Generalized definition of time delay in scattering theory

We advocate for the systematic use of a symmetrized definition of time delay in scattering theory. In two-body scattering processes, we show that the symmetrized time delay exists for arbitrary dilated spatial regions symmetric with respect to the origin. It is equal to the usual time delay plus a new contribution, which vanishes in the case of spherical spatial regions. We also prove that the symmetrized time delay is invariant under an appropriate mapping of time reversal. These results are also discussed in the context of classical scattering theory.Comment: 18 page

Time delay for one-dimensional quantum systems with steplike potentials

This paper concerns time-dependent scattering theory and in particular the concept of time delay for a class of one-dimensional anisotropic quantum systems. These systems are described by a Schr\"{o}dinger Hamiltonian $H = -\Delta + V$ with a potential $V(x)$ converging to different limits $V_{\ell}$ and $V_{r}$ as $x \to -\infty$ and $x \to +\infty$ respectively. Due to the anisotropy they exhibit a two-channel structure. We first establish the existence and properties of the channel wave and scattering operators by using the modern Mourre approach. We then use scattering theory to show the identity of two apparently different representations of time delay. The first one is defined in terms of sojourn times while the second one is given by the Eisenbud-Wigner operator. The identity of these representations is well known for systems where $V(x)$ vanishes as $|x| \to \infty$ ($V_\ell = V_r$). We show that it remains true in the anisotropic case $V_\ell \not = V_r$, i.e. we prove the existence of the time-dependent representation of time delay and its equality with the time-independent Eisenbud-Wigner representation. Finally we use this identity to give a time-dependent interpretation of the Eisenbud-Wigner expression which is commonly used for time delay in the literature.Comment: 48 pages, 1 figur

Scattering into Cones and Flux across Surfaces in Quantum Mechanics: a Pathwise Probabilistic Approach

We show how the scattering-into-cones and flux-across-surfaces theorems in Quantum Mechanics have very intuitive pathwise probabilistic versions based on some results by Carlen about large time behaviour of paths of Nelson diffusions. The quantum mechanical results can be then recovered by taking expectations in our pathwise statements.Comment: To appear in Journal of Mathematical Physic

Functional status in ICU survivors and out of hospital outcomes: a cohort study

OBJECTIVES: Functional status at hospital discharge may be a risk factor for adverse events among survivors of critical illness. We sought to examine the association between functional status at hospital discharge in survivors of critical care and risk of 90-day all-cause mortality after hospital discharge. DESIGN: Single-center retrospective cohort study. SETTING: Academic Medical Center. PATIENTS: Ten thousand three hundred forty-three adults who received critical care from 1997 to 2011 and survived hospitalization. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: The exposure of interest was functional status determined at hospital discharge by a licensed physical therapist and rated based on qualitative categories adapted from the Functional Independence Measure. The main outcome was 90-day post hospital discharge all-cause mortality. A categorical risk-prediction score was derived and validated based on a logistic regression model of the function grades for each assessment. In an adjusted logistic regression model, the lowest quartile of functional status at hospital discharge was associated with an increased odds of 90-day postdischarge mortality compared with patients with independent functional status (odds ratio, 7.63 [95% CI, 3.83-15.22; p < 0.001]). In patients who had at least 7 days of physical therapy treatment prior to hospital discharge (n = 2,293), the adjusted odds of 90-day postdischarge mortality in patients with marked improvement in functional status at discharge was 64% less than patients with no change in functional status (odds ratio, 0.36 [95% CI, 0.24-0.53]; p < 0.001). CONCLUSIONS: Lower functional status at hospital discharge in survivors of critical illness is associated with increased postdischarge mortality. Furthermore, patients whose functional status improves before discharge have decreased odds of postdischarge mortality.L30 TR001257 - NCATS NIH HH

Tennessee\u27s National Impact on Teacher Evaluation Law & Policy: An Assessment of Value-Added Model Litigation

Over the last decade or so, federal and state education policymakers embraced the use of value added models (VAMs) to evaluate teachers’ performance and make high-stakes employment decisions (e.g., tenure, merit pay, termination of employment). VAMs are complicated statistical models that attempt to estimate a teacher’s contribution to student test scores, particularly those in mathematics and reading. Educational researchers, as well as many teachers and unions, however, have objected to the use of VAMs noting that these models fail to adequately account for variables outside of teachers’ control that contribute to a student’s education performance. Subsequently, many teachers challenged the use of VAMs through the courts. This article assesses those challenges

Extreme Covariant Quantum Observables in the Case of an Abelian Symmetry Group and a Transitive Value Space

We represent quantum observables as POVMs (normalized positive operator valued measures) and consider convex sets of observables which are covariant with respect to a unitary representation of a locally compact Abelian symmetry group $G$. The value space of such observables is a transitive $G$-space. We characterize the extreme points of covariant observables and also determine the covariant extreme points of the larger set of all quantum observables. The results are applied to position, position difference and time observables.Comment: 23 page

Hardy-Carleman Type Inequalities for Dirac Operators

General Hardy-Carleman type inequalities for Dirac operators are proved. New inequalities are derived involving particular traditionally used weight functions. In particular, a version of the Agmon inequality and Treve type inequalities are established. The case of a Dirac particle in a (potential) magnetic field is also considered. The methods used are direct and based on quadratic form techniques

“Rational” Observational Systems of Educational Accountability and Reform

There is something incalculable about teacher expertise and whether it can be observed, detected, quantified, and as per current educational policies, used as an accountability tool to hold America’s public school teachers accountable for that which they do (or do not do well). In this commentary, authors (all of whom are former public school teachers) argue that rubric-based teacher observational systems, developed to assess the extent to which teachers adapt and follow sets of rubric-based rules, might actually constrain teacher expertise. Moreover, authors frame their comments using the Dreyfus Model (1980, 1986) to illustrate how observational systems and the rational conceptions on which they are based might be stifling educational progress and reform. Accessed 4,702 times on https://pareonline.net from August 20, 2015 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Do daily compensatory health beliefs predict intention to quit and smoking behavior? A daily diary study during smoking cessation

Compensatory health beliefs (CHBs) are a means to cope with motivational conflicts between intended health goals and the temptation for an unhealthy behavior. As CHBs can fluctuate on a daily basis, this study examined how daily CHBs are associated with daily intention to quit smoking and daily number of cigarettes smoked before and after a quit date at the between- and within-person level. The study comprised a prospective longitudinal design and investigated 83 women and 83 men for 32 consecutive days during an ongoing joint self-set quit attempt. Daily CHBs varied from day to day and between individuals. At the between-person level, higher women’s mean CHBs were associated with lower intention (b = −0.23, p = 0.04) and at the 10% level with more cigarettes smoked after the quit date (rate ratio (RR) = 1.92, p = 0.07). At the within-person level, women’s higher than usual CHBs were unrelated to intention to quit, but were related to less smoking before (RR = 0.96, p = 0.03) and at the 10% level after the quit date (RR = 0.91, p = 0.09). A marginally positive association between daily CHBs and smoking at the within-person level emerged for men. The negative effect of daily CHBs at the between-person level on smoking seems to unfold after the quit attempt and for women only