Quantum approach to the thermalization of the toppling pencil interacting with a finite bath

TL;DR

This paper explores quantum thermalization using a novel variational method, demonstrating that a small environment can effectively drive a bistable quantum system towards its ground state, with energy decay depending on the environment size.

Contribution

It applies the coupled coherent states method to study quantum thermalization in a bistable system coupled to a finite bath, offering a new computational approach.

Findings

Few environmental oscillators can induce thermalization of the system.

Long-time average energy decreases with increasing bath size.

Method overcomes exponential complexity in quantum dynamics simulations.

Abstract

We investigate the longstanding problem of thermalization of quantum systems coupled to an environment by focusing on a bistable quartic oscillator interacting with a finite number of harmonic oscillators. In order to overcome the exponential wall that one usually encounters in grid based approaches to solve the time-dependent Schr\"odinger equation of the extended system, methods based on the time-dependent variational principle are best suited. Here we will apply the method of coupled coherent states [D. V. Shalashilin and M. S. Child, J. Chem. Phys. {\bf 113}, 10028 (2000)]. By investigating the dynamics of an initial wavefunction on top of the barrier of the double well, it will be shown that only a handful of oscillators with suitably chosen frequencies, starting in their ground states, is enough to drive the bistable system close to its uncoupled ground state. The long-time average of the double-well energy is found to be a monotonously decaying function of the number of environmental oscillators in the parameter range that was numerically accessible.