Semiclassical quantization of nonadiabatic systems with hopping periodic orbits

TL;DR

This paper develops a semiclassical quantization method for nonadiabatic systems, extending Gutzwiller's trace formula to include hopping periodic orbits, and demonstrates its accuracy on a simple model.

Contribution

It introduces a novel semiclassical quantization condition for nonadiabatic systems using hopping periodic orbits, expanding the scope of quantum-classical correspondence.

Findings

Accurately reproduces quantum energy levels in a nonadiabatic model

Extends Gutzwiller's trace formula to nonadiabatic systems

Discusses chaotic dynamics in the classical limit of nonadiabatic systems

Abstract

We present a semiclassical quantization condition, i.e., quantum-classical correspondence, for steady states of nonadiabatic systems consisting of fast and slow degrees of freedom (DOFs) by extending Gutzwiller's trace formula to a nonadiabatic form. The quantum-classical correspondence indicates that a set of primitive hopping periodic orbits, which are invariant under time evolution in the phase space of the slow DOF, should be quantized. The semiclassical quantization is then applied to a simple nonadiabatic model and accurately reproduces exact quantum energy levels. In addition to the semiclassical quantization condition, we also discuss chaotic dynamics involved in the classical limit of nonadiabatic dynamics.