823 research outputs found
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 with a potential converging to different limits
and as and 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 vanishes as (). We show
that it remains true in the anisotropic case , 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
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
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
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
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“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
Spectrum generating algebra for the continuous spectrum of a free particle in Lobachevski space
In this paper, we construct a Spectrum Generating Algebra (SGA) for a quantum
system with purely continuous spectrum: the quantum free particle in a
Lobachevski space with constant negative curvature. The SGA contains the
geometrical symmetry algebra of the system plus a subalgebra of operators that
give the spectrum of the system and connects the eigenfunctions of the
Hamiltonian among themselves. In our case, the geometrical symmetry algebra is
and the SGA is . We start with a
representation of by functions on a realization of the
Lobachevski space given by a two sheeted hyperboloid, where the Lie algebra
commutators are the usual Poisson-Dirac brackets. Then, introduce a quantized
version of the representation in which functions are replaced by operators on a
Hilbert space and Poisson-Dirac brackets by commutators. Eigenfunctions of the
Hamiltonian are given and "naive" ladder operators are identified. The
previously defined "naive" ladder operators shift the eigenvalues by a complex
number so that an alternative approach is necessary. This is obtained by a non
self-adjoint function of a linear combination of the ladder operators which
gives the correct relation among the eigenfunctions of the Hamiltonian. We give
an eigenfunction expansion of functions over the upper sheet of two sheeted
hyperboloid in terms of the eigenfunctions of the Hamiltonian.Comment: 23 page
The various power decays of the survival probability at long times for free quantum particle
The long time behaviour of the survival probability of initial state and its
dependence on the initial states are considered, for the one dimensional free
quantum particle. We derive the asymptotic expansion of the time evolution
operator at long times, in terms of the integral operators. This enables us to
obtain the asymptotic formula for the survival probability of the initial state
, which is assumed to decrease sufficiently rapidly at large .
We then show that the behaviour of the survival probability at long times is
determined by that of the initial state at zero momentum . Indeed,
it is proved that the survival probability can exhibit the various power-decays
like for an arbitrary non-negative integers as ,
corresponding to the initial states with the condition as .Comment: 15 pages, to appear in J. Phys.
Magnetic transport in a straight parabolic channel
We study a charged two-dimensional particle confined to a straight
parabolic-potential channel and exposed to a homogeneous magnetic field under
influence of a potential perturbation . If is bounded and periodic along
the channel, a perturbative argument yields the absolute continuity of the
bottom of the spectrum. We show it can have any finite number of open gaps
provided the confining potential is sufficiently strong. However, if
depends on the periodic variable only, we prove by Thomas argument that the
whole spectrum is absolutely continuous, irrespectively of the size of the
perturbation. On the other hand, if is small and satisfies a weak
localization condition in the the longitudinal direction, we prove by Mourre
method that a part of the absolutely continuous spectrum persists
Local energy decay of massive Dirac fields in the 5D Myers-Perry metric
We consider massive Dirac fields evolving in the exterior region of a
5-dimensional Myers-Perry black hole and study their propagation properties.
Our main result states that the local energy of such fields decays in a weak
sense at late times. We obtain this result in two steps: first, using the
separability of the Dirac equation, we prove the absence of a pure point
spectrum for the corresponding Dirac operator; second, using a new form of the
equation adapted to the local rotations of the black hole, we show by a Mourre
theory argument that the spectrum is absolutely continuous. This leads directly
to our main result.Comment: 40 page
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