Transient features of quantum open maps

TL;DR

This paper investigates how short-term features of quantum open maps influence resonance distributions and eigenfunction localization, revealing sensitivity to initial conditions and delocalization effects at small opening areas.

Contribution

It demonstrates the impact of initial opening shape on quantum resonance distributions and phase space localization, highlighting transient effects in quantum open maps.

Findings

Resonance distributions depend on initial opening shape.

Eigenfunctions show delocalization when opening area is less than 5.

Short-term behaviors significantly influence quantum resonance properties.

Abstract

We study families of open chaotic maps that classically share the same asymptotic properties -- forward and backwards trapped sets, repeller dimensions, escape rate -- but differ in their short time behavior. When these maps are quantized we find that the fine details of the distribution of resonances and the corresponding eigenfunctions are sensitive to the initial shape and size of the openings. We study phase space localization of the resonances with respect to the repeller and find strong delocalization effects when the area of the openings is smaller than $\hbar$.