共查询到20条相似文献,搜索用时 906 毫秒
1.
A complex symplectic structure on a Lie algebra h is an integrable complex structure J with a closed non-degenerate (2,0)-form. It is determined by J and the real part Ω of the (2,0)-form. Suppose that h is a semi-direct product g?V, and both g and V are Lagrangian with respect to Ω and totally real with respect to J. This note shows that g?V is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω and J are isomorphic. 相似文献
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Fernando Etayo Gordejuela Pedro L. García Pérez Jaime Muñoz Masqué Javier Pérez Alvarez 《Journal of Geometry and Physics》2007
In this article we classify higher-order gauge invariant Lagrangian densities on the bundle of connections of a principal G-bundle π:P→M, in the case where the structure group is abelian. Also we show the strong obstruction for an analogous classification in the noncommutative case. 相似文献
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We study a class of complex structures on the generalized tangent bundle of a smooth manifold M endowed with a torsion free linear connection, ∇. We introduce the concept of ∇-integrability and we study integrability conditions. In the case of the generalized complex structures introduced by Hitchin (2003) in [2], we compare the two concepts of integrability. Moreover, as an application, we describe almost complex structures on the cotangent bundle of M induced by complex structures on the generalized tangent bundle of M. 相似文献
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Given a Poisson (or more generally Dirac) manifold P, there are two approaches to its geometric quantization: one involves a circle bundle Q over P endowed with a Jacobi (or Jacobi–Dirac) structure; the other one involves a circle bundle with a (pre)contact groupoid structure over the (pre)symplectic groupoid of P. We study the relation between these two prequantization spaces. We show that the circle bundle over the (pre)symplectic groupoid of P is obtained from the Lie groupoid of Q via an S1 reduction that preserves both the Lie groupoid and the geometric structures. 相似文献
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We provide generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Using quantum Tsallis entropy of order q, we first provide a generalized monogamy inequality of multi-qubit entanglement for q=2 or 3. This generalization encapsulates the multi-qubit CKW-type inequality as a special case. We further provide a generalized polygamy inequality of multi-qubit entanglement in terms of Tsallis-q entropy for 1≤q≤2 or 3≤q≤4, which also contains the multi-qubit polygamy inequality as a special case. 相似文献
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Let X be a smooth complex projective curve and S⊂X a finite subset. We show that an orthogonal or symplectic parabolic Higgs bundle on X with parabolic structure over S admits a Hermitian–Einstein connection if and only if it is polystable. 相似文献
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We study a matrix model obtained by dimensionally reducing Chern–Simons theory on S3. We find that the matrix integration is decomposed into sectors classified by the representation of SU(2). We show that the N -block sectors reproduce SU(N) Yang–Mills theory on S2 as the matrix size goes to infinity. 相似文献
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We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Zp) gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n dimensional vector space which we call Hn. The Zp gauge particles act on the vertex particles and thus Hn can be thought of as a C(Zp) module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n and p, though we believe this feature holds for all n>p. We will see that non-Abelian anyons of the quantum double of C(S3) are obtained as part of the vertex excitations of the model with n=6 and p=3. Ising anyons are obtained in the model with n=4 and p=2. The n=3 and p=2 case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Zp. This makes them possible candidates for realizing quantum computation. 相似文献
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The random-crystal field spin-1 Blume–Capel model is investigated by the lowest approximation of the cluster-variation method which is identical to the mean-field approximation. The crystal field is either turned on randomly with probability p or turned off with q=1−p in a bimodal distribution. Then the phase diagrams are constructed on the crystal field (Δ)–temperature (kT/J) planes for given values of p and on the (kT/J,p) planes for given Δ by studying the thermal variations of the order parameters. In the latter, we only present the second-order phase transition lines, because of the existence of irregular wiggly phase transitions which are not good enough to construct lines. In addition to these phase transitions, the model also yields tricritical points for all values of p and the reentrant behavior at lower p values. 相似文献
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Community detection is a very important problem in social network analysis. Classical clustering approach, K-means, has been shown to be very efficient to detect communities in networks. However, K-means is quite sensitive to the initial centroids or seeds, especially when it is used to detect communities. To solve this problem, in this study, we propose an efficient algorithm K-rank, which selects the top-K nodes with the highest rank centrality as the initial seeds, and updates these seeds by using an iterative technique like K-means. Then we extend K-rank to partition directed, weighted networks, and to detect overlapping communities. The empirical study on synthetic and real networks show that K-rank is robust and better than the state-of-the-art algorithms including K-means, BGLL, LPA, infomap and OSLOM. 相似文献
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Skeleton of weighted social network 总被引:1,自引:0,他引:1
In the literature of social networks, understanding topological structure is an important scientific issue. In this paper, we construct a network from mobile phone call records and use the cumulative number of calls as a measure of the weight of a social tie. We extract skeletons from the weighted social network on the basis of the weights of ties, and we study their properties. We find that strong ties can support the skeleton in the network by studying the percolation characters. We explore the centrality of w-skeletons based on the correlation between some centrality measures and the skeleton index w of a vertex, and we find that the average centrality of a w-skeleton increases as w increases. We also study the cumulative degree distribution of the successive w-skeletons and find that as w increases, the w-skeleton tends to become more self-similar. Furthermore, fractal characteristics appear in higher w-skeletons. We also explore the global information diffusion efficiency of w-skeletons using simulations, from which we can see that the ties in the high w-skeletons play important roles in information diffusion. Identifying such a simple structure of a w-skeleton is a step forward toward understanding and representing the topological structure of weighted social networks. 相似文献
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Unfolded equations of motion for symmetric massive bosonic fields of any spin in Minkowski and (A)dS spaces are presented. Manifestly gauge invariant action for a spin s?2 massive field in any dimension is constructed in terms of gauge invariant curvatures. 相似文献
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Let M be a symplectic symmetric space, and let ?:M→V be an extrinsic symplectic symmetric immersion in the sense of Krantz and Schwachhöfer (2010) [7], i.e., (V,Ω) is a symplectic vector space and ? is an injective symplectic immersion such that for each point p∈M, the geodesic symmetry in p is compatible with the reflection in the affine normal space at ?(p). 相似文献
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We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network. This set includes m “ambassador” nodes and l of each ambassador’s descendants where m and l are random variables selected from any choice of distributions pl and qm. The process mimics the tendency of authors to cite varying numbers of papers included in the bibliographies of the other papers they cite. We show that the degree distributions of the networks generated after a large number of iterations are scale-free and derive an expression for the power-law exponent. In a particular case of the model where the number of ambassadors is always the constant m and the number of selected descendants from each ambassador is the constant l, the power-law exponent is (2l+1)/l. For this example we derive expressions for the degree distribution and clustering coefficient in terms of l and m. We conclude that the proposed model can be tuned to have the same power law exponent and clustering coefficient of a broad range of the scale-free distributions that have been studied empirically. 相似文献
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We propose a one-parameter theory for gauge mediation of supersymmetry (SUSY) breaking. The spectrum of SUSY particles such as squarks and sleptons in the SUSY standard-model and the dynamics of SUSY-breaking sector are, in principle, determined only by one parameter in the theory, that is, the mass of messengers. Above the messenger threshold all gauge coupling and Yukawa coupling constants in the SUSY-breaking sector are on the infrared fixed point. We find that the present theory may predict a split spectrum of the standard-model SUSY particles, mgaugino<msfermion, where mgaugino and msfermion are SUSY-breaking masses for gauginos and squarks/sleptons, respectively. 相似文献
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Eigenfunctions of integrable planar billiards are studied — in particular, the number of nodal domains, ν of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrödinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and non-separable integrable billiards, ν satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of mmodkn, given a particular k, for a set of quantum numbers, m,n. Further, we observe that the patterns in a family are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. 相似文献