Related papers: Boltzmann equation and its cosmological applicatio…
We introduce a generalised relaxation-time-approximation form of the collision term in the Boltzmann kinetic equation that allows for using different relaxation times for elastic and inelastic collisions. The efficacy of the proposed…
A challenging problem in solving the Boltzmann equation numerically is that the velocity space is approximated by a finite region. Therefore, most methods are based on a truncation technique and the computational cost is then very high if…
A simple kinematical argument suggests that the classical approximation may be inadequate to describe the evolution of a system with an anisotropic particle distribution. In order to verify this quantitatively, we study the Boltzmann…
We derive the matching conditions for cosmological perturbations in a Friedmann Universe where the equation of state undergoes a sharp jump, for instance as a result of a phase transition. The physics of the transition which is needed to…
Starting with the relativistic Boltzmann equation where the collision term was generalized to include gradients of the phase-space distribution function, we recently presented a new derivation of the equations for the relativistic…
This talk provides a critical assessment of collisionless galactic dynamics, focusing on the interpretation and limitations of the collisionless Boltzmann equation and the physical mechanisms associated with collisionless relaxation.…
We consider the cosmological application of a (variant of) relatively newly proposed model \cite{1609.06915} unifying inflation, dark energy, dark matter, and the Higgs mechanism. The model was originally defined using additional…
Starting with the relativistic Boltzmann equation for a system of particles defined by a distribution function, we have derived the virial relation for a spherical structure within an expanding background in the context of general…
The modern cosmology is based on inflationary models with baryosynthesis and dark matter/energy.It implies extension of particle symmetry beyond the Standard model. Studies of physical basis of the modern cosmology combine direct searches…
This paper discusses the problem of inflation in the context of Friedmann-Robertson-Walker Cosmology. We show how, after a simple change of variables, one can quantize the problem in a way which parallels the classical discussion. The…
We obtain the conditions constituting a thermal equilibrium between two energy levels: (i) the total energy is equal in both levels; (ii) the temperature is equal for all particles. Exploiting these conditions, we derive a differential…
In this paper, we study the Boltzmann equation in a close to the hydrodynamic limit regime, set in bounded spatial domains with non-isothermal Maxwell boundary conditions. We establish the existence, uniqueness, and asymptotic stability of…
Fokker-Planck equation with the velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides the self-consistent and universal description of friction…
Improving upon the previous treatment by Mueller and Son, we derive the Boltzmann equation that results from a classical scalar field theory. This is obtained by starting from the corresponding quantum field theory and taking the classical…
Interband effects such as coherence/tunneling have recently been shown to give an important contribution to the charge and heat transport properties under certain conditions. These can be captured by adding corrective terms to the…
We derive semiclassical Boltzmann equations describing thermalization of an ensemble of excitons due to exciton-phonon interactions taking into account the fact that excitons are not ideal bosons but composite particles consisting of…
Quantum effects play an essential role in modern cosmology. Perhaps the most striking example comes from large-scale structures, generally assumed to originate from vacuum quantum fluctuations and stretched by an expansion phase. Inflation…
Consider a microscopic system of $N$ hard spheres that are initially independent (modulo the exclusion condition on particle positions) and identically distributed in $\mathbb{R}^3$. When the number $N$ of particles goes to infinity and the…
Particle interactions are key elements of many dynamical systems. In the context of systems described by a Boltzmann equation, such interactions may be described by a collision integral, a multidimensional integral over the momentum-phase…
From the microscopic theory, we derive a number conserving quantum kinetic equation, valid for a dilute Bose gas at any temperature, in which the binary collisions between the quasi-particles are mediated by phonon-like excitations (called…