Dattagupta S. Diffusion: Formalism and Applications

CRC Press, 2014. — 282 p.Within a unifying framework, Diffusion: Formalism and Applications covers both classical and quantum domains, along with numerous applications. The author explores the more than two centuries-old history of diffusion, expertly weaving together a variety of topics from physics, mathematics, chemistry, and biology.
The book examines the two distinct paradigms of diffusion—physical and stochastic—introduced by Fourier and Laplace and later unified by Einstein in his groundbreaking work on Brownian motion. The author describes the role of diffusion in probability theory and stochastic calculus and discusses topics in materials science and metallurgy, such as defect-diffusion, radiation damage, and spinodal decomposition. In addition, he addresses the impact of translational/rotational diffusion on experimental data and covers reaction-diffusion equations in biology. Focusing on diffusion in the quantum domain, the book also investigates dissipative tunneling, Landau diamagnetism, coherence-to-decoherence transition, quantum information processes, and electron localization.Classical Diffusion
Introduction to Brownian Motion.
Markov Processes.
Gaussian Processes.
Langevin Equations.
Fokker–Planck Equation.
Jump Diffusion.
Random Walk and Anomalous Diffusion.
Spectroscopic Structure Factor.
Rotational Diffusion of Molecules.
Order Parameter Diffusion.
Diffusion of Rapidly Driven Systems.
Quantum Diffusion
Quantum Langevin Equations.
Path Integral Treatment of Quantum Diffusion.
Quantum Continuous Time Random Walk Model.
Quantum Jump Models.
Quantum Diffusion: Decoherence and Localization.