Scarring for Quantum Maps with Simple Spectrum

TL;DR

This paper demonstrates that certain quantum maps with simple spectra still exhibit scarring, challenging the idea that high spectral multiplicities are necessary for quantum ergodicity failure.

Contribution

It introduces a family of quantum maps with simple spectra that still show scarring, contrasting previous examples where spectral multiplicity caused ergodicity failure.

Findings

Quantum maps with simple spectra can exhibit scarring.

Spectral simplicity does not prevent quantum ergodicity failure.

The maps' spectra are generically simple, yet they show invariant submanifold localization.

Abstract

We previously introduced a family of symplectic maps of the torus whose quantization exhibits scarring on invariant co-isotropic submanifolds. The purpose of this note is to show that in contrast to other examples, where failure of Quantum Unique Ergodicity is attributed to high multiplicities in the spectrum, for these examples the spectrum is (generically) simple.