  Here the problem considered is that of a pair of oscillators coupled to a
common heat bath. Many, if not most, discussions of a single operator coupled
to a bath have used the independent oscillator model of the bath. However, that
model has no notion of separation, so the question of phenomena when the
oscillators are near one another compared with when they are widely separated
cannot be addressed. Here the Lamb model of an oscillator attached to a
stretched string is generalized to illustrate some of these questions. The
coupled Langevin equations for a pair of oscillators attached to the string at
different points are derived and their limits for large and small separations
obtained. Finally, as an illustration of a different phenomenon, the
fluctuation force between a pair of masses attached to the string is
calculated, with closed form expressions for the force at small and large
separations.

Quantum Physics