Diffusion —— Formalism and Applications

----- 扩散：形式主义与应用

ISBN: 9781439895573 出版年：2013 页码：300 Dattagupta, Sushanta CRC Press

CLASSICAL DIFFUSION Introduction to Brownian Motion Introductory Remarks Fourier Equation Random Walk Random Walk on Lattice and Its Continuum Limit Einstein on Brownian Motion Concluding Remarks Markov Processes Genesis of Markov Concept Definition Stationary Markov Process Gaussian Processes Introduction Gaussian Stochastic Processes Stationary GaussMarkov Process Langevin Equations Introduction Free Particle in Momentum Space Free Particle in Position Space Harmonic Oscillator Diffusive Cyclotron Motion Fokker-Planck Equation Introduction FP Equation in Velocity FP Equation in Position: Stochastic Diffusion FP Equation in Force Field: Kramers Equation FP Equation in Force Field in High Friction Limit: Smoluchowski Equation FP Equation for Damped Harmonic Oscillator FP Equation for Cyclotron Motion Diffusion across Barrier Jump Diffusion Introduction Operator Notation Two-State Jump and Telegraph Processes Multi-State Jump Process KuboAnderson Process Interpolation Model Kangaroo Process Random Walk and Anomalous Diffusion Introduction to Continuous Time Random Walk (CTRW) Non-Markovian Diffusion in CTRW Scheme Spectroscopic Structure Factor Introductory Remarks Cyclotron Motion in Weak Collision and BoltzmannLorentz Models Neutron Scattering From a Damped Harmonic Oscillator Restricted Diffusion over Discrete Sites Unbounded Jump Diffusion in Empty Lattice Vacancy-Assisted Correlated Diffusion in Solids Rotational Diffusion of Molecules Introduction Extended Diffusion Models M Diffusion Model J Diffusion Model Interpolation Model Applications to Infrared and Raman Rotational Spectroscopy Order Parameter Diffusion CahnHilliard Equation Pattern Formation Jump Diffusion in Ising Model Relation with CH Equation ReactionDiffusion Models and Spatiotemporal Patterns Diffusion of Rapidly Driven System Introduction Langevin Equation in Over-Damped Case Langevin Equation for Arbitrary Damping Effective Diffusion in Periodic Potential QUANTUM DIFFUSION Quantum Langevin Equations Introduction Derivation of Classical Langevin Equation Quantum Generalization Free Particle Diffusive Quantum Cyclotron Motion Diffusive Landau Diamagnetism Path Integral Treatment of Quantum Diffusion Introduction Basic Model Ohmic Dissipation and Classical Limit Master Equation in High Temperature Limit Application to Dissipative Diamagnetism Quantum Continuous Time Random Walk Model Introduction Formulation Applications Finite Temperature Effects Quantum Jump Models Introduction Formalism Polaronic Transformation Qubit Neutron Structure Factor for H Diffusion in Metals Spin Relaxation of Muon Diffusion in Metals Quantum Diffusion: Decoherence and Localization Introductory Comments Landau-to-Bohrvan Leeuwen Transition of Diamagnetism Harmonic Oscillator in Quantum Diffusive Regime Decoherence in Spin Boson Model Dissipation-less Decoherence Retrieving Quantum Information Despite Decoherence Localization of Electronic States in Disordered Systems References appear at the end of each chapter.