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

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.

arXiv comment7 pages, 5 figures

References in corpus (13)

• Decoherence, einselection, and the quantum origins of the classical
• Observation of an exceptional point in a chaotic optical microcavity
• Boundary element method for resonances in dielectric microcavities
• Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities
• Observation of resonance trapping in an open microwave cavity
• Superradiance Transition in Transport Through Nanosystems
• Rabi Oscillations at Exceptional Points in Microwave Billiards
• Coupled non-identical microdisks: avoided crossing of energy levels and unidirectional far-field emission
• Scattering Experiments with Microwave Billiards at an Exceptional Point under Broken Time Reversal Invariance
• Entropy-power uncertainty relations : towards a tight inequality for all Gaussian pure states
• Dynamical stabilization and time in open quantum systems
• Non-Hermitian Hamiltonian and Lamb shift in circular dielectric microcavity
• Behavior of three modes of decay channels and their self-energies of elliptic dielectric microcavity

Cited by in corpus (9)

• Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions
• Indicators of wavefunction (de)localization in the avoided crossing in a quadrupole cavity
• Relative Entropy as a Measure of Difference Between Hermitian and Non-Hermitian Systems
• Observation of Electronic Modes in Open Cavity Resonator
• Entropic measure of directional emissions in microcavity lasers
• Entropic comparison of Landau-Zener and Demkov interactions in the phase space of a quadrupole billiard
• Hidden quantum-classical correspondence in chaotic billiards revealed by mutual information
• Topological Switching via Exceptional Point Pairs in an Optical Microcavity Laser
• Information-theoretic analysis of complex eigenmodes across avoided crossings in open microcavities