Abstract. Path-integral solutions to time-evolution equations in statistical physics have recently aroused great interest. The main problem in applying these methods is to find a valid propagator in the short-time regime of evolution. A new method is proposed to obtain a set of accurate short-time propagators by the construction of a simple auxiliary Fokker-Planck equation. This equation takes into account the full relevant functional dependence of the original drift and diffusion terms. By using a suitable decomposition of the drift and diffusion coefficients it is possible to derive a new representation of the Dirac -function. From this representation the short-time behaviour of the solutions is given not only for the infinitesimal time interval, but also for a discrete finite one which has a more practical numerical sense. This picture leads to accurate short-time propagators which include the prescribed boundary conditions.

Print publication: Issue 20 (21 May 1999)
Received 14 August 1998, in final form 23 February 1999