Scarring on invariant manifolds for perturbed quantized hyperbolic toral automorphisms

Abstract

We exhibit scarring for certain nonlinear ergodic toral automorphisms. There are perturbed quantized hyperbolic toral automorphisms preserving certain co-isotropic submanifolds. The classical dynamics is ergodic, hence in the semiclassical limit almost all eigenstates converge to the volume measure of the torus. Nevertheless, we show that for each of the invariant submanifolds, there are also eigenstates which localize and converge to the volume measure of the corresponding submanifold.

17 pages

References in corpus (3)

• Scarred eigenstates for quantum cat maps of minimal periods
• Quantization of multidimensional cat maps
• Long time propagation and control on scarring for perturbed quantized hyperbolic toral automorphisms

Cited by in corpus (5)

• Scarring for Quantum Maps with Simple Spectrum
• Joint Quasimodes, Positive Entropy, and Quantum Unique Ergodicity
• Quantisations of piecewise affine maps on the torus and their quantum limits
• On the fluctuations of matrix elements of the quantum cat map
• Maximal scarring for eigenfunctions of quantum graphs