133,137 research outputs found
Localization and pattern formation in Wigner representation via multiresolution
We present an application of variational-wavelet analysis to quasiclassical
calculations of solutions of Wigner equations related to nonlinear (polynomial)
dynamical problems. (Naive) deformation quantization, multiresolution
representations and variational approach are the key points. Numerical
calculations demonstrates pattern formation from localized eigenmodes and
transition from chaotic to localized (waveleton) types of behaviour.Comment: 3 pages, 3 figures, espcrc2.sty, Presented at VIII International
Workshop on Advanced Computing and Analysis Techniques in Physics Research,
Section III "Simulations and Computations in Theoretical Physics and
Phenomenology", ACAT'2002, June 24-28, 2002, Mosco
Homological scaffold via minimal homology bases
The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global features onto individual network components, unless one provides a principled way to make such a choice. In this paper, we apply recent advances in the computation of minimal homology bases to introduce a quasi-canonical version of the scaffold, called minimal, and employ it to analyze data both real and in silico. At the same time, we verify that, statistically, the standard scaffold is a good proxy of the minimal one for sufficiently complex networks
Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
We report new results and generalizations of our work on unextendible product
bases (UPB), uncompletable product bases and bound entanglement. We present a
new construction for bound entangled states based on product bases which are
only completable in a locally extended Hilbert space. We introduce a very
useful representation of a product basis, an orthogonality graph. Using this
representation we give a complete characterization of unextendible product
bases for two qutrits. We present several generalizations of UPBs to arbitrary
high dimensions and multipartite systems. We present a sufficient condition for
sets of orthogonal product states to be distinguishable by separable
superoperators. We prove that bound entangled states cannot help increase the
distillable entanglement of a state beyond its regularized entanglement of
formation assisted by bound entanglement.Comment: 24 pages RevTex, 15 figures; appendix removed, several small
corrections, to appear in Comm. Math. Phy
Effective Symmetries of the Minimal Supermultiplet of N = 8 Extended Worldline Supersymmetry
A minimal representation of the N = 8 extended worldline supersymmetry, known
as the `ultra-multiplet', is closely related to a family of supermultiplets
with the same, E(8) chromotopology. We catalogue their effective symmetries and
find a Spin(4) x Z(2) subgroup common to them all, which explains the
particular basis used in the original construction. We specify a constrained
superfield representation of the supermultiplets in the ultra-multiplet family,
and show that such a superfield representation in fact exists for all adinkraic
supermultiplets. We also exhibit the correspondences between these
supermultiplets, their Adinkras and the E(8) root lattice bases. Finally, we
construct quadratic Lagrangians that provide the standard kinetic terms and
afford a mixing of an even number of such supermultiplets controlled by a
coupling to an external 2-form of fluxes.Comment: 13 Figure
BBGKY Dynamics: from Localization to Pattern Formation
A fast and efficient numerical-analytical approach is proposed for modeling
complex behaviour in the BBGKY--hierarchy of kinetic equations. Our
calculations are based on variational and multiresolution approaches in the
basis of polynomial tensor algebras of generalized coherent states/wavelets. We
construct the representation for hierarchy of reduced distribution functions
via the multiscale decomposition in highly-localized eigenmodes. Numerical
modeling shows the creation of various internal structures from localized
modes, which are related to localized or chaotic type of behaviour and the
corresponding patterns (waveletons) formation. The localized pattern is a model
for energy confinement state (fusion) in plasma.Comment: 14 pages, 3 figures, ws-procs9x6.cls, presented at Workshop "Progress
in Nonequilibrium Greens Functions", Dresden, Germany, August 19-23, 200
Pattern Formation in Wigner-like Equations via Multiresolution
We present the application of the variational-wavelet analysis to the
quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and
related equations corresponding to the nonlinear (polynomial) dynamical
problems. (Naive) deformation quantization, the multiresolution representations
and the variational approach are the key points. We construct the solutions via
the multiscale expansions in the generalized coherent states or high-localized
nonlinear eigenmodes in the base of the compactly supported wavelets and the
wavelet packets. We demonstrate the appearance of (stable) localized patterns
(waveletons) and consider entanglement and decoherence as possible
applications.Comment: 15 pages, 6 figures, ws-procs9x6.cls, Presented at Joint 28th ICFA
Advanced Beam Dynamics & Advanced & Novel Accelerators Workshop on Quantum
Aspects of Beam Physics and Other Critical Issues of Beams in Physics and
Astrophysics, January 7-11, 2003, Hiroshima University, Higashi-Hiroshima,
Japa
Littlewood-Richardson Coefficients via Yang-Baxter Equation
The purpose of this paper is to present an interpretation for the
decomposition of the tensor product of two or more irreducible representations
of GL(N) in terms of a system of quantum particles. Our approach is based on a
certain scattering matrix that satisfies a Yang-Baxter type equation. The
corresponding piecewise-linear transformations of parameters give a solution to
the tetrahedron equation. These transformation maps are naturally related to
the dual canonical bases for modules over the quantum enveloping algebra
. A byproduct of our construction is an explicit description for the
cone of Kashiwara's parametrizations of dual canonical bases. This solves a
problem posed by Berenstein and Zelevinsky. We present a graphical
interpretation of the scattering matrices in terms of web functions, which are
related to honeycombs of Knutson and Tao.Comment: 24 page
Orthogonal multiplet bases in SU(Nc) color space
We develop a general recipe for constructing orthogonal bases for the
calculation of color structures appearing in QCD for any number of partons and
arbitrary Nc. The bases are constructed using hermitian gluon projectors onto
irreducible subspaces invariant under SU(Nc). Thus, each basis vector is
associated with an irreducible representation of SU(Nc). The resulting
multiplet bases are not only orthogonal, but also minimal for finite Nc. As a
consequence, for calculations involving many colored particles, the number of
basis vectors is reduced significantly compared to standard approaches
employing overcomplete bases. We exemplify the method by constructing multiplet
bases for all processes involving a total of 6 external colored partons.Comment: 50 pages, 2 figure
Classical and Quantum Ensembles via Multiresolution. I. BBGKY Hierarchy
A fast and efficient numerical-analytical approach is proposed for modeling
complex behaviour in the BBGKY hierarchy of kinetic equations. We construct the
multiscale representation for hierarchy of reduced distribution functions in
the variational approach and multiresolution decomposition in polynomial tensor
algebras of high-localized states. Numerical modeling shows the creation of
various internal structures from localized modes, which are related to
localized or chaotic type of behaviour and the corresponding patterns
(waveletons) formation. The localized pattern is a model for energy confinement
state (fusion) in plasma.Comment: 5 pages, 3 figures, espcrc2.sty, Presented at IX International
Workshop on Advanced Computing and Analysis Techniques in Physics Research,
Section III "Simulations and Computations in Theoretical Physics and
Phenomenology", ACAT 2003, December, 2003, KEK, Tsukub
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