Fain Irreversibilities in Quantum Mechanics

1. Auflage 2006
ISBN: 978-0-306-47128-5
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 113, 224 Seiten

Reihe: Fundamental Theories of Physics

This book presents a unified theoretical and conceptual framework for the description of various irreversible phenomena in quantum mechanics. The general theory of irreversible processes is applied to specific physical models and situations such as energy and electron transfer processes, tunnelling in condensed media, superradiance, etc. Special attention is given to memory effects in relaxation processes and dissipationless states in dissipative systems. A separate chapter is devoted to the problem of irreversibility in quantum measurements.

Audience: This book will be of interest to postgraduate students and specialists in quantum mechanics, statistical physics, and chemical physics. The work may serve as a complementary text for quantum mechanics courses.

Autoren/Hrsg.

Fain, B.

Fain, Benjamin

Inhaltsverzeichnis

1;CONTENTS;6
2;FOREWORD;8
3;INTRODUCTION;9
4;CHAPTER I QUANTUM- THEORETICAL BASIS. DENSITY MATRIX;11
4.1;1.1 Basic concepts;11
4.2;1.2 Various representations of physical quantities.;13
4.3;1.3 Quantum state and statistical ensembles;15
4.4;1.4 The wave function;16
4.5;1.5 Entropyofquantum ensembles;20
4.6;1.6 Pure and mixed states. Proper mixtures.;21
4.7;1.7 Transition probability per unit time;27
4.8;1.8 Continuous spectrum of energies and irreversibility;32
5;CHAPTER II QUANTUM THEORY OF RELAXATION PROCESSES;34
5.1;2.1 Exact equations describing temporal behavior of interacting dissipative and dynamic systems;35
5.2;2.2 Relaxation of the dissipative system. Markovian approximation;38
5.3;2.3 Equations for density matrix of dynamic systems;43
5.4;2.4 Generalized master equations;48
5.5;2.5 Time convolutionless equations. Argyres and Kelley projection operators and reduced dynamics.;51
5.6;2.6 Semigroup theory of irreversible processes;57
5.7;2.7 Master equations for dynamic systems;62
6;CHAPTER III INTERACTION WITH PHONONS AND MOLECULAR VIBRATIONS;74
6.1;3.1 Description of time- dependent electron- nuclear system in the Born- Oppenheimer approximation;74
6.2;3.2 Phonons. Phonon-phonon interaction and relaxation;76
6.3;3.3 Two-state electronic systems;80
6.4;3.4 Radiationless transitions. Basic models of electron and energy transfer;85
6.5;3.5 Tunneling in the condensed media;88
6.6;3.6 Equations ofmotion of the two-state electronic (nuclear) system interacting with vibrations of the medium;92
6.7;3.7 Calculation of rate coefficients;95
6.8;3.8 The energy gap law;102
7;CHAPTER IV INTERACTION WITH PHOTONS;116
7.1;4.1 Interaction of matter with the electromagnetic field;116
7.2;4.2 A system of two-level molecules interacting with the electromagnetic field;118
7.3;4.3 Quantum theory of spontaneous and stimulated emission in a system of two- level molecules;120
7.4;4.4 Spontaneous emission vs. vacuum fluctuations;123
7.5;4.5 Superradiance ( small volumes L ³ <<;125
7.6;4.6 Large sample superradiance;127
7.7;4.7 Time- development of the superradiance ( small volumes);132
7.8;4.8 Time-development of the superradiance (large volumes);138
8;CHAPTER V MEMORY EFFECTS IN RELAXATION PROCESSES, EXACT SOLUTIONS.;144
8.1;5.1 Time development of quantum systems: general relations;144
8.2;5.2 General criteria for emerging of dissipationless regimes;147
8.3;5.3 The configuration interaction between one discrete state and the continuum of the states;150
8.4;5.4 Spontaneous emission of bosons (phonons) and tunneling in the rotating wave approximation;152
8.5;5.5 Weak coupling case ( beyond RWA);160
8.6;5.6 Semiquantitive analysis of the dissipationless regime;166
8.7;5.7 Rotating wave, Markovian, and weak coupling approximations;172
8.8;5.8 Impossibility of exponential relaxation;180
9;CHAPTER VI QUANTUM MEASUREMENT AND IRREVERSIBILITY;182
9.1;6.1 Another view on quantum mechanics. EPR. Bell’s theorems. Nonlocality.;182
9.2;6.2 Reduction of wave-packet;191
9.3;6.3 Reduction of the wave packet as a result of interaction with the dissipative system;195
9.4;6.4 Measurement of spins in the Stern-Gerlach experiment;199
9.5;6.5 Realization of quantum measurement by the irreversible relaxation process;205
9.6;6.6 Gedanken experiment: measurement of the z-component of spin ½;207
10;CONCLUDING REMARKS;211
11;REFERENCES;214
12;INDEX;220

Leseproben

CHAPTER 1 QUANTUM-THEORETICAL BASIS. DENSITY MATRIX (p. 1-2)

The present chapter gives a short account of the basic concepts of quantum theory. Since our main purpose is quantum theory of irreversible processes, the use of the density matrix concept is indispensable. A conventional presentation of quantum theory principles uses the wave function as the basic characteristic of a quantum system. In this case the density matrix is, in a sense, a derivative of the wave function. In this chapter we consider the density matrix as a basic, primary characteristic of the quantum system [1], while the description by the wave function is a specific case of the description with aid of the density matrix. We realize that such an approach is a generalization of the conventional procedure. However, this generalization seems to be quite natural, and only due to historical reasons quantum theory text books use the wave function presentation. In this chapter we follow conventional (Copenhagen) interpretation of quantum mechanics. A different approach will be considered in the last chapter (Chapter VI).

1.1 Basic concepts

The nature of the phenomena occurring at the atomic level is very different from the nature of the phenomena of the macrocosm. For this reason the basic concepts of the classical theory proved to be invalid in describing the microcosm. The concept of the state of a physical system underwent a most radical re-examination. In classical physics it is assumed that the physical quantities (or properties of a system) found from various measurements made on a system are characteristics of the particular state of the system, that they are always present in a given system in a definite form and that this does not depend on the observational methods and equipment. In quantum physics they are at the same time characteristics of the methods and equipment used for the observations. In the microcosm we cannot ignore the effect of the measuring apparatus on the measured object. Therefore the concept of the quantum state takes into account both the object which is in this state and possible experimental devices used to make the measurement. Accordingly, the quantum theoretical description of quantum objects differs essentially from the classical description. Quantum theory, unlike the classical theory, is a statistical theory in principle. The laws of quantum theory do not govern the actual behavior of a particular object, but give the probabilities of the various ways in which the object may behave as a result of an interaction with its surroundings. The following postulates form the basis of the quantum description of physical phenomena.