Investigation of ground vibration from circular tunnels using a 2.5D FE/BE model of tunnel and ground

A numerical model of a circular tunnel using the 2.5D finite element and boundary element method is described. This makes use of the constant geometry in the axial direction so that a two-dimensional model is solved for a series of wavenumbers. The full 3D solution can be recovered by a Fourier transformation. The response of the tunnel structure is analysed first. Then, the vibration at certain points on the ground surface is predicted using the tunnel-soil model. Finally, a parametric study is carried out to show the influence of different aspects of tunnel design to the vibration in the ground

Observation of Andreev Surface Bound States in the 3-K phase Region of Sr_2RuO_4

The tunneling spectrum of the superconducting phase with T_c ~ 3.0 K has been measured in the Ru-embedded region of Sr_2RuO_4 using cleaved junctions. A sharp zero-bias conductance peak (ZBCP) has been observed below 3 K. All characteristics of this ZBCP suggest that it originates from Andreev surface bound states, indicating that the pairing in the 3-K phase is also non-s-wave. Below the bulk T_c of Sr_2RuO_4 (~1.5 K), a bell-shaped ZBCP was found. This supports that there is a phase transition in the 3-K phase region near the bulk T_c.Comment: 4 pages, to appear in Phys. Rev. Lett. 87 (2001

Amplifier for scanning tunneling microscopy at MHz frequencies

Conventional scanning tunneling microscopy (STM) is limited to a bandwidth of circa 1kHz around DC. Here, we develop, build and test a novel amplifier circuit capable of measuring the tunneling current in the MHz regime while simultaneously performing conventional STM measurements. This is achieved with an amplifier circuit including a LC tank with a quality factor exceeding 600 and a home-built, low-noise high electron mobility transistor (HEMT). The amplifier circuit functions while simultaneously scanning with atomic resolution in the tunneling regime, i.e. at junction resistances in the range of giga-ohms, and down towards point contact spectroscopy. To enable high signal-to-noise and meet all technical requirements for the inclusion in a commercial low temperature, ultra-high vacuum STM, we use superconducting cross-wound inductors and choose materials and circuit elements with low heat load. We demonstrate the high performance of the amplifier by spatially mapping the Poissonian noise of tunneling electrons on an atomically clean Au(111) surface. We also show differential conductance spectroscopy measurements at 3MHz, demonstrating superior performance over conventional spectroscopy techniques. Further, our technology could be used to perform impedance matched spin resonance and distinguish Majorana modes from more conventional edge states

Preasymptotic Convergence of Randomized Kaczmarz Method

Kaczmarz method is one popular iterative method for solving inverse problems, especially in computed tomography. Recently, it was established that a randomized version of the method enjoys an exponential convergence for well-posed problems, and the convergence rate is determined by a variant of the condition number. In this work, we analyze the preasymptotic convergence behavior of the randomized Kaczmarz method, and show that the low-frequency error (with respect to the right singular vectors) decays faster during first iterations than the high-frequency error. Under the assumption that the inverse solution is smooth (e.g., sourcewise representation), the result explains the fast empirical convergence behavior, thereby shedding new insights into the excellent performance of the randomized Kaczmarz method in practice. Further, we propose a simple strategy to stabilize the asymptotic convergence of the iteration by means of variance reduction. We provide extensive numerical experiments to confirm the analysis and to elucidate the behavior of the algorithms.Comment: 20 page

Hawking radiation from the Schwarzschild black hole with a global monopole via gravitational anomaly

Hawking flux from the Schwarzschild black hole with a global monopole is obtained by using Robinson and Wilczek's method. Adopting a dimension reduction technique, the effective quantum field in the (3+1)--dimensional global monopole background can be described by an infinite collection of the (1+1)--dimensional massless fields if neglecting the ingoing modes near the horizon, where the gravitational anomaly can be cancelled by the (1+1)--dimensional black body radiation at the Hawking temperature.Comment: 4 pages, no figure, 3nd revsion with one reference adde

Landau-Zener-Stuckelberg interference in a multi-anticrossing system

We propose a universal analytical method to study the dynamics of a multi-anticrossing system subject to driving by one single large-amplitude triangle pulse, within its time scales smaller than the dephasing time. Our approach can explain the main features of the Landau-Zener-Stuckelberg interference patterns recently observed in a tripartite system [Nature Communications 1:51 (2010)]. In particular, we focus on the effects of the size of anticrossings on interference and compare the calculated interference patterns with numerical simulations. In addition, Fourier transform of the patterns can extract information on the energy level spectrum.Comment: 6 pages, 5 figure