By Professor Sushanta Dattagupta, Professor Sanjay Puri (auth.)

From the sector of nonequilibrium statistical physics, this graduate- and research-level quantity treats the modeling and characterization of dissipative phenomena. various examples from diversified disciplines like condensed subject physics, fabrics technology, metallurgy, chemical physics and so on. are mentioned. Dattagupta employs the huge framework of stochastic procedures and grasp equation options to procure types for a variety of experimentally correct phenomena reminiscent of classical and quantum Brownian movement, spin dynamics, kinetics of section ordering, rest in glasses, dissipative tunneling. It offers a pedagogical exposition of present examine fabric and may be necessary to experimentalists, computational physicists and theorists.

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LAID) The term exp( -iLBt) drops out because of the cyclic property of the trace operation over the Hilbert space of the bath. , we assume that the subsystem is decoupled from the heat bath for t < O. The perturbation V, which couples the subsystem to the heat bath, is switched on at t = O. We are interested in the subsequent time-evolution of Ps (t). 13) where ZB = TrB (e-i3 1i B) is the partition function for the heat bath. 16) where the states Inb), In~), refer to the eigenstates of the bath Hamiltonian 'HB.

67) is now space- and time-dependent, and satisfies the fluctuation-dissipation relation: O(r,t) = 0, O(r', t')O(r", til) = 2rkB Tc5(r' - r")c5(t' - til). 69) constitute the so-called Model A of order-parameter kinetics, discussed by Halperin and Hohenberg in the context of dynamical critical phenomena [66]. 67) is referred to as the timedependent Ginzburg-Landau (TDGL) equation [68]. 67) is obtained by dropping the noise term as follows: ~1jJ(r t) = _rc5Q[1jJ] at' c51jJ . 70) exhibits purely relaxational dynamics, and is expected to be valid at low temperatures.

77) constitute Model B in the classification scheme of Halperin and Hohenberg [66]. 6 Modeling of Order-Parameter Kinetics 53 The TDGL and CRC equations (or Models A and B) represent the prototypical equations for order-parameter kinetics. In more complex physical situations, there may be multiple order parameters which satisfy different conservation laws. Let us focus on two examples here. First, consider the case of a binary (AB) mixture where one of the components (say, A) has an attached magnetic spin [77].