Comparative study of semiclassical approaches to quantum dynamics

TL;DR

This paper compares three semiclassical methods for simulating quantum dynamics, evaluating their accuracy and efficiency against exact quantum solutions in various one-dimensional systems.

Contribution

It provides a systematic analysis of the accuracy and computational performance of semiclassical approaches for quantum dynamics, with benchmarking against exact quantum results.

Findings

Semiclassical methods show varying accuracy depending on system features.

All approaches are computationally more efficient than exact quantum methods.

The study highlights the strengths and limitations of each semiclassical approach.

Abstract

Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to their numerical implementation. As test cases, we consider the time evolution of Gaussian wave packets in different one-dimensional geometries, whereby tunneling, resonance and anharmonicity effects are taken into account. The results and methods are benchmarked against an exact quantum mechanical treatment of the system, which is based on a highly efficient Chebyshev expansion technique of the time evolution operator.