Hamiltonian treatment of time dispersive and dissipative media within the linear response theory
arXiv:physics/0410127 · doi:10.1016/j.cam.2006.01.038
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.
12 pages, 1 figure, second revised version with clarifications of some points, improved discussion of weakly dispersive media, and discussion of dilation theory. 3rd revision a few typos corrected and discussion of canonical heat bath added