E. H. LIEB  Publications
 Second Order Radiative Corrections to the Magnetic Moment of a
Bound Electron, Phil. Mag. Vol. 46, 311316 (1955).
 A NonPerturbation Method for NonLinear Field Theories,
Proc. Roy. Soc. 241A, 339363 (1957).
 (with K. Yamazaki) Ground State Energy and Effective Mass of the
Polaron, Phys. Rev. 111, 728733 (1958).
 (with H. Koppe) Mathematical Analysis of a Simple Model Related
to the Stripping Reaction, Phys. Rev. 116, 367371 (1959).
 Hard Sphere Bose Gas  An Exact Momentum Space Formulation,
Proc. U.S. Nat. Acad. Sci. 46, 10001002 (1960).
 Operator Formalism in Statistical Mechanics, J. Math. Phys.
2, 341343 (1961).

(with D.C. Mattis) Exact Wave Functions in Superconductivity, J.
Math. Phys. 2, 602609 (1961).

(with T.D. Schultz and D.C. Mattis) Two Soluble Models of an
Antiferromagnetic Chain, Annals of Phys. (N.Y.) 16, 407466 (1961).

(with D.C. Mattis) Theory of Ferromagnetism and the Ordering of
Electronic Energy Levels, Phys. Rev. 125, 164172 (1962).

(with D.C. Mattis) Ordering Energy Levels of Interacting Spin
Systems, J. Math. Phys. 3, 749751 (1962).

New Method in the Theory of Imperfect Gases and Liquids, J.
Math. Phys. 4, 671678 (1963).

(with W. Liniger) Exact Analysis of an Interacting Bose Gas. I.
The General Solution and the Ground State, Phys. Rev. 130, 16051616
(1963).

Exact Analysis of an Interacting Bose Gas. II. The Excitation
Spectrum, Phys. Rev. 130, 16161624 (1963).

Simplified Approach to the Ground State Energy of an Imperfect
Bose Gas, Phys. Rev. 130, 25182528 (1963).

(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, A899A906 (1964).

(with W. Liniger) Simplified Approach to the Ground State
Energy of an Imperfect Bose Gas. III. Application to the OneDimensional
Model, Phys. Rev. 134, A312A315 (1964).

(with T.D. Schultz and D.C. Mattis) TwoDimensional Ising Model
as a Soluble Problem of Many Fermions, Rev. Mod. Phys. 36, 856871
(1964).

The Bose Fluid, Lectures in Theoretical Physics, Vol.
VIIC, (Boulder summer school), University of Colorado Press, 175224
(1965).

(with D.C. Mattis) Exact Solution of a ManyFermion System and
its Associated Boson Field, J. Math. Phys. 6, 304312 (1965).

(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, A129A130 (1965).

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

Proofs of Some Conjectures on Permanents, J. of Math. and
Mech. 16, 127139 (1966).

Quantum Mechanical Extension of the LebowitzPenrose Theorem on
the van der Waals Theory, J. Math. Phys. 7, 10161024 (1966).

(with D.C. Mattis) Theory of Paramagnetic Impurities in
Semiconductors, J. Math. Phys. 7, 20452052 (1966).

(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, 118122 (1966).

Some Comments on the OneDimensional ManyBody Problem,
unpublished Proceedings of Eastern Theoretical Physics Conference, New York
(1966).

Calculation of Exchange Second Virial Coefficient of a Hard
Sphere Gas by Path Integrals, J. Math. Phys. 8, 4352 (1967).

(with Z. Rieder and J.L. Lebowitz) Properties of a Harmonic
Crystal in a Stationary Nonequilibrium State, J. Math. Phys. 8,
10731078 (1967).

Exact Solution of the Problem of the Entropy of TwoDimensional
Ice, Phys. Rev. Lett. 18, 692694 (1967).

Exact Solution of the F Model of an Antiferroelectric, Phys.
Rev. Lett. 18, 10461048 (1967).

Exact Solution of the TwoDimensional Slater KDP Model of a
Ferroelectric, Phys. Rev. Lett. 19, 108110 (1967).

The Residual Entropy of Square Ice, Phys. Rev. 162,
162172 (1967).

Ice, Ferro and Antiferroelectrics, in Methods and
Problems in Theoretical Physics, in honour of R.E. Peierls,
proceedings of the 1967 Birmingham conference, (NorthHolland, 1970)
p. 2128.

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. 286306.

The Solution of the Dimer Problems by the Transfer Matrix
Method, J. Math. Phys. 8, 23392341 (1967).

(with M. Flicker) Delta Function Fermi Gas with Two Spin
Deviates, Phys. Rev. 161, 179188 (1967).

Concavity Properties and a Generating Function for Stirling
Numbers, J. Combinatorial Theory 5, 203206 (1968).

A Theorem on Pfaffians, J. Combinatorial Theory
5, 313319 (1968).

(with F.Y. Wu) Absence of Mott Transition in an Exact Solution
of the ShortRange OneBand Model in One Dimension, Phys. Rev. Lett.
20, 14451448 (1968). Errata:
Phys. Rev. Lett. 21, 192 (1968).

Two Dimensional Ferroelectric Models, J. Phys. Soc. (Japan)
26 (supplement), 9495 (1969).

(with W.A. Beyer) Clusters on a Thin Quadratic Lattice, Studies
in Appl. Math. 48, 7790 (1969).

(with C.J. Thompson) Phase Transition in Zero Dimensions: A
Remark on the Spherical Model, J. Math. Phys. 10, 14031406
(1969).

(with J.L. Lebowitz) The Existence of Thermodynamics for Real
Matter with Coulomb Forces, Phys. Rev. Lett. 22, 631634 (1969).

Two Dimensional Ice and Ferroelectric Models, in Lectures in
Theoretical Physics, XI D, (Boulder summer school) Gordon and Breach,
329354 (1969).

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. 163176.

Models, in Phase Transitions, proceedings of the 14th Solvay
Chemistry Conference, May 1969, (Interscience, 1971) p. 4556.

(with H. Araki) Entropy Inequalities, Commun. Math. Phys.
18, 160170 (1970).

(with O.J. Heilmann) Violation of the NonCrossing Rule: The
Hubbard Hamiltonian for Benzene, Trans. N.Y. Acad. Sci.33, 116149
(1970). Also in Annals N.Y. Acad. Sci. 172, 583617 (1971).
(Awarded the 1970 Boris Pregel award for research in chemical
physics.)

(with O.J. Heilmann) Monomers and Dimers, Phys. Rev. Lett.
24, 14121414 (1970).

Book Review of ``Statistical Mechanics'' by David Ruelle, Bull.
Amer. Math. Soc. 76, 683687 (1970).

(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, 155162 (1970).

(with D.B. Abraham, T. Oguchi and T. Yamamoto) On the Anomolous
Specific Heat of Sodium Trihydrogen Selenite, Progr. Theor. Phys. (Kyoto)
44, 11141115 (1970).

(with D.B. Abraham) Anomalous Specific Heat of Sodium
Trihydrogen Selenite  An Associated Combinatorial Problem, J. Chem. Phys.
54, 14461450 (1971).

(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, 1927 (1971).

(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. 281326.

(with H.N.V. Temperley) Relations between the
`Percolation' and `Colouring' Problem and Other GraphTheoretical
Problems Associated with Regular Planar Lattices: Some Exact Results
for the `Percolation' Problem, Proc. Roy. Soc. A322, 251280 (1971).

(with M. de Llano) Some Exact Results in the HartreeFock
Theory of a ManyFermion System at High Densities, Phys. Letts. 37B,
4749 (1971).

(with J.L. Lebowitz) The Constitution of Matter: Existence of
Thermodynamics for Systems Composed of Electrons and Nuclei, Adv. in
Math. 9, 316398 (1972).

(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. 331490.

(with D. Ruelle) A Property of Zeros of the Partition Function
for Ising Spin Systems, J. Math. Phys. 13, 781784 (1972).

(with O.J. Heilmann) Theory of MonomerDimer Systems, Commun.
Math. Phys. 25, 190232 (1972). Errata 27, 166 (1972).

(with M.L. Glasser and D.B. Abraham) Analytic Properties of the
Free Energy for the ``Ice'' Models, J. Math. Phys. 13, 887900
(1972).

(with D.W. Robinson) The Finite Group Velocity of Quantum Spin
Systems, Commun. Math. Phys. 28, 251257 (1972).

(with J.L. Lebowitz) Phase Transition in a Continuum Classical
System with Finite Interactions, Phys. Lett. 39A, 98100 (1972).

(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,
136161 (1973).

(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, 423460 (1973).

Convex Trace Functions and the WignerYanaseDyson Conjecture,
Adv. in Math. 11, 2671288 (1973).

(with M.B. Ruskai) A Fundamental Property of Quantum Mechanical
Entropy, Phys. Rev. Lett. 30, 434436 (1973).

(with M.B. Ruskai) Proof of the Strong Subadditivity of
QuantumMechanical Entropy, J. Math. Phys. 14, 19381941 (1973).

(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, 360404 (1973).

(with K. Hepp) Phase Transition in Reservoir Driven Open
Systems with Applications to Lasers and Superconductors, Helv. Phys.
Acta 46, 573602 (1973).

(with K. Hepp) The Equilibrium Statistical Mechanics of Matter
Interacting with the Quantized Radiation Field, Phys. Rev. A8,
25172525 (1973).

(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, 298316 (1973).

The Classical Limit of Quantum Spin Systems, Commun. Math.
Phys. 31, 327340 (1973).

(with B. Simon) ThomasFermi Theory Revisited, Phys. Rev. Lett.
31, 681683 (1973).

(with M.B. Ruskai) Some Operator Inequalities of the Schwarz
Type, Adv. in Math. 12, 269273 (1974).

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, 226236 (1974).

(with B. Simon) On Solutions to the HartreeFock Problem for
Atoms and Molecules, J. Chem. Physics 61, 735736 (1974).

ThomasFermi and HartreeFock Theory, lecture at the 1974
International Congress of Mathematicians, Vancouver, (Proceedings,
1975) Vol. 2, p. 383386.

Some Convexity and Subadditivity Properties of Entropy, Bull.
Amer. Math. Soc. 81, 113 (1975).

(with H.J. Brascamp and J.M. Luttinger) A General Rearrangement
Inequality for Multiple Integrals, Jour. Funct. Anal. 17,
227237 (1975).

(with H.J. Brascamp) Some Inequalities for Gaussian Measures
and the LongRange Order of the OneDimensional 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. 114.

(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, 178208 (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, (NorthHolland, 1982), p. 153177.

(with P. Hertel and W. Thirring) Lower Bound to the Energy of
Complex Atoms, J. Chem. Phys. 62, 33553356 (1975).

(with W. Thirring) Bound for the Kinetic Energy of Fermions
which Proves the Stability of Matter, Phys. Rev. Lett. 35, 687689
(1975). Errata 35, 1116 (1975).

(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. 393404.

(with H.J. Brascamp) Best Constants in Young's Inequality, Its
Converse and Its Generalization to More Than Three Functions, Adv. in Math.
20, 151172 (1976).

(with H.J. Brascamp) On Extensions of the BrunnMinkowski and
PrékopaLeindler Theorems, Including Inequalities for Log Concave
Functions and with an Application to the Diffusion Equation, J. Funct.
Anal. 22, 366389 (1976).

(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. 8390.

Inequalities for Some Operator and Matrix Functions, Adv. in
Math. 20, 174178 (1976).

(with H. Narnhofer) The Thermodynamic Limit for Jellium, J.
Stat. Phys. 12, 291310 (1975). Errata
J. Stat. Phys. 14, 465 (1976).

The Stability of Matter, Rev. Mod. Phys. 48, 553569 (1976).

Bounds on the Eigenvalues of the Laplace and Schrödinger
Operators, Bull. Amer. Math. Soc. 82, 751753 (1976).

(with F.J. Dyson and B. Simon) Phase Transitions in the Quantum
Heisenberg Model, Phys. Rev. Lett. 37, 120123 (1976). (See
no. 104.)

(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. 269303.

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

(with B. Simon) ThomasFermi Theory of Atoms, Molecules and
Solids, Adv. in Math. 23, 22116 (1977).

(with O. Lanford and J. Lebowitz) Time Evolution of Infinite
Anharmonic Oscillators, J. Stat. Phys. 16, 453461 (1977).

The Stability of Matter, proceedings of the Conference on the
Fiftieth Anniversary of the Schrödinger Equation, Acta Physica
Austriaca Suppl. XVII, 181207 (1977).

Existence and Uniqueness of the Minimizing Solution of
Choquard's NonLinear Equation, Studies in Appl. Math. 57, 93105
(1977).

(with J. Fröhlich) Existence of Phase Transitions for
Anisotropic Heisenberg Models, Phys. Rev. Lett. 38, 440442
(1977).

(with B. Simon) The HartreeFock Theory for Coulomb Systems,
Commun. Math. Phys. 53, 185194 (1977).

(with W. Thirring) A Lower Bound for Level Spacings, Annals of
Phys. (N.Y.) 103, 8896 (1977).

(with F. Dyson and B. Simon) Phase Transitions in Quantum Spin
Systems with Isotropic and NonIsotropic Interactions, J. Stat. Phys.
18, 335383 (1978).

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. 101166.

(with R. Benguria) ManyBody Atomic Potentials in ThomasFermi
Theory, Annals of Phys. (N.Y.) 110, 3445 (1978).

(with R. Benguria) The Positivity of the Pressure in
ThomasFermi Theory, Commun. Math. Phys. 63, 193218 (1978). Errata
71, 94 (1980).

(with M. de Llano) Solitons and the Delta Function Fermion Gas
in HartreeFock Theory, J. Math. Phys. 19, 860868 (1978).

(with J. Fröhlich) Phase Transitions in Anisotropic Lattice
Spin Systems, Commun. Math. Phys. 60, 233267 (1978).

(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, 134 (1978). (See
no. 124.)

(with M. Aizenman and E.B. Davies) Positive Linear Maps Which
are Order Bounded on C* Subalgebras, Adv. in Math. 28, 8486
(1978).

(with M. Aizenman) On SemiClassical Bounds for Eigenvalues
of Schrödinger Operators, Phys. Lett. 66A, 427429
(1978).

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, 5967
(1978).

Proof of an Entropy Conjecture of Wehrl, Commun. Math. Phys.
62, 3541 (1978).

(with B. Simon) Monotonicity of the Electronic Contribution
to the BornOppenheimer Energy, J. Phys. B. 11, L537L542
(1978).

(with O. Heilmann) Lattice Models for Liquid Crystals, J.
Stat. Phys. 20, 679693 (1979).

(with H. Brezis) Long Range Atomic Potentials in ThomasFermi
Theory, Commun. Math. Phys. 65, 231246 (1979).

The N^{5/3} Law for Bosons, Phys. Lett. 70A, 7173
(1979).

A Lower Bound for Coulomb Energies, Phys. Lett. 70A,
444446 (1979).

Why Matter is Stable, Kagaku 49, 301307 and 385388
(1979). (In Japanese).

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

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, 91102 (1980).

The Number of Bound States of OneBody Schrödinger Operators
and the Weyl Problem, proceedings of the American Mathematical Society
Symposia in Pure Mathematics, 36, 241252 (1980).

(with J. Fröhlich, R. Israel and B. Simon) Phase Transitions and
Reflection Positivity. II. Lattice Systems with ShortRange and
Coulomb Interactions. J. Stat. Phys. 22, 297347 (1980). (See
no. 110.)

Why Matter is Stable, Chinese Jour. Phys. 17, 4962
(1980). (English version of no. 120).

A Refinement of Simon's Correlation Inequality, Commun. Math.
Phys. 77, 127135 (1980).

(with B. Simon) Pointwise Bounds on Eigenfunctions and Wave
Packets in NBody Quantum Systems. VI. Asymptotics in the TwoCluster
Region, Adv. in Appl. Math. 1, 324343 (1980).

The Uncertainty Principle, article in Encyclopedia of
Physics, edited by R. Lerner and G. Trigg, (Addison Wesley,
1981), p. 10781079.

(with S. Oxford) An Improved Lower Bound on the Indirect
Coulomb Energy, Int. J. Quant. Chem. 19, 427439 (1981).

(with R. Benguria and H. Brezis) The
ThomasFermivon Weizsäecker Theory of Atoms and Molecules,
Commun. Math. Phys. 79, 167180 (1981).

(with M. Aizenman) The Third Law of Thermodynamics and the
Degeneracy of the Ground State for Lattice Systems, J. Stat. Phys.
24, 279297 (1981).

(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,
545566 (1981).

(with A. Sokal) A General LeeYang Theorem for OneComponent
and Multicomponent Ferromagnets, Commun. Math. Phys. 80, 153179
(1981).

Variational Principle for ManyFermion Systems, Phys. Rev.
Lett. 46, 457459 (1981). Errata 47, 69 (1981).

ThomasFermi and Related Theories of Atoms and Molecules, in
Rigorous Atomic and Molecular Physics, edited by G. Velo and
A. Wightman, (Plenum Press, 1981), p. 213308.

ThomasFermi and Related Theories of Atoms and Molecules,
Rev. Mod. Phys. 53, 603641 (1981). Errata 54, 311
(1982). (Revised version of no. 135.)

Statistical Theories of Large Atoms and Molecules, proceedings
of the 1981 Oaxtepec conference on Recent Progress in ManyBody Theories,
Springer Lecture Notes in Physics, 142, 336343 (1982).

Statistical Theories of Large Atoms and Molecules, Comments
Atomic and Mol. Phys. 11, 147155 (1982).

Analysis of the ThomasFermivon Weizsäcker Equation for an
Infinite Atom without Electron Repulsion, Commun. Math. Phys. 85,
1525 (1982).

(with D.A. Liberman) Numerical Calculation of the
ThomasFermivon Weizsäcker Function for an Infinite Atom without
Electron Repulsion, Los Alamos National Laboratory Report, LA9186MS
(1982).

Monotonicity of the Molecular Electronic Energy in the Nuclear
Coordinates, J. Phys. B.: At. Mol. Phys. 15, L63L66 (1982).

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

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. 111149.

An L^{p} Bound for the Riesz and Bessel Potentials of
Orthonormal Functions, J. Funct. Anal. 51, 159165 (1983).

(with H. Brezis) A Relation Between Pointwise Convergence of
Functions and Convergence of Functionals,
Proc. Amer. Math. Soc. 88, 486490 (1983).

(with R. Benguria) A Proof of the Stability of Highly
Negative Ions in the Absence of the Pauli Principle, Phys. Rev. Lett.
50, 17711774 (1983).

Sharp Constants in the HardyLittlewoodSobolev and Related
Inequalities, Annals of Math. 118, 349374 (1983).

Density Functionals for Coulomb Systems (a revised version of
no. 143), Int. Jour. Quant. Chem. 24, 243277 (1983). An expanded
version appears in Density Functional Methods in Physics,
edited by R. Dreizler and J. da Providencia, Plenum Nato ASI Series,
123, 3180 (1985).

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).

(with I. Daubechies) One Electron Relativistic Molecules with
Coulomb Interaction, Commun. Math. Phys. 90, 497510 (1983).

(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, 143148 (NorthHolland,
1984).

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,
403412 (NorthHolland, 1984).

On the Lowest Eigenvalue of the Laplacian for the Intersection
of Two Domains, Inventiones Math. 74, 441448 (1983).

(with J. Chayes and L. Chayes) The Inverse Problem in
Classical Statistical Mechanics, Commun. Math. Phys. 93, 57121
(1984).

On Characteristic Exponents in Turbulence, Commun. Math. Phys.
92, 473480 (1984).

Atomic and Molecular Negative Ions, Phys. Rev. Lett.
52, 315317 (1984).

Bound on the Maximum Negative Ionization of Atoms and
Molecules, Phys. Rev. 29A, 30183028 (1984).

(with W. Thirring) Gravitational Collapse in Quantum
Mechanics with Relativistic Kinetic Energy, Annals of Phys. (N.Y.)
155, 494512 (1984).

(with I.M. Sigal, B. Simon and W. Thirring) Asymptotic
Neutrality of LargeZ Ions, Phys. Rev. Lett. 52, 994996
(1984). (See no. 185.)

(with R. Benguria) The Most Negative Ion in the
ThomasFermivon Weizsäcker Theory of Atoms and Molecules,
J. Phys. B: At. Mol. Phys. 18, 10451059 (1985).
 (with H. Brezis) Minimum Action Solutions of Some Vector
Field Equations, Commun. Math. Phys. 96, 97113 (1984).
 (with H. Brezis) Sobolev Inequalities with Remainder Terms,
J. Funct. Anal. 62, 7386 (1985).
 Baryon Mass Inequalities in Quark Models, Phys. Rev. Lett.
54, 19871990 (1985).
 (with J. Fröhlich and M. Loss) Stability of Coulomb Systems
with Magnetic Fields I. The OneElectron Atom, Commun. Math. Phys.
104, 251270 (1986).
 (with M. Loss) Stability of Coulomb Systems with Magnetic
Fields II. The ManyElectron Atom and the OneElectron Molecule, Commun.
Math. Phys. 104, 271282 (1986).
 (with W. Thirring) Universal Nature of van der Waals Forces
for Coulomb Systems, Phys. Rev. A 34, 4046 (1986).
 Some GinzburgLandau Type VectorField 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, 105107
(1986).
 (with I. Affleck) A Proof of Part of Haldane's Conjecture on
Spin Chains, Lett. Math. Phys. 12, 5769 (1986).
 (with H. Brezis and JM. Coron) Estimations d'Energie pour des
Applications de R^{3} a Valeurs dans S^{2},
C.R. Acad. Sci. Paris
303, Ser. 1, 207210 (1986).
 (with H. Brezis and JM. Coron) Harmonic Maps with Defects,
Commun. Math. Phys. 107, 649705 (1986).
 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. 209214.
 (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, 19 (1986).
 (with T. Kennedy) An Itinerant Electron Model with
Crystalline or Magnetic Long Range Order, Physica 138A, 320358
(1986).
 (with T. Kennedy) A Model for Crystallization: A Variation
on the Hubbard Model, in proceedings of IUPAP Statphys 16 Conference,
Boston, Physica 140A, 240250 (1986).
 (with T. Kennedy) Proof of the Peierls Instability in One
Dimension, Phys. Rev. Lett. 59, 13091312 (1987).
 (with I. Affleck, T. Kennedy and H. Tasaki) Rigorous Results
on ValenceBond Ground States in Antiferromagnets, Phys. Rev. Lett.
59, 799802 (1987).
 (with H.T. Yau) The Chandrasekhar Theory of Stellar Collapse
as the Limit of Quantum Mechanics, Commun. Math. Phys. 112, 147174
(1987).
 (with H.T. Yau) A Rigorous Examination of the Chandrasekhar
Theory of Stellar Collapse, Astrophys. Jour. 323, 140144 (1987).
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Continuous, Jour. Amer. Math. Soc. 2, 683773 (1989). A
summary of this work (using `rectifiable currents') appears as The
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Mathematica, vol. XXX, Ist. Naz. Alta Matem. Francesco Severi Roma,
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 (with M. Aizenman) Magnetic Properties of Some
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Magnetic Field of a Neutron Star, Phys. Rev. Lett. 69, 749752
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Physics,
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1993), p. 221237. Also in Spectral Theory and Scattering Theory and
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Math. 23, 259274, Math. Soc. of Japan, Kinokuniya (1994).
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(a) Méthodes
SemiClassiques, Colloque Internatinal (Nantes 1991), Asterisque
210, 237246 (1991); (b) Some New Trends on Fluid Dynamics and
Theoretical Physics, edited by C.C. Lin and N. Hu,
(Peking University Press, 1993) p. 149157; (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,
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Hubbard Model, J. Math. Phys. 34, 891898 (1993).
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Math. Soc. Symposia in Pure Math. 54, part 2, 379384 (1993).
(Proceedings of Summer Research Institute on Differential Geometry at UCLA,
July 828, 1990.)
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 (with E. Carlen) Optimal TwoUniform Convexity and Fermion
Hypercontractivity, in Quantum and NonCommutative Analysis,
proceedings of the June 1992 Kyoto Conference, edited by H. Araki
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 (with M. Loss) Fluxes, Laplacians and Kasteleyn's Theorem,
Duke Math. Journal 71, 337363 (1993).
 (with V. Bach, R. Lewis and H. Siedentop) On the Number of Bound
States of a Bosonic NParticle Coulomb System,
Zeits. f. Math. 214, 441460 (1993).
 (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, 513591 (1994).
 (with J.P. Solovej and J. Yngvason) Asymptotics of Heavy Atoms
in High Magnetic Fields: II. Semiclassical Regions, Commun. Math. Phys.
161, 77124 (1994).
 (with V. Bach, M. Loss and J.P. Solovej) There are No Unfilled
Shells in Unrestricted HartreeFock Theory,
Phys. Rev. Lett. 72, 29812983 (1994).
 (with K. Ball and E. Carlen) Sharp Uniform Convexity and
Smoothness Inequalities for Trace Norms, Invent. Math. 115, 463482
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 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. 267278.
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proceedings of 1993 NATO ASI, edited by D. Baeriswyl et.al., (Plenum
Press, 1995), p. 119. A further revision appears in
proceedings of the XIth International Congress of Mathematical
Physics, Paris, 1994, edited by D. Iagolnitzer, (International
Press, 1995), p. 392412.
 (with V. Bach and J.P. Solovej) Generalized HartreeFock
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 (with M. Loss) Symmetry of the GinzburgLandau Minimizer in a
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 (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. 157172.
 (with J.P. Solovej and J. Yngvason) Ground States of Large
Quantum Dots in Magnetic Fields, Phys. Rev. B 51,
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 (with J. Freericks) The Ground State of a General
ElectronPhonon Hamiltonian is a Spin Singlet, Phys. Rev. B 51,
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 (with B. Nachtergaele) The Stability of the Peierls
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 (with B. Nachtergaele) Dimerization in RingShaped
Molecules: The Stability of the Peierls Instability, in
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Magnetic Fields, Phys. Rev. Lett. 75, 985989 (1995).
 (with O. J. Heilmann) Electron Density near the
Nucleus of a large Atom, Phys. Rev. A 52, 36283643 (1995).
 (with A. Iantchenko and H. Siedentop) Proof of a Conjecture
about Atomic and Molecular Cores Related to Scott's Correction,
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Errata 188, 499500 (1997).
 (with L. Cafarelli and D. Jerison) On the Case of Equality in
the BrunnMinkowski Inequality for Capacity, Adv. in Math. 117,
193207 (1996).
 (with M. Loss and H. Siedentop) Stability of Relativistic
Matter via ThomasFermi Theory, Helv. Phys. Acta 69,
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 Some of the Early History of Exactly Soluble Models, in
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of the Conference on Unconventional Quantum Liquids, Evora, Portugal,
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Conference on Unconventional Quantum Liquids, Evora, Portugal, 1996,
Zeits. f. Phys. B 933, 125126 (1997).
 (with M. Loss) book Analysis, American Mathematical
Society (1997).
 Doing Math with Fred, in In Memoriam Frederick J. Almgren
Jr., 19371997, Experimental Math. 6, 23 (1997).
 (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. 145167 (1997). This is a
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Thermodynamics, Notices of the Amer. Math. Soc. 45,
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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''.
 (with D. Hundertmark and L.E. Thomas) A Sharp Bound for an
Eigenvalue Moment of the OneDimensional Schroedinger Operator,
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 (with E. Carlen) A Minkowski Type Trace Inequality and
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 Some Problems in Statistical Mechanics that I would like to
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arXiv mathph/9908019, mp_arc 99304.
 (with P. Schupp) Singlets and Reflection Symmetric Spin
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 (with M. Loss) SelfEnergy of Electrons in
Nonperturbative QED, in Differential Equations and
Mathematical Physics, University of Alabama, Birmingham, 1999,
R. Weikard and G. Weinstein, eds. 279293, Amer. Math. Soc./Internat.
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H.D. Doebner, V.K. Dobrev, J.D. Hennig and W. Luecke, eds., pp. 101110,
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arXiv mathph/0002014, mp_arc 0063.
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of the GrossPitaevskii Energy Functional for a Twodimensional Bose
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arXiv condmat/0005026, mp_arc 00203.
 (with M. Griesemer and M. Loss) Ground States in
Nonrelativistic Quantum Electrodynamics, Invent. Math.
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 (with J.P. Solovej) Ground State Energy of the
OneComponent Charged Bose Gas, Commun. Math. Phys. 217, 127163
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arXiv condmat/0007425, mp_arc 00303.
 (with J. Yngvason) The Mathematics of the Second Law of
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A. Alon, J. Bourgain, A. Connes, M. Gromov and V. Milman, eds.,
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arXiv mathph/0107003, mp_arc 01243.
 (with J. Freericks and D. Ueltschi) Segregation in the
FalicovKimball Model, Commun. Math. Phys. 227, 243279 (2002).
arXiv mathph/0107003, mp_arc 01243.
 (with G.K. Pedersen) Convex Multivariable Trace Functions,
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 (with J. Freericks and D. Ueltschi) Phase Separation due
to Quantum Mechanical Correlations, Phys. Rev. Lett. 88, #106401
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 (with M. Loss) Stability of a Model of Relativistic Quantum
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arXiv mathph/0109002, mp_arc 01315.
 (with M. Loss) A Bound on Binding Energies and Mass
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108, 10571069 (2002). arXiv mathph/0110027.
 (with R. Seiringer) Proof of BoseEinstein Condensation
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88, #170409 (2002). arXiv mathph/0112032, mp_arc 02115.
 (with M. Loss) Stability of Matter in Relativistic Quantum
Mechanics, in Mathematical Results in Quantum Mechanics,
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 (with J.Yngvason) The Mathematical Structure of the Second
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2001, International Press, de Jong, et al eds.,
2002, pp. 89129 . arXiv mathph/0204007.
 (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.,
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 (with R. Seiringer and J. Yngvason) Poincare Inequalities
in Punctured Domains, Annals of Math. 158, 10671080 (2003).
arXiv math.FA/0205088.
 (with R. Seiringer and J. Yngvason) Superfluidity in Dilute
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arXiv condmat/0205570, mp_arc 02339.
 (with F.Y. Wu) The onedimensional Hubbard model: A
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Nonlinear Science, Proceedings of the International Conference Dedicated
to the 100th Anniversary of A.A. Andronov, Volume II, pp 582590,
Nizhny Novgorod, Institute of Applied Physics, University of Nizhny
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 (with R. Seiringer) Equivalent forms of the BessisMoussaVillani
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arXiv mathph/0210027.
 (with R. Seiringer and J. Yngvason) Onedimensional Bosons in
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 (with R. Seiringer and J. Yngvason) Onedimensional Behavior
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 (with R. Seiringer) BoseEinstein Condensation of Dilute
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 (with M. Loss) Existence of Atoms and Molecules in Nonrelativistic
Quantum Electrodynamics, Adv. Theor. Math. Phys. 7 , 667710 (2003).
arXiv mathph/0307046.
 (with J.P. Solovej) Ground State Energy of the TwoComponent
Charged Bose Gas,
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 (with J. Yngvason) The Entropy of Classical Thermodynamics,
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A.~Greven, G.~Keller and G. Warnecke eds., Princeton University Press,
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 (with M. Loss) A Note on Polarization Vectors in Quantum
Electrodynamics, Commun. Math. Phys. 252, 477483 (2004).
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 (with M. Aizenman, R. Seiringer, J.P. Solovej and J. Yngvason)
BoseEinstein Quantum Phase Transition in an Optical Lattice Model,
Phys. Rev. A 70 , 023612(112) (2004). arXiv condmat/0403240.
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 (with E. Carlen) Some Matrix Rearrangement Inequalities,
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 (with R. Seiringer, J.P. Solovej and J. Yngvason)
The QuantumMechanical ManyBody 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).
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 (with M. Loss) The Thermodynamic Limit
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 (with E. Carlen and M. Loss)
A Sharp analog of Young's Inequality on ${\bf S}^N$
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(with R. Seiringer and J.P. Solovej) Ground State Energy of the
Low Density Fermi Gas, Phys. Rev. A 71, 053605(113) (2005).
arXiv mathph/0412080.
 (with R. Seiringer) A Stronger Subadditivity of Entropy,
Phys. Rev. A 71, 062329(19) (2005). arXiv mathph/0412009.
 (with R. Seiringer and J. Yngvason) Justification of cNumber
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 (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 condmat/0610117.
 (with E. Carlen and M. Loss) An Inequality of Hadamard Type
for Permanents, Methods and Applications of Analysis
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 (with R. Seiringer) Derivation of the GrossPitaevskii Equation for
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 (with R.L. Frank, A. Laptev and R. Seiringer)
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 (with A. Giuliani and J.L. Lebowitz) Ising models with
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 (with D. Osherson and S. Weinstein) Elementary Proof of a
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 (with R. Seiringer and J.P. Solovej) GroundState 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,
239248 (2006).
 (with M. Aizenman, R. Seiringer, J.P. Solovej
and J. Yngvason) BoseEinstein 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, 199215, Springer (2006). arXiv condmat/0412034.
See #291.
 (with R. Seiringer and J. Yngvason) BoseEinstein Condensation
and Spontaneous Symmetry Breaking, in Proceedings of
the 21st Max Born Symposium, Wroclaw, Poland, June 2628, 2006.
Reports on Mathematical Physics. arXiv mathph/0610034.
 (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, 479489 (2007). arXiv
mathph/0610062.
 (with R.L. Frank and R. Seiringer) HardyLiebThirring
inequalities for fractional Schr\"odinger operators, Jour. Amer. Math.
Soc. (in press). arXiv math.SP/0610593.
 (with R.L. Frank, R. Seiringer and H. Siedentop) Mueller's
ExchangeCorrelation Energy in DensityMatrixFunctional Theory.
Phys. Rev. A 76, 052517 (2007). arXiv:0705.1587[condmat.strel].
 (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, JC Zambrini eds.,
437, 127158 (2007).
 (with A. Giuliani and J.L. Lebowitz) Striped Phases in Two
Dimensional Dipole Systems, Phys. Rev. B 76, 184426 (2007).
arXiv:0707.3760[condmat.statmech].
 (with J. Predd, R. Seiringer, D. Osherson, V. Poor, and S.
Kulkarni) Probabilistic Coherence and Proper Scoring Rules,
IEEE Trans. Information Theory 55, 47864792 (2009).
arXiv:0710.3183 [stat.ML]
 (with R.L. Frank and R. Seiringer) Number of Bound States of
Schroedinger Operators with MatrixValued Potentials, Lett. Math.
Phys. 82, 107116 (2007). arXiv:0710.1877 [mathph].
 (with S. Jansen and R. Seiler) Symmetry Breaking in
Laughlin's State on a Cylinder, Commun. Math. Phys.
285, 503535 (2009). arXiv:0711.1467[condmat.meshall].

(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[condmat.meshall].
 (with E. Carlen) A Minkowski Type Trace Inequality and
Strong Subadditivity of Quantum Entropy II: Convexity and concavity.
Lett. Math. Phys. 83, 107126 (2008) arXiv:math/0701352[math.OA].
 (with A. Giuliani and J.L. Lebowitz) Periodic minimizers in 1D
local mean field theory, Commun. Math. Phys.
286, 163177 (2009). arXiv:mathph/0712.2330, mparc 07307.
 (with E. Carlen) BrascampLieb Inequalities for
Noncommutative Integration, Documenta Math. 13, 553584
(2008). arxiv:0808.1060[math.FA].
 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. 2738 (2008).
 (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.
1091, 4454 (2009). arXiv:0811.3078.
 Quantum Mechanics, the Stability of Matter and Quantum
Electrodynamics, Contemporary Math 476, 133148 (2008). Lectures
at the fourth summer school in analysis and mathematical physics,
Cuernavaca, 2005.
 (with E. Carlen) Short Proofs of Theorems of Horn and Mirsky
on Diagonals and Eigenvalues of Matrices, Electronic Jour. Linear Alg.
18, 438441 (2009). arXiv:0904.0734.
 (with A. Giuliani and J. Lebowitz) Modulated Phases of a 1D
Sharp Interface Model in a Magnetic Field. Phys. Rev. B 80,
13442016 (2009). arXiv:0905.3758.
 (with R. Frank) Inversion Positivity and the Sharp
HardyLittlewoodSobolev Inequality, arXiv:0904.4275.
 (with R. Seiringer and J. Yngvason) Yrast Line of a Rapidly
Rotating Bose Gas: GrossPitaevskii 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.

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

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

(with R. Frank) Spherical reflection positivity and the
HardyLittlewoodSobolev inequality, Proceedings of International
Workshop on Concentration Functional Inequalities and Isoperimetry, Boca
Raton, 2009. Contemporary Mathematics 545, 89102 (2011).
arXiv:1003.5248.

(with C. Decker, R.J. McCann and B.K. Stephens)
Existence, Uniqueness, and Substitution Effects in the ChooSiow
Marriage Matching Model. Title changed to: Unique Equilibria and
Substitution Effects in a Stochastic Model of the Marriage
Market, J. Economic Theory 148, 778792 (2013)). arxiv:1012.1904.

(with R. Frank) Sharp Constants in Several Inequalities on
the Heisenberg Group, Annals of Math 176, 349381 (2012).
DOI 10.4007/annals.2012.176.1.6. arXiv:1009.1410.

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

(with R. Frank, R. Seiringer and L. Thomas) Stability and
Absence of Binding for MultiPolaron Systems, Publication
Math\'ematiques
de l'IHES 113, Number 1, 3967 (2011). . arxiv:1004.4892.

(with R. Frank, R. Seiringer and L. Thomas) Binding,
Stability,
and Nonbinding of Multipolaron Systems,
Proceedings of the conference QMath 11 (Hradec Kralove, September 2010).
World Scientific. arXiv:1010.0737.

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

(with R.Frank) A New, RearrangementFree Proof of the Sharp
HardyLittlewoodSobolev Inequality,
Operator Theory: Advances and
Applications, 219, 5567 (2011), Birkhauser. arXiv:1010.5821.

(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.

(with R. Frank, M. Lewin and R. Seiringer) A Positive
Density Analogue of the LiebThirring Inequality, (2011).
(A detailed version of previous item 338.) Duke Math. Jour.
162, 435494 (2013).
DOI 10.1215/001270942019477
arXiv: 1108.4246.

(with E. A. Carlen and D.CorderoErquasquin)
Asymmetric Covariance Estimates of BrascampLieb Type and Related
Inequalities for Logconcave Measuresi,
Ann. Inst. Henri Poincar\'e  Probabilit\'es et Statistiques
49, 1–12 (2013). DOI: 10.1214/11AIHP462.
arXiv:1106.0709.

(with R. Frank) Possible Lattice Distortions in the
Hubbard Model for Graphene, Phys. Rev. Lett. 107, 066801
(2011). arXiv:1105.0693.
 (with R. Frank and R. Seiringer) Binding of Polarons and
Atoms at Threshold, Commun. Math. Phys. 313, 405424 (2012).
DOI 10.1007/s0022001214369(2012). arXiv:1106.0729.

(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.

(with Y. Yang) NonAbelian Vortices in Supersymmetric Gauge
Field Theory via Direct Method, Commun. Math. Phys.
313,
445478 (2012). DOI: 10.1007/s0022000908389. arXiv:1106.1626.

(with R. Frank) Entropy and the Uncertainty Principle,
Annales Henri Poincare 13, 17111717 (2012). DOI 10.1007/s000230120175y.
arXiv:1109.1209.

(with R. Frank and R. Seiringer) Symmetry of Bipolaron
Bound States for Small Coulomb Repulsion, Commun. Math. Phys.,
319, 557573 (2013)
DOI: 10.1007/s002200121604y. arXiv:1201.3954.

(with E. Carlen) Bounds for Entanglement via an Extension
of Strong Subadditivity of Entropy, Lett. Math. Phys.
101, 111 (2012). DOI 10.1007/s1100501205656.. arXiv:1203.4719.

(with R. Frank) Extended Quantum Conditional Entropy and
Quantum Uncertainty Inequalities, Commun. Math. Phys. 323, 487495
(2013). ). arxiv:1204.0825.

(with R. Seiringer) Further Implications of the BessisMoussaVillani
Conjecture, J. Stat. Phys. 149, 8691 (2012). DOI:
10.1007/s1095501205858. arXiv:1206.0460.

(with J.P. Solovej) Proof of an Entropy Conjecture for Bloch
Coherent Spin States and its Generalizations, Acta Math.
212, 379398 (2014). DOI: 10.1007/s1151101401136.
arXiv:1208.3632.

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

(with R. Frank, R. Seiringer and L. Thomas) Ground State
Properties of MultiPolaron Systems, in Proceedings of ICMP12, Aalborg,
2012, 477485, World Scientific (2013). arXiv:1209:3717.

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

(with E. Carlen and R. Frank) Stability Estimates for the
Lowest Eigenvalue of a Schroedinger Operator,
Geometric and Functional
Analysis, 24, 6384 (2014). DOI: 10.1007/s000390140253z. arXiv:1301.5032.

(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.

(with A. Vershynina) Upper bounds on mixing rates,
Quantum Information and Computation
13, No.11 & 12, 09860994 (2013). arXiv:1302:3865.

(with R. Seiringer) Equivalence of Two Definitions of the
Effective Mass of a Polaron, J. Stat. Phys. 154,
Issue 12, 5157 (2014).
DOI 10.1007/s109550130791z.. arXiv:1304.1780.

(with A. Giuliani and R. Seiringer) Formation of Stripes
and Slabs near the Ferromagnetic Transition, Commun. Math. Phys.
331, 333350 (2014).
DOI: 10.1007/s0022001419232. arxiv:1304.6344.

(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.

(with R. Frank, M. Lewin and R. Seiringer) Strichartz
Inequality for Orthonormal Functions, Jour. European Math. Soc.,
16, 15071526 (2014). DOI 10.4171/JEMS/467. arXiv:1306.1309.

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

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

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

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

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

(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/s0022001626516.
arXiv:1403.3816.
 An Open Problem about ExchangeCorrelation Energy, in
"Manyelectron Approaches in Physics, Chemistry and Mathematics"
415416, V. Bach
and L. Delle Sitte, eds., Springer Mathematical Physics Studies (2014).
 (with M. Lewin) Improved LiebOxford ExchangeCorrelation
Inequality with Gradient Correction, Phys. Rev. A 91, 022507
(2015). DOI: http://dx.doi.org/10.1103/PhysRevA.91.022507.
arxiv:1408.3358.
 (with E. Carlen and R. Frank) Some Operator and Trace
Function Convexity Theorems. Lin. Alg. Appl. 490, 174185
(2016). DOI:10.1016/j.laa.2015.11.006.
arXiv:1409.0564.
 (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.
 (with A. Giuliani) Columnar Phase in Quantum Dimer Models.
J. Phys.A: Math. Theor. 48, 235203 (2015).
DOI:10.1088/17518113/48/23/235203. This paper was
chosen for J. Phys. A. Higlights of 2015.
arXiv: 1502.02254.
 (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.

(with J.P. Solovej) Proof of the Wehrltype Entropy
Conjecture for Symmmetric SU(N) Coherent States. Commun. Math. Phys.
348, 567578 (2016). DOI:10.1007/s0022001625969.
arXiv:1506.07633.

(with A. Giuliani and I. Jauslin) A Pfaffian Formula for
MonomerDimer Partition Functions, Jour. Stat. Phys. 163,
211–238, (2016). DOI:10.1007/s1095501614841. arXiv:1510.05027.

(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.

(with R. Frank and J. Sabin) Maximizers for the SteinTomas
Inequality, Geometric and Functional Analysis,
26, 10951134
(2016). DOI: 10.1007/s0003901603809. arXiv:1603.07658.
 (with R. Frank) A `LiquidSolid' Phase Transition
in a Simple Model for Swarming, based on the `no flatspots' theorem
for subharmonic functions, Indiana, Univ. Math. Journal. 67
15471569 (2018). DOI: 10.1512/iumj.2018.67.7398. arXiv:1607.07971.

(with N. Rougerie and J. Yngvason) Rigidity of the Laughlin
Liquid, J. Stat. Phys. 17, 544554 (2018) Journal of Statistical
Phyics DOI: 10.1007/s1095501820821. arXiv 1609.03818.

(with N. Rougerie and J. Yngvason) Local incompressibility
estimates for the laughlin phase, Commun. Math. Phys.
365 431470 (2018).
doi.org/10.1007/s0022001831651 arXiv:1701.09064.

(with E.~Carlen) A Dual Form of the Sharp Nash Inequality
and its Weighted Generalization, Bull. London Math. Soc. 51,
129144 (2019). DOI:110.1112/blms.12220 . arxiv: 1703,09325,

(with R. Frank) Norms of Quantum Gaussian Multimode
Channels, J. Math. Phys. 58, 062204 (2017). DOI 10.1063/1.4989809
arxiv:1704.08720.

(with M. Lewin and R. Seiringer) Statistical
Mechanics of the Uniform Electron Gas,
Journal de l'Ecole polytechnique
 Mathematiques, 5, 79116 (2018). arXiv:1705.10676.

(with I. Jauslin) Nematic Liquid Crystal Phase
in a System of Interacting Dimers and Monomers, Commun. Math. Phys.
(in press) arXiv:1709.05297.

(with E. Carlen) Some Trace Inequalities for Exponential
and Logarithmic Functions, Bull. Math. Sciences
DOI 10.1007/s1337301801233 (2018). arXiv:1709.05450.
Available online.

(with E. Carlen and R. Frank) Inequalities for Quantum
Divergences and the AudenaertDatta Conjecture, J. Phys. A: Math.
Theor. arXiv:1806.03985

(with R. Frank and E. Carlen) Inequalities for Lpnorms that
Sharpen the Triangle Inequality and Complement Hanner's Inequality.
arXiv:1807.05599.

(with R. Frank) Periodic Energy Minimizers for a
OneDimensional Liquid Drop Model. arXiv:1808.06172.

(with E. Carlen and R. Frank) Inequalities that
sharpen the triangle inequality for sums of N functions in Lp.
arXiv:1902.04399.
Last updated 8/2018