# Scarring in open chaotic systems: The local density of states

## TL;DR

This paper investigates how openings in chaotic quantum systems affect wavefunction scarring and local density of states, showing that strong coupling suppresses scarring effects and restores random matrix theory behavior.

## Contribution

It introduces a method to estimate the local density of states in open chaotic systems and demonstrates how openings influence scarring phenomena.

## Key findings

- Strong coupling suppresses energy dependence of local density of states
- Openings restore RMT behavior in chaotic systems
- Predictions validated on quantum maps with different openings

## Abstract

Chaotic Hamiltonians are known to follow Random Matrix Theory (RMT) ensembles in the apparent randomness of their spectra and wavefunction statistics. Deviations form RMT also do occur, however, due to system-specific properties, or as quantum signatures of classical chaos. Scarring, for instance, is the enhancement of wavefunction intensity near classical periodic orbits, and it can be characterized by a local density of states (or local spectrum) that clearly deviates from RMT expectations, by exhibiting a peaked envelope, which has been described semiclassically. Here, the system is connected to an opening, the local density of states is introduced for the resulting non-Hermitian chaotic Hamiltonian, and estimated a priori in terms of the Green's function of the closed system and the open channels. The predictions obtained are tested on quantum maps coupled both to a single-channel opening and to a Fresnel-type continuous opening. The main outcome is that strong coupling to the opening gradually suppresses the energy dependence of the local density of states due to scarring, and restores RMT behavior.