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

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

2004-10-18

arxiv.org/abs/physics/0410127v5

J. Comp. Appl. Math. 204 (2007), 199-208

Physics

Classical Physics

12 pages, 1 figure, second revised version with clarifications of some points, improved discussion of weakly dispersive media,

Scientific paper

10.1016/j.cam.2006.01.038

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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