Recent Developments in the Theory of Scarring

TL;DR

This paper reviews recent advances in understanding quantum wavefunction behavior near unstable periodic orbits in chaotic systems, highlighting how classical dynamics inform quantum properties and deviations from random matrix theory.

Contribution

It introduces a wavepacket dynamics framework that quantitatively links short-time classical behavior to long-time quantum properties, revealing new insights into scarring phenomena.

Findings

Quantum wavefunctions show non-random behavior near unstable periodic orbits.

Short-time classical dynamics can predict quantum intensity distributions and correlations.

Deviations from random matrix theory occur due to short unstable periodic orbits.

Abstract

We review recent progress in attaining a quantitative understanding of the scarring phenomenon, the non-random behavior of quantum wavefunctions near unstable periodic orbits of a classically chaotic system. The wavepacket dynamics framework leads to predictions about statistical long-time and stationary properties of quantum systems with chaotic classical analogues. Many long-time quantum properties can be quantitatively understood using only short-time classical dynamics information; these include wavefunction intensity distributions, intensity correlations in phase space and correlations between wavefunctions, and distributions of decay rates and conductance peaks in weakly open systems. Strong deviations from random matrix theory are predicted and observed in the presence of short unstable periodic orbits.