Weyl laws for open quantum maps
Zhenhao Li
Massachusetts Institute of Technology, Cambridge, USA
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Abstract
We find Weyl upper bounds for the quantum open baker’s map in the semiclassical limit. For the number of eigenvalues in an annulus, we derive the asymptotic upper bound , where is the dimension of the trapped set of the baker’s map and is the semiclassical parameter, which improves upon the previous result of . Furthermore, we derive a Weyl upper bound with explicit dependence on the inner radius of the annulus for quantum open baker’s maps with Gevrey cutoffs.
Cite this article
Zhenhao Li, Weyl laws for open quantum maps. J. Spectr. Theory 12 (2022), no. 4, pp. 1541–1566
DOI 10.4171/JST/441