Damped harmonic oscillator: pure states of the bath and exact master equations

Abstract

Time evolution of a harmonic oscillator linearly coupled to a heat bath is compared for three classes of initial states for the bath modes - grand canonical ensemble, number states and coherent states. It is shown that for a wide class of number states the behavior of the oscillator is similar to the case of the equilibrium bath. If the bath modes are initially in coherent states, then the variances of the oscillator coordinate and momentum, as well as its entanglement to the bath, asymptotically approach the same values as for the oscillator at zero temperature and the average coordinate and momentum show a Brownian-like behavior. We derive an exact master equation for the characteristic function of the oscillator valid for arbitrary factorized initial conditions. In the case of the equilibrium bath this equation reduces to an equation of the Hu-Paz-Zhang type, while for the coherent states bath it leads to an exact stochastic master equation with a multiplicative noise.

arXiv comment9 pages, submitted to Phys. Rev. E

References in corpus (4)

• Exact time evolution and master equations for the damped harmonic oscillator
• Quantum Brownian Motion in a Bath of Parametric Oscillators: A model for system-field interactions
• Decoherence and Initial Correlations in Quantum Brownian Motion
• Exact Diagonalization of Two Quantum Models for the Damped Harmonic Oscillator

Cited by in corpus (3)

• On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator
• Non-Markovian master equation for a damped oscillator with time-varying parameters
• Quantum master equations from classical Lagrangians with two stochastic forces