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We describe the temporal behavior of the dynamic elements of an exactly soluble quantum model. The model consists of a single two-level atom or spin interacting with a single mode of the quantized radiation field in the dipole approximation, the mode being initially in an arbitrary coherent state of excitation. We give new long-time numerical and closed-form approximate analytic solutions for the expectation values of the atomic dipole moment and the difference in population of the two atomic levels in the rotating wave approximation. The atomic dipoledipole correlation function is calculated. A11 of the results are obtained without semiclassical or decorrelation approximations. Unusual features found in the temporal behavior of this lossless model problem are "collapse, " i.e. , episodic nonexponential damping of both the atomic inversion and dipole moment, and two kinds of "revival" or partial recorrelation, in the dynamic evolution, during which the initial state is nearly recovered. We give analytic formulas for the collapse function, for both of the revival times, and for the envelope of the revival maxima. Some remarks are made about the nature of irreversibility in this exactly soluble and loss-free model. )Mary Street Jenkins Foundation Fellow, Puebla, Mexico. E. T. Jaynes, Microwave Laboratory Report No. 502, Stanford University, 1958 (unpublished). By rotating wave approximation one can understand the neglect of terms in the interaction Hamiltonian that are not approximately energy-conserving in lowest order.A more pictorial view based on spin precession is given in may texts on resonance physics, for example,

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In this paper we consider a magnetic analog of the double-Reissner-Nordström solution and construct the corresponding magnetic potential A ' in the explicit form. The behavior of the resulting solution under the Harrison transformation then naturally singles out the asymmetric black diholes-configurations composed of two nonextreme black holes possessing unequal masses, and charges equal in magnitude but opposite in sign-as its most general subclass for which equilibrium of the black-hole constituents can be achieved with the aid of the external magnetic (or electric) field. We also generalize the double-ReissnerNordström solution to dilaton gravity with arbitrary dilaton coupling, yielding the four-dimensional double-Gibbons-Maeda spacetime. The study of some physical properties of the solutions obtained leads, in particular, to very simple formulas for the areas of the horizons and surface gravities.

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