dorsal/arxiv
View SchemaExactly solvable path integral for open cavities in terms of quasinormal modes
| Authors | Alec Maassen van den Brink |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9905082 |
| URL | https://arxiv.org/abs/quant-ph/9905082 |
| DOI | 10.1103/PhysRevE.61.2367 |
| Journal | Phys.Rev.E61:2367-2375,2000 |
Abstract
We evaluate the finite-temperature Euclidean phase-space path integral for the generating functional of a scalar field inside a leaky cavity. Provided the source is confined to the cavity, one can first of all integrate out the fields on the outside to obtain an effective action for the cavity alone. Subsequently, one uses an expansion of the cavity field in terms of its quasinormal modes (QNMs)-the exact, exponentially damped eigenstates of the classical evolution operator, which previously have been shown to be complete for a large class of models. Dissipation causes the effective cavity action to be nondiagonal in the QNM basis. The inversion of this action matrix inherent in the Gaussian path integral to obtain the generating functional is therefore nontrivial, but can be accomplished by invoking a novel QNM sum rule. The results are consistent with those obtained previously using canonical quantization.
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"abstract": "We evaluate the finite-temperature Euclidean phase-space path integral for\nthe generating functional of a scalar field inside a leaky cavity. Provided the\nsource is confined to the cavity, one can first of all integrate out the fields\non the outside to obtain an effective action for the cavity alone.\nSubsequently, one uses an expansion of the cavity field in terms of its\nquasinormal modes (QNMs)-the exact, exponentially damped eigenstates of the\nclassical evolution operator, which previously have been shown to be complete\nfor a large class of models. Dissipation causes the effective cavity action to\nbe nondiagonal in the QNM basis. The inversion of this action matrix inherent\nin the Gaussian path integral to obtain the generating functional is therefore\nnontrivial, but can be accomplished by invoking a novel QNM sum rule. The\nresults are consistent with those obtained previously using canonical\nquantization.",
"arxiv_id": "quant-ph/9905082",
"authors": [
"Alec Maassen van den Brink"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevE.61.2367",
"journal_ref": "Phys.Rev.E61:2367-2375,2000",
"title": "Exactly solvable path integral for open cavities in terms of quasinormal modes",
"url": "https://arxiv.org/abs/quant-ph/9905082"
},
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