24 March 2015, King's College, Strand building, room S5.20.
A special talk:
Maciej Zworski (Berkeley)
Resonances as viscosity limits
Many physical systems can be described using evolution of states.
We observe correlations: one measures
the time evolution of one state against another state. The time representation
can be replaced by the frequency representation (by taking a Fourier transform)
which produces the power spectrum. The poles of power spectrum
appear in different settings and are called scattering poles (obstacle
scattering), quantum resonances (quantum scattering theory),
quasinormal modes (general relativity), Pollicott--Ruelle resonances
In practically all situations these poles 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 case of black box
Euclidean scattering. The method has also been numerically investigated
in the chemistry literature as an alternative to complex scaling.