Edge Channel Interference Controlled by Landau Level Filling

We study the visibility of Aharonov-Bohm interference in an electronic Mach-Zehnder interferometer (MZI) in the integer quantum Hall regime. The visibility is controlled by the filling factor $\nu$ and is observed only between $\nu \approx 2.0$ and 1.0, with an unexpected maximum near $\nu=1.5$. Three energy scales extracted from the temperature and voltage dependences of the visibility change in a very similar way with the filling factor, indicating that the different aspects of the interference depend sensitively on the local structure of the compressible and incompressible strips forming the quantum Hall edge channels.Comment: 5 pages, 5 figures, final version accepted for publication in Phys. Rev.

Counting Statistics and Dephasing Transition in an Electronic Mach-Zehnder Interferometer

It was recently suggested that a novel type of phase transition may occur in the visibility of electronic Mach-Zehnder Interferometers. Here, we present experimental evidence for the existence of this transition. The transition is induced by strongly non-Gaussian noise that originates from the strong coupling of a quantum point contact to the interferometer. We provide a transparent physical picture of the effect, by exploiting a close analogy to the neutrino-oscillations of particle physics. In addition, our experiment constitutes a probe of the singularity of the elusive full counting statistics of a quantum point contact.Comment: 7 pages, 4 figures (+Supplement 8 pages, 9 figures

Nonlocal vortex motion in mesoscopic amorphous Nb0.7Ge0.3 structures

We study nonlocal vortex transport in mesoscopic amorphous Nb0.7Ge0.3 samples. A dc current I is passed through a wire connected via a perpendicular channel, of a length L= 2-5 um, with a pair of voltage probes where a nonlocal response Vnl ~ I is measured. The maximum of Rnl=Vnl/I for a given temperature occurs at an L-independent magnetic field and is proportional to 1/L. The results are interpreted in terms of the dissipative vortex motion along the channel driven by a remote current, and can be understood in terms of a simple model.Comment: 4 pages, 3 figure

Tsunami observations by coastal ocean radar

When tsunami waves propagate across the open ocean, they are steered by the Coriolis effect and refraction due to gentle gradients in the bathymetry on scales longer than the wavelength. When the wave encounters steep gradients at the edges of continental shelves and at the coast, the wave becomes nonlinear and conservation of momentum produces squirts of surface current at the head of submerged canyons and in coastal bays. High frequency (HF) coastal ocean radar is well conditioned to observe the surface current bursts at the edge of the continental shelf and give a warning of 40 minutes to 2 hours when the shelf is 50 to 200km wide. The period of tsunami waves is invariant over changes in bathymetry and is in the range 2 to 30 minutes. Wavelengths for tsunamis (in 500 to 3000m depth) are in the range 8.5 to over 200 km, and on a shelf where the depth is about 50m (as in the Great Barrier Reef (GBR)) the wavelengths are in the range 2.5 to 30 km. In the use of HF radar technology, there is a trade-off between the precision of surface current speed measurements and time resolution. It is shown that the phased array HF ocean surface radar being deployed in the GBR and operating in a routine way for mapping surface currents, can resolve surface current squirts from tsunamis in the wave period range 20 to 30 minutes and in the wavelength range greater than about 6 km. An advantage in signal-to-noise ratio can be obtained from the prior knowledge of the spatial pattern of the squirts at the edge of the continental shelf, and it is estimated that, with this analysis, the time resolution of the GBR radar may be reduced to about 2.5 minutes, which corresponds to a capability to detect tsunamis at the shelf edge in the period range 5 to 30 minutes. It is estimated that the lower limit of squirt velocity detection at the shelf edge would correspond to a tsunami with water elevation of about 2.5 cm in the open ocean. This means that the GBR HF radar is well conditioned for use as a monitor of small, as well as larger, tsunamis and has the potential to contribute to the understanding of tsunami genesis research

A rarefaction-tracking method for hyperbolic conservation laws

We present a numerical method for scalar conservation laws in one space dimension. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compression waves. The solution is represented by particles that carry function values and move according to the method of characteristics. Between two neighboring particles, an interpolation is defined by an analytical similarity solution of the conservation law. An interaction of particles represents a collision of characteristics. The resulting shock is resolved by merging particles so that the total area under the function is conserved. The method is variation diminishing, nevertheless, it has no numerical dissipation away from shocks. Although shocks are not explicitly tracked, they can be located accurately. We present numerical examples, and outline specific applications and extensions of the approach.Comment: 21 pages, 7 figures. Similarity 2008 conference proceeding

An Unstaggered Constrained Transport Method for the 3D Ideal Magnetohydrodynamic Equations

Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with nonlinear numerical instabilities. One approach for controlling the discrete divergence is through a so-called constrained transport method, which is based on first predicting a magnetic field through a standard finite volume solver, and then correcting this field through the appropriate use of a magnetic vector potential. In this work we develop a constrained transport method for the 3D ideal MHD equations that is based on a high-resolution wave propagation scheme. Our proposed scheme is the 3D extension of the 2D scheme developed by Rossmanith [SIAM J. Sci. Comp. 28, 1766 (2006)], and is based on the high-resolution wave propagation method of Langseth and LeVeque [J. Comp. Phys. 165, 126 (2000)]. In particular, in our extension we take great care to maintain the three most important properties of the 2D scheme: (1) all quantities, including all components of the magnetic field and magnetic potential, are treated as cell-centered; (2) we develop a high-resolution wave propagation scheme for evolving the magnetic potential; and (3) we develop a wave limiting approach that is applied during the vector potential evolution, which controls unphysical oscillations in the magnetic field. One of the key numerical difficulties that is novel to 3D is that the transport equation that must be solved for the magnetic vector potential is only weakly hyperbolic. In presenting our numerical algorithm we describe how to numerically handle this problem of weak hyperbolicity, as well as how to choose an appropriate gauge condition. The resulting scheme is applied to several numerical test cases.Comment: 46 pages, 12 figure

A class of residual distribution schemes and their relation to relaxation systems

Residual distributions (RD) schemes are a class of of high-resolution finite volume methods for unstructured grids. A key feature of these schemes is that they make use of genuinely multidimensional (approximate) Riemann solvers as opposed to the piecemeal 1D Riemann solvers usually employed by finite volume methods. In 1D, LeVeque and Pelanti [J. Comp. Phys. 172, 572 (2001)] showed that many of the standard approximate Riemann solver methods (e.g., the Roe solver, HLL, Lax-Friedrichs) can be obtained from applying an exact Riemann solver to relaxation systems of the type introduced by Jin and Xin [Comm. Pure Appl. Math. 48, 235 (1995)]. In this work we extend LeVeque and Pelanti's results and obtain a multidimensional relaxation system from which multidimensional approximate Riemann solvers can be obtained. In particular, we show that with one choice of parameters the relaxation system yields the standard N-scheme. With another choice, the relaxation system yields a new Riemann solver, which can be viewed as a genuinely multidimensional extension of the local Lax-Friedrichs scheme. This new Riemann solver does not require the use Roe-Struijs-Deconinck averages, nor does it require the inversion of an m-by-m matrix in each computational grid cell, where $m$ is the number of conserved variables. Once this new scheme is established, we apply it on a few standard cases for the 2D compressible Euler equations of gas dynamics. We show that through the use of linear-preserving limiters, the new approach produces numerical solutions that are comparable in accuracy to the N-scheme, despite being computationally less expensive.Comment: 46 pages, 14 figure