Related papers: Difference Boltzmann Equation
Difference Kinetic Equations are derived quantum mechanically in a plane wavelets representation with account of two-particle correlations. It is shown that the set of plane wavelet orthonormal functions is complete. The set of ket vectors…
In the context of cosmological perturbation theory, we derive the second order Boltzmann equation describing the evolution of the distribution function of radiation without a specific gauge choice. The essential steps in deriving the…
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…
The notion of distance between a global Maxwellian function and an arbitrary solution $f$ (with the same total density $\rho$ at the fixed moment $t$) of Boltzmann equation is introduced. In this way we essentially generalize the important…
A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions…
Boltzmann's differential equation is replaced by the corresponding reciprocal symmetric finite difference equation. Finite difference translates discreteness of energy. Boltzmann's function, then, splits into two reciprocally related…
Collective orders and photo-induced phase transitions in quantum matter can evolve on timescales which are orders of magnitude slower than the femtosecond processes related to electronic motion in the solid. Quantum Boltzmann equations can…
The relativistic quantum Boltzmann equation (or the relativistic Uehling-Uhlenbeck equation) describes the dynamics of single-species fast-moving quantum particles. With the recent development of the relativistic quantum mechanics, the…
A linear Boltzmann equation with nonautonomous collision operator is rigorously derived in the Boltzmann-Grad limit for the deterministic dynamics of a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with…
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…
We present a concise derivation of the Boltzmann form for single-particle energy distributions in classical many-body Hamiltonian systems. The derivation relies on two physical facts: coarse-graining-scale invariance of the empirical…
We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff-Baym equations. Our method applies to a generic quantum field, coupled to a…
The Boltzmann equation is one of the most famous equations and has vast applications in modern science. In the current study, we take the randomness of binary collisions into consideration and generalize the classical Boltzmann equation…
We calculate the electronic transport properties of a system which is irradiated by a homogeneous microwave field. Within a Boltzmann equation approach, a general expression for the conductivity tensor is derived and evaluated for a quasi…
The Boltzmann kinetic equation is obtained from an integro-differential master equation that describes a stochastic dynamics in phase space of an isolated thermodynamic system. The stochastic evolution yields a generation of entropy,…
The differential equation for Boltzmann's function is replaced by the corresponding discrete finite difference equation. The difference equation is, then, symmetrized so that the equation remains invariant when step d is replaced by -d. The…
The quantum Boltzmann equation, or Fokker-Planck equation, has been used to successfully explain a number of experiments in semiconductor optics in the past two decades. This paper reviews some of the developments of this work, including…
This article investigates the full Boltzmann equation up to second order in the cosmological perturbations. Describing the distribution of polarized radiation by using a tensor valued distribution function, the second order Boltzmann…
A novel refinement of the conventional treatment of Kadanoff--Baym equations is suggested. Besides the Boltzmann equation another differential equation is used for calculating the evolution of the non-equilibrium two-point function.…
In this work we consider the classical non-linear Boltzmann equation, where the unknown is the distribution function $f$, which depends on the time $t$, the vector $\mathbf{x}$ (the position of a molecule) and its velocity $\mathbf{\xi}$.…