Asymptotic Completeness for Compton Scattering

Scattering in a model of a massive quantum-mechanical particle, an ``electron'', interacting with massless, relativistic bosons, ``photons'', is studied. The interaction term in the Hamiltonian of our model describes emission and absorption of ``photons'' by the ``electron''; but ``electron-positron'' pair production is suppressed. An ultraviolet cutoff and an (arbitrarily small, but fixed) infrared cutoff are imposed on the interaction term. In a range of energies where the propagation speed of the dressed ``electron'' is strictly smaller than the speed of light, unitarity of the scattering matrix is proven, provided the coupling constant is small enough; (asymptotic completeness of Compton scattering). The proof combines a construction of dressed one--electron states with propagation estimates for the ``electron'' and the ``photons''.Comment: gap of previous version closed, large parts rewritten, more general results and more comprehensive exposition. 64 pages, 3 figure

Perceptions and Attitudes of Dietetic Program Educators Regarding Use of Distance Education and Computer-Based Simulations in Dietetics Education

Distance education (DE) can address barriers to training nutrition professionals by offering a convenient, flexible and efficient way of learning. One particularly valuable teaching tool in DE is the use of computer-based simulations (CBS). CBS stimulates confidence building, acquisition of new knowledge, exposure to new and challenging patient cases in a safe learning environment, development of communication and critical thinking skills, and the cultivation of sensitivity towards patient needs. Despite the benefits, there is a lack of research examining dietetic educator’s perceptions of and experience with CBS. Goals of this study were to determine: 1) whether dietetic program educators were open to the idea of using CBS and how these responses varied in relation to different factors, and 2) dietetic program educators’ perceptions of the benefits and barriers of using CBS. Secondary data analyses were conducted on a15-item survey developed by the American Dietetic Association (ADA). Surveys contained two qualitative questions and 13 quantitative questions related to CBS. Surveys were e-mailed via the ADA listserv to 535 program directors, including Dietetic Internship Programs (DI), Coordinated Programs in Dietetics (CP), Didactic Programs in Dietetics (DPD), and the Dietetic Technician Programs (DT). A total of 165 individuals responded to the survey. The majority of respondents were open to the use of CBS (n=117) and a small number were not open (n=24). Respondents open to CBS were more likely to 1) not prefer face-to-face communication with their students and colleagues 2) currently be using online case studies and simulations 3) be using standardized patients in supervised practice 4) believe that dietetics education needs alternatives to traditional supervised practice such as CBS 5) believe that they have IT and financial support from their administration 6) have medical simulation laboratories available for dietetics students 7) believe that they had the technological skills needed to use CBS. Educators commented on the potential for CBS to address the shortage of preceptors and facilities available for supervised practice, in addition to enhancing and expediting learning in various settings. Perceived barriers, included the idea that technology impedes learning and a concern about the resources needed to implement CBS. Understanding the perspectives and practices of education program directors is a crucial component of furthering the process of incorporating CBS into nutrition education. This is exciting new terrain for nutrition education and moving forward with research in both distance education and CBS will be beneficial to enhancing nutrition and dietetics education in DE, traditional classroom settings and in supervised practice

Rayleigh Scattering at Atoms with Dynamical Nuclei

Scattering of photons at an atom with a dynamical nucleus is studied on the subspace of states of the system with a total energy below the threshold for ionization of the atom (Rayleigh scattering). The kinematics of the electron and the nucleus is chosen to be non-relativistic, and their spins are neglected. In a simplified model of a hydrogen atom or a one-electron ion interacting with the quantized radiation field in which the helicity of photons is neglected and the interactions between photons and the electron and nucleus are turned off at very high photon energies and at photon energies below an arbitrarily small, but fixed energy (infrared cutoff), asymptotic completeness of Rayleigh scattering is established rigorously. On the way towards proving this result, it is shown that, after coupling the electron and the nucleus to the photons, the atom still has a stable ground state, provided its center of mass velocity is smaller than the velocity of light; but its excited states are turned into resonances. The proof of asymptotic completeness then follows from extensions of a positive commutator method and of propagation estimates for the atom and the photons developed in previous papers. The methods developed in this paper can be extended to more realistic models. It is, however, not known, at present, how to remove the infrared cutof

Zooming in on local level statistics by supersymmetric extension of free probability

We consider unitary ensembles of Hermitian NxN matrices H with a confining potential NV where V is analytic and uniformly convex. From work by Zinn-Justin, Collins, and Guionnet and Maida it is known that the large-N limit of the characteristic function for a finite-rank Fourier variable K is determined by the Voiculescu R-transform, a key object in free probability theory. Going beyond these results, we argue that the same holds true when the finite-rank operator K has the form that is required by the Wegner-Efetov supersymmetry method of integration over commuting and anti-commuting variables. This insight leads to a potent new technique for the study of local statistics, e.g., level correlations. We illustrate the new technique by demonstrating universality in a random matrix model of stochastic scattering.Comment: 38 pages, 3 figures, published version, minor changes in Section

Mean-field dynamics of fermions with relativistic dispersion

We extend the derivation of the time-dependent Hartree-Fock equation recently obtained by Benedikter et al. ["Mean-field evolution of fermionic systems," Commun. Math. Phys. (to be published)] to fermions with a relativistic dispersion law. The main new ingredient is the propagation of semiclassical commutator bounds along the pseudo-relativistic Hartree-Fock evolution. (C) 2014 AIP Publishing LLC