The scar mechanism revisited

TL;DR

This paper revisits the mechanisms behind quantum scars in chaotic systems, analyzing how unstable periodic orbits and homoclinic tori influence quantum density distribution and transport.

Contribution

It provides a detailed analysis of the relationship between classical recurrences, quantum interference, and secondary transport mechanisms like homoclinic tori in quantum scarring.

Findings

Quantum density accumulates along scars via constructive interference.

Homoclinic tori play a significant role in quantum transport.

Relationship between primary scars and secondary transport mechanisms is clarified.

Abstract

Unstable periodic orbits are known to originate scars on some eigenfunctions of classically chaotic systems through recurrences causing that some part of an initial distribution of quantum probability in its vicinity returns periodically close to the initial point. In the energy domain, these recurrences are seen to accumulate quantum density along the orbit by a constructive interference mechanism when the appropriate quantization (on the action of the scarring orbit) is fulfilled. Other quantized phase space circuits, such as those defined by homoclinic tori, are also important in the coherent transport of quantum density in chaotic systems. The relationship of this secondary quantum transport mechanism with the standard mechanism for scarring is here discussed and analyzed.