Phys. Rev. Lett. 76, 1453–1456 (1996)Overcoming the Wall in the Semiclassical Baker's MapReceived 5 September 1995; published in the issue dated 26 February 1996 A major barrier in semiclassical calculations for chaotic systems is the exponential increase in the number of terms at long times. Using an analogy with spin-chain partition functions, we overcome this “exponential 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. This method enables us to obtain semiclassical results up to the Heisenberg time and beyond, providing new insight as to the accuracy of the semiclassical approximation. The semiclassical result is often correct; its breakdown is nonuniform. © 1996 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.76.1453
DOI:
10.1103/PhysRevLett.76.1453
PACS:
05.45.+b, 03.65.Sq
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