Stochastic representation of the quantum quartic oscillator

Gennaro Tucci, Stefano De Nicola, Sascha Wald, Andrea Gambassi

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Abstract

Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic processes has been proposed. Here we provide first steps towards the extension of this stochastic approach to bosonic systems by considering the one-dimensional quantum quartic oscillator. We show how to exactly parameterize the time evolution of this prototypical model via the dynamics of a set of classical variables. We interpret these variables as stochastic processes, which allows us to propose a novel way to numerically simulate the time evolution of the system. We benchmark our findings by considering analytically solvable limits and providing alternative derivations of known results.
Original languageEnglish
Number of pages34
JournalSciPost Physics Core
Volume6
Issue number2
DOIs
Publication statusPublished - 14 Apr 2023

Bibliographical note

This is an Open Access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/4.0/),
which permits unrestricted use, distribution, and reproduction in any medium,
provided the original work is properly cited.

Keywords

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Nuclear and High Energy Physics
  • Statistical and Nonlinear Physics

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