Quaternionic potentials in non-relativistic quantum mechanics

We discuss the Schrodinger equation in presence of quaternionic potentials. The study is performed analytically as long as it proves possible, when not, we resort to numerical calculations. The results obtained could be useful to investigate an underlying quaternionic quantum dynamics in particle physics. Experimental tests and proposals to observe quaternionic quantum effects by neutron interferometry are briefly reviewed.Comment: 21 pages, 16 figures (ps), AMS-Te

Questions of quality in repositories of open educational resources: a literature review

Open educational resources (OER) are teaching and learning materials which are freely available and openly licensed. Repositories of OER (ROER) are platforms that host and facilitate access to these resources. ROER should not just be designed to store this content – in keeping with the aims of the OER movement, they should support educators in embracing open educational practices (OEP) such as searching for and retrieving content that they will reuse, adapt or modify as needed, without economic barriers or copyright restrictions. This paper reviews key literature on OER and ROER, in order to understand the roles ROER are said or supposed to fulfil in relation to furthering the aims of the OER movement. Four themes which should shape repository design are identified, and the following 10 quality indicators (QI) for ROER effectiveness are discussed: featured resources; user evaluation tools; peer review; authorship of the resources; keywords of the resources; use of standardised metadata; multilingualism of the repositories; inclusion of social media tools; specification of the creative commons license; availability of the source code or original files. These QI form the basis of a method for the evaluation of ROER initiatives which, in concert with considerations of achievability and long-term sustainability, should assist in enhancement and development. Keywords: open educational resources; open access; open educational practice; repositories; quality assuranc

Continuous approximation of binomial lattices

A systematic analysis of a continuous version of a binomial lattice, containing a real parameter $\gamma$ and covering the Toda field equation as $\gamma\to\infty$, is carried out in the framework of group theory. The symmetry algebra of the equation is derived. Reductions by one-dimensional and two-dimensional subalgebras of the symmetry algebra and their corresponding subgroups, yield notable field equations in lower dimensions whose solutions allow to find exact solutions to the original equation. Some reduced equations turn out to be related to potentials of physical interest, such as the Fermi-Pasta-Ulam and the Killingbeck potentials, and others. An instanton-like approximate solution is also obtained which reproduces the Eguchi-Hanson instanton configuration for $\gamma\to\infty$. Furthermore, the equation under consideration is extended to $(n+1)$--dimensions. A spherically symmetric form of this equation, studied by means of the symmetry approach, provides conformally invariant classes of field equations comprising remarkable special cases. One of these $(n=4)$ enables us to establish a connection with the Euclidean Yang-Mills equations, another appears in the context of Differential Geometry in relation to the socalled Yamabe problem. All the properties of the reduced equations are shared by the spherically symmetric generalized field equation.Comment: 30 pages, LaTeX, no figures. Submitted to Annals of Physic

Soybean, 1962-1966

Cover title."University of Missouri Agricultural Experiment Station in cooperation with Agricultural Research Service, U.S. Dept. Agriculture.

Quantum noise and mixedness of a pumped dissipative non-linear oscillator

Evolutions of quantum noise, characterized by quadrature squeezing parameter and Fano factor, and of mixedness, quantified by quantum von Neumann and linear entropies, of a pumped dissipative non-linear oscillator are studied. The model can describe a signal mode interacting with a thermal reservoir in a parametrically pumped cavity with a Kerr non-linearity. It is discussed that the initial pure states, including coherent states, Fock states, and finite superpositions of coherent states evolve into the same steady mixed state as verified by the quantum relative entropy and the Bures metric. It is shown analytically and verified numerically that the steady state can be well approximated by a nonclassical Gaussian state exhibiting quadrature squeezing and sub-Poissonian statistics for the cold thermal reservoir. A rapid increase is found in the mixedness, especially for the initial Fock states and superpositions of coherent states, during a very short time interval, and then for longer evolution times a decrease in the mixedness to the same, for all the initial states, and relatively low value of the nonclassical Gaussian state.Comment: 10 pages, 12 figure

Independent ferroelectric contributions and rare-earth-induced polarization reversal in multiferroic TbMn2O5

Three independent contributions to the magnetically induced spontaneous polarization of multiferroic TbMn2O5 are uniquely separated by optical second harmonic generation and an analysis in terms of Landau theory. Two of them are related to the magnetic Mn3+/4+ order and are independent of applied fields of up to 7 T. The third contribution is related to the long-range antiferromagnetic Tb3+ order. It shows a drastic decrease upon the application of a magnetic field and mediates the change of sign of the spontaneous electric polarization in TbMn2O5. The close relationship between the rare-earth long-range order and the non-linear optical properties points to isotropic Tb-Tb exchange and oxygen spin polarization as mechanism for this rare-earth induced ferroelectricity.Comment: 8 pages, 5 figure

Protein-responsive ribozyme switches in eukaryotic cells

Genetic devices that directly detect and respond to intracellular concentrations of proteins are important synthetic biology tools, supporting the design of biological systems that target, respond to or alter specific cellular states. Here, we develop ribozyme-based devices that respond to protein ligands in two eukaryotic hosts, yeast and mammalian cells, to regulate the expression of a gene of interest. Our devices allow for both gene-ON and gene-OFF response upon sensing the protein ligand. As part of our design process, we describe an in vitro characterization pipeline for prescreening device designs to identify promising candidates for in vivo testing. The in vivo gene-regulatory activities in the two types of eukaryotic cells correlate with in vitro cleavage activities determined at different physiologically relevant magnesium concentrations. Finally, localization studies with the ligand demonstrate that ribozyme switches respond to ligands present in the nucleus and/or cytoplasm, providing new insight into their mechanism of action. By extending the sensing capabilities of this important class of gene-regulatory device, our work supports the implementation of ribozyme-based devices in applications requiring the detection of protein biomarkers

Second harmonic generation on incommensurate structures: The case of multiferroic MnWO4

A comprehensive analysis of optical second harmonic generation (SHG) on an incommensurate (IC) magnetically ordered state is presented using multiferroic MnWO4 as model compound. Two fundamentally different SHG contributions coupling to the primary IC magnetic order or to secondary commensurate projections of the IC state, respectively, are distinguished. Whereas the latter can be described within the formalism of the 122 commensurate magnetic point groups the former involves a breakdown of the conventional macroscopic symmetry analysis because of its sensitivity to the lower symmetry of the local environment in a crystal lattice. Our analysis thus foreshadows the fusion of the hitherto disjunct fields of nonlinear optics and IC order in condensed-matter systems

Investigation of the quasifission process by theoretical analysis of experimental data of fissionlike reaction products

The fusion excitation function is the important quantity in planning experiments for the synthesis of superheavy elements. Its values seem to be determined by the experimental study of the hindrance to complete fusion by the observation of mass, angular and energy distributions of the fissionlike fragments. There is ambiguity in establishment of the reaction mechanism leading to the observed binary fissionlike fragments. The fissionlike fragments can be produced in the quasifission, fast fission, and fusion-fission processes which have overlapping in the mass (angular, kinetic energy) distributions of fragments. The branching ratio between quasifission and complete fusion strongly depends on the characteristics of the entrance channel. In this paper we consider a wide set of reactions (with different mass asymmetry and mass symmetry parameters) with the aim to explain the role played by many quantities on the reaction mechanisms. We also present the results of study of the $^{48}$Ca+$^{249}$Bk reaction used to synthesize superheavy nuclei with Z = 117 by the determination of the evaporation residue cross sections and the effective fission barriers $$ of excited nuclei formed along the de-excitation cascade of the compound nucleus.Comment: 21 pages, 15 figures, 2 table

Timelapse

We discuss the existence in an arbitrary frame of a finite time for the transformation of an initial quantum state into another e.g. in a decay. This leads to the introduction of a timelapse $\tilde{\tau}$ in analogy with the lifetime of a particle. An argument based upon the Heisenberg uncertainty principle suggests the value of $\tilde{\tau}=1 / M_0$. Consequences for the exponential decay formula and the modifications that $\tilde{\tau}$ introduces into the Breit-Wigner mass formula are described.Comment: 5 pages [2 figs], ReV-Te