Read e-book online Irreversibilities in Quantum Mechanics (Fundamental Theories PDF

By B. Fain

ISBN-10: 0306471280

ISBN-13: 9780306471285

ISBN-10: 079236581X

ISBN-13: 9780792365815

Provides a a theoretical and conceptual framework for the outline of irreversible phenomena in quantum mechanics. With purposes to precise actual types and simulations, and detailed consciousness given to reminiscence results in rest methods and dissipationless states in dissipative platforms.

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Example text

14), r << 1, are discussed in Appendix A to this chapter. It is clear from physical considerations that fast relaxation of the dissipative system would destroy the correlation created by the interaction between the dynamic and dissipative subsystems. s. of Eq. 1 1). The problem of the factorization approximation does not exist in the works of van Hove [16], Zwanzig [10,11], and Fain [20,21]. Van Hove and Zwanzig considered the relaxation dissipative system (the diagonal part of its density matrix while Fain derived equations for the diagonal in Greek indices part of the density matrix An important comment has to be made.

2). This Hamiltonian describes the system of interest, or dynamic system, whose Hamiltonian is E, interacting with the dissipative system - thermal bath - with Hamiltonian F + G. 14). 14) without the term is usually called the Redfield equation. This equation has certain limitations. (1) It has been derived in the weak coupling approximation, using only terms up to the second order of the interacting energy V. 17). 14) has been derived in the Markovian approximation. There is another approach to the irreversible processes which have been developed during the last decades [39-42].

However, a closer examination shows [45] that the two formulations are, in general, mutually exclusive, with the Redfield equations not conforming a completely positive semigroup. It does not mean that the Redfield equations of motion cannot preserve positivity for a certain subset of initial states. However, positivity cannot be satisfied for all initial states. A paper [36] of Suarez et al. provides concrete examples of solutions of the Redfield equations which break the positivity; that is, they lead to negative values for population probabilities.

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Irreversibilities in Quantum Mechanics (Fundamental Theories of Physics) by B. Fain

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