相关论文: A geometric derivation of the linear Boltzmann equ…
In this article it is shown that the fundamental equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of curved space-time. We further generalize the results to…
A time-reversal symmetry relation is established for out-of-equilibrium dilute or rarefied gases described by the fluctuating Boltzmann equation. The relation is obtained from the associated coarse-grained master equation ruling the random…
The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. From the mathematical point of view, the existence of global smooth solutions for arbitrary initial data is an…
In a recent paper we give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Here we present our results in the simplified case of a…
We attempt to construct a gravitational coupling by pre-selecting an energy-momentum tensor as the source for gravitational field. The energy-momentum tensor we take is a recently derived new expression motivated by joint localization of…
It is a fundamental problem in mathematical physics to derive macroscopic transport equations from microscopic models. In this paper we derive the linear Boltzmann equation in the low-density limit of a damped quantum Lorentz gas for a…
The zero temperature relaxational dynamics of a particle in a short range correlated random potential is addressed. We derive a set of "two-times" mean-field dynamical equations, accounting for a possible mean displacement of the particle…
This paper's objective is to improve the existing proof of the derivation of the Rayleigh--Boltzmann equation from the nonideal Rayleigh gas [6], yielding a far faster convergence rate. This equation is a linear version of the Boltzmann…
We show that the spatially homogeneous Boltzmann equation evolves as the gradient flow of the entropy with respect to a suitable geometry on the space of probability measures which takes the collision process into account. This gradient…
A manifestly covariant, or geometric, field theory for relativistic classical particle-field system is developed. The connection between space-time symmetry and energy-momentum conservation laws for the system is established geometrically…
We review the derivation of the Boltzmann equation and its cosmological applications in this paper. The derivation of the Boltzmann equation, especially the collision term, is discussed in detail in the language of the quantum field theory…
In this paper, we present a rigorous derivation of a new kinetic equation describing the limiting behavior of a classical system of particles with three particle elastic instantaneous interactions, which are modeled using a non-symmetric…
We present a derivation of a Boltzmann equation for the QCD plasma, starting from the quantum field equations. The derivation is based on a gauge covariant gradient expansion which takes consistently into account all possible dependences on…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
We develop an unified algebraic approach to the description of gauge interactions within the framework of a new concept of quantum mechanics. The next step in generalizing the space-time and the action vector space is made. The gauge field…
We study the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no…
In this paper we consider a large system of Bosons or Fermions. We start with an initial datum which is compatible with the Bose-Einstein, respectively Fermi-Dirac, statistics. We let the system of interacting particles evolve in a…
We study the kinetic theory of a weakly interacting quantum field. Assuming a state that is close to homogeneous and stationary, we derive a closed kinetic equation for the rate of change of the occupation numbers, perturbatively in the…
The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metrics leads to new contributions to the in-band energy operator in…