Date: Thu, 30 Jan 14 01:19:35 GMT Subject: math-ph daily 9 new + 6 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 Tue 28 Jan 14 21:00:00 GMT to Wed 29 Jan 14 21:00:00 GMT ------------------------------------------------------------------------------ \\ arXiv:1401.7393 Date: Wed, 29 Jan 2014 02:24:19 GMT (18kb) Title: Two-Component Spinors in Spacetimes with Torsionful Affinities Authors: J.G. Cardoso Categories: math-ph gr-qc math.MP Comments: About 19 pages, 14 references \\ The essentially unique torsionful version of the classical two-component spinor formalisms of Infeld and van der Waerden is exhibited. All the metric spinors and connecting objects that arise here are formally the same as the ones borne by the traditional formalisms. Any spin-affine connection appears to possess a torsional part which is conveniently taken as a suitable asymmetric contribution. Such a torsional affine contribution thus supplies a gauge-invariant potential that may carry an observable character, and thereby effectively takes over the role of any trivially realizable symmetric contribution. The overall curvature spinors for any spin-affine connection accordingly emerge from the irreducible decomposition of a mixed world-spin object which in turn comes out of the action on elementary spinors of a typical torsionful second-order covariant derivative operator. It is pointed out that the new theoretical framework supposedly should afford both a physical characterization of the cosmic dark energy and a description of the propagation of gravitons in torsional regions of the universe. \\ ( http://arxiv.org/abs/1401.7393 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:1401.7477 Date: Wed, 29 Jan 2014 11:51:07 GMT (541kb) Title: Iterative construction of eigenfunctions of the monodromy matrix for SL(2,C) magnet Authors: S.E. Derkachov, A.N. Manashov Categories: math-ph math.MP Comments: 27 pages, 8 figures \\ We present an iterative method for constructing eigenfunctions of the monodromy matrix elements of the SL(2,C) spin chains. Such eigenfunctions form a convenient basis for studies of both closed and open spin chains. We construct the eigenfunctions in an explicit form and calculate the corresponding scalar products (Sklyanin's measure). \\ ( http://arxiv.org/abs/1401.7477 , 541kb) ------------------------------------------------------------------------------ \\ arXiv:1401.7507 Date: Wed, 29 Jan 2014 13:20:52 GMT (620kb) Title: Analytic matrix elements for the two-electron atomic basis with logarithmic terms Authors: Evgeny Z. Liverts and Nir Barnea Categories: math-ph math.MP physics.atom-ph physics.comp-ph Comments: 19 pages, 1 table, 5 figures \\ The two-electron problem for the helium-like atom/ions in $S$-state is considered. The basis containing the integer powers of $\ln r$, where $r$ is a radial variable of the Fock expansion, is studied. In this basis, the analytic expressions for the matrix elements of the corresponding Hamiltonian are presented. These expressions include only special functions presented by the built-in $Mathematica$ codes, what enables very fast and accurate computation of the matrix elements. The decisive contribution of the correct logarithmic terms to the behavior of the two-electron wave function in the vicinity of the triple-coalescence point is reaffirmed. \\ ( http://arxiv.org/abs/1401.7507 , 620kb) ------------------------------------------------------------------------------ \\ arXiv:1401.7523 Date: Wed, 29 Jan 2014 14:36:25 GMT (904kb) Title: On Hyperbolicity of 13-Moment System Authors: Zhenning Cai and Yuwei Fan and Ruo Li Categories: math-ph math.MP Comments: 19 pages, 3 figures MSC-class: 82C40, 35L60 \\ We point out that the thermodynamic equilibrium is not an interior point of the hyperbolicity region of Grad's 13-moment system. With a compact expansion of the phase density, which is compacter than Grad's expansion, we derived a modified 13-moment system. The new 13-moment system admits the thermodynamic equilibrium as an interior point of its hyperbolicity region. We deduce a concise criterion to ensure the hyperbolicity, thus the hyperbolicity region can be quantitatively depicted. \\ ( http://arxiv.org/abs/1401.7523 , 904kb) ------------------------------------------------------------------------------ \\ arXiv:1401.7563 Date: Wed, 29 Jan 2014 15:57:56 GMT (26kb) Title: Optimal space of linear classical observables for Maxwell $k$-forms via spacelike and timelike compact de Rham cohomologies Authors: Marco Benini Categories: math-ph gr-qc hep-th math.MP Comments: 26 pages MSC-class: 81T20, 81T13, 14F40 \\ Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact support systems. These cohomology groups are shown to be isomorphic respectively to the usual de Rham cohomology of a spacelike Cauchy surface and its counterpart with compact support. Furthermore, an analog of the usual Poincar\'e duality for de Rham cohomology is shown to hold for the case with non-standard supports as well. We apply these results to find optimal spaces of linear observables for analogs of arbitrary degree $k$ of both the vector potential and the Faraday tensor. The term optimal has to be intended in the following sense: The spaces of linear observables we consider distinguish between different configurations; in addition to that, there are no redundant observables. This last point in particular heavily relies on the analog of Poincar\'e duality for the new cohomology groups. \\ ( http://arxiv.org/abs/1401.7563 , 26kb) ------------------------------------------------------------------------------ \\ arXiv:1401.7606 Date: Wed, 29 Jan 2014 17:41:10 GMT (7kb) Title: An exact solution of the Currie-Hill equations in 1 + 1 dimensional Minkowski space Authors: Janos Balog Categories: math-ph hep-th math.MP Comments: 9 pages, LaTeX \\ We present an exact two-particle solution of the Currie-Hill equations of Predictive Relativistic Mechanics in $1 + 1$ dimensional Minkowski space. The instantaneous accelerations are given in terms of elementary functions depending on the relative particle position and velocities. The general solution of the equations of motion is given and by studying the global phase space of this system it is shown that this is a subspace of the full kinematic phase space. \\ ( http://arxiv.org/abs/1401.7606 , 7kb) ------------------------------------------------------------------------------ \\ arXiv:1401.7624 Date: Tue, 28 Jan 2014 13:50:08 GMT (339kb) Title: Correlation Functions of XX0 Heisenberg Chain, q-Binomial Determinants, and Random Walks Authors: N. M. Bogoliubov, C. Malyshev Categories: math-ph cond-mat.stat-mech hep-th math.CO math.MP Comments: 27 pages, 2 figures, LaTeX Journal-ref: Nuclear Physics B 879 [FS] (2014) 268-291 \\ The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-factors and of the thermal correlation functions are obtained. The q-binomial determinants enable the connection of the form-factors with the generating functions both of boxed plane partitions and of self-avoiding lattice paths. The asymptotical behavior of the thermal correlation functions is studied in the limit of low temperature provided that the characteristic parameters of the system are large enough. \\ ( http://arxiv.org/abs/1401.7624 , 339kb) ------------------------------------------------------------------------------ \\ arXiv:1401.7629 Date: Wed, 29 Jan 2014 19:20:06 GMT (29kb) Title: Quantization and dynamisation of Trace-Poisson brackets Authors: Jean Avan, Eric Ragoucy and Vladimir Rubtsov Categories: math-ph math.MP Comments: 26 pages Report-no: LAPTH-007/14 \\ The quantization problem for the trace-bracket algebra, derived from double Poisson brackets, is discussed. We obtain a generalization of the boundary YBE (or so-called ABCD-algebra) for the quantization of quadratic trace-brackets. A dynamical deformation is proposed on the lines of Gervais-Neveu-Felder dynamical quantum algebras. \\ ( http://arxiv.org/abs/1401.7629 , 29kb) ------------------------------------------------------------------------------ \\ arXiv:1401.7655 Date: Wed, 29 Jan 2014 20:43:32 GMT (4653kb) Title: Fourier-space inversion of the star transform Authors: Fan Zhao, John C. Schotland and Vadim A. Markel Categories: math-ph math.MP physics.med-ph \\ We define the star transform as a generalization of the broken ray transform introduced by us previously. The advantages of using the star transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium separately and simultaneously (from the same data) and the possibility to utilize scattered radiation which, in the case of the conventional X-ray tomography, is discarded. In this paper, we derive the star transform from physical principles, discuss its mathematical properties and analyze numerical stability of inversion. In particular, it is shown that stable inversion of the star transform can be obtained only for configurations involving odd number of rays. Several computationally-efficient inversion algorithms are derived and tested numerically. \\ ( http://arxiv.org/abs/1401.7655 , 4653kb) %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- ------------------------------------------------------------------------------ \\ arXiv:1304.7926 (*cross-listing*) Date: Tue, 30 Apr 2013 09:13:44 GMT (31kb) Date (revised v2): Wed, 10 Jul 2013 09:57:27 GMT (32kb) Title: How to detect a genuine quantum pump effect in graphene? Authors: Colin Benjamin Categories: cond-mat.mes-hall cond-mat.mtrl-sci math-ph math.MP quant-ph Comments: 5 Pages and 5 figures. Accepted for publication in Applied Physics Letters Journal-ref: Appl. Phys. Lett. 103, 043120 (2013) DOI: 10.1063/1.4816761 \\ Quantum pumping in graphene has been predicted in recent years. Till date there have been no experiments indicating a graphene based quantum pump. This is not uncommon as in case of other non-Dirac behavior showing materials it has not yet been unambiguously experimentally detected. The reason being that in experiments with such materials the rectification effect overshadows the pumped current. In this work we answer the question posed in the title by taking recourse to "strain". We show that the symmetries of the rectified and pumped currents towards strain reversal can effectively distinguish between the two. \\ ( http://arxiv.org/abs/1304.7926 , 32kb) ------------------------------------------------------------------------------ \\ arXiv:1401.6709 (*cross-listing*) Date: Mon, 27 Jan 2014 00:42:46 GMT (2632kb,D) Title: Transmutations of supersymmetry through soliton scattering, and self-consistent condensates Authors: Adrian Arancibia and Mikhail S. Plyushchay Categories: hep-th math-ph math.MP nlin.SI quant-ph Comments: 26 pages, 4 figures \\ We consider the two most general families of the (1+1)D Dirac systems with transparent scalar potentials, and two related families of the paired reflectionless Schrodinger operators. The ordinary N=2 supersymmetry for such Schrodinger pairs is enlarged up to an exotic N=4 nonlinear centrally extended supersymmetric structure, which involves two bosonic integrals composed from the Lax-Novikov operators for the stationary Korteweg-de Vries hierarchy. Each associated single Dirac system displays a proper N=2 nonlinear supersymmetry with a non-standard grading operator. One of the two families of the first and second order systems exhibits the unbroken supersymmetry, while another is described by the broken exotic supersymmetry. The two families are shown to be mutually transmuted by applying a certain limit procedure to the soliton scattering data. We relate the topologically trivial and nontrivial transparent potentials with self-consistent inhomogeneous condensates in Bogoliubov-de Gennes and Gross-Neveu models, and indicate the exotic N=4 nonlinear supersymmetry of the paired reflectionless Dirac systems. \\ ( http://arxiv.org/abs/1401.6709 , 2632kb) ------------------------------------------------------------------------------ \\ arXiv:1401.7579 (*cross-listing*) Date: Tue, 28 Jan 2014 17:01:26 GMT (6309kb,D) Title: Transformation elastodynamics and cloaking for flexural waves Authors: D. J. Colquitt, M. Brun, M. Gei, A. B. Movchan, N. V. Movchan, and I. S. Jones Categories: physics.class-ph cond-mat.mtrl-sci math-ph math.MP Comments: 18 pages, 6 figures \\ The paper addresses an important issue of cloaking transformations for fourth-order partial differential equations representing flexural waves in thin elastic plates. It is shown that, in contrast with the Helmholtz equation, the general form of the partial differential equation is not invariant with respect to the cloaking transformation. The significant result of this paper is the analysis of the transformed equation and its interpretation in the framework of the linear theory of pre-stressed plates. The paper provides a formal framework for transformation elastodynamics as applied to elastic plates. Furthermore, an algorithm is proposed for designing a square cloak for flexural waves, which employs a regularised push-out transformation. Illustrative numerical examples show high accuracy and efficiency of the proposed cloaking algorithm. In particular, a physical configuration involving a perturbation of an interference pattern generated by two coherent sources is presented. It is demonstrated that the perturbation produced by a cloaked defect is negligibly small even for such a delicate interference pattern. \\ ( http://arxiv.org/abs/1401.7579 , 6309kb) ------------------------------------------------------------------------------ \\ arXiv:1401.7581 (*cross-listing*) Date: Wed, 29 Jan 2014 16:43:45 GMT (29kb) Title: One-dimensional Schroedinger operators with delta-prime-interactions on Cantor-type sets Authors: Jonathan Eckhardt, Aleksey Kostenko, Mark Malamud, and Gerald Teschl Categories: math.SP math-ph math.MP Comments: 29 pages MSC-class: Primary 34L40, 81Q10, Secondary 34L05, 34L20 \\ We introduce a novel approach for defining a $\delta'$-interaction on a subset of the real line of Lebesgue measure zero which is based on Sturm-Liouville differential expression with measure coefficients. This enables us to establish basic spectral properties (e.g., self-adjointness, lower semiboundedness and spectral asymptotics) of Hamiltonians with $\delta'$-interactions concentrated on sets of complicated structures. \\ ( http://arxiv.org/abs/1401.7581 , 29kb) ------------------------------------------------------------------------------ \\ arXiv:1401.7627 (*cross-listing*) Date: Wed, 29 Jan 2014 19:11:39 GMT (29kb,D) Title: Point and surface interactions in quantum mechanics: resolving the paradox Authors: Rutger-Jan Lange Categories: quant-ph math-ph math.MP MSC-class: 81-XX, 81Q05, 81Q10, 81Q15, 81Q80, 46Fxx, 46Lxx, 46-XX, 35-XX, 35Dxx, 35Pxx, 35Qxx, 31Bxx, 31Cxx \\ This paper develops a distributional theory for the Schr\"odinger equation with point interactions in $d=1$, and surface interactions in $d>1$. Currently, there is no generally accepted method whereby singular potentials can be translated into a set of boundary conditions, and vice versa. We aim to fill that void. In one dimension, we consider the singular potential $\delta^{(n)}(x)$. The resulting wave function $\psi$ generally has a discontinuous value and discontinuous derivatives. For such functions, the term $\delta^{(n)}(x)\,\psi(x)$ is not generally defined. To obtain meaningful solutions to the Schr\"odinger equation, therefore, a distributional theory is required that allows test functions to have a jump in the value and in all derivatives. By developing this theory, we establish a one-to-one correspondence between singular potentials and boundary conditions. By properly defining the $\delta^{(1)}(x)$-potential, in the sense of allowing discontinuous solutions, we derive a closed-form solution to the time-dependent propagator, thereby resolving a longstanding paradox. Finally, we show that surface delta potentials and surface delta prime potentials in $d>1$ can reproduce solutions to the classical Dirichlet, Neumann and Robin boundary value problems. \\ ( http://arxiv.org/abs/1401.7627 , 29kb) ------------------------------------------------------------------------------ \\ arXiv:1401.7658 (*cross-listing*) Date: Wed, 29 Jan 2014 20:46:22 GMT (39kb) Title: Upper bounds on error probabilities and asymptotic error exponents in quantum multiple state discrimination Authors: Koenraad M.R. Audenaert and Mil\'an Mosonyi Categories: quant-ph math-ph math.MP Comments: 46 pages \\ We consider the multiple hypothesis testing problem for symmetric quantum state discrimination between r given states \sigma_1,...,\sigma_r. By splitting up the overall test into multiple binary tests in various ways we obtain a number of upper bounds on the optimal error probability in terms of the binary error probabilities. These upper bounds allow us to deduce various bounds on the asymptotic error rate, for which it has been hypothesised that it is given by the multi-hypothesis quantum Chernoff bound (or Chernoff divergence) C(\sigma_1,...,\sigma_r), as recently introduced by Nussbaum and Szko{\l}a in analogy with Salikhov's classical multi-hypothesis Chernoff bound. This quantity is defined as the minimum of the pairwise binary Chernoff divergences min_{j