Eigenvalue attraction in open quantum systems, biophysical systems, and Parity-Time symmetric materials

TL;DR

This paper explores how eigenvalues and their conjugates attract in various physical systems by deriving second derivative expressions that account for inertial forces and interactions among eigenvalues.

Contribution

It introduces a novel analytical framework for understanding eigenvalue attraction in open quantum, biophysical, and Parity-Time symmetric systems.

Findings

Eigenvalues exhibit attraction behavior influenced by inertial and inter-eigenvalue forces.

Derived explicit formulas for the second derivatives of eigenvalues.

Applicable to diverse physical systems with complex spectra.

Abstract

We investigate eigenvalue attraction for open quantum systems, biophysical systems, and for Parity-Time symmetric materials. To determine whether an eigenvalue and its complex conjugate of a real matrix attract, we derive expressions for the second derivative of eigenvalues, which is dependent upon contributions from inertial forces, attraction between an eigenvalue and its complex conjugate, as well as the force of the remaining eigenvalues in the spectrum.