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A numerical perspective on Hartree−Fock−Bogoliubov theory

Mathieu Lewin, Séverine Paul (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The method of choice for describing attractive quantum systems is Hartree−Fock−Bogoliubov (HFB) theory. This is a nonlinear model which allows for the description of pairing effects, the main explanation for the superconductivity of certain materials at very low temperature. This paper is the first study of Hartree−Fock−Bogoliubov theory from the point of view of numerical analysis. We start by discussing its proper discretization and then analyze the convergence of the simple fixed point (Roothaan)...

Introduction to magnetic resonance imaging for mathematicians

Charles L. Epstein (2004)

Annales de l’institut Fourier

The basic concepts and models used in the study of nuclear magnetic resonance are introduced. A simple imaging experiment is described, as well as, the reduction of the problem of selective excitation to a classical problem in inverse scattering.

Limit distributions of many-particle spectra and q-deformed Gaussian variables

Piotr Śniady (2006)

Banach Center Publications

We find the limit distributions for a spectrum of a system of n particles governed by a k-body interaction. The hamiltonian of this system is modelled by a Gaussian random matrix. We show that the limit distribution is a q-deformed Gaussian distribution with the deformation parameter q depending on the fraction k/√n. The family of q-deformed Gaussian distributions include the Gaussian distribution and the semicircular law; therefore our result is a generalization of the results of Wigner [Wig1,...

Weak interaction limit for nuclear matter and the time-dependent Hartree-Fock equation

Bernard Ducomet (2010)

Applications of Mathematics

We consider an effective model of nuclear matter including spin and isospin degrees of freedom, described by an N -body Hamiltonian with suitably renormalized two-body and three-body interaction potentials. We show that the corresponding mean-field theory (the time-dependent Hartree-Fock approximation) is “exact” as N tends to infinity.

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