Time-dependent properties of non-equilibrium systems can be calculated from their molecular models using the techniques of non-equilibrium statistical mechanics (NESM). It is possible to present a pedagogical introduction to many of the concepts and practical application of the techniques to the engineering students of third and fourth year of our B.Tech. programme. No prior knowledge of quantum mechanics and statistical mechanics is required. However, familiarity with elementary classical thermodynamics is essential.
In this course we shall look at the non-equilibrium phenomena from a physicist's perspective focusing on the generic common features of each phenomenon, exhibited by a wide variety of (apparently diverse) systems and try to explain the origin of the "unity" among the apparent "diversity". The students will not only get a glimpse of the expanding frontiers of contemporary fundamental research in NESM but will also get training in using the powerful techniques of NESM in applied research which is intrinsically interdisciplinary.
INTRODUCTION: Examples of non-equilibrium phenomena(i) Glass transition; (ii) Nucleation; (iii) Phase separation; Experimental probes: Dynamic scattering; inelastic neutron scattering (3)
THEORETICAL TOOLS: Two alternative theoretical approaches ( a ) Langevin equation-dissipation, nonlinearity and noise; Illustration with translational Brownian motion; ( b) Fokker-Planck equation-diffusion and drift; Illustration with (i) translational Brownian motion, (ii) rotational Brownian motion. Master equation-loss and gain of probabilities; concept of detailed balance (9).
META-STABILITY AND BI-STABILITY: Kramers' theory of thermally activated barrier crossing-applications in (i) chemical reactions (ii) rock magnetism. "Enhancing signals with the help of noise (!)" - applications of stochastic resonance in (a) nonlinear optics, (b) solid state devices, (c) neuro-science, (d) molecular motors and biological locomotion. Becker-Doring Theory of homogeneous nucleation and its modern extensions-applications in (a) condensation and (b) crystallization (12).
UNSTABLE STATES: Allen-Cahn scenario of interfacial dynamics and domain growth-applications to domain growth in quenched magnets; Lifshitz-Slyozov arguments for phase separation and its generalizations-applications to (a) alloys, (b) fluid mixtures, (c) polymer mixtures. Theory of phase separation controlled by topological defects- application to liquid crystals. Theory of coarsening of Cellular Patterns- applications to soap froths (e.g., shaving foams) (12).
NON-EQUILIBRIUM STEADY-STATES IN DRIVEN SYSTEM: Driven systems of interacting particles - applications to vehicular traffic;
Driven surfaces- applications in molecular beam epitaxy (MBE) (4).
At present there is no single book which can serve as the text book for the entire course. However, the first item in the list below will cover a large part of the course. The other items in the bibliography will serve as the text for a few other parts. Some pedagogical review articles published very recently will also be used for some specific topics.
Bibiliography