Spectral behavior of contractive noise

TL;DR

This paper investigates the spectral properties of quantum systems under contractive noise, revealing a power-law growth of long-lived resonances with no link to classical fractal dimensions, challenging existing fractal Weyl law predictions.

Contribution

It demonstrates that the number of long-lived resonances grows as a power law in 7, independent of the classical attractor4s fractal dimension, contradicting previous fractal Weyl law expectations.

Findings

Long-lived resonances grow as a power law in 7.

No correlation between resonance growth exponent and classical fractal dimension.

Challenges the applicability of the fractal Weyl law to contractive noise systems.

Abstract

We study the behavior of the spectra corresponding to quantum systems subjected to a contractive noise, i.e. the environment reduces the accessible phase space of the system, but the total probability is conserved. We find that the number of long lived resonances grows as a power law in $\hbar$ but surprisingly there is no relationship between the exponent of this power law and the fractal dimension of the corresponding classical attractor. This is in disagreement with the predictions of the fractal Weyl law which has been established for open systems where the probability is lost under the effect of a projective noise.