Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

We apply the semi-classical limit of the generalized SO(3) map for representation of variable-spin systems in a four-dimensional symplectic manifold and approximate their evolution terms of effective classical dynamics on T*S2. Using the asymptotic form of the star-product, we manage to “quantize” one of the classical dynamic variables and introduce a discretized version of the Truncated Wigner Approximation (TWA). Two emblematic examples of quantum dynamics (rotor in an external field and two coupled spins) are analyzed, and the results of exact, continuous, and discretized versions of TWA are compared.

High-cadence observations and variable spin behaviour of magnetar Swift J1818.0−1607 after its outburst

ABSTRACT We report on multifrequency radio observations of the new magnetar Swift J1818.0−1607, following it for more than one month with high cadence. The observations commenced less than 35 h after its registered first outburst. We obtained timing, polarization, and spectral information. Swift J1818.0−1607 has an unusually steep spectrum for a radio emitting magnetar and also has a relatively narrow and simple pulse profile. The position angle swing of the polarization is flat over the pulse profile, possibly suggesting that our line of sight grazes the edge of the emission beam. This may also explain the steep spectrum. The spin evolution shows large variation in the spin-down rate, associated with four distinct timing events over the course of our observations. Those events may be related to the appearance and disappearance of a second pulse component. The first timing event coincides with our actual observations, while we did not detect significant changes in the emission properties that could reveal further magnetospheric changes. Characteristic ages inferred from the timing measurements over the course of months vary by nearly an order of magnitude. A longer-term spin-down measurement over approximately 100 d suggests a characteristic age of about 500 yr, larger than previously reported. Though Swift J1818.0−1607 could still be one of the youngest neutron stars (and magnetars) detected so far, we caution using the characteristic age as a true-age indicator given the caveats behind its calculation.

Diamagnetism versus paramagnetism of charged ideal spin-1/2 fermions in a harmonic trap under a uniform magnetic field

Magnetic properties of harmonically trapped charged ideal spin-1/2 fermions in a uniform magnetic field are studied. It is shown that the magnetism of charged spin-1/2 fermions can be explained by a competition between the diamagnetic and paramagnetic effects, where a variable spin factor is introduced to describe the strength of paramagnetic effect. As the spin factor increases, a crossover from diamagnetic region to paramagnetic region appears. Moreover, the critical values of spin factor are obtained at low-temperature and under weak magnetic field, respectively. Spin-1/2 fermions display distinct magnetic behaviors from spinless case.