Barnett, S. M. , Cresser, J. D. and Croke, S. (2024) Revisiting the damped quantum harmonic oscillator. Physica Scripta, 99(2), 025109. (doi: 10.1088/1402-4896/ad1902)
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Abstract
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.
| Item Type: | Articles |
|---|---|
| Additional Information: | This work was supported, in part, by the Royal Society through the award to SMB of a Research Professorship, RP150122. |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Barnett, Professor Stephen and Cresser, Dr James and Croke, Dr Sarah |
| Authors: | Barnett, S. M., Cresser, J. D., and Croke, S. |
| College/School: | College of Science and Engineering > School of Physics and Astronomy |
| Journal Name: | Physica Scripta |
| Publisher: | IOP Publishing |
| ISSN: | 0031-8949 |
| ISSN (Online): | 1402-4896 |
| Published Online: | 11 January 2024 |
| Copyright Holders: | Copyright © 2024 The Author(s) |
| First Published: | First published in Physica Scripta 99(2):025109 |
| Publisher Policy: | Reproduced under a Creative Commons license |
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