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

An hphp-Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems

In this paper we develop an $hp$-adaptive procedure for the numerical solution of general, semilinear elliptic boundary value problems in 1d, with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton method and an $hp$-version adaptive finite element discretization (based on a robust a posteriori residual analysis), thereby leading to a fully $hp$-adaptive Newton-Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples.Comment: arXiv admin note: text overlap with arXiv:1408.522

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

Independent electrons model for open quantum systems: Landauer-Buettiker formula and strict positivity of the entropy production

A general argument leading from the formula for currents through an open noninteracting mesoscopic system given by the theory of non-equilibrium steady states (NESS) to the Landauer-Buettiker formula is pointed out. Time reversal symmetry is not assumed. As a consequence it follows that, as far as the system has a nontrivial scattering theory and the reservoirs have different temperatures and/or chemical potentials, the entropy production is strictly positive.Comment: 12 pages. Submitted for publication in J. Math. Phys. on 2006-06-05. Revision and extension of: G. Nenciu, A general proof of Landauer-Buettiker formula, [math-ph/0603030

Scanning Tunneling Microscopy of Biological Macromolecular Structures Coated with a Conducting Film

We have studied the capability of scanning tunneling microscopy (STM) to reveal the three-dimensional structure of biological macromolecular structures that have been rendered conductive by metal-coating. The sample preparation used has been derived from a well established method in transmission electron microscopy (TEM). It includes adsorption, freezing and dehydration by vacuum-sublimation, followed by metal-shadowing of the specimen. As an alternative to adsorption and coating, fluid biomaterials can be replaced by conductive freeze-fracture replica. We give an introduction into the sample preparation of metal-coated specimens and discuss how each step can affect the structural preservation and thereby the quality of the data. Some aspects of the data acquisition and the quantitative evaluation of STM data are shown. Possible contributions of STM in the biological macromolecular research are pointed out

On the Lax-Phillips scattering theory

We give a simple description of the wave operators appearing in the Lax-Phillips scattering theory. This is used to derive a relation between the scattering matrix and a kind of time delay operator and to characterize all scattering systems having the same scattering operato

On the exit statistics theorem of many particle quantum scattering

We review the foundations of the scattering formalism for one particle potential scattering and discuss the generalization to the simplest case of many non interacting particles. We point out that the "straight path motion" of the particles, which is achieved in the scattering regime, is at the heart of the crossing statistics of surfaces, which should be thought of as detector surfaces. We sketch a proof of the relevant version of the many particle flux across surfaces theorem and discuss what needs to be proven for the foundations of scattering theory in this context.Comment: 15 pages, 4 figures; to appear in the proceedings of the conference "Multiscale methods in Quantum Mechanics", Accademia dei Lincei, Rome, December 16-20, 200

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

Photon position measure

The positive operator valued measure (POVM) for a photon counting array detector is derived and found to equal photon flux density integrated over pixel area and measurement time. Since photon flux density equals number density multiplied by the speed of light, this justifies theoretically the observation that a photon counting array provides a coarse grained measurement of photon position. The POVM obtained here can be written as a set of projectors onto a basis of localized states, consistent with the description of photon position in a recent quantum imaging proposal [M. Tsang, Phys. Rev. Lett. \textbf{102}, 253601 (2009)]. The wave function that describes a photon counting experiment is the projection of the photon state vector onto this localized basis. Collapse is to the electromagnetic vacuum and not to a localized state, thus violating the text book rules of quantum mechanics but compatible with the theory of generalized observables and the nonlocalizability of an incoming photon