# Lyapunov exponents and Hamiltonian poles in a non Hermitian dynamics

## TL;DR

This paper establishes a link between Hamiltonian poles and Lyapunov exponents in non-Hermitian quantum dynamics, demonstrating that decay times relate inversely to Lyapunov exponents through a phase space volume formalism.

## Contribution

It introduces a novel formalism connecting Hamiltonian poles and Lyapunov exponents in non-Hermitian quantum systems, simplifying previous semiclassical approaches.

## Key findings

- Decay time is inversely proportional to Lyapunov exponents.
- Formalism accurately characterizes the Gamow model behavior.
- Results align with semiclassical quantum resonance theory.

## Abstract

By means of expressing volumes in phase space in terms of traces of quantum operators, a relationship between the Hamiltonian poles and the Lyapunov exponents in a non Hermitian quantum dynamics, is presented. We illustrate the formalism by characterizing the behavior of the Gamow model whose dissipative decay time, measured by its decoherence time, is found to be inversely proportional to the Lyapunov exponents of the unstable periodic orbits. The results are in agreement with those obtained by means of the semiclassical periodic-orbit approach in quantum resonances theory but using a simpler mathematics.