Memory functions, projection operators, and the defect technique : some tools of the trade for the condensed matter physicist
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書誌事項
Memory functions, projection operators, and the defect technique : some tools of the trade for the condensed matter physicist
（Lecture notes in physics, v. 982）
Springer, c2021
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LNP 982
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注記
Includes bibliographical references (p. 353-370) and index
内容説明・目次
内容説明
This book provides a graduate-level introduction to three powerful and closely related techniques in condensed matter physics: memory functions, projection operators, and the defect technique. Memory functions appear in the formalism of the generalized master equations that express the time evolution of probabilities via equations non-local in time, projection operators allow the extraction of parts of quantities, such as the diagonal parts of density matrices in statistical mechanics, and the defect technique allows solution of transport equations in which the translational invariance is broken in small regions, such as when crystals are doped with impurities. These three methods combined form an immensely useful toolkit for investigations in such disparate areas of physics as excitation in molecular crystals, sensitized luminescence, charge transport, non-equilibrium statistical physics, vibrational relaxation, granular materials, NMR, and even theoretical ecology. This book explains the three techniques and their interrelated nature, along with plenty of illustrative examples. Graduate students beginning to embark on a research project in condensed matter physics will find this book to be a most fruitful source of theoretical training.
目次
Dedication page
Acknowledgments
Foreword
Authors' Preface
1 The Memory Function Formalism: What and Why
1.1 Introduction to Memory Functions
1.2 An Example of How Memory Functions Arise: the Railway-Track Model
1.3 An Overview of Areas in which the Memory Formalism Helps
2 Zwanzig's Projection Operators: How They Yield Memories
2.1 The Derivation of the Master Equation: a Central Problem in Quantum Statistical Mechanics
2.2 Memories from Projection Operators that Diagonalize the Density Matrix
2.3 Two Simple Examples of Projections and an Exercise
2.3.1 Evolution of a Simple Complex Quantity
2.3.2 Projection Operators for Quantum Control of Dynamic Localization
2.3.3 Exercise for the Reader: the Open Trimer
2.4 What is Missing from the Projection Derivation of the Master Equation
3 Building Coarse-Graining into the Projection Technique
3.1 The Need to Coarse-Grain
3.2 Constructing the Coarse-Graining Projection Operator
3.3 Generalization of the F orster-Dexter Theory of Excitation Transfer
3.4 Obtaining Realistic Memory Functions
3.5 Implementing a General Plan
3.5.1 Example in an Unrelated Area: Ferromagnetism
4 Features of Memory Functions and Relations to Other Entities
4.1 Resolution of the Perrin-F orster-Davydov Puzzle
4.2 Relations Among Theories of Excitation Transfer
4.3 Long-range Transfer Rates as a Consequence of Strong Intersite Coupling
4.4 Connection of Memories to Neutron Scattering and Velocity Auto-Correlation Functions, and Pausing Time Distributions
5 Applications to Experiments: Transient Gratings, Ronchi Rulings, and Depolarization
5.1 Non-drastic Experiments: Fluorescence Depolarization as an Example
5.2 Ronchi Rulings for Measuring Coherence of Triplet Excitons
5.3 Fayer's Transient Gratings: an Ideal Experiment for Measuring Coherence of Singlet Excitons
6 Projection Operators for Various Contexts
6.1 Projections for the Theory of Electrical Resistivity
6.2 Projections that Integrate in Classical Systems
6.2.1 The BBGKY Hierarchy
6.2.2 Torrey-Bloch Equation for NMR Microscopy
6.3 Projections for Quantum Control of Dynamic Localization
6.4 Projections for the Railway-Track Model of Chapter 2
7 Memories and Projections in Nonlinear Equations of Motion
7.1 Extended Nonlinear Systems and the Physical Pendulum
7.2 Nonlinear Waves in Reaction Di_usion systems
7.3 Spatial Memories: Inuence Functions in the Fisher Equation
8 NMR Microsocopy and Granular Compaction
8.1 Pulsed Gradient NMR Signals in Con_ned Geometries
8.2 Analytic Solutions of a Generalized Torrey-Bloch Equation
8.3 Non-local Analysis of Stress Distribution in Compacted Sand
8.4 Spatial Memories and Correlations in the Theory of Granular Materials
9 Projections/Memories for Microscopic Treatment of Vibrational Relaxation
9.1 The Importance of Vibrational Relaxation
9.2 The Montroll-Shuler Equation and its Generalization to the Coherent Domain
9.3 Reservoir E_ects in Vibrational Relaxation
9.4 Approach to Equilibrium of a Simpler System: a Non-Degenerate Dimer
10 The Montroll Defect Technique
10.1 Introduction: Experiments that Modify Substantially
10.2 Overview of the Defect Technique and Simple Cases
10.2.1 Trapping at a Single Site
10.2.2 How Laplace Inversion may be avoided in Some Situations
10.2.3 Trapping at More than 1 Site: Exercise for the Reader
10.3 Coherence E_ects on Sensitized Luminescence
10.4 End-Detectors in a Simpson Geometry
10.5 High Defect Concentration: the _-function Approach
10.6 Periodically Arranged Defects
10.7 Remarks
11 The Defect Technique in the Continuum
11.1 General Discussion
11.2 Higher Dimensional Systems
11.3 A Theory of Coalescence of Signaling Receptor Clusters in Immune Cells
11.4 The Defect Technique with the Smoluchowski Equation
11.5 Momentum-Space Theory of Capture
12 A Mathematical Approach to Non-Physical Defects
12.1 Introduction
12.2 Exciton Annihilation in Translationally Invariant Crystals
12.3 Scattering Function from the Stochastic Liouville Equation with its Terms viewed as Defects
12.4 Transmission of Infection in the Spread of Epidemics
13 Memory Functions from Static Disorder: E_ective Medium Approach
13.1 Introduction
13.2 Various Descriptions of Disorder
13.3 E_ective Medium Approach: Philosophy and Prescription
13.4 Examination of its Validity and Extension of its Applications
14 Concluding Remarks
14.1 What We Have Learnt
Bibliography
Bibliography
Author index
Subject index
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