Graduate Student Seminar: Eigenvectors for graphs from quantized interval maps, Speaker: Laura Shou

Eigenvectors for graphs from quantized interval maps

Abstract: In this talk I will discuss the eigenvectors of 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 (2001)] as a model for quantum chaos on graphs. The resulting unitary matrices are sparse, yet numerically exhibit CUE random matrix behavior. To analyze the eigenvectors, I prove a pointwise Weyl law with shrinking spectral windows. This implies a stronger version of the quantum ergodic theorem for these models, and shows in the semiclassical limit that a family of randomly perturbed quantizations has approximately Gaussian eigenvectors.

Laura Shou is a PhD candidate in the Mathematics Department at Princeton University. She her undergrad in math at Caltech and then studied mathematical physics in Munich, Germany.