Asymptotics of large eigenvalues for a class of band matrices

We investigate the asymptotic behaviour of large eigenvalues for a class of finite difference self-adjoint operators with compact resolvent in $l^2$

A Physical Realization of the Generalized PT-, C-, and CPT-Symmetries and the Position Operator for Klein-Gordon Fields

Generalized parity (P), time-reversal (T), and charge-conjugation (C)operators were initially definedin the study of the pseudo-Hermitian Hamiltonians. We construct a concrete realization of these operators for Klein-Gordon fields and show that in this realization PT and C operators respectively correspond to the ordinary time-reversal and charge-grading operations. Furthermore, we present a complete description of the quantum mechanics of Klein-Gordon fields that is based on the construction of a Hilbert space with a relativistically invariant, positive-definite, and conserved inner product. In particular we offer a natural construction of a position operator and the corresponding localized and coherent states. The restriction of this position operator to the positive-frequency fields coincides with the Newton-Wigner operator. Our approach does not rely on the conventional restriction to positive-frequency fields. Yet it provides a consistent quantum mechanical description of Klein-Gordon fields with a genuine probabilistic interpretation.Comment: 20 pages, published versio

Quantum Inverse Square Interaction

Hamiltonians with inverse square interaction potential occur in the study of a variety of physical systems and exhibit a rich mathematical structure. In this talk we briefly mention some of the applications of such Hamiltonians and then analyze the case of the N-body rational Calogero model as an example. This model has recently been shown to admit novel solutions, whose properties are discussed.Comment: Talk presented at the conference "Space-time and Fundamental Interactions: Quantum Aspects" in honour of Prof. A.P.Balachandran's 65th birthday, Vietri sul Mare, Italy, 26 - 31 May, 2003, Latex file, 9 pages. Some references added in the replaced versio

The organizational dynamics enabling patient portal impacts upon organizational performance and patient health: a qualitative study of Kaiser Permanente.

BackgroundPatient portals may lead to enhanced disease management, health plan retention, changes in channel utilization, and lower environmental waste. However, despite growing research on patient portals and their effects, our understanding of the organizational dynamics that explain how effects come about is limited.MethodsThis paper uses qualitative methods to advance our understanding of the organizational dynamics that influence the impact of a patient portal on organizational performance and patient health. The study setting is Kaiser Permanente, the world's largest not-for-profit integrated delivery system, which has been using a portal for over ten years. We interviewed eighteen physician leaders and executives particularly knowledgeable about the portal to learn about how they believe the patient portal works and what organizational factors affect its workings. Our analytical framework centered on two research questions. (1) How does the patient portal impact care delivery to produce the documented effects?; and (2) What are the important organizational factors that influence the patient portal's development?ResultsWe identify five ways in which the patient portal may impact care delivery to produce reported effects. First, the portal's ability to ease access to services improves some patients' satisfaction as well as changes the way patients seek care. Second, the transparency and activation of information enable some patients to better manage their care. Third, care management may also be improved through augmented patient-physician interaction. This augmented interaction may also increase the 'stickiness' of some patients to their providers. Forth, a similar effect may be triggered by a closer connection between Kaiser Permanente and patients, which may reduce the likelihood that patients will switch health plans. Finally, the portal may induce efficiencies in physician workflow and administrative tasks, stimulating certain operational savings and deeper involvement of patients in medical decisions. Moreover, our analysis illuminated seven organizational factors of particular importance to the portal's development--and thereby ability to impact care delivery: alignment with financial incentives, synergy with existing IT infrastructure and operations, physician-led governance, inclusive decision making and knowledge sharing, regional flexibility to implementation, continuous innovation, and emphasis on patient-centered design.ConclusionsThese findings show how organizational dynamics enable the patient portal to affect care delivery by summoning organization-wide support for and use of a portal that meets patient needs

The heat kernel of the compactified D=11 supermembrane with non-trivial winding

We study the quantization of the regularized hamiltonian, $H$, of the compactified D=11 supermembrane with non-trivial winding. By showing that $H$ is a relatively small perturbation of the bosonic hamiltonian, we construct a Dyson series for the heat kernel of $H$ and prove its convergence in the topology of the von Neumann-Schatten classes so that $e^{-Ht}$ is ensured to be of finite trace. The results provided have a natural interpretation in terms of the quantum mechanical model associated to regularizations of compactified supermembranes. In this direction, we discuss the validity of the Feynman path integral description of the heat kernel for D=11 supermembranes and obtain a matrix Feynman-Kac formula.Comment: 19 pages. AMS LaTeX. A whole new section was added and some other minor changes in style where mad

Spectral Analysis of a Two Body Problem with Zero Range Perturbation

We consider a class of singular, zero-range perturbations of the Hamiltonian of a quantum system composed by a test particle and a harmonic oscillators in dimension one, two and three and we study its spectrum. In facts we give a detailed characterization of point spectrum and its asymptotic behavior with respect to the parameters entering the Hamiltonian. We also partially describe the positive spectrum and scattering properties of the Hamiltonian.Comment: Version submitted for publication, AMStex, 22 page

Coupled anharmonic oscillators: the Rayleigh-Ritz approach versus the collocation approach

For a system of coupled anharmonic oscillators we compare the convergence rate of the variational collocation approach presented recently by Amore and Fernandez (2010 Phys.Scr.81 045011) with the one obtained using the optimized Rayleigh-Ritz (RR) method. The monotonic convergence of the RR method allows us to obtain more accurate results at a lower computational cost.Comment: 7 pages, 1 figur

A Number-Theoretic Error-Correcting Code

In this paper we describe a new error-correcting code (ECC) inspired by the Naccache-Stern cryptosystem. While by far less efficient than Turbo codes, the proposed ECC happens to be more efficient than some established ECCs for certain sets of parameters. The new ECC adds an appendix to the message. The appendix is the modular product of small primes representing the message bits. The receiver recomputes the product and detects transmission errors using modular division and lattice reduction

Edge Currents for Quantum Hall Systems, I. One-Edge, Unbounded Geometries

Devices exhibiting the integer quantum Hall effect can be modeled by one-electron Schroedinger operators describing the planar motion of an electron in a perpendicular, constant magnetic field, and under the influence of an electrostatic potential. The electron motion is confined to unbounded subsets of the plane by confining potential barriers. The edges of the confining potential barrier create edge currents. In this, the first of two papers, we prove explicit lower bounds on the edge currents associated with one-edge, unbounded geometries formed by various confining potentials. This work extends some known results that we review. The edge currents are carried by states with energy localized between any two Landau levels. These one-edge geometries describe the electron confined to certain unbounded regions in the plane obtained by deforming half-plane regions. We prove that the currents are stable under various potential perturbations, provided the perturbations are suitably small relative to the magnetic field strength, including perturbations by random potentials. For these cases of one-edge geometries, the existence of, and the estimates on, the edge currents imply that the corresponding Hamiltonian has intervals of absolutely continuous spectrum. In the second paper of this series, we consider the edge currents associated with two-edge geometries describing bounded, cylinder-like regions, and unbounded, strip-like, regions.Comment: 68 page