Quantum dynamics of the damped harmonic oscillator
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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.
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
New Journal of Physics
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