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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 Trapped…
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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 next…
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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 matrices…
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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 range…
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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 allows…
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The kernel of Dirac operators on $\S^3$ and $\R^3$
TLDR
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 is described.
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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 the…
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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 rigorous…
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Asymptotics for Bosonic atoms
It was proved by Benguria and Lieb that for an atom where the ‘electrons’ do not satisfy the exclusion principle, the critical electron number Nc, i.e., the maximal number of electrons the atom can…
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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 is…
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