Probabilistic Weyl laws for quantized tori

Abstract

For the Toeplitz quantization of complex-valued functions on a $2n$-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical experiments the same Weyl law also holds for ``false'' eigenvalues created by pseudospectral effects.

33 pages, 3 figures, v2 corrected listed title

References in corpus (3)

• Pseudospectra of semi-classical (pseudo)differential operators
• Distribution of resonances for open quantum maps
• Weyl laws for partially open quantum maps

Cited by in corpus (7)

• Two point eigenvalue correlation for a class of non-selfadjoint operators under random perturbations
• Almost sure Weyl law for quantized tori
• Uniform observable error bounds of Trotter formulae for the semiclassical Schrödinger equation
• Observable Error Bounds of the Time-splitting Scheme for Quantum-Classical Molecular Dynamics
• Particle Trajectories for Quantum Maps
• Discrete Superconvergence Analysis for Quantum Magnus Algorithms of Unbounded Hamiltonian Simulation
• An exotic calculus of Berezin-Toeplitz operators