Angle-resolved photoemission studies of the superconducting gap symmetry in Fe-based superconductors

The superconducting gap is the fundamental parameter that characterizes the superconducting state, and its symmetry is a direct consequence of the mechanism responsible for Cooper pairing. Here we discuss about angle-resolved photoemission spectroscopy measurements of the superconducting gap in the Fe-based high-temperature superconductors. We show that the superconducting gap is Fermi surface dependent and nodeless with small anisotropy, or more precisely, a function of momentum. We show that while this observation is inconsistent with weak coupling approaches for superconductivity in these materials, it is well supported by strong coupling models and global superconducting gaps. We also suggest that the strong anisotropies measured by other probes sensitive to the residual density of states are not related to the pairing interaction itself, but rather emerge naturally from the smaller lifetime of the superconducting Cooper pairs that is a direct consequence of the momentum dependent interband scattering inherent to these materials.Comment: 7 pages, 5 figure

Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms

Let $l$ and $m$ be two integers with $l>m\ge 0$, and let $a$ and $b$ be integers with $a\ge 1$ and $a+b\ge 1$. In this paper, we prove that $\log {\rm lcm}_{mn<i\le ln}\{ai+b\} =An+o(n)$, where $A$ is a constant depending on $l, m$ and $a$.Comment: 8 pages. To appear in Archiv der Mathemati

Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations

Using a one-dimensional macromolecule in aqueous solution as an illustration, we demonstrate that the relative entropy from information theory, $\sum_k p_k\ln(p_k/p_k^*)$, has a natural role in the energetics of equilibrium and nonequilibrium conformational fluctuations of the single molecule. It is identified as the free energy difference associated with a fluctuating density in equilibrium, and is associated with the distribution deviate from the equilibrium in nonequilibrium relaxation. This result can be generalized to any other isothermal macromolecular systems using the mathematical theories of large deviations and Markov processes, and at the same time provides the well-known mathematical results with an interesting physical interpretations.Comment: 5 page

The most plausible explanation of the cyclical period changes in close binaries: the case of the RS CVn-type binary WW Dra

We searched the orbital period changes in 182 EA-type (including the 101 Algol systems used by \cite{hal89}), 43 EB-type and 53 EW-type binaries with known both the mass ratio and the spectral type of their secondary components. We reproduced and improved the same diagram as Hall's (1989) according to the new collected data. Our plots do not support the conclusion derived by \cite{hal89} that all cases of cyclical period changes are restricted to binaries having the secondary component with spectral types later than F5. The presence of period changes also among stars with secondary component of early type indicates that the magnetic activity is one cause, but not the only one, for the period variation. It is discovered that cyclic period changes, likely due to the presence of a third body are more frequent in EW-type binaries among close binaries. Therefore, the most plausible explanation of the cyclical period changes is the LTTE via the presence of a third body. By using the century-long historical record of the times of light minimum, we analyzed the cyclical period change in the Algol binary WW Dra. It is found that the orbital period of the binary shows a $\sim112.2 \textbf{\textrm{yr}}$ cyclic variation with an amplitude of $\sim0.1977\textbf{\textrm{days}}$. The cyclic oscillation can be attributed to the LTTE via a third body with a mass no less than $6.43 M_{\odot}$. However, no spectral lines of the third body were discovered indicating that it may be a candidate black hole. The third body is orbiting the binary at a distance shorter than 14.4 AU and it may play an important role in the evolution of this system.Comment: 9 pages, 5 figures, published by MNRA

Stochastic Physics, Complex Systems and Biology

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated equilibrium, spontaneous random "mutations" and "adaptations". On an evlutionary time scale it produces sustainable diversity among individuals in a homogeneous population rather than convergence as usually predicted by a deterministic dynamics. The emergent discrete states in such a system, i.e., attractors, have natural robustness against both internal and external perturbations. Phenotypic states of a biological cell, a mesoscopic nonlinear stochastic open biochemical system, could be understood through such a perspective.Comment: 10 page

Neutrino fluence after r-process freeze-out and abundances of Te isotopes in presolar diamonds

Using the data of Richter et al. (1998) on Te isotopes in diamond grains from a meteorite, we derive bounds on the neutrino fluence and the decay timescale of the neutrino flux relevant for the supernova r-process. Our new bound on the neutrino fluence F after freeze-out of the r-process peak at mass number A = 130 is more stringent than the previous bound F < 0.045 (in units of 10**37 erg/cm**2) of Qian et al. (1997) and Haxton et al. (1997) if the neutrino flux decays on a timescale tau > 0.65 s. In particular, it requires that a fluence of F = 0.031 be provided by a neutrino flux with tau < 0.84 s. Such a fluence may be responsible for the production of the solar r-process abundances at A = 124-126 (Qian et al. 1997; Haxton et al. 1997). Our results are based on the assumption that only the stable nuclei implanted into the diamonds are retained while the radioactive ones are lost from the diamonds upon decay after implantation (Ott 1996). We consider that the nanodiamonds are condensed in an environment with C/O > 1 in the expanding supernova debris or from the exterior H envelope. The implantation of nuclei would have occurred 10**4-10**6 s after r-process freeze-out. This time interval may be marginally sufficient to permit adequate cooling upon expansion for the formation of diamond grains. The mechanisms of preferential retention/loss of the implanted nuclei are not well understood.Comment: AASTeX, 11 pages, 3 Postscript figure

The least common multiple of a sequence of products of linear polynomials

Let $f(x)$ be the product of several linear polynomials with integer coefficients. In this paper, we obtain the estimate: $\log {\rm lcm}(f(1), ..., f(n))\sim An$ as $n\rightarrow\infty$, where $A$ is a constant depending on $f$.Comment: To appear in Acta Mathematica Hungaric