Date: Wed, 30 May 07 00:00:32 GMT Subject: math-ph daily 1 new + 8 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 Mon 28 May 07 20:00:03 GMT to Tue 29 May 07 20:00:03 GMT ------------------------------------------------------------------------------ \\ arXiv:0705.4218 Date: Tue, 29 May 2007 13:33:14 GMT (17kb) Title: $PT$ symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum Authors: E.Caliceti, S.Graffi, J.Sjoestrand Categories: math-ph math.MP Comments: 20 pages \\ Consider in $L^2(R^d)$, $d\geq 1$, the operator family $H(g):=H_0+igW$. $\ds H_0= a^\ast_1a_1+... +a^\ast_da_d+d/2$ is the quantum harmonic oscillator with rational frequencies, $W$ a $P$ symmetric bounded potential, and $g$ a real coupling constant. We show that if $|g|<\rho$, $\rho$ being an explicitly determined constant, the spectrum of $H(g)$ is real and discrete. Moreover we show that the operator $\ds H(g)=a^\ast_1 a_1+a^\ast_2a_2+ig a^\ast_2a_1$ has real discrete spectrum but is not diagonalizable. \\ ( http://arxiv.org/abs/0705.4218 , 17kb) %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- ------------------------------------------------------------------------------ \\ arXiv:0705.3236 (*cross-listing*) Date: Tue, 22 May 2007 19:19:46 GMT (15kb) Title: Eigenvectors of Baxter-Bazhanov-Stroganov \tau^(2)(t_q) model with fixed-spin boundary conditions Authors: N.Z. Iorgov, V.N. Shadura, Yu.V. Tykhyy Categories: nlin.SI cond-mat.stat-mech math-ph math.MP Comments: 14 pages, paper submitted to Proceedings of the International Workshop "Classical and Quantum Integrable Systems" (Dubna, January, 2007) \\ The aim of this contribution is to give the explicit formulas for the eigenvectors of the transfer-matrix of Baxter-Bazhanov-Stroganov (BBS) model (N-state spin model) with fixed-spin boundary conditions. These formulas are obtained by a limiting procedure from the formulas for the eigenvectors of periodic BBS model. The latter formulas were derived in the framework of the Sklyanin's method of separation of variables. In the case of fixed-spin boundaries the corresponding T-Q Baxter equations for the functions of separated variables are solved explicitly. As a particular case we obtain the eigenvectors of the Hamiltonian of Ising-like Z_N quantum chain model. \\ ( http://arxiv.org/abs/0705.3236 , 15kb) ------------------------------------------------------------------------------ \\ arXiv:0705.3340 (*cross-listing*) Date: Wed, 23 May 2007 11:33:38 GMT (107kb) Title: Renormalized Quantum Yang-Mills Fields in Curved Spacetime Authors: Stefan Hollands Categories: gr-qc hep-th math-ph math.MP Comments: Latex 115pp, no figures, review style presentation \\ We present a proof that quantum Yang-Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime. To this end, we construct the non-commutative algebra of observables, in the sense of formal power series. This algebra contains all gauge invariant, renormalized, interacting quantum field operators (polynomials in the field strength and its derivatives), and all their relations such as commutation relations or operator product expansion. It can be viewed as a deformation quantization of the Poisson algebra of classical Yang-Mills theory equipped with the Peierls bracket. The algebra is constructed as the cohomology of an auxiliary algebra describing a gauge fixed theory with ghosts and anti-fields. A key technical difficulty is to establish a suitable hierarchy of Ward identities at the renormalized level that ensure conservation of the interacting BRST-current, and that the interacting BRST-charge is nilpotent. The algebra of physical interacting field observables is obtained as the cohomology of this charge. As a consequence of our constructions, we can prove that the operator product expansion closes on the space of gauge invariant operators. Similarly, the renormalization group flow is proved not to leave the space of gauge invariant operators. \\ ( http://arxiv.org/abs/0705.3340 , 107kb) ------------------------------------------------------------------------------ \\ arXiv:0705.3897 (*cross-listing*) Date: Sat, 26 May 2007 15:28:58 GMT (313kb) Title: A remark on quantum gravity Authors: Dirk Kreimer Categories: hep-th gr-qc math-ph math.MP Comments: 9p, several eps figures \\ We discuss the structure of Dyson--Schwinger equations in quantum gravity and conclude in particular that all relevant skeletons are of first order in the loop number. There is an accompanying sub Hopf algebra on gravity amplitudes equivalent to identities between n-graviton scattering amplitudes which generalize the Slavnov Taylor identities. These identities map the infinite number of charges and finite numbers of skeletons in gravity to an infinite number of skeletons and a finite number of charges needing renormalization. Our analysis suggests that gravity, regarded as a probability conserving but perturbatively non-renormalizable theory, is renormalizable after all, thanks to the structure of its Dyson--Schwinger equations. \\ ( http://arxiv.org/abs/0705.3897 , 313kb) ------------------------------------------------------------------------------ \\ arXiv:0705.4033 (*cross-listing*) Date: Mon, 28 May 2007 11:33:36 GMT (9kb) Title: Mapping out of equilibrium into equilibrium: the macroscopic fluctuations of simple transport models Authors: Julien Tailleur, Jorge Kurchan, Vivien Lecomte Categories: cond-mat.stat-mech math-ph math.MP nlin.SI \\ We study a simple transport model driven out of equilibrium by reservoirs at the boundaries, corresponding to the hydrodynamic limit of the Symmetric Simple Exclusion Process (SSEP). We show that a non-local transformation of densities and currents maps the large deviations of the model into those of an open, isolated chain satisfying detailed balance, where rare fluctuations are the time-reversals of relaxations. We argue that the existence of such a mapping is the immediate reason why it is possible in this model -- as well as for other cases solved through the Macroscopic Fluctuation Theory [1] -- to obtain an explicit solution for the large-deviation function of densities through elementary changes of variables. \\ ( http://arxiv.org/abs/0705.4033 , 9kb) ------------------------------------------------------------------------------ \\ arXiv:0705.4125 (*cross-listing*) Date: Tue, 29 May 2007 01:06:06 GMT (19kb) Title: Upgrading Local Ergodic Theorem for planar semi-dispersing billiards Authors: N. Chernov, N. Simanyi Categories: math.DS math-ph math.MP Comments: 16 pages, 1 figure MSC-class: 37D50; 34D05 \\ Local Ergodic Theorem (also known as `Fundamental Theorem') gives sufficient conditions under which a phase point has an open neighborhood that belongs (mod 0) to one ergodic component. This theorem is a key ingredient of many proofs of ergodicity for billiards and, more generally, for smooth hyperbolic maps with singularities. However the proof of that theorem relies upon a delicate assumption (Chernov-Sinai Ansatz), which is difficult to check for some physically relevant models, including gases of hard balls. Here we give a proof of Local Ergodic Theorem for two dimensional billiards without using Ansatz. \\ ( http://arxiv.org/abs/0705.4125 , 19kb) ------------------------------------------------------------------------------ \\ arXiv:0705.4181 (*cross-listing*) Date: Tue, 29 May 2007 10:07:14 GMT (11kb) Title: Asymptotics of the eigenvalues of elliptic systems with fast oscillating coefficients Authors: D. Borisov Categories: math.SP math-ph math.MP \\ We consider singularly perturbed second order elliptic system in the whole space with fast oscillating coefficients. We construct the complete asymptotic expansions for the eigenvalues converging to the isolated ones of the homogenized system, as well as the complete asymptotic expansions for the associated eigenfunctions. \\ ( http://arxiv.org/abs/0705.4181 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:0705.4186 (*cross-listing*) Date: Tue, 29 May 2007 10:32:06 GMT (17kb) Title: (Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms Authors: A. Klimyk and J. Patera Categories: math.CA math-ph math.MP Comments: 25 pages, no figures \\ Four families of special functions, depending on n variables, are studied. We call them symmetric and antisymmetric multivariate sine and cosine functions. They are given as determinants or antideterminants of matrices, whose matrix elements are sine or cosine functions of one variable each. These functions are eigenfunctions of the Laplace operator, satisfying specific conditions at the boundary of a certain domain F of the n-dimensional Euclidean space. Discrete and continuous orthogonality on F of the functions within each family, allows one to introduce symmetrized and antisymmetrized multivariate Fourier-like transforms, involving the symmetric and antisymmetric multivariate sine and cosine functions. \\ ( http://arxiv.org/abs/0705.4186 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:0705.4271 (*cross-listing*) Date: Tue, 29 May 2007 18:42:04 GMT (36kb) Title: Existence and convergence properties of physical measures for certain dynamical systems with holes Authors: Henk Bruin, Mark Demers, Ian Melbourne Categories: math.DS math-ph math.MP Comments: 35 pages MSC-class: 37A30; 37D35; 37E05 \\ We study two classes of dynamical systems with holes: expanding maps of the interval and Misiurewicz maps. In both cases, we prove that there is a natural absolutely continuous conditionally invariant measure $\mu$ (a.c.c.i.m.) with the physical property that strictly positive Holder continuous functions converge to the density of $\mu$ under the renormalized dynamics of the system. In addition, we construct an invariant measure $\nu$, supported on the Cantor set of points that never escape from the system, that is ergodic and enjoys exponential decay of correlations for Holder observables. We show that $\nu$ satisfies an equilibrium principle which implies that the escape rate formula, familiar to the thermodynamic formalism, holds outside the usual setting. In particular, it holds for Misiurewicz maps with holes, which are not uniformly hyperbolic and do not admit a finite Markov partition. We use a general framework of Young towers with holes and first prove results about the a.c.c.i.m. and the invariant measure on the tower. Then we show how to transfer results to the original dynamical system. This approach can be expected to generalize to other dynamical systems than the two above classes. \\ ( http://arxiv.org/abs/0705.4271 , 36kb) %%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%% ------------------------------------------------------------------------------ \\ arXiv:math-ph/0405052 replaced with revised version Tue, 29 May 2007 14:34:29 GMT (220kb) Title: Height fluctuations in the honeycomb dimer model Authors: Richard Kenyon Categories: math-ph math.MP math.PR Comments: 39 pages. Expanded and revised version MSC-class: 82B20 \\ ( http://arxiv.org/abs/math-ph/0405052 , 220kb) ------------------------------------------------------------------------------ \\ arXiv:math-ph/0703033 replaced with revised version Tue, 29 May 2007 09:45:09 GMT (29kb) Title: Does there exist the Lebesgue measure in the infinite-dimensional space? Authors: Anatoly Vershik Categories: math-ph math.MP math.PR Comments: 35 pp. Ref 39 MSC-class: 22E45,46G12,46G20 \\ ( http://arxiv.org/abs/math-ph/0703033 , 29kb) ------------------------------------------------------------------------------ \\ arXiv:math/0302148 (*cross-listing*) replaced with revised version Tue, 29 May 2007 17:12:57 GMT (27kb) Title: Selberg Type Integrals Associated with $sl_3$ Authors: V.Tarasov and A.Varchenko Categories: math.QA math-ph math.MP math.RT Comments: Errata added; 13 pages, amstex.tex 2.2 and amssym.tex required Journal-ref: Lett. Math. Phys. 65 (2003), no. 3, 173--185 \\ ( http://arxiv.org/abs/math/0302148 , 27kb) ------------------------------------------------------------------------------ \\ arXiv:quant-ph/0609178 (*cross-listing*) replaced with revised version Tue, 29 May 2007 09:47:38 GMT (383kb) Title: Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous variable systems Authors: Gerardo Adesso, Marie Ericsson, Fabrizio Illuminati Categories: quant-ph cond-mat.other math-ph math.MP physics.optics Comments: 8 pages, 4 figures. Extended version. Added discussion about entanglement sharing and its promiscuous structure in qudits and non-Gaussian states \\ ( http://arxiv.org/abs/quant-ph/0609178 , 383kb) %%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%--- 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. E-mail submissions have been discontinued in favor of better support for Web submissions. See http://arXiv.org/help/uploads