Description
Book SynopsisWithin 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 diffusionphysical and stochasticintroduced 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 d
Trade Review
"The book is written in a light style, that is to say, it is not overly weighed down with technicalities. It reviews the most basic formulas and their performances in various settings and thus supplies a handy overview of the diffusion theory in action. An impressive attempt is made in Part II to provide a guided tour of diffusions in the quantum setting. The book should be mostly useful for physicists interested in getting first glimpses of diffusion theory." -Mathematical Reviews, August 2015 "Some chapters contain exercises that make the book useful for the beginners. But the other chapters can be interesting to the experts as well." -Yuri E. Gliklikh, Zentralblatt MATH 1295
Table of Contents
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 System. 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.
