Quantum spin dynamics

Abstract:

We calculate the gradient of the radiation field generated by a polarization current with a superluminally rotating distribution pattern and show that the absolute value of this gradient increases as R(7/2) with distance R, within the sharply focused subbeams that constitute the overall radiation beam from such a source. In addition to supporting the earlier finding that the azimuthal and polar widths of these subbeams become narrower (as R(-3) and R(-1), respectively) with distance from the source, this result implies that the boundary contribution to the solution of the wave equation governing the radiation field does not always vanish in the limit where the boundary tends to infinity (as is commonly assumed in textbooks and the published literature). While the boundary contribution to the retarded solution for the potential can always be rendered equal to zero by means of a gauge transformation that preserves the Lorenz condition, the boundary contribution to the retarded solution of the wave equation for the field may be neglected only if it diminishes with distance faster than the contribution of the source density. In the case of a rotating superluminal source, however, the boundary term in the retarded solution for the field is by a factor of the order of R(1/2)larger than the source term of this solution, in the limit where the boundary tends to infinity. This result explains why an argument based on the solution of the wave equation governing the field in which the boundary term is neglected [such as that presented by Hannay, J. Opt. Soc. A 23, 1530 (2006)] misses the nonspherical decay of the field that is generated by a rotating superluminal source. The only way one can calculate the free-space radiation field of an accelerated superluminal source is via the retarded solution for the potential. Our findings have implications also for the observations of the pulsar emission: The more distant a pulsar, the narrower and brighter its giant pulses should be.

Abstract:

The focusing of the radiation generated by a polarization current with a superluminally rotating distribution pattern is of a higher order in the plane of rotation than in other directions. Consequently, our previously published [J. Opt. Soc. Am. A24, 2443 (2007)] asymptotic approximation to the value of this field outside the equatorial plane breaks down as the line of sight approaches a direction normal to the rotation axis, i.e., is nonuniform with respect to the polar angle. Here we employ an alternative asymptotic expansion to show that, though having a rate of decay with frequency (mu) that is by a factor of order mu(2/3) slower, the equatorial radiation field has the same dependence on distance as the nonspherically decaying component of the generated field in other directions: It, too, diminishes as the inverse square root of the distance from its source. We also briefly discuss the relevance of these results to the giant pulses received from pulsars: The focused, nonspherically decaying pulses that arise from a superluminal polarization current in a highly magnetized plasma have a power-law spectrum (i.e., a flux density S infinity mu(alpha)) whose index (alpha) is given by one of the values -2/3, -2, -8/3, or -4.

Abstract:

A photo-switchable fullerene dimer and its analogous nitrogen endohedral species have been synthesized and characterized. Irradiation by ultraviolet and visible light has been used to switch between the trans and cis isomers of both the C60- and N@C60- based dimers. Environmental perturbations experienced by the encapsulated nitrogen atom upon switching between the two isomers in degassed carbon disulfide has been determined by pulse electron paramagnetic resonance. Both T1 and T2 electron spin relaxation times of the two isomers of the endohedral fullerene containing dimer revealed a biexponential decay. Although the zero field splitting parameter Deff for both isomers in solution was similar, around 13.0 MHz, the molecular rotation correlation time τC of the trans and cis isomers was calculated to be 37.2 ± 1.6 and 34.8 ± 2.7 ps, respectively. © 2008 American Chemical Society.