# Classical properties of the leading eigenstates of quantum dissipative systems

## TL;DR

This paper explores how classical stable structures influence the quantum eigenstates in dissipative systems, revealing a simple scarring phenomenon and linking classical periodic orbits to quantum decay behavior.

## Contribution

It demonstrates that classical isoperiodic stable structures determine the phase and localization of quantum eigenstates in dissipative systems, extending the understanding of quantum-classical correspondence.

## Key findings

- Eigenstates' phase is determined by nearby classical stable structures
- Eigenvectors are strongly localized on classical periodic orbits
- Presence of a simple scarring phenomenon in dissipative quantum systems

## Abstract

By analyzing a paradigmatic example of the theory of dissipative systems -- the classical and quantum dissipative standard map -- we are able to explain the main features of the decay to the quantum equilibrium state. The classical isoperiodic stable structures typically present in the parameter space of these kind of systems play a fundamental role. In fact, we have found that the period of stable structures that are near in this space determines the phase of the leading eigenstates of the corresponding quantum superoperator. Moreover, the eigenvectors show a strong localization on the corresponding periodic orbits (limit cycles). We show that this sort of scarring phenomenon (an established property of Hamiltonian and projectively open systems) is present in the dissipative case and it is of extreme simplicity.