Complexity of spectral sequences: semiclassical approach

TL;DR

This paper discusses the complexity involved in semiclassical evaluation of quantum spectra, highlighting differences in spectral complexity among chaotic systems compared to integrable ones.

Contribution

It introduces the idea that quantum spectra of chaotic systems vary in complexity, providing a new perspective on spectral analysis in semiclassical regimes.

Findings

Quantum spectra of chaotic systems differ in complexity.

Semiclassical evaluation is more challenging for nonintegrable systems.

Spectral complexity varies among chaotic systems.

Abstract

It has been long recognized that the task of semiclassical evaluation of quantum spectra for the classically nonintegrable systems is fundamentally more complex than for the classically integrable ones. Below it is argued that the quantum spectra of the chaotic systems can differ among themselves by level of their complexity.