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Ground State Energy of the Low Density Fermi Gas
Elliott H. Lieb, Robert Seiringer, Jan Philip Solovej
Recent developments in the physics of low density trapped gases make it worthwhile to verify old, well known results that, while plausible, were based on perturbation theory and as…
A Stronger Subadditivity of Entropy
Elliott H. Lieb, Robert Seiringer
The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[ρ]= - Tr (ρ\ln ρ) of a density matrix ρ_{123} on the…
Justification of c-Number Substitutions in Bosonic Hamiltonians
Elliott H. Lieb, Robert Seiringer, Jakob Yngvason
The validity of substituting a c-number for the mode operator is established rigorously in full generality, thereby verifying one aspect of Bogoliubov's 1947 theory…
Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice
M. Aizenman, E. H. Lieb, R. Seiringer +2
One of the most remarkable recent developments in the study of ultracold Bose gases is the observation of a reversible transition from a Bose Einstein condensate to a state compose…
A Sharp analog of Young's Inequality on and Related Entropy Inequalities
Eric Carlen, Elliott Lieb, Michael Loss
We prove a sharp analog of Young's inequality on , and deduce from it certain sharp entropy inequalities. The proof turns on constructing a nonlinear heat flow that drives tri…
The thermodynamic limit for matter interacting with Coulomb forces and with the quantized electromagnetic field: I. The lower bound
Elliott H. Lieb, Michael Loss
The proof of the existence of the thermodynamic limit for electrons and nuclei interacting via the Coulomb potential, in the framework of non-relativistic quantum mechanics, was ac…
The Quantum-mechanical Many Body Problem: The Bose Gas
Elliott H. Lieb, Robert Seiringer, Jan Philip Solovej +1
This article gives a detailed presentation of the authors' recent results on the ground state properties of the Bose gas. It is a much expanded version of a talk given by one of th…
Bose-Einstein Quantum Phase Transition in an Optical Lattice Model
Michael Aizenman, Elliott H. Lieb, Robert Seiringer +2
Bose-Einstein condensation (BEC) in cold gases can be turned on and off by an external potential, such as that presented by an optical lattice. We present a model of this phenomeno…
Some Matrix Rearrangement Inequalities
Eric Carlen, Elliott H. Lieb
We investigate a rearrangement inequality for pairs of n-square matrices: Let |A\|_p denote the C^p trace norm of an n-square matrix A. Consider the quantity |A+B|_p^p + |A-B|_p^p.…
A Note on Polarization Vectors in Quantum Electrodynamics
Elliott H. Lieb, Michael Loss
A photon of momentum k can have only two polarization states, not three. Equivalently, one can say that the magnetic vector potential A must be divergence free in the Coulomb gauge…
Quantum Mechanics, The Stability of Matter and Quantum Electrodynamics
Elliott H. Lieb
Much progress has been made in the last few decades in developing the necessary mathematics for understanding the full implications of the quantum-mechanical many-body problem and…