Related papers: Approach to equilibrium for the phonon Boltzmann e…
We consider stationary and propagating solutions for a Bose-Einstein condensate in a periodic optical potential with an additional confining optical or magnetic potential. Using an effective mass approximation we express the condensate…
We analyze a simple example of wave equation with a time-dependent damping term, whose coefficient decays at infinity at the scale-invariant rate and includes an oscillatory component that is integrable but not absolutely integrable. We…
The convergence of the Boltzmann equaiton to the compressible Euler equations when the Knudsen number tends to zero has been a long standing open problem in the kinetic theory. In the setting of Riemann solution that contains the generic…
The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and…
We derive an inequality relating the finite-frequency linear response and fluctuations of an observable in a physical system. The relation holds for arbitrary observables and perturbations in general Markovian dynamics, including over- and…
We study steady Boltzmann equation in half-space, which arises in the Knudsen boundary layer problem, with diffusive reflection boundary conditions. Under certain admissible conditions and the source term decaying exponentially, we…
The paper is devoted to constructing the global solutions around global Maxwellians to the initial-boundary value problem on the Boltzmann equation in general bounded domains with isothermal diffuse reflection boundaries. We allow a class…
The work describes an analogy-based small oscillations analysis of a standard static equilibrium lab problem. In addition to force analysis, a potential energy function for the system is developed, and by drawing out mathematical…
In this paper, we present a critical collection of essential mathematical tools and techniques for the analysis of Boltzmann-type kinetic equations, which in recent years have established themselves as a flexible and powerful paradigm to…
We present an analytical study of a nonlinear oscillator subject to an additive Ornstein-Uhlenbeck noise. Known results are mainly perturbative and are restricted to the large dissipation limit (obtained by neglecting the inertial term) or…
We study the asymptotic behavior of the spectrum of a quantum system which is a perturbation of a spherically symmetric anharmonic oscillator in dimension 2. We prove that a large part of its eigenvalues can be obtained by Bohr-Sommerfeld…
A system of linear differential equations with oscillatory decreasing coefficients is considered. The coefficients has the form $t^{-\alpha}a(t)$,~$\alpha>0$, where $a(t)$ is trigonometric polynomial with an arbitrary set of frequencies.…
In this paper we consider the global stability of solutions of an affine stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
We propose a formal expansion of multiple relaxation times lattice Boltzmann schemes in terms of a single infinitesimal numerical variable. The result is a system of partial differential equations for the conserved moments of the lattice…
The influence of quantized electromagnetic fields on a nonrelativistic charged particle moving near a conducting plate is studied. We give a field-theoretic derivation of the nonlinear, non-Markovian Langevin equation of the particle by the…
A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into…
A class of asymptotically autonomous systems on the plane with oscillatory coefficients is considered. It is assumed that the limiting system is Hamiltonian with a stable equilibrium. The effect of damped multiplicative stochastic…
We study nonlinear phonon excitations in a one-dimensional quantum nonlinear lattice model using numerical exact diagonalization. We find that multi-phonon bound states exist as eigenstates which are natural counterparts of breather…
We derive and solve a Boltzmann equation governing the cosmological evolution of the number density of current carrying cosmic string loops, whose centrifugally supported equilibrium configurations are also referred to as vortons. The phase…
In this note, we present a general way to construct spectral methods for the collision operator of the Boltzmann equation which preserves exactly the Maxwellian steady-state of the system. We show that the resulting method is able to…