18,863 research outputs found

    Arithmetic Properties of Overpartition Pairs

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    Bringmann and Lovejoy introduced a rank for overpartition pairs and investigated its role in congruence properties of ppˉ(n)\bar{pp}(n), the number of overpartition pairs of n. In particular, they applied the theory of Klein forms to show that there exist many Ramanujan-type congruences for the number ppˉ(n)\bar{pp}(n). In this paper, we shall derive two Ramanujan-type identities and some explicit congruences for ppˉ(n)\bar{pp}(n). Moreover, we find three ranks as combinatorial interpretations of the fact that ppˉ(n)\bar{pp}(n) is divisible by three for any n. We also construct infinite families of congruences for ppˉ(n)\bar{pp}(n) modulo 3, 5, and 9.Comment: 19 page

    Finite-volume two-pion energies and scattering in the quenched approximation

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    We investigate how L\"uscher's relation between the finite-volume energy of two pions at rest and pion scattering lengths has to be modified in quenched QCD. We find that this relation changes drastically, and in particular, that ``enhanced finite-volume corrections" of order L0=1L^0=1 and L−2L^{-2} occur at one loop (LL is the linear size of the box), due to the special properties of the η′\eta' in the quenched approximation. We define quenched pion scattering lengths, and show that they are linearly divergent in the chiral limit. We estimate the size of these various effects in some numerical examples, and find that they can be substantial.Comment: 22 pages, uuencoded, compressed postscript fil

    Geodesics in the space of measure-preserving maps and plans

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    We study Brenier's variational models for incompressible Euler equations. These models give rise to a relaxation of the Arnold distance in the space of measure-preserving maps and, more generally, measure-preserving plans. We analyze the properties of the relaxed distance, we show a close link between the Lagrangian and the Eulerian model, and we derive necessary and sufficient optimality conditions for minimizers. These conditions take into account a modified Lagrangian induced by the pressure field. Moreover, adapting some ideas of Shnirelman, we show that, even for non-deterministic final conditions, generalized flows can be approximated in energy by flows associated to measure-preserving maps

    Finite Temperature QCD with Wilson Quarks: A Study with a Renormalization Group Improved Gauge Action

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    Finite temperature transition in lattice QCD with degenerate Wilson quarks is investigated on an Nt=4N_t=4 lattice, using a renormalization group improved gauge action. We find the following for the NF=2N_F=2 case: 1) The transition is smooth for a wide range of the quark mass. 2) The chiral transition is continuous. 3) The chiral condensation well satisfies a scaling relation with the critical exponents of the 3 dimensional O(4)O(4) spin model. For NF=3N_F=3, we find that the chiral transition is of first order.Comment: 4 pages (6 figures), Postscript file, Contribution to Lattice 95 proceeding

    The Kaon B-parameter with the Wilson Quark Action using Chiral Ward Identities

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    We present a detailed description of the method and results of our calculation of the kaon B parameter using the Wilson quark action in quenched QCD at β=5.9−6.5\beta=5.9-6.5. The mixing problem of the Δs=2\Delta s=2 four-quark operators is solved non-perturbatively with full use of chiral Ward identities. We find BK(NDR,2GeV)=0.562(64)B_K(NDR, 2 GeV)=0.562(64) in the continuum limit, which agrees with the value obtained with the Kogut-Susskind quark action.Comment: 10 pages, latex source-file, 10 figures as epsf-file, uses espcrc2.sty. Talk given at International Workshop on Lattice QCD on Parallel Computers, 10-15 Mar 1997, Tsukuba, Japa

    Conformal or Walking? Monte Carlo renormalization group studies of SU(3) gauge models with fundamental fermions

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    Strongly coupled gauge systems with many fermions are important in many phenomenological models. I use the 2-lattice matching Monte Carlo renormalization group method to study the fixed point structure and critical indexes of SU(3) gauge models with 8 and 12 flavors of fundamental fermions. With an improved renormalization group block transformation I am able to connect the perturbative and confining regimes of the N_f=8 flavor system, thus verifying its QCD-like nature. With N_f=12 flavors the data favor the existence of an infrared fixed point and conformal phase, though the results are also consistent with very slow walking. I measure the anomalous mass dimension in both systems at several gauge couplings and find that they are barely different from the free field value.Comment: 26 pages, 11 figure
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