Related papers: Landau kinetic equation for dry aligning active mo…
We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…
Landau damping is calculated using real variables, clarifying the physical mechanism.
The Boltzmann equation for excess Cooper pairs above T_c is derived in the framework of the time-dependent Ginzburg-Landau (TDGL) theory using Langevin's approach of the stochastic differential equation. The Newton dynamic equation for the…
In this paper we propose an alternative to the coupling of Berkes, Liu and Wu [1] to obtain strong approximations for partial sums of dependent sequences. The main tool is a new Rosen-thal type inequality expressed in terms of the coupling…
The Balescu-Lenard equation from plasma physics is widely considered to include a highly accurate correction to Landau's fundamental collision operator. Yet so far it has seen very little mathematical study. We perform an extensive…
The Fokker-Planck equation for a heavy particle in a granular fluid is derived from the Liouville equation. The host fluid is assumed to be in its homogeneous cooling state and all interactions are idealized as smooth, inelastic hard…
We study slowly moving solutions of the real Ginzburg-Landau equation on the line, by a method due to J. Carr and R.L. Pego. These are functions taking alternately positive or negative values on large intervals. A consequence of our…
Starting from an approximate microscopic model of a trapped Bose-condensed gas at finite temperatures, we derive an equation of motion for the condensate wavefunction and a quantum kinetic equation for the distribution function for the…
The linearized Boltzmann equation is considered to describe small spatial perturbations of the homogeneous cooling state. The corresponding macroscopic balance equations for the density, temperature, and flow velocity are derived from it as…
We consider the Landau-Zener problem for a Bose-Einstein condensate in a linearly varying two-level system, for the full many-particle system as well and in the mean-field approximation. The many-particle problem can be solved approximately…
A convenient form of kinetic equation is derived for pair annihilation of heavy stable particles relevant to the dark matter problem in cosmology. The kinetic equation thus derived extends the on-shell Boltzmann equation in a most…
We consider a kinetic model of self-propelled particles with alignment interaction and with precession about the alignment direction. We derive a hydrodynamic system for the local density and velocity orientation of the particles. The…
The balance equations for thermodynamic quantities are derived from the nonlocal quantum kinetic equation. The nonlocal collisions lead to molecular contributions to the observables and currents. The corresponding correlated part of the…
We consider quantum rotors or Ising spins in a transverse field on a $d$-dimensional lattice, with random, frustrating, short-range, exchange interactions. The quantum dynamics are associated with a finite moment of inertia for the rotors,…
Quasiparticle dynamics in relativistic plasmas associated with hot, weakly-coupled gauge theories (such as QCD at asymptotically high temperature $T$) can be described by an effective kinetic theory, valid on sufficiently large time and…
The Lowest Landau Level (LLL) equation emerges as an accurate approximation for a class of dynamical regimes of Bose-Einstein Condensates (BEC) in two-dimensional isotropic harmonic traps in the limit of weak interactions. Building on…
We provide a rigorous justification of the linearized Boltzmann- and Landau equations from interacting particle systems with long-range interaction. The result shows that the fluctuations of Hamiltonian $N$- particle systems governed by…
The time-dependent Ginzburg-Landau equation and the Boltzmann transport equation for one-dimensional charge-density-wave (CDW) conductors are derived from a microscopic model by applying the Keldysh Green's function approach under a…
In the Landau-de Gennes theory on nematic liquid crystals, the well-known Landau-de Gennes energy depends on four elastic constants; $L_1$, $L_2$, $L_3$, $L_4$. For the general case of $L_4\neq 0$, Ball-Majumdar \cite {BM} found an example…
Landau damping in weakly interacting Bose gases is investigated by means of perturbation theory. Our approach points out the crucial role played by Bose-Einstein condensation and yields an explicit expression for the decay rate of…