Toward a grand theory of irreversibility
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From: "Juan R." González-Álvarez on 7 Jun 2010 11:21 TOWARD A GRAND THEORY OF IRREVERSIBILITY --- This is only an excerpt, the complete news, equations and figure are available in below links. --- An introduction to the new fine-grained theory was given in the second part: "Trajectory branching in Liouville space as the source of irreversibility". As was said therein, the new theory may be considered a generalization of the fine-grained theory developed during last decades by the Brussels-Austin School. In this third part, I will sketch how the new theory reproduces the known pragmatic and semiphenomenological quantum approaches developed in the last decades by at least six communities: NMR chemists, quantum optics, condensed matter physicists, mathematical physicists, astrophysicists, and condensed phase chemical physicists and physical chemists. Among other approaches, I consider Redfield, Agarwal, Caldeira & Leggett, Lindblad, Zwanzig PO, and Gamow theory. For instance, the Lindblad equation of his semigroup theory can be obtained in the weak interaction limit of a Markovian approximation to the equation of motion 3 (see figure) for a system interacting, through a factorized system-bath interaction Hamiltonian, with a heat bath at thermodynamic equilibrium, if one takes the limit of ultrashort reservoir correlation time. A broad set of generalizations of the Lindblad equation are at our hand now. One can add non-Markovian corrections to it, fluctuating corrections... There exists very important physics associated to the Vlasov term, which is ignored in Lindblad's semigroup approach. Moreover, the Lindblad model is purely formal, without making any specific model for the dissipative interactions; therefore, in practical calculations, the choice of the Lindblad operators A_m as well as of the prefactor c(m,m) has to be guided either by intuition or by previous phenomenological knowledge. An additional advantage of the new theory is evident here, because both the prefactor and the Lindblad operators can be obtained from first principles of the new theory. For illustration I give the operator for the case of quantum Brownian motion. The advantages of this new theory of irreversibility over the coarse-grained approaches are numerous. In this event, I give a list of advantages over Zwanzig & Mori projection operator formalism: REFERENCES Phase space approach to theories of quantum dissipation 1997: J. Chem. Phys. 107(13), 5236—5253. Kohen, D.; Marston, C. C.; Tannor, D. J. Nonequilibrium Statistical Mechanics 2001: Oxford University Press, Oxford. Zwanzig, Robert. A consistent description of kinetics and hydrodynamics of systems of interacting particles by means of the nonequilibrium statistical operator method 1998: Condensed Matter Physics 1, 4(16) 687–750. Tokarchuk, M. V.; Omelyan, I. P.; Kobryn, A. E. Nonequilibrium Statistical Mechanics, Ensemble Method 1998: Kluwer Academic Publishers, Dordrecht. Eu, Byung Chan. The Quantum Theory of Fields, Volume 1 Foundations 1996: Cambridge University Press, Cambridge; Reprinted with corrections. Weinberg, Steven. Gamow vectors In Semigroup Representations of the Poincaré Group and Relativistic Gamow Vectors 2008: arXiv:hep-th/9911059v1. Bohm, A.; Kaldass, H.; Wickramasekara, S.; Kielanowski, P. ################## FULL NEWS AND BLOG ################## http://www.canonicalscience.org/publications/canonicalsciencetoday/canonicalsciencetoday.html http://www.canonicalscience.org/publications/canonicalsciencetoday/20100607.html -- http://www.canonicalscience.org/ BLOG: http://www.canonicalscience.org/publications/canonicalsciencetoday/canonicalsciencetoday.html
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