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Hamiltonian treatment of time dispersive and dissipative media within the linear response theory

A. Figotin·J. H. Schenker
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Abstract

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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A. Figotin, J. H. Schenker. 2006-01-24. Hamiltonian treatment of time dispersive and dissipative media within the linear response theory. https://doi.org/10.1016/j.cam.2006.01.038

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