Quantum dynamics of the damped harmonic oscillator

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 Kramers-Kronig relations. This approach offers an alternative description of nano-mechanical oscillators and opto-mechanical systems.

31 pages

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Cited by in corpus (14)

• Open quantum system dynamics and the mean force Gibbs state
• Thermal energies of classical and quantum damped oscillators coupled to reservoirs
• On the lagrangian description of dissipative systems
• Lie transformation method on quantum state evolution of a general time-dependent driven and damped parametric oscillator
• Quantum electrodynamics of lossy magnetodielectric samples in vacuum: modified Langevin noise formalism
• Complex semiclassical theory for non-Hermitian quantum systems
• Damped vacuum states of light
• Stochastic simulation of dissipative quantum oscillators
• Damped oscillators within the general theory of Casimir and van der Waals forces
• Quantum dissipation of planar harmonic systems: Maxwell-Chern-Simons theory
• Absorption in dipole-lattice models of dielectrics
• Quantum theory of a strongly-dissipative scalar field
• Quantization of nonlinear non-Hamiltonian systems
• Hamiltonian of mean force and a damped harmonic oscillator in an anisotropic medium