Tunneling and the Band Structure of Chaotic Systems

TL;DR

This paper uses semiclassical periodic orbit theory, including complex orbits, to analyze tunneling effects on the band structure of chaotic systems, validated by the kicked-Harper model.

Contribution

It introduces a method incorporating complex orbits into semiclassical analysis to accurately describe tunneling and band structures in chaotic systems.

Findings

Excellent agreement with numerical simulations

Effective description of tunneling mechanisms

Applicable to extreme quantum regimes

Abstract

We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex orbits. These turn out to be fundamental for a proper description of the band structure since they incorporate conduction processes through tunneling mechanisms. The results obtained, illustrated with the kicked-Harper model, are in excellent agreement with numerical simulations, even in the extreme quantum regime.