801 research outputs found

    Affine Jacobians of Spectral Curves and Integrable Models

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    We explicitly construct the algebraic model of affine Jacobian of a generic algebraic curve of high genus and use it to compute the Euler characteristic of the Jacobian and investigate its structure.Comment: 30 pages; acknoledgements adde

    On quantization of affine Jacobi varieties of spectral curves

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    A quantum integrable model related to Uq(sl^(N))U_q(\hat{sl}(N)) is considered. A reduced model is introduced which allows interpretation in terms of quantized affine Jacobi variety. Closed commutation relations for observables of reduced model are found.Comment: To be published in "Como Proceedings"; 10 pages, 1 figur

    Remarks on rotating shallow-water magnetohydrodynamics

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    International audienceWe show how the rotating shallow-water MHD model, which was proposed in the solar tachocline context, may be systematically derived by vertical averaging of the full MHD equations for the rotating magneto fluid under the influence of gravity. The procedure highlights the main approximations and the domain of validity of the model, and allows for multi-layer generalizations and, hence, inclusion of the baroclinic effects. A quasi-geostrophic version of the model, both in barotropic and in baroclinic cases, is derived in the limit of strong rotation. The basic properties of the model(s) are sketched, including the stabilizing role of magnetic fields in the baroclinic version. © 2013. CC Attribution 3.0 License

    Magnetic-field Induced Screening Effect and Collective Excitations

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    We explicitly construct the fermion propagator in a magnetic field background B to take the lowest Landau-level approximation. We analyze the energy and momentum dependence in the polarization tensor and discuss the collective excitations. We find there appear two branches of collective modes in one of two transverse gauge particles; one represents a massive and attenuated gauge particle and the other behaves similar to the zero sound at finite density.Comment: 5 pages, 3 figures; references on the zero sound added and typos correcte

    Integer Quantum Hall Transition and Random SU(N) Rotation

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    We reduce the problem of integer quantum Hall transition to a random rotation of an N-dimensional vector by an su(N) algebra, where only N specially selected generators of the algebra are nonzero. The group-theoretical structure revealed in this way allows us to obtain a new series of conservation laws for the equation describing the electron density evolution in the lowest Landau level. The resulting formalism is particularly well suited to numerical simulations, allowing us to obtain the critical exponent \nu numerically in a very simple way. We also suggest that if the number of nonzero generators is much less than N, the same model, in a certain intermediate time interval, describes percolating properties of a random incompressible steady two-dimensional flow. In other words, quantum Hall transition in a very smooth random potential inherits certain properties of percolation.Comment: 4 pages, 1 figur

    Quantization of the N=2 Supersymmetric KdV Hierarchy

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    We continue the study of the quantization of supersymmetric integrable KdV hierarchies. We consider the N=2 KdV model based on the sl(1)(2∣1)sl^{(1)}(2|1) affine algebra but with a new algebraic construction for the L-operator, different from the standard Drinfeld-Sokolov reduction. We construct the quantum monodromy matrix satisfying a special version of the reflection equation and show that in the classical limit, this object gives the monodromy matrix of N=2 supersymmetric KdV system. We also show that at both the classical and the quantum levels, the trace of the monodromy matrix (transfer matrix) is invariant under two supersymmetry transformations and the zero mode of the associated U(1) current.Comment: LaTeX2e, 12 page

    Beta-gamma systems and the deformations of the BRST operator

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    We describe the relation between simple logarithmic CFTs associated with closed and open strings, and their "infinite metric" limits, corresponding to the beta-gamma systems. This relation is studied on the level of the BRST complex: we show that the consideration of metric as a perturbation leads to a certain deformation of the algebraic operations of the Lian-Zuckerman type on the vertex algebra, associated with the beta-gamma systems. The Maurer-Cartan equations corresponding to this deformed structure in the quasiclassical approximation lead to the nonlinear field equations. As an explicit example, we demonstrate, that using this construction, Yang-Mills equations can be derived. This gives rise to a nontrivial relation between the Courant-Dorfman algebroid and homotopy algebras emerging from the gauge theory. We also discuss possible algebraic approach to the study of beta-functions in sigma-models.Comment: LaTeX2e, 15 pages; minor revision, typos corrected, Journal of Physics A, in pres
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