A nearly closed ballistic billiard with random boundary transmission

A variety of mesoscopic systems can be represented as a billiard with a random coupling to the exterior at the boundary. Examples include quantum dots with multiple leads, quantum corrals with different kinds of atoms forming the boundary, and optical cavities with random surface refractive index. The specific example we study is a circular (integrable) billiard with no internal impurities weakly coupled to the exterior by a large number of leads with one channel open in each lead. We construct a supersymmetric nonlinear $\sigma$-model by averaging over the random coupling strengths between bound states and channels. The resulting theory can be used to evaluate the statistical properties of any physically measurable quantity in a billiard. As an illustration, we present results for the local density of states.Comment: 5 pages, 1 figur

Scalar and vector Keldysh models in the time domain

The exactly solvable Keldysh model of disordered electron system in a random scattering field with extremely long correlation length is converted to the time-dependent model with extremely long relaxation. The dynamical problem is solved for the ensemble of two-level systems (TLS) with fluctuating well depths having the discrete Z_2 symmetry. It is shown also that the symmetric TLS with fluctuating barrier transparency may be described in terms of the planar Keldysh model with dime-dependent random planar rotations in xy plane having continuous SO(2) symmetry. The case of simultaneous fluctuations of the well depth and barrier transparency is subject to non-abelian algebra. Application of this model to description of dynamic fluctuations in quantum dots and optical lattices is discussed.Comment: 6 pages, 5 eps figures. Extended version of the paper to be published in JETP Lett 89 (2009

Longitudinal Data with Follow-up Truncated by Death: Match the Analysis Method to Research Aims

Diverse analysis approaches have been proposed to distinguish data missing due to death from nonresponse, and to summarize trajectories of longitudinal data truncated by death. We demonstrate how these analysis approaches arise from factorizations of the distribution of longitudinal data and survival information. Models are illustrated using cognitive functioning data for older adults. For unconditional models, deaths do not occur, deaths are independent of the longitudinal response, or the unconditional longitudinal response is averaged over the survival distribution. Unconditional mod- els, such as random effects models fit to unbalanced data, may implicitly impute data beyond the time of death. Fully conditional models stratify the longitudinal response trajectory by time of death. Fully conditional models are effective for describing in- dividual trajectories, in terms of either aging (age, or years from baseline) or dying (years from death). Causal models (principal stratification) as currently applied are fully conditional models, since group differences at one timepoint are described for a cohort that will survive past a later timepoint. Partly conditional models summarize the longitudinal response in the dynamic cohort of survivors. Partly conditional models are serial cross-sectional snapshots of the response, reflecting the average response in survivors at a given timepoint rather than individual trajectories. Joint models of sur- vival and longitudinal response describe the evolving health status of the entire cohort. Researchers using longitudinal data should consider which method of accommodating deaths is consistent with research aims, and use analysis methods accordingly

Finite Size Corrections for the Pairing Hamiltonian

We study the effects of superconducting pairing in small metallic grains. We show that in the limit of large Thouless conductance one can explicitly determine the low energy spectrum of the problem as an expansion in the inverse number of electrons on the grain. The expansion is based on the formal exact solution of the Richardson model. We use this expansion to calculate finite size corrections to the ground state energy, Matveev-Larkin parameter, and excitation energies.Comment: 22 pages, 1 figur

VACUUM CASTING OF ALUMINUM-SILICON COATING ON TUBALLOY URANIUM . Final Report on a part of P.A. No. 390-ML-54-S F.S. 17

Welding is used to fabricate titanium and titanium-alloy components for air-frames, Jet engines, missiles, and chemical equipment. Annong the most important considerations in adapting titanium and its alloys to welded components is to use proper welding procedures and to select alloys that have the required weld-joint properties. The chemical and metallurgical characteristics that affect the selection of welding processes and alloys are discussed. Also, information is presented on surface preparation, welding procedures, and quality control. In addition, detailed data on the mechanical properties of welded joints in the commercial grades of titanium and titanium alloys and how these properties are affected by heat treatment and elevated temperatures are presented. (auth

Nonequilibrium theory of Coulomb blockade in open quantum dots

We develop a non-equilibrium theory to describe weak Coulomb blockade effects in open quantum dots. Working within the bosonized description of electrons in the point contacts, we expose deficiencies in earlier applications of this method, and address them using a 1/N expansion in the inverse number of channels. At leading order this yields the self-consistent potential for the charging interaction. Coulomb blockade effects arise as quantum corrections to transport at the next order. Our approach unifies the phase functional and bosonization approaches to the problem, as well as providing a simple picture for the conductance corrections in terms of renormalization of the dot's elastic scattering matrix, which is obtained also by elementary perturbation theory. For the case of ideal contacts, a symmetry argument immediately allows us to conclude that interactions give no signature in the averaged conductance. Non-equilibrium applications to the pumped current in a quantum pump are worked out in detail.Comment: Published versio

Quantum dots with two electrons: Singlet-triplet transitions

The magnetic character of the ground-state of two electrons on a double quantum dot, connected in series to left and right single-channel leads, is considered. By solving exactly for the spectrum of the two interacting electrons, it is found that the coupling to the continuum of propagating states on the leads, in conjunction with the electron-electron interactions, may result in a delocalization of the bound state of the two electrons. This, in turn, reduces significantly the range of the Coulomb interaction parameters over which singlet-triplet transitions can be realized. It is also found that the coupling to the leads favors the singlet ground-state.Comment: 8 pages, submitted to Phys. Rev.