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On the relaxation to quantum-statistical equilibrium of the Wigner-Weisskopf atom in a one-dimensional radiation field. V. Exact solution for infinite systems

par Davidson, Russel ;Kozak, John
Référence Journal of mathematical physics, 14, 4, page (423-431)
Publication Publié, 1973

Article révisé par les pairs

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Résumé :

In pursuit of the study begun in the preceding paper of the spontaneous emission of a Wigner-Weisskopf atom in a one-dimensional radiation field, the exact solution of this problem in the thermodynamic limit of a system of infinite extent is examined. The analysis reveals the existence in general of three contributions to the probability of the atom's being excited at any moment: a constant contribution and two sorts of time-dependent ones, exponential and nonexponential. For a specific choice of coupling function, this probability is written down in closed form. The link between the constant contribution and the appearance of ghost states and ergodicity is investigated, and criteria given to determine when this contribution does not arise. A numerical study is made of the expressions obtained, and the nonexponential part of the solution compared with approximations for it which have been previously obtained by various means. It is concluded that the predictions of the weak-coupling Prigogine-Résibois master equation are inadequate except when the model is ergodic in a certain sense, and some suggestions are made concerning the relevance of these studies to nonequilibrium statistical mechanics. Copyright © 1973 by the American Institute of Physics.