  Non-equilibrium path integral methods for computing quantum free energy
differences are applied to a quantum particle trapped in a harmonic well of
uniformly changing strength with the purpose of establishing the convergence
properties of the work distribution and free energy as the number of degrees of
freedom M in the regularized path integrals goes to infinity. The work
distribution is found to converge when M tends to infinity regardless of the
switching speed, leading to finite results for the free energy difference when
the Jarzynski non-equilibrium work relation or the Crooks fluctuation relation
are used. The nature of the convergence depends on the regularization method.
For the Fourier method, the convergence of the free energy difference and work
distribution go as 1/M, while both quantities converge as 1/M^2 when the bead
regularization procedure is used. The implications of these results to more
general systems are discussed.
