Path Integral Construction of Quantum Propagators for Time-Dependent Potentials to Evaluate Work Statistics

The path integral approach to quantum mechanics is an alternative to the Schrödinger equation for finding quantum propagators. This approach generalizes the action principle in classical mechanics with a sum over the infinite number of possible trajectories. It can also be used to calculate the propagator in the case of a time-dependent potential. Here, I describe several of these potentials and illustrate the case of a particle in a rigid box with one wall moving uniformly in time, using a semi-classical approximation. Time-dependent potentials can be used in quantum thermodynamics as a work parameter, which does work on the system when controlled by an external agent. This leads to a path integral approach to quantum thermodynamics. I illustrate the calculation of the work statistics for the rigid box with one wall moving uniformly in time.