Small scale quantum ergodicity in cat maps. II. Quasimodes that are not equidistributed at the logarithmical scales

2020/05/01 by Xiaolong Han, Han, Xiaolong
Mathematics · Physics and Astronomy · #11F25 #35P20 #37D20 #58G25 #81Q50 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2005.00648

openalex publication_date 2020/05/01 · openalex created_date 2020/05/13 · openalex updated_date 2026/07/28

Abstract

In this series, we investigate quantum ergodicity at small scales for linear hyperbolic maps of the torus ("cat maps'"). In Part II of the series, we construct quasimodes that are quantum ergodic but are not equidistributed at the logarithmical scales.

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