Harmonic Crystals in the Half-Space, I. Convergence to Equilibrium

Abstract

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 Rosenblatt or Ibragimov type. We study the distribution ${\mu }_t$ of the solution at time $t\in \mathbb{R}$. The main result is the convergence of ${\mu }_t$ to a Gaussian measure as $t\to \infty$ which is time stationary with a covariance inherited from the initial (in general, non-Gaussian) measure.

References in corpus (2)

• Local stationarity for lattice dynamics in the harmonic approximation
• On a Two-Temperature Problem for Wave Equation

Cited by in corpus (4)

• On convergence to equilibrium for one-dimensional chain of harmonic oscillators in the half-line
• Lattice Dynamics in the Half-Space, II. Energy Transport Equation
• On the energy current for harmonic crystals
• Large-time asymptotic behavior of the infinite system of harmonic oscillators