Biomedical subjects

Elliott H Lieb

Publications and source records attributed to Elliott H Lieb.

5 recordsLinked to original sources

PubMed2005

Justification of c-number substitutions in bosonic Hamiltonians.

The validity of substituting a c-number z for the k=0 mode operator a(0) is established rigorously in full generality, thereby verifying one aspect of Bogoliubov's 1947 theory. This substitution not only yields the correct value of thermodynamic quantities such as the pressure or ground state energy, but also the value of |z|(2) that maximizes the partition function equals the true amount of condensation in the presence of a gauge-symmetry-breaking term. This point had previously been elusive.

Journal Article↗

PubMed2003

One-dimensional bosons in three-dimensional traps.

Recent experimental and theoretical work has indicated conditions in which a trapped, low density Bose gas ought to behave like the 1D delta-function Bose gas solved by Lieb and Liniger. Up until now, the theoretical arguments have been based on variational/perturbative ideas or numerical investigations. There are four parameters: density, transverse and longitudinal dimensions, and scattering length. In this paper we explicate five parameter regions in which various types of 1D or 3D behavior occur in the ground state. Our treatment is based on a rigorous analysis of the many-body Schrödinger equation.

Journal Article↗

PubMed2002

Polarization of interacting bosons with spin.

We prove that in the absence of explicit spin-dependent forces one of the ground states of interacting bosons with spin is always fully polarized. Generally, this state is degenerate with other states, but one can specify the exact degeneracy. For T>0, the magnetization and zero-field susceptibility exceed that of a pure paramagnet. The results are relevant to experimental work on triplet superconductivity and condensation of atoms with spin. They eliminate the possibility, raised in some theoretical speculations, that the ground state or positive temperature state might be antiferromagnetic.

Journal Article↗

PubMed2002

Proof of Bose-Einstein condensation for dilute trapped gases.

The ground state of bosonic atoms in a trap has been shown experimentally to display Bose-Einstein condensation (BEC). We prove this fact theoretically for bosons with two-body repulsive interaction potentials in the dilute limit, starting from the basic Schrödinger equation; the condensation is 100% into the state that minimizes the Gross-Pitaevskii energy functional. This is the first rigorous proof of BEC in a physically realistic, continuum model.

Journal Article↗

PubMed2002

Phase separation due to quantum mechanical correlations.

Can phase separation be induced by strong electron correlations? We present a theorem that affirmatively answers this question in the Falicov-Kimball model away from half filling, for any dimension. In the ground state the itinerant electrons are spatially separated from the classical particles.

Journal Article↗