Evaluation of the smoothed interference pattern under conditions of ray chaos

A ray-based approach has been considered for evaluation of the coarse-grain ed Wigner function. From the viewpoint of wave propagation theory this func tion represents the local spectrum of the wave field smoothed over some spa tial and angular scales. A very simple formula has been considered which ex presses the smoothed Wigner function through parameters of ray trajectories . Although the formula is ray-based, it nevertheless has no singularities a t caustics and its numerical implementation does not require looking for ei genrays. These advantages are especially important under conditions of ray chaos when fast growing numbers of eigenrays and caustics are the important factors spoiling applicability of standard semiclassical approaches alread y at short ranges. Similar factors restrict applicability of some semiclass ical predictions in quantum mechanics at times exceeding the so-called "log arithm break time." Numerical calculations have been carried out for a part icular model of range-dependent waveguide where ray trajectories exhibit ch aotic motion. These calculations have confirmed our conjecture that by choo sing large enough smoothing scales, i.e., by sacrificing small details of t he interference pattern, one can substantially enhance the validity region of ray theory. (C) 2000 American Institute of Physics. [S1054-1500(00)00301 -3].