相关论文: Generalization of Boltzmann Equilibration Dynamics
In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the…
In this paper we show global well-posedness near vacuum for the binary-ternary Boltzmann equation. The binary-ternary Boltzmann equation provides a correction term to the classical Boltzmann equation, taking into account both binary and…
A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the…
We study the role of electron-electron interactions for spin polarized transport using the Boltzmann equation and derive a set of coupled transport equations. For spin polarized transport the electron-electron interactions are important,…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…
The Boltzmann distribution predicts the collective behavior of systems at thermodynamic equilibrium as a function of their constituent parts. Yet most systems in nature are not at equilibrium, and a unified theory of their behavior does not…
There are three levels of description in classical statistical mechanics, the microscopic/dynamic, the macroscopic/statistical and the thermodynamic. At one end there is a well-used concept of equilibrium in thermodynamics and at the other…
In this paper we present a new derivation of the $H$-theorem and the corresponding collisional equilibrium velocity distributions, within the framework of Tsallis' nonextensive thermostatistics. Unlike previous works, in our derivation we…
The dynamics of a Bose-Einstein condensate is studied theoretically in a combined periodic plus harmonic external potential. Different dynamical regimes of stable and unstable collective dipole and Bloch oscillations are analysed in terms…
We present a kinetic description of Bose-Einstein condensation for particle systems being out of thermal equilibrium, which may happen for gluons produced in the early stage of ultra-relativistic heavy-ion collisions. The dynamics of bosons…
A recent kinetic approach for Vicsek-like models of active particles is reviewed. The theory is based on an exact Chapman-Kolmogorov equation in phase space. It can handle discrete time dynamics and "exotic" multi-particle interactions. A…
Correlations born before the onset of hydrodynamic flow can leave observable traces on the final state particles. Measurement of these correlations can yield important information on the isotropization and thermalization process. Starting…
This paper deals with a Boltzmann-type kinetic model describing the interplay between vehicle dynamics and safety aspects in vehicular traffic. Sticking to the idea that the macroscopic characteristics of traffic flow, including the…
It is well known that due to its divergence at large impact parameters, the Boltzmann collision integral in the kinetic equation for 3D systems of particles interacting through a $1/r$ potential must be replaced by a Balescu-Lenard-like…
Generic models of propelled particle systems posit that the emergence of polar order is driven by the competition between local alignment and noise. Although this notion has been confirmed employing the Boltzmann equation, the range of…
This paper considers a system of Boltzmann equations modelling the mixture of monatomic and polyatomic gases in an $L^{2}-L^{\infty}$ perturbation theory around global modified Maxwellians accounting for the internal energy of the mixture…
Boltzmann's Principle S = k ln W was repeatedly criticized by Einstein since it lacked a proper dynamical foundation in view of the thermal motion of the particles, out of which a physical system consists. This suggests, in particular, that…
This article deals with the issues of global-in-time existence and asymptotic analysis of a fluid-particle interaction model in the so-called bubbling regime. The mixture occupies the physical space $\Omega \subset \mathbb{R}^3$ which may…
We show that by integrating out the electric field and incorporating proper boundary conditions, a semiclassical Boltzmann equation can describe electron transport properties, continuously from the diffusive to ballistic regimes. General…
Systems with long range interactions display some anomalies when its dynamics and thermodynamics are studied below certain conditions. Among these anomalies are the quasi- stationary states, which are exacerbated because of special initial…