Origin of the $1/f^{\alpha}$-Spectral-Noise in Chaotic and Regular Quantum Systems

TL;DR

This paper investigates the origin of 1/f^α spectral noise in quantum systems, linking it to classical invariant manifolds and quantum interference, and predicts a universal spectral exponent in the presence of decoherence.

Contribution

It establishes a connection between spectral noise and classical invariant manifolds, analyzing the transition from order to chaos through Floquet quasienergy statistics.

Findings

Spectral noise origin linked to quantum interference of invariant manifolds.

Order-to-chaos transition characterized by Floquet quasienergy statistics.

Decoherence leads to a universal spectral exponent α=2 in both chaotic and integrable systems.

Abstract

Based on the connection between the spectral form factor and the probability to return, the origin of the $1/f^\alpha$-noise in fully chaotic and fully integrable systems is traced to the quantum interference between invariant manifolds of the classical dynamics and the dimensionality of those invariant manifolds. This connection and the order-to-chaos transition are analyzed in terms of the statistics of Floquet's quasienergies of a classically chaotic driving non-linear system. An immediate prediction of the connection established here is that in the presence of decoherence, the spectral exponent $\alpha$ takes the same value, $\alpha=2$, for both, fully chaotic and fully integrable systems.