The Shannon entropy and avoided crossings in closed and open quantum billiards

TL;DR

This paper explores how Shannon entropy relates to avoided crossings in dielectric microcavities, revealing opposite behavior to atomic physics and linking entropy changes to symmetry breaking and collective Lamb shifts.

Contribution

It demonstrates the connection between Shannon entropy and avoided crossings in both open and closed quantum billiards, highlighting effects of symmetry breaking and collective Lamb shifts.

Findings

Shannon entropy increases near avoided crossings in dielectric microcavities.

Opposite entropy behavior observed compared to atomic physics.

Entropy changes linked to symmetry breaking and Lamb shifts.

Abstract

The relation between the Shannon entropy and avoided crossings is investigated in dielectric microcavities. The Shannon entropy of probability density for eigenfunctions in an open elliptic billiard as well as a closed quadrupole billiard increases as the center of avoided crossing is approached. These results are opposite to those of atomic physics for electrons. It is found that the collective Lamb shift of the open quantum system and the symmetry breaking in the closed chaotic quantum system give equivalent effects to the Shannon entropy.