Overcoming the Wall in the Semiclassical Baker's Map

L. Kaplan and E. J. Heller
Phys. Rev. Lett. 76, 1453 – Published 26 February 1996
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Abstract

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 Nstate 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.

  • Received 5 September 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.1453

©1996 American Physical Society

Authors & Affiliations

L. Kaplan

  • Department of Physics, Harvard University, Cambridge, Massachusetts 02138

E. J. Heller

  • Department of Physics, Harvard University and Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138

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Vol. 76, Iss. 9 — 26 February 1996

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