Quantum dynamics of the damped harmonic oscillator

T. G. Philbin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)
5 Downloads (Pure)

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 languageEnglish
Article number083043
Number of pages31
JournalNew Journal of Physics
Volume14
DOIs
Publication statusPublished - 31 Aug 2012

Keywords

  • Ground-state
  • Brownian-motion
  • Quantitization
  • System
  • Mechanics

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