Date: Thu, 28 Aug 08 00:00:25 GMT Subject: math-ph daily 4 new + 6 crosses received by eprepget ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Send any complaints regarding submissions directly to submitter. ------------------------------------------------------------------------------ Point your www client at http://arXiv.org/ To unsubscribe, e-mail To: math-ph@arXiv.org, Subject: cancel ------------------------------------------------------------------------------ received by eprepget from Tue 26 Aug 08 20:00:02 GMT to Wed 27 Aug 08 20:00:03 GMT ------------------------------------------------------------------------------ \\ arXiv:0808.3654 Date: Wed, 27 Aug 2008 08:58:20 GMT (10kb) Title: Gauge symmetries of systems with a finite number of degrees of freedom Authors: Farhang Loran Categories: math-ph math.MP Comments: 15 pages, Int. J. Mod. Phys. A MSC-class: 81T70, 70H45 \\ For systems with a finite number of degrees of freedom, it is shown in [arXiv:hep-th/0303014] that first class constraints are Abelianizable if the Faddeev-Popov determinant is not vanishing for some choice of subsidiary constraints. Here, for irreducible first class constraint systems with SO(3) or SO(4) gauge symmetries, including a subset of coordinates in the fundamental representation of the gauge group, we explicitly determine the Abelianizable and non-Abelianizable classes of constraints. For the Abelianizable class, we explicitly solve the constraints to obtain the equivalent set of Abelian first class constraints. We show that for non-Abelianizable constraints there exist residual gauge symmetries which results in confinement-like phenomena. \\ ( http://arxiv.org/abs/0808.3654 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:0808.3661 Date: Wed, 27 Aug 2008 09:25:40 GMT (7kb) Title: The stability of growing networks Authors: Zhenting Hou; Xiangxing Kong; Qinggui Zhao Categories: math-ph math.MP math.PR Comments: 9 pages MSC-class: 05C80; 60C05 \\ In this paper we abstract a kind of stochastic processes from evolving processes of growing networks, which are called as growing network Markov chains, threrefore the existence of the steady degree distribution and the formulas of the degree distribution are transformed to the corresponding problems of growing network Markov chains. We divide growing network markov chains into two classes: non-multiple and multiple, and then, obtain the condition in which the steady degree distribution exists and the exact formulas respectively, and then applied it to the various growing networks. So we have rigorous, exact and united solution of the steady degree distribution of the growing networks. \\ ( http://arxiv.org/abs/0808.3661 , 7kb) ------------------------------------------------------------------------------ \\ arXiv:0808.3714 Date: Wed, 27 Aug 2008 13:58:54 GMT (2kb) Title: On nonadiabatic calculation of dipole moments Authors: Francisco M. Fernandez Categories: math-ph math.MP \\ We discuss a recent nonadiabatic calculation of dipole moments and argue that the trial functions used by the authors do not appear to satisfy the Hellmann-Feynman theorem \\ ( http://arxiv.org/abs/0808.3714 , 2kb) ------------------------------------------------------------------------------ \\ arXiv:0808.3740 Date: Wed, 27 Aug 2008 16:30:53 GMT (12kb) Title: The Lie Algebra of Local Killing Fields Authors: Richard Atkins Categories: math-ph math.MP Comments: 20 pages MSC-class: 53B99 \\ We present an algebraic procedure that finds the Lie algebra of the local Killing fields of a smooth metric. In particular, we determine the number of independent local Killing fields about a given point on the manifold. Metrics of constant curvature, locally symmetric spaces and surfaces are also discussed. \\ ( http://arxiv.org/abs/0808.3740 , 12kb) %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- ------------------------------------------------------------------------------ \\ arXiv:0807.5113 (*cross-listing*) Date: Thu, 31 Jul 2008 17:13:33 GMT (24kb) Date (revised v2): Fri, 22 Aug 2008 13:15:12 GMT (24kb) Title: Topological branes, p-algebras and generalized Nahm equations Authors: Giulio Bonelli, Alessandro Tanzini and Maxim Zabzine Categories: hep-th math-ph math.MP Comments: 20 pages \\ Inspired by the recent advances in multiple M2-brane theory, we consider the generalizations of Nahm equations for arbitrary p-algebras. We construct the topological p-algebra quantum mechanics associated to them and we show that this can be obtained as a truncation of the topological p-brane theory previously studied by the authors. The resulting topological p-algebra quantum mechanics is discussed in detail and the relation with the M2-M5 system is pointed out in the p=3 case, providing a geometrical argument for the emergence of the 3-algebra structure in the Bagger-Lambert-Gustavsson theory \\ ( http://arxiv.org/abs/0807.5113 , 24kb) ------------------------------------------------------------------------------ \\ arXiv:0808.2327 (*cross-listing*) Date: Mon, 18 Aug 2008 02:14:47 GMT (24kb) Title: Deformed boson-fermion correspondence, Q-bosons, and topological strings on the conifold Authors: Piotr Su{\l}kowski Categories: hep-th cond-mat.other math-ph math.MP Comments: 20 pages, 1 figure Report-no: BONN-TH-2008-09 \\ We consider two different physical systems for which the basis of the Hilbert space can be parametrized by Young diagrams: free complex fermions and the phase model of strongly correlated bosons. Both systems have natural deformations parametrized by a parameter Q: the former one is related to the deformed boson-fermion correspondence introduced by N. Jing, while the latter is the so-called Q-boson, arising also in the context of quantum groups. We show that both deformations are equivalent and can be realized in the same way in the algebra of Hall-Littlewood symmetric functions. Without a deformation, these reduce to Schur functions, which can be used to construct a generating function of plane partitions, reproducing a topological string partition function on $C^3$. A deformation of both systems leads then to a deformed generating function, which reproduces topological string partition function of the conifold, with the deformation parameter Q identified with the size of $P^1$. \\ ( http://arxiv.org/abs/0808.2327 , 24kb) ------------------------------------------------------------------------------ \\ arXiv:0808.3435 (*cross-listing*) Date: Tue, 26 Aug 2008 03:03:03 GMT (22kb) Title: Rank-three Killing-Yano tensor and separability of the massive Dirac's equation in the general 5-dimensional Kerr-(anti-)de Sitter black hole background Authors: Shuang-Qing Wu Categories: hep-th gr-qc math-ph math.MP quant-ph Comments: 26 pages, use JHEP3.cls. Paper companied to arXiv:0807.2114 [hep-th] \\ It is shown that the Dirac equation is separable by variables in a five-dimensional rotating Kerr-(anti-)de Sitter black hole with two independent angular momenta. A first-order symmetry operator that commutes with the Dirac operator is constructed in terms of a rank-three Killing-Yano tensor whose square is a second-order symmetric Stackel-Killing tensor admitted by the five-dimensional Kerr-(anti-)de Sitter spacetime. \\ ( http://arxiv.org/abs/0808.3435 , 22kb) ------------------------------------------------------------------------------ \\ arXiv:0808.3486 (*cross-listing*) Date: Tue, 26 Aug 2008 12:13:30 GMT (241kb) Title: On functions of Jacobi-Weierstrass (I) and equation of Painleve Authors: Yu.V.Brezhnev Categories: math.CA hep-th math-ph math.DS math.MP Comments: In Russian; 33 pages; 1 figure \\ The paper is an essentially extended version of the work math.CA/0601371, supplemented with an application. We present new results in the theory of classical $\theta$-functions of Jacobi and $\sigma$-functions of Weierstrass: ordinary differential equations and series expansions. We also give the extension of canonical $\theta$-functions and consider an application to the sixth Painlev\'e equation (P6). Picard--Hitchin's general solution of P6 is represented explicitly in a form of logarithmic derivative of a corresponding $\tau$-function (Painlev\'e's form). \\ ( http://arxiv.org/abs/0808.3486 , 241kb) ------------------------------------------------------------------------------ \\ arXiv:0808.3721 (*cross-listing*) Date: Wed, 27 Aug 2008 19:35:08 GMT (49kb) Title: Integral formulation of 3-D Navier-Stokes and longer time existence of smooth solutions Authors: O. Costin, G. Luo and S. Tanveer Categories: math.AP math-ph math.MP MSC-class: 76D03, 76D05, 35Q3 \\ We consider the 3-D Navier-Stokes initial value problem, $$ v_t - \nu \Delta v = -\mathcal{P} [ v \cdot \nabla v ] + f , v(x, 0) = v_0 (x), x \in \mathbb{T}^3 (*) $$ where $\mathcal{P}$ is the Hodge projection. We assume that the Fourier transform norms $ \| {\hat f} \|_{l^1 (\mathbb{Z}^3)}$ and $\| {\hat v}_0 \|_{l^{1} (\mathbb{Z}^3)}$ are finite. Using an inverse Laplace transform approach, we prove that an integral equation equivalent to (*) has a unique solution ${\hat U} (k, q)$, exponentially bounded for $q$ in a sector centered on $\RR^+$, where $q$ is the inverse Laplace dual to $1/t^n$ for $n \ge 1$. This implies in particular local existence of a classical solution to (*) for $t \in (0, T)$, where $T$ depends on $\| {\hat v}_0 \|_{l^{1}}$ and $\| {\hat f} \|_{l^1}$. Global existence of the solution to NS follows if $\| {\hat U} (\cdot, q) \|_{l^1}$ has subexponential bounds as $q\to\infty$. If $f=0$, then the converse is also true: if NS has global solution, then there exists $n \ge 1 $ for which $\| {\hat U} (\cdot, q) \|$ necessarily decays. We show the exponential growth rate bound of U, \alpha, can be better estimated based on the values of ${\hat U}$ on a finite interval $[0,q_0]$. We also show how the integral equation can be solved numerically with controlled errors. Preliminary numerical calculations suggest that this approach gives an existence time that substantially exceeds classical estimate. \\ ( http://arxiv.org/abs/0808.3721 , 49kb) ------------------------------------------------------------------------------ \\ arXiv:0808.3737 (*cross-listing*) Date: Wed, 27 Aug 2008 16:18:58 GMT (13kb) Title: Asymptotic behavior of eigenvalues of Schr\"odinger type operators with degenerate kinetic energy Authors: Christian Hainzl, Robert Seiringer Categories: math.SP math-ph math.MP \\ We study the eigenvalues of Schr\"odinger type operators $T + \lambda V$ and their asymptotic behavior in the small coupling limit $\lambda \to 0$, in the case where the symbol of the kinetic energy, $T(p)$, strongly degenerates on a non-trivial manifold of codimension one. \\ ( http://arxiv.org/abs/0808.3737 , 13kb) %%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%% ------------------------------------------------------------------------------ \\ arXiv:math/0608357 (*cross-listing*) replaced with revised version Wed, 27 Aug 2008 11:28:40 GMT (58kb) Title: Coincidence of Lyapunov exponents for random walks in weak random potentials Authors: Markus Flury Categories: math.PR math-ph math.MP Comments: Published in at http://dx.doi.org/10.1214/00-AOP368 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) Report-no: IMS-AOP-AOP368 MSC-class: 60K37 (Primary) 34D08, 60K35 (Secondary) Journal-ref: Annals of Probability 2008, Vol. 36, No. 4, 1528-1583 DOI: 10.1214/00-AOP368 \\ ( http://arxiv.org/abs/math/0608357 , 58kb) ------------------------------------------------------------------------------ \\ arXiv:0708.2614 (*cross-listing*) replaced with revised version Wed, 27 Aug 2008 01:32:04 GMT (20kb) Title: On the blow up phenomenon for the $L^2$-critical focusing Hartree equation in $\Bbb R^4$ Authors: Changxing Miao, Guixiang Xu and Lifeng Zhao Categories: math.AP math-ph math.MP Comments: 25pages MSC-class: 35Q40, 35Q55, 47J35 \\ ( http://arxiv.org/abs/0708.2614 , 20kb) ------------------------------------------------------------------------------ \\ arXiv:0802.0695 (*cross-listing*) replaced with revised version Wed, 27 Aug 2008 14:59:58 GMT (20kb) Title: Superpositions of Probability Distributions Authors: Petr Jizba and Hagen Kleinert Categories: cond-mat.other cond-mat.stat-mech math-ph math.MP quant-ph Comments: 23 pages, RevTeX, minor changes, accepted to Phys. Rev. E \\ ( http://arxiv.org/abs/0802.0695 , 20kb) ------------------------------------------------------------------------------ \\ arXiv:0808.3149 replaced with revised version Tue, 26 Aug 2008 22:40:43 GMT (11kb) Title: The Time Inversion for a Modified Oscillator Authors: Ricardo Cordero-Soto and Sergei K. Suslov Categories: math-ph math.MP Comments: 9 pages, no figures \\ ( http://arxiv.org/abs/0808.3149 , 11kb) %%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%--- For subscribe options to combined physics archives, e-mail To: physics@arXiv.org, Subject: subscribe ----------------------------------------------------------------------------- For help on viewing and making submissions, see http://arXiv.org/help/ For a list of archive mirror sites, see http://arXiv.org/servers.html ----------------------------------------------------------------------------- Third-party submissions cause excessive problems. Author self-submissions are exceedingly preferred. 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