Title: Eigenstates of quantized baker’s map

 

Abstract:

Quantized baker’s map is a model for quantum chaos on the torus. I will introduce the background and model, and then discuss applications of windowed spectral projection estimates to the eigenstates and statistics of random band-limited states in this model. Afterwards, I will discuss generic random eigenbases of a different quantization, the Walsh-quantized A-baker’s map, which has high degeneracies in its spectrum. For generic random eigenbases, similar techniques show Gaussian value statistics and phase space equidistribution with high probability in the semiclassical limit.