E. H. LIEB -- Publications

Publications of Elliott H. Lieb

  1. Second Order Radiative Corrections to the Magnetic Moment of a Bound Electron, Phil. Mag. Vol. 46, 311-316 (1955).

  2. A Non-Perturbation Method for Non-Linear Field Theories, Proc. Roy. Soc. 241A, 339-363 (1957).

  3. (with K. Yamazaki) Ground State Energy and Effective Mass of the Polaron, Phys. Rev. 111, 728-733 (1958).

  4. (with H. Koppe) Mathematical Analysis of a Simple Model Related to the Stripping Reaction, Phys. Rev. 116, 367-371 (1959).

  5. Hard Sphere Bose Gas - An Exact Momentum Space Formulation, Proc. U.S. Nat. Acad. Sci. 46, 1000-1002 (1960).

  6. Operator Formalism in Statistical Mechanics, J. Math. Phys. 2, 341-343 (1961).

  7. (with D.C. Mattis) Exact Wave Functions in Superconductivity, J. Math. Phys. 2, 602-609 (1961).

  8. (with T.D. Schultz and D.C. Mattis) Two Soluble Models of an Antiferromagnetic Chain, Annals of Phys. (N.Y.) 16, 407-466 (1961).

  9. (with D.C. Mattis) Theory of Ferromagnetism and the Ordering of Electronic Energy Levels, Phys. Rev. 125, 164-172 (1962).

  10. (with D.C. Mattis) Ordering Energy Levels of Interacting Spin Systems, J. Math. Phys. 3, 749-751 (1962).

  11. New Method in the Theory of Imperfect Gases and Liquids, J. Math. Phys. 4, 671-678 (1963).

  12. (with W. Liniger) Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State, Phys. Rev. 130, 1605-1616 (1963).

  13. Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum, Phys. Rev. 130, 1616-1624 (1963).

  14. Simplified Approach to the Ground State Energy of an Imperfect Bose Gas, Phys. Rev. 130, 2518-2528 (1963).

  15. (with A. Sakakura) Simplified Approach to the Ground State Energy of an Imperfect Bose Gase. II. The Charged Bose Gas at High Density, Phys. Rev. 133, A899-A906 (1964).

  16. (with W. Liniger) Simplified Approach to the Ground State Energy of an Imperfect Bose Gas. III. Application to the One-Dimensional Model, Phys. Rev. 134, A312-A315 (1964).

  17. (with T.D. Schultz and D.C. Mattis) Two-Dimensional Ising Model as a Soluble Problem of Many Fermions, Rev. Mod. Phys. 36, 856-871 (1964).

  18. The Bose Fluid, Lectures in Theoretical Physics, Vol. VIIC, (Boulder summer school), University of Colorado Press, 175-224 (1965).

  19. (with D.C. Mattis) Exact Solution of a Many-Fermion System and its Associated Boson Field, J. Math. Phys. 6, 304-312 (1965).

  20. (with S.Y. Larsen, J.E. Kilpatrick and H.F. Jordan) Suppression at High Temperature of Effects Due to Statistics in the Second Virial Coefficient of a Real Gas, Phys. Rev. 140, A129-A130 (1965).

  21. (with D.C. Mattis) Book Mathematical Physics in One Dimension (Academic Press, New York, 1966).

  22. Proofs of Some Conjectures on Permanents, J. of Math. and Mech. 16, 127-139 (1966).

  23. Quantum Mechanical Extension of the Lebowitz-Penrose Theorem on the van der Waals Theory, J. Math. Phys. 7, 1016-1024 (1966).

  24. (with D.C. Mattis) Theory of Paramagnetic Impurities in Semiconductors, J. Math. Phys. 7, 2045-2052 (1966).

  25. (with T. Burke and J.L. Lebowitz) Phase Transition in a Model Quantum System: Quantum Corrections to the Location of the Critical Point, Phys. Rev. 149, 118-122 (1966).

  26. Some Comments on the One-Dimensional Many-Body Problem, unpublished Proceedings of Eastern Theoretical Physics Conference, New York (1966).

  27. Calculation of Exchange Second Virial Coefficient of a Hard Sphere Gas by Path Integrals, J. Math. Phys. 8, 43-52 (1967).

  28. (with Z. Rieder and J.L. Lebowitz) Properties of a Harmonic Crystal in a Stationary Nonequilibrium State, J. Math. Phys. 8, 1073-1078 (1967).

  29. Exact Solution of the Problem of the Entropy of Two-Dimensional Ice, Phys. Rev. Lett. 18, 692-694 (1967).

  30. Exact Solution of the F Model of an Antiferroelectric, Phys. Rev. Lett. 18, 1046-1048 (1967).

  31. Exact Solution of the Two-Dimensional Slater KDP Model of a Ferroelectric, Phys. Rev. Lett. 19, 108-110 (1967).

  32. The Residual Entropy of Square Ice, Phys. Rev. 162, 162-172 (1967).

  33. Ice, Ferro- and Antiferroelectrics, in Methods and Problems in Theoretical Physics, in honour of R.E. Peierls, proceedings of the 1967 Birmingham conference, (North-Holland, 1970) p. 21-28.

  34. Exactly Soluble Models, in Mathematical Methods in Solid State and Superfluid Theory, proceedings of the 1967 Scottish Universities' Summer School of Physics, (Oliver and Boyd, Edinburgh, 1969) p. 286-306.

  35. The Solution of the Dimer Problems by the Transfer Matrix Method, J. Math. Phys. 8, 2339-2341 (1967).

  36. (with M. Flicker) Delta Function Fermi Gas with Two Spin Deviates, Phys. Rev. 161, 179-188 (1967).

  37. Concavity Properties and a Generating Function for Stirling Numbers, J. Combinatorial Theory 5, 203-206 (1968).

  38. A Theorem on Pfaffians, J. Combinatorial Theory 5, 313-319 (1968).

  39. (with F.Y. Wu) Absence of Mott Transition in an Exact Solution of the Short-Range One-Band Model in One Dimension, Phys. Rev. Lett. 20, 1445-1448 (1968). Errata: Phys. Rev. Lett. 21, 192 (1968).

  40. Two Dimensional Ferroelectric Models, J. Phys. Soc. (Japan) 26 (supplement), 94-95 (1969).

  41. (with W.A. Beyer) Clusters on a Thin Quadratic Lattice, Studies in Appl. Math. 48, 77-90 (1969).

  42. (with C.J. Thompson) Phase Transition in Zero Dimensions: A Remark on the Spherical Model, J. Math. Phys. 10, 1403-1406 (1969).

  43. (with J.L. Lebowitz) The Existence of Thermodynamics for Real Matter with Coulomb Forces, Phys. Rev. Lett. 22, 631-634 (1969).

  44. Two Dimensional Ice and Ferroelectric Models, in Lectures in Theoretical Physics, XI D, (Boulder summer school) Gordon and Breach, 329-354 (1969).

  45. Survey of the One Dimensional Many Body Problem and Two Dimensional Ferroelectric Models, in Contemporary Physics: Trieste Symposium 1968, International Atomic Energy Agency, Vienna, 1969, Vol. 1, p. 163-176.

  46. Models, in Phase Transitions, proceedings of the 14th Solvay Chemistry Conference, May 1969, (Interscience, 1971) p. 45-56.

  47. (with H. Araki) Entropy Inequalities, Commun. Math. Phys. 18, 160-170 (1970).

  48. (with O.J. Heilmann) Violation of the Non-Crossing Rule: The Hubbard Hamiltonian for Benzene, Trans. N.Y. Acad. Sci.33, 116-149 (1970). Also in Annals N.Y. Acad. Sci. 172, 583-617 (1971). (Awarded the 1970 Boris Pregel award for research in chemical physics.)

  49. (with O.J. Heilmann) Monomers and Dimers, Phys. Rev. Lett. 24, 1412-1414 (1970).

  50. Book Review of ``Statistical Mechanics'' by David Ruelle, Bull. Amer. Math. Soc. 76, 683-687 (1970).

  51. (with J.L. Lebowitz) Thermodynamic Limit for Coulomb Systems, in Systèmes a un Nombre Infini de Degrés de Liberté, Colloques Internationaux de Centre National de la Recherche Scientifique 181, 155-162 (1970).

  52. (with D.B. Abraham, T. Oguchi and T. Yamamoto) On the Anomolous Specific Heat of Sodium Trihydrogen Selenite, Progr. Theor. Phys. (Kyoto) 44, 1114-1115 (1970).

  53. (with D.B. Abraham) Anomalous Specific Heat of Sodium Trihydrogen Selenite -- An Associated Combinatorial Problem, J. Chem. Phys. 54, 1446-1450 (1971).

  54. (with O.J. Heilmann, D. Kleitman and S. Sherman) Some Positive Definite Functions on Sets and Their Application to the Ising Model, Discrete Math. 1, 19-27 (1971).

  55. (with Th. Niemeijer and G. Vertogen) Models in Statistical Mechanics, in Statistical Mechanics and Quantum Field Theory, proceedings of 1970 Ecole d'Eté de Physique Théorique (Les Houches), (Gordon and Breach, 1971) p. 281-326.

  56. (with H.N.V. Temperley) Relations between the `Percolation' and `Colouring' Problem and Other Graph-Theoretical Problems Associated with Regular Planar Lattices: Some Exact Results for the `Percolation' Problem, Proc. Roy. Soc. A322, 251-280 (1971).

  57. (with M. de Llano) Some Exact Results in the Hartree-Fock Theory of a Many-Fermion System at High Densities, Phys. Letts. 37B, 47-49 (1971).

  58. (with J.L. Lebowitz) The Constitution of Matter: Existence of Thermodynamics for Systems Composed of Electrons and Nuclei, Adv. in Math. 9, 316-398 (1972).

  59. (with F.Y. Wu) Two Dimensional Ferroelectric Models, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. Green (Academic, 1972), Vol. 1, p. 331-490.

  60. (with D. Ruelle) A Property of Zeros of the Partition Function for Ising Spin Systems, J. Math. Phys. 13, 781-784 (1972).

  61. (with O.J. Heilmann) Theory of Monomer-Dimer Systems, Commun. Math. Phys. 25, 190-232 (1972). Errata 27, 166 (1972).

  62. (with M.L. Glasser and D.B. Abraham) Analytic Properties of the Free Energy for the ``Ice'' Models, J. Math. Phys. 13, 887-900 (1972).

  63. (with D.W. Robinson) The Finite Group Velocity of Quantum Spin Systems, Commun. Math. Phys. 28, 251-257 (1972).

  64. (with J.L. Lebowitz) Phase Transition in a Continuum Classical System with Finite Interactions, Phys. Lett. 39A, 98-100 (1972).

  65. (with J.L. Lebowitz) Lectures on the Thermodynamic Limit for Coulomb Systems, in Statistical Mechanics and Mathematical Problems, Battelle 1971 Recontres, Springer Lecture Notes in Physics 20, 136-161 (1973).

  66. (with J.L. Lebowitz) Lectures on the Thermodynamic Limit for Coulomb Systems, in Lectures in Theoretical Physics XIV B, (Boulder summer school), Colorado Associated University Press, 423-460 (1973).

  67. Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture, Adv. in Math. 11, 267-1288 (1973).

  68. (with M.B. Ruskai) A Fundamental Property of Quantum Mechanical Entropy, Phys. Rev. Lett. 30, 434-436 (1973).

  69. (with M.B. Ruskai) Proof of the Strong Subadditivity of Quantum-Mechanical Entropy, J. Math. Phys. 14, 1938-1941 (1973).

  70. (with K. Hepp) On the Superradiant Phase Transition for Molecules in a Quantized Radiation Field: The Dicke Maser Model, Annals of Phys. (N.Y.) 76, 360-404 (1973).

  71. (with K. Hepp) Phase Transition in Reservoir Driven Open Systems with Applications to Lasers and Superconductors, Helv. Phys. Acta 46, 573-602 (1973).

  72. (with K. Hepp) The Equilibrium Statistical Mechanics of Matter Interacting with the Quantized Radiation Field, Phys. Rev. A8, 2517-2525 (1973).

  73. (with K. Hepp) Constructive Macroscopic Quantum Electrodynamics, in Constructive Quantum Field Theory, proceedings of the 1973 Erice Summer School, edited by G. Velo and A. Wightman, Springer Lecture Notes in Physics 25, 298-316 (1973).

  74. The Classical Limit of Quantum Spin Systems, Commun. Math. Phys. 31, 327-340 (1973).

  75. (with B. Simon) Thomas-Fermi Theory Revisited, Phys. Rev. Lett. 31, 681-683 (1973).

  76. (with M.B. Ruskai) Some Operator Inequalities of the Schwarz Type, Adv. in Math. 12, 269-273 (1974).

  77. Exactly Soluble Models in Statistical Mechanics, lecture given at the 1973 I.U.P.A.P. van der Waals Centennial Conference on Statistical Mechanics, Physica 73, 226-236 (1974).

  78. (with B. Simon) On Solutions to the Hartree-Fock Problem for Atoms and Molecules, J. Chem. Physics 61, 735-736 (1974).

  79. Thomas-Fermi and Hartree-Fock Theory, lecture at the 1974 International Congress of Mathematicians, Vancouver, (Proceedings, 1975) Vol. 2, p. 383-386.

  80. Some Convexity and Subadditivity Properties of Entropy, Bull. Amer. Math. Soc. 81, 1-13 (1975).

  81. (with H.J. Brascamp and J.M. Luttinger) A General Rearrangement Inequality for Multiple Integrals, Jour. Funct. Anal. 17, 227-237 (1975).

  82. (with H.J. Brascamp) Some Inequalities for Gaussian Measures and the Long-Range Order of the One-Dimensional Plasma, in Functional Integration and its Applications, proceedings of the Conference on Functional Integration, Cumberland Lodge, England, edited by A.M. Arthurs, (Clarendon Press, 1975), p. 1-14.

  83. (with K. Hepp) The Laser: A Reversible Quantum Dynamical System with Irreversible Classical Macroscopic Motion, in Dynamical Systems, Battelle 1974 Rencontres, Springer Lecture Notes in Physics 38, 178-208 (1975). Also appears in Melting, Localization and Chaos, proceedings of the 9th Midwest Solid State Theory Symposium, 1981, edited by R. Kalia and P. Vashishta, (North-Holland, 1982), p. 153-177.

  84. (with P. Hertel and W. Thirring) Lower Bound to the Energy of Complex Atoms, J. Chem. Phys. 62, 3355-3356 (1975).

  85. (with W. Thirring) Bound for the Kinetic Energy of Fermions which Proves the Stability of Matter, Phys. Rev. Lett. 35, 687-689 (1975). Errata 35, 1116 (1975).

  86. (with H.J. Brascamp and J.L. Lebowitz) The Statistical Mechanics of Anharmonic Lattices, in Proceedings of the 40th session of the International Statistics Institute, Warsaw, 1975 , Vol. 9, p. 393-404.

  87. (with H.J. Brascamp) Best Constants in Young's Inequality, Its Converse and Its Generalization to More Than Three Functions, Adv. in Math. 20, 151-172 (1976).

  88. (with H.J. Brascamp) On Extensions of the Brunn-Minkowski and Prékopa-Leindler Theorems, Including Inequalities for Log Concave Functions and with an Application to the Diffusion Equation, J. Funct. Anal. 22, 366-389 (1976).

  89. (with J.F. Barnes and H.J. Brascamp) Lower Bounds for the Ground State Energy of the Schrödinger Equation Using the Sharp Form of Young's Inequality, in Studies in Mathematical Physics, edited by E. Lieb, B. Simon, and A. Wightman, (Princeton Press, 1976), p. 83-90.

  90. Inequalities for Some Operator and Matrix Functions, Adv. in Math. 20, 174-178 (1976).

  91. (with H. Narnhofer) The Thermodynamic Limit for Jellium, J. Stat. Phys. 12, 291-310 (1975). Errata J. Stat. Phys. 14, 465 (1976).

  92. The Stability of Matter, Rev. Mod. Phys. 48, 553-569 (1976).

  93. Bounds on the Eigenvalues of the Laplace and Schrödinger Operators, Bull. Amer. Math. Soc. 82, 751-753 (1976).

  94. (with F.J. Dyson and B. Simon) Phase Transitions in the Quantum Heisenberg Model, Phys. Rev. Lett. 37, 120-123 (1976). (See no. 104.)

  95. (with W. Thirring) Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities, in Studies in Mathematical Physics, edited E. Lieb, B. Simon, and A. Wightman, (Princeton University Press, 1976), p. 269-303.

  96. (with B. Simon and A. Wightman) Book Studies in Mathematical Physics: Essays in Honor of Valentine Bargmann, (Princeton University Press, 1976).

  97. (with B. Simon) Thomas-Fermi Theory of Atoms, Molecules and Solids, Adv. in Math. 23, 22-116 (1977).

  98. (with O. Lanford and J. Lebowitz) Time Evolution of Infinite Anharmonic Oscillators, J. Stat. Phys. 16, 453-461 (1977).

  99. The Stability of Matter, proceedings of the Conference on the Fiftieth Anniversary of the Schrödinger Equation, Acta Physica Austriaca Suppl. XVII, 181-207 (1977).

  100. Existence and Uniqueness of the Minimizing Solution of Choquard's Non-Linear Equation, Studies in Appl. Math. 57, 93-105 (1977).

  101. (with J. Fröhlich) Existence of Phase Transitions for Anisotropic Heisenberg Models, Phys. Rev. Lett. 38, 440-442 (1977).

  102. (with B. Simon) The Hartree-Fock Theory for Coulomb Systems, Commun. Math. Phys. 53, 185-194 (1977).

  103. (with W. Thirring) A Lower Bound for Level Spacings, Annals of Phys. (N.Y.) 103, 88-96 (1977).

  104. (with F. Dyson and B. Simon) Phase Transitions in Quantum Spin Systems with Isotropic and Non-Isotropic Interactions, J. Stat. Phys. 18, 335-383 (1978).

  105. Many Particle Coulomb Systems, in Statistical Mechanics, proceedings of the 1976 International Mathematics Summer Center (CIME), Session on Statistical Mechanics, Ciclo, Italy, 1976, edited by G. Gallavotti, (Liguore Editore, Naples, 1978), p. 101-166.

  106. (with R. Benguria) Many-Body Atomic Potentials in Thomas-Fermi Theory, Annals of Phys. (N.Y.) 110, 34-45 (1978).

  107. (with R. Benguria) The Positivity of the Pressure in Thomas-Fermi Theory, Commun. Math. Phys. 63, 193-218 (1978). Errata 71, 94 (1980).

  108. (with M. de Llano) Solitons and the Delta Function Fermion Gas in Hartree-Fock Theory, J. Math. Phys. 19, 860-868 (1978).

  109. (with J. Fröhlich) Phase Transitions in Anisotropic Lattice Spin Systems, Commun. Math. Phys. 60, 233-267 (1978).

  110. (with J. Fröhlich, R. Israel and B. Simon) Phase Transitions and Reflection Positivity. I. General Theory and Long Range Lattice Models, Commun. Math. Phys. 62, 1-34 (1978). (See no. 124.)

  111. (with M. Aizenman and E.B. Davies) Positive Linear Maps Which are Order Bounded on C* Subalgebras, Adv. in Math. 28, 84-86 (1978).

  112. (with M. Aizenman) On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators, Phys. Lett. 66A, 427-429 (1978).

  113. New Proofs of Long Range Order, proceedings of the International Conference on Mathematical Problems in Theoretical Physics, June, 1977, Springer Lecture Notes in Physics, 80, 59-67 (1978).

  114. Proof of an Entropy Conjecture of Wehrl, Commun. Math. Phys. 62, 35-41 (1978).

  115. (with B. Simon) Monotonicity of the Electronic Contribution to the Born-Oppenheimer Energy, J. Phys. B. 11, L537-L542 (1978).

  116. (with O. Heilmann) Lattice Models for Liquid Crystals, J. Stat. Phys. 20, 679-693 (1979).

  117. (with H. Brezis) Long Range Atomic Potentials in Thomas-Fermi Theory, Commun. Math. Phys. 65, 231-246 (1979).

  118. The N5/3 Law for Bosons, Phys. Lett. 70A, 71-73 (1979).

  119. A Lower Bound for Coulomb Energies, Phys. Lett. 70A, 444-446 (1979).

  120. Why Matter is Stable, Kagaku 49, 301-307 and 385-388 (1979). (In Japanese).

  121. The Number of Bound States of One-Body Schrödinger Operators and the Weyl Problem, Symposium of the Research Institute of Mathematical Sciences, Kyoto University, 1979.

  122. Some Open Problems About Coulomb Systems, in proceedings of the Conference of the International Association of Mathematical Physics, Lausanne, 1979, Springer Lecture Notes in Physics, 116, 91-102 (1980).

  123. The Number of Bound States of One-Body Schrödinger Operators and the Weyl Problem, proceedings of the American Mathematical Society Symposia in Pure Mathematics, 36, 241-252 (1980).

  124. (with J. Fröhlich, R. Israel and B. Simon) Phase Transitions and Reflection Positivity. II. Lattice Systems with Short-Range and Coulomb Interactions. J. Stat. Phys. 22, 297-347 (1980). (See no. 110.)

  125. Why Matter is Stable, Chinese Jour. Phys. 17, 49-62 (1980). (English version of no. 120).

  126. A Refinement of Simon's Correlation Inequality, Commun. Math. Phys. 77, 127-135 (1980).

  127. (with B. Simon) Pointwise Bounds on Eigenfunctions and Wave Packets in N-Body Quantum Systems. VI. Asymptotics in the Two-Cluster Region, Adv. in Appl. Math. 1, 324-343 (1980).

  128. The Uncertainty Principle, article in Encyclopedia of Physics, edited by R. Lerner and G. Trigg, (Addison Wesley, 1981), p. 1078-1079.

  129. (with S. Oxford) An Improved Lower Bound on the Indirect Coulomb Energy, Int. J. Quant. Chem. 19, 427-439 (1981).

  130. (with R. Benguria and H. Brezis) The Thomas-Fermi-von Weizsäecker Theory of Atoms and Molecules, Commun. Math. Phys. 79, 167-180 (1981).

  131. (with M. Aizenman) The Third Law of Thermodynamics and the Degeneracy of the Ground State for Lattice Systems, J. Stat. Phys. 24, 279-297 (1981).

  132. (with J. Bricmont, J. Fontaine, J. Lebowitz and T. Spencer) Lattice Systems with a Continuous Symmetry III. Low Temperature Asymptotic Expansion for the Plane Rotator Model, Commun. Math. Phys. 78, 545-566 (1981).

  133. (with A. Sokal) A General Lee-Yang Theorem for One-Component and Multi-component Ferromagnets, Commun. Math. Phys. 80, 153-179 (1981).

  134. Variational Principle for Many-Fermion Systems, Phys. Rev. Lett. 46, 457-459 (1981). Errata 47, 69 (1981).

  135. Thomas-Fermi and Related Theories of Atoms and Molecules, in Rigorous Atomic and Molecular Physics, edited by G. Velo and A. Wightman, (Plenum Press, 1981), p. 213-308.

  136. Thomas-Fermi and Related Theories of Atoms and Molecules, Rev. Mod. Phys. 53, 603-641 (1981). Errata 54, 311 (1982). (Revised version of no. 135.)

  137. Statistical Theories of Large Atoms and Molecules, proceedings of the 1981 Oaxtepec conference on Recent Progress in Many-Body Theories, Springer Lecture Notes in Physics, 142, 336-343 (1982).

  138. Statistical Theories of Large Atoms and Molecules, Comments Atomic and Mol. Phys. 11, 147-155 (1982).

  139. Analysis of the Thomas-Fermi-von Weizsäcker Equation for an Infinite Atom without Electron Repulsion, Commun. Math. Phys. 85, 15-25 (1982).

  140. (with D.A. Liberman) Numerical Calculation of the Thomas-Fermi-von Weizsäcker Function for an Infinite Atom without Electron Repulsion, Los Alamos National Laboratory Report, LA-9186-MS (1982).

  141. Monotonicity of the Molecular Electronic Energy in the Nuclear Coordinates, J. Phys. B.: At. Mol. Phys. 15, L63-L66 (1982).

  142. Comment on ``Approach to Equilibrium of a Boltzmann Equation Solution'', Phys. Rev. Lett. 48, 1057 (1982).

  143. Density Functionals for Coulomb Systems, in Physics as Natural Philosophy: Essays in honor of Laszlo Tisza on his 75th Birthday, edited by A. Shimony and H. Feshbach, (M.I.T. Press, 1982), p. 111-149.

  144. An Lp Bound for the Riesz and Bessel Potentials of Orthonormal Functions, J. Funct. Anal. 51, 159-165 (1983).

  145. (with H. Brezis) A Relation Between Pointwise Convergence of Functions and Convergence of Functionals, Proc. Amer. Math. Soc. 88, 486-490 (1983).

  146. (with R. Benguria) A Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle, Phys. Rev. Lett. 50, 1771-1774 (1983).

  147. Sharp Constants in the Hardy-Littlewood-Sobolev and Related Inequalities, Annals of Math. 118, 349-374 (1983).

  148. Density Functionals for Coulomb Systems (a revised version of no. 143), Int. Jour. Quant. Chem. 24, 243-277 (1983). An expanded version appears in Density Functional Methods in Physics, edited by R. Dreizler and J. da Providencia, Plenum Nato ASI Series, 123, 31-80 (1985).

  149. The Significance of the Schrödinger Equation for Atoms, Molecules and Stars, lecture given at the Schrödinger Symposium, Dublin Institute of Advanced Studies, October 1983, (unpublished).

  150. (with I. Daubechies) One Electron Relativistic Molecules with Coulomb Interaction, Commun. Math. Phys. 90, 497-510 (1983).

  151. (with I. Daubechies) Relativistic Molecules with Coulomb Interaction, in Differential Equations, proceedings of the Conference held at the University of Alabama, Birmingham, 1983, edited by I. Knowles and R. Lewis, Math. Studies Series, 92, 143-148 (North-Holland, 1984).

  152. Some Vector Field Equations, in Differential Equations, proceedings of the Conference held at the University of Alabama, Birmingham, 1983, edited by I. Knowles and R. Lewis, Math. Studies Series 92, 403-412 (North-Holland, 1984).

  153. On the Lowest Eigenvalue of the Laplacian for the Intersection of Two Domains, Inventiones Math. 74, 441-448 (1983).

  154. (with J. Chayes and L. Chayes) The Inverse Problem in Classical Statistical Mechanics, Commun. Math. Phys. 93, 57-121 (1984).

  155. On Characteristic Exponents in Turbulence, Commun. Math. Phys. 92, 473-480 (1984).

  156. Atomic and Molecular Negative Ions, Phys. Rev. Lett. 52, 315-317 (1984).

  157. Bound on the Maximum Negative Ionization of Atoms and Molecules, Phys. Rev. 29A, 3018-3028 (1984).

  158. (with W. Thirring) Gravitational Collapse in Quantum Mechanics with Relativistic Kinetic Energy, Annals of Phys. (N.Y.) 155, 494-512 (1984).

  159. (with I.M. Sigal, B. Simon and W. Thirring) Asymptotic Neutrality of Large-Z Ions, Phys. Rev. Lett. 52, 994-996 (1984). (See no. 185.)

  160. (with R. Benguria) The Most Negative Ion in the Thomas-Fermi-von Weizsäcker Theory of Atoms and Molecules, J. Phys. B: At. Mol. Phys. 18, 1045-1059 (1985).

  161. (with H. Brezis) Minimum Action Solutions of Some Vector Field Equations, Commun. Math. Phys. 96, 97-113 (1984).

  162. (with H. Brezis) Sobolev Inequalities with Remainder Terms, J. Funct. Anal. 62, 73-86 (1985).

  163. Baryon Mass Inequalities in Quark Models, Phys. Rev. Lett. 54, 1987-1990 (1985).

  164. (with J. Fröhlich and M. Loss) Stability of Coulomb Systems with Magnetic Fields I. The One-Electron Atom, Commun. Math. Phys. 104, 251-270 (1986).

  165. (with M. Loss) Stability of Coulomb Systems with Magnetic Fields II. The Many-Electron Atom and the One-Electron Molecule, Commun. Math. Phys. 104, 271-282 (1986).

  166. (with W. Thirring) Universal Nature of van der Waals Forces for Coulomb Systems, Phys. Rev. A 34, 40-46 (1986).

  167. Some Ginzburg-Landau Type Vector-Field Equations, in Nonlinear systems of Partial Differential Equations in Applied Mathematics, edited by B. Nicolaenko, D. Holm and J. Hyman, Amer. Math. Soc. Lectures in Appl. Math. 23, Part 2, 105-107 (1986).

  168. (with I. Affleck) A Proof of Part of Haldane's Conjecture on Spin Chains, Lett. Math. Phys. 12, 57-69 (1986).

  169. (with H. Brezis and J-M. Coron) Estimations d'Energie pour des Applications de R3 a Valeurs dans S2, C.R. Acad. Sci. Paris 303, Ser. 1, 207-210 (1986).

  170. (with H. Brezis and J-M. Coron) Harmonic Maps with Defects, Commun. Math. Phys. 107, 649-705 (1986).

  171. Some Fundamental Properties of the Ground States of Atoms and Molecules, in Fundamental Aspects of Quantum Theory, edited by V. Gorini and A. Frigerio, Nato ASI Series B, (Plenum Press, 1986), Vol. 144, p. 209-214.

  172. (with T. Kennedy) A Model for Crystallization: A Variation on the Hubbard Model, in Statistical Mechanics and Field Theory: Mathematical Aspects, Springer Lecture Notes in Physics 257, 1-9 (1986).

  173. (with T. Kennedy) An Itinerant Electron Model with Crystalline or Magnetic Long Range Order, Physica 138A, 320-358 (1986).

  174. (with T. Kennedy) A Model for Crystallization: A Variation on the Hubbard Model, in proceedings of IUPAP Statphys 16 Conference, Boston, Physica 140A, 240-250 (1986).

  175. (with T. Kennedy) Proof of the Peierls Instability in One Dimension, Phys. Rev. Lett. 59, 1309-1312 (1987).

  176. (with I. Affleck, T. Kennedy and H. Tasaki) Rigorous Results on Valence-Bond Ground States in Antiferromagnets, Phys. Rev. Lett. 59, 799-802 (1987).

  177. (with H.-T. Yau) The Chandrasekhar Theory of Stellar Collapse as the Limit of Quantum Mechanics, Commun. Math. Phys. 112, 147-174 (1987).

  178. (with H.-T. Yau) A Rigorous Examination of the Chandrasekhar Theory of Stellar Collapse, Astrophys. Jour. 323, 140-144 (1987).

  179. (with F. Almgren) Singularities of Energy Minimizing Maps from the Ball to the Sphere, Bull. Amer. Math. Soc. 17, 304-306 (1987). (See no. 190.)

  180. Bounds on Schrödinger Operators and Generalized Sobolev Type Inequalities, Proceedings of the International Conference on Inequalities, University of Birmingham, England, 1987, Marcel Dekker Lecture Notes in Pure and Appl. Math., edited by W.N. Everitt, Vol. 129, p. 123-133 (1991).

  181. (with I. Affleck, T. Kennedy and H. Tasaki) Valence Bond Ground States in Isotropic Quantum Antiferromagnets, Commun. Math. Phys. 115, 477-528 (1988).

  182. (with T. Kennedy and H. Tasaki) A Two Dimensional Isotropic Quantum Antiferromagnet with Unique Disordered Ground State, J. Stat. Phys. 53, 383-416 (1988).

  183. (with T. Kennedy and S. Shastry) Existence of Néel Order in Some Spin 1/2 Heisenberg Antiferromagnets, J. Stat. Phys. 53, 1019-1030 (1988).

  184. (with T. Kennedy and S. Shastry) The XY Model has Long-Range Order for all Spins and all Dimensions Greater than One, Phys. Rev. Lett. 61, 2582-2584 (1988).

  185. (with I.M. Sigal, B. Simon and W. Thirring) Approximate Neutrality of Large-Z Ions, Commun. Math. Phys. 116, 635-644 (1988). (See no. 159.)

  186. (with H.-T. Yau) The Stability and Instability of Relativistic Matter, Commun. Math. Phys. 118, 177-213 (1988).

  187. (with H.-T. Yau) Many-Body Stability Implies a Bound on the Fine Structure Constant, Phys. Rev. Lett. 61, 1695-1697 (1988).

  188. (with J. Conlon and H.-T. Yau) The N7/5 Law for Charged Bosons, Commun. Math. Phys. 116, 417-448 (1988).

  189. (with F. Almgren and W. Browder) Co-area, Liquid Crystals, and Minimal Surfaces, in Partial Differential Equations, edited by S.S. Chern, Springer Lecture Notes in Math. 1306, 1-22 (1988).

  190. (with F. Almgren) Singularities of Energy Minimizing Maps from the Ball to the Sphere: Examples, Counterexamples and Bounds, Ann. of Math. 128, 483-530 (1988).

  191. (with F. Almgren) Counting Singularities in Liquid Crystals, in IXth International Congress on Mathematical Physics, B. Simon, A. Truman, I.M. Davies eds., Hilger, 396-409 (1989). This also appears in: Symposia Mathematica, vol. XXX, Ist. Naz. Alta Matem. Francesco Severi Roma, 103-118, Academic Press (1989); Variational Methods, H. Berestycki, J-M. Coron, I. Ekeland eds., Birkhäuser, 17-36 (1990); How many singularities can there be in an energy minimizing map from the ball to the sphere?, in Ideas and Methods in Mathematical Analysis, Stochastics, and Applications, S. Albeverio, J.E. Fenstad, H. Holden, T. Lindstrom eds., Cambridge Univ. Press, vol. 1, 394-408 (1992).

  192. (with F. Almgren) Symmetric Decreasing Rearrangement can be Discontinuous, Bull. Amer. Math. Soc. 20, 177-180 (1989).

  193. (with F. Almgren) Symmetric Decreasing Rearrangement is Sometimes Continuous, Jour. Amer. Math. Soc. 2, 683-773 (1989). A summary of this work (using `rectifiable currents') appears as The (Non)continuity of Symmetric Decreasing Rearrangement in Symposia Mathematica, vol. XXX, Ist. Naz. Alta Matem. Francesco Severi Roma, 89-102, Academic Press (1989) and in Variational Methods, H. Berestycki, J-M. Coron, I. Ekeland eds., Birkhäuser, 3-16 (1990).

  194. Two Theorems on the Hubbard Model, Phys. Rev. Lett. 62, 1201-1204 (1989). Errata 62, 1927 (1989).

  195. (with J. Conlon and H.-T. Yau) The Coulomb Gas at Low Temperature and Low Density, Commun. Math. Phys. 125, 153-180 (1989).

  196. Gaussian Kernels have only Gaussian Maximizers, Invent. Math. 102, 179-208 (1990).

  197. Kinetic Energy Bounds and their Application to the Stability of Matter, in Schrödinger Operators, proceedings Sønderborg Denmark 1988, edited by H. Holden and A. Jensen, Springer Lecture Notes in Physics 345, 371-382 (1989). Expanded version of no. 180.

  198. The Stability of Matter: From Atoms to Stars, 1989 Gibbs Lecture, Bull. Amer. Math. Soc. 22, 1-49 (1990).

  199. Integral Bounds for Radar Ambiguity Functions and Wigner Distributions, J. Math. Phys. 31, 594-599 (1990).

  200. On the Spectral Radius of the Product of Matrix Exponentials, Linear Alg. and Appl.141, 271-273 (1990).

  201. (with M. Aizenman) Magnetic Properties of Some Itinerant-Electron Systems at T > 0, Phys. Rev. Lett. 65, 1470-1473 (1990).

  202. (with H. Siedentop) Convexity and Concavity of Eigenvalue Sums, J. Stat. Phys. 63, 811-816 (1991).

  203. (with J.P. Solovej) Quantum Coherent Operators: A Generalization of Coherent States, Lett. Math. Phys. 22, 145-154 (1991).

  204. The Flux-Phase Problem on Planar Lattices, proceedings of the Conference on Physics in Two Dimensions, Neuchatel, August 1991, Helv. Phys. Acta 65, 247-255 (1992).

  205. Atome in starken Magnetfeldern, Physikalische Blätter 48, 549-552 (1992). Translation by H. Siedentop of the Max-Planck medal lecture (1 April 1992) ``Atoms in strong magnetic fields''.

  206. Absence of Ferromagnetism for One-Dimensional Itinerant Electrons, in Probabilistic Methods in Mathematical Physics, proceedings of the International Workshop Siena, May 1991, edited by F. Guerra, M. Loffredo and C. Marchioro, (World Scientific, 1992), p. 290-294. A shorter version appears in Rigorous Results in Quantum Dynamics, edited by J. Dittrich and P. Exner, (World Scientific, 1991) p. 243-245.

  207. (with J.P. Solovej and J. Yngvason) Heavy Atoms in the Magnetic Field of a Neutron Star, Phys. Rev. Lett. 69, 749-752 (1992).

  208. (with J.P. Solovej) Atoms in the Magnetic Field of a Neutron Star, in Differential Equations with Applications to Mathematical Physics, edited by W.F. Ames, J.V. Herod and E.M. Harrell II, (Academic Press, 1993), p. 221-237. Also in Spectral Theory and Scattering Theory and Applications, edited by K. Yajima,, Advanced Studies in Pure Math. 23, 259-274, Math. Soc. of Japan, Kinokuniya (1994). This is a summary of nos. 215, 216. Earlier summaries also appear in: (a) Méthodes Semi-Classiques, Colloque Internatinal (Nantes 1991), Asterisque 210, 237-246 (1991); (b) Some New Trends on Fluid Dynamics and Theoretical Physics, edited by C.C. Lin and N. Hu, (Peking University Press, 1993) p. 149-157; (c) proceedings of the International Symposium on Advanced Topics of Quantum Physics, Shanxi, Beijing, edited by J.Q. Lang, M.L. Wang, S.N. Qiao and D.C. Su, (Science Press, 1993), p. 5-13.

  209. (with M. Loss and R. McCann) Uniform Density Theorem for the Hubbard Model, J. Math. Phys. 34, 891-898 (1993).

  210. Remarks on the Skyrme Model, in Proceedings of the Amer. Math. Soc. Symposia in Pure Math. 54, part 2, 379-384 (1993). (Proceedings of Summer Research Institute on Differential Geometry at UCLA, July 8-28, 1990.)

  211. (with E. Carlen) Optimal Hypercontractivity for Fermi Fields and Related Non-Commutative Integration Inequalities, Commun. Math. Phys. 155, 27-46 (1993).

  212. (with E. Carlen) Optimal Two-Uniform Convexity and Fermion Hypercontractivity, in Quantum and Non-Commutative Analysis, proceedings of the June 1992 Kyoto Conference, edited by H. Araki et.al., (Kluwer, 1993), p. 93-111. (Condensed version of no. 211.)

  213. (with M. Loss) Fluxes, Laplacians and Kasteleyn's Theorem, Duke Math. Journal 71, 337-363 (1993).

  214. (with V. Bach, R. Lewis and H. Siedentop) On the Number of Bound States of a Bosonic N-Particle Coulomb System, Zeits. f. Math. 214, 441-460 (1993).

  215. (with J.P. Solovej and J. Yngvason) Asymptotics of Heavy Atoms in High Magnetic Fields: I. Lowest Landau Band Region, Commun. Pure Appl. Math. 47, 513-591 (1994).

  216. (with J.P. Solovej and J. Yngvason) Asymptotics of Heavy Atoms in High Magnetic Fields: II. Semiclassical Regions, Commun. Math. Phys. 161, 77-124 (1994).

  217. (with V. Bach, M. Loss and J.P. Solovej) There are No Unfilled Shells in Unrestricted Hartree-Fock Theory, Phys. Rev. Lett. 72, 2981-2983 (1994).

  218. (with K. Ball and E. Carlen) Sharp Uniform Convexity and Smoothness Inequalities for Trace Norms, Invent. Math. 115, 463-482 (1994).

  219. Coherent States as a Tool for Obtaining Rigorous Bounds, Proceedings of the Symposium on Coherent States, Past, Present and Future, Oak Ridge, edited by D.H. Feng, J. Klauder and M.R. Strayer, (World Scientific, 1994), p. 267-278.

  220. The Hubbard model -- Some Rigorous Results and Open Problems, in Advances in Dynamical Systems and Quantum Physics, proceedings of 1993 Conference in honor of G.F. Dell'Antonio, edited by S. Albeverio et.al., (World Scientific, 1995), p. 173-193. A revised version appears in The Hubbard Model, proceedings of 1993 NATO ASI, edited by D. Baeriswyl et.al., (Plenum Press, 1995), p. 1-19. A further revision appears in proceedings of the XIth International Congress of Mathematical Physics, Paris, 1994, edited by D. Iagolnitzer, (International Press, 1995), p. 392-412.

  221. (with V. Bach and J.P. Solovej) Generalized Hartree-Fock Theory of the Hubbard Model, J. Stat. Phys. 76, 3-90 (1994).

  222. The Flux Phase of the Half-Filled Band, Phys. Rev. Lett. 73, 2158-2161 (1994).

  223. (with M. Loss) Symmetry of the Ginzburg-Landau Minimizer in a Disc, Math. Res. Lett. 1, 701-715 (1994).

  224. (with J.P. Solovej and J. Yngvason) Quantum Dots, in proceedings of the Conference on Partial Differential Equations and Mathematical Physics, University of Alabama, Birmingham, 1994, edited by I. Knowles, (International Press, 1995), p. 157-172.

  225. (with J.P. Solovej and J. Yngvason) Ground States of Large Quantum Dots in Magnetic Fields, Phys. Rev. B 51, 10646-10665 (1995).

  226. (with J. Freericks) The Ground State of a General Electron-Phonon Hamiltonian is a Spin Singlet, Phys. Rev. B 51, 2812-2821 (1995).

  227. (with B. Nachtergaele) The Stability of the Peierls Instability for Ring Shaped Molecules, Phys. Rev. B 51, 4777-4791 (1995).

  228. (with B. Nachtergaele) Dimerization in Ring-Shaped Molecules: The Stability of the Peierls Instability, in proceedings of the XIth International Congress of Mathematical Physics, Paris, 1994, edited by D. Iagolnitzer, 1995), p. 423-431.

  229. (with B. Nachtergaele) Bond Alternation in Ring-Shaped Molecules: The Stability of the Peierls Instability, proceedings of the Conference The Chemical Bond, Copenhagen 1994, Int. J. Quant. Chem. 58, 699-706 (1996).

  230. Fluxes and Dimers in the Hubbard Model, in Proceedings of the International Congress of Mathematicians, Zürich, 1994, edited by S.D. Chatterji, (Birkhäuser, 1995), Vol. 2, p. 1279-1280.

  231. (with M. Loss and J. P. Solovej) Stability of Matter in Magnetic Fields, Phys. Rev. Lett. 75, 985-989 (1995).

  232. (with O. J. Heilmann) Electron Density near the Nucleus of a large Atom, Phys. Rev. A 52, 3628-3643 (1995).

  233. (with A. Iantchenko and H. Siedentop) Proof of a Conjecture about Atomic and Molecular Cores Related to Scott's Correction, J. reine u. ang. Math. 472, 177-195 (1996).

  234. (with L. Thomas) Exact Ground State Energy of the Strong-Coupling Polaron, Commun. Math. Phys. 183, 511-519 (1997). Errata 188, 499-500 (1997).

  235. (with L. Cafarelli and D. Jerison) On the Case of Equality in the Brunn-Minkowski Inequality for Capacity, Adv. in Math. 117, 193-207 (1996).

  236. (with M. Loss and H. Siedentop) Stability of Relativistic Matter via Thomas-Fermi Theory, Helv. Phys. Acta 69, 974-984 (1996).

  237. Some of the Early History of Exactly Soluble Models, in Proceedings of the 1996 Northeastern University conference on Exactly Soluble Models, Int. Jour. Mod. Phys. B 11, 3-10 (1997).

  238. (with H. Siedentop and J. P. Solovej) Stability and Instability of Relativistic Electrons in Magnetic Fields, J. Stat. Phys. 89, 37-59 (1997).

  239. (with H. Siedentop and J-P. Solovej) Stability of Relativistic Matter with Magnetic Fields, Phys. Rev. Lett. 79, 1785-1788 (1997).

  240. Stability of Matter in Magnetic Fields, in Proceedings of the Conference on Unconventional Quantum Liquids, Evora, Portugal, 1996, Zeits. f. Phys. B 933, 271-274 (1997).

  241. Birmingham in the Good Old Days, in proceedings of the Conference on Unconventional Quantum Liquids, Evora, Portugal, 1996, Zeits. f. Phys. B 933, 125-126 (1997).

  242. (with M. Loss) book Analysis, American Mathematical Society (1997).

  243. Doing Math with Fred, in In Memoriam Frederick J. Almgren Jr., 1937-1997, Experimental Math. 6, 2-3 (1997).

  244. (with J.P. Solovej and J. Yngvason) Asymptotics of Natural and Artificial Atoms in Strong Magnetic Fields, in The Stability of Matter: From Atoms to Stars, Selecta of E. H. Lieb, W. Thirring ed., second edition, Springer Verlag, pp. 145-167 (1997). This is a summary of nos. 207, 208, 215, 216, 224, 225.

  245. Stability and Instability of Relativistic Electrons in Classical Electromagnetic Fields, in proceedings of Conference on Partial Differential Equations and Mathematical Physics, Georgia Inst. of Tech., March, 1997, Amer. Math. Soc. Contemporary Math. series, E. Carlen, E. Harrell, M. Loss eds., 217, 99-108 (1998).

  246. (with J. Yngvason) Ground State Energy of the Low Density Bose Gas, Phys. Rev. Lett. 80, 2504-2507 (1998). arXiv math-ph/9712138, mp_arc 97-631. http://www.ams.org/notices/199805/lieb.pdf

  247. (with J. Yngvason) A guide to Entropy and the Second Law of Thermodynamics, Notices of the Amer. Math. Soc. 45, 571-581 (1998). arXiv math-ph/9805005, mp_arc 98-339. http://www.ams.org/notices/199805/lieb.pdf. See no. 266. This paper received the American Mathematical Society 2002 Levi Conant prize for ``the best expository paper published in either the Notices of the AMS or the Bulletin of the AMS in the preceding five years''.

  248. (with D. Hundertmark and L.E. Thomas) A Sharp Bound for an Eigenvalue Moment of the One-Dimensional Schroedinger Operator, Adv. Theor. Math. Phys. 2, 719- 731 (1998). arXiv math-ph/9806012, mp_arc 98-753.

  249. (with E. Carlen) A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy, in Amer. Math. Soc. Transl. (2), 189, 59-69 (1999). arXiv math/0701352.

  250. (with J. Yngvason) The Physics and Mathematics of the Second Law of Thermodynamics, Physics Reports 310, 1-96 (1999). arXiv cond-mat/9708200, mp_arc 97-457.

  251. Some Problems in Statistical Mechanics that I would like to see Solved, 1998 IUPAP Boltzmann prize lecture, Physica A 263, 491-499 (1999).

  252. (with P. Schupp) Ground State Properties of a Fully Frustrated Quantum Spin System, Phys. Rev. Lett. 83, 5362-5365 (1999). arXiv math-ph/9908019, mp_arc 99-304.

  253. (with P. Schupp) Singlets and Reflection Symmetric Spin Systems, Physica A 279, 378-385 (2000). arXiv math-ph/9910037, mp_arc 99-404.

  254. (with R. Seiringer and J.Yngvason) Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional, Phys. Rev. A 61, 043602-1 -- 043602-13 (2000). arXiv math-ph/9908027, mp_arc 99-312.

  255. (with J. Yngvason) The Ground State Energy of a Dilute Bose Gas, in Differential Equations and Mathematical Physics, University of Alabama, Birmingham, 1999, R. Weikard and G. Weinstein, eds., 295-306, Amer. Math. Soc./Internat. Press (2000). arXiv math-ph/9910033, mp_arc 99-401.

  256. (with M. Loss) Self-Energy of Electrons in Non-perturbative QED, in Differential Equations and Mathematical Physics, University of Alabama, Birmingham, 1999, R. Weikard and G. Weinstein, eds. 279-293, Amer. Math. Soc./Internat. Press (2000). arXiv math-ph/9908020, mp_arc 99-305.

  257. (with R. Seiringer and J. Yngvason) The Ground State Energy and Density of Interacting Bosons in a Trap, in Quantum Theory and Symmetries, Goslar, 1999, H.-D. Doebner, V.K. Dobrev, J.-D. Hennig and W. Luecke, eds., pp. 101-110, World Scientific (2000). arXiv math-ph/9911026, mp_arc 99-439.

  258. (with J. Yngvason) The Ground State Energy of a Dilute Two-dimensional Bose Gas, J. Stat. Phys. 103, 509-526 (2001). arXiv math-ph/0002014, mp_arc 00-63.

  259. (with J. Yngvason) A Fresh Look at Entropy and the Second Law of Thermodynamics, Physics Today, 53, 32-37 (April 2000). arXiv math-ph/0003028, mp_arc 00-123. See also 53, 11-14, 106 (October 2000).

  260. Lieb-Thirring Inequalities, in Encyclopaedia of Mathematics, Supplement vol. 2, pp. 311-313, Kluwer (2000). arXiv math-ph/0003039, mp_arc 00-132.

  261. Thomas-Fermi Theory, in Encyclopaedia of Mathematics, Supplement vol. 2, pp. 455-457, Kluwer (2000). arXiv math-ph/0003040, mp_arc 00-131.

  262. (with H. Siedentop) Renormalization of the Regularized Relativistic Electron-Positron Field, Commun. Math. Phys. 213, 673-684 (2000). arXiv math-ph/0003001, mp_arc 00-98.

  263. (with R. Seiringer and J. Yngvason) A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-dimensional Bose Gas, Commun. Math. Phys. 224, 17-31 (2001). arXiv cond-mat/0005026, mp_arc 00-203.

  264. (with M. Griesemer and M. Loss) Ground States in Non-relativistic Quantum Electrodynamics, Invent. Math. 145, 557-595 (2001). arXiv math-ph/0007014, mp_arc 00-313.

  265. (with J.P. Solovej) Ground State Energy of the One-Component Charged Bose Gas, Commun. Math. Phys. 217, 127-163 (2001). Errata 225, 219-221 (2002). arXiv cond-mat/0007425, mp_arc 00-303.

  266. (with J. Yngvason) The Mathematics of the Second Law of Thermodynamics, in Visions in Mathematics, Towards 2000, A. Alon, J. Bourgain, A. Connes, M. Gromov and V. Milman, eds., GAFA 2000, no. 1, Birkhauser, p. 334-358 (2000). mp_arc 00-332. See no. 247.

  267. The Bose Gas: A Subtle Many-Body Problem, in Proceedings of the XIII International Congress on Mathematical Physics, London, A. Fokas, et al. eds. International Press, pp. 91-111, 2001. arXiv math-ph/0107003, mp_arc 01-243.

  268. (with J. Freericks and D. Ueltschi) Segregation in the Falicov-Kimball Model, Commun. Math. Phys. 227, 243-279 (2002). arXiv math-ph/0107003, mp_arc 01-243.

  269. (with G.K. Pedersen) Convex Multivariable Trace Functions, Reviews in Math. Phys. 14, 1-18 (2002). arXiv math.OA/0107062.

  270. (with J. Freericks and D. Ueltschi) Phase Separation due to Quantum Mechanical Correlations, Phys. Rev. Lett. 88, #106401 (2002). arXiv cond-mat/0110251.

  271. (with M. Loss) Stability of a Model of Relativistic Quantum Electrodynamics, Commun. Math. Phys. 228, 561-588 (2002). arXiv math-ph/0109002, mp_arc 01-315.

  272. (with M. Loss) A Bound on Binding Energies and Mass Renormalization in Models of Quantum Electrodynamics, J. Stat. Phys. 108, 1057-1069 (2002). arXiv math-ph/0110027.

  273. (with R. Seiringer) Proof of Bose-Einstein Condensation for Dilute Trapped Gases, Phys. Rev. Lett. , Phys. Rev. Lett. 88, #170409 (2002). arXiv math-ph/0112032, mp_arc 02-115.

  274. (with M. Loss) Stability of Matter in Relativistic Quantum Mechanics, in Mathematical Results in Quantum Mechanics, Proceedings of QMath8, Taxco, Amer. Math. Soc. Contemporary Mathematics series, pp. 225-238, 2002.

  275. (with J.Yngvason) The Mathematical Structure of the Second Law of Thermodynamics, in Current Developments in Mathematics 2001, International Press, de Jong, et al eds., 2002, pp. 89-129 . arXiv math-ph/0204007.

  276. (with R. Seiringer, J.P. Solovej and J. Yngvason) The Ground State of the Bose Gas, in Currrent Developments in Mathematics 2001, International Press, de Jong, et al eds., 2002, pp. 131-178. arXiv math-ph/0204027, mp_arc 02-183.

  277. (with R. Seiringer and J. Yngvason) Poincare Inequalities in Punctured Domains, Annals of Math. 158, 1067-1080 (2003). arXiv math.FA/0205088.

  278. (with R. Seiringer and J. Yngvason) Superfluidity in Dilute Trapped Bose Gases, Phys. Rev. B 66, #134529 (2002). arXiv cond-mat/0205570, mp_arc 02-339.

  279. (with F.Y. Wu) The one-dimensional Hubbard model: A reminiscence, Physica A 321, 1-27 (2003). arXiv cond-mat/0207529.

  280. (with E. Eisenberg) Polarization of interacting bosons with spin, Phys. Rev. Lett. 89, #220403 (2002). arXiv cond-mat/0207042, mp_arc 02-446.

  281. The Stability of Matter and Quantum Electrodynamics, Proceedings of the Heisenberg symposium, Munich, Dec. 2001, Fundamental Physics--Heisenberg and Beyond , G. Buschhorn and J. Wess, eds., pp. 53-68, Springer (2004). arXiv math-ph/0209034. A modified version appears in the Milan Journal of Mathematics 71 , 199-217 (2003). A further modification appears in the Jahresbericht of the German Math. Soc. JB 106 , 93-110 (2004) (Teubner). arXiv math-ph/0401004.

  282. (with R. Seiringer and J. Yngvason) Two-dimensional Gross-Pitaevskii Theory, in: A.G. Litvak (editor). Progress in Nonlinear Science, Proceedings of the International Conference Dedicated to the 100th Anniversary of A.A. Andronov, Volume II, pp 582--590, Nizhny Novgorod, Institute of Applied Physics, University of Nizhny Novgorod, 2002.

  283. (with R. Seiringer) Equivalent forms of the Bessis-Moussa-Villani Conjecture, J. Stat. Phys. 115 , 185-190 (2004). arXiv math-ph/0210027.

  284. (with R. Seiringer and J. Yngvason) One-dimensional Bosons in Three-dimensional Traps, Phys. Rev. Lett. 91, #150401 (2003). arXiv cond-mat/0304071.

  285. (with R. Seiringer and J. Yngvason) One-dimensional Behavior of Dilute, Trapped Bose Gases. Commun. Math. Phys. 244, 347-393 (2004). arXiv math-ph/0305025.

  286. (with R. Seiringer) Bose-Einstein Condensation of Dilute Gases in Traps, in Differential Equations and Mathematical Physics, proceedings of a conference in Univ. of Birmingham, 2002, Amer. Math. Soc. Contemporary Math. series, Y. Karpeshina, G. Stolz, R. Weikard, Y. Zeng, eds., 327, 239-250 (2003).

  287. (with M. Loss) Existence of Atoms and Molecules in Non-relativistic Quantum Electrodynamics, Adv. Theor. Math. Phys. 7 , 667-710 (2003). arXiv math-ph/0307046.

  288. (with J.P. Solovej) Ground State Energy of the Two-Component Charged Bose Gas, Commun. Math. Phys. 252, 485-534 (2004). arXiv math-phys/0311010, mp\_arc 03-490.

  289. (with J. Yngvason) The Entropy of Classical Thermodynamics, in Entropy, the proceedings of a conference in Dresden, 2000, A.~Greven, G.~Keller and G. Warnecke eds., Princeton University Press, pp. 147-196 (2003).

  290. (with M. Loss) A Note on Polarization Vectors in Quantum Electrodynamics, Commun. Math. Phys. 252, 477-483 (2004). arXiv math-ph/0401016.

  291. (with M. Aizenman, R. Seiringer, J.P. Solovej and J. Yngvason) Bose-Einstein Quantum Phase Transition in an Optical Lattice Model, Phys. Rev. A 70 , 023612-(1-12) (2004). arXiv cond-mat/0403240. See #306.

  292. (with E. Carlen) Some Matrix Rearrangement Inequalities, Annali di Matematica Pura ed Applicada 185 Supplement, 315-324 (2006). arXiv math.OA/0402239.

  293. (with R. Seiringer, J.P. Solovej and J. Yngvason) The Quantum-Mechanical Many-Body Problem: The Bose Gas, Proceedings of the conference `Perspectives in Analysis', KTH Stockholm, 2003, M.~Benedicks, P.~Jones and S.~Smirnov, eds., Springer Verlag (in press). arxiv math-ph/0405004.

  294. (with M. Loss) The Thermodynamic Limit for Matter Interacting with Coulomb Forces and with the Quantized Electromagnetic Field: I. The Lower Bound, Commun. Math. Phys. 258 , 675-695 (2005). arXiv math-ph/0408001.

  295. (with E. Carlen and M. Loss) A Sharp analog of Young's Inequality on ${\bf S}^N$ and Related Entropy Inequalities, Jour. Geom. Anal. 14 , 487-520 (2004). arXiv math.FA/0408030.

  296. (with R. Seiringer and J.P. Solovej) Ground State Energy of the Low Density Fermi Gas, Phys. Rev. A 71, 053605-(1-13) (2005). arXiv math-ph/0412080.

  297. (with R. Seiringer) A Stronger Subadditivity of Entropy, Phys. Rev. A 71, 062329-(1-9) (2005). arXiv math-ph/0412009.

  298. (with R. Seiringer and J. Yngvason) Justification of c-Number Substitutions in Bosonic Hamiltonians, Phys. Rev. Lett. 94, 080401--1-4 (2005). arXiv math-ph/0412023.

  299. (with R. Seiringer, J.P. Solovej and J. Yngvason) The Mathematics of the Bose Gas and its Condensation, vol. 34, Oberwolfach Seminars Series, Birkhaeuser (2005). arXiv cond-mat/0610117.

  300. (with E. Carlen and M. Loss) An Inequality of Hadamard Type for Permanents, Methods and Applications of Analysis 13, 1-18 (2006). arXiv math.CA/0508096.

  301. (with R. Seiringer) Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases, Commun. Math. Phys. 264, 505-537 (2006). arXiv math-ph/0504042.

  302. (with V. Bach and M. Travaglia) Ferromagnetism of the Hubbard Model at Strong Coupling in the Hartree-Fock Approximation, Rev. Math. Phys. 18, 519-543 (2006). arXiv cond-mat/0506695.

  303. (with R.L. Frank, A. Laptev and R. Seiringer) Lieb-Thirring inequalities for Schroedinger operators with complex-valued potentials, Lett. Math. Phys. 77, 309-316 (2006). arXiv math-ph/0605017.

  304. (with A. Giuliani and J.L. Lebowitz) Ising models with long-range dipolar and short range ferromagnetic interactions, Phys. Rev. B 74, 064420--1-11 (2006). arXiv cond-mat/0604668.

  305. (with D. Osherson and S. Weinstein) Elementary Proof of a Theorem of Jean Ville. arXiv cs.CC/0607054.

  306. (with R. Seiringer and J.P. Solovej) Ground-State Energy of a Dilute Fermi Gas, in Recent Advances in Differential Equations and Mathematical Physics, proceedings of a conference at the Univ. of Birmingham, 2005, Amer. Math. Soc. Contemporary Math. series, N. Chernov, Y. Karpeshina, I. Knowles, R. Lewis, R. Weikard eds., 412, 239-248 (2006).

  307. (with M. Aizenman, R. Seiringer, J.P. Solovej and J. Yngvason) Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice, in Mathematical Physics of Quantum Mechanics, J. Asch and A. Joye Eds., Lecture Notes in Physics 690, 199-215, Springer (2006). arXiv cond-mat/0412034. See #291.

  308. (with R. Seiringer and J. Yngvason) Bose-Einstein Condensation and Spontaneous Symmetry Breaking, in Proceedings of the 21st Max Born Symposium, Wroclaw, Poland, June 26--28, 2006. Reports on Mathematical Physics. arXiv math-ph/0610034.

  309. (with R.L. Frank and R. Seiringer} Stability of Relativistic Matter with Magnetic Fields for Nuclear Charges up to the Critical Value, Commun. Math. Phys. 275, 479-489 (2007). arXiv math-ph/0610062.

  310. (with R.L. Frank and R. Seiringer) Hardy-Lieb-Thirring inequalities for fractional Schr\"odinger operators, Jour. Amer. Math. Soc. (in press). arXiv math.SP/0610593.

  311. (with R.L. Frank, R. Seiringer and H. Siedentop) Mueller's Exchange-Correlation Energy in Density-Matrix-Functional Theory. Phys. Rev. A 76, 052517 (2007). arXiv:0705.1587[cond-mat.str-el].

  312. (with J. Yngvason) A Second Look at the Second Law of Thermodynamics, in Prospects in Mathematical Physics `Young Researcher's Symposium', 14th International Congress on Mathematical Physics, Lisbon 2003, Amer. Math. Soc. Contemporary Math. series, J.C. Mourao, J.P. Nunes, R. Picken, J-C Zambrini eds., 437, 127-158 (2007).

  313. (with A. Giuliani and J.L. Lebowitz) Striped Phases in Two Dimensional Dipole Systems, Phys. Rev. B 76, 184426 (2007). arXiv:0707.3760[cond-mat.stat-mech].

  314. (with J. Predd, R. Seiringer, D. Osherson, V. Poor, and S. Kulkarni) Probabilistic Coherence and Proper Scoring Rules, IEEE Trans. Information Theory 55, 4786-4792 (2009). arXiv:0710.3183 [stat.ML]

  315. (with R.L. Frank and R. Seiringer) Number of Bound States of Schroedinger Operators with Matrix-Valued Potentials, Lett. Math. Phys. 82, 107-116 (2007). arXiv:0710.1877 [math-ph].

  316. (with S. Jansen and R. Seiler) Symmetry Breaking in Laughlin's State on a Cylinder, Commun. Math. Phys. 285, 503-535 (2009). arXiv:0711.1467[cond-mat.mes-hall].

  317. (with S. Jansen and R. Seiler) Laughlin's Function on a Cylinder: Plasma Analogy and Representation as a Quantum Polymer Physica Status Solidi (b) 245, No. 2, 439–446 (2008). Special issue on Quantum Hall systems. arXiv:0802.2208[cond-mat.mes-hall].

  318. (with E. Carlen) A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and concavity. Lett. Math. Phys. 83, 107-126 (2008) arXiv:math/0701352[math.OA].

  319. (with A. Giuliani and J.L. Lebowitz) Periodic minimizers in 1D local mean field theory, Commun. Math. Phys. 286, 163-177 (2009). arXiv:math-ph/0712.2330, mp-arc 07-307.

  320. (with E. Carlen) Brascamp-Lieb Inequalities for Non-commutative Integration, Documenta Math. 13, 553-584 (2008). arxiv:0808.1060[math.FA].

  321. What if Boltzmann had known about quantum Mechanics?, in Boltzmann's Legacy, G. Gallavotti, W. Reiter and J. Yngvason, eds. ESI Lectures in Mathematics and Physics, European Math. Soc. Publishing House, pp. 27-38 (2008).

  322. (with A. Giuliani and J.L. Lebowitz) Pattern formation in Systems with Competing Interactions, Proceedings of the 10th Granada Seminar on Computational Physics, Amer. Inst. Phys.. arXiv:0811.3078.

  323. Quantum Mechanics, the Stability of Matter and Quantum Electrodynamics, Contemporary Math 476, 133-148 (2008). Lectures at the fourth summer school in analysis and mathematical physics, Cuernavaca, 2005.

  324. (with E. Carlen) Short Proofs of Theorems of Horn and Mirsky on Diagonals and Eigenvalues of Matrices, Electronic Jour. Linear Alg. 18, 438-441 (2009). arXiv:0904.0734.

  325. (with A. Giuliani and J. Lebowitz) Modulated Phases of a 1D Sharp Interface Model in a Magnetic Field. Phys. Rev. B 80, 134420-1-6 (2009). arXiv:0905.3758.

  326. (with R. Frank) Inversion Positivity and the Sharp Hardy-Littlewood-Sobolev Inequality, arXiv:0904.4275.

  327. (with R. Seiringer and J. Yngvason) Yrast Line of a Rapidly Rotating Bose Gas: Gross--Pitaevskii Regime, Phys. Rev. A 79, 06326 (2009). Also selected for the July 2009 issue of Virtual Journal of Atomic Quantum Fluids, http://www.vjaqf.org. arXiv:0904.1750.

  328. (with R. Seiringer) The Stability of Matter in Quantum Mechanics, 293 pages, Cambridge University Press (2010).

  329. (with R. Frank and R. Seiringer) Equivalence of Sobolev Inequalities and Lieb-Thirring Inequalities, Proceedings of the XVI International Congress on Mathematical Physics, Prague, 2009. P. Exner ed., World Scientific. arXiv:0909.5449.

  330. (with R. Frank) Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality, Proceedings of International Workshop on Concentration Functional Inequalities and Isoperimetry, Boca Raton, 2009. Contemporary Mathematics 545, 89-102 (2011). arXiv:1003.5248.

  331. (with C. Decker, R.J. McCann and B.K. Stephens) Existence, Uniqueness, and Substitution Effects in the Choo-Siow Marriage Matching Model. Title changed to: Unique Equilibria and Substitution Effects in a Stochastic Model of the Marriage Market, J. Economic Theory 148, 778-792 (2013)). arxiv:1012.1904.

  332. (with R. Frank) Sharp Constants in Several Inequalities on the Heisenberg Group, Annals of Math 176, 349-381 (2012). DOI 10.4007/annals.2012.176.1.6. arXiv:1009.1410.

  333. (with R. Frank, R. Seiringer and L. Thomas) Bi-Polaron and $N$-Polaron Binding Energies, Phys. Rev. Lett. 104, 210402 (2010). arXiv:1004.1196.

  334. (with R. Frank, R. Seiringer and L. Thomas) Stability and Absence of Binding for Multi-Polaron Systems, Publication Math\'ematiques de l'IHES 113, Number 1, 39-67 (2011). . arxiv:1004.4892.

  335. (with R. Frank, R. Seiringer and L. Thomas) Binding, Stability, and Non-binding of Multi-polaron Systems, Proceedings of the conference QMath 11 (Hradec Kralove, September 2010). World Scientific. arXiv:1010.0737.

  336. (with Y. Ostrover) Localization of Multi-dimensional Wigner Distributions, Jour. Math. Phys. 51, 102101 (2010). arXiv:1007.1796.

  337. (with R.Frank) A New, Rearrangement-Free Proof of the Sharp Hardy-Littlewood-Sobolev Inequality, Operator Theory: Advances and Applications, 219, 55-67 (2011), Birkhauser. arXiv:1010.5821.

  338. (with R. Frank, M. Lewin and R. Seiringer) Energy Cost to Make a Hole in the Fermi Sea, Phys. Rev. Lett. 106, 150402 (2011). arXiv:1102.1414.

  339. (with R. Frank, M. Lewin and R. Seiringer) A Positive Density Analogue of the Lieb-Thirring Inequality, (2011). (A detailed version of previous item 338.) Duke Math. Jour. 162, 435-494 (2013). DOI 10.1215/00127094-2019477 arXiv: 1108.4246.

  340. (with E. A. Carlen and D.Cordero-Erquasquin) Asymmetric Covariance Estimates of Brascamp-Lieb Type and Related Inequalities for Log-concave Measuresi, Ann. Inst. Henri Poincar\'e - Probabilit\'es et Statistiques 49, 1–12 (2013). DOI: 10.1214/11-AIHP462. arXiv:1106.0709.

  341. (with R. Frank) Possible Lattice Distortions in the Hubbard Model for Graphene, Phys. Rev. Lett. 107, 066801 (2011). arXiv:1105.0693.

  342. (with R. Frank and R. Seiringer) Binding of Polarons and Atoms at Threshold, Commun. Math. Phys. 313, 405-424 (2012). DOI 10.1007/s00220-012-1436-9(2012). arXiv:1106.0729.

  343. (with A. Giuliani and J. Lebowitz) Checkerboards, Stripes and Corner Energies in Spin Models with Competing Interactions, Phys. Rev. B 84, 064205 (2011). arXiv:1106.0922.

  344. (with Y. Yang) Non-Abelian Vortices in Supersymmetric Gauge Field Theory via Direct Method, Commun. Math. Phys. 313, 445-478 (2012). DOI: 10.1007/s00220-009-0838-9. arXiv:1106.1626.

  345. (with R. Frank) Entropy and the Uncertainty Principle, Annales Henri Poincare 13, 1711-1717 (2012). DOI 10.1007/s00023-012-0175-y. arXiv:1109.1209.

  346. (with R. Frank and R. Seiringer) Symmetry of Bipolaron Bound States for Small Coulomb Repulsion, Commun. Math. Phys., 319, 557-573 (2013) DOI: 10.1007/s00220-012-1604-y. arXiv:1201.3954.

  347. (with E. Carlen) Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy, Lett. Math. Phys. 101, 1-11 (2012). DOI 10.1007/s11005-012-0565-6.. arXiv:1203.4719.

  348. (with R. Frank) Extended Quantum Conditional Entropy and Quantum Uncertainty Inequalities, Commun. Math. Phys. 323, 487-495 (2013). ). arxiv:1204.0825.

  349. (with R. Seiringer) Further Implications of the Bessis-Moussa-Villani Conjecture, J. Stat. Phys. 149, 86-91 (2012). DOI: 10.1007/s10955-012-0585-8. arXiv:1206.0460.

  350. (with J.P. Solovej) Proof of an Entropy Conjecture for Bloch Coherent Spin States and its Generalizations, Acta Math. 212, 379-398 (2014). DOI: 10.1007/s11511-014-0113-6. arXiv:1208.3632.

  351. (with O. Lazarev) A Smooth, Complex Generalization of the Hobby-Rice Theorem, Indiana Univ. Math. Jour. 62, 1350021 (2014). arXiv:1205.5059.

  352. (with R. Frank, R. Seiringer and L. Thomas) Ground State Properties of Multi-Polaron Systems, in Proceedings of ICMP12, Aalborg, 2012, 477-485, World Scientific (2013). arXiv:1209:3717.

  353. (with E. Carlen and J. Lebowitz) On an Extension Problem for Density Matrices, Jour. Math. Phys. 54, 062103 (2013) arXiv:1301:4605

  354. (with E. Carlen and R. Frank) Stability Estimates for the Lowest Eigenvalue of a Schroedinger Operator, J. Geometric and Functional Analysis, 24, 63-84 (2014). DOI: 10.1007/s00039-014-0253-z. arXiv:1301.5032.

  355. (with J. Bellazzini, R. Frank and R. Seiringer) Existence of ground states at the binding threshold, Rev. Math. Phys. 26, 1350021 (2014). DOI: 10.1142/S0129055X13500219. arXiv:1301.5370.

  356. (with A. Vershynina) Upper bounds on mixing rates, Quantum Information and Computation 13, No.11 & 12, 0986-0994 (2013). arXiv:1302:3865.

  357. (with R. Seiringer) Equivalence of Two Definitions of the Effective Mass of a Polaron, J. Stat. Phys. 154, Issue 1-2, 51-57 (2014). DOI 10.1007/s10955-013-0791-z.. arXiv:1304.1780.

  358. (with A. Giuliani and R. Seiringer) Formation of Stripes and Slabs near the Ferromagnetic Transition, Commun. Math. Phys. 331, 333-350 (2014). DOI: 10.1007/s00220-014-1923-2. arxiv:1304.6344.

  359. (with A. Giuliani and R. Seiringer) Realization of Stripes and Slabs in Two and Three Dimensions, Phys. Rev. B, 88, 064401 (2013). DOI: 10.1103/PhysRevB.88.064401. arXiv:1305.5323.

  360. (with R. Frank, M. Lewin and R. Seiringer) Strichartz Inequality for Orthonormal Functions, Jour. European Math. Soc., 16, 1507-1526 (2014). DOI 10.4171/JEMS/467. arXiv:1306.1309.

  361. (with J. Yngvason) The Entropy Concept for Non-Equilibrium States, Proc. Roy. Soc. A469: 20130408 (2013). Doi.org/10.1098/rspa.2013.0408. arXiv:1305.3912.

  362. (with R. Schrader) Current Densities in Density Functional Theory. Phys. Rev. A 88, 032516 (2013). Listed as "Editor's suggestion". DOI: 10.1103/PhysRevA.88.032516. arXiv:1308.2664.

  363. (with R. Frank) Monotonicity of a Relative Renyi Entropy, Jour. Math. Phys. 54, 122201 (2013). DOI: 10.1063/1.4838835. arXiv:1306.5358

  364. (with Y. Li and C. Wu) Exact Results on Itinerant Ferromagnetism in Two- and Three-Dimensional Multi-orbital Systems, Phys. Rev. Lett. 112, 068103 (2014). DOI:10.1103/PhysRevLett.112.217201. arXiv:1310.4391.

  365. (with J. Yngvason) Entropy Meters and the Entropy of Non-extensive Systems, Proc. Roy. Soc. A 470 20140192 (2014). DOI:10.1098/rspa.2014.0192. arXiv:1403.0902.

  366. (with E. Carlen) Remainder Terms for Some Quantum Entropy Inequalities, Jour. Math. Phys. 55, 042201 (2014); DOI:10.1063/1.4871575. arXiv:1402.3840.

  367. (with E. Carlen and R. Reuvers) Entropy and Entanglement Bounds for Reduced Density Matrices of Fermionic States, Commun. Math.Phys. 344, 655–671 (2016). DOI 10.1007/s00220-016-2651-6. arXiv:1403.3816.

  368. An Open Problem about Exchange-Correlation Energy, in "Many-electron Approaches in Physics, Chemistry and Mathematics" 415-416, V. Bach and L. Delle Sitte, eds., Springer Mathematical Physics Studies (2014).

  369. (with M. Lewin) Improved Lieb-Oxford Exchange-Correlation Inequality with Gradient Correction, Phys. Rev. A 91, 022507 (2015). DOI: http://dx.doi.org/10.1103/PhysRevA.91.022507. arxiv:1408.3358.

  370. (with E. Carlen and R. Frank) Some Operator and Trace Function Convexity Theorems. Lin. Alg. Appl. 490, 174-185 (2016). DOI:10.1016/j.laa.2015.11.006. arXiv:1409.0564.

  371. (with R. Benguria and R. Frank) Ground State Energy of Large Polaron Systems, J. Math. Phys. 56 , 021901 (2015) ; http://dx.doi.org/10.1063/1.4908125 . arXiv: 1409.5415.

  372. (with A. Giuliani) Columnar Phase in Quantum Dimer Models. J. Phys.A: Math. Theor. 48, 235203 (2015). DOI:10.1088/1751-8113/48/23/235203. This paper was chosen for J. Phys. A. Higlights of 2015. arXiv: 1502.02254.

  373. (with R. Frank) A Compactness Lemma and its Application to the Existence of Minimizers for the Liquid Drop Model, SIAM Jour. Math. Analysis 47, 4436–4450 (2015). DOI. 10.1137/15M1010658. arXiv:1503.00192.

  374. (with J.P. Solovej) Proof of the Wehrl-type Entropy Conjecture for Symmmetric SU(N) Coherent States. Commun. Math. Phys. 348, 567-578 (2016). DOI:10.1007/s00220-016-2596-9. arXiv:1506.07633.

  375. (with A. Giuliani and I. Jauslin) A Pfaffian Formula for Monomer-Dimer Partition Functions, Jour. Stat. Phys. 163, 211–238, (2016). DOI:10.1007/s10955-016-1484-1. arXiv:1510.05027.

  376. (with E. Carlen and M. Loss) On a Quantum Entropy Power Inequality of Audenaert, Datta and Ozols, J. Math. Phys. 57, 062203 (2016); DOI: 10.1063/1.4953638. arXiv:1603.07043.

  377. (with R. Frank and J. Sabin) Maximizers for the Stein-Tomas Inequality, Geometric and Functional Analysis, {\bf 26}, 1095-1134 (2016). DOI: 10.1007/s00039-016-0380-9. arXiv:1603.07658.

  378. (with R. Frank) A `Liquid-Solid' Phase Transition in a Simple Model for Swarming, based on the `no flat-spots' theorem for subharmonic functions, Indiana, Univ. Math. Journal. arXiv:1607.07971.

  379. (with N. Rougerie and J. Yngvason) Rigidity of the Laughlin Liquid. arXiv 1609.03818.

  380. (with N. Rougerie and J. Yngvason) Local incompressibility estimates for the laughlin phase. arXiv:1701.09064.

  381. (with R. Frank) Norms of quantum Gaussian multi-mode channels. J. Math. Phys. arxiv:1704.08720.

  382. (with M. Lewin and R. Seiringer) Statistical Mechanics of the Uniform Electron Gas. arXiv:1705.10676.

  383. (with Ian Jauslin) Nematic liquid crystal phase in a system of interacting dimers and monomers, arXiv:1709.05297.

  384. (with Eric Carlen) Some trace inequalities for exponential and logarithmic functions, arXiv:1709.05450.


Last updated