Path integral approach to driven quantum harmonic oscillator using Markov chain Monte Carlo methods

TL;DR

This paper uses Markov chain Monte Carlo methods to simulate driven quantum harmonic oscillators, accurately reproducing theoretical expectations for different driving forces and system parameters.

Contribution

It introduces a path integral approach combined with Metropolis algorithm simulations to study driven quantum harmonic oscillators, including both constant and time-dependent forces.

Findings

Accurate expectation values of position for various parameters.

Coherent states obtained under constant forcing.

Simulation results match theoretical predictions almost exactly.

Abstract

We have simulated the ground states of quantum harmonic oscillators driven either by constant forces of different magnitudes or time-dependent driving forces. The expectation values of position for various combinations of mass, natural angular frequency, and the coupling constant $\lambda$ were calculated for both driving modes. For constant forcing, coherent states were obtained. The results for both forcing scenarios match the theoretically expected values almost exactly. For the simulations, the Metropolis algorithm was implemented on a discrete time lattice to evaluate the imaginary time path integral of the systems.