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

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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 Schrödinger 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. 113, 10028 (2000)0021-960610.1063/1.1322075]. By investigating the dynamics of an initial wave function 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.


Original languageEnglish
Article number022201
Number of pages11
JournalPhysical Review A
Issue number2
Publication statusPublished - 2 Feb 2022

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WOS 000751936600004


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