Related papers: The relativistic quantum Boltzmann equation near e…
A theory of quantum jumps is developed by using a new asymmetric equation, which is complementary to the Schr\"odinger equation. The new equation displays Bohr's rules for quantum jumps, and its solutions demonstrate that once a quantum…
The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start from the standard Boltzmann equation, averaging over frequencies leads to appearance of fractional derivative. This fact is in accordance…
Bohmian mechnaics is the most naively obvious embedding imaginable of Schr\"odingers's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…
The Boltzmann equation is a powerful theoretical tool for modeling the collective dynamics of quantum many-body systems subject to external perturbations. Analysis of the equation gives access to linear response properties including…
This paper is concerned with the relativistic Boltzmann equation without angular cutoff. We establish the global-in-time existence, uniqueness, and asymptotic stability for solutions nearby the relativistic Maxwellian. We work in the case…
It is shown that the Foldy-Wouthuysen transformation for relativistic particles in strong external fields provides the possibility of obtaining a meaningful classical limit of the relativistic quantum mechanics. The full agreement between…
The two-dimensional, periodic Lorentz gas, is the dynamical system corresponding with the free motion of a point particle in a planar system of fixed circular obstacles centered at the vertices of a square lattice in the Euclidian plane.…
We consider M systems (each an electron in a long square cylinder) uniformly arranged on a ring and with Coulomb interactions. Exact straightforward numerical time-dependent perturbation calculation of a single N-level ($\lesssim 7$)…
The Choh Uhlenbeck equation was the first successful generalization of the Boltzmann equation to include triple collisions in a systematic manner. Detailed analysis of its triple collision term has led to the important concept of ring…
We prove that for a combined system of classical and quantum particles, it is possible to write a dynamics for the classical particles that incorporates in a natural way the Boltzmann equilibrium population for the quantum subsystem. In…
Spectral methods, thanks to their high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the collisional kinetic equations of Boltzmann type, such as the Boltzmann-Nordheim equation. This…
We consider the long time evolution of a quantum particle weakly interacting with a phonon field. We show that in the weak coupling limit the Wigner distribution of the electron density matrix converges to the solution of the linear…
We study the far-from-equilibrium statistical mechanics of periodically driven fermionic atoms in a lossy optical resonator. We show that the interplay of the Fermi surface with cavity losses leads to sub-natural cavity linewidth narrowing,…
We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in…
We propose a BGK model of the quantum Boltzmann equation for gas mixtures. We also provide a sufficient condition that guarantees the existence of equilibrium coefficients so that the model shares the same conservation laws and $H$-theorem…
In rotationally symmetric domains, the Boltzmann equation with specular reflection boundary condition has a special type of equilibrium states called the rotational local Maxwellian which, unlike the uniform Maxwellian, has an additional…
We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…
A simplified relativistic kinetic theory for gases with internal degrees of freedom, based on a BGK-type collision term, is considered. First the Boltzmann equation is rewritten in tetrad form and then thermal coefficients are determined to…
Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…