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.
Original language | English |
---|---|
Article number | 083043 |
Number of pages | 31 |
Journal | New Journal of Physics |
Volume | 14 |
DOIs | |
Publication status | Published - 31 Aug 2012 |
Keywords
- Ground-state
- Brownian-motion
- Quantitization
- System
- Mechanics