Spatial Correlation in Quantum Chaotic Systems with Time-reversal Symmetry: Theory and Experiment

TL;DR

This paper investigates spatial correlations in quantum chaotic systems with time-reversal symmetry, revealing long-range oscillations and predictability of wavefunction behavior, supported by theoretical analysis and microwave cavity experiments.

Contribution

It introduces a supermatrix method to analyze wavefunction correlations and demonstrates long-range Friedel oscillations in chaotic systems with experimental validation.

Findings

Existence of long-range Friedel oscillations in wavefunction density

High predictability of wavefunction spatial dependence with large fluctuations

Excellent agreement between theory and microwave cavity experiments

Abstract

The correlation between the values of wavefunctions at two different spatial points is examined for chaotic systems with time-reversal symmetry. Employing a supermatrix method, we find that there exist long-range Friedel oscillations of the wave function density for a given eigenstate, although the background wavefunction density fluctuates strongly. We show that for large fluctuations, once the value of the wave function at one point is known, its spatial dependence becomes highly predictable for increasingly large space around this point. These results are compared with the experimental wave functions obtained from billiard-shaped microwave cavities and very good agreement is demonstrated.