The superslow pulsation X-ray pulsars in high mass X-ray binaries

There exists a special class of X-ray pulsars that exhibit very slow pulsation of $P_{\rm spin}>1000$ s in the high mass X-ray binaries (HMXBs). We have studied the temporal and spectral properties of these superslow pulsation neutron star binaries in hard X-ray bands with INTEGRAL observations. Long-term monitoring observations find spin period evolution of two sources: spin-down trend for 4U 2206+54 ($P_{\rm spin}\sim 5560$ s with $\dot{P}_{\rm spin}\sim 4.9\times 10^{-7}$ s s$^{-1}$) and long-term spin-up trend for 2S 0114+65 ($P_{\rm spin}\sim 9600$ s with $\dot{P}_{\rm spin}\sim -1\times 10^{-6}$ s s$^{-1}$) in the last 20 years. A Be X-ray transient, SXP 1062 ($P_{\rm spin}\sim 1062$ s), also showed a fast spin-down rate of $\dot{P}_{\rm spin}\sim 3\times 10^{-6}$ s s$^{-1}$ during an outburst. These superslow pulsation neutron stars cannot be produced in the standard X-ray binary evolution model unless the neutron star has a much stronger surface magnetic field ($B>10^{14}$ G). The physical origin of the superslow spin period is still unclear. The possible origin and evolution channels of the superslow pulsation X-ray pulsars are discussed. Superslow pulsation X-ray pulsars could be younger X-ray binary systems, still in the fast evolution phase preceding the final equilibrium state. Alternatively, they could be a new class of neutron star system $-$ accreting magnetars.Comment: 4 pages, 3 figures. Oral talk for the Proceedings of IAUS 291 "Neutron Stars and Pulsars: Challenges and Opportunities after 80 years", J. van Leeuwen (ed.

Supercritical Nonlinear Schr\"odinger equations: Quasi-Periodic Solutions

We construct time quasi-periodic solutions to the energy supercritical nonlinear Schr\"odinger equations on the torus in arbitrary dimensions. This introduces a new approach, which could have general applicability.Comment: 62 pages; Duke Math. J. (to appear

B \to D'_0 (D'_1)\ell \bar \nu decays in HQEFT

Semileptonic B decays into excited charmed mesons $D'_0$ and $D'_1$ are studied in the framework of heavy quark effective field theory (HQEFT) up to order $1/m_Q$. They are characterized by a single leading Isgur-Wise function $\tau$ and several wave functions arising at $1/m_Q$ order. $\tau$ and the $1/m_Q$ order functions $\chi^b_0$, $\chi^c_0$ related to the kinetic energy operators are evaluated through QCD sum rule approach; zero recoil values of the $1/m_Q$ order functions $\kappa_1$, $\kappa_2$, $\kappa'_1$ and $\kappa'_2$ are extracted from the meson masses; and the branching ratios are found to be suppressed by the $1/m_Q$ corrections. It is concluded that the next leading order wave functions can be significant. However it does not change the previous prediction that the production rate of $j_l^P=3/2^+$ charmed mesons dominates over that of $1/2^+$ doublets.Comment: 20 pages, 10 figure

Modeling two-state cooperativity in protein folding

A protein model with the pairwise interaction energies varying as local environment changes, i.e., including some kinds of collective effect between the contacts, is proposed. Lattice Monte Carlo simulations on the thermodynamical characteristics and free energy profile show a well-defined two-state behavior and cooperativity of folding for such a model. As a comparison, related simulations for the usual G\={o} model, where the interaction energies are independent of the local conformations, are also made. Our results indicate that the evolution of interactions during the folding process plays an important role in the two-state cooperativity in protein folding.Comment: 5 figure