Revisiting the damped quantum harmonic oscillator
| Autor: | Barnett, Stephen M., Cresser, James D., Croke, Sarah |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We reanalyse the quantum damped harmonic oscillator, introducing three less than common features. These are (i) the use of a continuum model of the reservoir rather than an ensemble of discrete oscillators, (ii) an exact diagonalisation of the Hamiltonian by adapting a technique pioneered by Fano, and (iii) the use of the thermofield technique for describing a finite temperature reservoir. We recover in this way a number of well-known and some, perhaps, less familiar results. An example of the latter is an ab initio proof that the oscillator relaxes to the mean-force Gibbs state. We find that special care is necessary when comparing the damped oscillator with its undamped counterpart as the former has two distinct natural frequencies, one associated with short time evolution and the other with longer times. Comment: 38 pages, 6 figures. This article, part review and part new results, is a contribution to the special issue of Physica Scripta "Challenges in quantum dynamics'', in honour of Professor Igor Jex on the occasion of his 60th birthday. arXiv admin note: substantial text overlap with arXiv:1508.02442 |
| Databáze: | arXiv |
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