dorsal/arxiv
View SchemaQuantum damped oscillator I: dissipation and resonances
| Authors | Dariusz Chruscinski, Jacek Jurkowski |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506007 |
| URL | https://arxiv.org/abs/quant-ph/0506007 |
| DOI | 10.1016/j.aop.2005.11.004 |
| Journal | Ann. Phys. 321 (2006) 854-874 |
Abstract
Quantization of a damped harmonic oscillator leads to so called Bateman's dual system. The corresponding Bateman's Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states which are responsible for the irreversible quantum dynamics of a damped harmonic oscillator.
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"abstract": "Quantization of a damped harmonic oscillator leads to so called Bateman\u0027s\ndual system. The corresponding Bateman\u0027s Hamiltonian, being a self-adjoint\noperator, displays the discrete family of complex eigenvalues. We show that\nthey correspond to the poles of energy eigenvectors and the corresponding\nresolvent operator when continued to the complex energy plane. Therefore, the\ncorresponding generalized eigenvectors may be interpreted as resonant states\nwhich are responsible for the irreversible quantum dynamics of a damped\nharmonic oscillator.",
"arxiv_id": "quant-ph/0506007",
"authors": [
"Dariusz Chruscinski",
"Jacek Jurkowski"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.aop.2005.11.004",
"journal_ref": "Ann. Phys. 321 (2006) 854-874",
"title": "Quantum damped oscillator I: dissipation and resonances",
"url": "https://arxiv.org/abs/quant-ph/0506007"
},
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