Indefinitely Oscillating Martingales

We construct a class of nonnegative martingale processes that oscillate indefinitely with high probability. For these processes, we state a uniform rate of the number of oscillations and show that this rate is asymptotically close to the theoretical upper bound. These bounds on probability and expectation of the number of upcrossings are compared to classical bounds from the martingale literature. We discuss two applications. First, our results imply that the limit of the minimum description length operator may not exist. Second, we give bounds on how often one can change one's belief in a given hypothesis when observing a stream of data.Comment: ALT 2014, extended technical repor

B→DsπB \to D_s \pi and the tree amplitude in B→π+π−B \to \pi^+ \pi^-

The recently-observed decay $B^0 \to D_s^+ \pi^-$ is expected to proceed mainly by means of a tree amplitude in the factorization limit: $B^0 \to \pi^- {(W^+)}^*$, ${(W^+)}^* \to D_s^+$. Under this assumption, we predict the corresponding contribution of the tree amplitude to $B^0 \to \pi^+ \pi^-$. We indicate the needed improvements in data that will allow a useful estimate of this amplitude with errors comparable to those accompanying other methods. Since the factorization hypothesis for this process goes beyond that proved in most approaches, we also discuss independent tests of this hypothesis.Comment: 7 pages, LaTeX, 1 figure, to be submitted to Phys. Rev. D (Brief Reports

Band-dependent quasiparticle dynamics in the hole-doped Ba-122 iron pnictides

We report on band-dependent quasiparticle dynamics in the hole-doped Ba-122 pnictides measured by ultrafast pump-probe spectroscopy. In the superconducting state of the optimal and over hole-doped samples, we observe two distinct relaxation processes: a fast component whose decay rate increases linearly with excitation density and a slow component whose relaxation is independent of excitation strength. We argue that these two components reflect the recombination of quasiparticles in the two hole bands through intraband and interband processes. We also find that the thermal recombination rate of quasiparticles increases quadratically with temperature in all samples. The temperature and excitation density dependence of the decays indicates fully gapped hole bands and nodal or very anisotropic electron bands.United States. Department of Energy (Grant No. DE-FG02-08ER46521)National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (award number DMR - 0819762

Thermodynamic perturbation theory for dipolar superparamagnets

Thermodynamic perturbation theory is employed to derive analytical expressions for the equilibrium linear susceptibility and specific heat of lattices of anisotropic classical spins weakly coupled by the dipole-dipole interaction. The calculation is carried out to the second order in the coupling constant over the temperature, while the single-spin anisotropy is treated exactly. The temperature range of applicability of the results is, for weak anisotropy (A/kT << 1), similar to that of ordinary high-temperature expansions, but for moderately and strongly anisotropic spins (A/kT > 1) it can extend down to the temperatures where the superparamagnetic blocking takes place (A/kT \sim 25), provided only the interaction strength is weak enough. Besides, taking exactly the anisotropy into account, the results describe as particular cases the effects of the interactions on isotropic (A = 0) as well as strongly anisotropic (A \to \infty) systems (discrete orientation model and plane rotators).Comment: 15 pages, 3 figure

Nonlinear Dynamical Stability of Newtonian Rotating White Dwarfs and Supermassive Stars

We prove general nonlinear stability and existence theorems for rotating star solutions which are axi-symmetric steady-state solutions of the compressible isentropic Euler-Poisson equations in 3 spatial dimensions. We apply our results to rotating and non-rotating white dwarf, and rotating high density supermassive (extreme relativistic) stars, stars which are in convective equilibrium and have uniform chemical composition. This paper is a continuation of our earlier work ([28])

Low-Mass Baryon-Antibaryon Enhancements in B Decays

The nature of low-mass baryon-antibaryon enhancements seen in B decays is explored. Three possibilities include (i) states near threshold as found in a model by Nambu and Jona-Lasinio, (ii) isoscalar states with $J^{PC} = 0^{\pm +}$ coupled to a pair of gluons, and (iii) low-mass enhancements favored by the fragmentation process. Ways of distinguishing these mechanisms using angular distributions and flavor symmetry are proposed.Comment: 8 pages, LaTeX, no figures, to be submitted to Phys. Rev. D. One reference adde

Existence and Nonlinear Stability of Rotating Star Solutions of the Compressible Euler-Poisson Equations

We prove existence of rotating star solutions which are steady-state solutions of the compressible isentropic Euler-Poisson (EP) equations in 3 spatial dimensions, with prescribed angular momentum and total mass. This problem can be formulated as a variational problem of finding a minimizer of an energy functional in a broader class of functions having less symmetry than those functions considered in the classical Auchmuty-Beals paper. We prove the nonlinear dynamical stability of these solutions with perturbations having the same total mass and symmetry as the rotating star solution. We also prove local in time stability of W^{1, \infty}(\RR^3) solutions where the perturbations are entropy-weak solutions of the EP equations. Finally, we give a uniform (in time) a-priori estimate for entropy-weak solutions of the EP equations

Density functional study of Aun_n (n=2-20) clusters: lowest-energy structures and electronic properties

We have investigated the lowest-energy structures and electronic properties of the Au$_n$(n=2-20) clusters based on density functional theory (DFT) with local density approximation. The small Au$_n$ clusters adopt planar structures up to n=6. Tabular cage structures are preferred in the range of n=10-14 and a structural transition from tabular cage-like structure to compact near-spherical structure is found around n=15. The most stable configurations obtained for Au$_{13}$ and Au$_{19}$ clusters are amorphous instead of icosahedral or fcc-like, while the electronic density of states sensitively depend on the cluster geometry. Dramatic odd-even alternative behaviors are obtained in the relative stability, HOMO-LUMO gaps and ionization potentials of gold clusters. The size evolution of electronic properties is discussed and the theoretical ionization potentials of Au$_n$ clusters compare well with experiments.Comment: 6 pages, 7 figure

Scaling behavior of the dipole coupling energy in two-dimensional disordered magnetic nanostructures

Numerical calculations of the average dipole-coupling energy $\bar E_\mathrm{dip}$ in two-dimensional disordered magnetic nanostructures are performed as function of the particle coverage $C$. We observe that $\bar E_\mathrm{dip}$ scales as $\bar E_\mathrm{dip}\propto C^{\alpha^*}$ with an unusually small exponent $\alpha^*\simeq 0.8$--1.0 for coverages $C\lesssim20$. This behavior is shown to be primarly given by the contributions of particle pairs at short distances, which is intrinsically related to the presence of an appreciable degree of disorder. The value of $\alpha^*$ is found to be sensitive to the magnetic arrangement within the nanostructure and to the degree of disorder. For large coverages $C\gtrsim20$ we obtain $\bar E_\mathrm{dip}\propto C^\alpha$ with $\alpha=3/2$, in agreement with the straighforward scaling of the dipole coupling as in a periodic particle setup. Taking into account the effect of single-particle anisotropies, we show that the scaling exponent can be used as a criterion to distinguish between weakly interacting ($\alpha^* \simeq 1.0$) and strongly interacting ($\alpha^* \simeq 0.8$) particle ensembles as function of coverage.Comment: accepted for publication in Phys.Rev.