Stochastic Representation of the Quantum Quartic Oscillator

TL;DR

This paper extends a stochastic classical representation approach from quantum spin systems to the quantum quartic oscillator, enabling new numerical simulation methods for bosonic quantum dynamics.

Contribution

It introduces an exact stochastic parameterization of the quantum quartic oscillator's dynamics, bridging a gap in classical simulation techniques for bosonic quantum systems.

Findings

Successfully parameterized the oscillator's evolution with classical stochastic variables

Validated the approach against analytically solvable cases

Provided alternative derivations of known quantum results

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.