Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 204, Issue 2, Pages 199-208Publisher
ELSEVIER
DOI: 10.1016/j.cam.2006.01.038
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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. (c) 2006 Elsevier B.V. All rights reserved.
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