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

Stereological analysis of hippocampus in rat treated with chemotherapeutic agent oxaliplatin

Background: Oxaliplatin (OX) has been widely used for treatment of colorectal and other cancers. Adverse effect of OX and other anticancer agents on cognition have been reported, but studies on the effects of chemotherapy on brain structure are scarce. This study describes the morphometrical features of the hippocampus structures in rat following OX treatment using design-based stereological methods. Materials and methods: Ten male Wistar rats were randomised into two groups. The rats from OX group received 2.4 mg/kg OX in vehicle for 5 consecutive days every week for 2 weeks intraperitoneally. Controls received vehicle only. Cavalieri’s method and the optical fractionator method were used for volume and neuron estimation, respectively. Results: Cavalieri’s method was used to estimate volume and showed that the volume of the hippocampus was significantly decreased in OX group (31.84 ± ± 1.24 mm3) compared with the vehicle control group (36.95 ± 3.48 mm3). The optical fractionator method was used to estimate neuron number and showed that the number of neurons in dentate gyrus, cornu ammonis 1 and 3 in OX group (8.147 ± 2.84 × 105, 4.257 ± 0.59 × 105 and 2.133 ± 0.22 × 105, respectively) did not differ from those of vehicle control group (7.36 ± 1.42 × 105, 3.521 ± ± 0.54 × 105 and 1.989 ± 0.46 × 105, respectively). Conclusions: These findings suggested that OX treatment induces loss of hippocampal volume without neuronal loss which might help to clarify the mechanism by which OX affects cognition and to improve preventive treatment strategies

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

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

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

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

The role of auditory cortices in the retrieval of single-trial auditory-visual object memories.

Single-trial encounters with multisensory stimuli affect both memory performance and early-latency brain responses to visual stimuli. Whether and how auditory cortices support memory processes based on single-trial multisensory learning is unknown and may differ qualitatively and quantitatively from comparable processes within visual cortices due to purported differences in memory capacities across the senses. We recorded event-related potentials (ERPs) as healthy adults (n = 18) performed a continuous recognition task in the auditory modality, discriminating initial (new) from repeated (old) sounds of environmental objects. Initial presentations were either unisensory or multisensory; the latter entailed synchronous presentation of a semantically congruent or a meaningless image. Repeated presentations were exclusively auditory, thus differing only according to the context in which the sound was initially encountered. Discrimination abilities (indexed by d') were increased for repeated sounds that were initially encountered with a semantically congruent image versus sounds initially encountered with either a meaningless or no image. Analyses of ERPs within an electrical neuroimaging framework revealed that early stages of auditory processing of repeated sounds were affected by prior single-trial multisensory contexts. These effects followed from significantly reduced activity within a distributed network, including the right superior temporal cortex, suggesting an inverse relationship between brain activity and behavioural outcome on this task. The present findings demonstrate how auditory cortices contribute to long-term effects of multisensory experiences on auditory object discrimination. We propose a new framework for the efficacy of multisensory processes to impact both current multisensory stimulus processing and unisensory discrimination abilities later in time

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 $\psi (x)$, which is assumed to decrease sufficiently rapidly at large $|x|$. We then show that the behaviour of the survival probability at long times is determined by that of the initial state $\psi$ at zero momentum $k=0$. Indeed, it is proved that the survival probability can exhibit the various power-decays like $t^{-2m-1}$ for an arbitrary non-negative integers $m$ as $t \to \infty$, corresponding to the initial states with the condition $\hat{\psi} (k) = O(k^m)$ as $k\to 0$.Comment: 15 pages, to appear in J. Phys.

“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