2004/04/30 by Alex Figotin, A. Figotin, Jeffrey H. Schenker +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Electromagnetic Simulation and Numerical Methods #Microwave Imaging and Scattering Analysis #math-ph #math.MP #msc:34A30 #msc:47DO6 #msc:70J10 #msc:78A25 #msc:82CO3
paper · pdf · doi:10.1007/s10955-004-8783-7
published as J. Stat. Phys. 118 (2005), 199 · LaTeX, 57 Pages, incorporated revisions corresponding with published version
arxiv created 2004/12/16 · openalex publication_date 2005/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system -- which we show is essentially unique. We illustrate the method by applying it to the spectral analysis of time dispersive dielectrics and the damped oscillator with retarded friction. In particular, we obtain a conservative extension of the Maxwell equations which is equivalent to the original Maxwell equations for a dispersive and lossy dielectric medium.