539 citations · 6.8k across the 160 of their papers we have counts for
74 papers · 1 filter
A trace inequality of Ando, Hiai and Okubo and a monotonicity property of the Golden-Thompson inequality
Eric A. Carlen, Elliott H. Lieb
The Golden-Thompson trace inequality which states that has proved to be very useful in quantum statistical mechanics. Golden used it to show that t…
Improved Lieb-Oxford bound on the indirect and exchange energies
Mathieu Lewin, Elliott H. Lieb, Robert Seiringer
The Lieb-Oxford inequality provides a lower bound on the Coulomb energy of a classical system of identical charges only in terms of their one-particle density. We prove here a…
Analysis of a simple equation for the ground state of the Bose gas II: Monotonicity, Convexity and Condensate Fraction
Eric A. Carlen, Ian Jauslin, Elliott H. Lieb
In a recent paper we studied an equation (called the "simple equation") introduced by one of us in 1963 for an approximate correlation function associated to the ground state of an…
Universal Functionals in Density Functional Theory
Mathieu Lewin, Elliott H. Lieb, Robert Seiringer
In this chapter we first review the Levy-Lieb functional, which gives the lowest kinetic and interaction energy that can be reached with all possible quantum states having a given…
Analysis of a simple equation for the ground state energy of the Bose gas
Eric Carlen, Ian Jauslin, Elliott H. Lieb
In 1963 a partial differential equation with a convolution non-linearity was introduced in connection with a quantum mechanical many-body problem, namely the gas of bosonic particl…
Wehrl-type coherent state entropy inequalities for and its subgroup
Elliott H. Lieb, Jan Philip Solovej
We discuss the Wehrl-type entropy inequality conjecture for the group and for its subgroup (or affine group), their representations on , and th…
The Local Density Approximation in Density Functional Theory
Mathieu Lewin, Elliott H. Lieb, Robert Seiringer
We give the first mathematically rigorous justification of the Local Density Approximation in Density Functional Theory. We provide a quantitative estimate on the difference betwee…
Divergence of the effective mass of a polaron in the strong coupling limit
Elliott H. Lieb, Robert Seiringer
We consider the Fröhlich model of a polaron, and show that its effective mass diverges in the strong coupling limit.
Periodic energy minimizers for a one-dimensional liquid drop model
Rupert L. Frank, Elliott H. Lieb
We reprove a result by Ren and Wei concerning the periodicity of minimizers of a one-dimensional liquid drop model in the neutral case. Our proof works for general boundary conditi…
Inequalities for quantum divergences and the Audenaert-Datta conjecture
Eric A. Carlen, Rupert L. Frank, Elliott H. Lieb
Given two density matrices and , there are a number of different expressions that reduce to the -Rényi relative entropy of with respect to in the classical case;…
Some trace inequalities for exponential and logarithmic functions
Eric A. Carlen, Elliott H. Lieb
Consider a function of pairs of positive matrices with values in the positive matrices such that whenever and commute Our first main result gives…
Nematic liquid crystal phase in a system of interacting dimers and monomers
Ian Jauslin, Elliott H. Lieb
We consider a monomer-dimer system with a strong attractive dimer-dimer interaction that favors alignment. In 1979, Heilmann and Lieb conjectured that this model should exhibit a n…
Statistical Mechanics of the Uniform Electron Gas
Mathieu Lewin, Elliott H. Lieb, Robert Seiringer
In this paper we define and study the classical Uniform Electron Gas (UEG), a system of infinitely many electrons whose density is constant everywhere in space. The UEG is defined…
Norms of quantum Gaussian multi-mode channels
Rupert L. Frank, Elliott H. Lieb
We compute the norm of a general Gaussian gauge-covariant multi-mode channel for any , where is a Schatten space. As…
Local incompressibility estimates for the Laughlin phase
Elliott Lieb, Nicolas Rougerie, Jakob Yngvason
We prove sharp density upper bounds on optimal length-scales for the ground states of classical 2D Coulomb systems and generalizations thereof. Our method is new, based on an auxil…
Rigidity of the Laughlin liquid
Elliott Lieb, Nicolas Rougerie, Jakob Yngvason
We consider general N-particle wave functions that have the form of a product of the Laughlin state with filling factor and an analytic function of the N variables. This i…
On a Quantum Entropy Power Inequality of Audenaert, Datta and Ozols
Eric A. Carlen, Elliott H. Lieb, Michael Loss
We give a short proof of a recent inequality of Audenaert, Datta and Ozols, and determine cases of equality.
A Pfaffian formula for monomer-dimer partition functions
Alessandro Giuliani, Ian Jauslin, Elliott H. Lieb
We consider the monomer-dimer partition function on arbitrary finite planar graphs and arbitrary monomer and dimer weights, with the restriction that the only non-zero monomer weig…
Proof of the Wehrl-type Entropy Conjecture for Symmmetric SU(N) Coherent States
Elliott H. Lieb, Jan Philip Solovej
The Wehrl entropy conjecture for coherent (highest weight) states in representations of the Heisenberg group, which was proved in 1978 and recently extended by us to the group $SU(…
A compactness lemma and its application to the existence of minimizers for the liquid drop model
Rupert L. Frank, Elliott H. Lieb
The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an interesting problem in the calculus of variations: Find a set with given…
Ground state energy of large polaron systems
Rafael D. Benguria, Rupert L. Frank, Elliott H. Lieb
The last unsolved problem about the many-polaron system, in the Pekar-Tomasevich approximation, is the case of bosons with the electron-electron Coulomb repulsion of strength exact…
Some Operator and Trace Function Convexity Theorems
Eric A. Carlen, Rupert L. Frank, Elliott H. Lieb
We consider convex trace functions where and are positive matrices and ask when these functions are convex or conca…
Improved Lieb-Oxford exchange-correlation inequality with gradient correction
Mathieu Lewin, Elliott H. Lieb
We prove a Lieb-Oxford-type inequality on the indirect part of the Coulomb energy of a general many-particle quantum state, with a lower constant than the original statement but in…
Entropy Meters and the Entropy of Non-extensive Systems
Elliott H. Lieb, Jakob Yngvason
In our derivation of the second law of thermodynamics from the relation of adiabatic accessibility of equilibrium states we stressed the importance of being able to scale a system'…