Date: Thu, 27 Dec 18 01:49:47 GMT Subject: math-ph daily 13 new + 19 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 Fri 21 Dec 18 19:00:00 GMT to Wed 26 Dec 18 19:00:00 GMT ------------------------------------------------------------------------------ \\ arXiv:1812.09354 Date: Fri, 21 Dec 2018 19:47:08 GMT (427kb,D) Title: Compatibility Conditions for Discrete Planar Structure Authors: Andrejs Treibergs, Andrej Cherkaev, Predrag Krtolica Categories: math-ph math.MP \\ Compatibility conditions are investigated for planar network structures consisting of nodes and connecting bars; these conditions restrict the elongations of bars and are analogous to the compatibility conditions of deformation in continuum mechanics. The requirement that the deformations remain planar imposes compatibility. Compatibility for structures with prescribed lengths and its linearization is considered. For triangulated structures, compatibility is expressed as a polynomial equation in the lengths of edges of the star domain surrounding each interior node. The continuum limits of the conditions coincide with those in the continuum problems. The compatibility equations may be summed along a closed curve to give conditions analogous to Gauss-Bonnet integral formula. There are rigid trusses without compatibility conditions in contrast to continuous materials. The compatibility equations around a hole involve the edges in the neighborhood surrounding the hole. The number of compatibility conditions is the number of bars that may be removed from a structure while keeping it rigid; this number measures the structural resilience. An asymptotic density of compatibility conditions is analyzed. \\ ( https://arxiv.org/abs/1812.09354 , 427kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09390 Date: Fri, 21 Dec 2018 22:09:03 GMT (44kb) Title: Decay of the Local Energy for the Charged Klein-Gordon Equation in the Exterior De Sitter-Reissner-Nordstr\"om Spacetime Authors: Nicolas Besset Categories: math-ph math.MP \\ We show decay of the local energy of solutions of the charged Klein-Gordon equation in the exterior De Sitter-Reissner-Nordstr\"om spacetime by means of a resonance expansion of the local propagator. \\ ( https://arxiv.org/abs/1812.09390 , 44kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09399 Date: Fri, 21 Dec 2018 22:37:33 GMT (641kb,D) Title: On rotationally invariant integrable and superintegrable systems in magnetic fields with non-subgroup type integrals Authors: Sebastien Bertrand, Libor \v{S}nobl Categories: math-ph math.MP MSC-class: 37J35, 78A25 \\ The aim of the present article is to construct quadratically integrable three dimensional systems in non-vanishing magnetic fields which possess so-called non-subgroup type integrals. The presence of such integrals means that the system possesses a pair of integrals of motion in involution which are (at most) quadratic in momenta and whose leading order terms, that are necessarily elements of the enveloping algebra of the Euclidean algebra, are not quadratic Casimir operators of a chain of its subalgebras. By imposing in addition that one of the integrals has the leading order term $L_z^2$ we can consider three such commuting pairs: circular parabolic, oblate spheroidal and prolate spheroidal. We find all possible integrable systems possessing such structure of commuting integrals and describe their Hamiltonians and their integrals. We show that our assumptions imply the existence of a first order integral $L_z $, i.e. rotational invariance, of all such systems. As a consequence, the Hamilton--Jacobi equation of each of these systems with magnetic field separates in the corresponding coordinate system, as it is known to be the case for all quadratically integrable systems without magnetic field, and in contrast with the subgroup type, i.e. Cartesian, spherical and cylindrical, cases, with magnetic fields. We also look for superintegrable systems within the circular parabolic integrable class. Assuming the additional integral to be first order we demonstrate that only previously known systems exist. However, for a particular second order ansatz for the sought integral ($L^2+\ldots$) we find a minimally quadratically superintegrable system. It is not quadratically maximally superintegrable but appears to possess bounded closed trajectories, hinting at hypothetical higher order superintegrability. \\ ( https://arxiv.org/abs/1812.09399 , 641kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09685 Date: Sun, 23 Dec 2018 10:29:12 GMT (7kb) Title: The Static Elliptic $N$-soliton Solutions of the KdV Equation Authors: Masahito Hayashi, Kazuyasu Shigemoto and Takuya Tsukioka Categories: math-ph math.MP Comments: 8 pages \\ Regarding $N$-soliton solutions, the trigonometric type, the hyperbolic type, and the exponential type solutions are well studied. While for the elliptic type solution, we know only the one-soliton solution so far. Using the commutative B\"{a}cklund transformation, we have succeeded in constructing the KdV static elliptic $N$-soliton solution, which means that we have constructed infinitely many solutions for the $\wp$-function type differential equation. \\ ( https://arxiv.org/abs/1812.09685 , 7kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09709 Date: Sun, 23 Dec 2018 13:42:56 GMT (17kb) Title: Poisson Structure of the Three-Dimensional Euler Equations in Fourier Space Authors: Holger R. Dullin, James D. Meiss, and Joachim Worthington Categories: math-ph math.DS math.MP \\ We derive a Poisson structure in the space of Fourier modes for the Euler equations in vorticity formulation on a three-dimensional periodic domain. This allows us to analyse the structure of the Euler equations using a Hamiltonian framework. The Poisson structure is then restricted to the divergence-free subspace on which the dynamics of the Euler equations takes place, reducing the size of the system of ODEs by a third. The divergence-free subspace is realised as a subspace define by sub-Casimirs, which are invariants which are Casimirs only after restriction to the subspace. The Poisson structure is shown to have the helicity as a Casimir invariant. We conclude by showing that periodic shear flows in three dimensions are equilibria that correspond to singular points of the Poisson structure, and hence the usual approach to study their nonlinear stability through the Energy-Casimir method fails. \\ ( https://arxiv.org/abs/1812.09709 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09765 Date: Sun, 23 Dec 2018 20:00:49 GMT (590kb) Title: Construction of non-PT-symmetric complex potentials with all-real spectra Authors: Jianke Yang Categories: math-ph math.MP physics.optics Comments: 22 pages, 6 figures Journal-ref: book chapter in "Parity-time Symmetry and Its Applications" (D. Christodoulides and J. Yang (eds.), Springer 2018), pp. 513-534 DOI: 10.1007/978-981-13-1247-2_18 \\ We review recent work on the generalization of PT symmetry. We show that, in addition to PT-symmetric complex potentials, there are also large classes of non-PT-symmetric complex potentials which also feature all-real spectra. In addition, some classes of these non-PT-symmetric potentials allow phase transitions which do or do not go through exceptional points. These non-PT-symmetric potentials are constructed by a variety of methods, such as the symmetry and supersymmetry methods and the soliton theory. A generalization of PT symmetry in multi-dimensions is also reviewed. \\ ( https://arxiv.org/abs/1812.09765 , 590kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09795 Date: Sun, 23 Dec 2018 23:26:32 GMT (341kb,D) Title: Triangular Schlesinger systems and superelliptic curves Authors: Vladimir Dragovi\'c, Renat Gontsov, Vasilisa Shramchenko Categories: math-ph math.MP Comments: 27 pages, 2 figures \\ We study the Schlesinger system of partial differential equations in the case when the unknown matrices of arbitrary size $(p\times p)$ are triangular and the eigenvalues of each matrix, called the exponents of the system, form an arithmetic progression with a rational difference $q$, the same for all matrices. Such a system possesses a family of solutions expressed via periods of meromorphic differentials on the Riemann surfaces of superelliptic curves. We determine the values of the difference $q$, for which our solutions lead to explicit polynomial solutions of the Schlesinger system. As an application of the $(2\times2)$-case, we obtain explicit rational solutions of Painlev\'e VI equations as well as a class of Liouvillian solutions for various Painlev\'e VI equations. Using similar methods, we provide algebraic solutions of particular Garnier systems. \\ ( https://arxiv.org/abs/1812.09795 , 341kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09893 Date: Mon, 24 Dec 2018 11:27:11 GMT (779kb,D) Title: Information geometric duality of $\phi$-deformed exponential families Authors: Jan Korbel, Rudolf Hanel, Stefan Thurner Categories: math-ph math.MP Comments: 9 pages, 2 figures \\ In the world of generalized entropies---which, for example, play a role in physical systems with sub- and super-exponential phasespace growth per degree of freedom---there are two ways for implementing constraints in the maximum entropy principle: linear- and escort constraints. Both appear naturally in different contexts. Linear constraints appear e.g. in physical systems, when additional information about the system is available through higher moments. Escort distributions appear naturally in the context of multifractals and information geometry. It was shown recently that there exists a fundamental duality that relates both approaches on the basis of the corresponding deformed logarithms (deformed-log duality). Here we show that there exists another duality that arises in the context of information geometry, relating the Fisher information of $\phi$-deformed exponential families that correspond to linear constraints (as studied by J. Naudts), with those that are based on escort constraints (as studied by S.-I. Amari). We explicitly demonstrate this information geometric duality for the case of $(c,d)$-entropy that covers all situations that are compatible with the first three Shannon-Khinchin axioms, and that include Shannon, Tsallis, Anteneodo-Plastino entropy, and many more as special cases. Finally, we discuss the relation between the deformed-log duality and the information geometric duality, and mention that the escort distributions arising in the two dualities are generally different and only coincide for the case of the Tsallis deformation. \\ ( https://arxiv.org/abs/1812.09893 , 779kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10019 Date: Tue, 25 Dec 2018 03:28:01 GMT (123kb,D) Title: Are almost-symmetries almost linear? Authors: Javier Cuesta, Michael M. Wolf Categories: math-ph math.MP quant-ph Comments: 8 pages, 1 figure \\ It $d-$pends. Wigner's symmetry theorem implies that transformations that preserve transition probabilities of pure quantum states are linear maps on the level of density operators. We investigate the stability of this implication. On the one hand, we show that any transformation that preserves transition probabilities up to an additive $\varepsilon$ in a separable Hilbert space admits a weak linear approximation, i.e. one relative to any fixed observable. This implies the existence of a linear approximation that is $4\sqrt{\varepsilon} d$-close in Hilbert-Schmidt norm, with $d$ the Hilbert space dimension. On the other hand, we prove that a linear approximation that is close in norm and independent of $d$ does not exist in general. To this end, we provide a lower bound that depends logarithmically on $d$. \\ ( https://arxiv.org/abs/1812.10019 , 123kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10132 Date: Tue, 25 Dec 2018 16:27:25 GMT (13kb) Title: On critical value of the coupling constant in exterior elliptic problems Authors: R.Puri, B.Vainberg Categories: math-ph math.MP MSC-class: 35J25, 35P15, 47A10, 47D07 \\ We consider exterior elliptic problems with coefficients stabilizing at infinity and study the critical value $\beta_{cr}$ of the coupling constant (the coefficient at the potential) that separates operators with a discrete spectrum and those without it. The dependence of $\beta_{cr}$ on the boundary condition and on the distance between the boundary and the support of the potential is described. The discrete spectrum of a non-symmetric operator with the FKW boundary condition (that appears in diffusion processes with traps) is also investigated. \\ ( https://arxiv.org/abs/1812.10132 , 13kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10274 Date: Wed, 26 Dec 2018 09:54:13 GMT (61kb) Title: Finite-size scaling of free energy in the dimer model on a hexagonal domain Authors: Anton Nazarov Categories: math-ph cond-mat.stat-mech math.MP Comments: 11 pages, 1 figure, submitted to "Theoretical and mathematical physics", based on MQFT-2018 conference talk MSC-class: 82B20 \\ We consider dimer model on a hexagonal lattice. This model can be seen as a "pile of cubes in the corner". The energy of configuration is given by the volume of the pile and the partition function is computed by the classical MacMahon formula or, more formally, by the determinant of Kasteleyn matrix. We use the expression for the partition function to derive the scaling behavior of free energy in the limit of lattice mesh tending to zero and temperature tending to infinity. We discuss the universality and physical meaning of expansion coefficients. \\ ( https://arxiv.org/abs/1812.10274 , 61kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10275 Date: Wed, 26 Dec 2018 09:54:34 GMT (13kb,D) Title: Crossover phenomena in the critical behavior for long-range models with power-law couplings Authors: Akira Sakai Categories: math-ph math.MP math.PR Comments: 11 pages, 6 diagram pictures in equations MSC-class: 60K35, 82B20, 82B27, 82B41, 82B43 \\ This is a short review of the two papers on the $x$-space asymptotics of the critical two-point function $G_{p_c}(x)$ for the long-range models of self-avoiding walk, percolation and the Ising model on $\mathbb{Z}^d$, defined by the translation-invariant power-law step-distribution/coupling $D(x)\propto|x|^{-d-\alpha}$ for some $\alpha>0$. Let $S_1(x)$ be the random-walk Green function generated by $D$. We have shown that $\bullet~~S_1(x)$ changes its asymptotic behavior from Newton ($\alpha>2$) to Riesz ($\alpha<2$), with log correction at $\alpha=2$; $\bullet~~G_{p_c}(x)\sim\frac{A}{p_c}S_1(x)$ as $|x|\to\infty$ in dimensions higher than (or equal to, if $\alpha=2$) the upper critical dimension $d_c$ (with sufficiently large spread-out parameter $L$). The model-dependent $A$ and $d_c$ exhibit crossover at $\alpha=2$. The keys to the proof are (i) detailed analysis on the underlying random walk to derive sharp asymptotics of $S_1$, (ii) bounds on convolutions of power functions (with log corrections, if $\alpha=2$) to optimally control the lace-expansion coefficients $\pi_p^{(n)}$, and (iii) probabilistic interpretation (valid only when $\alpha\le2$) of the convolution of $D$ and a function $\varPi_p$ of the alternating series $\sum_{n=0}^\infty(-1)^n\pi_p^{(n)}$. We outline the proof, emphasizing the above key elements for percolation in particular. \\ ( https://arxiv.org/abs/1812.10275 , 13kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10362 Date: Wed, 26 Dec 2018 16:24:27 GMT (42kb) Title: Crossing invariant correlation functions at $c=1$ from isomonodromic $\tau$ functions Authors: Pavlo Gavrylenko, Raoul Santachiara Categories: math-ph math.MP Comments: 36 pages \\ We present an approach that gives rigorous construction of a class of crossing invariant functions in $c=1$ CFTs from the weakly invariant distributions on the moduli space $\mathcal M_{0,4}^{SL(2,\mathbb{C})}$ of $SL(2,\mathbb{C})$ flat connections on the sphere with four punctures. By using this approach we show how to obtain correlation functions in the Ashkin-Teller and the Runkel-Watts theory. Among the possible crossing-invariant theories, we obtain also the analytic Liouville theory, whose consistence was assumed only on the basis of numerical tests. \\ ( https://arxiv.org/abs/1812.10362 , 42kb) %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- ------------------------------------------------------------------------------ \\ arXiv:1812.08616 (*cross-listing*) Date: Thu, 20 Dec 2018 14:52:09 GMT (43kb) Title: Non-commutative Fourier transform for the Lorentz group via the Duflo map Authors: Daniele Oriti, Giacomo Rosati Categories: hep-th gr-qc math-ph math.MP \\ We defined a non-commutative algebra representation for quantum systems whose phase space is the cotangent bundle of the Lorentz group, and the non-commutative Fourier transform ensuring the unitary equivalence with the standard group representation. Our construction is from first principles in the sense that all structures are derived from the choice of quantization map for the classical system, the Duflo quantization map. \\ ( https://arxiv.org/abs/1812.08616 , 43kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09515 (*cross-listing*) Date: Sat, 22 Dec 2018 12:00:28 GMT (29kb,D) Title: Flat $\mathfrak{so}(p,q)$-Connections for Manifolds of Non-Euclidean Signature Authors: Arash Ranjbar and Jorge Zanelli Categories: hep-th math-ph math.DG math.MP Comments: 25 pages, 2 figures \\ The well-known fact that $S^1$, $S^3$ and $S^7$ are parallelizable manifolds admitting flat connections is revisited. The role of torsion in the construction of those flat connections is made explicit, and the possibilities allowed by different metric signatures are examined. A necessary condition for parallelizability in an open region is that the torsion tensor must be covariantly constant. This property can be used to obtain a relation between a torsion-free and flat connections. Our treatment covers Riemannian and pseudo-Riemannian (non-Euclidean signature) hyperbolic manifolds of dimensions three and seven. Apart from the spherical cases mentioned above, the explicit flat $\mathfrak{so}(p,q)$ connections with $p+q=3,7$ are constructed for the coset manifolds $SO(p,q+1)/SO(p,q)$ or $SO(p+1,q)/SO(p,q)$. \\ ( https://arxiv.org/abs/1812.09515 , 29kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09667 (*cross-listing*) Date: Sun, 23 Dec 2018 07:35:00 GMT (59kb,D) Title: Dirichlet p-Laplacian eigenvalues and Cheeger constants on symmetric graphs Authors: Bobo Hua and Lili Wang Categories: math.SP math-ph math.AP math.CO math.DG math.MP Comments: 32 pages \\ In this paper, we study eigenvalues and eigenfunctions of $p$-Laplacians with Dirichlet boundary condition on graphs. We characterize the first eigenfunction (and the maximum eigenfunction for a bipartite graph) via the sign condition. By the uniqueness of the first eigenfunction of $p$-Laplacian, as $p\to 1,$ we identify the Cheeger constant of a symmetric graph with that of the quotient graph. By this approach, we calculate various Cheeger constants of spherically symmetric graphs. \\ ( https://arxiv.org/abs/1812.09667 , 59kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09679 (*cross-listing*) Date: Sun, 23 Dec 2018 09:55:22 GMT (70kb,A) Title: The image of the Burnside ring in the Representation ring for binary Platonic groups Authors: Simon Burton, Hisham Sati, Urs Schreiber Categories: math.RT math-ph math.AT math.GR math.MP Comments: 44 pages, Python code attached as ancillary file \\ We describe an efficient algorithm that computes, for any finite group G, the linear span of its virtual permutation representations inside all its linear representations, hence the image of the canonical morphism $\beta$ from the Burnside ring to the representation ring. We use this to determine the image and cokernel of $\beta$ for binary Platonic groups, hence for finite subgroups of SU(2), over $k \in \{\mathbb{Q}, \mathbb{R}, \mathbb{C}\}$. We find explicitly that for the three exceptional subgroups and for the first seven binary dihedral subgroups, $\beta$ surjects onto the sub-lattice of the real representation ring spanned by the integer-valued characters. We conjecture that, generally, this holds true for all the binary dihedral groups. \\ ( https://arxiv.org/abs/1812.09679 , 70kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09791 (*cross-listing*) Date: Sun, 23 Dec 2018 22:50:04 GMT (23kb) Title: Twisted De Rham complex on line and $\widehat{frak{sl}_2}$ singular vectors Authors: Alexey Slinkin and Alexander Varchenko Categories: math.AG math-ph math.MP math.QA Comments: Latex, 29 pages \\ We consider two complexes. The first complex is the twisted De Rham complex of scalar meromorphic differential forms on projective line, holomorphic on the complement to a finite set of points. The second complex is the chain complex of the Lie algebra of $\frak{sl}_2$-valued algebraic functions on the same complement, with coefficients in a tensor product of contragradient dual Verma modules over the affine Lie algebra $\widehat{frak{sl}_2}$. In [SV2] a construction of a monomorphism of the first complex to the second was suggested. It was indicated in [SV2] that under this monomorphism the existence of singular vectors in the Verma modules (the Malikov-Feigin-Fuchs singular vectors) is reflected in the relations between the cohomology classes of the De Rham complex. In this paper we prove the results formulated in [SV2]. \\ ( https://arxiv.org/abs/1812.09791 , 23kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09850 (*cross-listing*) Date: Mon, 24 Dec 2018 07:31:19 GMT (26kb) Title: Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models Authors: Marta Lewicka Categories: math.AP math-ph math.MP Comments: 23 pages \\ This paper concerns the variational description of prestrained materials, in the context of dimension reduction for thin films $\Omega^h=\omega\times (-\frac{h}{2}, \frac{h}{2})$. Given a Riemann metric $G$ on $\Omega^1$, we study the question of what is the infimum of the averaged pointwise deficit of a given immersion from being an orientation-preserving isometric immersion of $G_{\mid \Omega^h}$ on $\Omega^h,$ over all weakly regular immersions. This deficit is measured by the non-Euclidean energies $\mathcal{E}^h$, which can be seen as modifications of the classical nonlinear three-dimensional elasticity. Building on our previous results, we complete the scaling analysis of $\mathcal{E}^h$ and the derivation of $\Gamma$-limits of the scaled energies $h^{-2n}\mathcal{E}^h$, for all $n\geq 1$. We show the energy quantisation in the sense that the even powers $2n$ of $h$ are indeed the only possible ones (all of them are also attained). For each $n$, we identify the equivalent conditions for the validity of the corresponding scaling, in terms of the vanishing of appropriate Riemann curvatures of $G$ to certain orders, and in terms of the matched isometry expansions. We also establish the asymptotic behaviour of the minimizing immersions as $h\to 0$. \\ ( https://arxiv.org/abs/1812.09850 , 26kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09898 (*cross-listing*) Date: Mon, 24 Dec 2018 11:36:49 GMT (14kb) Title: Analysis and boundary value problems on domains with a smooth set of singular points: an approach via bounded geometry Authors: Bernd Ammann, Nadine Grosse, Victor Nistor Categories: math.AP math-ph math.DG math.MP Comments: 8 pages, announcement with sketches of the proofs and a summary in French \\ We prove well-posedness and regularity results for elliptic boundary value problems on certain domains with a smooth set of singular points. Our class of domains contains the class of domains with isolated oscillating conical singularities, and hence they generalize the classical results of Kondratiev on domains with conical singularities. The proofs are based on conformal changes of metric, on the differential geometry of manifolds with boundary and bounded geometry, and on our earlier results on manifolds with boundary and bounded geometry. \\ ( https://arxiv.org/abs/1812.09898 , 14kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09919 (*cross-listing*) Date: Mon, 24 Dec 2018 13:27:44 GMT (411kb,D) Title: Algebraic Structures in the Coupling of Gravity to Gauge Theories Authors: David Prinz Categories: hep-th gr-qc math-ph math.MP Comments: 50 pages, 259 Feynman diagrams MSC-class: 16, 53, 81, 83 \\ This article is an extension of the authors second master thesis [1]. It aims to introduce the theory of perturbatively quantized General Relativity coupled to Spinor Electrodynamics, provide the results thereof and set the notation to serve as a starting point for further research in this direction. It includes the differential geometric and Hopf algebraic background, as well as the corresponding Lagrange density and some renormalization theory. Then, a particular problem in the renormalization of Quantum General Relativity coupled to Quantum Electrodynamics is addressed and solved by a generalization of Furry's Theorem. Next, the restricted combinatorial Green's functions for all two-loop propagator and all one-loop divergent subgraphs thereof are presented. Finally, relations between these one-loop restricted combinatorial Green's functions necessary for multiplicative renormalization are discussed. One of those relations suggests that it is unphysical to consider the coupling to Spinor Electrodynamics alone and instead consider the coupling to the whole Electroweak Sector. \\ ( https://arxiv.org/abs/1812.09919 , 411kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09995 (*cross-listing*) Date: Mon, 24 Dec 2018 22:44:27 GMT (13kb) Title: Jordan operator algebras revisited Authors: David P. Blecher and Zhenhua Wang Categories: math.OA math-ph math.FA math.MP Comments: 10 pages \\ Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with a^2 in A for all a in A. In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory of associative operator algebras, in particularly surprisingly much of the associative theory from several recent papers of the first author and coauthors, generalizes to Jordan operator algebras. In the present paper we complete this task, giving several results which generalize the associative case in these papers, relating to unitizations, real positivity, hereditary subalgebras, and a couple of other topics. We also solve one of the three open problems stated at the end of our earlier joint paper on Jordan operator algebras. \\ ( https://arxiv.org/abs/1812.09995 , 13kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10043 (*cross-listing*) Date: Tue, 25 Dec 2018 06:02:27 GMT (20kb) Title: Q-operator for the quantum NLS model Authors: N. Belousov, S. Derkachov Categories: hep-th math-ph math.MP \\ In this paper we show that the operator introduced by A. A. Tsvetkov enjoys all the needed properties of a Q-operator. It is shown that the Q-operator of the XXX spin chain with generic values of spin turns into Tsvetkov's operator in the continuum limit for large spin. \\ ( https://arxiv.org/abs/1812.10043 , 20kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10091 (*cross-listing*) Date: Tue, 25 Dec 2018 11:19:57 GMT (1494kb) Title: Quantum information measures of the Aharonov-Bohm ring in uniform magnetic fields Authors: O. Olendski Categories: quant-ph cond-mat.mes-hall math-ph math.MP Comments: 11 figures, 1 table \\ Shannon quantum information entropies $S_{\rho,\gamma}$, Fisher informations $I_{\rho,\gamma}$, Onicescu energies $O_{\rho,\gamma}$ and complexities $e^SO$ are calculated both in position (subscript $\rho$) and momentum ($\gamma$) spaces for azimuthally symmetric 2D nanoring that is placed into combination of transverse uniform magnetic field $\bf B$ and Aharonov-Bohm (AB) flux $\phi_{AB}$ and whose potential profile is modeled by superposition of quadratic and inverse quadratic dependencies on radius $r$. Increasing intensity $B$ flattens momentum waveforms $\Phi_{nm}({\bf k})$ and in the limit of infinitely large fields they turn to zero, what means that the position wave functions $\Psi_{nm}({\bf r})$, which are their Fourier counterparts, tend in this limit to the $\delta$-functions. Position (momentum) Shannon entropy depends on the field $B$ as a negative (positive) logarithm of $\omega_{eff}\equiv\left(\omega_0^2+\omega_c^2/4\right)^{1/2}$, where $\omega_0$ determines the quadratic steepness of the confining potential and $\omega_c$ is a cyclotron frequency. This makes the sum ${S_\rho}_{nm}+{S_\gamma}_{nm}$ a field-independent quantity that increases with the principal $n$ and azimuthal $m$ quantum numbers and does satisfy entropic uncertainty relation. Position Fisher information does not depend on $m$, linearly increases with $n$ and varies as $\omega_{eff}$ whereas its $n$ and $m$ dependent Onicescu counterpart ${O_\rho}_{nm}$ changes as $\omega_{eff}^{-1}$. The products ${I_\rho}_{nm}{I_\gamma}_{nm}$ and ${O_\rho}_{nm}{O_\gamma}_{nm}$ are $B$-independent quantities. A dependence of the measures on the ring geometry is discussed. It is argued that a variation of the position Shannon entropy or Onicescu energy with the AB field uniquely determines an associated persistent current as a function of $\phi_{AB}$ at $B=0$. An inverse statement is correct too. \\ ( https://arxiv.org/abs/1812.10091 , 1494kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10145 (*cross-listing*) Date: Tue, 25 Dec 2018 17:57:55 GMT (81kb,AD) Title: Efficiently computable bounds for magic state distillation Authors: Xin Wang, Mark M. Wilde, Yuan Su Categories: quant-ph cs.IT math-ph math.IT math.MP Comments: 16 pages, 1 figure \\ Magic state manipulation is a crucial component in the leading approaches to realizing scalable, fault-tolerant, and universal quantum computation. Related to magic state manipulation is the resource theory of magic states, for which one of the goals is to characterize and quantify quantum "magic." In this paper, we introduce the family of thauma measures to quantify the amount of magic in a quantum state, and we exploit this family of measures to address several open questions in the resource theory of magic states. As a first application, we use the min-thauma to bound the regularized relative entropy of magic. As a consequence of this bound, we find that two classes of states with maximal mana, a previously established magic measure, cannot be interconverted in the asymptotic regime at a rate equal to one. This result resolves a basic question in the resource theory of magic states and reveals a fundamental difference between the resource theory of magic states and other resource theories such as entanglement and coherence. As a second application, we establish the hypothesis testing thauma as an efficiently computable benchmark for the one-shot distillable magic, which in turn leads to a variety of bounds on the rate at which magic can be distilled, as well as on the overhead of magic state distillation. Finally, we prove that the max-thauma can outperform mana in benchmarking the efficiency of magic state distillation. \\ ( https://arxiv.org/abs/1812.10145 , 81kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10156 (*cross-listing*) Date: Tue, 25 Dec 2018 19:11:25 GMT (514kb,D) Title: Deep neural networks are biased towards simple functions Authors: Giacomo De Palma, Bobak Toussi Kiani and Seth Lloyd Categories: stat.ML cond-mat.dis-nn cs.LG math-ph math.MP quant-ph \\ We prove that the binary classifiers of bit strings generated by random wide deep neural networks are biased towards simple functions. The simplicity is captured by the following two properties. For any given input bit string, the average Hamming distance of the closest input bit string with a different classification is at least $\sqrt{n\left/\left(2\pi\ln n\right)\right.}$, where $n$ is the length of the string. Moreover, if the bits of the initial string are flipped randomly, the average number of flips required to change the classification grows linearly with $n$. On the contrary, for a uniformly random binary classifier, the average Hamming distance of the closest input bit string with a different classification is one, and the average number of random flips required to change the classification is two. These results are confirmed by numerical experiments on deep neural networks with two hidden layers, and settle the conjecture stating that random deep neural networks are biased towards simple functions. The conjecture that random deep neural networks are biased towards simple functions was proposed and numerically explored in [Valle P\'erez et al., arXiv:1805.08522] to explain the unreasonably good generalization properties of deep learning algorithms. By providing a precise characterization of the form of this bias towards simplicity, our results open the way to a rigorous proof of the generalization properties of deep learning algorithms in real-world scenarios. \\ ( https://arxiv.org/abs/1812.10156 , 514kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10168 (*cross-listing*) Date: Tue, 25 Dec 2018 21:25:32 GMT (11kb) Title: Extended supersymmetric Calogero model Authors: Sergey Krivonos, Olaf Lechtenfeld, Alexander Provorov, Anton Sutulin Categories: hep-th math-ph math.MP Comments: 1+7 pages \\ We present a surprising redefinition of matrix fermions which brings the supercharges of the $\cal N$-extended supersymmetric $A_{n-1}$ Calogero model introduced in [1] to the standard form maximally cubic in the fermions. The complexity of the model is transferred to a non-canonical and nonlinear conjugation property of the fermions. Employing the new cubic supercharges, we apply a supersymmetric generalization of a "folding" procedure for $A_{2n-1}\oplus A_1$ to explicitly construct the supercharges and Hamiltonian for arbitrary even-$\cal N$ supersymmetric extensions of the $B_n$, $C_n$ and $D_n$ rational Calogero models. We demonstrate that all considered models possess a dynamical $osp({\cal N}|2)$ superconformal symmetry. \\ ( https://arxiv.org/abs/1812.10168 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10287 (*cross-listing*) Date: Wed, 26 Dec 2018 12:01:23 GMT (875kb) Title: Toric Quiver Asymptotics and Mahler Measure: $\mathcal{N}=2$ BPS States Authors: Ali Zahabi Categories: hep-th math-ph math.MP Comments: 25 pages, 12 figures \\ BPS sector in $\mathcal{N}=2$, four-dimensional toric quiver gauge theories has previously been studied using crystal melting model and dimer model. We introduce the Mahler measure associated to statistical dimer model to study large $N$ limit of these quiver gauge theories. In this limit, generating function of BPS states in a general toric quiver theory is studied and entropy, growth rate of BPS states and free energy of the quiver are obtained in terms of the Mahler measure. Moreover, a possible third-order phase transition in toric quivers is discussed. Explicit computations of profile function, entropy density, BPS growth rate and phase structure of quivers are presented in concrete examples of clover $\mathbb{C}^3$, and resolved conifold $\mathcal{C}$ quivers. Finally, BPS growth rates of Hirzebruch $\mathbb{F}_0$, and $\mathbb{C}^3/ \mathbb{Z}^2\times \mathbb{Z}^2$ orbifold quivers are obtained and a possible interpretation of the results for certain BPS black holes is discussed. \\ ( https://arxiv.org/abs/1812.10287 , 875kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10314 (*cross-listing*) Date: Wed, 26 Dec 2018 13:50:04 GMT (51kb,D) Title: Non-convex 4d polytopes in Spin Foam Models Authors: Benjamin Bahr Categories: gr-qc math-ph math.MP Comments: 25 pages, 17 figures (14 images, 3 tables) \\ In this article we consider non-convex $4d$ polytopes in $\mathbb{R}^4$. The paper consist of two parts: Firstly, we extend the proof of the formula for the $4d$ volume in terms of $2d$ face bivectors and boundary graph crossings from convex to non-convex polytopes. Secondly, we consider the EPRL-FK spin foam model, and demonstrate that there exists boundary data which leads to non-convex $4d$ polytopes in the asymptotic analysis of the vertex amplitude. \\ ( https://arxiv.org/abs/1812.10314 , 51kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10373 (*cross-listing*) Date: Wed, 26 Dec 2018 16:59:12 GMT (1775kb) Title: Dissipative spin chain as a non-Hermitian Kitaev ladder Authors: Naoyuki Shibata and Hosho Katsura Categories: cond-mat.stat-mech cond-mat.str-el math-ph math.MP quant-ph Comments: 5+6 pages, 4 figures \\ We derive exact results for the Lindblad equation for a quantum spin chain (one-dimensional quantum compass model) with dephasing noise. The system possesses doubly degenerate nonequilibrium steady states due to the presence of a conserved charge commuting with the Hamiltonian and Lindblad operators. We show that the system can be mapped to a non-Hermitian Kitaev model on a two-leg ladder, which is solvable by representing the spins in terms of Majorana fermions. This allows us to study the Liouvillian gap, the inverse of relaxation time, in detail. We find that the Liouvillian gap increases monotonically when the dissipation strength $ \gamma $ is small, while it decreases monotonically for large $ \gamma $, implying a kind of phase transition in the first decay mode. The Liouvillian gap and the transition point are obtained in closed form in the case where the spin chain is critical. We also obtain the explicit expression for the autocorrelator of the edge spin. The result implies the suppression of decoherence when the spin chain is in the topological regime. \\ ( https://arxiv.org/abs/1812.10373 , 1775kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10376 (*cross-listing*) Date: Wed, 26 Dec 2018 17:00:40 GMT (86kb,D) Title: Extreme gaps between eigenvalues of Wigner matrices Authors: Paul Bourgade Categories: math.PR math-ph math.MP \\ This paper proves universality of the distribution of the smallest and largest gaps between bulk eigenvalues of generalized Wigner matrices, from the symmetric and Hermitian classes. The assumptions on the distribution of the matrix elements are a subexponential decay and some smoothness of the density. The proof relies on the Erd{\H o}s-Schlein-Yau dynamic approach. We exhibit a new observable that satisfies a stochastic advection equation and reduces local relaxation of the Dyson Brownian motion to a maximum principle. \\ ( https://arxiv.org/abs/1812.10376 , 86kb) ------------------------------------------------------------------------------ \\ arXiv:1812.10406 (*cross-listing*) Date: Wed, 19 Dec 2018 17:24:05 GMT (14kb) Title: Wave breaking in a class of non-local conservation laws Authors: Yongki Lee Categories: math.AP math-ph math.MP MSC-class: 35L65, 35L67 \\ For models describing water waves, Constantin and Escher's works have long been considered as the cornerstone method for proving wave breaking phenomena. Their rigorous analytic proof shows that if the lowest slope of flows can be controlled by its highest slope initially, then the wave-breaking occur for the Whitham-type equation. Since this breakthrough, there have been numerous refined wave-breaking results established by generalizing the kernel which describes the dispersion relation of water waves. Even though the proofs of these involve a system of coupled Riccati-type differential inequalities, however, little or no attention has been made to a generalization of this Riccati-type system. In this work, from a rich class of non-local conservation laws, a Riccati-type system that governs the flow's gradient is extracted and investigated. The system's leading coefficient functions are allowed to change their values and signs over time as opposed to the ones in many of other previous works are fixed constants. Up to the author's knowledge, the blow-up analysis upon this structural generalization is new and is of theoretical interest in itself as well as its application to various non-local flow models. The theory is illustrated via the Whitham-type equation with nonlinear drift. Our method is applicable to a large class of non-local conservation laws. \\ ( https://arxiv.org/abs/1812.10406 , 14kb) %%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%% ------------------------------------------------------------------------------ \\ arXiv:1510.08723 (*cross-listing*) replaced with revised version Sat, 22 Dec 2018 10:32:22 GMT (510kb,D) Title: Scaling limits of random normal matrix processes at singular boundary points Authors: Yacin Ameur, Nam-Gyu Kang, Nikolai Makarov, and Aron Wennman Categories: math.PR math-ph math.CV math.MP Comments: Expanded and enhanced MSC-class: Primary: 60B20, Secondary: 60G55, 81T40, 30C40, 30D15, 35R09 \\ ( https://arxiv.org/abs/1510.08723 , 510kb) ------------------------------------------------------------------------------ \\ arXiv:1704.02750 replaced with revised version Sat, 22 Dec 2018 08:55:43 GMT (21kb) Title: 4D limit of melting crystal model and its integrable structure Authors: Kanehisa Takasaki Categories: math-ph hep-th math.MP math.QA nlin.SI Comments: latex2e using packages amsmath,amssymb,amsthm, 35 pages, no figure; (v2) the title is changed and an appendix is added; (v3) texts in Introduction and Sect. 4.2 are modified, a few typos are corrected, final version for publication MSC-class: 14N35, 37K10, 39A13 DOI: 10.1016/j.geomphys.2018.12.012 \\ ( https://arxiv.org/abs/1704.02750 , 21kb) ------------------------------------------------------------------------------ \\ arXiv:1705.03104 (*cross-listing*) replaced with revised version Sun, 23 Dec 2018 14:14:04 GMT (166kb,D) Title: Sharp phase transition for the random-cluster and Potts models via decision trees Authors: Hugo Duminil-Copin, Aran Raoufi, Vincent Tassion Categories: math.PR math-ph math.MP Comments: 16 pages, 3 figures \\ ( https://arxiv.org/abs/1705.03104 , 166kb) ------------------------------------------------------------------------------ \\ arXiv:1707.06225 (*cross-listing*) replaced with revised version Tue, 25 Dec 2018 20:04:09 GMT (1384kb,D) Title: Waves along fractal coastlines: From fractal arithmetic to wave equations Authors: Marek Czachor Categories: math.DS math-ph math.MP nlin.CD nlin.PS Comments: First version of the paper was submitted to arXiv on 9 Jul 2017 \\ ( https://arxiv.org/abs/1707.06225 , 1384kb) ------------------------------------------------------------------------------ \\ arXiv:1709.06081 replaced with revised version Wed, 26 Dec 2018 02:10:04 GMT (150kb) Title: Open problem in orthogonal polynomials Authors: A. D. Alhaidari Categories: math-ph math.MP quant-ph Comments: 7 pages, 1 table, 17 references MSC-class: 42C05, 33C47, 33C45, 33D45 \\ ( https://arxiv.org/abs/1709.06081 , 150kb) ------------------------------------------------------------------------------ \\ arXiv:1712.08657 (*cross-listing*) replaced with revised version Sat, 22 Dec 2018 10:52:22 GMT (152kb) Title: Two-point boundary correlation functions of dense loop models Authors: Alexi Morin-Duchesne, Jesper Lykke Jacobsen Categories: cond-mat.stat-mech hep-th math-ph math.MP Comments: 49 pages. v2: minor changes Journal-ref: SciPost Phys. 4, 034 (2018) DOI: 10.21468/SciPostPhys.4.6.034 \\ ( https://arxiv.org/abs/1712.08657 , 152kb) ------------------------------------------------------------------------------ \\ arXiv:1802.08911 (*cross-listing*) replaced with revised version Fri, 21 Dec 2018 19:05:31 GMT (338kb,D) Title: Conformal bootstrap for percolation and polymers Authors: Andre LeClair and Joshua Squires Categories: hep-th cond-mat.stat-mech math-ph math.MP Comments: 25 pages, 10 figures. v2: published version Journal-ref: J. Stat. Mech. (2018) 123105 DOI: 10.1088/1742-5468/aaf10a \\ ( https://arxiv.org/abs/1802.08911 , 338kb) ------------------------------------------------------------------------------ \\ arXiv:1804.05782 (*cross-listing*) replaced with revised version Sat, 22 Dec 2018 16:41:49 GMT (48kb,D) Title: Non-commutative waves for gravitational anyons Authors: Sergio Inglima and Bernd Schroers Categories: hep-th gr-qc math-ph math.MP Comments: 36 pages, 2 figures; minor corrections and additional references (version to appear in Letters in Mathematical Physics) \\ ( https://arxiv.org/abs/1804.05782 , 48kb) ------------------------------------------------------------------------------ \\ arXiv:1804.08587 replaced with revised version Sun, 23 Dec 2018 08:49:59 GMT (169kb,D) Title: The random normal matrix model: insertion of a point charge Authors: Yacin Ameur, Nam-Gyu Kang, Seong-Mi Seo Categories: math-ph math.CV math.MP math.PR Comments: In this version, we have expanded the range of possible singularities, so that we in particular include the full, two-parametric family of Mittag-Leffler fields \\ ( https://arxiv.org/abs/1804.08587 , 169kb) ------------------------------------------------------------------------------ \\ arXiv:1808.00306 (*cross-listing*) replaced with revised version Wed, 26 Dec 2018 18:33:47 GMT (38kb,D) Title: Equilibrium fluctuation for an anharmonic chain with boundary conditions in the Euler scaling limit Authors: Stefano Olla and Lu Xu Categories: math.PR cond-mat.stat-mech math-ph math.MP \\ ( https://arxiv.org/abs/1808.00306 , 38kb) ------------------------------------------------------------------------------ \\ arXiv:1808.03961 (*cross-listing*) replaced with revised version Sun, 23 Dec 2018 21:54:27 GMT (57kb,D) Title: Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I Authors: Kirill Cherednichenko, Yulia Ershova, Alexander Kiselev Categories: math.AP cond-mat.mtrl-sci math-ph math.MP Comments: 35 pages, 1 figure \\ ( https://arxiv.org/abs/1808.03961 , 57kb) ------------------------------------------------------------------------------ \\ arXiv:1811.00331 (*cross-listing*) replaced with revised version Sun, 23 Dec 2018 11:18:29 GMT (266kb,D) Title: Superconvergence of Topological Entropy in the Symbolic Dynamics of Substitution Sequences Authors: Leon Zaporski, Felix Flicker Categories: nlin.CD math-ph math.MP Comments: This version: updated figures and added discussion of generalised time quasilattices. 17 pages, 4 figures \\ ( https://arxiv.org/abs/1811.00331 , 266kb) ------------------------------------------------------------------------------ \\ arXiv:1811.02631 (*cross-listing*) replaced with revised version Tue, 25 Dec 2018 16:17:54 GMT (35kb) Title: The complex sinh-Gordon model: form factors of descendant operators and current-current perturbations Authors: Michael Lashkevich and Yaroslav Pugai Categories: hep-th math-ph math.MP nlin.SI Comments: 31 pages; v2: references added; v3: many misprints corrected \\ ( https://arxiv.org/abs/1811.02631 , 35kb) ------------------------------------------------------------------------------ \\ arXiv:1811.04536 replaced with revised version Wed, 26 Dec 2018 05:09:36 GMT (23kb) Title: Classification of the orthogonal separable webs for the Hamilton-Jacobi and Laplace-Beltrami equations on 3-dimensional Hyperbolic and de Sitter spaces Authors: Carlos Valero, Raymond G. McLenaghan Categories: math-ph math.MP \\ ( https://arxiv.org/abs/1811.04536 , 23kb) ------------------------------------------------------------------------------ \\ arXiv:1811.06449 (*cross-listing*) replaced with revised version Mon, 24 Dec 2018 16:28:07 GMT (1075kb) Title: Trends in supersymmetric quantum mechanics Authors: David J. Fernandez C Categories: quant-ph hep-th math-ph math.MP Comments: 33 pages, 2 figures, submitted as a contribution to the monographic volume "Integrability, Supersymmetry and Coherent States", a volume in honour of Professor V\'eronique Hussin, small changes done, references added \\ ( https://arxiv.org/abs/1811.06449 , 1075kb) ------------------------------------------------------------------------------ \\ arXiv:1811.09692 (*cross-listing*) replaced with revised version Mon, 24 Dec 2018 17:59:23 GMT (37kb) Title: Anderson localization for two interacting quasiperiodic particles Authors: Jean Bourgain, Ilya Kachkovskiy Categories: math.SP math-ph math.MP Comments: Some notation has been revised, and the referee's suggestions addressed. The result now covers a larger class of interaction potentials. To appear in Geometric and Functional Analysis \\ ( https://arxiv.org/abs/1811.09692 , 37kb) ------------------------------------------------------------------------------ \\ arXiv:1812.03486 (*cross-listing*) replaced with revised version Sat, 22 Dec 2018 04:46:25 GMT (11kb) Title: Some aspects of number theory related to phase operators Authors: F. Bouzeffour and M. Garayev Categories: math.FA math-ph math.MP math.OA Comments: 12 \\ ( https://arxiv.org/abs/1812.03486 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:1812.03767 replaced with revised version Wed, 26 Dec 2018 12:50:39 GMT (18kb) Title: Matrix product solution to the reflection equation associated with a coideal subalgebra of $U_q(A^{(1)}_{n-1})$ Authors: Atsuo Kuniba, Masato Okado and Akihito Yoneyama Categories: math-ph math.MP math.QA nlin.SI Comments: 11 pages, v2: minor corrections MSC-class: 17B37, 17B80 \\ ( https://arxiv.org/abs/1812.03767 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:1812.04561 (*cross-listing*) replaced with revised version Wed, 26 Dec 2018 03:46:39 GMT (53kb,D) Title: Absence of Finite Temperature Phase Transitions in the X-Cube Model and its $\mathbb{Z}_{p}$ Generalization Authors: Zack Weinstein, Emilio Cobanera, Gerardo Ortiz, Zohar Nussinov Categories: cond-mat.stat-mech hep-th math-ph math.MP quant-ph Comments: 66 pages, 18 figures \\ ( https://arxiv.org/abs/1812.04561 , 53kb) ------------------------------------------------------------------------------ \\ arXiv:1812.05516 (*cross-listing*) replaced with revised version Sat, 22 Dec 2018 10:20:04 GMT (63kb,D) Title: Multiplicative Hitchin Systems and Supersymmetric Gauge Theory Authors: Chris Elliott and Vasily Pestun Categories: math.AG hep-th math-ph math.MP math.QA Comments: 54 pages. Several references added and updated \\ ( https://arxiv.org/abs/1812.05516 , 63kb) ------------------------------------------------------------------------------ \\ arXiv:1812.08291 replaced with revised version Mon, 24 Dec 2018 17:52:19 GMT (458kb) Title: Unphysical energy sheets and resonances in the Friedrichs-Faddeev model Authors: Alexander K. Motovilov Categories: math-ph math.MP \\ ( https://arxiv.org/abs/1812.08291 , 458kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09022 replaced with revised version Mon, 24 Dec 2018 12:49:05 GMT (135kb,D) Title: Vacuum energy for generalised Dirac combs at $T = 0$ Authors: Michael Bordag, Jose M Mu\~noz-Casta\~neda and Luc\'ia Santamar\'ia-Sanz Categories: math-ph cond-mat.stat-mech math.MP quant-ph Comments: 13 pages, 3 figures. Bibliography and Acknowledgements minor corrections have been included \\ ( https://arxiv.org/abs/1812.09022 , 135kb) ------------------------------------------------------------------------------ \\ arXiv:1812.09316 replaced with revised version Tue, 25 Dec 2018 09:29:27 GMT (0kb,I) Title: Exact solution of an integrable $J_1-J_2$ spin chain model Authors: Yi Qiao, Zhirong Xin, Junpeng Cao, Wen-Li Yang, Kangjie Shi and Yupeng Wang Categories: math-ph cond-mat.stat-mech math.MP nlin.SI Comments: The model has been studied. We appreciate Prof. Hosho Katsura for pointing out for us \\ ( https://arxiv.org/abs/1812.09316 , 0kb) %%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%--- 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/