Complex-valued second difference as a measure of stabilization of complex dissipative statistical systems: Girko ensemble

TL;DR

This paper investigates the stability of eigenenergies in quantum dissipative systems modeled by complex Ginibre ensemble Hamiltonians, revealing stable eigenenergy structures and drawing analogies with electrical charge systems.

Contribution

It introduces a novel analysis of eigenenergy stability in dissipative quantum systems using complex Ginibre ensemble, highlighting structural stability and charge analogies.

Findings

Eigenenergies form stable structures in the Ginibre ensemble

Analogy established between eigenenergy systems and electrical charges

Provides insights into dissipation effects on quantum system stability

Abstract

A quantum statistical system with energy dissipation is studied. Its statistics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble. The eigenenergies are shown to form stable structure. Analogy of Wigner and Dyson with system of electrical charges is drawn.