Related papers: On the Convergence to a Statistical Equilibrium fo…
We consider the Dirac equation in $\R^3$ with a potential, and study the distribution $\mu_t$ of the random solution at time $t\in\R$. The initial measure $\mu_0$ has zero mean, a translation-invariant covariance, and a finite mean charge…
We consider the dynamics of a harmonic crystal in $d$ dimensions with $n$ components, $d,n$ arbitrary, $d,n\ge 1$, and study the distribution $\mu_t$ of the solution at time $t\in\R$. The initial measure $\mu_0$ has a translation-invariant…
The paper considers the wave equation, with constant or variable coefficients in $\R^n$, with odd $n\geq 3$. We study the asymptotics of the distribution $\mu_t$ of the random solution at time $t\in\R$ as $t\to\infty$. It is assumed that…
Consider the Klein-Gordon equation (KGE) in $\R^n$, $n\ge 2$, with constant or variable coefficients. We study the distribution $\mu_t$ of the random solution at time $t\in\R$. We assume that the initial probability measure $\mu_0$ has zero…
We consider the Hamiltonian system consisting of a Klein-Gordon vector field and a particle in $\R^3$. The initial date of the system is a random function with a finite mean density of energy which also satisfies a Rosenblatt- or…
For a system consisting of several Dirac fields and a particle, we study the Cauchy problem with random initial data. We assume that the initial measure has zero mean value, a finite mean charge density, a translation-invariant covariance…
Consider the wave equation with constant or variable coefficients in $\R^3$. The initial datum is a random function with a finite mean density of energy that also satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition. The random…
We consider the dynamics of a harmonic crystal in the half-space with zero boundary condition. It is assumed that the initial date is a random function with zero mean, finite mean energy density which also satisfies a mixing condition of…
We consider a linear Hamiltonian system consisting of a classical particle and a scalar field describing by the wave or Klein-Gordon equations with variable coefficients. The initial data of the system are supposed to be a random function…
We consider the dynamics of a field coupled to a harmonic crystal with $n$ components in dimension $d$, $d,n\ge 1$. The crystal and the dynamics are translation-invariant with respect to the subgroup $\Z^d$ of $\R^d$. The initial data is a…
We consider the dynamics of a harmonic crystal in $d$ dimensions with $n$ components,$d,n \ge 1$. The initial date is a random function with finite mean density of the energy which also satisfies a Rosenblatt- or Ibragimov-Linnik-type…
The initial-boundary value problem for an infinite one-dimensional chain of harmonic oscillators on the half-line is considered. The large time asymptotic behavior of solutions is studied. The initial data of the system are supposed to be a…
We establish soliton-like asymptotics for finite energy solutions to the Dirac equation coupled to a relativistic particle. Any solution with initial state close to the solitary manifold, converges in long time limit to a sum of traveling…
We present direct and elementary commutator techniques for the Dirac equation with long-range electric and mass perturbations. The main results are absence of generalized eigenfunctions and locally uniform resolvent estimates, both in terms…
We use the Fourier based Gabetta-Toscani-Wennberg (GTW) metric $d_2$ to study the rate of convergence to equilibrium for the Kac model in $1$ dimension. We take the initial velocity distribution of the particles to be a Borel probability…
The Dirac equation, usually obtained by `quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic…
Let $f(\cdot,t)$ be the probability density function which represents the solution of Kac's equation at time $t$, with initial data $f_0$, and let $g_{\sigma}$ be the Gaussian density with zero mean and variance $\sigma^2$, $\sigma^2$ being…
Concentration of measure is a phenomenon in which a random variable that depends in a smooth way on a large number of independent random variables is essentially constant. The random variable will "concentrate" around its median or…
Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward an equilibrium or towards the set of equilibria (quasiconvergence). In this paper, we provide new formulations of…
The Dirac method of quantizing Hamiltonian systems with constraints is applied to the massless Thirring model. We solve the quantum Hamiltonian equation for the energy-momentum tensor and obtain a violation of the classical conservation…