Academic Journal
Spectral Theory of Time Dispersive and Dissipative Systems: Spectral theory of time dispersive and dissipative systems
| Τίτλος: | Spectral Theory of Time Dispersive and Dissipative Systems: Spectral theory of time dispersive and dissipative systems |
|---|---|
| Συγγραφείς: | Alexander Figotin, Jeffrey H. Schenker |
| Πηγή: | Journal of Statistical Physics. 118:199-263 |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | Springer Science and Business Media LLC, 2005. |
| Έτος έκδοσης: | 2005 |
| Θεματικοί όροι: | 34A30, 47DO6, 82CO3, 78A25, 70J10, Applications of operator theory to differential and integral equations, FOS: Physical sciences, spectral theory, Mathematical Physics (math-ph), 01 natural sciences, Applications of operator theory in statistical physics, time dispersive dissipative dielectric medium, time dispersive dissipative systems, Lamb model, Quantum dynamics and nonequilibrium statistical mechanics (general), Maxwell equations, 0101 mathematics, PDEs in connection with optics and electromagnetic theory, conservative extension, Mathematical Physics |
| Περιγραφή: | 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. LaTeX, 57 Pages, incorporated revisions corresponding with published version |
| Τύπος εγγράφου: | Article Other literature type |
| Περιγραφή αρχείου: | application/xml |
| Γλώσσα: | English |
| ISSN: | 1572-9613 0022-4715 |
| DOI: | 10.1007/s10955-004-8783-7 |
| DOI: | 10.48550/arxiv.math-ph/0404070 |
| Σύνδεσμος πρόσβασης: | http://arxiv.org/pdf/math-ph/0404070 http://arxiv.org/abs/math-ph/0404070 https://arxiv.org/abs/math-ph/0404070 https://arxiv.org/pdf/math-ph/0404070 https://www.math.uci.edu/~afigotin/papers/Figotin%20Schenker%20Spectral%20Theory%20of%20Time%20Dispersive%20and%20Dissipative%20JSP%202005.pdf http://users.math.msu.edu/users/jeffrey/Reprints/JSPV118P199.pdf https://core.ac.uk/display/100831837 https://users.math.msu.edu/users/jeffrey/Reprints/JSPV118P199.pdf https://ui.adsabs.harvard.edu/abs/2005JSP...118..199F/abstract https://link.springer.com/article/10.1007/s10955-004-8783-7 |
| Rights: | Springer TDM arXiv Non-Exclusive Distribution |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....c40fa3a80a3e2708bbfc6a70eb7af2cb |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 15729613 00224715 |
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| DOI: | 10.1007/s10955-004-8783-7 |