Right eigenvalue equation in quaternionic quantum mechanics

We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n-dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations. Our discussion is also extended to complex linear operators, whose spectrum is characterized by 2n complex eigenvalues. We show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products. Finally, we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution.Comment: 24 pages, AMS-Te

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

Quaternionic Electroweak Theory and CKM Matrix

We find in our quaternionic version of the electroweak theory an apparently hopeless problem: In going from complex to quaternions, the calculation of the real-valued parameters of the CKM matrix drastically changes. We aim to explain this quaternionic puzzle.Comment: 8, Revtex, Int. J. Theor. Phys. (to be published

Relativistic tunneling through opaque barriers

We propose an analytical study of relativistic tunneling through opaque barriers. We obtain a closed formula for the phase time. This formula is in excellent agreement with the numerical simulations and corrects the standard formula obtained by the stationary phase method. An important result is found when the upper limit of the incoming energy distribution coincides with the upper limit of the tunneling zone. In this case, the phase time is proportional to the barrier width.Comment: 11 pages, 3 figure

Resonant laser tunnelling

We propose an experiment involving a gaussian laser tunneling through a twin barrier dielectric structure. Of particular interest are the conditions upon the incident angle for resonance to occur. We provide some numerical calculations for a particular choice of laser wave length and dielectric refractive index which confirm our expectations.Comment: 15 pages, 6 figure

Expertise locale et étrangère en Palestine: faiblesse, fragmentation et séduction des pratiques urbanistiques

Based on research and intervention direct experiences of the authors in the OPT, this paper offers a contribution about the circulation and exchange of knowledge in the framework of international cooperation, strictly related to the urban planning field of practices. By the effects of the Israeli occupation and the spatial nature of this conflict, in fact, Palestine could be considered as an extreme case of dependence by the International cooperation – above all from the point of view of public legitimacy and economic support – also for the ordinary activities in urban and regional planning and regulation of spaces. The long history of international cooperation, however, does not seem to have contributed so far to diminish weaknesses, fragmentation and the ability to intervene by professionals and local institutions that in this context are the desired outcome of the occupation itself. This poses a crucial question for theoretical reflections as well as for the international cooperation practices, which has led the authors to discuss the ways in which the knowledge of international experts is combined with local ones, starting from analogies and differences in the most widespread ways of thinking and to act in the context of international cooperation related to the planning of the city and the territory. Then 6 " portrait-type of planners", 3 of local planners and 3 of international planners were elaborated, to summarize references and experiences useful to highlight dynamics that seem peculiar and which try to reconnect the training paths, the available networks and the guidelines for action in order to highlight the critical elements of the most frequent and widespread practices. From the effort of synthesis of the peculiarities of the many subjects met and interviewed and the comparison between the portraits it is possible to trac

Imaginary in all directions: an elegant formulation of special relativity and classical electrodynamics

A suitable parameterization of space-time in terms of one complex and three quaternionic imaginary units allows Lorentz transformations to be implemented as multiplication by complex-quaternionic numbers rather than matrices. Maxwell's equations reduce to a single equation.Comment: 8 page

Well posedness and smoothing effect of Schrödinger-Poisson equation

In this work we take under consideration the Cauchy problem for the Schrödinger-Poisson type equation i t u=- x2 u+V (u) u-f (∫u∫2) u, where f represents a local nonlinear interaction (we take into account both attractive and repulsive models) and V is taken as a suitable solution of the Poisson equation V=12 ∫x∫ (C- ∫u∫2), C Cc∞ is the doping profile or impurities. We show that this problem is locally well posed in the weighted Sobolev spaces Hs { Hs (R): (1+ x2) 12 ∫∫2 <∞} with s1, which means the local existence, uniqueness, and continuity of the solution with respect to the initial data. Moreover, under suitable assumptions on the local interaction, we show the existence of global solutions. Finally, we establish that for s1 local in time and space, smoothing effects are present in the solution; more precisely, in this problem there is locally a gain of half a derivative. © 2007 American Institute of Physics.Fil:De Leo, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Rial, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Phases and Transitions in Phantom Nematic Elastomer Membranes

Motivated by recently discovered unusual properties of bulk nematic elastomers, we study a phase diagram of liquid-crystalline polymerized phantom membranes, focusing on in-plane nematic order. We predict that such membranes should enerically exhibit five phases, distinguished by their conformational and in-plane orientational properties, namely isotropic-crumpled, nematic-crumpled, isotropic-flat, nematic-flat and nematic-tubule phases. In the nematic-tubule phase, the membrane is extended along the direction of {\em spontaneous} nematic order and is crumpled in the other. The associated spontaneous symmetries breaking guarantees that the nematic-tubule is characterized by a conformational-orientational soft (Goldstone) mode and the concomitant vanishing of the in-plane shear modulus. We show that long-range orientational order of the nematic-tubule is maintained even in the presence of harmonic thermal luctuations. However, it is likely that tubule's elastic properties are ualitatively modified by these fluctuations, that can be studied using a nonlinear elastic theory for the nematic tubule phase that we derive at the end of this paper.Comment: 12 pages, 4 eps figures. To appear in PR

Revealing the tidal scars of the Small Magellanic Cloud

Due to their close proximity, the Large and Small Magellanic Clouds (SMC/LMC) provide natural laboratories for understanding how galaxies form and evolve. With the goal of determining the structure and dynamical state of the SMC, we present new spectroscopic data for $\sim$ 3000 SMC red giant branch stars observed using the AAOmega spectrograph at the Anglo-Australian Telescope. We complement our data with further spectroscopic measurements from previous studies that used the same instrumental configuration and proper motions from the \textit{Gaia} Data Release 2 catalogue. Analysing the photometric and stellar kinematic data, we find that the SMC centre of mass presents a conspicuous offset from the velocity centre of its associated \mbox{H\,{\sc i}} gas, suggesting that the SMC gas is likely to be far from dynamical equilibrium. Furthermore, we find evidence that the SMC is currently undergoing tidal disruption by the LMC within 2\,kpc of the centre of the SMC, and possibly all the way in to the very core. This is evidenced by a net outward motion of stars from the SMC centre along the direction towards the LMC and apparent tangential anisotropy at all radii. The latter is expected if the SMC is undergoing significiant tidal stripping, as we demonstrate using a suite of $N$-body simulations of the SMC/LMC system disrupting around the Milky Way. These results suggest that dynamical models for the SMC that assume a steady state will need to be revisited.Comment: Revised version submitted to MNRAS after referee report, 18 pages, 18 figure