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Feynman Integral and Random Dynamics in Quantum Physics : A Probabilistic Approach to Quantum Dynamics : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - Zbigniew Haba

Feynman Integral and Random Dynamics in Quantum Physics : A Probabilistic Approach to Quantum Dynamics

MATHEMATICS AND ITS APPLICATIONS (KLUWER )

Hardcover

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This volume presents a mathematical theory of the Feynman integral based on probabilistic methods, which is applied to controllable approximations to Hamiltonian and dissipative quantum dynamics. A wide range of methods of random dynamical systems is discussed for models of quantum physics. The probabilistic method is considered an efficient tool for analytic and numerical approximations of the dynamics of large complex quantum systems.

Foreword
Introduction
Basic Notation
Preliminariesp. 1
Markov chainsp. 13
Stochastic differential equationsp. 31
Semi-groups and the Trotter product formulap. 41
The Feynman integralp. 45
Feynman integral and stochastic differential equationsp. 79
Random perturbations of the classical mechanicsp. 89
Complex dynamics and coherent statesp. 117
Quantum non-linear oscillationsp. 141
Feynman integral on analytic submanifoldsp. 159
Interaction with the environmentp. 169
Lindblad equation and stochastic Schrodinger equationp. 185
Hamiltonian time evolution of the density matrixp. 251
Stochastic representation of the Lindblad time evolutionp. 257
Decoherence and estimates on dissipative dynamicsp. 277
Diffusive behaviour of the Wigner function and decoherencep. 283
Scattering and tunnelling in an environmentp. 291
The Feynman integral in quantum field theoryp. 303
The phase space methods in QFTp. 313
Computer simulations of quantum random dynamicsp. 331
The Bibliographyp. 353
Indexp. 363
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792357353
ISBN-10: 0792357353
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 367
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.77 x 17.15  x 1.91
Weight (kg): 0.77