Dual Spaces Structure of Quantum Kinetic Equations

Kinetic Equations for Quantum Many-Particle Systems

Approximate solution of dual integral equations

‎We study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎These equations will be converted to a system of‎ ‎singular integral equations with Cauchy type kernels‎. ‎Using‎ ‎Chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of Cauchy type singular integral equation which will ...

Quantum Kinetic Equations and Dark Matter Abundances Reconsidered

Starting from a Caldeira-Leggett model for the interaction of a system with an environment, Joichi, Matsumoto, and Yoshimura have reconsidered the derivation of the quantum Boltzmann equation. They find an extra term that accounts for the effects of virtual particles, and which drastically changes the results for relic densities of stable, weakly interacting massive particles (WIMPs), and for t...

On Kinetic Flux Vector Splitting Schemes for Quantum Euler Equations∗

The kinetic flux vector splitting (KFVS) scheme, when used for quantum Euler equations, as was done by Yang et al [22], requires the integration of the quantum Maxwellians (Bose-Einstein and Fermi-Dirac distributions), giving a numerical flux much more complicated than the classical counterpart. As a result, a nonlinear 2 by 2 system that connects the macroscopic quantities temperature and fuga...

Kinetic equations

Kinetic theory is a way of describing the time evolution of a system consisting of a large number of elementary objects which may be called particles. The mathematical study of such systems leads to a class of partial differential equations called kinetic equations. Equations of this type have many applications in physics and other sciences. The ’particles’ could for instance be electrons, star...