Mathematics Colloquia and Seminars

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It is well known that for systems in one spatial dimension the Bohr-Sommerfeld quantization condition applies successfully to determine the spectrum of quantum observables whose energy surfaces are real one-dimensional curves. In this talk we shall discuss the spectrum of non-selfadjoint perturbations of semiclassical operators with periodic Hamilton flows. In dimension two we shall show that complex curves can be used to give a precise description of the entire spectrum in some region of the complex plane, going beyond the corresponding results in the self-adjoint theory. Applications of our results include barrier top resonances for Schr\"odinger operators and eigenfrequencies for dissipative wave equations on Zoll surfaces. This is a joint work with Johannes Sj\"ostrand.