# Elliott H. Lieb

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American mathematical physicist and professor of mathematics and physics at Princeton University

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## Why Is Elliott H. Lieb Influential?

(Suggest an Edit or Addition)According to Wikipedia, Elliott Hershel Lieb is an American mathematical physicist and professor of mathematics and physics at Princeton University who specializes in statistical mechanics, condensed matter theory, and functional analysis.

## Elliott H. Lieb's Published Works

### Published Works

- Two Soluble Models of an Antiferromagnetic Chain (1961) (2749)
- A Relation Between Pointwise Convergence of Functions and Convergence of Functionals (1983) (1972)
- EXACT ANALYSIS OF AN INTERACTING BOSE GAS. I. THE GENERAL SOLUTION AND THE GROUND STATE (1963) (1746)
- Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension (1968) (1741)
- Analysis, Second edition (2001) (1317)
- Rigorous results on valence-bond ground states in antiferromagnets. (1987) (1303)
- Two theorems on the Hubbard model. (1989) (1285)
- Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities (1983) (1253)
- The finite group velocity of quantum spin systems (1972) (1067)
- Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation (1977) (1001)
- Density Functionals for Coulomb Systems (1983) (988)
- On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation (1976) (962)
- Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum (1963) (930)
- Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem (1971) (910)
- Valence bond ground states in isotropic quantum antiferromagnets (1988) (899)
- On the superradiant phase transition for molecules in a quantized radiation field: the dicke maser model (1973) (692)
- Two-Dimensional Ising Model as a Soluble Problem of Many Fermions (1964) (665)
- Exact Solution of a Many-Fermion System and Its Associated Boson Field (1965) (652)
- Quantum Dots (1993) (647)
- Thomas-fermi and related theories of atoms and molecules (1981) (619)
- The Thomas-Fermi theory of atoms, molecules and solids (1977) (589)
- Inequalities for the Moments of the Eigenvalues of the Schrodinger Hamiltonian and Their Relation to Sobolev Inequalities (2002) (577)
- Ordering Energy Levels of Interacting Spin Systems (1962) (550)
- Convex trace functions and the Wigner-Yanase-Dyson conjecture (1973) (527)
- The Mathematics of the Bose Gas and its Condensation (2005) (525)
- Bosons in a trap: A rigorous derivation of the Gross-Pitaevskii energy functional (1999) (480)
- Harmonic maps with defects (1986) (479)
- Theory of monomer-dimer systems (1972) (450)
- Proof of the strong subadditivity of quantum‐mechanical entropy (1973) (450)
- Properties of a Harmonic Crystal in a Stationary Nonequilibrium State (1967) (410)
- The Hartree-Fock theory for Coulomb systems (1977) (407)
- Best Constants in Young's Inequality, Its Converse, and Its Generalization to More than Three Functions (1976) (405)
- The physics and mathematics of the second law of thermodynamics (Physics Reports 310 (1999) 1–96)☆ (1997) (392)
- The Stability of Matter in Quantum Mechanics (2009) (388)
- The classical limit of quantum spin systems (1973) (366)
- Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter (1975) (353)
- The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics (1987) (351)
- Residual Entropy of Square Ice (1967) (347)
- A general rearrangement inequality for multiple integrals (1974) (344)
- Proof of Bose-Einstein condensation for dilute trapped gases. (2001) (335)
- Theory of Ferromagnetism and the Ordering of Electronic Energy Levels (1962) (331)
- Sharp uniform convexity and smoothness inequalities for trace norms (1994) (323)
- Entropy inequalities (1970) (304)
- Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators (2006) (301)
- Exact Solution of the Problem of the Entropy of Two-Dimensional Ice (1967) (300)
- Phase transitions in quantum spin systems with isotropic and nonisotropic interactions (1978) (270)
- Proof of an entropy conjecture of Wehrl (1978) (266)
- Gaussian kernels have only Gaussian maximizers (1990) (263)
- Improved Lower Bound on the Indirect Coulomb Energy (1981) (258)
- Exact Solution of the F Model of An Antiferroelectric (1967) (258)
- Symmetric decreasing rearrangement is sometimes continuous (1989) (251)
- A proof of part of Haldane's conjecture on spin chains (1986) (247)
- Bounds on the eigenvalues of the Laplace and Schroedinger operators (1976) (245)
- Monotonicity of a relative Rényi entropy (2013) (235)
- Ground states in non-relativistic quantum electrodynamics (2000) (233)
- On the lowest eigenvalue of the Laplacian for the intersection of two domains (1983) (232)
- Generalized Hartree-Fock theory and the Hubbard model (1993) (228)
- The stability and instability of relativistic matter (1988) (220)
- Flux phase of the half-filled band. (1994) (216)
- A Fundamental Property of Quantum-Mechanical Entropy (1973) (214)
- Equilibrium Statistical Mechanics of Matter Interacting with the Quantized Radiation Field (1973) (212)
- Exact Solution of the Two-Dimensional Slater KDP Model of a Ferroelectric (1967) (211)
- The Stability of Matter: From Atoms to Stars (2001) (210)
- The Thomas—Fermi—von Weizsäcker Theory of Atoms and Molecules (1981) (201)
- Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases (2005) (190)
- An itinerant electron model with crystalline or magnetic long range order (1986) (187)
- The Number of Bound States of One-Body Schroedinger Operators and the Weyl Problem (代数解析学の最近の発展) (1979) (185)
- Phase Transitions and Reflection Positivity . I . General Theory and Long Range Lattice Models (1978) (184)
- Ground State Energy of the Low Density Bose Gas (1997) (180)
- A Rigorous Derivation¶of the Gross–Pitaevskii Energy Functional¶for a Two-dimensional Bose Gas (2000) (176)
- Bound on the maximum negative ionization of atoms and molecules (1984) (172)
- Minimum action solutions of some vector field equations (1984) (169)
- Sobolev inequalities with remainder terms (1985) (164)
- Phase transitions and reflection positivity. I. General theory and long range lattice models (1978) (164)
- The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei (1972) (163)
- Sharp constants in several inequalities on the Heisenberg group (2010) (161)
- Variational principle for many-fermion systems (1981) (150)
- A general Lee-Yang theorem for one-component and multicomponent ferromagnets (1981) (149)
- Thomas-Fermi Theory Revisited (1973) (148)
- Stability of Coulomb systems with magnetic fields (1986) (148)
- Phase transitions in anisotropic lattice spin systems (1978) (146)
- Integral bounds for radar ambiguity functions and Wigner distributions (1990) (146)
- The XY model has long-range order for all spins and all dimensions greater than one. (1988) (142)
- A sharp analog of Young’s inequality on SN and related entropy inequalities (2004) (142)
- Monomers and Dimers (1970) (134)
- The stability of matter (1976) (134)
- On semi-classical bounds for eigenvalues of Schrödinger operators (1978) (133)
- A Fresh Look at Entropy and the Second Law of Thermodynamics (2000) (131)
- Existence of Néel order in some spin-1/2 Heisenberg antiferromagnets (1988) (131)
- Existence of Thermodynamics for Real Matter with Coulomb Forces (1969) (129)
- Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions (1994) (128)
- Probabilistic Coherence and Proper Scoring Rules (2007) (127)
- Some Convexity and Subadditivity Properties of Entropy (1975) (119)
- Inversion positivity and the sharp Hardy–Littlewood–Sobolev inequality (2009) (119)
- Mathematical Physics in One Dimension: Exactly Soluble Models of Interacting Particles (1967) (117)
- Theory of monomer-dimer systems (1972) (116)
- A lower bound for Coulomb energies (1979) (114)
- Exact Ground State Energy of the Strong-Coupling Polaron (1995) (114)
- A refinement of Simon's correlation inequality (1980) (110)
- Gravitational collapse in quantum mechanics with relativistic kinetic energy (1984) (109)
- A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity (2007) (109)
- Lieb–Thirring Inequalities for Schrödinger Operators with Complex-valued Potentials (2006) (105)
- Asymptotics of heavy atoms in high magnetic fields: I. Lowest landau band regions (1994) (105)
- The Ground State Energy of a Dilute Two-Dimensional Bose Gas (2000) (103)
- Ground State Energy of the Two-Component Charged Bose Gas (2003) (99)
- Fluxes, Laplacians, and Kasteleyn’s theorem (1992) (99)
- A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator (1998) (96)
- On characteristic exponents in turbulence (1984) (95)
- Optimal hypercontractivity for fermi fields and related non-commutative integration inequalities (1992) (93)
- VIOLATION OF THE NONCROSSING RULE: THE HUBBARD HAMILTONIAN FOR BENZENE * (1971) (93)
- Ground State Energy of the One-Component Charged Bose Gas (2000) (92)
- Some operator inequalities of the schwarz type (1974) (92)
- Monotonicity of the electronic contribution to the Born-Oppenheimer energy (1978) (90)
- A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality (2010) (89)
- A Guide to Entropy and the Second Law of Thermodynamics (1998) (89)
- One-electron relativistic molecules with Coulomb interaction (1983) (83)
- Phase Transitions in Reservoir-Driven Open Systems with Applications to Lasers and Superconductors (1973) (83)
- Stability of coulomb systems with magnetic fields (1986) (82)
- Two-Dimensional Ferroelectric Models (2004) (82)
- Solution of the Dimer Problem by the Transfer Matrix Method (1967) (82)
- Proofs of some Conjectures on Permanents (1966) (81)
- There are no unfilled shells in unrestricted Hartree-Fock theory. (1993) (79)
- Existence of Atoms and Molecules in Non-Relativistic Quantum Electrodynamics (2003) (79)
- The thermodynamic limit for jellium (1975) (79)
- Justification of c-number substitutions in bosonic Hamiltonians. (2004) (77)
- Bose-Einstein quantum phase transition in an optical lattice model (2004) (77)
- Some problems in statistical mechanics that I would like to see solved (1999) (75)
- The stability of matter in magnetic fields (1995) (73)
- Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas (1963) (73)
- Innovation in Crop Protection: Trends in Research. (2000) (70)
- Identification of T=0 and T=1 bands in the N=Z=37 nucleus 74Rb. (1996) (70)
- Search for bound states of the eta meson in light nuclei. (1988) (69)
- Ground-State Energy and Effective Mass of the Polaron (1958) (68)
- Quantum-Mechanical Extension of the Lebowitz-Penrose Theorem on the Van Der Waals Theory (1966) (67)
- Co-Area, Liquid Crystals, and Minimal Surfaces (1988) (66)
- Müller’s exchange-correlation energy in density-matrix-functional theory (2007) (64)
- On the Case of Equality in the Brunn-Minkowski Inequality for Capacity (1996) (64)
- Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds (1988) (64)
- The entropy concept for non-equilibrium states (2013) (64)
- Stability Estimates for the Lowest Eigenvalue of a Schrödinger Operator (2013) (63)
- Some inequalities for Gaussian measures and the long-range order of the one-dimensional plasma (2002) (63)
- Irradiation effects in Ag-Fe bilayers: Ion-beam mixing, recrystallization, and surface roughening. (1996) (63)
- Concavity properties and a generating function for stirling numbers (1968) (63)
- Time evolution of infinite anharmonic systems (1977) (62)
- Proof of the Peierls instability in one dimension. (1987) (62)
- Equivalent Forms of the Bessis–Moussa–Villani Conjecture (2002) (62)
- Ground states of large quantum dots in magnetic fields. (1995) (59)
- Proof of the stability of highly negative ions in the absence of the pauli principle (1983) (59)
- Lattice systems with a continuous symmetry (1981) (58)
- One-Dimensional Behavior of Dilute, Trapped Bose Gases (2003) (58)
- Heavy atoms in the strong magnetic field of a neutron star. (1992) (58)
- A Compactness Lemma and Its Application to the Existence of Minimizers for the Liquid Drop Model (2015) (57)
- The Hubbard model: Some Rigorous Results and Open Problems (1993) (57)
- The third law of thermodynamics and the degeneracy of the ground state for lattice systems (1981) (56)
- The Thomas-Fermi-von Weizsäcker theory of atoms and molecules (1981) (56)
- TheN7/5 law for charged bosons (1988) (56)
- Phase Transitions and Reflection Positivity . II . Lattice Systems with Short-Range and Coulomb Interactions (1979) (56)
- Unique equilibria and substitution effects in a stochastic model of the marriage market (2010) (55)
- Phase transitions and reflection positivity. II. Lattice systems with short-range and Coulomb interactions (1980) (55)
- A two-dimensional isotropic quantum antiferromagnet with unique disordered ground state (1988) (54)
- One-dimensional bosons in three-dimensional traps. (2003) (54)
- Exact Ground State Energy of the Strong-Coupling Polaron (1995) (53)
- Phase Transitions in the Quantum Heisenberg Model (1976) (53)
- Extended Quantum Conditional Entropy and Quantum Uncertainty Inequalities (2012) (52)
- Stability of the Peierls instability for ring-shaped molecules. (1994) (52)
- Strichartz inequality for orthonormal functions (2013) (52)
- Stability and instability of relativistic electrons in classical electromagnetic fields (1996) (52)
- Proof of an entropy conjecture for Bloch coherent spin states and its generalizations (2012) (51)
- On solutions to the Hartree‐Fock problem for atoms and molecules (1974) (51)
- Ground-state energy of the low-density Fermi gas (2004) (51)
- A positive density analogue of the Lieb-Thirring inequality (2011) (51)
- Phase transition in a continuum classical system with finite interactions (1972) (50)
- Ising models with long-range antiferromagnetic and short-range ferromagnetic interactions (2006) (50)
- Remainder terms for some quantum entropy inequalities (2014) (50)
- Polarization of interacting bosons with spin. (2002) (48)
- Asymptotic Neutrality of Large- Z Ions (1984) (48)
- Long range atomic potentials in Thomas-Fermi theory (1979) (46)
- The inverse problem in classical statistical mechanics (1984) (45)
- Approximate neutrality of large-Z ions (1988) (45)
- Perturbed angular-correlation experiments on 111In in oxidized fcc metals and their oxides. (1987) (45)
- Stability of a Model of Relativistic Quantum Electrodynamics (2001) (45)
- Phase separation due to quantum mechanical correlations. (2001) (44)
- Calculation of Exchange Second Virial Coefficient of a Hard‐Sphere Gas by Path Integrals (1967) (43)
- Maximizers for the Stein–Tomas Inequality (2016) (43)
- Lattice models for liquid crystals (1979) (43)
- Symmetry of the Ginzburg Landau Minimizer in a Disc (1994) (42)
- Improved Lieb-Oxford exchange-correlation inequality with gradient correction (2014) (41)
- Segregation in the Falicov--Kimball Model (2001) (41)
- Erratum: Bound for the Kinetic Energy of Fermions which Proves the Stability of Matter. (Physical Review Letters) (1975) (40)
- Universal nature of van der Waals forces for Coulomb systems. (1986) (40)
- Delta-Function Fermi Gas with Two-Spin Deviates (1967) (40)
- Ground state of a general electron-phonon Hamiltonian is a spin singlet. (1994) (40)
- The Mathematical Structure of the Second Law of Thermodynamics (2002) (40)
- A Bound on Binding Energies and Mass Renormalization in Models of Quantum Electrodynamics (2001) (40)
- Striped phases in two-dimensional dipole systems (2007) (39)
- An Inequality of Hadamard Type for Permanents (2005) (38)
- Stability of Relativistic Matter with Magnetic Fields for Nuclear Charges up to the Critical Value (2006) (38)
- Ion-beam mixing of Ag/Fe and In/Fe layers studied by hyperfine techniques. (1996) (37)
- Magnetic properties of some itinerant-electron systems at T>0. (1990) (36)
- Stability and absence of binding for multi-polaron systems (2010) (36)
- Ground State Properties of a Fully Frustrated Quantum Spin System (1999) (35)
- Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy (2012) (35)
- Studies in mathematical physics : essays in honor of Valentine Bargmann (2015) (35)
- Statistical Mechanics of the Uniform Electron Gas (2017) (34)
- Erratum: Thomas-Fermi and related theories of atoms and molecules (1982) (34)
- Yrast line of a rapidly rotating Bose gas: Gross-Pitaevskii regime (2009) (33)
- The ground state of the Bose gas (2002) (33)
- Poincare Inequalities in Punctured Domains (2002) (33)
- A Rigorous Examination of the Chandrasekhar Theory of Stellar Collapse (1987) (33)
- Periodic Minimizers in 1D Local Mean Field Theory (2007) (32)
- Superfluidity in dilute trapped Bose gases (2002) (32)
- The Coulomb Gas at low temperature and low density (1989) (32)
- Renormalization of the Regularized Relativistic Electron-Positron Field (2000) (32)
- An Lp Bound for the Riesz and Bessel Potentials of Orthonormal Functions (1983) (32)
- Checkerboards, stripes, and corner energies in spin models with competing interactions (2011) (32)
- Existence of Phase Transitions for Anisotropic Heisenberg Models (1977) (31)
- Non-Abelian Vortices in Supersymmetric Gauge Field Theory via Direct Methods (2011) (31)
- The most negative ion in the Thomas-Fermi-von Weizsäcker theory of atoms and molecules (1985) (31)
- The local density approximation in density functional theory (2019) (31)
- Energy cost to make a hole in the Fermi sea. (2011) (30)
- Entropy meters and the entropy of non-extensive systems (2014) (30)
- A `liquid-solid' phase transition in a simple model for swarming (2016) (30)
- New Method in the Theory of Imperfect Gases and Liquids (1963) (30)
- The Statistical Mechanics of Anharmonic Lattices (1975) (29)
- Floating Wigner crystal with no boundary charge fluctuations (2019) (29)
- Bipolaron and N-polaron binding energies. (2010) (28)
- Lieb-Thirring Inequalities (2000) (28)
- Relaxation of electronic defects in pure and doped La2O3 observed by perturbed angular correlations. (1996) (28)
- Equivalence of Sobolev inequalities and Lieb-Thirring inequalities (2009) (28)
- Erratum to: The N 7/5 Law for Charged Bosons (1991) (28)
- A Note on Polarization Vectors in Quantum Electrodynamics (2004) (28)
- Quantum coherent operators: A generalization of coherent states (1991) (28)
- Self-Energy of Electrons in Non-Perturbative QED (1999) (27)
- Suppression at High Temperature of Effects Due to Statistics in the Second Virial Coefficient of a Real Gas (1965) (27)
- Uniform density theorem for the Hubbard model (1993) (27)
- E2 and E3 transitions from quadrupole-octupole coupled states in 144Nd. (1994) (27)
- Kinetic Energy Bounds and Their Application to the Stability of Matter (1989) (27)
- Electric-field gradients at 111Cd in delafossite oxides ABO2 (A=Ag, Cu; B=Al, Cr, Fe, In, Nd, Y). (1996) (26)
- Some Operator and Trace Function Convexity Theorems (2014) (26)
- Local incompressibility estimates for the Laughlin phase (2017) (26)
- Stability of Relativistic Matter via Thomas-Fermi Theory (1996) (26)
- Yrast transition strengths and band structure of 75Br. (1985) (26)
- Lower bound to the energy of complex atoms (1975) (26)
- The Stability of Matter and Quantum Electrodynamics (2002) (26)
- Exact Results for Itinerant Ferromagnetism in Multiorbital Systems on Square and Cubic Lattices (2013) (25)
- Exactly soluble models (1974) (25)
- Stability of Relativistic Matter with Magnetic Fields (1997) (25)
- Current densities in density-functional theory (2013) (25)
- Universal Functionals in Density Functional Theory (2019) (24)
- A model for crystallization: A variation on the Hubbard model (1986) (24)
- Fission of heavy nuclei induced by stopped antiprotons. I. Inclusive characteristics of fission fragments. (1994) (24)
- Hyperfine interactions of 111Cd in Ga2O3. (1993) (24)
- Inequalities for quantum divergences and the Audenaert–Datta conjecture (2018) (24)
- Solitons and the delta function fermion gas in Hartree–Fock theory (1978) (23)
- Electron density near the nucleus of a large atom. (1995) (23)
- Symmetry Breaking in Laughlin’s State on a Cylinder (2007) (23)
- Atomic and Molecular Negative Ions (1984) (23)
- The Stability of Matter in Quantum Mechanics: List of Symbols (2009) (23)
- Stronger subadditivity of entropy (2004) (22)
- Rigidity of the Laughlin Liquid (2016) (22)
- Lieb-Robinson bounds (2013) (22)
- Baryon mass inequalities in quark models. (1985) (22)
- Many-body stability implies a bound on the fine-structure constant. (1988) (21)
- Exact Wave Functions in Superconductivity (1961) (21)
- The law for bosons (1979) (21)
- Proof of spherical flocking based on quantitative rearrangement inequalities (2019) (21)
- The Bose Fluid* † (1965) (20)
- The Ground State Energy and Density of Interacting Bosons in a Trap (1999) (20)
- CONVEX MULTIVARIABLE TRACE FUNCTIONS (2001) (20)
- Signature inversion caused by triaxiality and unpaired band crossings in 72Br (2000) (19)
- Lifetime and g-factor measurements of yrast states in 134Nd and 136Nd. (1987) (19)
- Electron density near the nucleus of a large atom (1995) (18)
- Thomas-Fermi and Hartree-Fock Theory* (1975) (18)
- Numerical calculation of the Thomas-Fermi-von Weizsacker function for an infinite atom without electron repulsion (1982) (17)
- Bose-Einstein Condensation and Spontaneous Symmetry Breaking (2006) (17)
- Possible lattice distortions in the hubbard model for graphene. (2011) (17)
- Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality (2010) (17)
- On an extension problem for density matrices (2013) (17)
- Binding of Polarons and Atoms at Threshold (2011) (17)
- High spin states and shell model description of the neutron deficient nuclei 90Ru and 91Ru. (1994) (17)
- Divergence of the Effective Mass of a Polaron in the Strong Coupling Limit (2019) (17)
- Inequalities for Some Operator and Matrix Functions (1976) (17)
- The Ground State Energy of a Dilute Bose Gas (1999) (17)
- Modulated phases of a one-dimensional sharp interface model in a magnetic field (2009) (16)
- Analysis of the Thomas-Fermi-von Weizsäcker equation for an infinite atom without electron repulsion (1982) (16)
- The positivity of the pressure in Thomas-Fermi theory (1978) (16)
- Lectures on the Thermodynamic Limit for Coulomb Systems (1973) (16)
- SIMPLIFIED APPROACH TO THE GROUND-STATE ENERGY OF AN IMPERFECT BOSE GAS. II. CHARGED BOSE GAS AT HIGH DENSITY (1964) (16)
- A Property of Zeros of the Partition Function for Ising Spin Systems (1972) (15)
- The N Law for Charged Bosons (2004) (15)
- Existence of ground states for negative ions at the binding threshold (2013) (15)
- The Thermodynamic Limit for Matter Interacting with Coulomb Forces and with the Quantized Electromagnetic Field: I. The Lower Bound (2004) (15)
- Formation of Stripes and Slabs Near the Ferromagnetic Transition (2013) (15)
- Theory of Paramagnetic Impurities in Semiconductors (1966) (15)
- The laser: A reversible quantum dynamical system with irreversible classical macroscopic motion (1982) (15)
- On the number of bound states of a bosonicN-particle Coulomb system (1993) (15)
- Wehrl-type coherent state entropy inequalities for SU(1,1) and its $AX+B$ subgroup (2021) (15)
- Coherent States as a Tool for Obtaining Rigorous Bounds (1994) (14)
- Number of Bound States of Schrödinger Operators with Matrix-Valued Potentials (2007) (14)
- Proof of a conjecture about atomic and molecular cores related to Scott's correction. (1996) (14)
- A theorem on Pfaffians (1968) (14)
- A Pfaffian Formula for Monomer–Dimer Partition Functions (2015) (14)
- Electric-field gradients in Sm2O3, Gd2O3, and Ho2O3 measured with perturbed-angular-correlation spectroscopy. (1992) (14)
- The Quantum-Mechanical Many-Body Problem: The Bose Gas (2004) (14)
- Comment on "approach to equilibrium of a boltzmann-equation solution" (1982) (14)
- Entropy and the Uncertainty Principle (2011) (13)
- Symmetric Decreasing Rearrangement Can Be Discontinuous (1989) (13)
- Phase Transition in Zero Dimensions: A Remark on the Spherical Model (1969) (13)
- Quantum Mechanics, The Stability of Matter and Quantum Electrodynamics (2004) (13)
- Dipole transition strengths and level densities in A <= 80 odd-odd nuclei obtained from thermal neutron capture. (1986) (13)
- Ground-state energy of the low-density Fermi gas (13 pages) (2005) (12)
- Absolute B(E1) values in the shape transitional 148-152Sm isotopes. (1993) (12)
- New proofs of long range order (1978) (12)
- Universal nature of van der Waals forces for Coulomb Systems (1986) (12)
- Asymmetric Covariance Estimates of Brascamp-Lieb Type and Related Inequalities for Log-concave Measures (2011) (12)
- Some trace inequalities for exponential and logarithmic functions (2017) (11)
- Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. VI. Asymptotics in the two-cluster region (1980) (11)
- Systematic behavior of the neutron-deficient molybdenum nuclei. (1991) (11)
- FERROMAGNETISM OF THE HUBBARD MODEL AT STRONG COUPLING IN THE HARTREE–FOCK APPROXIMATION (2005) (11)
- Symmetry of Bipolaron Bound States for Small Coulomb Repulsion (2012) (11)
- Monotonicity of the molecular electronic energy in the nuclear coordinates (1982) (11)
- Inequalities : selecta of Elliott H. Lieb (2002) (11)
- Boson effective charges for light Se, Kr, and Sr isotopes. (1990) (10)
- Realization of stripes and slabs in two and three dimensions (2013) (10)
- Transition probabilities between high spin states in 88Mo and 90Mo. (1994) (10)
- Brascamp--Lieb inequalities for non-commutative integration (2008) (10)
- Multiple Coulomb excitation of the transitional nucleus 82Kr. (1985) (10)
- Elementary Proof of a Theorem of Jean Ville (2006) (10)
- Equivalence of Two Definitions of the Effective Mass of a Polaron (2013) (10)
- On a quantum entropy power inequality of Audenaert, Datta, and Ozols (2016) (10)
- Many-body atomic potentials in Thomas-Fermi theory (1978) (10)
- Some exact results in the Hartree-Fock theory of a many-fermion system at high densities (1971) (9)
- Norms of quantum Gaussian multi-mode channels (2017) (9)
- Ground state properties of multi-polaron systems (2012) (9)
- The thermodynamic limit for jellium (1975) (9)
- The Ancestry of the ‘Anyon’ (1990) (9)
- SIMPLIFIED APPROACH TO THE GROUND-STATE ENERGY OF AN IMPERFECT BOSE GAS. III. APPLICATION TO THE ONE-DIMENSIONAL MODEL (1964) (9)
- Singlets and reflection symmetric spin systems (1999) (9)
- A smooth complex generalization of the Hobby-Rice theorem (2012) (9)
- A note on a theorem of M. Christ (2019) (9)
- Constructive macroscopic quantum electrodynamics (1973) (9)
- Analysis of a simple equation for the ground state energy of the Bose gas (2019) (9)
- The Bose Gas: A Subtle Many-Body Problem (2000) (9)
- Phase Transition in a Model Quantum System: Quantum Corrections to the Location of the Critical Point (1966) (9)
- Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice (2004) (9)
- Perturbed angular correlation measurements in 2D spin-frustrated CuFeO2. (1996) (9)
- Some open problems about Coulomb systems (1980) (9)
- Spectroscopy of high spin states in 73Br. (1987) (8)
- Entropy and Entanglement Bounds for Reduced Density Matrices of Fermionic States (2014) (8)
- Asymptotics of Natural and Artificial Atoms in Strong Magnetic Fields (1997) (8)
- Singularities of energy-minimizing maps from the ball to the sphere (1987) (8)
- Conversion electron and yrast state measurements in 73Br. (1990) (8)
- Proof of the Wehrl-type Entropy Conjecture for Symmetric $${SU(N)}$$SU(N) Coherent States (2015) (8)
- Laughlin's function on a cylinder: plasma analogy and representation as a quantum polymer (2008) (8)
- Analytic Properties of the Free Energy for the (1972) (8)
- Some matrix rearrangement inequalities (2004) (8)
- SHORT PROOFS OF THEOREMS OF MIRSKY AND HORN ON DIAGONALS AND EIGENVALUES OF MATRICES (2009) (8)
- Pattern formation in systems with competing interactions (2008) (8)
- Bond alternation in ring‐shaped molecules: The stability of the Peierls instability (1996) (8)
- Periodic minimizers in 1 D local mean field theory (2007) (8)
- Upper bounds on mixing rates (2013) (8)
- Convexity and concavity of eigenvalue sums (1991) (7)
- Proof of a conjecture about atomic and molecular cores related to Scott’s correction (1996) (7)
- Ground-State Energy of a Dilute Fermi Gas (2005) (7)
- Symmetry of the Ginzburg-Landau minimizer in a disc (1995) (6)
- Condensed Matter Physics and Exactly Soluble Models: Selecta of Elliott H. Lieb (2004) (6)
- A non-perturbation method for non-linear field theories (1957) (6)
- The most negative ion in the Thomas-Fermi-von Weizsacker theory of atoms and molecules (1985) (6)
- Periodic energy minimizers for a one-dimensional liquid drop model (2018) (6)
- Matrix and Operator Trace Inequalities (2013) (6)
- Proof of the Wehrl-type Entropy Conjecture for Symmetric SU ( N ) Coherent States (2016) (5)
- Simplified approach to the repulsive Bose gas from low to high densities and its numerical accuracy (2020) (5)
- On the Anomalous Specific Heat of Sodium Trihydrogen Selenite (1970) (5)
- Rotational bands in 76Rb. (1995) (5)
- Analysis of a Simple Equation for the Ground State of the Bose Gas II: Monotonicity, Convexity, and Condensate Fraction (2020) (5)
- Atoms in the Magnetic Field of a Neutron Star (1993) (5)
- On the extension of the FKG inequality to n functions (2021) (4)
- The Mathematics of the Second Law of Thermodynamics (2010) (4)
- Inequalities for $$L^p$$-Norms that Sharpen the Triangle Inequality and Complement Hanner’s Inequality (2018) (4)
- Localization of Multi-Dimensional Wigner Distributions (2010) (4)
- Anomalous specific heat of sodium trihydrogen selenite - An associated combinatorial problem (1971) (4)
- Nematic Liquid Crystal Phase in a System of Interacting Dimers and Monomers (2017) (4)
- Strong Subadditivity of Quantum Entropy (2013) (4)
- Bose-Einstein Condensation of Dilute Gases in Traps (2002) (4)
- On the Convolution Inequality f ≥ f ⋆ f (2020) (4)
- Binding, Stability, and Non-binding of Multi-polaron Systems (2010) (4)
- Bounds on Schrödinger operators and generalized Sobolev type inequalities (1986) (4)
- Further Implications of the Bessis–Moussa–Villani Conjecture (2012) (4)
- THE (NON)CONTINUITY OF SYMMETRIC DECREASING REARRANGEMENT (2002) (4)
- Proof of the Strong Scott Conjecture for Atomic and Molecular Cores (1995) (3)
- Positive Linear Maps which are Order Bounded on C* Subalgebras (1978) (3)
- MATHEMATICAL ANALYSIS OF A SIMPLE MODEL RELATED TO THE STRIPPING REACTION (1959) (3)
- Erratum: ``The positivity of the pressure in Thomas-Fermi theory'' (1980) (3)
- Columnar phase in quantum dimer models (2015) (3)
- High spin states in 78Sr. (1984) (3)
- Thomas-Fermi Theory (2000) (3)
- Existence of Néel order in some spin-½ Heisenberg antiferromagnets (1988) (3)
- Clusters on a Thin Quadratic Lattice (Transfer Matrix Technique) (1969) (3)
- On the spectral radius of the product of matrix exponentials (1990) (3)
- Chapter 1 – WITHDRAWN: Classical Statistical Mechanics (1966) (3)
- Some Vector Field Equations (1984) (3)
- Improved Lieb–Oxford bound on the indirect and exchange energies (2022) (2)
- Optimal Two—Uniform Convexity and Fermion Hypercontractivity (1993) (2)
- Entropy Revisited, Gorilla and All (2000) (2)
- Inequalities that sharpen the triangle inequality for sums of $N$ functions in $L^p$ (2019) (2)
- Why Matter is Stable (1979) (2)
- Some positive definite functions on sets and their application to the Ising model (1971) (2)
- Mixed Function Oxidation (2003) (2)
- A Gaussian refinement of the Lieb-Robinson bound (2013) (2)
- Some of the Early History of Exactly Soluble Models (1997) (2)
- Counting Singularities in Liquid Crystals (1990) (2)
- HARD SPHERE BOSE GAS: AN EXACT MOMENTUM SPACE FORMULATION. (1960) (2)
- XXXVI. Second-order radiative corrections to the magnetic moment of a bound electron (1955) (2)
- A Wehrl-type entropy inequality for the affine AX+B group (2019) (2)
- Entropy bounds for reduced density matrices of fermionic states (2014) (1)
- A fresh look at a simplified approach to the Bose gas. (2020) (1)
- Statistical mechanics : selecta of Elliott H. Lieb (2004) (1)
- Relativistic Molecules with Coulomb Interaction (1984) (1)
- WITHDRAWN: Front Matter (1966) (1)
- A Model of Itinerant Ferromagnetism in Two- and Three- Dimensional Multi-orbital Systems (2013) (1)
- Exact Results of Itinerant Ferromagnetism in Multi-orbital Hubbard Systems (2014) (1)
- Pattern formation in systems with competing interactions 1 (2008) (1)
- Statistical theories of large atoms and molecules (1981) (1)
- The positivity of the pressure in Thomas Fermi theory (1978) (1)
- The Stability of Matter in Quantum Mechanics: Preface (2009) (1)
- Lower Bound for the Ground State Energy of the Schrodinger Equation Using the Sharp Form of Young's Inequality (2015) (1)
- A ug 2 00 5 AN INEQUALITY OF HADAMARD TYPE FOR PERMANENTS (2008) (1)
- A dual form of the sharp Nash inequality and its weighted generalization (2017) (1)
- 0 00 70 14 v 1 1 1 Ju l 2 00 0 Ground States in Non-relativistic Quantum Electrodynamics (2000) (1)
- Non-Abelian Vortices in Supersymmetric Gauge Field Theory via Direct Methods (2012) (1)
- The Stability of Matter in Quantum Mechanics: Electrostatic Inequalities (2009) (1)
- Ferromagnetism of the Low-Density Hubbard Model in the Hartree-Fock Approximation (2005) (1)
- Coincidence analyzing-power measurements of the reaction 12C(p (1992) (1)
- Identification of Transcription Factor EGL-27::GFP Binding Regions in L1 (2011) (1)
- Identification of Transcription Factor GEI-1::GFP Binding Regions in L4 (2011) (1)
- Chapter Eight. The Entropy of Classical Thermodynamics (2014) (1)
- Identical bands in 77Sr, 78Sr, and 78Rb: Evidence for a very good spectator orbital. (1994) (1)
- Pion-nucleus single charge exchange induced by stopped negative pions. (1996) (1)
- Identification of Transcription Factor LIN-15B::GFP Binding Regions in L3 (2011) (1)
- Ground state energy of large polaron systems (2014) (1)
- Binding of Polarons and Atoms at Threshold (2012) (0)
- Regularity of solutions of Poisson’s equation (2001) (0)
- M ay 2 00 0 A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-dimensional Bose Gas (1999) (0)
- Further Implications of the Bessis–Moussa–Villani Conjecture (2012) (0)
- One-Dimensional Behavior of Dilute, Trapped (2003) (0)
- Large atoms in large magnetic fields (1992) (0)
- EXISTENCE AND UNIQUENESS OF MINIMIZERS FOR THE NONLINEAR HARTREE EQUATION (2018) (0)
- PHYSICAL REVIEW LETTERS 30 JANUARY 1984 Atomic and Molecular Negative Ions (0)
- Potential theory and Coulomb energies (2001) (0)
- Nematic Liquid Crystal Phase in a System of Interacting Dimers and Monomers (2018) (0)
- The Stability of Matter in Quantum Mechanics: Prologue (2009) (0)
- b-Quark Asymmetry in DELPHI (1993) (0)
- Liquid crystals and the Heilmann-Lieb model (2018) (0)
- Erratum: Commun. Math. Phys. 215, 197–216 (2000) (2002) (0)
- The Ground State of the Bose GasE (2009) (0)
- SOME COMMENTS ON THE ONE-DIMENSIONAL MANY-BODY PROBLEM. (1965) (0)
- WITHDRAWN: Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State (1966) (0)
- O A ] 1 6 Se p 20 01 CONVEX MULTIVARIABLE TRACE FUNCTIONS (2008) (0)
- inequality for orthonormal functions (2014) (0)
- Quantum Phases of Cold Bosons in an Optical Lattice (2009) (0)
- Some Fundamental Properties of the Ground States of Atoms and Molecules (1986) (0)
- Entropy in Quantum Mechanics: Advances (2013) (0)
- ofInteracting B osons in a Trap (2021) (0)
- The Stability of Matter in Quantum Mechanics: Many-Particle Systems and Stability of the Second Kind (2009) (0)
- A Pfaffian Formula for Monomer–Dimer Partition Functions (2016) (0)
- The Dirac Operator and the Brown–Ravenhall Model (2009) (0)
- WITHDRAWN: The Disordered Chain of Harmonic Oscillators (1966) (0)
- One-dimensional behavior of dilute Bose gases in traps (2006) (0)
- I Is a Quantization. 4. If We Modify the Multiplication of Links in F I (0)
- A simple proof of Horn's Theorem (2009) (0)
- The Stability of Matter in Quantum Mechanics: Magnetic Fields and the Pauli Operator (2009) (0)
- Doing Math with Fred (1997) (0)
- Talenti’s comparison theorem revisited (2018) (0)
- Short proofs of theorems of Horn and Mirsky on diagonals and eigenvalues of matrices (2009) (0)
- GAS AN D IT S CON DEN SAT ION (2006) (0)
- A Short Appreciation of Freeman Dyson’s Long Career in Mathematical Physics (2004) (0)
- The Fourier transform (2001) (0)
- Local incompressibility estimates for the Laughlin phase (2018) (0)
- Chapter 5 – WITHDRAWN: The Bose Gas (1966) (0)
- Birmingham in the good old days (1996) (0)
- Chapter 6 – WITHDRAWN: Magnetism (1966) (0)
- Measure and integration (2001) (0)
- Formation of Stripes and Slabs Near the Ferromagnetic Transition (2014) (0)
- Fluxes and Dimers in the Hubbard Model (1995) (0)
- Entropy and Entanglement Bounds for Reduced Density Matrices of Fermionic States (2016) (0)
- Valence Bond Spin Models: Ground States and Excitations (1989) (0)
- Extended Quantum Conditional Entropy and Quantum Uncertainty Inequalities (2013) (0)
- Many Particle Coulomb Systems (2010) (0)
- How Much Energy Does it Cost to Make a Hole in the Fermi Sea (2011) (0)
- 21C-5 ON THE INTERACTION OF A POLARON WITH A PERIODIC POTENTIAL (1958) (0)
- Walter Eduard Thirring (2015) (0)
- Survey of the one-dimensional many-body problem and two-dimensional ferro-electric models (1969) (0)
- 200-MeV- pi +-induced single-nucleon removal from 24Mg. (1985) (0)
- The Stability of Matter in Quantum Mechanics: Gravitational Stability of White Dwarfs and Neutron Stars (2009) (0)
- Rigidity of the Laughlin Liquid (2018) (0)
- Identification of Transcription Factor CEH-30::GFP Binding Regions in Late Embyros (2011) (0)
- The Ionization Problem, and the Dependence of the Energy on N and M Separately (2009) (0)
- 2 7 Ju n 20 05 Ferromagnetism of the Low-Density Hubbard Model in the Hartree-Fock Approximation (2005) (0)
- Stability of Non-Relativistic Matter (2009) (0)
- INEQUALITIES FüR THE MOMENTS OF THE EIGENVALDES OF THE SCHRÖDINGER HAMILTONIAN AND THEIR RELATION (1997) (0)
- The Stability of Matter in Quantum Mechanics: Lieb–Thirring and Related Inequalities (2009) (0)
- Stripe formation at the ferromagnetic transition (2013) (0)
- Equivalence of Two Definitions of the Effective Mass of a Polaron (2013) (0)
- A trace inequality of Ando, Hiai, and Okubo and a monotonicity property of the Golden–Thompson inequality (2022) (0)
- The Sobolev spaces ¹ and ^{12} (2001) (0)
- Stability of Relativistic Matter (2009) (0)
- PHYSICAL REVIEW LETTERS (1991) (0)
- The Stability of Matter in Quantum Mechanics: Bibliography (2009) (0)
- Symmetry of Bipolaron Bound States for Small Coulomb Repulsion (2012) (0)
- Walter Thirring (1987) (0)
- E-GEOD-25798.processed.2.zip (2011) (0)
- On the convolution inequality $f \geq f\star f$ (2020) (0)
- A lower bound for level spacings (1977) (0)
- Introduction to the calculus of variations (2001) (0)
- WITHDRAWN: Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum (1966) (0)
- WITHDRAWN: Two Soluble Models of an Antiferromagnetic Chain (1966) (0)
- Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy (2012) (0)
- finland Informally Notifies Germany of Desire for Peace-Official Affirms (2011) (0)
- More about Eigenvalues (2001) (0)
- Random Surfaces Enumerating Algebraic Curves (2005) (0)
- Operator Formalism in Statistical Mechanics (1961) (0)
- Electromagnetic transition strengths between high spin states in 79Sr and 80Sr. (1990) (0)
- WITHDRAWN: The Many-Fermion Problem (1966) (0)
- Review: David Ruelle, Statistical Mechanics (1970) (0)
- Electromagnetic decay properties of high spin states in 4391Tc48. (1994) (0)
- Calcul Des Variations. —Estimations d’énergie pour des applications de R3 à (2002) (0)
- E-GEOD-25798.additional.1.zip (2011) (0)
- Entropy and the Uncertainty Principle (2012) (0)
- Parabolic mirror objective with high numerical aperture for imaging and spectroscopy at the nanometer scale (2002) (0)
- WITHDRAWN: PERSPECTIVES IN PHYSICS: A Series of Reprint Collections (1966) (0)
- Identification of Transcription Factor MEP-1::GFP Binding Regions in Embryos (2011) (0)
- Lieb-Liniger model of a Bose Gas (2008) (0)
- Divergence of the Effective Mass of a Polaron in the Strong Coupling Limit (2019) (0)
- Large Atoms in the Magnetic Field of a Neutron Star (1994) (0)
- Communications in Mathematical Physics Segregation in the Falicov – Kimball Model (2002) (0)
- E-GEOD-25800.processed.1.zip (2011) (0)
- Maximizers for the Stein–Tomas Inequality (2016) (0)
- Chapter 3 – WITHDRAWN: Electron Energy Bands in Ordered and Disordered Crystals (1966) (0)
- High spin shell model states in the isotope 4390Tc47. (1993) (0)
- WITHDRAWN: Time-Dependent Phenomena (1966) (0)
- Seniority v=5 states in 4189Nb48. (1993) (0)
- Stability Estimates for the Lowest Eigenvalue of a Schrödinger Operator (2014) (0)
- Maay-Body Stability ImpDes a Bound on the FiDe-Structare Constant (1991) (0)
- Quantized Electromagnetic Fields and Stability of Matter (2009) (0)
- FA ] 2 A ug 2 00 4 A Sharp analog of Young ’ s Inequality on S N and Related Entropy Inequalities (2018) (0)
- What if Boltzmann had known about quantum mechanics (2008) (0)
- Periodic energy minimizers for a one-dimensional liquid drop model (2019) (0)
- J ul 2 00 1 CONVEX MULTIVARIABLE TRACE FUNCTIONS (2009) (0)
- One-dimensional strongly interacting electrons with single impurity: conductance reemergence (2019) (0)
- The Stability of Matter in Quantum Mechanics: Introduction to Elementary Quantum Mechanics and Stability of the First Kind (2009) (0)
- The Stability of Matter in Quantum Mechanics: An Estimation of the Indirect Part of the Coulomb Energy (2009) (0)
- Letter to the Editor: Monotonicity of the molecular electronic energy in the nuclear coordinates (2005) (0)
- Communications in Mathematical Physics Periodic Minimizers in 1 D Local Mean Field Theory (2008) (0)
- In Memoriam: Memories of Andrew Lenard (2020) (0)
- Erratum: Simplified approach to the repulsive Bose gas from low to high densities and its numerical accuracy [Phys. Rev. A 103 , 053309 (2021)] (2021) (0)
- The Stability of Matter in Quantum Mechanics: The Thermodynamic Limit for Coulomb Systems (2009) (0)

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