Rigorous statistical detection and characterization of a deviation from the Gutenberg-Richter distribution above magnitude 8 in subduction zones

We present a quantitative statistical test for the presence of a crossover c0 in the Gutenberg-Richter distribution of earthquake seismic moments, separating the usual power law regime for seismic moments less than c0 from another faster decaying regime beyond c0. Our method is based on the transformation of the ordered sample of seismic moments into a series with uniform distribution under condition of no crossover. The bootstrap method allows us to estimate the statistical significance of the null hypothesis H0 of an absence of crossover (c0=infinity). When H0 is rejected, we estimate the crossover c0 using two different competing models for the second regime beyond c0 and the bootstrap method. For the catalog obtained by aggregating 14 subduction zones of the Circum Pacific Seismic Belt, our estimate of the crossover point is log(c0) =28.14 +- 0.40 (c0 in dyne-cm), corresponding to a crossover magnitude mW=8.1 +- 0.3. For separate subduction zones, the corresponding estimates are much more uncertain, so that the null hypothesis of an identical crossover for all subduction zones cannot be rejected. Such a large value of the crossover magnitude makes it difficult to associate it directly with a seismogenic thickness as proposed by many different authors in the past. Our measure of c0 may substantiate the concept that the localization of strong shear deformation could propagate significantly in the lower crust and upper mantle, thus increasing the effective size beyond which one should expect a change of regime.Comment: pdf document of 40 pages including 5 tables and 19 figure

On the Timescale for the Formation of Protostellar Cores in Magnetic Interstellar Clouds

We revisit the problem of the formation of dense protostellar cores due to ambipolar diffusion within magnetically supported molecular clouds, and derive an analytical expression for the core formation timescale. The resulting expression is similar to the canonical expression = t_{ff}^2/t_{ni} ~ 10 t_{ni} (where t_{ff} is the free-fall time and t_{ni} is the neutral-ion collision time), except that it is multiplied by a numerical factor C(\mu_{c0}), where \mu_{c0} is the initial central mass-to-flux ratio normalized to the critical value for gravitational collapse. C(\mu_{c0}) is typically ~ 1 in highly subcritical clouds (\mu_{c0} << 1), although certain conditions allow C(\mu_{c0}) >> 1. For clouds that are not highly subcritical, C(\mu_{c0}) can be much less than unity, with C(\mu_{c0}) --> 0 for \mu_{c0} --> 1, significantly reducing the time required to form a supercritical core. This, along with recent observations of clouds with mass-to-flux ratios close to the critical value, may reconcile the results of ambipolar diffusion models with statistical analyses of cores and YSO's which suggest an evolutionary timescale \~ 1 Myr for objects of mean density ~ 10^4 cm^{-3}. We compare our analytical relation to the results of numerical simulations, and also discuss the effects of dust grains on the core formation timescale.Comment: 11 pages, 2 figures, accepted for publication in the Astrophysical Journa

Gap States in Dilute Magnetic Alloy Superconductors

We study states in the superconducting gap induced by magnetic impurities using self-consistent quantum Monte Carlo with maximum entropy and formally exact analytic continuation methods. The magnetic impurity susceptibility has different characteristics for T_{0} \alt T_{c0} and T_{0} \agt T_{c0} ($T_{0}$: Kondo temperature, $T_{c0}$: superconducting transition temperature) due to the crossover between a doublet and a singlet ground state. We systematically study the location and the weight of the gap states and the gap parameter as a function of $T_{0}/T_{c0}$ and the concentration of the impurities.Comment: 4 pages in ReVTeX including 4 encapsulated Postscript figure

Charmed quark component of the photon wave function

We determine the c-anti-c component of the photon wave function on the basis of (i) the data on the transitions e+ e- -> J/psi(3096), psi(3686), psi(4040), psi(4415), (ii) partial widths of the two-photon decays eta_{c0}(2979), chi_{c0}(3415), chi_{c2}(3556) -> gamma-gamma, and (iii) wave functions of the charmonium states obtained by solving the Bethe-Salpeter equation for the c-anti-c system. Using the obtained c-anti-c component of the photon wave function we calculate the gamma-gamma decay partial widths for radial excitation 2S state, eta_{c0}(3594) -> gamma-gamma, and 2P states chi_{c0}(3849), chi_{c2}(3950) -> gamma-gamma.Comment: 20 pages, 8 figure

Annihilation Rate of Heavy 0^{++} P-wave Quarkonium in Relativistic Salpeter Method

Two-photon and two-gluon annihilation rates of P-wave scalar charmonium and bottomonium up to third radial excited states are estimated in the relativistic Salpeter method. We solved the full Salpeter equation with a well defined relativistic wave function and calculated the transition amplitude using the Mandelstam formalism. Our model dependent estimates for the decay widths: $\Gamma(\chi_{c0} \to 2\gamma)=3.78$ keV, $\Gamma(\chi'_{c0} \to 2\gamma)=3.51$ keV, $\Gamma(\chi_{b0} \to 2\gamma)=48.8$ eV and $\Gamma(\chi'_{b0} \to 2\gamma)=50.3$ eV. We also give estimates of total widths by the two-gluon decay rates: $\Gamma_{tot}(\chi_{c0})=10.3$ MeV, $\Gamma_{tot}(\chi'_{c0})=9.61$ MeV, $\Gamma_{tot}(\chi_{b0})=0.887$ MeV and $\Gamma_{tot}(\chi'_{b0})=0.914$ MeV.Comment: 8 pages, 1 figure, 4 table

Hall coefficient in heavy fermion metals

Experimental studies of the antiferromagnetic (AF) heavy fermion metal $\rm YbRh_2Si_2$ in a magnetic field $B$ indicate the presence of a jump in the Hall coefficient at a magnetic-field tuned quantum state in the zero temperature limit. This quantum state occurs at $B\geq B_{c0}$ and induces the jump even though the change of the magnetic field at $B=B_{c0}$ is infinitesimal. We investigate this by using the model of heavy electron liquid with the fermion condensate. Within this model the jump takes place when the magnetic field reaches the critical value $B_{c0}$ at which the ordering temperature $T_N(B=B_{c0})$ of the AF transition vanishes. We show that at $B\to B_{c0}$, this second order AF phase transition becomes the first order one, making the corresponding quantum and thermal critical fluctuations vanish at the jump. At $T\to0$ and $B=B_{c0}$, the Gr\"uneisen ratio as a function of temperature $T$ diverges. We demonstrate that both the divergence and the jump are determined by the specific low temperature behavior of the entropy $S(T)\propto S_0+a\sqrt{T}+bT$ with $S_0$, $a$ and $b$ are temperature independent constants.Comment: 5 pages, 2 figure