World Scientific Series in Contemporary Chemical Physics - Vol. 10
THE LANGEVIN EQUATION
With Applications in Physics, Chemistry and Electrical Engineering
by W T Coffey (Trinity College, Dublin), Yu P Kalmykov (Russian Acad. Sci., Moscow) & J T Waldron (Dublin City Univ., Dublin)
The book is suitable for a lecture course on the theory of Brownian motion, being based on final year undergraduate lectures given at Trinity College, Dublin. Topics that are discussed include: white noise; the Chapman-Kolmogorov equation – Kramers-Moyal expansion; the Langevin equation; the Fokker-Planck equation; Brownian motion of a free particle; spectral density and the Wiener-Khintchin theorem – Brownian motion in a potential application to the Josephson effect, ring laser gyro; Brownian motion in two dimensions; harmonic oscillators; itinerant oscillators; linear response theory; rotational Brownian motion; application to loss processes in dielectric and ferrofluids; superparamagnetism and nonlinear relaxation processes.
As the first elementary book on the Langevin equation approach to Brownian motion, this volume attempts to fill in all the missing details which students find particularly hard to comprehend from the fundamental papers contained in the Dover reprint — Selected Papers on Noise and Stochastic Processes, ed. N Wax (1954) – together with modern applications particularly to relaxation in ferrofluids and polar dielectrics.
Contents:
- Historical Background and Introductory Concepts
- Langevin
Equations and Methods of Solution
- The Brownian Motion of a Free Particle and a Harmonic Oscillator
- The Itinerant Oscillator Model
- Two-Dimensional Rotational Brownian Motion in N-Fold Cosine Potentials
- The Brownian Motion in a Tilted Cosine Potential: Application to the Josephson Tunnelling Junction
- Three-Dimensional Rotational Brownian Motion in an External Potential with Application to the Theory of Dielectric and Magnetic Relaxation
- Rotational Brownian Motion in an External Potential — Matrix Continued Fraction Solution
- Numerical Solutions for Non-Axially Symmetric Problems
- Inertial Langevin Equations: Application to the Theory of Dielectric and Kerr-Effect Relaxation
- Linear Response Theory and the Fokker-Planck Operator
Readership: Physicists, chemists, electrical engineers, statisticians
and undergraduates.
"I found this book a valuable addition to my library. It will be of interest to researchers and advanced students and the material could be used as the text for a course for advanced undergraduates and graduate students."
Irwin Oppenheim (MIT)
Journal of Statistical Physics, 1997 |
| 428pp |
Pub. date: Jul 1996 |
|
