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Jan 2013

Volume 54, Issue 1, Articles (01xxxx)

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J. Math. Phys. 54, 013701 (2013); http://dx.doi.org/10.1063/1.4772611 (14 pages)

K. Sakkaravarthi and T. Kanna
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Announcement: Journal of Mathematical Physics introduces two new sections: Many-Body and Condensed Matter Physics and Representation Theory and Algebraic Methods

Bruno Nachtergaele, Editor

J. Math. Phys. 54, 010201 (2013); http://dx.doi.org/10.1063/1.4774284 (2 pages)

Online Publication Date: 22 January 2013

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05.30.-d Quantum statistical mechanics
02.10.-v Logic, set theory, and algebra
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back to top Partial Differential Equations

Characterisation and representation of non-dissipative electromagnetic medium with two Lorentz null cones

Matias F. Dahl

J. Math. Phys. 54, 011501 (2013); http://dx.doi.org/10.1063/1.4773832 (23 pages)

Online Publication Date: 10 January 2013

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We study Maxwell's equations on a 4-manifold N with a medium that is non-dissipative and has a linear and pointwise response. In this setting, the medium can be represented by a suitable math-tensor on the 4-manifold N. Moreover, in each cotangent space on N, the medium defines a Fresnel surface. Essentially, the Fresnel surface is a tensorial analogue of the dispersion equation that describes the response of the medium for signals in the geometric optics limit. For example, in an isotropic medium the Fresnel surface is at each point a Lorentz null cone. In a recent paper, Lindell, Favaro, and Bergamin introduced a condition that constrains the polarisation for plane waves. In this paper we show (under suitable assumptions) that a slight strengthening of this condition gives a complete pointwise characterisation of all medium tensors for which the Fresnel surface is the union of two distinct Lorentz null cones. This is, for example, the behaviour in uniaxial media such as calcite. Moreover, using the representation formulas from Lindell et al. we obtain a closed form representation formula that pointwise parameterises all medium tensors for which the Fresnel surface is the union of two distinct Lorentz null cones. Both the characterisation and the representation formula are tensorial and do not depend on local coordinates.
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03.50.De Classical electromagnetism, Maxwell equations
42.15.-i Geometrical optics

Remarks on the regularity criteria of generalized MHD and Navier-Stokes systems

Kazuo Yamazaki

J. Math. Phys. 54, 011502 (2013); http://dx.doi.org/10.1063/1.4773833 (16 pages)

Online Publication Date: 11 January 2013

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We study the regularity criteria of the three dimensional generalized magnetohydrodynamics (MHD) and Navier-Stokes systems. In particular, we show that the regularity criteria of the generalized MHD system may be reduced to depend only on two diagonal entries of the Jacobian matrix of the velocity vector field or one vorticity component and one entry of the Jacobian matrix of the velocity vector field.
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47.10.ad Navier-Stokes equations
47.65.-d Magnetohydrodynamics and electrohydrodynamics
02.10.Yn Matrix theory

Global existence for a coupled system of Schrödinger equations with power-type nonlinearities

Nghiem V. Nguyen, Rushun Tian, Bernard Deconinck, and Natalie Sheils

J. Math. Phys. 54, 011503 (2013); http://dx.doi.org/10.1063/1.4774149 (19 pages)

Online Publication Date: 14 January 2013

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In this manuscript, we consider the Cauchy problem for a Schrödinger system with power-type nonlinearitiesmathwhere uj:mathN×math→math, ψj0:mathN→math for j = 1, 2, …, m and ajk = akj are positive real numbers. Global existence for the Cauchy problem is established for a certain range of p. A sharp form of a vector-valued Gagliardo-Nirenberg inequality is deduced, which yields the minimal embedding constant for the inequality. Using this minimal embedding constant, global existence for small initial data is shown for the critical case p = 1 + 2/N. Finite-time blow-up, as well as stability of solutions in the critical case, is discussed.
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03.65.Ge Solutions of wave equations: bound states
02.30.Hq Ordinary differential equations

Nodal soliton solutions for quasilinear Schrödinger equations with critical exponent

Yinbin Deng, Shuangjie Peng, and Jixiu Wang

J. Math. Phys. 54, 011504 (2013); http://dx.doi.org/10.1063/1.4774153 (27 pages)

Online Publication Date: 14 January 2013

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This paper is concerned with constructing nodal radial solutions for quasilinear Schrödinger equations in mathN with critical growth which have appeared as several models in mathematical physics. For any given integer k ⩾ 0, by using a change of variables and minimization argument, we obtain a sign-changing minimizer with k nodes of a minimization problem. Since the critical exponent appears and the lower order term may change sign, we should use more delicate arguments.
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05.45.Yv Solitons
05.70.Jk Critical point phenomena
02.60.Lj Ordinary and partial differential equations; boundary value problems
02.60.Pn Numerical optimization

The existence of steady solutions for a class of Schrödinger equations in nonlinear optical lattices

Ruifeng Zhang, Hong Wang, and Rentao Liu

J. Math. Phys. 54, 011505 (2013); http://dx.doi.org/10.1063/1.4769384 (7 pages)

Online Publication Date: 30 January 2013

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We address the impact of nonlocality in the physical features exhibited by solitons in photorefractive optical lattice. We use the method of calculus of variations to develop an existence theory for the steady state solutions of a nonlinear Schrödinger equation modeling light waves propagating in nonlinear optical lattices. We show via a mountain-pass argument that there exist steady state solutions realizing a continuous spectrum of energy points or wavenumbers.
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03.65.Ge Solutions of wave equations: bound states
03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations
02.30.Xx Calculus of variations
back to top Quantum Mechanics (General and Nonrelativistic)

Uncertainties of coherent states for a generalized supersymmetric annihilation operator

Mordechai Kornbluth and Fredy Zypman

J. Math. Phys. 54, 012101 (2013); http://dx.doi.org/10.1063/1.4772607 (13 pages)

Online Publication Date: 4 January 2013

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This study presents supersymmetric coherent states that are eigenstates of a general four-parameter family of annihilation operators. The elements of this family are defined as operators in Fock space that transform a subspace of a definite number of particles into a subspace with one particle removed. The emphasis is on classifying parameter space in various regions according to the uncertainty bounds of the corresponding coherent states. Specifically, the uncertainty in position-momentum is analyzed, with specific focus on characterizing regions of minimum uncertainty states, regions where the uncertainties are bounded from above, and where they grow unbound.
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03.65.Ta Foundations of quantum mechanics; measurement theory
03.65.Ge Solutions of wave equations: bound states

Tunneling resonances in systems without a classical trapping

D. Borisov, P. Exner, and A. Golovina

J. Math. Phys. 54, 012102 (2013); http://dx.doi.org/10.1063/1.4773098 (19 pages)

Online Publication Date: 4 January 2013

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In this paper, we analyze a free quantum particle in a straight Dirichlet waveguide which has at its axis two Dirichlet barriers of lengths ℓ± separated by a window of length 2a. It is known that if the barriers are semi-infinite, i.e., we have two adjacent waveguides coupled laterally through the boundary window, the system has for any a > 0 a finite number of eigenvalues below the essential spectrum threshold. Here, we demonstrate that for large but finite ℓ± the system has resonances which converge to the said eigenvalues as ℓ± → ∞, and derive the leading term in the corresponding asymptotic expansion.
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03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)
02.10.Ud Linear algebra
02.60.Lj Ordinary and partial differential equations; boundary value problems

Time fractional Schrödinger equation: Fox's H-functions and the effective potential

Selçuk Ş. Bayın

J. Math. Phys. 54, 012103 (2013); http://dx.doi.org/10.1063/1.4773100 (18 pages)

Online Publication Date: 4 January 2013

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After introducing the formalism of the general space and time fractional Schrödinger equation, we concentrate on the time fractional Schrödinger equation and present new results via the elegant language of Fox's H-functions. We show that the general time dependent part of the wave function for the separable solutions of the time-fractional Schrödinger equation is the Mittag-Leffler function with an imaginary argument by two different methods. After separating the Mittag-Leffler function into its real and imaginary parts, in contrast to existing works, we show that the total probability is ⩽1 and decays with time. Introducing the effective potential approach, we also write the Mittag-Leffler function with an imaginary argument as the product of its purely decaying and purely oscillating parts. In the light of these, we reconsider the simple box problem.
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03.65.Ge Solutions of wave equations: bound states
02.30.Sa Functional analysis
02.60.Lj Ordinary and partial differential equations; boundary value problems

Non-Hermitian oscillator and R-deformed Heisenberg algebra

R. Roychoudhury, B. Roy, and P. P. Dube

J. Math. Phys. 54, 012104 (2013); http://dx.doi.org/10.1063/1.4773097 (11 pages)

Online Publication Date: 7 January 2013

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A non-Hermitian generalized oscillator model, generally known as the Swanson model, has been studied in the framework of R-deformed Heisenberg algebra. The non-Hermitian Hamiltonian is diagonalized by generalized Bogoliubov transformation. A set of deformed creation annihilation operators is introduced whose algebra shows that the transformed Hamiltonian has conformal symmetry. The spectrum is obtained using algebraic technique. The superconformal structure of the system is also worked out in detail. An anomaly related to the spectrum of the Hermitian counterpart of the non-Hermitian Hamiltonian with generalized ladder operators is shown to occur and is discussed in position dependent mass scenario.
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03.65.Ge Solutions of wave equations: bound states
02.10.Yn Matrix theory
03.65.Fd Algebraic methods

Quantum dynamics in phase space: Moyal trajectories 2

G. Braunss

J. Math. Phys. 54, 012105 (2013); http://dx.doi.org/10.1063/1.4773229 (14 pages)

Online Publication Date: 7 January 2013

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Continuing a previous paper [G. Braunss, J. Phys. A: Math. Theor. 43, 025302 (2010)10.1088/1751-8113/43/2/025302] where we had calculated ℏ2-approximations of quantum phase space viz. Moyal trajectories of examples with one and two degrees of freedom, we present in this paper the calculation of ℏ2-approximations for four examples: a two-dimensional Toda chain, the radially symmetric Schwarzschild field, and two examples with three degrees of freedom, the latter being the nonrelativistic spherically Coulomb potential and the relativistic cylinder symmetrical Coulomb potential with a magnetic field H. We show in particular that an ℏ2-approximation of the nonrelativistic Coulomb field has no singularity at the origin (r = 0) whereas the classical trajectories are singular at r = 0. In the third example, we show in particular that for an arbitrary function γ(H, z) the expression β ≡ pz + γ(H, z) is classically (ℏ = 0) a constant of motion, whereas for ℏ ≠ 0 this holds only if γ(H, z) is an arbitrary polynomial of second order in z. This statement is shown to extend correspondingly to a cylinder symmetrical Schwarzschild field with a magnetic field. We exhibit in detail a number of properties of the radially symmetric Schwarzschild field. We exhibit finally the problems of the nonintegrable Hénon-Heiles Hamiltonian and give a short review of the regular Hilbert space representation of Moyal operators.
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03.65.Aa Quantum systems with finite Hilbert space
02.10.De Algebraic structures and number theory
03.65.Fd Algebraic methods
03.65.Vf Phases: geometric; dynamic or topological
04.20.Cv Fundamental problems and general formalism
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
back to top Quantum Mechanics

Asymptotically minimal uncertainty states for time-dependent oscillators

Predrag Punoševac and Sam L. Robinson

J. Math. Phys. 54, 012106 (2013); http://dx.doi.org/10.1063/1.4773874 (16 pages)

Online Publication Date: 10 January 2013

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We consider the time-dependent Schrödinger equation in one spatial dimension with a time-dependent quadratic Hamiltonian and, under appropriate assumptions on the coefficient functions in the Hamiltonian, construct solutions that approach minimal uncertainty states for large times.
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03.65.Ge Solutions of wave equations: bound states
03.65.Sq Semiclassical theories and applications

Three-dimensional shape invariant non-separable model with equidistant spectrum

M. S. Bardavelidze, F. Cannata, M. V. Ioffe, and D. N. Nishnianidze

J. Math. Phys. 54, 012107 (2013); http://dx.doi.org/10.1063/1.4774292 (11 pages)

Online Publication Date: 16 January 2013

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A class of three-dimensional models, which satisfy supersymmetric intertwining relations with the simplest—oscillator-like—variant of shape invariance, is constructed. It is proved that the models are not amenable to the conventional separation of variables for the complex potentials, but their spectra are real and equidistant (such as, for isotropic harmonic oscillator). The special case of such potential with quadratic interaction is solved completely. The Hamiltonian of the system is non-diagonalizable, and its wave functions and associated functions are built analytically. The symmetry properties of the model and degeneracy of energy levels are studied.
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03.65.Ge Solutions of wave equations: bound states
03.65.Ta Foundations of quantum mechanics; measurement theory

High-energy analysis and Levinson's theorem for the selfadjoint matrix Schrödinger operator on the half line

Tuncay Aktosun and Ricardo Weder

J. Math. Phys. 54, 012108 (2013); http://dx.doi.org/10.1063/1.4773904 (27 pages)

Online Publication Date: 17 January 2013

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The matrix Schrödinger equation with a selfadjoint matrix potential is considered on the half line with the general selfadjoint boundary condition at the origin. When the matrix potential is integrable, the high-energy asymptotics are established for the related Jost matrix, the inverse of the Jost matrix, and the scattering matrix. Under the additional assumption that the matrix potential has a first moment, Levinson's theorem is derived, relating the number of bound states to the change in the argument of the determinant of the scattering matrix.
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03.65.Ge Solutions of wave equations: bound states
03.65.Nk Scattering theory
02.10.Yn Matrix theory
03.65.Fd Algebraic methods

Generalized Kepler problems. I. Without magnetic charges

Guowu Meng

J. Math. Phys. 54, 012109 (2013); http://dx.doi.org/10.1063/1.4775343 (25 pages)

Online Publication Date: 17 January 2013

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For each simple euclidean Jordan algebra V of rank ρ and degree δ, we introduce a family of classical dynamic problems. These dynamical problems all share the characteristic features of the Kepler problem for planetary motions, such as the existence of Laplace-Runge-Lenz vector and hidden symmetry. After suitable quantizations, a family of quantum dynamic problems, parametrized by the nontrivial Wallach parameter ν, is obtained. Here, ν∈W(V): = {kmath∣k = 1,...,(ρ−1)}∪((ρ−1)math,∞) and was introduced by N. Wallach to parametrize the set of nontrivial scalar-type unitary lowest weight representations of the conformal group of V. For the quantum dynamic problem labelled by ν, the bound state spectra is −math, I = 0, 1, … and its Hilbert space of bound states gives a new realization for the afore-mentioned representation labelled by ν. A few results in the literature about these representations become more explicit and more refined. The Lagrangian for a classical Kepler-type dynamic problem introduced here is still of the simple form: ½‖math‖2+math. Here, math is the velocity of a unit-mass particle moving on the space consisting of V’s semi-positive elements of a fixed rank, and r is the inner product of x with the identity element of V.
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03.65.Fd Algebraic methods
03.65.Ge Solutions of wave equations: bound states

Variance of the quantum dwell time for a nonrelativistic particle

G. E. Hahne

J. Math. Phys. 54, 012110 (2013); http://dx.doi.org/10.1063/1.4776657 (16 pages)

Online Publication Date: 24 January 2013

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Muñoz, Seidel, and Muga [Phys. Rev. A 79, 012108 (2009)10.1103/PhysRevA.79.012108], following an earlier proposal by Pollak and Miller [Phys. Rev. Lett. 53, 115 (1984)10.1103/PhysRevLett.53.115] in the context of a theory of a collinear chemical reaction, showed that suitable moments of a two-flux correlation function could be manipulated to yield expressions for the mean quantum dwell time and mean square quantum dwell time for a structureless particle scattering from a time-independent potential energy field between two parallel lines in a two-dimensional spacetime. The present work proposes a generalization to a charged, nonrelativistic particle scattering from a transient, spatially confined electromagnetic vector potential in four-dimensional spacetime. The geometry of the spacetime domain is that of the slab between a pair of parallel planes, in particular, those defined by constant values of the third (z) spatial coordinate. The mean Nth power, N = 1, 2, 3, …, of the quantum dwell time in the slab is given by an expression involving an N-flux-correlation function. All these means are shown to be nonnegative. The N = 1 formula reduces to an S-matrix result published previously [G. E. Hahne, J. Phys. A 36, 7149 (2003)10.1088/0305-4470/36/25/316]; an explicit formula for N = 2, and of the variance of the dwell time in terms of the S-matrix, is worked out. A formula representing an incommensurability principle between variances of the output-minus-input flux of a pair of dynamical variables (such as the particle's time flux and others) is derived.
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03.65.Nk Scattering theory
02.10.Yn Matrix theory
03.65.Fd Algebraic methods

Fractional Schrödinger equation for a particle moving in a potential well

Yuri Luchko

J. Math. Phys. 54, 012111 (2013); http://dx.doi.org/10.1063/1.4777472 (10 pages)

Online Publication Date: 23 January 2013

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In this paper, the fractional Schrödinger equation that contains the quantum Riesz fractional derivative instead of the Laplace operator is revisited for the case of a particle moving in the infinite potential well. In the recent papers [M. Jeng, S.-L.-Y. Xu, E. Hawkins, and J. M. Schwarz, “On the nonlocality of the fractional Schrödinger equation,” J. Math. Phys. 51, 062102 (2010)10.1063/1.3430552] and [S. S. Bayin, “On the consistency of the solutions of the space fractional Schrödinger equation,” J. Math. Phys. 53, 042105 (2012)10.1063/1.4705268] published in this journal, controversial opinions regarding solutions to the fractional Schrödinger equation for a particle moving in the infinite potential well that were derived by Laskin [“Fractals and quantum mechanics,” Chaos 10, 780–790 (2000)10.1063/1.1050284] have been given. In this paper, a thorough mathematical treatment of these matters is provided. The problem under consideration is reformulated in terms of three integral equations with the power kernels. Even if the equations look not very complicated, no solution to these equations in explicit form is known. Still, the obtained equations are used to show that the eigenvalues and eigenfunctions of the fractional Schrödinger equation for a particle moving in the infinite potential well given by Laskin [“Fractals and quantum mechanics,” Chaos 10, 780–790 (2000)10.1063/1.1050284] and many other papers by different authors cannot be valid as has been first stated by Jeng et al. [“On the nonlocality of the fractional Schrödinger equation,” J. Math. Phys. 51, 062102 (2010)10.1063/1.3430552].
Show PACS
03.65.Ge Solutions of wave equations: bound states
02.10.Ud Linear algebra
02.30.Rz Integral equations
03.65.Fd Algebraic methods

Uncertainty relation for non-Hamiltonian quantum systems

Vasily E. Tarasov

J. Math. Phys. 54, 012112 (2013); http://dx.doi.org/10.1063/1.4776653 (13 pages)

Online Publication Date: 25 January 2013

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General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schrödinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications.
Show PACS
03.65.Ge Solutions of wave equations: bound states
02.10.Ud Linear algebra
03.65.Fd Algebraic methods
back to top Quantum Information and Computation

A hierarchy of topological tensor network states

Oliver Buerschaper, Juan Martín Mombelli, Matthias Christandl, and Miguel Aguado

J. Math. Phys. 54, 012201 (2013); http://dx.doi.org/10.1063/1.4773316 (46 pages)

Online Publication Date: 23 January 2013

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We present a hierarchy of quantum many-body states among which many examples of topological order can be identified by construction. We define these states in terms of a general, basis-independent framework of tensor networks based on the algebraic setting of finite-dimensional Hopf C*-algebras. At the top of the hierarchy we identify ground states of new topological lattice models extending Kitaev's quantum double models [Ann. Phys. 303, 2 (2003)10.1016/S0003-4916(02)00018-0]. For these states we exhibit the mechanism responsible for their non-zero topological entanglement entropy by constructing an entanglement renormalization flow. Furthermore, we argue that the hierarchy states are related to each other by the condensation of topological charges.
Show PACS
03.65.Fd Algebraic methods
03.65.Ta Foundations of quantum mechanics; measurement theory
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
05.70.Ce Thermodynamic functions and equations of state
02.10.Ud Linear algebra
02.20.-a Group theory
02.40.Re Algebraic topology
back to top Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory

N = 2 gauge theories: Congruence subgroups, coset graphs, and modular surfaces

Yang-Hui He and John McKay

J. Math. Phys. 54, 012301 (2013); http://dx.doi.org/10.1063/1.4772976 (24 pages)

Online Publication Date: 4 January 2013

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We establish a correspondence between generalized quiver gauge theories in four dimensions and congruence subgroups of the modular group, hinging upon the trivalent graphs, which arise in both. The gauge theories and the graphs are enumerated and their numbers are compared. The correspondence is particularly striking for genus zero torsion-free congruence subgroups as exemplified by those which arise in Moonshine. We analyze in detail the case of index 24, where modular elliptic K3 surfaces emerge: here, the elliptic j-invariants can be recast as dessins d'enfant, which dictate the Seiberg-Witten curves.
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11.15.-q Gauge field theories
02.10.Ox Combinatorics; graph theory

Dimensional reduction without continuous extra dimensions

Ali H. Chamseddine, J. Fröhlich, B. Schubnel, and D. Wyler

J. Math. Phys. 54, 012302 (2013); http://dx.doi.org/10.1063/1.4771877 (17 pages)

Online Publication Date: 7 January 2013

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We describe a novel approach to dimensional reduction in classical field theory. Inspired by ideas from noncommutative geometry, we introduce extended algebras of differential forms over space-time, generalized exterior derivatives, and generalized connections associated with the “geometry” of space-times with discrete extra dimensions. We apply our formalism to theories of gauge- and gravitational fields and find natural geometrical origins for an axion- and a dilaton field, as well as a Higgs field.
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11.10.Nx Noncommutative field theory
03.50.-z Classical field theories
14.80.Va Axions and other Nambu-Goldstone bosons (Majorons, familons, etc.)
11.15.-q Gauge field theories
02.40.Gh Noncommutative geometry
02.10.-v Logic, set theory, and algebra

Classical limit of the Nelson model with cutoff

Marco Falconi

J. Math. Phys. 54, 012303 (2013); http://dx.doi.org/10.1063/1.4775716 (30 pages)

Online Publication Date: 17 January 2013

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In this paper we analyze the classical limit of the Nelson model with cutoff, when both non-relativistic and relativistic particles number goes to infinity. We prove convergence of quantum observables to the solutions of classical equations, and find the evolution of quantum fluctuations around the classical solution. Furthermore, we analyze the convergence of transition amplitudes of normal ordered products of creation and annihilation operators between different types of initial states. In particular, the limit of normal ordered products between states with a fixed number of both relativistic and non-relativistic particles yields an unexpected quantum residue: instead of the product of classical solutions we obtain an average of the product of solutions corresponding to varying initial conditions.
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03.65.Ta Foundations of quantum mechanics; measurement theory
03.65.Sq Semiclassical theories and applications

New proofs for the two Barnes lemmas and an additional lemma

Bernd Jantzen

J. Math. Phys. 54, 012304 (2013); http://dx.doi.org/10.1063/1.4775770 (7 pages)

Online Publication Date: 17 January 2013

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Mellin–Barnes (MB) representations have become a widely used tool for the evaluation of Feynman loop integrals appearing in perturbative calculations of quantum field theory. Some of the MB integrals may be solved analytically in closed form with the help of the two Barnes lemmas which have been known in mathematics already for one century. The original proofs of these lemmas solve the integrals by taking infinite series of residues and summing these up via hypergeometric functions. This paper presents new, elegant proofs for the Barnes lemmas which only rely on the well-known basic identity of MB representations, avoiding any series summations. They are particularly useful for presenting and proving the Barnes lemmas to students of quantum field theory without requiring knowledge on hypergeometric functions. The paper also introduces and proves an additional lemma for a MB integral ∫dz involving a phase factor exp (±iπz).
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11.10.-z Field theory
02.30.Uu Integral transforms
back to top General Relativity and Gravitation

Noncommutative residue and sub-Dirac operators for foliations

Jian Wang and Yong Wang

J. Math. Phys. 54, 012501 (2013); http://dx.doi.org/10.1063/1.4773878 (35 pages)

Online Publication Date: 11 January 2013

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In this paper, we define lower dimensional volumes associated with sub-Dirac operators for foliations. In some cases, we compute these lower dimensional volumes. We also prove the Kastler-Kalau-Walze type theorems for foliations with or without boundary. As a corollary, we give an explanation of the gravitational action for the Robertson-Walker space [a, b] ×f M3.
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02.40.-k Geometry, differential geometry, and topology
back to top Dynamical Systems

Hamiltonian integrability of two-component short pulse equations

J. C. Brunelli and S. Sakovich

J. Math. Phys. 54, 012701 (2013); http://dx.doi.org/10.1063/1.4773363 (12 pages)

Online Publication Date: 4 January 2013

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We obtain the bi-Hamiltonian structure for some of the two-component short pulse equations proposed in the literature to generalize the original short pulse equation when polarized pulses propagate in anisotropic media.
Show PACS
03.65.Ge Solutions of wave equations: bound states
02.30.Rz Integral equations
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