539 citations · 6.8k across the 160 of their papers we have counts for
6 papers · 1 filter
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…
A dual form of the sharp Nash inequality and its weighted generalization
Eric A. Carlen, Elliott H. Lieb
The well known duality between the Sobolev inequality and the Hardy-Littlewood-Sobolev inequality suggests that the Nash inequality could also have an interesting dual form, even t…
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…