A set of oscillators in a common bath

Abstract

The well-known model of a heavy oscillator interacting with a bath of light oscillators is extended to several heavy oscillators. New features appear when they are in resonance. These are worked out for the case of two identical oscillators, with the following conclusions. If initially one of them is excited its damping is slowed down by the presence of the other. If initially both are excited their emitted field exhibits second order coherence and therefore “interference between photons”. If initially the bath is in thermal equilibrium the oscillators end up by being thermally excited and uncorrelated. Finally the formulation in terms of a Langevin equation is discussed.