  We determine the frequency-dependent response characteristics of a quantum
system to a driven Caldeira-Leggett bath. The bath degrees of freedom are
explicitly driven by an external time-dependent force, in addition to the
direct time-dependent forcing of the system itself. After general
considerations of driven Caldeira-Leggett baths, we consider the Rubin model of
a chain of quantum particles coupled by linear springs as an important model of
a quantum dissipative system. We show that in the presence of time-dependent
driving of the chain, this model can be mapped to a quantum system which
couples to a driven Caldeira-Leggett bath. The effect of the bath driving is
captured by a time-dependent force on the central system, which is, in
principle, non-Markovian in nature. We study two specific examples, the exactly
solvable case of a harmonic potential, and a quantum two-state system for which
we assume a weak system-bath coupling. We evaluate the dynamical response to a
periodic driving of the system and the bath. The dynamic susceptibility is
shown to be altered qualitatively by the bath drive: The dispersive part is
enhanced at low frequencies and acquires a maximum at zero frequency. The
absorptive part develops a shoulder-like behavior in this frequency regime.
These features seem to be generic for quantum systems in a driven
Caldeira-Leggett bath.
