Time-dependent quantum Monte Carlo and the stochastic quantization

TL;DR

This paper explores the connection between time-dependent quantum Monte Carlo (TDQMC) and stochastic quantization, demonstrating how TDQMC enables practical simulation of many-body quantum dynamics by guiding particles in physical space.

Contribution

It establishes the relationship between TDQMC and stochastic quantization, highlighting the advantages of TDQMC for simulating time evolution of correlated quantum systems.

Findings

Successfully calculated ground states of a 1D Helium atom

Simulated the dipole moment evolution under ultrashort laser pulse

Demonstrated feasibility of TDQMC for complex quantum dynamics

Abstract

We examine the relation between the recently proposed time-dependent quantum Monte Carlo (TDQMC) method and the principles of stochastic quantization. In both TDQMC and stochastic quantization particle motion obeys stochastic guidance equations to preserve quantum equilibrium. In this way the probability density of the Monte Carlo particles corresponds to the modulus square of the many-body wave function at all times. However, in TDQMC the motion of particles and guide waves occurs in physical space unlike in stochastic quantization where it occurs in configuration space. Hence the practical calculation of time evolution of many-body fully correlated quantum systems becomes feasible within the TDQMC methodology. We illustrate the TDQMC technique by calculating the symmetric and antisymmetric ground state of a model one-dimensional Helium atom, and the time evolution of the dipole moment when the atom is irradiated by a strong ultrashort laser pulse.