One and two dimensional tunnel junction arrays in weak Coulomb blockade regime-absolute accuracy in thermometry

We have investigated one and two dimensional (1D and 2D) arrays of tunnel junctions in partial Coulomb blockade regime. The absolute accuracy of the Coulomb blockade thermometer is influenced by the external impedance of the array, which is not the same in the different topologies of 1D and 2D arrays. We demonstrate, both by experiment and by theoretical calculations in simple geometries, that the 1D structures are better in this respect. Yet in both 1D and 2D, the influence of the environment can be made arbitrarily small by making the array sufficiently large.Comment: 11 pages, 3 figure

FLOQUET PROBLEM AND CENTER MANIFOLD REDUCTION FOR ORDINARY DIFFERENTIAL OPERATORS WITH PERIODIC COEFFICIENTS IN HILBERT SPACES

A first order differential equation with a periodic operator coefficient acting in a pair of Hilbert spaces is considered. This setting models both elliptic equations with periodic coefficients in a cylinder and parabolic equations with time periodic coefficients. Our main results are a construction of a pointwise projector and a spectral splitting of the system into a finite-dimensional system of ordinary differential equations with constant coefficients and an infinite-dimensional part whose solutions have better properties in a certain sense. This complements the well-known asymptotic results for periodic hypoelliptic problems in cylinders and for elliptic problems in quasicylinders obtained by P. Kuchment and S. A. Nazarov, respectively. As an application, a center manifold reduction is presented for a class of nonlinear ordinary differential equations in Hilbert spaces with periodic coefficients. This result generalizes the known case with constant coefficients explored by A. Mielke.Peer reviewe

Spectral theory of Toeplitz and Hankel operators on the Bergman space A1

The Fredholm properties of Toeplitz operators on the Bergman space A2 have been well-known for continuous symbols since the 1970s. We investigate the case p=1 with continuous symbols under a mild additional condition, namely that of the logarithmic vanishing mean oscillation in the Bergman metric. Most differences are related to boundedness properties of Toeplitz operators acting on Ap that arise when we no longer have 1<p<∞; in particular bounded Toeplitz operators on A1 were characterized completely very recently but only for bounded symbols. We also consider compactness of Hankel operators on A1

Asymptotics of the spectrum of the mixed boundary value problem for the Laplace operator in a thin spindle-shaped domain

Free access to full-text articles is allowed 3 years after publication of the corresponding issue. Access to full-text articles of this issue will be allowed starting from April 1, 2024The asymptotics is examined for solutions to the spectral problem for the Laplace operator in a d-dimensional thin, of diameter O(h), spindle-shaped domain Omega(h) with the Dirichlet condition on small, of size h +0, an ordinary differential equation on the axis (-1, 1) (sic) z of the spindle arises with a coefficient degenerating at the points z = +/- 1 and moreover, without any boundary condition because the requirement on the boundedness of eigenfunctions makes the limit spectral problem well-posed. Error estimates are derived for the one-dimensional model but in the case of d = 3 it is necessary to construct boundary layers near the sets Gamma(h)(+/-) and in the case of d = 2 it is necessary to deal with selfadjoint extensions of the differential operator. The extension parameters depend linearly on In h so that its eigenvalues are analytic functions in the variable 1/vertical bar ln h vertical bar As a result, in all dimensions the one-dimensional model gets the power-law accuracy O(h(delta)d ) with an exponent delta(d) > 0. First (the smallest) eigenvalues, positive in Omega(h) and null in (-1, 1), require individual treatment. Also, infinite asymptotic series are discussed, as well as the static problem (without the spectral parameter) and related shapes of thin domains.Peer reviewe

Electron energy relaxation by phonons in the Kondo condensate

We have used normal metal-insulator-superconductor tunnel junctions as thermometers at sub-Kelvin temperatures to study the electron-phonon (e-p) interaction in thin Aluminum films doped with Manganese, as a function of Manganese concentration. Mn in Al is known to be a Kondo impurity with extremely high Kondo temperature $T_K \sim$ 500 K, thus our results probe the e-p coupling in the fully spin compensated, unitary limit. The temperature dependence of the e-p interaction is consistent with the existing theory for disordered metals, however full theory including the Kondo effect has not been worked out yet. The strength of the interaction decreases with increasing Manganese concentration, providing a means to improve sensitivity of detectors and efficiency of solid state coolers

New results and open problems on Toeplitz operators in Bergman spaces

We discuss some of the recent progress in the field of Toeplitz operators acting on Bergman spaces of the unit disk, formulate some new results, and describe a list of open problems -- concerning boundedness, compactness and Fredholm properties -- which was presented at the conference "Recent Advances in Function Related Operator Theory'' in Puerto Rico in March 2010

Origin of the hysteresis in bilayer 2D systems in the quantum Hall regime

The hysteresis observed in the magnetoresistance of bilayer 2D systems in the quantum Hall regime is generally attributed to the long time constant for charge transfer between the 2D systems due to the very low conductivity of the quantum Hall bulk states. We report electrometry measurements of a bilayer 2D system that demonstrate that the hysteresis is instead due to non-equilibrium induced current. This finding is consistent with magnetometry and electrometry measurements of single 2D systems, and has important ramifications for understanding hysteresis in bilayer 2D systems.Comment: 4 pages, 3 figs. Accepted for publication in PR

Electrometry using the quantum Hall effect in a bilayer 2D electron system

We discuss the development of a sensitive electrometer that utilizes a two-dimensional electron gas (2DEG) in the quantum Hall regime. As a demonstration, we measure the evolution of the Landau levels in a second, nearby 2DEG as the applied perpendicular magnetic field is changed, and extract an effective mass for electrons in GaAs that agrees within experimental error with previous measurements.Comment: 3.5 pages, 3 figures, submitted to APL