2022/01/19 by Alex V. Plyukhin
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Anharmonicity #Brownian motion #Ergodic theory #Ergodicity #Harmonic oscillator #Parametric oscillator #Quantum many-body systems #Relaxation (psychology) #Thermal equilibrium #cond-mat.stat-mech #math-ph #math.MP #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.105.014121
published as Phys. Rev. E 105, 014121 (2022)
arxiv created 2022/01/19 · openalex publication_date 2022/01/19 · openalex created_date 2022/01/25 · arxiv updated 2022/02/02 · openalex updated_date 2026/08/05
We consider an open (Brownian) classical harmonic oscillator in contact with a non-Markovian thermal bath and described by the generalized Langevin equation. When the bath's spectrum has a finite upper cutoff frequency, the oscillator may have ergodic and nonergodic configurations. In ergodic configurations (when they exist, they correspond to lower oscillator frequencies) the oscillator demonstrates conventional relaxation to thermal equilibrium with the bath. In nonergodic configurations (which correspond to higher oscillator frequencies) the oscillator in general does not thermalize but relaxes to periodically correlated (cyclostationary) states whose statistics vary periodically in time. For a specific dissipation kernel in the Langevin equation, we evaluate explicitly relevant relaxation functions, which describe the evolution of mean values and time correlations. When the oscillator frequency is switched from a lower value to higher one, the oscillator may show parametric ergodic to nonergodic transitions with equilibrium initial and cyclostationary final states. These transitions are shown to resemble phase transitions of the second kind.