| Автор | A J van Wonderen |
| Автор | L G Suttorp |
| Дата выпуска | 2004-11-19 |
| dc.description | The Ullersma model for the damped harmonic oscillator is coupled to the quantized electromagnetic field. All material parameters and interaction strengths are allowed to depend on position. The ensuing Hamiltonian is expressed in terms of canonical fields, and diagonalized by performing a normal-mode expansion. The commutation relations of the diagonalizing operators are in agreement with the canonical commutation relations. For the proof we replace all sums of normal modes by complex integrals with the help of the residue theorem. The same technique helps us to explicitly calculate the quantum evolution of all canonical and electromagnetic fields. We identify the dielectric constant and the Green function of the wave equation for the electric field. Both functions are meromorphic in the complex frequency plane. The solution of the extended Ullersma model is in keeping with well-known phenomenological rules for setting up quantum electrodynamics in an absorptive and spatially inhomogeneous dielectric. To establish this fundamental justification, we subject the reservoir of independent harmonic oscillators to a continuum limit. The resonant frequencies of the reservoir are smeared out over the real axis. Consequently, the poles of both the dielectric constant and the Green function unite to form a branch cut. Performing an analytic continuation beyond this branch cut, we find that the long-time behaviour of the quantized electric field is completely determined by the sources of the reservoir. Through a Riemann–Lebesgue argument we demonstrate that the field itself tends to zero, whereas its quantum fluctuations stay alive. We argue that the last feature may have important consequences for application of entanglement and related processes in quantum devices. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Копирайт | 2004 IOP Publishing Ltd |
| Название | The oscillator model for dissipative QED in an inhomogeneous dielectric |
| Тип | paper |
| DOI | 10.1088/0305-4470/37/46/002 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 37 |
| Первая страница | 11101 |
| Последняя страница | 11122 |
| Аффилиация | A J van Wonderen; Instituut voor Theoretische Fysica, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands |
| Аффилиация | L G Suttorp; Instituut voor Theoretische Fysica, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands |
| Выпуск | 46 |
