Weak-field Hall effect and static polarizability of Bloch electrons

A theory of the weak field Hall effect of Bloch electrons based on the analysis of the forces acting on electrons is presented. It is argued that the electric current is composed of two contributions, that driven by the electric field along current flow and the non-dissipative contribution originated in demagnetization currents. The Hall resistance as a function of the electron concentration for the tight-binding model of a crystal with square lattice and body-centered cubic lattice is described in detail. For comparison the effect of strong magnetic fields is also discussed

A transmission problem across a fractal self-similar interface

We consider a transmission problem in which the interior domain has infinitely ramified structures. Transmission between the interior and exterior domains occurs only at the fractal component of the interface between the interior and exterior domains. We also consider the sequence of the transmission problems in which the interior domain is obtained by stopping the self-similar construction after a finite number of steps; the transmission condition is then posed on a prefractal approximation of the fractal interface. We prove the convergence in the sense of Mosco of the energy forms associated with these problems to the energy form of the limit problem. In particular, this implies the convergence of the solutions of the approximated problems to the solution of the problem with fractal interface. The proof relies in particular on an extension property. Emphasis is put on the geometry of the ramified domain. The convergence result is obtained when the fractal interface has no self-contact, and in a particular geometry with self-contacts, for which an extension result is proved

Clockwise Stellar Disk and the Dark Mass in the Galactic Center

Two disks of young stars have recently been discovered in the Galactic Center. The disks are rotating in the gravitational field of the central black hole at radii r=0.1-0.3 pc and thus open a new opportunity to measure the central mass. We find that the observed motion of stars in the clockwise disk implies M=4.3+/-0.5 million solar masses for the fiducial distance to the Galactic Center R_0=8 kpc and derive the scaling of M with R_0. As a tool for our estimate we use orbital roulette, a recently developed method. The method reconstructs the three-dimensional orbits of the disk stars and checks the randomness of their orbital phases. We also estimate the three-dimensional positions and orbital eccentricities of the clockwise-disk stars.Comment: Comments: 16 pages, 5 figures, ApJ, in pres

Photo-assisted Andreev reflection as a probe of quantum noise

Andreev reflection, which corresponds to the tunneling of two electrons from a metallic lead to a superconductor lead as a Cooper pair (or vice versa), can be exploited to measure high frequency noise. A detector is proposed, which consists of a normal lead--superconductor circuit, which is capacitively coupled to a mesoscopic circuit where noise is to be measured. We discuss two detector circuits: a single normal metal -- superconductor tunnel junction and a normal metal separated from a superconductor by a quantum dot operating in the Coulomb blockade regime. A substantial DC current flows in the detector circuit when an appropriate photon is provided or absorbed by the mesoscopic circuit, which plays the role of an environment for the junction to which it couples. Results for the current can be cast in all cases in the form of a frequency integral of the excess noise of the environment weighted by a kernel which is specific to the transport process (quasiparticle tunneling, Andreev reflection,...) which is considered. We apply these ideas to the measurement of the excess noise of a quantum point contact and we provide numerical estimates of the detector current.Comment: 19 pages, 11 figure

Volatility in coral cover erodes niche structure, but not diversity, in reef fish assemblages

The world’s coral reefs are experiencing increasing volatility in coral cover, largely because of anthropogenic environmental change, highlighting the need to understand how such volatility will influence the structure and dynamics of reef assemblages. These changes may influence not only richness or evenness but also the temporal stability of species’ relative abundances (temporal beta-diversity). Here, we analyzed reef fish assemblage time series from the Great Barrier Reef to show that, overall, 75% of the variance in abundance among species was attributable to persistent differences in species’ long-term mean abundances. However, the relative importance of stochastic fluctuations in abundance was higher on reefs that experienced greater volatility in coral cover, whereas it did not vary with drivers of alpha-diversity. These findings imply that increased coral cover volatility decreases temporal stability in relative abundances of fishes, a transformation that is not detectable from static measures of biodiversity