Generalized Filinov transformation of the semiclassical initial value representation

An efficient method is proposed for the practical solution of the "sign" pr oblem for integrals involved in the semiclassical initial value representat ion. It is based on a generalization of the conventional Filinov filtering procedure which has the (approximate) effect of incorporating complex initi al conditions into the phase space average; it does this by including an ex plicit oscillatory term in the filtering function that partially cancels th e oscillatory part of the original integrand. A systematic procedure is als o described for making an optimal choice of the "smoothing parameters," thu s removing this arbitrariness in the overall approach. Tests on systems wit h chaotic dynamics demonstrate the accuracy and efficiency of the method. ( C) 2001 American Institute of Physics.