Avoided level crossings in open quantum systems

TL;DR

This paper investigates how avoided level crossings in open quantum systems affect complex eigenvalues, wavefunction mixing, and symmetry influences, especially at high level densities where overlapping effects and environmental couplings become significant.

Contribution

It introduces a model simulating wavefunction mixing around avoided crossings using Gaussian distributions and explores the impact of overlapping crossings and symmetries in open quantum systems.

Findings

Overlapping Gaussian distributions lead to new effects in eigenvalue behavior.

Imaginary coupling terms significantly influence the avoided crossing phenomena.

Symmetries affect the characteristics of multi-level avoided crossings.

Abstract

At high level density, two states avoid usually crossing at the critical value $a_{\rm cr}$ of the parameter $a$ by which the system is controlled. The wavefunctions of the two states are mixed in a finite parameter range around $a_{\rm cr}$. This holds true for discrete states as well as for narrow resonance states which are coupled via the environment of scattering wavefunctions. We study the influence of avoided level crossings onto four overlapping complex eigenvalues of a symmetric non-Hermitian operator. The mixing of the two wavefunctions around $a_{\rm cr}$ is simulated, in each case, by assuming a Gaussian distribution around $a_{\rm cr}$. At high level density, the Gaussian distributions related to avoided crossings of different levels may overlap. Here, new effects arise, especially from the imaginary part of the coupling term via the environment. The results show, moreover, the influence of symmetries onto the multi-level avoided crossing phenomenon.