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Alexander Figotin's Abstract
HAMILTONIAN TREATMENT OF TIME DISPERSIVE AND DISSIPATIVE MEDIA
WITHIN LINEAR RESPONSE THEORY
We develop a Hamiltonian theory for a time dispersive and dissipative (TDD)
inhomogeneous medium, as described by a linear response equation respecting
causality and power dissipation. The canonical Hamiltonian constructed here
exactly reproduces the original dissipative evolution after integrating out
auxiliary fields. In particular, for a dielectric medium we obtain a simple
formula for the Hamiltonian and closed form expressions for the energy
density and energy flux involving the auxiliary fields. The developed
approach also allows to treat a long standing problem of scattering from a
lossy non-spherical obstacle and, more generally, wave propagation in TDD
media.
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