Transport Equations Including Many-Particle Correlations for an Arbitrary Quantum System: A General Formalism

Kinetic Equations for Quantum Many-Particle Systems

Quantification of correlations in quantum many-particle systems.

We introduce a well-defined and unbiased measure of the strength of correlations in quantum many-particle systems which is based on the relative von Neumann entropy computed from the density operator of correlated and uncorrelated states. The usefulness of this general concept is demonstrated by quantifying correlations of interacting electrons in the Hubbard model and in a series of transition...

New existence results for a coupled system of nonlinear differential equations of arbitrary order

This paper studies the existence of solutions for a coupled system of nonlinear fractional differential equations. New existence and uniqueness results are established using Banach fixed point theorem. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. Some illustrative examples are also presented.

One particle equations for many particle quantum systems : the MCTHDF method

This contribution is devoted to the mathematical analysis of more or less sophisticated approximations of the time evolution of systems of N quantum particles. New results for the Multiconfiguration Time Dependent Hartree Fock (MCTDHF) method (which cover the material of the talk given by the first author at the “Non linear waves conference in honor of Walter Strauss”) are summarized and compar...

A ‎N‎ote On ‎`‎A New Method For Solving An Arbitrary Fully Fuzzy Linear System'‎

In cite{beh}, the authors claimed by a counterexample that the cross product definition in cite{molo} is not correct and thus the proposed technique is false. In this note, we show that this assertion is ‎incorrect.