9,505 research outputs found
Hypersymmetry: a Z_3-graded generalization of supersymmetry
We propose a generalization of non-commutative geometry and gauge theories
based on ternary Z_3-graded structures. In the new algebraic structures we
define, we leave all products of two entities free, imposing relations on
ternary products only. These relations reflect the action of the Z_3-group,
which may be either trivial, i.e. abc=bca=cab, generalizing the usual
commutativity, or non-trivial, i.e. abc=jbca, with j=e^{(2\pi i)/3}. The usual
Z_2-graded structures such as Grassmann, Lie and Clifford algebras are
generalized to the Z_3-graded case. Certain suggestions concerning the eventual
use of these new structures in physics of elementary particles are exposed
Z_3-graded exterior differential calculus and gauge theories of higher order
We present a possible generalization of the exterior differential calculus,
based on the operator d such that d^3=0, but d^2\not=0. The first and second
order differentials generate an associative algebra; we shall suppose that
there are no binary relations between first order differentials, while the
ternary products will satisfy the cyclic relations based on the representation
of cyclic group Z_3 by cubic roots of unity. We shall attribute grade 1 to the
first order differentials and grade 2 to the second order differentials; under
the associative multiplication law the grades add up modulo 3. We show how the
notion of covariant derivation can be generalized with a 1-form A, and we give
the expression in local coordinates of the curvature 3-form. Finally, the
introduction of notions of a scalar product and integration of the Z_3-graded
exterior forms enables us to define variational principle and to derive the
differential equations satisfied by the curvature 3-form. The Lagrangian
obtained in this way contains the invariants of the ordinary gauge field tensor
F_{ik} and its covariant derivatives D_i F_{km}.Comment: 13 pages, no figure
Mesoscopic molecular ions in Bose-Einstein condensates
We study the possible formation of large (mesoscopic) molecular ions in an
ultracold degenerate bosonic gas doped with charged particles (ions). We show
that the polarization potentials produced by the ionic impurities are capable
of capturing hundreds of atoms into loosely bound states. We describe the
spontaneous formation of these hollow molecular ions via phonon emission and
suggest an optical technique for coherent stimulated transitions of free atoms
into a specific bound state. These results open up new interesting
possibilities for manipulating tightly confined ensembles.Comment: 4 pages (two-columns), 2 figure
Fourier transform spectroscopy and coupled-channel deperturbation treatment of the A1Sigma+ ~ b3Pi complex of KCs molecule
The laser induced fluorescence (LIF) spectra A1Sigma ~ b3Pi --> X1Sigma+ of
KCs dimer were recorded in near infrared region by Fourier Transform
Spectrometer with a resolution of 0.03 cm-1. Overall more than 200 LIF spectra
were rotationally assigned to 39K133Cs and 41K133Cs isotopomers yielding with
the uncertainty of 0.003-0.01 cm-1 more than 3400 rovibronic term values of the
strongly mixed singlet A1Sigma+ and triplet b3Pi states. Experimental data
massive starts from the lowest vibrational level v_A=0 of the singlet and
nonuniformly cover the energy range from 10040 to 13250 cm-1 with rotational
quantum numbers J from 7 to 225. Besides of the dominating regular A1Sigma+ ~
b3P Omega=0 interactions the weak and local heterogenous A1S+ ~ b3P Omega=1
perturbations have been discovered and analyzed. Coupled-channel deperturbation
analysis of the experimental 39K133Cs e-parity termvalues of the A1S+ ~ b3P
complex was accomplished in the framework of the phenomenological 4 x 4
Hamiltonian accounting implicitly for regular interactions with the remote
states manifold. The resulting diabatic potential energy curves of the
interacting states and relevant spin-orbit coupling matrix elements defined
analytically by Expanded Morse Oscillators model reproduce 95% of experimental
data field of the 39K133Cs isotopomer with a standard deviation of 0.004 cm-1
which is consistent with the uncertainty of the experiment. Reliability of the
derived parameters was additionally confirmed by a good agreement between the
predicted and experimental termvalues of 41K133Cs isotopomer. Calculated
intensity distributions in the A ~ b --> X LIF progressions are also consistent
with their experimental counterparts.Comment: 17 pages, 14 figure
Synchronous Behavior of Two Coupled Electronic Neurons
We report on experimental studies of synchronization phenomena in a pair of
analog electronic neurons (ENs). The ENs were designed to reproduce the
observed membrane voltage oscillations of isolated biological neurons from the
stomatogastric ganglion of the California spiny lobster Panulirus interruptus.
The ENs are simple analog circuits which integrate four dimensional
differential equations representing fast and slow subcellular mechanisms that
produce the characteristic regular/chaotic spiking-bursting behavior of these
cells. In this paper we study their dynamical behavior as we couple them in the
same configurations as we have done for their counterpart biological neurons.
The interconnections we use for these neural oscillators are both direct
electrical connections and excitatory and inhibitory chemical connections: each
realized by analog circuitry and suggested by biological examples. We provide
here quantitative evidence that the ENs and the biological neurons behave
similarly when coupled in the same manner. They each display well defined
bifurcations in their mutual synchronization and regularization. We report
briefly on an experiment on coupled biological neurons and four dimensional ENs
which provides further ground for testing the validity of our numerical and
electronic models of individual neural behavior. Our experiments as a whole
present interesting new examples of regularization and synchronization in
coupled nonlinear oscillators.Comment: 26 pages, 10 figure
The cubic chessboard
We present a survey of recent results, scattered in a series of papers that
appeared during past five years, whose common denominator is the use of cubic
relations in various algebraic structures. Cubic (or ternary) relations can
represent different symmetries with respect to the permutation group S_3, or
its cyclic subgroup Z_3. Also ordinary or ternary algebras can be divided in
different classes with respect to their symmetry properties. We pay special
attention to the non-associative ternary algebra of 3-forms (or ``cubic
matrices''), and Z_3-graded matrix algebras. We also discuss the Z_3-graded
generalization of Grassmann algebras and their realization in generalized
exterior differential forms. A new type of gauge theory based on this
differential calculus is presented. Finally, a ternary generalization of
Clifford algebras is introduced, and an analog of Dirac's equation is
discussed, which can be diagonalized only after taking the cube of the
Z_3-graded generalization of Dirac's operator. A possibility of using these
ideas for the description of quark fields is suggested and discussed in the
last Section.Comment: 23 pages, dedicated to A. Trautman on the occasion of his 64th
birthda
Anisotropic composite polymer for high magnetic force in microfluidic systems
International audienceAnisotropic carbonyl iron-PolyDiMethylSiloxane (PDMS) composites were developed and implemented in microfluidic devices to serve as magnetic flux concentrators. These original materials provide technological solutions for heterogeneous integration with PDMS. Besides microfabrication advantages, they offer interesting modular magnetic properties. Applying an external magnetic field during the PDMS reticulation leads to the formation of 1D-agglomerates of magnetic particles, organized in the non-magnetic polymer matrix. This induces an increase of susceptibility as compared to composites with randomly dispersed particles. In this report, we explored the gain in reachable magnetophoretic forces in operating microfluidic devices, from the study of magnetic micro-beads motion injected in the microchannel. We show that even at relatively large distances from the magnetically-functionalized channel wall, the anisotropic composite leads to a factor two increase in the magnetophoretic force. Finally, further investigations based on finite element description suggest that the measured benefit of anisotropic composite polymers does not only rely on the global susceptibility increase but also on the local magnetic field gradients originating from the microstructure
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