Scattering in one dimension: The coupled Schroedinger equation, threshold behaviour and Levinson's theorem

We formulate scattering in one dimension due to the coupled Schr\"{o}dinger equation in terms of the $S$ matrix, the unitarity of which leads to constraints on the scattering amplitudes. Levinson's theorem is seen to have the form $\eta(0) = \pi (n_b + 1/2 n - 1/2 N)$, where $\eta(0)$ is the phase of the $S$ matrix at zero energy, $n_b$ the number of bound states with nonzero binding energy, $n$ the number of half-bound states, and $N$ the number of coupled equations. In view of the effects due to the half-bound states, the threshold behaviour of the scattering amplitudes is investigated in general, and is also illustrated by means of particular potential models.Comment: to appear in Journal of Mathematic Physics, RevTex, 16 pages, 3 figures (PostScript

Evidence on a DSGE Business Cycle model subject to Neutral and Investment-Specific Technology Shocks using Bayesian Model Averaging

The empirical support for a DSGE type of real business cycle model with two technology shocks is evaluated using a Bayesian model averaging procedure that makes use of a finite mixture of many models within the class of vector autoregressive (VAR) processes. The linear VAR model is extended to permit equilibrium restrictions and restrictions on long-run responses to technology shocks apart from having a range of lag structures and deterministic processes. These model features are weighted as posterior probabilites and computed using MCMC and analytical methods. Uncertainty exists as to the most appropriate model for our data, with five models receiving significant support. The model set used has substantial implications for the results obtained. We do find support for a number of features implied by the real business cycle model. Business cycle volatility seems more due to investment specific technology shocks than neutral technology shocks and this result is robust to model specification. These techonolgy schocks appear to account for all stochastic trends in our system after 1984. we provide evidence on the uncertainty bands associated with these results.

Model Uncertainty and Bayesian Model Averaging in Vector Autoregressive Processes

Economic forecasts and policy decisions are often informed by empirical analysis based on econometric models. However, inference based upon a single model, when several viable models exist, limits its usefulness. Taking account of model uncertainty, a Bayesian model averaging procedure is presented which allows for unconditional inference within the class of vector autoregressive (VAR) processes. Several features of VAR process are investigated. Measures on manifolds are employed in order to elicit uniform priors on subspaces defined by particular structural features of VARs. The features considered are the number and form of the equilibrium economic relations and deterministic processes. Posterior probabilities of these features are used in a model averaging approach for forecasting and impulse response analysis. The methods are applied to investigate stability of the "Great Ratios" in U.S. consumption, investment and income, and the presence and effects of permanent shocks in these series. The results obtained indicate the feasibility of the proposed method.Posterior probability; Grassman manifold; Orthogonal group; Cointegration; Model averaging; Stochastic trend; Impulse response; Vector autoregressive model.

Improper priors with well defined Bayes Factors

While some improper priors have attractive properties, it is generally claimed that Bartlett’s paradox implies that using improper priors for the parameters in alternative models results in Bayes factors that are not well defined, thus preventing model comparison in this case. In this paper we demonstrate, using well understood principles underlying what is already common practice, that this latter result is not generally true and so expand the class of priors that may be used for computing posterior odds to two classes of improper priors: the shrink age prior; and a prior based upon a nesting argument. Using a new representation of the issue of undefined Bayes factors, we develop classes of improper priors from which well defined Bayes factors result. However, as the use of such priors is not free of problems, we include discussion on the issues with using such priors for model comparison.Improper prior; Bayes factor; marginal likelihood; shrinkage prior; measure

Free initial wave packets and the long-time behavior of the survival and nonescape probabilities

The behavior of both the survival S(t) and nonescape P(t) probabilities at long times for the one-dimensional free particle system is shown to be closely connected to that of the initial wave packet at small momentum. We prove that both S(t) and P(t) asymptotically exhibit the same power-law decrease at long times, when the initial wave packet in momentum representation behaves as O(1) or O(k) at small momentum. On the other hand, if the integer m becomes greater than 1, S(t) and P(t) decrease in different power-laws at long times.Comment: 4 pages, 3 figures, Title and organization changed, however the results not changed, To appear in Phys. Rev.

WKB approximation for multi-channel barrier penetrability

Using a method of local transmission matrix, we generalize the well-known WKB formula for a barrier penetrability to multi-channel systems. We compare the WKB penetrability with a solution of the coupled-channels equations, and show that the WKB formula works well at energies well below the lowest adiabatic barrier. We also discuss the eigen-channel approach to a multi-channel tunneling, which may improve the performance of the WKB formula near and above the barrier.Comment: 15 pages, 4 eps figure

Atomic quasi-Bragg diffraction in a magnetic field

We report on a new technique to split an atomic beam coherently with an easily adjustable splitting angle. In our experiment metastable helium atoms in the |{1s2s}^3S_1 M=1> state diffract from a polarization gradient light field formed by counterpropagating \sigma^+ and \sigma^- polarized laser beams in the presence of a homogeneous magnetic field. In the near-adiabatic regime, energy conservation allows the resonant exchange between magnetic energy and kinetic energy. As a consequence, symmetric diffraction of |M=0> or |M=-1> atoms in a single order is achieved, where the order can be chosen freely by tuning the magnetic field. We present experimental results up to 6th order diffraction (24 \hbar k momentum splitting, i.e., 2.21 m/s in transverse velocity) and present a simple theoretical model that stresses the similarity with conventional Bragg scattering. The resulting device constitutes a flexible, adjustable, large-angle, three-way coherent atomic beam splitter with many potential applications in atom optics and atom interferometry.Comment: 4 pages, 5 figure

Anomalous Fisher-like zeros for the canonical partition function of noninteracting fermions

Noninteracting fermions, placed in a system with a continuous density of states, may have zeros in the $N$-fermion canonical partition function on the positive real $\beta$ axis (or very close to it), even for a small number of particles. This results in a singular free energy, and instability in other thermal properties of the system. In the context of trapped fermions in a harmonic oscillator, these zeros are shown to be unphysical. By contrast, similar bosonic calculations with continuous density of states yield sensible results.Noninteracting fermions, placed in a system with a continuous density of states yield sensible results.Comment: 5 pages and 5 figure

Health care reform and financial crisis in the Netherlands:consequences for the financial arena of health care organizations

Over the past decade, many health care systems across the Global North have implemented elements of market mechanisms while also dealing with the consequences of the financial crisis. Although effects of these two developments have been researched separately, their combined impact on the governance of health care organizations has received less attention. The aim of this study is to understand how health care reforms and the financial crisis together shaped new roles and interactions within health care. The Netherlands – where dynamics between health care organizations and their financial stakeholders (i.e., banks and health insurers) were particularly impacted – provides an illustrative case. Through semi-structured interviews, additional document analysis and insights from institutional change theory, we show how banks intensified relationship management, increased demands on loan applications and shifted financial risks onto health care organizations, while health insurers tightened up their monitoring and accountability practices towards health care organizations. In return, health care organizations were urged to rearrange their operations and become more risk-minded. They became increasingly dependent on banks and health insurers for their existence. Moreover, with this study, we show how institutional arenas come about through both the long-term efforts of institutional agents and unpredictable implications of economic and societal crises.<br/