An Approximation Scheme for Reflected Stochastic Differential Equations

In this paper we consider the Stratonovich reflected stochastic differential equation $dX_t=\sigma(X_t)\circ dW_t+b(X_t)dt+dL_t$ in a bounded domain \O which satisfies conditions, introduced by Lions and Sznitman, which are specified below. Letting $W^N_t$ be the $N$-dyadic piecewise linear interpolation of $W_t$ what we show is that one can solve the reflected ordinary differential equation $\dot X^N_t=\sigma(X^N_t)\dot W^N_t+b(X^N_t)+\dot L^N_t$ and that the distribution of the pair $(X^N_t,L^N_t)$ converges weakly to that of $(X_t,L_t)$. Hence, what we prove is a distributional version for reflected diffusions of the famous result of Wong and Zakai. Perhaps the most valuable contribution made by our procedure derives from the representation of $\dot X^N_t$ in terms of a projection of $\dot W_t^N$. In particular, we apply our result in hand to derive some geometric properties of coupled reflected Brownian motion in certain domains, especially those properties which have been used in recent work on the "hot spots" conjecture for special domain.Comment: 26 pages, 4 figure

Dependence of the superconducting critical temperature on the number of layers in homologous series of high-Tc cuprates

We study a model of $n$-layer high-temperature cuprates of homologous series like HgBa_2Ca_(n-1)Cu_nO_(2+2n+\delta) to explain the dependence of the critical temperature Tc(n) on the number $n$ of Cu-O planes in the elementary cell. Focusing on the description of the high-temperature superconducting system in terms of the collective phase variables, we have considered a semi-microscopic anisotropic three-dimensional vector XY model of stacked copper-oxide layers with adjustable parameters representing microscopic in-plane and out-of-plane phase stiffnesses. The model captures the layered composition along c-axis of homologous series and goes beyond the phenomenological Lawrence-Doniach model for layered superconductors. Implementing the spherical closure relation for vector variables we have solved the phase XY model exactly with the help of transfer matrix method and calculated Tc(n) for arbitrary block size $n$, elucidating the role of the c-axis anisotropy and its influence on the critical temperature. Furthermore, we accommodate inhomogeneous charge distribution among planes characterized by the charge imbalance coefficient $R$ being the function of number of layers $n$. By making a physically justified assumption regarding the doping dependence of the microscopic phase stiffnesses, we have calculated the values of parameter $R$ as a function of block size $n$ in good agreement with the nuclear magnetic resonance data of carrier distribution in multilayered high-Tc cuprates.Comment: 15 pages, 10 figures. Submitted to Physical Review

Magnetization vector in the reversible region of a highly anisotropic cuprate superconductor: anisotropy factor and the role of 2D vortex fluctuations

By using a high quality Tl2Ba2Ca2Cu3O10 (Tl-2223) single crystal as an example, the magnetization vector was probed in the reversible region of highly anisotropic cuprate superconductors. For that, we have measured its components along and transverse to the applied magnetic field for different crystal orientations. The analysis shows that the angular dependence of the perpendicular component of the magnetization vector follows the one predicted by a London-like approach which includes a contribution associated with the thermal fluctuations of the 2D vortex positions. For the Tl-2223 crystal studied here, a lower bound for the anisotropy factor was estimated to be about 190.Comment: 6 pages, 3 figure

Evolution of Fermion Pairing from Three to Two Dimensions

We follow the evolution of fermion pairing in the dimensional crossover from 3D to 2D as a strongly interacting Fermi gas of $^6$Li atoms becomes confined to a stack of two-dimensional layers formed by a one-dimensional optical lattice. Decreasing the dimensionality leads to the opening of a gap in radio-frequency spectra, even on the BCS-side of a Feshbach resonance. The measured binding energy of fermion pairs closely follows the theoretical two-body binding energy and, in the 2D limit, the zero-temperature mean-field BEC-BCS theory.Comment: 5 pages, 4 figure

Overcoming the boundary layer turbulence at Dome C: ground-layer adaptive optics versus tower

The unique atmospheric conditions present at sites such as Dome C on the Antarctic plateau are very favorable for high spatial resolution astronomy. At Dome C, the majority of the optical turbulence is confined to a 30 to 40 m thick stable boundary layer that results from the strong temperature inversion created by the heat exchange between the air and the ice-covered ground. To fully realize the potential of the exceptionally calm free atmosphere, this boundary layer must be overcome. In this article we compare the performance of two methods proposed to beat the boundary layer: mounting a telescope on a tower that physically puts it above the turbulent layer, and installing a telescope at ground level with a ground-layer adaptive optics system. A case is also made to combine these two methods to further improve the image quality

Fluctuations in superconducting rings with two order parameters

Starting from the Ginzburg-Landau energy functional, we discuss how the presence of two order parameters and the coupling between them influence a superconducting ring in the fluctuative regime. Our method is exact, but requires numerical implementation. We also study approximations for which some analytic expressions can be obtained, and check their ranges of validity. We provide estimates for the temperature ranges where fluctuations are important, calculate the persistent current in magnesium diboride rings as a function of temperature and enclosed flux, and point out its additional dependence on the cross-section area of the ring. We find temperature regions in which fluctuations enhance the persistent currents and regions where they inhibit the persistent current. The presence of two order parameters that can fluctuate independently always leads to larger averages of the order parameters at Tc, but only for appropriate parameters this yields larger persistent current. In cases of very different material parameters for the two coupled condensates, the persistent current is inhibited

Extragalactic Radio Sources and the WMAP Cold Spot

We detect a dip of 20-45% in the surface brightness and number counts of NVSS sources smoothed to a few degrees at the location of the WMAP cold spot. The dip has structure on scales of approximately 1-10 degrees. Together with independent all-sky wavelet analyses, our results suggest that the dip in extragalactic brightness and number counts and the WMAP cold spot are physically related, i.e., that the coincidence is neither a statistical anomaly nor a WMAP foreground correction problem. If the cold spot does originate from structures at modest redshifts, as we suggest, then there is no remaining need for non-Gaussian processes at the last scattering surface of the CMB to explain the cold spot. The late integrated Sachs-Wolfe effect, already seen statistically for NVSS source counts, can now be seen to operate on a single region. To create the magnitude and angular size of the WMAP cold spot requires a ~140 Mpc radius completely empty void at z<=1 along this line of sight. This is far outside the current expectations of the concordance cosmology, and adds to the anomalies seen in the CMB.Comment: revised version, ApJ, in pres

Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas

The coupling of the spin of electrons to their motional state lies at the heart of recently discovered topological phases of matter. Here we create and detect spin-orbit coupling in an atomic Fermi gas, a highly controllable form of quantum degenerate matter. We reveal the spin-orbit gap via spin-injection spectroscopy, which characterizes the energy-momentum dispersion and spin composition of the quantum states. For energies within the spin-orbit gap, the system acts as a spin diode. To fully inhibit transport, we open an additional spin gap, thereby creating a spin-orbit coupled lattice whose spinful band structure we probe. In the presence of s-wave interactions, such systems should display induced p-wave pairing, topological superfluidity, and Majorana edge states

Free-electron lasers : echoes of photons past

High-harmonic generation is an established method to significantly upshift laser photon energies. Now, researchers at the SLAC National Accelerator Laboratory have used echo concepts to generate coherent high-harmonic output from an electron-beam light source