Fast converging path integrals for time-dependent potentials: I. Recursive calculation of short-time expansion of the propagator

We calculate the short-time expansion of the propagator for a general many-body quantum system in a time-dependent potential to orders that have not yet been accessible before. To this end the propagator is expressed in terms of a discretized effective potential, for which we derive and analytically solve a set of efficient recursion relations. Such a discretized effective potential can be used to substantially speed up numerical Monte-Carlo simulations for path integrals, or to set up various analytic approximation techniques to study dynamic properties of quantum systems in timedependent potentials. The analytically derived results are numerically verified by treating several simple one-dimensional models.

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