Quantum statistical theory of damped, driven Morse oscillator: Bistable features and spectral characteristics

Abstract

A new quantum statistical formulation of a damped classically driven Morse oscillator is presented. The theory is based on the realization of the Morse oscillator in terms of generators of an SU(2) Lie algebra, which allows us to construct the spin coherent states for the Morse oscillator. The c-number equivalents of the master equation in the form of the Fokker–Planck and Langevin equations have been derived and solved in the mean field limit to demonstrate the existence of multiple steady states and the associated molecular bistability. The nonstationary solution derived under adiabatic elimination of relevant variable and secular approximation is also presented. Some spectral characteristics such as shift and linewidth due to phase fluctuations have been calculated.