On the peculiarities in the rotational frequency evolution of isolated neutron stars

The measurements of pulsar frequency second derivatives have shown that they are $10^2-10^6$ times larger than expected for standard pulsar spin-down law, and are even negative for about half of pulsars. We explain these paradoxical results on the basis of the statistical analysis of the rotational parameters $\nu$, $\dot \nu$ and $\ddot \nu$ of the subset of 295 pulsars taken mostly from the ATNF database. We have found a strong correlation between $\ddot \nu$ and $\dot \nu$ for both $\ddot\nu > 0$ and $\ddot\nu < 0$, as well as between $\nu$ and $\dot\nu$. We interpret these dependencies as evolutionary ones due to $\dot\nu$ being nearly proportional to the pulsars' age. The derived statistical relations as well as "anomalous" values of $\ddot\nu$ are well described by assuming the long-time variations of the spin-down rate. The pulsar frequency evolution, therefore, consists of secular change of $\nu_{ev}(t)$, $\dot\nu_{ev}(t)$ and $\ddot\nu_{ev}(t)$ according to the power law with $n \approx 5$, the irregularities, observed within a timespan as a timing noise, and the variations on the timescale larger than that timespan -- several tens of years.Comment: 4 pages, 3 figures. Accepted for publication in ApSS, in the proceedings of the conference "Isolated Neutron Stars: from the Interior to the Surface", London, April 2006; eds. S. Zane, R. Turolla and D. Pag

Ginzburg-Landau theory of vortices in a multi-gap superconductor

The Ginzburg-Landau functional for a two-gap superconductor is derived within the weak-coupling BCS model. The two-gap Ginzburg-Landau theory is, then, applied to investigate various magnetic properties of MgB2 including an upturn temperature dependence of the transverse upper critical field and a core structure of an isolated vortex. Orientation of vortex lattice relative to crystallographic axes is studied for magnetic fields parallel to the c-axis. A peculiar 30-degree rotation of the vortex lattice with increasing strength of an applied field observed by neutron scattering is attributed to the multi-gap nature of superconductivity in MgB2.Comment: 11 page

Upper critical field in dirty two-band superconductors: breakdown of the anisotropic Ginzburg-Landau theory

We investigate the upper critical field in a dirty two-band superconductor within quasiclassical Usadel equations. The regime of very high anisotropy in the quasi-2D band, relevant for MgB$_{2}$, is considered. We show that strong disparities in pairing interactions and diffusion constant anisotropies for two bands influence the in-plane $H_{c2}$ in a different way at high and low temperatures. This causes temperature-dependent $H_{c2}$ anisotropy, in accordance with recent experimental data in MgB$_{2}$. The three-dimensional band most strongly influences the in-plane $H_{c2}$ near $T_{c}$, in the Ginzburg-Landau (GL) region. However, due to a very large difference between the c-axis coherence lengths in the two bands, the GL theory is applicable only in an extremely narrow temperature range near $T_c$. The angular dependence of $H_{c2}$ deviates from a simple effective-mass law even near $T_c$.Comment: 12 pages, 5 figures, submitted to Phys.Rev.