Pointwise Weyl law for graphs from quantized interval maps

Abstract

We prove an analogue of the pointwise Weyl law for families of unitary matrices obtained from quantization of one-dimensional interval maps. This quantization for interval maps was introduced by Pakoński et al. [J. Phys. A: Math. Gen. 34 9303-9317 (2001)] as a model for quantum chaos on graphs. Since we allow shrinking spectral windows in the pointwise Weyl law, as a consequence we obtain for these models a strengthening of the quantum ergodic theorem from Berkolaiko et al. [Commun. Math. Phys. 273 137-159 (2007)], and show in the semiclassical limit that a family of randomly perturbed quantizations has approximately Gaussian eigenvectors. We also examine further the specific case where the interval map is the doubling map.

final version

References in corpus (3)

• Form factor for a family of quantum graphs: An expansion to third order
• Quantum ergodicity on graphs
• Quantum ergodicity for expanding quantum graphs in the regime of spectral delocalization

Cited by in corpus (1)

• Eigenstates and spectral projection for quantized baker's map