Entropic comparison of Landau-Zener and Demkov interactions in the phase space of a quadrupole billiard

TL;DR

This paper compares Landau-Zener and Demkov interactions in a chaotic billiard using information theory, revealing distinct entropy behaviors and Fisher information differences that could indicate scar formation.

Contribution

It introduces an entropic analysis of avoided crossings in chaotic billiards, highlighting differences between Landau-Zener and Demkov interactions in phase space.

Findings

Shannon entropy increases near Landau-Zener crossings

Shannon entropy decreases after Demkov crossings with deformation

Fisher information is larger for Landau-Zener interactions

Abstract

We investigate two types of avoided crossings in a chaotic billiard within the framework of information theory. The Shannon entropy in the phase space for the Landau--Zener interaction increases as the center of the avoided crossing is approached. Meanwhile, that for the Demkov interaction decreases as the center of avoided crossing is passed by with an increase in the deformation parameter. This feature can provide a new indicator for scar formation. In addition, it is found that the Fisher information of the Landau--Zener interaction is significantly larger than that of the Demkov interaction.