10,286 research outputs found
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
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