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

ISBN-10: 3642057993

ISBN-13: 9783642057991

ISBN-10: 3662067587

ISBN-13: 9783662067581

From the sphere of nonequilibrium statistical physics, this graduate- and research-level quantity treats the modeling and characterization of dissipative phenomena. numerous examples from diversified disciplines like condensed topic physics, fabrics technological know-how, metallurgy, chemical physics and so forth. are mentioned. Dattagupta employs the large framework of stochastic approaches and grasp equation innovations to acquire types for quite a lot of experimentally suitable phenomena similar to classical and quantum Brownian movement, spin dynamics, kinetics of part ordering, leisure in glasses, dissipative tunneling. It presents a pedagogical exposition of present learn fabric and may be priceless to experimentalists, computational physicists and theorists.

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A well-known S. , Dissipative Phenomena in Condensed Matter © Springer-Verlag Berlin Heidelberg 2004 32 2 Kinetic Ising Models example in statistical physics is the lattice-gas model of the liquid-vapor phase transition [38-41J. In this model, each lattice site is occupied by either an atom (A) or a vacancy (V). The lattice gas is described by occupation variables, with values ni = 0 or 1 when the site i is occupied by V or A. An equivalent description arises if we introduce spin variables mi = 2ni - 1, which assume values m = ±l.

85) 0 -00 Furthermore, the quantities W ( -111) and W (11 - 1) are related by a detailed-balance factor. 87) -00 Next, we use the cyclic property of the trace operation to obtain J h? 92) 1. , fluctuations in the bath have very short life-times. 93) can be further simplified as W( -111) 2g2 + W(1I- 1) ~ t;! 1 00 dT(b(T)b(O)). 97) then yield (cf. 61)) W(-111) W(11-1) = ApeQ(l) , = ApeQ(-l). 100) The important point here is that A is independent of the magnetic field H. Thus, the quantities W (-111) and W (11 - 1), which are interpreted as transition probabilities, depend on the subsystem energy (characterized by H in the present case) only through the equilibrium probabilities peQ (±l).

65) is usually referred to as the Onsager equation or the LandauKhalatnikov equation. , the order parameter 'ljJ is spatially homogeneous as in Sect. 5. , near the critical point of a phase transition [66] or in phase ordering problems [67]. 67) where 1jJ(r, t) is now a function of space r and time t. 58). 9). 68) accounts for surface tension due to inhomogeneities in the order parameter. The parameter K measures the strength of the surface tension. 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).

### Dissipative Phenomena in Condensed Matter: Some Applications by Professor Sushanta Dattagupta, Professor Sanjay Puri (auth.)

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