SIGNATURES OF CHAOS IN THE MODULUS AND PHASE OF TIME-DEPENDENT WAVE-FUNCTIONS

For a classically chaotic two-dimensional bound system, based on the a ssumption that an initially-well-localized, semiclassical wave packet can be represented by a superposition of a large number of random plan e waves at fixed times, we show that the modulus and phase of the wave function are independent random functions having a Rayleigh and a uni form one-point spatial distribution function, respectively. These pred ictions are confirmed through our numerical wave-packet study for one- quarter of the Sinai billiard. Streamline vortices can form around wav e-function nodes, a fact first discovered by Dirac in 1931. For a clas sically chaotic billiard, the random plane-wave superposition approxim ation predicts that both the number of nodal points and the maximum nu mber of vortices in a wave packet with initial wave number k is N, whe re N refers to the Nth eigenstate with wave number k(N) which is close st to k.