Dissipative Quantum Chaos and Decoherence

✍ Scribed by Daniel Braun (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2001
• Tongue: English
• Leaves: 125
• Series: Springer Tracts in Modern Physics 172
• Edition: 1
• Category: Library

✦ Synopsis

Dissipative Quantum Chaos and Decoherence provides an over- view of the state of the art of research in this exciting field. The main emphasis is on the development of a semiclassical formalism that allows one to incorporate the effect of dissipation and decoherence in a precise, yet tractable way into the quantum mechanics of classically chaotic systems. The formalism is employed to reveal how the spectrum of the quantum mechanical propagator of a density matrix is determined by the spectrum of the corresponding classical propagator of phase space density. Simple quantum--classical hybrid formulae for experimentally relevant correlation functions and time-dependent expectation values of observables are derived. The problem of decoherence is treated in detail, and highly unexpected cases of very slow decoherence are revealed, with important consequences for the long-debated realizability of Schrödinger cat states as well as for the construction of quantum computers.

✦ Table of Contents

Introduction....Pages 1-5
Classical Maps....Pages 7-19
Unitary Quantum Maps....Pages 21-29
Dissipation in Quantum Mechanics....Pages 31-49
Decoherence....Pages 51-62
Dissipative Quantum Maps....Pages 63-73
Semiclassical Analysis of Dissipative Quantum Maps....Pages 75-117
Saddle-Point Method for a Complex Function of Several Arguments....Pages 119-120
The Determinant of a Tridiagonal, Periodically Continued Matrix....Pages 121-121
Partial Classical Maps and Stability Matrices for the Dissipative Kicked Top....Pages 123-124

✦ Subjects

Complexity; Quantum Optics, Quantum Electronics, Nonlinear Optics