The Spectrum of an Almost Maximally Open Quantized Cat Map

Autor:	Borns-Weil, Yonah
Rok vydání:	2022
Předmět:	Mathematics - Spectral Theory Mathematical Physics 81Q50 (Primary) 47B28 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We consider eigenvalues of a quantized cat map (i.e. hyperbolic symplectic integer matrix), cut off in phase space to include a fixed point as its only periodic orbit on the torus. We prove a simple formula for the eigenvalues on both the quantized real line and the quantized torus in the semiclassical limit as $h\to0$. We then consider the case with no fixed points, and prove a superpolynomial decay bound on the eigenvalues. The results are illustrated with numerical calculations. Comment: 35 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.13898 Zobrazit plný text záznamu View this record from Arxiv