Localized Mode and Nonergodicity of a Harmonic Oscillator Chain

Abstract

We present a simple and microscopic physical model that breaks the ergodicity. Our model consists of coupled classical harmonic oscillators, and the motion of the tagged particle obeys the generalized Langevin equation satisfying the second fluctuation dissipation theorem. It is found that although the nonergodicity strength, which is expected to detect the ergodicity breaking, for this model vanishes, the velocity auto correlation function of the tagged particle asymptotically oscillates. We analyze the model by using the molecular dynamics and the exact diagonalization as well as the rigorous mapping to the generalized Langevin equation. Our analysis reveals that the asymptotic oscillation is caused by a localized mode with an isolated frequency from the continuous phonon spectrum.

References in corpus (11)

• Chaos and Quantum Thermalization
• Memory Effects In Nonequilibrium Quantum Impurity Models
• Molecular hydrodynamics from memory kernels
• Khinchin theorem and anomalous diffusion
• The Generalized Langevin Equation: An efficient approach to non-equilibrium molecular dynamics of open systems
• Violation of the fluctuation-dissipation theorem for fast superdiffusion
• Intermediate dynamics between Newton and Langevin
• Necessity of Eigenstate Thermalization
• Thermalization without eigenstate thermalization hypothesis after a quantum quench
• Entropy, non-ergodicity and non-Gaussian behaviour in ballistic transport
• Nonergodic solutions of the generalized Langevin equation

Cited by in corpus (5)

• Nonergodic Brownian oscillator
• Non-Clausius heat transfer: the example of harmonic chain with an impurity
• Emergent time crystal from a fractional Langevin equation with white and colored noise
• Dynamics of micro and nanoscale systems in the weak-memory regime: A mathematical framework beyond the Markov approximation
• Nonergodic Brownian oscillator: High-frequency response