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Quantum dynamics of the damped harmonic oscillator

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philbin2012newjphys083043.pdf (892.2Kb)
Date
31/08/2012
Author
Philbin, T. G.
Keywords
Ground-state
Brownian-motion
Quantitization
System
Mechanics
QC Physics
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Abstract
The quantum theory of the damped harmonic oscillator has been a subject of continual investigation since the 1930s. The obstacle to quantization created by the dissipation of energy is usually dealt with by including a discrete set of additional harmonic oscillators as a reservoir. But a discrete reservoir cannot directly yield dynamics such as Ohmic damping (proportional to velocity) of the oscillator of interest. By using a continuum of oscillators as a reservoir, we canonically quantize the harmonic oscillator with Ohmic damping and also with general damping behaviour. The dynamics of a damped oscillator is determined by an arbitrary effective susceptibility that obeys the Kramers-Kronig relations. This approach offers an alternative description of nano-mechanical oscillators and opto-mechanical systems.
Citation
Philbin , T G 2012 , ' Quantum dynamics of the damped harmonic oscillator ' , New Journal of Physics , vol. 14 , 083043 . https://doi.org/10.1088/1367-2630/14/8/083043
Publication
New Journal of Physics
Status
Peer reviewed
DOI
https://doi.org/10.1088/1367-2630/14/8/083043
ISSN
1367-2630
Type
Journal article
Rights
2012 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/4761

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