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Scattering resonances as viscosity limits

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If you have a question about this talk, please contact Harsha Hutridurga.

In practically all situations scattering resonances can be defined as limits of L2 eigenvalues of operators which regularize the Hamiltonian at infinity. For instance, Pollicott–Ruelle resonances in the theory of dynamical systems are given by viscosity limits: adding a Laplacian to the generator of an Anosov flow gives an operator with a discrete spectrum; letting the coupling constant go to zero turns eigenvalues into the resonances (joint work with S. Dyatlov). This principle seems to apply in all other settings where resonances can be defined and I will explain it in the simplest case of scattering by compactly supported potentials. The method has also been numerically investigated in the chemistry literature as an alternative to complex scaling.

This talk is part of the Partial Differential Equations seminar series.

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