OVERCOMING THE WALL IN THE SEMICLASSICAL BAKERS MAP

A major barrier in semiclassical calculations for chaotic systems is t he exponential increase in the number of terms at long times. Using an analogy with spin-chain partition functions, we overcome this ''expon ential wall'' for the baker's map, reducing to order NT3/2 the number of operations needed to evolve an N-state system for T time steps. Thi s method enables us to obtain semiclassical results up to the Heisenbe rg time and beyond, providing new insight as to the accuracy of the se miclassical approximation. The semiclassical result is often correct; its breakdown is nonuniform.