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Scar intensity statistics in the position representation.

K Damborsky¹, L Kaplan

¹Department of Physics, Tulane University, New Orleans, Louisiana 70118, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 21, 2006

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We predict wave function intensities on chaotic system orbits. Our findings detail how system size and orbit instability affect these distributions, revealing insights into quantum scarring effects.

Area of Science:

Quantum chaos
Wave function analysis
Statistical mechanics

Background:

Chaotic ballistic systems exhibit complex wave function behavior.
Understanding wave function intensity distribution on periodic orbits is crucial for quantum mechanics.
Previous studies have explored scarring but lacked general predictions for intensity distributions.

Purpose of the Study:

To derive general predictions for wave function intensity distributions.
To analyze the influence of system size and orbital instability.
To investigate deviations from the semiclassical limit.

Main Methods:

Derivation of analytical expressions for wave function intensity distributions.
Analysis of periodic orbits in chaotic systems.

Related Experiment Videos

Development of limiting expressions for asymptotic and perturbative regimes.

Main Results:

Obtained general predictions dependent on effective system size, instability exponent, and focal point proximity.
Derived asymptotic probability distribution for rare high-intensity events.
Developed a perturbative formula for weak scarring limits.
Identified a single scaling variable (lambdaN) for finite system size deviations.

Conclusions:

The study provides a comprehensive framework for understanding wave function intensities in chaotic systems.
Results offer insights into quantum scarring and deviations from semiclassical predictions.
The findings are applicable to various chaotic ballistic systems.