Computational applications of the Many Interacting Worlds interpretation of quantum mechanics

TL;DR

This paper introduces an extended Many Interacting Worlds algorithm that uses kernel functions to simulate quantum nuclear dynamics in higher dimensions, enabling more accurate quantum molecular simulations beyond previous approximations.

Contribution

The paper presents a novel extension of the Many Interacting Worlds approach using kernel functions, allowing for n-dimensional quantum simulations and ground state searches.

Findings

Algorithm performs well in different potentials and dimensions.

Compared favorably to original approach and exact solutions.

Enables quantum molecular dynamics simulations in higher dimensions.

Abstract

While historically many quantum mechanical simulations of molecular dynamics have relied on the Born-Oppenheimer approximation to separate electronic and nuclear behavior, recently a lot of interest has arisen towards quantum effects in nuclear dynamics as well. Due to the computational difficulty of solving the Schroedinger equation in full, these effects are often treated with approximate quasi-classical methods. In this paper we present a new algorithm to tackle these problems, using an extension to the Many Interacting Worlds approach to quantum mechanics. This technique uses a kernel function to rebuild the probability density and therefore, at a difference with the approximation presented in the original paper, can be naturally extended to n-dimensional systems. This opens up the possibility of performing quantum ground state searches with steepest descent methods as well as real time quantum molecular dynamics simulations. The behavior of the algorithm is studied in different potentials and numbers of dimensions and compared both to the original approach and to exact Schroedinger equation solutions whenever possible.