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

Canonical analysis based on scatter matrices.

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix are considered in more detail. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimator and S-estimates through theoretical and simulation studies. The theory is illustrated by an example.Canonical correlations; Canonical variables; Canonical vectors; Covariance; Covariance determinant estimator; Determinant estimator; Distribution; Efficiency; Estimator; Functions; Influence function; Matrix; Scatter; Shape matrix; Sign covariance mix; Simulation; Studies; Theory; Tyler's estimate;

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

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

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

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

Influence of temperature gradients on tunnel junction thermometry below 1 K: cooling and electron-phonon coupling

We have studied thermal gradients in thin Cu and AlMn wires, both experimentally and theoretically. In the experiments, the wires were Joule heated non-uniformly at sub-Kelvin temperatures, and the resulting temperature gradients were measured using normal metal-insulator-superconducting tunnel junctions. The data clearly shows that even in reasonably well conducting thin wires with a short ($\sim 10 \mu$m) non-heated portion, significant temperature differences can form. In most cases, the measurements agree well with a model which includes electron-phonon interaction and electronic thermal conductivity by the Wiedemann-Franz law.Comment: J. Low Temp. Phys. in pres

Canonical analysis based on scatter matrices.

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example.Canonical correlations; Canonical variables; Canonical vectors; Covariance; Covariance determinant estimator; Determinant estimator; Distribution; Efficiency; Estimator; Functions; Influence function; Matrix; Principal components; Scatter; Shape matrix; Sign; Sign covariance mix; Simulation; Studies; Theory; Tyler's estimate; Variance;

Asymptotic expansions of the solutions of the Cauchy problem for nonlinear parabolic equations

Let $u$ be a solution of the Cauchy problem for the nonlinear parabolic equation $$\partial_t u=\Delta u+F(x,t,u,\nabla u) \quad in \quad{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad in \quad{\bf R}^N,$$ and assume that the solution $u$ behaves like the Gauss kernel as $t\to\infty$. In this paper, under suitable assumptions of the reaction term $F$ and the initial function $\varphi$, we establish the method of obtaining higher order asymptotic expansions of the solution $u$ as $t\to\infty$. This paper is a generalization of our previous paper, and our arguments are applicable to the large class of nonlinear parabolic equations