Stochastic Processes in Chemical Physics
1st Edition
Published on 8. September 2009
391 pages
978-0-470-14400-8 (ISBN)
Description
The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.
K. E. Shuler is the author of Stochastic Processes in Chemical Physics, Volume 15, published by Wiley.
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Kurt E. Shuler
Advances in Chemical Physics: v. 15
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12/1969
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Content
- Stochastic Processes in Chemical Physics
- CONTENTS
- Probabilistic and Dynamic Approaches to the Theory of Stochastic Processes
- I. Introduction
- II. Probabilistic Preliminaries
- III. Master Equations
- IV. Langevin Equation
- Quantum States and Dissipative Processes
- I. Introduction
- II. Einstein's Theory of Spontaneous Emission in Unstable Particles
- III. Mechanisms of Dissipation
- IV. Probability Amplitudes and Quantum Time
- V. Quantum States of Finite Lifetime
- VI. Kinetic Equations : Feynman Diagrams and Correlation Diagrams
- VII. Boltzmann Approximation
- VIII. Physical Particles and Entropy
- IX. Kinetic Equations and Quantum States
- X. Conclusions and Perspectives
- Relaxed Motion in Irreversible Molecular Statistics
- I. The Basic Enigma
- II. The Basic Macroscopic Functions
- III. The Boundary Forces
- IV. The information Content of Probability Statements
- V. Heuristic Introduction to Relaxed Motion
- VI. Plan of Explicit Calculation
- VII. Solution in a Siniplitied Case: "Vestiginal Forces"
- VIII-IX. Calculation of the Information Integrals
- X. The Variational Principle
- XI. The Linear Approximation
- XII. Generalization
- Thermal Fluctuations in Nonlinear Systems
- I. Introduction: The Linear Case
- II. The Nonlinear Problem
- III. The Master Equation
- IV. Expansion of the Master Equation
- V. Additional Remarks
- VI. The Microscopic Description
- VII. The Microscopic Equations of Motion
- Error Bounds and Spectral Densities
- I. lntroduction
- II. Properties of Spectral Densities
- III. Error Bounds for Averages of Spectral Densities
- A. Error Bounds for the Response to a Damped Harmonic Perturbation
- B. Error Bounds for Cumulative Distribution
- C. Error Bounds for Second-Order Perturbation Energies
- IV. Extrapolation Methods for Spectral Densities
- V. Summary and Discussion
- A Stochastic Theory of Line Shape
- I. Introduction
- II. Random Frequency Modulation
- III. Two, Simple Examples
- a. Two State Jump Modulation
- b. Gaussian Modulation
- IV. Collapse of an NMR Multiplet
- V. Low Field Spin Resonance
- VI. Spectrum of Excitations to a Doublet with a Random Modulation
- VII. Random Stark Modulation of a Hydrogen Atom
- VIII. Line Shape of Mossbauer Spectra
- IX. Concluding Remarks
- A Stochastic Model for Neutron Scattering by Simple Liquids
- I. Model Calculations
- II. Scattering from H2 in Liquid Argon
- Fluctuations in Autocorrelation Functions in Diffusing Systems
- I. Introduction
- II. Definitions
- III. Method
- IV. Results
- A. Harmonically Bound Particle
- B. Particle in a Box
- C. Plane Rotor
- D. Spherical Rotor
- V. Relaxation Times
- VI. Discussion
- Stochastic Theory of Chemical Rate Processes
- I. Introduction
- II. Random Walk Model of Unimolecular Decomposition
- III. Exactly Solvable Elementary Reactions
- IV. Selected Applications
- A. Kinetics of Reactant Isolation
- B. Reaction Kinetics on Linear Lattices with Neighbor Effects
- C. Kinetics of Photochemical Reactions in Nucleic Acid Derivatives
- D. Nucleation Theory
- The Kinetics of Biopolymerization on Nucleic Acid Templates
- I. Introduction
- II. DNA Replication
- III. Protein Synthesis
- Some Models for the Decay of Initial Correlations in Dynamical Systems
- I. Introduction
- II. The Independent Random Walk Model
- III. Harmonic Oscillator Models
- IV. The One-Dimensional Ising Model
- Vibrational Relaxation of a Gas of Diatomic Molecules
- I. Introduction
- II. The Master Equation
- III. The Linear Equation
- IV Qualitative Features of the Linear Equation
- V. The Monte Carlo Process
- VI. Discussion
- Self-Avoiding Walks on Lattices
- I. Introduction
- II. Random Walks, Restricted Walks, and Self-Avoiding Walks
- III. Methods of Investigating Self-Avoiding Walks
- A. Rigorous Analysis
- B. Monte Carlo
- C. Exact Enumeration
- D. Transition Matrix
- IV. Properties of Self-Avoiding Walks
- A. Number of Walks of n Steps
- B. Number of Polygonal Closures of n Steps
- C. Mean Square Length
- D. Probability Distribution of End Points
- E. Mean Square Radius of Gyration
- F. Correlation Between Steps
- G. Passage from a Restricted to a Self-Avoiding Walk
- V. Analogy with the Ising Model
- VI. Continuum Models
- VII. Conclusions
- Non-Self Intersecting Random Walks on Lattices with Near-Neighbor Interactions
- I. Introduction
- II. Thermodynamic Properties of Self-Interacting Chains from the Monte Carlo Computations
- III. Stochastic Model for Restricted Self-Avoiding Chains with Nearest-Neighbor Interactions
- A. General Considerations
- B. Derivation of the Chain Partition Function
- IV. Preliminary Results
- Reversible Kinetics on Linear Lattices with Neighbor Effects
- I. General Considerations
- II. Derivation of Kinetics
- Ill. Equilibrium Relations
- IV. Numerical Approximations
- V. Some Applications
- Stochastic Models for Chain Dynamics
- I. Introduction
- II. Freely Jointed Chain
- III. One-Dimensional Chain with Correlations
- IV . Discussion
- Langevin Theory of Polymer Dynamics in Dilute Solution
- I. Introduction
- II. Hydrodynamic Interaction
- III. Fokker-Planck Equation
- IV. Langevin Equation
- Toeplitz Determinants: Some Applications, Theorems and Conjectures
- I. Introduction and Examples
- A. Random Walk
- B. Prediction Theory
- C. Ising Model Correlation Functions
- D. Dimers on a Plane Lattice
- II. Previous Results
- III. Extensions of the Classical Theorem
- IV. Special Results and Conjectures
- V. Summary
- A New Series Expansion for Path Integrals in Statistical hlechanics
- Brownian Motion and Indeterminacy Relations
- I . Introduction
- II. The Burgers Equation Approach
- III. The Kramers Equation Approach
- Author Index
- Curnulative lndex to Volumes I-XIV and XV
