Download Irreversibilities in Quantum Mechanics (Fundamental Theories by B. Fain PDF

By B. Fain

Offers a a theoretical and conceptual framework for the outline of irreversible phenomena in quantum mechanics. With functions to precise actual types and simulations, and targeted cognizance given to reminiscence results in rest methods and dissipationless states in dissipative structures.

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15). , for values 1). e. for large enough t, the transition probability is proportional to time t and it is possible to introduce the transition probability per unit time (which itself does not depend on time). 16) depend on the actual properties of the system under investigation. 19) is not satisfied then there is no time-independent transition probability per unit time. 21) there is no time-independent transition probability per unit time. 12) the transition probability is proportional to t².

2). 3), are diagonal in m and indices respectively). 13) DL0 =L0D . 6) by L0. 11) Here the Markovian approximation for the dissipative system is assumed [the fourth term in the right hand side of Eq. 11)]. 12) However, under certain conditions such a reduction can be approximately performed [17,18]. These conditions correspond to the fast relaxation of the dissipative system in comparison with the relaxation of the dynamic subsystem. 13) where is the characteristic relaxation time of the dynamic system.

19). Such an approximation is justified provided second and higher order terms may be neglected. 19) are decaying fast Let us assume that sums over functions enough, being the characteristic decay time. 26) the transition probabilities per unit time do not depend on time. 16) respectively. e. 6) using the Born and the Markovian approximation. 29) corresponding to RPA at the initial time t = t0. Of course, such an assumption is not a very satisfactory one. g. 17)]. However, the sums which are inherent in the first term in the right hand side of Eq.

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