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The Mathematics of the Bose Gas and its Condensation
The Dilute Bose Gas in 3D.- The Dilute Bose Gas in 2D.- Generalized Poincare Inequalities.- Bose-Einstein Condensation and Superfluidity for Homogeneous Gases.- Gross-Pitaevskii Equation for TrappedExpand
Generalized Hartree-Fock theory and the Hubbard model
The familiar unrestricted Hartree-Fock variational principles is generalized to include quasi-free states. As we show, these are in one-to-one correspondence with the one-particle density matricesExpand
Bogoliubov Spectrum of Interacting Bose Gases
We study the large-N limit of a system of N bosons interacting with a potential of intensity 1/N. When the ground state energy is to the first order given by Hartree's theory, we study the nextExpand
Quantum Dots
Quantum dots (QDs) are a unique type of nanocrystalline semiconductor whose electronic and optical properties are dependent on the size and shape of the dots. Diameters of these particles can rangeExpand
The kernel of Dirac operators on $\S^3$ and $\R^3$
In this paper we describe an intrinsically geometric way of producing magnetic fields on $\S^3$ and $\R^3$ for which the corresponding Dirac operators have a non-trivial kernel. In many cases we areExpand
Proof of the ionization conjecture in a reduced Hartree-Fock model
SummaryThe ionization conjecture for atomic models states that the ionization energy and maximal excess charge are bounded by constants independent of the nuclear charge. We prove this for theExpand
A CORRELATION ESTIMATE WITH APPLICATIONS TO QUANTUM SYSTEMS WITH COULOMB INTERACTIONS
We consider some two-body operators acting on a Fock space with either fermionic or no statistics. We prove that they are bounded below by one-body operators which mimic exchange effects. This allowsExpand
Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions
The ground state energy of an atom of nuclear chargeZe in a magnetic fieldB is exactly evaluated to leading order asZ→∞ in the following three regions:B≪Z4/3,B≈Z4/3 andZ4/3≪B≪Z3. In each case this isExpand
The Mean-Field Approximation in Quantum Electrodynamics. The no-photon case
We study the mean-field approximation of quantum electrodynamics (QED) by means of a thermodynamic limit. The QED Hamiltonian is written in Coulomb gauge and does not contain any normal ordering orExpand
The BCS Functional for General Pair Interactions
The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorousExpand
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