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 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

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

Helical structures from an isotropic homopolymer model

We present Monte Carlo simulation results for square-well homopolymers at a series of bond lengths. Although the model contains only isotropic pairwise interactions, under appropriate conditions this system shows spontaneous chiral symmetry breaking, where the chain exists in either a left- or a right-handed helical structure. We investigate how this behavior depends upon the ratio between bond length and monomer radius.Comment: 10 pages, 3 figures, accepted for publication by Physical Review Letter

A Magellanic Origin for the Warp of the Galaxy

We show that a Magellanic Cloud origin for the warp of the Milky Way can explain most quantitative features of the outer HI layer recently identified by Levine, Blitz & Heiles (2005). We construct a model similar to that of Weinberg (1998) that produces distortions in the dark matter halo, and we calculate the combined effect of these dark-halo distortions and the direct tidal forcing by the Magellanic Clouds on the disk warp in the linear regime. The interaction of the dark matter halo with the disk and resonances between the orbit of the Clouds and the disk account for the large amplitudes observed for the vertical m=0,1,2 harmonics. The observations lead to six constraints on warp forcing mechanisms and our model reasonably approximates all six. The disk is shown to be very dynamic, constantly changing its shape as the Clouds proceed along their orbit. We discuss the challenges to MOND placed by the observations.Comment: 4 pages, 3 figures, submitted to ApJ Letters. Additional graphics, 3d visualizations and movies available at http://www.astro.umass.edu/~weinberg/lm

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

Phonon resonances in atomic currents through Bose-Fermi mixtures in optical lattices

We present an analysis of Bose-Fermi mixtures in optical lattices for the case where the lattice potential of the fermions is tilted and the bosons (in the superfluid phase) are described by Bogoliubov phonons. It is shown that the Bogoliubov phonons enable hopping transitions between fermionic Wannier-Stark states; these transitions are accompanied by energy dissipation into the superfluid and result in a net atomic current along the lattice. We derive a general expression for the drift velocity of the fermions and find that the dependence of the atomic current on the lattice tilt exhibits negative differential conductance and phonon resonances. Numerical simulations of the full dynamics of the system based on the time-evolving block decimation algorithm reveal that the phonon resonances should be observable under the conditions of a realistic measuring procedure.Comment: 8 pages, 5 figure

Introduction to cross LAK 2016: Learning analytics across spaces

For the LAK (Learning Analytics and Knowledge) community, it is highly important to pay attention to the development and deployment of learning analytics solutions for blended learning scenarios where students work at diverse digital and physical learning spaces and interact in different modalities. This workshop has been a first attempt in gathering the sub-community of LAK researchers, learning scientists and researchers from other communities, interested in ubiquitous, mobile and/or face-to-face learning analytics. It was clear for all the attendees that a key concern that has not been deeply explored yet is associated with the mechanisms to integrate and coordinate learning analytics to provide continued support to learning across digital and physical spaces. The two main goals of the workshop were to share perspectives and identify a set of guidelines that could be offered to teachers, researchers or designers to create and connect Learning Analytics solutions according to the pedagogical needs and contextual constraints to provide support across digital and physical learning spaces