569 research outputs found
Effects and detection of quantum noise
No full textThis thesis is about random fluctuations over time (or noise) of electric currents and voltages occuring in small (mesoscopic) electronic devices with typical sizes of micro- to nanometre. Even though the theory presented is of a more general nature, research into such systems has been greatly pushed forward by the prospect of building a quantum computer. There are two important aspects to noise which are addressed in this work. The first can be summarised as detection and refers to the idea, that the fluctuations carry information about the microscopic details (geometric design, scattering, temperature) of transport which causes them. The theoretical problem we investigate is then to relate detector signals to fundamental properties of the sample. Secondly, fluctuations can trigger a variety of processes in the environment. Depending on the system one may wish to enhance or diminish such effects. To achieve this goal we study noise-induced effects and the coupling between noise sources and their environment. The precise way in which these fluctuations occur can be found from the theory of Full Counting Statistics (FCS) which provides a cornerstone for this thesis. In chapter 3 the effect of a weak electromagnetic environment on the Full Counting Statistics of a coherent conductor is investigated. We obtain explicit expressions for the correction to the FCS which are further studied by analytical and numerical means. We also present a reinterpretation of the correction in terms of elementary physical events. The major result in that chapter is a universal relation for Full Counting Statistics which holds at arbitrary voltage, temperature and with no regard to the concrete realization of the contact. For FCS this relation takes the form of detailed balance. In chapter 4 we investigate the detection of finite frequency noise using a quantum tunnelling detector. We focus on a concrete experimental setup consisting of a coherent conductor taking the role of the noise source and a tunnel junction (the detector) which is capacitively coupled to it. We show that the detector rate in a certain parameter range is dominated by a two-photon process and a process involving two interacting electrons in the coherent conductor. We find an explicit analytical expression for the detector signal in terms of system parameters: tunnel coupling, transmissions, environment, voltage over the conductor and coupling parameter. Our results facilitate the detection of many-particle events in the context of quantum transport, particularly electron-electron interactions. The non-Gaussian higher moments of the distribution of current fluctuations in a mesoscopic conductor contain more information than is present in average current and noise. However they are inherently difficult to measure. In order to facilitate such experiments, we propose a completely new way for measuring the Full Counting Statistics in chapter 5. We study threshold detection with a Josephson junction coupled to a mesoscopic conductor. We show that the detailed dependence of the junction's escape rate is sensitive to the distinct FCS of specific conductors (tunnel junction, diffusive, ballistic). We also address issues related to the measurement procedure notably feedback and dispersiveness of the detector. Our theoretical results facilitate a new type of electric noise measurement: direct measurement of the full distribution of transferred charge.Applied Science
A streamline-diffusion methods for nonconforming finite element approximations applied to convection-diffusion problems
No full textWe consider a nonconforming streamline-diffusion finite element method for solving convection-diffusion problems. The theoretical and numerical investigation for triangular and tetrahedral meshes recently given by John, Maubach and Tobiska has shown that the usual application of the SDFEM gives not a sufficient stabilization. Additional parameter dependent jump terms have been proposed which preserve the same order of convergence as in the conforming case. The error analysis has been essentially based on the existence of a conforming finite element subspace of the nonconforming space. Thus, the analysis can be applied for example to the Crouzeix/Raviart element but not to the nonconforming quadrilateral elements proposed by Rannacher and Turek. In this paper, parameter free new jump terms are developed which allow to handle both the triangular and the quadrilateral case. Numerical experiments support the theoretical predictions. (orig.)Available from TIB Hannover: RR 4487(1997,35) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman
Computations of flows with interfaces using arbitrary Lagrangian Eulerian method
No full textThis work is devoted to the accurate simulation of incompressible two phase flows. The core of our methodology is the use of interface resolving meshes and the arbitrary Lagrangian-Eulerian (ALE) description of the fluid kinematics. Our numerical scheme is based on second order finite elements, a fractional step ? time discretisation, and a special approximation of the curvature to incorporate surface tension effects. We demonstrate the potential of the proposed numerical method by the simulation of a rising bubble and the Rayleigh-Taylor instability problem
Quantitative benchmark computations of two-dimensional bubble dynamics
No full textBenchmark configurations for quantitative validation and comparison of incompressible interfacial flow codes, which model two-dimensional bubbles rising in liquid columns, are proposed. The benchmark quantities: circularity, center of mass, and mean rise velocity are defined and measured to monitor convergence toward a reference solution. Comprehensive studies are undertaken by three independent research groups, two representing Eulerian level set finite-element codes and one representing an arbitrary Lagrangian-Eulerian moving grid approach.
The first benchmark test case considers a bubble with small density and viscosity ratios, which undergoes moderate shape deformation. The results from all codes agree very well allowing for target reference values to be established. For the second test case, a bubble with a very low density compared to that of the surrounding fluid, the results for all groups are in good agreement up to the point of break up, after which all three codes predict different bubble shapes. This highlights the need for the research community to invest more effort in obtaining reference solutions to problems involving break up and coalescence.
Other research groups are encouraged to participate in these benchmarks by contacting the authors and submitting their own data. The reference data for the computed benchmark quantities can also be supplied for validation purposes
Inelastic interaction corrections and universal relations for full counting statistics in a quantum contact
No full textTowards experimental observation of full counting statistics
No full textWe discuss how threshold detectors can be used for a direct measurement of the full counting statistics (FCS) of current fluctuations and how to implement Josephson junctions in this respect. We propose a scheme to characterize the full counting statistics from the current dependence of the escape rate measured. We illustrate the scheme with explicit results for tunnel, diffusive and quasi-ballistic mesoscopic conductors.Kavli Institute of NanoscienceApplied Science
A coupled multigrid method for nonconforming finite element discretizations of the 2D-Stokes equation
No full textAbstract This paper investigates a multigrid method for the solution of the saddle point formulation of the discrete Stokes equation obtained with inf±sup stable nonconforming ®nite elements of lowest order. A smoother proposed by Braess and Sarazin (1997) is used and L 2 -projection as well as simple averaging are considered as prolongation. The W-cycle convergence in the L 2 -norm of the velocity with a rate independently of the level and linearly decreasing with increasing number of smoothing steps is proven. Numerical tests con®rm the theoretically predicted results
The Martian Thermosphere/Ionosphere at High and Low Solar Activities
No full textWe compare here models of the thermosphere/ionosphere of Mars at low and high solar activities, and we present heating rates and efficiencies due to the absorption of solar radiation in the 18 to 2000 Å range. Using neutral model densities from the NCAR Mars Thermospheric General Circulation Model (MTGCM) of Bougher and co-workers, and solar fluxes from W. K. Tobiska, we have modeled the density profiles of 14 ions and 5 minor neutral species. We predict the variations in the ion densities with solar activity, and describe the sources and sinks of the ions. The major sources and sinks differ in some respects from those for the Venus ionosphere, and these differences are discussed as well. We find that the predicted total electron density profile computed using solar fluxes from Tobiska is somewhat different from that obtained using the fluxes of Hinteregger. One possible conclusion is that, at the time of Mariners 6 and 7, the soft x-ray fluxes were midway between those of the Tobiska and Hinteregger spectra
Stoffel, A„ Finite Elemente und Wärmeleitung. Eine Einfuhrung. Weinheim etc., VCH Verlagsgesellschaft 1992. V, 144 S., DM 46.‐. ISBN 3‐527‐28252‐1
No full text- …
