Shannon entropy and avoided crossings in closed and open quantum billiards

2018/01/31 by Kyu-Won Park, Songky Moon, Younghoon Shin +3
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Mathematical Dynamics and Fractals #Mathematics #Physics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Statistical physics #Theoretical physics #nlin.CD #quant-ph

paper · pdf · doi:10.1103/physreve.97.062205

published as Phys. Rev. E 97, 062205 (2018) · 7 pages, 5 figures

arxiv created 2018/03/12 · openalex publication_date 2018/06/12 · arxiv updated 2018/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The relation between Shannon entropy and avoided crossings is investigated in dielectric microcavities. The Shannon entropy of the probability density for eigenfunctions in an open elliptic billiard as well as a closed quadrupole billiard increases as the center of the 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 have equivalent effects on the Shannon entropy.

Citations

• Periodic Orbits and Classical Quantization Conditions
• A Mathematical Theory of Communication
• Formation of Long-Lived, Scarlike Modes near Avoided Resonance Crossings in Optical Microcavities
• Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws
• Decoherence, einselection, and the quantum origins of the classical