Dedication page
Acknowledgments
Foreword
Authors' Preface
1 The Memory Function Formalism: What and Why
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
2.3.2 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 Forster-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
4.2 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
10.6 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
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
Show more
Dedication page
Acknowledgments
Foreword
Authors' Preface
1 The Memory Function Formalism: What and Why
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
2.3.2 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 Forster-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
4.2 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
10.6 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
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
Show moreChapter 1. The Memory Function Formalism: What and Why.- Chapter 2. Zwanzig’s Projection Operators: How They Yield Memories.- Chapter 3. Building Coarse-Graining into Projections and Generalizing Energy Transfer Theory.- Chapter 4. Relations of Memories to Other Entities and GME Solutions for the Linear Chain.- Chapter 5. Direct Determination of Frenkel Exciton Coherence from Ronchi Ruling and Transient Grating Experiments.- Chapter 6. Application to Charges Moving in Crystals: Resolution of the Mobility Puzzle in Naphthalene and Related Results.- Chapter 7. Projections and Memories for Microscopic Treatment of Vibrational Relaxation.- Chapter 8. Projection Operators for Various Contexts.- Chapter 9. Spatial Memories and Granular Compaction.- Chapter 10. Memories and Projections in Nonlinear Equations of Motion.- Chapter 11. The Montroll Defect Technique and its Application to Molecular Crystals.- Chapter 12. The Defect Technique in the Continuum.- Chapter 13. Memory Functions fromStatic Disorder: Effective Medium Theory.- Chapter 14. Effective Medium Theory Application to Molecular Movement in Cell Membranes.- Chapter 15. A Mathematical Approach to Non-Physical Defects.- Chapter 16. Concluding Remarks.
V. M. (Nitant) Kenkre is Distinguished Professor (Emeritus) of Physics at the University of New Mexico (UNM), USA, retired since 2016. His undergraduate studies were at IIT, Bombay (India) and his graduate work took place at SUNY Stony Brook (USA). He was elected Fellow of the American Physical Society in 1998, Fellow of the American Association for Advancement of Science in 2005 and has won an award from his University for his international work. He was the Director of two Centers at UNM: the Center for Advanced Studies for 4 years and then the Founding Director of the Consortium of the Americas for Interdisciplinary Science for 16 years. He was given the highest faculty research award of his University in 2004 and supervised the Ph.D. research of 25 doctoral scientists and numerous postdoctoral researchers.
Through 270 published papers, his research achievements include formalistic contributions to non- equilibrium statistical mechanics, particularly quantum transport theory, observations in sensitized luminescence and exciton/electron dynamics in molecular solids, and solutions to cross-disciplinary puzzles arising in spread of epidemics, energy transfer in photosynthetic systems, statistical mechanics of granular materials, and the theory of microwave sintering of ceramics.
He has interests in comparative religion, literature and visual art, and has often lectured on the first of these. His most recent coauthored book is Theory of the Spread of Epidemics and Movement Ecology of Animals (Cambridge University Press, 2020). He has also coauthored a book on exciton dynamics (Springer, 1982), coedited another on modern challenges in statistical mechanics (AIP, 2003), and published a book on his poetry entitled Tinnitus, and two on philosophy: The Pragmatic Geeta, and What is Hinduism.
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