Dynamics of a Maximally Open Quantized Cat Map

The HADES seminar on Tuesday, February 22 will be at 3:30 pm in Room 740.

Speaker: Yonah Borns-Weil

Abstract: Quantum dynamics is concerned with quantum analogues of classical dynamical systems. A common situation is scattering theory, in which the Hamiltonian dynamics of scattered particles are replaced by wavefunctions obeying the Schrödinger equation. When time is discretized, the analogues are open quantum maps, which are Fourier integral operators arising from phase space diffeomorphisms that are then “opened” by sending some regions to “infinity.” In this talk, we analyze a simple open quantum map, based on the classical Arnol’d cat map. We shall show using the method of Grushin problems that the spectrum has a very simple form in the semiclassical regime as h approaches 0. Emphasis will be given to motivation and interpretations of the result.

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