The unusual nature of the quantum Baker's transformation

Journal Article · Mon Apr 01 04:00:00 EST 1991 · Annals of Physics (New York); (United States)

DOI:https://doi.org/10.1016/0003-4916(91)90184-A· OSTI ID:5675312

O'Connor, P W; Tomsovic, S ^[1]

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1. Univ. of Washington, Seattle (United States)

The authors investigate the quantum Baker's transformation which has been introduced as a paradigm for studies of the quantum mechanics of classically chaotic systems. A semiclassical theory of the dynamics, good to times logarithmic in {h bar}, is given in the form of a linear wave packet dynamics. The consequences for the implied heavy eigenfunction scarring and for the trace of the propagator are compared to the quantum results. Unexpectedly, the semiclassical trace remains accurate beyond this logarithmic time. Some exotic quantum properties are found that cannot be explained by the short time semiclassics. Further study reveals level clustering, large recurrences in the trace of the propagator, and excesses of small eigenvector components. Many of the unusual behaviors have a very strong and peculiar {h bar} dependence.

• OSTI ID: 5675312
• Journal Information: Annals of Physics (New York); (United States), Journal Name: Annals of Physics (New York); (United States) Vol. 207:1; ISSN 0003-4916; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CLASSICAL MECHANICS
DYNAMICS
EIGENFUNCTIONS
FUNCTIONS
GREEN FUNCTION
INSTABILITY
MECHANICS
PROPAGATOR
QUANTUM MECHANICS
SEMICLASSICAL APPROXIMATION
STOCHASTIC PROCESSES
TIME DEPENDENCE
TRANSFORMATIONS
WAVE PACKETS