Scarring for Quantum Maps with Simple Spectrum

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.

5 pages

References in corpus (2)

• Entropy of semiclassical measures of the Walsh-quantized baker's map
• Scarring on invariant manifolds for perturbed quantized hyperbolic toral automorphisms

Cited by in corpus (3)

• Scarred eigenstates for arithmetic toral point scatterers
• Periodic orbits in cosmological billiards: the Selberg trace formula for asymptotic Bianchi IX universes, evidence for scars in the wavefunction of the quantum universe and large-scale structure anisotropies of the present universe
• Superscars for Arithmetic Point Scatterers II