4,027 research outputs found

    (In)commensurability, scaling and multiplicity of friction in nanocrystals and application to gold nanocrystals on graphite

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    The scaling of friction with the contact size AA and (in)commensurabilty of nanoscopic and mesoscopic crystals on a regular substrate are investigated analytically for triangular nanocrystals on hexagonal substrates. The crystals are assumed to be stiff, but not completely rigid. Commensurate and incommensurate configurations are identified systematically. It is shown that three distinct friction branches coexist, an incommensurate one that does not scale with the contact size (A0A^0) and two commensurate ones which scale differently (with A1/2A^{1/2} and AA) and are associated with various combinations of commensurate and incommensurate lattice parameters and orientations. This coexistence is a direct consequence of the two-dimensional nature of the contact layer, and such multiplicity exists in all geometries consisting of regular lattices. To demonstrate this, the procedure is repeated for rectangular geometry. The scaling of irregularly shaped crystals is also considered, and again three branches are found (A1/4,A3/4,AA^{1/4}, A^{3/4}, A). Based on the scaling properties, a quantity is defined which can be used to classify commensurability in infinite as well as finite contacts. Finally, the consequences for friction experiments on gold nanocrystals on graphite are discussed

    Constructing quantum vertex algebras

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    This is a sequel to \cite{li-qva}. In this paper, we focus on the construction of quantum vertex algebras over \C, whose notion was formulated in \cite{li-qva} with Etingof and Kazhdan's notion of quantum vertex operator algebra (over \C[[h]]) as one of the main motivations. As one of the main steps in constructing quantum vertex algebras, we prove that every countable-dimensional nonlocal (namely noncommutative) vertex algebra over \C, which either is irreducible or has a basis of PBW type, is nondegenerate in the sense of Etingof and Kazhdan. Using this result, we establish the nondegeneracy of better known vertex operator algebras and some nonlocal vertex algebras. We then construct a family of quantum vertex algebras closely related to Zamolodchikov-Faddeev algebras.Comment: 37 page

    Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case

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    This is the first in a series of papers in which we study vertex-algebraic structure of Feigin-Stoyanovsky's principal subspaces associated to standard modules for both untwisted and twisted affine Lie algebras. A key idea is to prove suitable presentations of principal subspaces, without using bases or even ``small'' spanning sets of these spaces. In this paper we prove presentations of the principal subspaces of the basic A_1^(1)-modules. These convenient presentations were previously used in work of Capparelli-Lepowsky-Milas for the purpose of obtaining the classical Rogers-Ramanujan recursion for the graded dimensions of the principal subspaces.Comment: 20 pages. To appear in International J. of Mat

    Crossover in the Slow Decay of Dynamic Correlations in the Lorentz Model

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    The long-time behavior of transport coefficients in a model for spatially heterogeneous media in two and three dimensions is investigated by Molecular Dynamics simulations. The behavior of the velocity auto-correlation function is rationalized in terms of a competition of the critical relaxation due to the underlying percolation transition and the hydrodynamic power-law anomalies. In two dimensions and in the absence of a diffusive mode, another power law anomaly due to trapping is found with an exponent -3 instead of -2. Further, the logarithmic divergence of the Burnett coefficient is corroborated in the dilute limit; at finite density, however, it is dominated by stronger divergences.Comment: Full-length paragraph added that exemplifies the relevance for dense fluids and makes a connection to recently observed, novel long-time tails in a hard-sphere flui

    Non Abelian Sugawara Construction and the q-deformed N=2 Superconformal Algebra

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    The construction of a q-deformed N=2 superconformal algebra is proposed in terms of level 1 currents of Uq(su^(2)){\cal{U}}_{q} ({\widehat{su}}(2)) quantum affine Lie algebra and a single real Fermi field. In particular, it suggests the expression for the q-deformed Energy-Momentum tensor in the Sugawara form. Its constituents generate two isomorphic quadratic algebraic structures. The generalization to Uq(su^(N+1)){\cal{U}}_{q} ({\widehat{su}}(N+1)) is also proposed.Comment: AMSLATEX, 21page

    Hard thermal effective action in QCD through the thermal operator

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    Through the application of the thermal operator to the zero temperature retarded Green's functions, we derive in a simple way the well known hard thermal effective action in QCD. By relating these functions to forward scattering amplitudes for on-shell particles, this derivation also clarifies the origin of important properties of the hard thermal effective action, such as the manifest Lorentz and gauge invariance of its integrand.Comment: 6 pages, contribution of the quarks to the effective action included and one reference added, version to be published in Phys. Rev.

    The 3-graviton vertex function in thermal quantum gravity

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    The high temperature limit of the 3-graviton vertex function is studied in thermal quantum gravity, to one loop order. The leading (T4T^4) contributions arising from internal gravitons are calculated and shown to be twice the ones associated with internal scalar particles, in correspondence with the two helicity states of the graviton. The gauge invariance of this result follows in consequence of the Ward and Weyl identities obeyed by the thermal loops, which are verified explicitly.Comment: 19 pages, plain TeX, IFUSP/P-100

    Non-linear electromagnetic interactions in thermal QED

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    We examine the behavior of the non-linear interactions between electromagnetic fields at high temperature. It is shown that, in general, the log(T) dependence on the temperature of the Green functions is simply related to their UV behavior at zero-temperature. We argue that the effective action describing the nonlinear thermal electromagnetic interactions has a finite limit as T tends to infinity. This thermal action approaches, in the long wavelength limit, the negative of the corresponding zero-temperature action.Comment: 7 pages, IFUSP/P-111

    A central extension of \cD Y_{\hbar}(\gtgl_2) and its vertex representations

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    A central extension of \cD Y_{\hbar}(\gtgl_2) is proposed. The bosonization of level 11 module and vertex operators are also given.Comment: 10 pages, AmsLatex, to appear in Lett. in Math. Phy

    Dynamical transitions in incommensurate systems

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    In the dynamics of the undamped Frenkel-Kontorova model with kinetic terms, we find a transition between two regimes, a floating incommensurate and a pinned incommensurate phase. This behavior is compared to the static version of the model. A remarkable difference is that, while in the static case the two regimes are separated by a single transition (the Aubry transition), in the dynamical case the transition is characterized by a critical region, in which different phenomena take place at different times. In this paper, the generalized angular momentum we have previously introduced, and the dynamical modulation function are used to begin a characterization of this critical region. We further elucidate the relation between these two quantities, and present preliminary results about the order of the dynamical transition.Comment: 7 pages, 6 figures, file 'epl.cls' necessary for compilation provided; subm. to Europhysics Letter
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