On convergence to equilibrium for one-dimensional chain of harmonic oscillators in the half-line

Abstract

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 random function which has some mixing properties. We study the distribution ${\mu }_t$ of the random solution at time moments $t\in \mathbb{R}$. The main result is the convergence of ${\mu }_t$ to a Gaussian probability measure as $t\to \infty$. We find stationary states in which there is a non-zero energy current at origin.

29 pages; corrected condition C on the constants of the system; added Remark 2.11 on the limiting energy current; corrected typos; results unchanged

References in corpus (1)

• On the Convergence to a Statistical Equilibrium in the Crystal Coupled to a Scalar Field

Cited by in corpus (1)

• Controllability in tunable chains of coupled harmonic oscillators