Related papers: Properties of the Boltzmann equation in the classi…
We present new analytic solutions to the relativistic Boltzmann equation within the relaxation time approximation. We first obtain spherically expanding solutions which are the kinetic counterparts of the exact solutions of the…
We study the emergence of Boltzmann's law for the "single particle energy distribution" in a closed system of interacting classical spins. It is shown that for a large number of particles Boltzmann's law may occur, even if the interaction…
The velocity and absorption coefficient for the plane sound waves in a classical gas are obtained by solving the Boltzmann kinetic equation, which describes the reaction of the single-particle distribution function to a periodic external…
Ultraviolet self-interaction energies in field theory sometimes contain meaningful physical quantities. The self-energies in such as classical electrodynamics are usually subtracted from the rest mass. For the consistent treatment of…
The known nonlinear kinetic equations (in particular, the wave kinetic equation and the quantum Nordheim -- Uehling -- Uhlenbeck equations) are considered as a natural generalization of the classical spatially homogeneous Boltzmann…
The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent…
The Boltzmann equation is the traditional framework in which one extends the time-dependent mean field classical description of a many-body system to include the effect of particle-particle collisions in an approximate manner. A…
We show that the widely used relaxation time approximation to the relativistic Boltzmann equation contains basic flaws, being incompatible with microscopic and macroscopic conservation laws. We propose a new approximation that fixes such…
The Boltzmann equation is essential for gas thermodynamics,as it models how the molecular density distribution $F(t,x,v)$ changes over time. However, existing research primarily focuses on the single species Boltzmann equation, while…
In many physical problems it is not possible to find an exact solution. However, when some parameter in the problem is small, one can obtain an approximate solution by expanding in this parameter. This is the basis of perturbative methods,…
The Boltzmann equation models gas dynamics in the low density or high Mach number regime, using a statistical description of molecular interactions. Planar shock wave solutions have been constructed for the Boltzmann equation for hard…
The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and related with them physical aspects. Based on the vacuum field theory no-geometry approach, developed in \cite{BPT,BPT1},…
The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system of equations describing in terms of ray trajectories a very wide family of wave-like phenomena (including diffraction and interference) going much beyond…
It is well known that a minimal distance emerges in quantum field theories owing to the need to regularize the UV divergences. The macroscopical limit at large minimal distance, weak spatial resolution, is investigated for a self…
This paper is to study the inelastic Boltzmann equation without Grad's angular cutoff assumption, where the well-posedness theory of the solution to the initial value problem is established for the Maxwellian molecules in a space of…
Dynamical symmetries of the collisionless Boltzmann transport equation, or Vlasov equation, but under the influence of an external driving force, are derived from non-standard representations of the $2D$ conformal algebra. In the case…
We propose a novel approach in the study of transport phenomena in dense systems or systems with long range interactions where multiple particle interactions must be taken into consideration. Within Boltzmann's kinetic formalism, we study…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
To calculate the baryon asymmetry in the baryogenesis via leptogenesis scenario one usually uses Boltzmann equations with transition amplitudes computed in vacuum. However, the hot and dense medium and, potentially, the expansion of the…