Simulation of wavepacket tunneling of interacting identical particles

TL;DR

This paper introduces a novel quantum molecular dynamics method based on the Wigner representation to simulate the tunneling of interacting identical particles, capturing exchange and interaction effects.

Contribution

The paper presents a new Wigner-based quantum molecular dynamics approach for simulating nonstationary tunneling of interacting identical particles.

Findings

Analysis of the roles of direct and exchange interactions in tunneling.

Calculation of tunneling times for interacting particles.

Demonstration of the method's ability to incorporate exchange effects.

Abstract

We demonstrate a new method of simulation of nonstationary quantum processes, considering the tunneling of two {\it interacting identical particles}, represented by wave packets. The used method of quantum molecular dynamics (WMD) is based on the Wigner representation of quantum mechanics. In the context of this method ensembles of classical trajectories are used to solve quantum Wigner-Liouville equation. These classical trajectories obey Hamilton-like equations, where the effective potential consists of the usual classical term and the quantum term, which depends on the Wigner function and its derivatives. The quantum term is calculated using local distribution of trajectories in phase space, therefore classical trajectories are not independent, contrary to classical molecular dynamics. The developed WMD method takes into account the influence of exchange and interaction between particles. The role of direct and exchange interactions in tunneling is analyzed. The tunneling times for interacting particles are calculated.