title: Dissipative dynamics of a harmonic oscillator: a nonperturbative approach.
abstract: Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of noninteracting oscillators. We follow a nonperturbative approach, proposed earlier by us for the free Brownian particle. The diffusion constants are calculated analytically and the positivity of the master equation is shown to hold above a critical temperature. We compare the long time behavior of the average kinetic and potential energies with known thermodynamic results. In the limit of vanishing oscillator frequency of the system, we recover the results of the free Brownian particle.
authors.affiliation: Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Mohanpur 741252, India.
authors.forename: Jishad
authors.initials: J
authors.lastname: Kumar
authors.forename: S
authors.initials: S
authors.lastname: Sinha
authors.forename: P A
authors.initials: PA
authors.lastname: Sreeram