• Corpus ID: 252090156

Infinite Chain of Harmonic Oscillators Under the Action of the Stationary Stochastic Force

@inproceedings{Lykov2022InfiniteCO,
  title={Infinite Chain of Harmonic Oscillators Under the Action of the Stationary Stochastic Force},
  author={Alexandr Lykov and Margarita Melikian},
  year={2022}
}
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of positive definite potential and initial conditions lying in l 2 ( Z )-space the perpesentation of the deviations of the particles from their equilibrium points are found. Precisely, deviation of each particle could be represented as the sum of some stationary process… 
View PDF on arXiv

References

SHOWING 1-10 OF 40 REFERENCES

Energy growth of infinite harmonic chain under microscopic random influence

Infinite harmonic chains of point particles with finite range translation invariant interaction have considered. It is assumed that the only one particle influenced by the white noise. We studied…

Harmonic Chain with Weak Dissipation

We consider finite harmonic chain (consisting of N classical particles) plus dissipative force acting on one particle (called dissipating particle) only. We want to prove that "in the generic case"…

Non-equilibrium dynamics of one-dimensional infinite particle systems with a hard-core interaction

An infinite system of Newton's equation of motion is considered for one-dimensional particles interacting by a finite-range hard-core potential of singularity like an inverse power of distance…

Convergence to stationary states for infinite harmonic systems

We study the evolution of the states for one-dimensional infinite harmonic systems, interacting through a translation invariant force of rapid decrease. We prove that for a large class of initial…

Exact time evolution of a classical harmonic-oscillator chain.

It is shown that the finite diffusion constant and the divergence in the mean-square displacement of a tagged oscillator arise from the zero-frequency mode present in the chain with periodic boundary conditions, which should hold for the harmonic-oscillator model in higher dimensions.

Hydrodynamic Limit for a Disordered Harmonic Chain

We consider a one-dimensional unpinned chain of harmonic oscillators with random masses. We prove that after hyperbolic scaling of space and time the distributions of the elongation, momentum, and…

Stationary non-equilibrium states of infinite harmonic systems

We investigate the existence, properties and approach to stationary non-equilibrium states of infinite harmonic crystals. For classical systems these stationary states are, like the Gibbs states,…

Convergence to Gibbs Equilibrium — Unveiling the Mystery

We consider general hamiltonian systems with quadratic interaction potential and N < 1 degrees of freedom, only m of which have contact with external world, that is subjected to damping and random…

One-dimensional harmonic lattice caricature of hydrodynamics

We derive the hydrodynamic (Euler) approximation for the harmonic time evolution of infinite classical oscillator system on one-dimensional lattice ℤ1 It is known that equilibrium (i.e.,…

Time evolution and ergodic properties of harmonic systems

We prove the existence of a time evolution and of a stationary equilibrium measure for the infinite harmonic crystal. The ergodic properties of the system are shown to be related in a simple way to…