Stationary phase slip state in quasi-one-dimensional rings

The nonuniform superconducting state in a ring in which the order parameter vanishing at one point is studied. This state is characterized by a jump of the phase by $\pi$ at the point where the order parameter becomes zero. In uniform rings such a state is a saddle-point state and consequently unstable. However, for non-uniform rings with e.g. variations of geometrical or physical parameters or with attached wires this state can be stabilized and may be realized experimentally.Comment: 6 pages, 7 figures, RevTex 4.0 styl

Data compression and regression based on local principal curves.

Frequently the predictor space of a multivariate regression problem of the type y = m(x_1, …, x_p ) + ε is intrinsically one-dimensional, or at least of far lower dimension than p. Usual modeling attempts such as the additive model y = m_1(x_1) + … + m_p (x_p ) + ε, which try to reduce the complexity of the regression problem by making additional structural assumptions, are then inefficient as they ignore the inherent structure of the predictor space and involve complicated model and variable selection stages. In a fundamentally different approach, one may consider first approximating the predictor space by a (usually nonlinear) curve passing through it, and then regressing the response only against the one-dimensional projections onto this curve. This entails the reduction from a p- to a one-dimensional regression problem. As a tool for the compression of the predictor space we apply local principal curves. Taking things on from the results presented in Einbeck et al. (Classification – The Ubiquitous Challenge. Springer, Heidelberg, 2005, pp. 256–263), we show how local principal curves can be parametrized and how the projections are obtained. The regression step can then be carried out using any nonparametric smoother. We illustrate the technique using data from the physical sciences

Density-functional study of Cu atoms, monolayers, and coadsorbates on polar ZnO surfaces

The structure and electronic properties of single Cu atoms, copper monolayers and thin copper films on the polar oxygen and zinc terminated surfaces of ZnO are studied using periodic density-functional calculations. We find that the binding energy of Cu atoms sensitively depends on how charge neutrality of the polar surfaces is achieved. Bonding is very strong if the surfaces are stabilized by an electronic mechanism which leads to partially filled surface bands. As soon as the surface bands are filled (either by partial Cu coverage, by coadsorbates, or by the formation of defects), the binding energy decreases significantly. In this case, values very similar to those found for nonpolar surfaces and for copper on finite ZnO clusters are obtained. Possible implications of these observations concerning the growth mode of copper on polar ZnO surfaces and their importance in catalysis are discussed.Comment: 6 pages with 2 postscript figures embedded. Uses REVTEX and epsf macro

Mechanical On-Chip Microwave Circulator

Nonreciprocal circuit elements form an integral part of modern measurement and communication systems. Mathematically they require breaking of time-reversal symmetry, typically achieved using magnetic materials and more recently using the quantum Hall effect, parametric permittivity modulation or Josephson nonlinearities. Here, we demonstrate an on-chip magnetic-free circulator based on reservoir engineered optomechanical interactions. Directional circulation is achieved with controlled phase-sensitive interference of six distinct electro-mechanical signal conversion paths. The presented circulator is compact, its silicon-on-insulator platform is compatible with both superconducting qubits and silicon photonics, and its noise performance is close to the quantum limit. With a high dynamic range, a tunable bandwidth of up to 30 MHz and an in-situ reconfigurability as beam splitter or wavelength converter, it could pave the way for superconducting qubit processors with integrated and multiplexed on-chip signal processing and readout.Comment: References have been update