57,314 research outputs found

    On correlation functions of integrable models associated to the six-vertex R-matrix

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    We derive an analog of the master equation obtained recently for correlation functions of the XXZ chain for a wide class of quantum integrable systems described by the R-matrix of the six-vertex model, including in particular continuum models. This generalized master equation allows us to obtain multiple integral representations for the correlation functions of these models. We apply this method to derive the density-density correlation functions of the quantum non-linear Schrodinger model.Comment: 21 page

    Point interactions in one dimension and holonomic quantum fields

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    We introduce and study a family of quantum fields, associated to delta-interactions in one dimension. These fields are analogous to holonomic quantum fields of M. Sato, T. Miwa and M. Jimbo. Corresponding field operators belong to an infinite-dimensional representation of the group SL(2,\Rb) in the Fock space of ordinary harmonic oscillator. We compute form factors of such fields and their correlation functions, which are related to the determinants of Schroedinger operators with a finite number of point interactions. It is also shown that these determinants coincide with tau functions, obtained through the trivialization of the det∗\mathrm{det}^*-bundle over a Grassmannian associated to a family of Schroedinger operators.Comment: 17 page

    Syntomic cohomology and Beilinson's Tate conjecture for K₂

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    On the Magnetic Excitation Spectra of High Tc Cu Oxides up to the Energies far above the Resonance Energy

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    Magnetic excitation spectra c"(q,w) of YBa2Cu3Oy and La214 systems have been studied. For La1.88Sr0.12CuO4, c"(q,w) have been measured up to ~30 meV and existing data have been analyzed up to the energy w~150 meV by using the phenomenological expression of the generalized magnetic susceptibility c(q,w)=c0(q,w)/{1+J(q)c0(q,w)}, where c0(q,w) is the susceptibility of the electrons without the exchange coupling J(q) among them. In the relatively low energy region up to slightly above the resonance energy Er, it has been reported by the authors' group that the expression can explain characteristics of the q- and w-dependence of the spectra of YBa2Cu3Oy (YBCO or YBCOy). Here, it is also pointed out that the expression can reproduce the rotation of four incommensurate peaks of c"(q,w) within the a*-b* plane about (p/a, p/a) {or so-called (p, p)} point by 45 degree, which occurs as w goes to the energy region far above Er from E below Er. For La2-xSrxCuO4 and La2-xBaxCuO4, agreements between the observed results and the calculations are less satisfactory than for YBCO, indicating that we have to take account of the existence of the "stripes" to consistently explain the observed c"(q,w) of La214 system especially near x=1/8.Comment: 14 pages, 5 figure

    Driven localized excitations in the acoustic spectrum of small nonlinear macroscopic and microscopic lattices

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    Both bright and dark traveling, locked, intrinsic localized modes (ILMs) have been generated with a spatially uniform driver at a frequency in the acoustic spectrum of a nonlinear micromechanical cantilever array. Complementary numerical simulations show that a minimum density of modes, hence array size, is required for the formation of such locked smoothly running excitations. Additional simulations on a small 1-D antiferromagnetic spin system are used to illustrate that such uniformly driven running ILMs should be a generic feature of a nanoscale atomic lattice.Comment: Physical Review Letters, accepte

    The Multicomponent KP Hierarchy: Differential Fay Identities and Lax Equations

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    In this article, we show that four sets of differential Fay identities of an NN-component KP hierarchy derived from the bilinear relation satisfied by the tau function of the hierarchy are sufficient to derive the auxiliary linear equations for the wave functions. From this, we derive the Lax representation for the NN-component KP hierarchy, which are equations satisfied by some pseudodifferential operators with matrix coefficients. Besides the Lax equations with respect to the time variables proposed in \cite{2}, we also obtain a set of equations relating different charge sectors, which can be considered as a generalization of the modified KP hierarchy proposed in \cite{3}.Comment: 19 page