Dynamical evolution of quantum oscillators towards equilibrium

TL;DR

This paper demonstrates how large quantum oscillator systems naturally evolve towards equilibrium through their intrinsic quantum dynamics, with small subsystems reaching a thermal state without additional assumptions.

Contribution

It provides a novel example of quantum equilibration emerging from pure dynamics in large oscillator systems, highlighting entanglement and thermalization mechanisms.

Findings

Small subsystems approach thermal equilibrium without external postulates

Subsystems exhibit entanglement with the rest of the system

Oscillators relax into states of the Boltzmann canonical form

Abstract

A pure quantum state of large number N of oscillators, interacting via harmonic coupling, evolves such that any small subsystem n<<N of the global state approaches equilibrium. This provides a novel example where equilibration emerges as a natural phenomena under quantum dynamics alone, with no necessity to bring in any additional statistical postulates. Mixedness of equilibrated subsystems consisting of 1, 2, ....., n<<N clearly indicates that small subsystems are entangled with the rest of the state i.e., the bath. Every single mode oscillator is found to relax in a mixed density matrix of the Boltzmann canonical form. In two oscillator equilibrated subsystems, intra-entanglement within the `system' oscillators is found to exist when the magnitude of the squeezing parameter of the bath is comparable in magnitude with that of the coupling strength.