On the Flux-Across-Surfaces Theorem

The quantum probability flux of a particle integrated over time and a distant surface gives the probability for the particle crossing that surface at some time. We prove the free Flux-Across-Surfaces Theorem, which was conjectured by Combes, Newton and Shtokhamer, and which relates the integrated quantum flux to the usual quantum mechanical formula for the cross section. The integrated quantum flux is equal to the probability of outward crossings of surfaces by Bohmian trajectories in the scattering regime.Comment: 13 pages, latex, 1 figure, very minor revisions, to appear in Letters in Mathematical Physics, Vol. 38, Nr.

Scattering of massive Dirac fields on the Schwarzschild black hole spacetime

With a generally covariant equation of Dirac fields outside a black hole, we develop a scattering theory for massive Dirac fields. The existence of modified wave operators at infinity is shown by implementing a time-dependent logarithmic phase shift from the free dynamics to offset a long-range mass term. The phase shift we obtain is a matrix operator due to the existence of both positive and negative energy wave components.Comment: LaTex, 17 page

H\"older continuity of the IDS for matrix-valued Anderson models

We study a class of continuous matrix-valued Anderson models acting on L^{2}(\R^{d})\otimes \C^{N}. We prove the existence of their Integrated Density of States for any $d\geq 1$ and $N\geq 1$. Then for $d=1$ and for arbitrary $N$, we prove the H\"older continuity of the Integrated Density of States under some assumption on the group $G_{\mu_{E}}$ generated by the transfer matrices associated to our models. This regularity result is based upon the analoguous regularity of the Lyapounov exponents associated to our model, and a new Thouless formula which relates the sum of the positive Lyapounov exponents to the Integrated Density of States. In the final section, we present an example of matrix-valued Anderson model for which we have already proved, in a previous article, that the assumption on the group $G_{\mu_{E}}$ is verified. Therefore the general results developed here can be applied to this model

Matrix exponential-based closures for the turbulent subgrid-scale stress tensor

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy

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

Scattering theory for arbitrary potentials

The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. New definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a Coulomb tail are presented. It is shown that for the Coulomb potential the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure.Comment: To be published in Phys Rev

Fermi-Walker gauge in 2+1 dimensional gravity.

It is shown that the Fermi-Walker gauge allows the general solution of determining the metric given the sources, in terms of simple quadratures. We treat the general stationary problem providing explicit solving formulas for the metric and explicit support conditions for the energy momentum tensor. The same type of solution is obtained for the time dependent problem with circular symmetry. In both cases the solutions are classified in terms of the invariants of the Wilson loops outside the sources. The Fermi-Walker gauge, due to its physical nature, allows to exploit the weak energy condition and in this connection it is proved that, both for open and closed universes with rotational invariance, the energy condition imply the total absence of closed time like curves. The extension of this theorem to the general stationary problem, in absence of rotational symmetry is considered. At present such extension is subject to some assumptions on the behavior of the determinant of the dreibein in this gauge. PACS number: 0420Comment: 28 pages, RevTex, no figure

A quasi classical approach to electron impact ionization

A quasi classical approximation to quantum mechanical scattering in the Moeller formalism is developed. While keeping the numerical advantage of a standard Classical--Trajectory--Monte--Carlo calculation, our approach is no longer restricted to use stationary initial distributions. This allows one to improve the results by using better suited initial phase space distributions than the microcanonical one and to gain insight into the collision mechanism by studying the influence of different initial distributions on the cross section. A comprehensive account of results for single, double and triple differential cross sections for atomic hydrogen will be given, in comparison with experiment and other theories.Comment: 21 pages, 10 figures, submitted to J Phys

Stakeholders' perspectives of mobile x-ray services in support of healthcare-in-place in residential aged care facilities: a qualitative study

Background: There is interest in reducing avoidable emergency department presentations from residential aged care facilities (RACF). Mobile x-ray services may enable the delivery of healthcare in residential aged care facilities. Accordingly, the Australian Government in November 2019 introduced a Medicare Benefit Schedule rebate providing for a ‘call-out’ fee payable to radiology service providers. This study aims to understand stakeholder perspectives on the benefits of mobile x-ray services and the factors influencing their adoption by RACFs. Design, setting, participants: Twenty-two semi-structured interviews were conducted between October 2020 and February 2021 with a range of stakeholders involved in healthcare delivery to residents: a) general practitioners; b) emergency department clinicians; c) paramedic clinicians; d) a hospital avoidance clinician; e) radiology clinicians and managers; and f ) aged care clinicians and managers. Thematic analysis was conducted. Results: Mobile x-ray services were considered valuable for RACF residents. Lack of timely general practitioner in person assessment and referral, as well as staffing deficits in residential aged care facilities, reduces optimal use of mobile x-ray services and results in potentially unnecessary hospital transfers. Conclusions: The use of mobile x-ray services, as a hospital avoidance strategy, depends on the capacity of RACFs to provide more complex healthcare-in-place. However, this requires greater access to general practitioners for in-person assessment and referral, adequate staffing numbers and appropriately skilled nursing staff within residential aged care facilities.Joanne Dollard, Jane Edwards, Lalit Yadav, Virginie Gaget, David Tivey, Maria Inacio, Guy Maddern, and Renuka Visvanatha