On the quantum baker`s map and its unusual traces

Journal Article · Mon May 01 04:00:00 EDT 1995 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1995.1035· OSTI ID:165247

Lakshminarayan, A ^[1]

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1. Physical Research Laboratory, Navarangapura, Ahmedabad, 380009 (India)

The quantum baker`s map is the quantization of a simple classically chaotic system and has many generic features that have been studied over the last few years. While there exists a semiclassical theory of this map, a more rigorous study of the same revealed some unexpected features which indicated that correction terms of the order of log({h_bar}) had to be included in the periodic orbit sum. Such singular semiclassical behaviour was also found in the simplest traces of the quantum map. In this note we study the quantum mechanics of a baker`s map which is obtained by {ital reflecting} the classical map about its edges in an effort to understand and circumvent these anomalies. This leads to a {ital real} quantum map with traces that follow the usual Gutzweiller--Tabor like semiclassical formulae. We develop the relevant semiclassical periodic orbit sum for this map which is closely related to that of the usual baker`s map, with the important difference that the propagators leading to this sum have no anomalous traces. {copyright} 1995 Academic Press, Inc.

• OSTI ID: 165247
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 239; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
MAPS
ORBITS
PROPAGATOR
QUANTIZATION
SEMICLASSICAL APPROXIMATION