Elements of Nonequilibrium Statistical Mechanics

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ISBN 9781420074192
Cat# AB7419

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Features

  • Introduces the Langevin equation, the mean-squared displacement of the Langevin equation, and the generalized Langevin equation
  • Covers the fluctuation-dissipation relationship, velocity autocorrelation function, and Markov processes
  • Explains Fokker-Planck equation and the Ornstein-Uhlenbeck distribution
  • Examines Brownian motion and diffusion in a force field
  • Concludes with the power spectrum of a random process and the Kubo-Green formula
  • Summary

    This book deals with the basic principles, techniques, and advances being made--both experimentally and theoretically--in the study of nonequilibrium phenomena, particularly in statistical physics, chemical physics, biological physics, complex systems, and several other areas. Accessible to senior undergraduate students and post-graduate students, this self-contained book offers a choice of topics that enables them to form a coherent picture of the subject. Coverage includes equations and formulas for calculating distribution, diffusion, and dynamic mobility under different conditions. The book concludes with a generalized Langevin equation and the power spectrum of pulse sequences.

    Table of Contents

    Introduction
    The Langevin Equation
    The Fluctuation-dissipation relationship
    The Velocity autocorrelation function
    Markov Processes
    The Fokker-Planck equation and the Ornstein-Uhlenbeck distribution
    Mean-squared displacement from the Langevin equation
    The Fokker Planck equation in phase space
    The diffusion equation
    Brownian motion
    Diffusion in a force field
    The Kubo-Green formula
    The dynamic mobility as a generalized susceptibility
    Power spectrum of a random process
    The generalized Langevin equation
    Power spectrum of a random pulse sequence
    Bibliography
    Index

    Author Bio(s)

    V. Balakrishnan has been a professor at the Department of Physics, Indian Institute of Technology, Madras, since 1980. He joined IIT Madras after working for some years at the Tata Institute of Fundamental Research (Mumbai) and the Reactor Research Centre, Department of Atomic Energy (kalpakkam). He was educated at the University of Delhi and Brandeis University, USA, from where he got his PhD in theoretical high energy phyisics in 1970. His research interests have spanned many areas over the years, including high energy physics, many-body theory, condensed matter physics, stochastic processes, probabilistic techniques, quantum dynamics, nonlinear dynamics and chaos. He has published numerous research papers in these areas, a number of popular pedagogic articles, and has co-authored a monograph titled Beyond the Crystalline State on certain aspects of condensed matter physics. Over the past three decades, Professor Balakrishnan has taught a wide variety of extremely popular courses at the undergraduate and post-graduate levels, comprising all the standard subjects in physics, as well as some new, non-traditional ones. In addition to receiving accolades for his teaching at IIT Madras, his lectures at numerous courses sponsored by the UGC, DST (SERC), and the International Center for Theoretical Physics (ICTP) have been well-received by their attendees. Dr. Balakrishnan has held visiting positions at several institutions abroad. He is a Fellow of the Indian Academy of Sciences.