7,915 research outputs found

    Semiclassical Inequivalence of Polygonalized Billiards

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    Polygonalization of any smooth billiard boundary can be carried out in several ways. We show here that the semiclassical description depends on the polygonalization process and the results can be inequivalent. We also establish that generalized tangent-polygons are closest to the corresponding smooth billiard and for de Broglie wavelengths larger than the average length of the edges, the two are semiclassically equivalent.Comment: revtex, 4 ps figure

    Reconstructing vector bundles on curves from their direct image on symmetric powers

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    Let CC be an irreducible smooth complex projective curve, and let EE be an algebraic vector bundle of rank rr on CC. Associated to EE, there are vector bundles Fn(E){\mathcal F}_n(E) of rank nrnr on Sn(C)S^n(C), where Sn(C)S^n(C) is nthsymmetricpowerof-th symmetric power of C.Weprovethefollowing:Let. We prove the following: Let E_1and and E_2betwosemistablevectorbundleson be two semistable vector bundles on C,with, with {\rm genus}(C)\, \geq\, 2.If. If {\mathcal F}_n(E_1)\,= \, {\mathcal F}_n(E_2)forafixed for a fixed n,then, then E_1 \,=\, E_2$

    Parameters and pitfalls in dark energy models with time varying equation of state

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    Are geometrical summaries of the CMB and LSS sufficient for estimating cosmological parameters? And how does our choice of a dark energy model impact the current constraints on standard cosmological parameters? We address these questions in the context of the widely used CPL parametrization of a time varying equation of state w in a cosmology allowing spatial curvature. We study examples of different behavior allowed in a CPL parametrization in a phase diagram, and relate these to effects on the observables. We examine parameter constraints in such a cosmology by combining WMAP5, SDSS, SNe, HST data sets by comparing the power spectra. We carefully quantify the differences of these constraints to those obtained by using geometrical summaries for the same data sets. We find that (a) using summary parameters instead of the full data sets give parameter constraints that are similar, but with discernible differences, (b) due to degeneracies, the constraints on the standard parameters broaden significantly for the same data sets. In particular, we find that in the context of CPL dark energy, (i) a Harrison-Zeldovich spectrum cannot be ruled out at 2σ2\sigma levels with our current data sets. and (ii) the SNe IA, HST, and WMAP 5 data are not sufficient to constrain spatial curvature; we additionally require the SDSS DR4 data to achieve this.Comment: 20 pages, 11 figures, Submitted to Astrophysical Journa

    Anomaly in the electronic structure of a BCS superconductor, ZrB(12)

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    We investigate the electronic structure of a complex conventional superconductor, ZrB12 employing high resolution photoemission spectroscopy and ab initio band structure calculations. The experimental valence band spectra could be described reasonably well within the local density approximation. Energy bands close to the Fermi level possess t_(2g) symmetry and the Fermi level is found to be in the proximity of quantum fluctuation regime. The spectral lineshape in the high resolution spectra is complex exhibiting signature of a deviation from Fermi liquid behavior. A dip at the Fermi level emerges above the superconducting transition temperature that gradually grows with the decrease in temperature. The spectral simulation of the dip and spectral lineshape based on a phenomenological self energy suggests a finite electron pair lifetime and a pseudogap above the superconducting transition temperature.Comment: 8 figure

    Periodic Orbits in Polygonal Billiards

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    We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed new light on the proliferation law and its variation with the genus of the invariant surface. Finally, we deal with correlations in the length spectrum and find that long orbits display Poisson fluctuations.Comment: 30 pages (Latex) including 11 figure

    Sculpting the band gap: a computational approach

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    Materials with optimized band gap are needed in many specialized applications. In this work, we demonstrate that Hellmann-Feynman forces associated with the gap states can be used to find atomic coordinates with a desired electronic density of states. Using tight-binding models, we show that this approach can be used to arrive at electronically designed models of amorphous silicon and carbon. We provide a simple recipe to include a priori electronic information in the formation of computer models of materials, and prove that this information may have profound structural consequences. An additional example of a graphene nanoribbon is provided to demonstrate the applicability of this approach to engineer 2-dimensional materials. The models are validated with plane-wave density functional calculations.Comment: Submitted to Physical Review Letters on June 12, 201

    Can Inflation solve the Hierarchy Problem?

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    Inflation with tunneling from a false to a true vacuum becomes viable in the presence of a scalar field that slows down the initial de Sitter phase. As a by-product this field also sets dynamically the value of the Newton constant observed today. This can be very large if the tunneling rate (which is exponentially sensitive to the barrier) is small enough. Therefore along with Inflation we also provide a natural dynamical explanation for why gravity is so weak today. Moreover we predict a spectrum of gravity waves peaked at around 0.1 mHz, that will be detectable by the planned space inteferometer LISA. Finally we discuss interesting predictions on cosmological scalar and tensor fluctuations in the light the WMAP 3-year data.Comment: 7 pages. Replaced version with comparison with WMAP 3-year dat

    Equivariant vector bundles on complete symmetric varieties of minimal rank

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    Let XX be the wonderful compactification of a complex symmetric space G/HG/H of minimal rank. For a point xGx\,\in\, G, denote by ZZ be the closure of BxH/HBxH/H in XX, where BB is a Borel subgroup of GG. The universal cover of GG is denoted by G~\widetilde{G}. Given a G~\widetilde{G} equivariant vector bundle EE on X,X, we prove that EE is nef (respectively, ample) if and only if its restriction to ZZ is nef (respectively, ample). Similarly, EE is trivial if and only if its restriction to ZZ is so

    On equivariant principal bundles over wonderful compactifications

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    Let GG be a simple algebraic group of adjoint type over C\mathbb C, and let MM be the wonderful compactification of a symmetric space G/HG/H. Take a G~\widetilde G--equivariant principal RR--bundle EE on MM, where RR is a complex reductive algebraic group and G~\widetilde G is the universal cover of GG. If the action of the isotropy group H~\widetilde H on the fiber of EE at the identity coset is irreducible, then we prove that EE is polystable with respect to any polarization on MM. Further, for wonderful compactification of the quotient of PSL(n,C)\text{PSL}(n,{\mathbb C}), n4n\,\neq\, 4 (respectively, PSL(2n,C)\text{PSL}(2n,{\mathbb C}), n2n \geq 2) by the normalizer of the projective orthogonal group (respectively, the projective symplectic group), we prove that the tangent bundle is stable with respect to any polarization on the wonderful compactification

    The electron-phonon coupling is large for localized states

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    From density functional calculations, we show that localized states stemming from defects or topological disorder exhibit an anomalously large electron-phonon coupling. We provide a simple analysis to explain the observation and perform a detailed study on an interesting system: amorphous silicon. We compute first principles deformation potentials (by computing the sensitivity of specific electronic eigenstates to individual classical normal modes of vibration). We also probe thermal fluctuations in electronic eigenvalues by first principles thermal simulation. We find a strong correlation between a static property of the network [localization, as gauged by inverse participation ratio (IPR)] and a dynamical property (the amplitude of thermal fluctuations of electron energy eigenvalues) for localized electron states. In particular, both the electron-phonon coupling and the variance of energy eigenvalues are proportional to the IPR of the localized state. We compare the results for amorphous Si to photoemission experiments. While the computations are carried out for silicon, very similar effects have been seen in other systems with disorder.Comment: 5 pages, 3 PostScript figure
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