  The imaginary-time path integral representation of the canonical partition
function of a quantum system and non-equilibrium work fluctuation relations are
combined to yield methods for computing free energy differences in quantum
systems using non-equilibrium processes. The path integral representation is
isomorphic to the configurational partition function of a classical field
theory, to which a natural but fictitious Hamiltonian dynamics is associated.
It is shown that if this system is prepared in an equilibrium state, after
which a control parameter in the fictitious Hamiltonian is changed in a finite
time, then formally the Jarzynski non-equilibrium work relation and the Crooks
fluctuation relation are shown to hold, where work is defined as the change in
the energy as given by the fictitious Hamiltonian. Since the energy diverges
for the classical field theory in canonical equilibrium, two regularization
methods are introduced which limit the number of degrees of freedom to be
finite. The numerical applicability of the methods is demonstrated for a
quartic double-well potential with varying asymmetry. A general parameter-free
smoothing procedure for the work distribution functions is useful in this
context.
