876,459 research outputs found

    A scaling theory of quantum breakdown in solids

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    We propose a new scaling theory for general quantum breakdown phenomena. We show, taking Landau-Zener type breakdown as a particular example, that the breakdown phenomena can be viewed as a quantum phase transition for which the scaling theory is developed. The application of this new scaling theory to Zener type breakdown in Anderson insulators, and quantum quenching has been discussed.Comment: 3 page

    Scaling Behavior in String Theory

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    In Calabi--Yau compactifications of the heterotic string there exist quantities which are universal in the sense that they are present in every Calabi--Yau string vacuum. It is shown that such universal characteristics provide numerical information, in the form of scaling exponents, about the space of ground states in string theory. The focus is on two physical quantities. The first is the Yukawa coupling of a particular antigeneration, induced in four dimensions by virtue of supersymmetry. The second is the partition function of the topological sector of the theory, evaluated on the genus one worldsheet, a quantity relevant for quantum mirror symmetry and threshold corrections. It is shown that both these quantities exhibit scaling behavior with respect to a new scaling variable and that a scaling relation exists between them as well.Comment: 10pp, 4 eps figures (essential

    Scaling and Asymptotic Scaling in the SU(2) Gauge Theory

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    We determine the critical couplings for the deconfinement phase transition in SU(2)SU(2) gauge theory on Nτ×Nσ3N_\tau \times N_\sigma^3 lattices with Nτ=8N_\tau = 8 and 16 and NσN_\sigma varying between 16 and 48. A comparison with string tension data shows scaling of the ratio Tc/σT_c / \sqrt{\sigma} in the entire coupling regime β=2.30−2.75\beta =2.30-2.75, while the individual quantities still exhibit large scaling violations. We find Tc/σ=0.69(2)T_c / \sqrt{\sigma}=0.69(2). We also discuss in detail the extrapolation of Tc/LambdaMˉSˉT_c / Lambda_{\rm{\bar{M} \bar{S}}} and σ/LambdaMˉSˉ\sqrt{\sigma} / Lambda_{\rm{\bar{M}\bar{S}}} to the continuum limit. Our result, which is consistent with the above ratio, is Tc/LambdaMˉSˉ=1.23(11)T_c / Lambda_{\rm{\bar{M}\bar{S}}} = 1.23(11) and σ/LambdaMˉSˉ=1.79(12)\sqrt{\sigma} / Lambda_{\rm{\bar{M}\bar{S}}} = 1.79(12). We also comment upon corresponding results for SU(3)SU(3) gauge theory and four flavour QCD.Comment: 27 pages with 9 postscript figures included. Plain TeX file (needed macros are included). BI-TP 92-26, FSU-SCRI-92-103, HLRZ-92-39 (Quote of UKQCD string tension, and accordingly Figs. 5 and 7a, plus a few typo's corrected.

    Effects of gauge theory based number scaling on geometry

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    Effects of local availability of mathematics (LAM) and space time dependent number scaling on physics and, especially, geometry are described. LAM assumes separate mathematical systems as structures at each space time point. Extension of gauge theories to include freedom of choice of scaling for number structures, and other structures based on numbers, results in a space time dependent scaling factor based on a scalar boson field. Scaling has no effect on comparison of experimental results with one another or with theory computations. With LAM all theory expressions are elements of mathematics at some reference point. Changing the reference point introduces (external) scaling. Theory expressions with integrals or derivatives over space or time include scaling factors (internal scaling) that cannot be removed by reference point change. Line elements and path lengths, as integrals over space and/or time, show the effect of scaling on geometry. In one example, the scaling factor goes to 0 as the time goes to 0, the big bang time. All path lengths, and values of physical quantities, are crushed to 0 as tt goes to 0. Other examples have spherically symmetric scaling factors about some point, x.x. In one type, a black scaling hole, the scaling factor goes to infinity as the distance, dd, between any point yy and xx goes to 0. For scaling white holes, the scaling factor goes to 0 as dd goes to 0. For black scaling holes, path lengths from a reference point, zz, to yy become infinite as yy approaches x.x. For white holes, path lengths approach a value much less than the unscaled distance from zz to x.x.Comment: 22 pages, 4 figures; to appear in proceedings, Quantum information and computation XI, SPIE conference proceedings, Vol. 8749, May 1-3, Baltimore, M

    Scaling theory of driven polymer translocation

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    We present a theoretical argument to derive a scaling law between the mean translocation time Ï„\tau and the chain length NN for driven polymer translocation. This scaling law explicitly takes into account the pore-polymer interactions, which appear as a correction term to asymptotic scaling and are responsible for the dominant finite size effects in the process. By eliminating the correction-to-scaling term we introduce a rescaled translocation time and show, by employing both the Brownian Dynamics Tension Propagation theory [Ikonen {\it et al.}, Phys. Rev. E {\bf 85}, 051803 (2012)] and molecular dynamics simulations that the rescaled exponent reaches the asymptotic limit in a range of chain lengths that is easily accessible to simulations and experiments. The rescaling procedure can also be used to quantitatively estimate the magnitude of the pore-polymer interaction from simulations or experimental data. Finally, we also consider the case of driven translocation with hydrodynamic interactions (HIs). We show that by augmenting the BDTP theory with HIs one reaches a good agreement between the theory and previous simulation results found in the literature. Our results suggest that the scaling relation between Ï„\tau and NN is retained even in this case.Comment: 5 pages, 4 figure
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