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Measuring scars of periodic orbits.

L Kaplan¹, E J Heller

¹Department of Physics and Society of Fellows, Harvard University, Cambridge, MA 02138, USA. kaplan@physics.harvard.edu

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

|April 24, 2002

Summary

This study introduces a new universal measure for periodic orbit scarring in quantum chaotic systems. This method enhances the detection of scars induced by unstable periodic orbits and their dynamics.

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Quantum Lissajous Scars.

Physical review letters·2019

Area of Science:

Quantum mechanics
Classical and quantum chaos
Statistical physics

Background:

Periodic orbit scarring is a key correction to random matrix theory predictions for quantum eigenstates.
Understanding eigenfunction scarring is crucial for analyzing classically chaotic systems.

Purpose of the Study:

To clarify concepts and effects of eigenfunction scarring.
To propose a universal measure for quantifying scar strength.
To investigate the role of periodic orbits and their dynamics in scar formation.

Main Methods:

Development of a universal scar measure incorporating periodic orbits and linearized dynamics.
Analysis of scar strength using eigenstate overlaps and inverse participation ratios.
Examination of off-resonance scars near unstable periodic orbits.

Main Results:

The proposed universal scar measure effectively quantifies scarring.
Enhanced scarring strength is observed, particularly for longer periodic orbits.
Off-resonance scars are identified adjacent to unstable periodic orbits.

Conclusions:

The new measure provides a robust tool for studying eigenfunction scarring.
Periodic orbit dynamics significantly influence quantum eigenstate structure.
This work advances the understanding of quantum manifestations of classical chaos.

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