Date: Mon, 29 Sep 14 00:18:30 GMT Subject: math-ph daily 9 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 Thu 25 Sep 14 20:00:00 GMT to Fri 26 Sep 14 20:00:00 GMT ------------------------------------------------------------------------------ \\ arXiv:1409.7439 Date: Thu, 25 Sep 2014 23:23:39 GMT (10kb) Title: Quasi-exact-solvability of the $A_{2}$ Elliptic model: algebraic form, $sl(3)$ hidden algebra, polynomial eigenfunctions Authors: Vladimir V. Sokolov and Alexander V. Turbiner Categories: math-ph hep-th math.MP nlin.SI quant-ph Comments: 13 pages Report-no: IHES/P/14/29 \\ The potential of the $A_2$ quantum elliptic model (3-body Calogero elliptic model) is defined by the pairwise three-body interaction through Weierstrass $\wp$-function and has a single coupling constant. A change of variables has been found, which are $A_2$ elliptic invariants. In those, the potential becomes a rational function, while the flat space metric as well as its associated vector are polynomials in two variables. It is shown the model possesses the hidden $sl_3$ algebra - the Hamiltonian is an element of the universal enveloping algebra $U_{sl_3}$ for arbitrary coupling constant - being equivalent to $sl_3$-quantum top. The integral in a form of the third order differential operator with polynomial coefficients is constructed explicitly, being also an element of the universal enveloping algebra $U_{sl_3}$. It is shown that there exists a discrete sequence of coupling constants for which a finite number of polynomial eigenfunctions up to a (non-singular) gauge factor occur. \\ ( http://arxiv.org/abs/1409.7439 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:1409.7470 Date: Fri, 26 Sep 2014 05:19:34 GMT (5kb) Title: On a conjectural solution to open KdV and Virasoro Authors: Hua-Zhong Ke Categories: math-ph math.AG math.MP math.SG Comments: 6 pages. Comments are welcome! \\ In this note, we present a recursive formula for the full partition function Z of descendent integrals over moduli spaces of open and closed Riemann surfaces, assuming the conjecture recently proposed by Pandharipande, Solomon and Tessler that Z satisfies the open KdV and Virasoro equations. \\ ( http://arxiv.org/abs/1409.7470 , 5kb) ------------------------------------------------------------------------------ \\ arXiv:1409.7525 Date: Fri, 26 Sep 2014 10:18:10 GMT (2251kb,D) Title: On a Class of Nonlocal Wave Equations from Applications Authors: Horst Reinhard Beyer, Burak Aksoylu, Fatih Celiker Categories: math-ph math.MP Comments: 36 pages, 8 figures MSC-class: 47G10, 35L05, 74B99 \\ We study equations from the area of peridynamics, which is an extension of elasticity. The governing equations form a system of nonlocal wave equations. Its governing operator is found to be a bounded, linear and self-adjoint operator on a Hilbert space. We study the well-posedness and stability of the associated initial value problem. We solve the initial value problem by applying the functional calculus of the governing operator. In addition, we give a series representation of the solution in terms of spherical Bessel functions. For the case of scalar valued functions, the governing operator turns out as functions of the Laplace operator. This result enables the comparison of peridynamic solutions to those of classical elasticity as well as the introduction of local boundary conditions into the nonlocal theory. The latter is studied in a companion paper. \\ ( http://arxiv.org/abs/1409.7525 , 2251kb) ------------------------------------------------------------------------------ \\ arXiv:1409.7534 Date: Fri, 26 Sep 2014 11:09:56 GMT (64kb) Title: Next Order Asymptotics and Renormalized Energy for Riesz Interactions Authors: Mircea Petrache and Sylvia Serfaty Categories: math-ph math.MP math.PR \\ We study systems of $n$ points in the Euclidean space of dimension $d \ge 1$ interacting via a Riesz kernel $|x|^{-s}$ and confined by an external potential, in the regime where $d-2\le s0,\\ +\infty &\text{if} &\det F\leq 0, \end{array}\right.\quad \end{align*} based on the Hencky-logarithmic strain tensor $\log U$. Here, $\mu>0$ is the infinitesimal shear modulus, $\kappa>0$ is the infinitesimal bulk modulus, $k,\widehat{k}$ are dimensionless fitting parameters, $F=\nabla \varphi$ is the gradient of deformation, $U=\sqrt{F^T F}$ is the right stretch tensor and ${\rm dev}_n\log {U}$ is the deviatoric part of the strain tensor $\log U$. Based on the multiplicative decomposition $F=F_e\, F_p$, we couple these energies with some isotropic elasto-plastic flow rules $F_p\,\frac{\rm d}{{\rm d t}}[F_p^{-1}]\in-\partial \chi({\rm dev}_3 \Sigma_{e})$ defined in the plastic distortion $F_p$, where $\partial \chi$ is the subdifferential of the indicator function $\chi$ of the convex elastic domain $\mathcal{E}_{\rm e}(W_{\rm iso},{\Sigma_{e}},\frac{1}{3}{\boldsymbol{\sigma}}_{\!\mathbf{y}}^2)$ in the mixed-variant $\Sigma_{e}$-stress space and $\Sigma_{e}=F_e^T D_{F_e} W_{\rm iso}(F_e)$. While $W_{_{\rm eH}}$ may loose ellipticity, we show that loss of ellipticity is effectively prevented by the coupling with plasticity, since the ellipticity domain of $W_{_{\rm eH}}$ on the one hand, and the elastic domain in $\Sigma_{e}$-stress space on the other hand, are closely related. We also review in detail existing isotropic elasto-plastic models based on 6-dimensional flow rules for the positive definite plastic metric tensor $C_p=F_p^T\, F_p$ and highlight their properties and interconnections. \\ ( http://arxiv.org/abs/1409.7555 , 68kb) ------------------------------------------------------------------------------ \\ arXiv:1409.7608 Date: Fri, 26 Sep 2014 15:51:06 GMT (22kb) Title: Lower bounds for resonance counting functions for obstacle scattering in even dimensions Authors: T. J. Christiansen Categories: math-ph math.MP math.SP MSC-class: 35P25, 47A40, 58J50 \\ In even dimensional Euclidean scattering, the resonances lie on the logarithmic cover of the complex plane. This paper studies resonances for obstacle scattering in ${\mathbb R}^d$ with Dirchlet or admissable Robin boundary conditions, when $d$ is even. Set $n_m(r)$ to be the number of resonances with norm at most $r$ and argument between $m\pi$ and $(m+1)\pi$. Then $\lim\sup _{r\rightarrow \infty}\frac{\log n_m(r)}{\log r}=d$ if $m\in {\mathbb Z}\setminus \{ 0\}$. \\ ( http://arxiv.org/abs/1409.7608 , 22kb) ------------------------------------------------------------------------------ \\ arXiv:1409.7647 Date: Fri, 26 Sep 2014 17:45:59 GMT (23kb) Title: On the bi-Hamiltonian Geometry of WDVV Equations Authors: M.V. Pavlov, R.F. Vitolo Categories: math-ph math.MP nlin.SI Comments: 21 pages MSC-class: 37K05, 37K10, 37K20, 37K25 \\ We consider the WDVV associativity equations in the four dimensional case. These nonlinear equations of third order can be written as a pair of six component commuting two-dimensional non-diagonalizable hydrodynamic type systems. We prove that these systems possess a compatible pair of local homogeneous Hamiltonian structures of Dubrovin--Novikov type (of first and third order, respectively). \\ ( http://arxiv.org/abs/1409.7647 , 23kb) %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- ------------------------------------------------------------------------------ \\ arXiv:1409.7424 (*cross-listing*) Date: Thu, 25 Sep 2014 21:22:40 GMT (11kb) Title: Eigenfunction Statistics for Anderson Model with H\"{o}lder continuous single site Potential Authors: Dhriti Ranjan Dolai and Anish Mallick Categories: math.SP math-ph math.MP \\ We consider random Schr\"{o}dinger operators on $\ell^2(\mathbb{Z}^d)$ when the distribution of single site potentials is $\alpha$-H\"{o}lder continuous ($0<\alpha\leq 1$). In localized regime we study the distribution of eigenfunctions simultaneously in space and energy. In a certain scaling limit we prove limits point are Poisson. \\ ( http://arxiv.org/abs/1409.7424 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:1409.7468 (*cross-listing*) Date: Fri, 26 Sep 2014 04:36:45 GMT (21kb) Title: Intermittence and time fractional stochastic partial differential equations Authors: Jebessa B. Mijena and Erkan Nane Categories: math.PR math-ph math.AP math.MP Comments: 20 pages, Submitted for publication. arXiv admin note: text overlap with arXiv:1409.7366 MSC-class: 60H15 \\ We consider time fractional stochastic heat type equation $$\partial^\beta_tu(t,x)=-\nu(-\Delta)^{\alpha/2} u_t(x)+I^{1-\beta}_t[\sigma(u)\stackrel{\cdot}{W}(t,x)]$$ in $(d+1)$ dimensions, where $\nu>0$, $\beta\in (0,1)$, $\alpha\in (0,2]$, $d<\min\{2,\beta^{-1}\}\a$, $\partial^\beta_t$ is the Caputo fractional derivative, $-(-\Delta)^{\alpha/2} $ is the generator of an isotropic stable process, $\stackrel{\cdot}{W}(t,x)$ is space-time white noise, and $\sigma:\RR{R}\to\RR{R}$ is Lipschitz continuous. The time fractional stochastic heat type equations might be used to model phenomenon with random effects with thermal memory. We prove: (i) absolute moments of the solutions of this equation grows exponentially; and (ii) the distances to the origin of the farthest high peaks of those moments grow exactly linearly with time. These results extend the results of Foondun and Khoshnevisan \cite{foondun-khoshnevisan-09} %(Mohammud Foondun and Davar Khoshnevisan, Intermittence and nonlinear parabolic %stochastic partial differential equations, Electron. J. Probab. 14 (2009), no. 21, 548--568) and Conus and Khoshnevisan \cite{conus-khoshnevisan} % (On the existence and position of the farthest peaks of a family of stochastic %heat and wave equations, Probab. Theory Related Fields 152 (2012), no. 3-4, 681--701) on the parabolic stochastic heat equations. \\ ( http://arxiv.org/abs/1409.7468 , 21kb) ------------------------------------------------------------------------------ \\ arXiv:1409.7500 (*cross-listing*) Date: Fri, 26 Sep 2014 08:49:26 GMT (308kb,D) Title: On the broken ray transform Authors: Joonas Ilmavirta Categories: math.DG math-ph math.AP math.MP Comments: 37 pages, 5 figures, only contains the introductory part Report-no: University of Jyv\"askyl\"a, Department of Mathematics and Statistics, Report 140, 2014 \\ This PhD thesis studies the broken ray transform, a generalization of the geodesic X-ray transform where geodesics are replaced with broken rays that reflect on a part of the boundary. The fundamental question is whether this transform is injective. We employ four different methods to approach this question, and each of them gives interesting results. Direct calculation can be used in a ball, where the geometry is particularly simple. If the reflecting part of the boundary is (piecewise) flat, a reflection argument can be used to reduce the problem to the usual X-ray transform. In some geometries one can use broken rays near the boundary to determine the values of the unknown function at the reflector, and even construct its Taylor series. One can also use energy estimates -- which in this context are known as Pestov identities -- to show injectivity in the presence of one convex reflecting obstacle. Many of these methods work also on Riemannian manifolds. We also discuss the periodic broken ray transform, where the integrals are taken over periodic broken rays. The broken ray transform and its periodic version have applications in other inverse problems, including Calder\'on's problem and problems related to spectral geometry. A more detailed abstract can be found in the PDF file. This version only contains the introductory parts of the thesis. The full thesis also contains five articles. \\ ( http://arxiv.org/abs/1409.7500 , 308kb) ------------------------------------------------------------------------------ \\ arXiv:1409.7539 (*cross-listing*) Date: Fri, 26 Sep 2014 11:33:56 GMT (657kb,D) Title: Exploring SU(3) Structure Moduli Spaces with Integrable G2 Structures Authors: Xenia de la Ossa, Magdalena Larfors, Eirik E. Svanes Categories: hep-th math-ph math.MP Comments: 53 pages, 5 figures Report-no: UUITP-11/14 \\ We study the moduli space of SU(3) structure manifolds X that form the internal compact spaces in four-dimensional N=1/2 domain wall solutions of heterotic supergravity with flux. Together with the direction perpendicular to the four-dimensional domain wall, X forms a non-compact 7-manifold Y with torsionful G2 structure. We use this G2 embedding to explore how X(t) varies along paths C(t) in the SU(3) structure moduli space. Our analysis includes the Bianchi identities which strongly constrain the flow. We show that requiring that the SU(3) structure torsion is preserved along the path leads to constraints on the G2 torsion and the embedding of X in Y. Furthermore, we study flows along which the torsion classes of X go from zero to non-zero values. In particular, we present evidence that the flow of half-flat SU(3) structures may contain Calabi-Yau loci, in the presence of non-vanishing H-flux. \\ ( http://arxiv.org/abs/1409.7539 , 657kb) ------------------------------------------------------------------------------ \\ arXiv:1409.7658 (*cross-listing*) Date: Fri, 26 Sep 2014 18:21:16 GMT (89kb) Title: Isotropic realizability of current fields in R^3 Authors: Marc Briane (IRMAR), Graeme W. Milton Categories: math.AP math-ph math.MP Comments: 22 pages \\ This paper deals with the isotropic realizability of a given regular divergence free field j in R^3 as a current field, namely to know when j can be written as sigma Du for some isotropic conductivity sigma, and some gradient field Du. The local isotropic realizability in R^3 is obtained by Frobenius' theorem provided that j and curl j are orthogonal in R^3. A counter-example shows that Frobenius' condition is not sufficient to derive the global isotropic realizability in R^3. However, assuming that (j, curl j, j x curl j) is an orthogonal basis of R^3, an admissible conductivity sigma is constructed from a combination of the three dynamical flows along the directions j/|j|, curl j/|curl j| and (j/|j|^2) x curl j. When the field j is periodic, the isotropic realizability in the torus needs in addition a boundedness assumption satisfied by the flow along the third direction (j/|j|^2) x \curl j. Several examples illustrate the sharpness of the realizability conditions. \\ ( http://arxiv.org/abs/1409.7658 , 89kb) %%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%% ------------------------------------------------------------------------------ \\ arXiv:0910.3831 replaced with revised version Fri, 26 Sep 2014 01:00:56 GMT (44kb) Title: Definition and characterization of supersmooth functions on superspace based on Fr\'echet-Grassmann algebra Authors: Atsushi Inoue Categories: math-ph math.MP Comments: 41 pages, 2 figures MSC-class: 58C50, 46S10, 58A50, 17A01 \\ ( http://arxiv.org/abs/0910.3831 , 44kb) ------------------------------------------------------------------------------ \\ arXiv:1405.7375 (*cross-listing*) replaced with revised version Fri, 26 Sep 2014 17:58:59 GMT (188kb,D) Title: Tensor Network Contractions for #SAT Authors: Jacob D. Biamonte, Jason Morton, Jacob W. Turner Categories: quant-ph cs.CC cs.LO math-ph math.MP Comments: 16 pages, 8 diagrams ACM-class: F.2; F.2.1; F.4 \\ ( http://arxiv.org/abs/1405.7375 , 188kb) ------------------------------------------------------------------------------ \\ arXiv:1406.2381 (*cross-listing*) replaced with revised version Fri, 26 Sep 2014 07:46:54 GMT (141kb) Title: Instanton moduli spaces and $\mathscr W$-algebras Authors: Alexander Braverman, Michael Finkelberg and Hiraku Nakajima Categories: math.QA hep-th math-ph math.AG math.MP math.RT Comments: 117 pages; v2, 120 pages, definition of the inner product corrected MSC-class: Primary 17B69, Secondary 14D21, 14J60 \\ ( http://arxiv.org/abs/1406.2381 , 141kb) ------------------------------------------------------------------------------ \\ arXiv:1406.6240 (*cross-listing*) replaced with revised version Fri, 26 Sep 2014 08:54:24 GMT (10kb) Title: On a stability property of Skyrme-related energy functionals Authors: Radu Slobodeanu Categories: math.DG hep-th math-ph math.MP Comments: 10 pages, includes minor corrections; match the published version (Quart.J.Math.) DOI: 10.1093/qmath/hau024 \\ ( http://arxiv.org/abs/1406.6240 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:1408.1645 replaced with revised version Fri, 26 Sep 2014 17:01:05 GMT (33kb,D) Title: Pure quasifree states of the Dirac field from the fermionic projector Authors: Christopher J. Fewster and Benjamin Lang Categories: math-ph math.MP Comments: v2 26pp. New results added concerning fluctuations of Wick polynomials \\ ( http://arxiv.org/abs/1408.1645 , 33kb) ------------------------------------------------------------------------------ \\ arXiv:1409.0570 (*cross-listing*) replaced with revised version Fri, 26 Sep 2014 19:49:56 GMT (81kb,D) Title: Multivariate orthogonal polynomial and integrable systems Authors: Gerardo Ariznabarreta and Manuel Ma\~nas Categories: math.CA math-ph math.MP math.RA nlin.SI Comments: In this second version we have improved Section 5 and corrected some missprints MSC-class: 15A23, 33C45, 37K10, 37L60, 42C05, 46L55 \\ ( http://arxiv.org/abs/1409.0570 , 81kb) ------------------------------------------------------------------------------ \\ arXiv:1409.0652 replaced with revised version Fri, 26 Sep 2014 18:15:34 GMT (28kb) Title: The limit of small Rossby numbers for randomly forced quasi-geostrophic equation on $\beta$-plane Authors: Sergei Kuksin and Alberto Maiocchi Categories: math-ph math.MP \\ ( http://arxiv.org/abs/1409.0652 , 28kb) ------------------------------------------------------------------------------ \\ arXiv:1409.3034 replaced with revised version Fri, 26 Sep 2014 10:41:45 GMT (13kb) Title: New Algebraic Structures from Hermitian One-Matrix Model Authors: Xiang-Mao Ding, Yuping Li and Lingxian Meng Categories: math-ph hep-th math.MP Comments: 1+16 pages, several types corrected, a little modification \\ ( http://arxiv.org/abs/1409.3034 , 13kb) ------------------------------------------------------------------------------ \\ arXiv:1409.3562 (*cross-listing*) replaced with revised version Fri, 26 Sep 2014 19:47:15 GMT (36kb) Title: Strong converse exponent for classical-quantum channel coding Authors: Milan Mosonyi and Tomohiro Ogawa Categories: quant-ph cs.IT math-ph math.IT math.MP Comments: v3: Considerably revised, many technical details fixed, the assumption of the finiteness of the input alphabet removed. 34 pages \\ ( http://arxiv.org/abs/1409.3562 , 36kb) ------------------------------------------------------------------------------ \\ arXiv:1409.6851 (*cross-listing*) replaced with revised version Fri, 26 Sep 2014 09:42:07 GMT (14kb) Title: Gauge theory of quantum gravity Authors: Cao H. Nam Categories: hep-th gr-qc math-ph math.MP Comments: 11 pages, discussions and references added, a mistake of Eq. (10) corrected, results unchanged \\ ( http://arxiv.org/abs/1409.6851 , 14kb) %%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%--- 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