Date: Fri, 29 Mar 13 00:06:50 GMT Subject: math-ph daily 3 new + 5 crosses received by eprepget ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Send any comments regarding submissions directly to submitter. ------------------------------------------------------------------------------ Archives at http://arxiv.org/ To unsubscribe, e-mail To: math-ph@arXiv.org, Subject: cancel ------------------------------------------------------------------------------ received by eprepget from Wed 27 Mar 13 20:00:00 GMT to Thu 28 Mar 13 20:00:00 GMT ------------------------------------------------------------------------------ \\ arXiv:1303.7028 Date: Thu, 28 Mar 2013 03:16:10 GMT (17kb) Title: Zeta regularized products, Riemann zeta zeros and prime number spectra Authors: G. Menezes, B. F. Svaiter and N. F. Svaiter Categories: math-ph hep-th math.MP math.NT \\ The Riemann hypothesis states that all nontrivial zeros of the zeta function lie in the critical line $\Re(s)=1/2$. Hilbert and P\'olya suggested that one possible way to prove the Riemann hypothesis is to interpret the nontrivial zeros in the light of spectral theory. Following this approach, we associate such a numerical sequence with the discrete spectrum of a linear differential operator. We discuss a necessary condition that such a sequence of numbers should obey in order to be associated with the spectrum of a linear differential operator of a system with countably infinite number of degrees of freedom. The sequence of nontrivial zeros is zeta regularizable. Then, functional integrals associated with hypothetical systems described by self-adjoint operators whose spectra is given by the sequence of the nontrivial zeros of the Riemann zeta function could be constructed. In addition, we demonstrate that if one considers the same situation with primes numbers, the associated functional integral cannot be constructed, due to the fact that the sequence of prime numbers is not zeta regularizable. \\ ( http://arxiv.org/abs/1303.7028 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1303.7150 Date: Thu, 28 Mar 2013 15:33:53 GMT (11kb) Title: New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems Authors: I. Marquette, C. Quesne Categories: math-ph math.MP quant-ph Comments: 16 pages Report-no: ULB/229/CQ/13/1 \\ New ladder operators are constructed for a rational extension of the harmonic oscillator associated with type III Hermite exceptional orthogonal polynomials and characterized by an even integer $m$. The eigenstates of the Hamiltonian separate into $m+1$ infinite-dimensional unitary irreducible representations of the corresponding polynomial Heisenberg algebra. These ladder operators are used to construct a higher-order integral of motion for two superintegrable two-dimensional systems separable in cartesian coordinates. The polynomial algebras of such systems provide for the first time an algebraic derivation of the whole spectrum through their finite-dimensional unitary irreducible representations. \\ ( http://arxiv.org/abs/1303.7150 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:1303.7182 Date: Thu, 28 Mar 2013 17:04:43 GMT (364kb,D) Title: A solution space for a system of null-state partial differential equations II Authors: Steven M. Flores, Peter Kleban Categories: math-ph cond-mat.stat-mech hep-th math.MP Comments: This article is the a sequel to "A solution space for a system of null-state partial differential equations I" (http://arxiv.org/abs/1212.2301), and it references version 2 of its prequel. Currently, we have only posted version 1 of the prequel, but soon, we will update it to version 2. This update will include only minor revisions \\ In this second of two articles, we study a system of 2N+3 linear homogeneous second-order partial differential equations (PDEs) in 2N variables that arise in conformal field theory (CFT) and multiple Schramm-Loewner Evolution (SLE). In CFT, these are null-state equations and Ward identities. They govern partition functions central to the characterization of a statistical cluster or loop model such as percolation, or more generally the Potts models and O(n) models, at the statistical mechanical critical point in the continuum limit. (SLE partition functions also satisfy these equations.) The partition functions for critical lattice models contained in a polygon P with 2N sides exhibiting a free/fixed side-alternating boundary condition are proportional to the CFT correlation function ^P, where the w_i are the vertices of P and psi_1^c is a one-leg corner operator. Partition functions conditioned on crossing events in which clusters join the fixed sides of P in some specified connectivity are also proportional to this correlation function. When conformally mapped onto the upper half-plane, methods of CFT show that this correlation function satisfies the system of PDEs that we consider. This article is the second of two papers in which we completely characterize the space of all solutions for this system of PDEs that grow no faster than a power-law. In the first article, we proved, to within a precise conjecture, that the dimension of this solution space is no more than C_N, the Nth Catalan number. In this article, we use those results to prove that if this conjecture is true, then this solution space has dimension C_N and is spanned by solutions that can be constructed with the CFT Coulomb gas (contour integral) formalism. \\ ( http://arxiv.org/abs/1303.7182 , 364kb) %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- ------------------------------------------------------------------------------ \\ arXiv:1303.7053 (*cross-listing*) Date: Thu, 28 Mar 2013 07:00:32 GMT (273kb) Title: Non-Hermitian $\cal PT$-symmetric quantum mechanics of relativistic particles with the restriction of mass Authors: V.N.Rodionov Categories: quant-ph hep-ph hep-th math-ph math.MP Comments: 14 pages, 3 figures \\ The modified Dirac equations for the massive particles with the replacement of the physical mass $m$ with the help of the relation $m\rightarrow m_1+ \gamma_5 m_2$ are investigated. It is shown that for a fermion theory with a $\gamma_5$-mass term, the limiting of the mass specter by the value $ m_{max}= {m_1}^2/2m_2$ takes place. In this case the different regions of the unbroken $\cal PT$ symmetry may be expressed by means of the restriction of the physical mass $m\leq m_{max}$. It should be noted that in the approach which was developed by C.Bender et al. for the $\cal PT$-symmetric version of the massive Thirring model with $\gamma_5$-mass term, the region of the unbroken $\cal PT$-symmetry was found in the form $m_1\geq m_2$ \cite{ft12}. However on the basis of the mass limitation $m\leq m_{max}$ we obtain that the domain $m_1\geq m_2$ consists of two different parametric sectors: i) $0\leq m_2 \leq m_1/\sqrt{2}$ -this values of mass parameters $m_1,m_2$ correspond to the traditional particles for which in the limit $m_{max}\rightarrow \infty$ the modified models are converting to the ordinary Dirac theory with the physical mass $m$; ii)$m_1/\sqrt{2}\leq m_2 \leq m_1$ - this is the case of the unusual particles for which equations of motion does not have a limit, when $m_{max}\rightarrow \infty$. The presence of this possibility lets hope for that in Nature indeed there are some "exotic fermion fields". As a matter of fact the formulated criterions may be used as a major test in the process of the division of considered models into ordinary and exotic fermion theories. It is tempting to think that the quanta of the exotic fermion field have a relation to the structure of the "dark matter". \\ ( http://arxiv.org/abs/1303.7053 , 273kb) ------------------------------------------------------------------------------ \\ arXiv:1303.7120 (*cross-listing*) Date: Thu, 28 Mar 2013 13:39:08 GMT (11kb) Title: Pre-acceleration from Landau-Lifshitz Series Authors: Sen Zhang Categories: hep-th math-ph math.MP physics.class-ph physics.plasm-ph Comments: 16 pages Report-no: OIQP-13-05 \\ The Landau-Lifshitz equation is considered as an approximation of the Abraham-Lorentz-Dirac equation. It is derived from the Abraham-Lorentz-Dirac equation by treating radiation reaction terms as a perturbation. However, while the Abraham-Lorentz-Dirac equation has pathological solutions of pre-acceleration and runaway, the Landau-Lifshitz equation and its finite higher order extensions are free of these problems. So it seems mysterious that the property of solutions of these two equations is so different. In this paper we show that the problems of pre-acceleration and runaway appear when one consider a series of all-order perturbation which we call it the Landau-Lifshitz series. We show that the Landau-Lifshitz series diverges in general. Hence a resummation is necessary to obtain a well-defined solution from the Landau-Lifshitz series. This resummation leads the pre-accelerating and the runaway solutions. The analysis is focusing on the non-relativistic case, but we can extend the results obtained here to relativistic case at least in one dimension. \\ ( http://arxiv.org/abs/1303.7120 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:1303.7126 (*cross-listing*) Date: Thu, 28 Mar 2013 14:00:01 GMT (56kb) Title: Witten's top Chern class via cosection localization Authors: Huai-Liang Chang, Jun Li, Wei-Ping Li Categories: math.AG math-ph math.MP Comments: 35 pages MSC-class: 14N35 \\ For a Landau Ginzburg space ([C^n/G],W), we construct the Witten's top Chern classes as algebraic cycles via cosection localized virtual cycles in case all sectors are narrow. We verify all axioms of such classes. We derive an explicit formula of such classes in the free case. We prove that this construction is equivalent to the prior constructions of Polishchuk-Vaintrob, of Chiodo and of Fan-Jarvis-Ruan. \\ ( http://arxiv.org/abs/1303.7126 , 56kb) ------------------------------------------------------------------------------ \\ arXiv:1303.7185 (*cross-listing*) Date: Thu, 28 Mar 2013 17:08:59 GMT (25kb,D) Title: Noncommutative gauge theories on $\mathbb{R}^2_\theta$ as matrix models Authors: Pierre Martinetti, Patrizia Vitale and Jean-Christophe Wallet Categories: hep-th math-ph math.MP Comments: 20 pages Report-no: LPT-13-04 \\ We study a class of noncommutative gauge theory models on 2-dimensional Moyal space from the viewpoint of matrix models and explore some related properties. Expanding the action around symmetric vacua generates non local matrix models with polynomial interaction terms. For a particular vacuum, we can invert the kinetic operator which is related to a Jacobi operator. The resulting propagator can be expressed in terms of Chebyschev polynomials of second kind. We show that non vanishing correlations exist at large separations. General considerations on the kinetic operators stemming from the other class of symmetric vacua, indicates that only one class of symmetric vacua should lead to fast decaying propagators. The quantum stability of the vacuum is briefly discussed. \\ ( http://arxiv.org/abs/1303.7185 , 25kb) ------------------------------------------------------------------------------ \\ arXiv:1303.7198 (*cross-listing*) Date: Thu, 28 Mar 2013 18:41:22 GMT (14kb) Title: Harmonic functions of general graph Laplacians Authors: Bobo Hua and Matthias Keller Categories: math.MG math-ph math.MP math.PR Comments: 13 pages \\ We study harmonic functions on general weighted graphs which allow for a compatible intrinsic metric. We prove an $L^{p}$ Liouville type theorem which is a quantitative integral $L^{p}$ estimate of harmonic functions analogous to Karp's theorem for Riemannian manifolds. As corollaries we obtain Yau's $L^{p}$-Liouville type theorem on graphs, identify the domain of the generator of the semigroup on $L^{p}$ and get a criterion for recurrence. As a side product, we show an analogue of Yau's $L^{p}$ Caccioppoli inequality. Furthermore, various quantitative results for graphs of finite measure are obtained. \\ ( http://arxiv.org/abs/1303.7198 , 14kb) %%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%% ------------------------------------------------------------------------------ \\ arXiv:1203.0262 (*cross-listing*) replaced with revised version Wed, 27 Mar 2013 21:15:46 GMT (19kb) Title: Reversibility conditions for quantum channels and their applications Authors: M.E. Shirokov Categories: quant-ph math-ph math.MP Comments: 28 pages, this version contains strengthened results of the previous one and of arXiv:1106.3297; to appear in Sbornik: Mathematics, 204:7 (2013) \\ ( http://arxiv.org/abs/1203.0262 , 19kb) ------------------------------------------------------------------------------ \\ arXiv:1207.2751 replaced with revised version Thu, 28 Mar 2013 16:23:59 GMT (32kb) Title: A Rigorous Path Integral for N=1 Supersymmetic Quantum Mechanics on a Riemannian Manifold Authors: Dana Fine and Stephen Sawin Categories: math-ph hep-th math.DG math.MP Comments: Minor changes in introduction, exposition and title based on referees' comments MSC-class: 81Q60, 81Q35, 53Z05, 58J20 \\ ( http://arxiv.org/abs/1207.2751 , 32kb) ------------------------------------------------------------------------------ \\ arXiv:1211.5010 (*cross-listing*) replaced with revised version Thu, 28 Mar 2013 13:50:09 GMT (20kb) Title: Noncommutative peak interpolation revisited Authors: David P. Blecher Categories: math.OA math-ph math.FA math.MP Comments: To appear. 7 pages MSC-class: 46L85, 46L52, 47L30, 46L07 (primary), 32T40, 46H10, 47L50, 47L55 (secondary) \\ ( http://arxiv.org/abs/1211.5010 , 20kb) ------------------------------------------------------------------------------ \\ arXiv:1212.3178 (*cross-listing*) replaced with revised version Thu, 28 Mar 2013 10:30:48 GMT (17kb) Title: Parafermionic excitations and critical exponents of random cluster and O(n) models Authors: Gesualdo Delfino Categories: hep-th cond-mat.stat-mech math-ph math.MP Comments: 13 pages, 4 figures. Published version with typo corrected and reference added Journal-ref: Annals of Physics 333 (2013) 1-11 DOI: 10.1016/j.aop.2013.02.009 \\ ( http://arxiv.org/abs/1212.3178 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1302.1797 replaced with revised version Thu, 28 Mar 2013 17:41:18 GMT (19kb) Title: On wave propagation in viscoelastic media with concave creep compliance Authors: Andrzej Hanyga Categories: math-ph math.MP Comments: 14 pp, 2 figures MSC-class: 74D05, 74J05, 42A99 \\ ( http://arxiv.org/abs/1302.1797 , 19kb) ------------------------------------------------------------------------------ \\ arXiv:1303.2036 replaced with revised version Thu, 28 Mar 2013 12:36:49 GMT (9kb) Title: The Einstein-Hilbert action of the space of holomorphic maps from S^2 to CP^k Authors: L.S. Alqahtani Categories: math-ph math.MP Comments: 12 pages - updated version \\ ( http://arxiv.org/abs/1303.2036 , 9kb) ------------------------------------------------------------------------------ \\ arXiv:1303.6913 replaced with revised version Thu, 28 Mar 2013 12:38:32 GMT (12595kb,D) Title: Perturbation analysis for an imperfect interface crack problem using weight function techniques Authors: A. Vellender, G. Mishuris, A. Piccolroaz Categories: math-ph math.MP Comments: Corrected abstract \\ ( http://arxiv.org/abs/1303.6913 , 12595kb) ------------------------------------------------------------------------------ \\ arXiv:1303.6917 (*cross-listing*) replaced with revised version Thu, 28 Mar 2013 00:53:53 GMT (18kb) Title: Is there life beyond Quantum Mechanics? Authors: Anton Kapustin Categories: quant-ph hep-th math-ph math.MP Comments: 23 pages, latex \\ ( http://arxiv.org/abs/1303.6917 , 18kb) %%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%--- 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