Unidirectional invisibility induced by PT-symmetric periodic structures.
Lin, Zin; Ramezani, Hamidreza; Eichelkraut, Toni; Kottos, Tsampikos; Cao, Hui; Christodoulides, Demetrios N
2011-05-27
Parity-time (PT) symmetric periodic structures, near the spontaneous PT-symmetry breaking point, can act as unidirectional invisible media. In this regime, the reflection from one end is diminished while it is enhanced from the other. Furthermore, the transmission coefficient and phase are indistinguishable from those expected in the absence of a grating. The phenomenon is robust even in the presence of Kerr nonlinearities, and it can also effectively suppress optical bistabilities. © 2011 American Physical Society
Scattering properties of PT- symmetric layered periodic structures
Shramkova, O. V.; Tsironis, G. P.
2016-10-01
The optical properties of PT-symmetric periodic stacks of the layers with balanced loss and gain are examined. We demonstrate that the tunnelling phenomenon in periodic structures is connected with excitation of surface waves at the boundaries separating gain and loss regions within each unit cell and tunnelling conditions for periodic stacks can be reduced to the conditions for one period. Alternatively, it is shown that coherent perfect absorber laser states are mediated by excitation of surface modes localised at all internal boundaries of the structure. The effects of structure parameters, angles, direction of incidence on the resonant phenomena and spontaneous symmetry breaking transition are determined. It is shown that structural periodicity significantly increases the number of resonant phenomena, especially in stacks with high real and imaginary parts of dielectric permittivity of the layers.
Longhi, Stefano
2017-01-01
We consider wave transport phenomena in a PT -symmetric extension of the periodically kicked quantum rotator model and reveal that dynamical localization assists the unbroken PT phase. In the delocalized (quantum resonance) regime, PT symmetry is always in the broken phase and ratchet acceleration arises as a signature of unidirectional non-Hermitian transport. An optical implementation of the periodically kicked PT -symmetric Hamiltonian, based on transverse beam propagation in a passive optical resonator with combined phase and loss gratings, is suggested to visualize acceleration modes in fractional Talbot cavities.
On PT-Symmetric Periodic Potential, Quark Confinement, and Other Impossible Pursuits
Directory of Open Access Journals (Sweden)
Christianto V.
2009-01-01
Full Text Available As we know, it has been quite common nowadays for particle physicists to think of six impossible things before breakfast, just like what their cosmology fellows used to do. In the present paper, we discuss a number of those impossible things, including PT-symmetric periodic potential, its link with condensed matter nuclear science, and possible neat link with Quark confinement theory. In recent years, the PT-symmetry and its related periodic potential have gained considerable interests among physicists. We begin with a review of some results from a preceding paper discussing derivation of PT-symmetric periodic potential from biquaternion Klein-Gordon equation and proceed further with the remaining issues. Further observation is of course recommended in order to refute or verify this proposition.
Classical irregular blocks, Hill's equation and PT-symmetric periodic complex potentials
Piatek, Marcin; Pietrykowski, Artur R.
2016-07-01
The Schrödinger eigenvalue problems for the Whittaker-Hill potential {Q}_2(x) = 1/2{h}^2 cos 4x + 4hμ cos 2x and the periodic complex potential {Q}_1(x)=1/4{h}^2{e}^{-} 4ix} + 2{h}^2 cos 2x are studied using their realizations in two-dimensional conformal field theory (2dCFT). It is shown that for the weak coupling (small) h ∈ ℝ and non-integer Floquet parameter ν ∉ ℤ spectra of hamiltonians ℋi = - d2/d x 2 + Q i( x), i = 1, 2 and corresponding two linearly independent eigenfunctions are given by the classical limit of the "single flavor" and "two flavors" ( N f = 1 , 2) irregular conformal blocks. It is known that complex nonhermitian hamiltonians which are PT-symmetric (= invariant under simultaneous parity P and time reversal T transformations) can have real eigenvalues. The hamiltonian ℋ1 is PT-symmetric for h, x ∈ ℝ. It is found that ℋ1 has a real spectrum in the weak coupling region for ν ∈ ℝ ℤ. This fact in an elementary way follows from a definition of the N f = 1 classical irregular block. Thus, ℋ1 can serve as yet another new model for testing postulates of PT-symmetric quantum mechanics.
Longhi, Stefano
2016-01-01
We consider wave transport phenomena in a $\\mathcal{PT}$-symmetric extension of the periodically-kicked quantum rotator model and reveal that dynamical localization assists the unbroken $\\mathcal{PT}$ phase. In the delocalized (quantum resonance) regime, $\\mathcal{PT}$ symmetry is always in the broken phase and ratchet acceleration arises as a signature of unidirectional non-Hermitian transport. An optical implementation of the periodically-kicked $\\mathcal{PT}$-symmetric Hamiltonian, based on transverse beam propagation in a passive optical resonator with combined phase and loss gratings, is suggested to visualize acceleration modes in fractional Talbot cavities.
Solitons in PT-symmetric periodic systems with the logarithmically saturable nonlinearity
Zhan, Kaiyun; Tian, Hao; Li, Xin; Xu, Xianfeng; Jiao, Zhiyong; Jia, Yulei
2016-09-01
We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain.
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Amore, Paolo, E-mail: paolo.amore@gmail.com [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima (Mexico); Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar [INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina); Garcia, Javier [INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina); Gutierrez, German [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima (Mexico)
2014-04-15
We study both analytically and numerically the spectrum of inhomogeneous strings with PT-symmetric density. We discuss an exactly solvable model of PT-symmetric string which is isospectral to the uniform string; for more general strings, we calculate exactly the sum rules Z(p)≡∑{sub n=1}{sup ∞}1/E{sub n}{sup p}, with p=1,2,… and find explicit expressions which can be used to obtain bounds on the lowest eigenvalue. A detailed numerical calculation is carried out for two non-solvable models depending on a parameter, obtaining precise estimates of the critical values where pair of real eigenvalues become complex. -- Highlights: •PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. •We study PT-symmetric strings with complex density. •They exhibit regions of unbroken PT symmetry. •We calculate the critical parameters at the boundaries of those regions. •There are exact real sum rules for some particular complex densities.
Bender, Carl M.
2015-07-01
The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian H = p2 + ix3, which is obviously not Dirac Hermitian, has a positive real discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory. Evidently, the axiom of Dirac Hermiticity is too restrictive. While H = p2 + ix3 is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined parity P (space reflection) and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past few years, some of these properties have been verified in laboratory experiments. A particularly interesting PT-symmetric Hamiltonian is H = p2 - x4, which contains an upside-down potential. This potential is discussed in detail, and it is explained in intuitive as well as in rigorous terms why the energy levels of this potential are real, positive, and discrete. Applications of PT-symmetry in quantum field theory are also discussed.
Classical irregular blocks, Hill's equation and PT-symmetric periodic complex potentials
Piatek, Marcin
2016-01-01
The Schroedinger eigenvalue problems for the Whittaker-Hill potential $Q_{2}(x)=\\tfrac{1}{2} h^2\\cos4x+4h\\mu\\cos2x$ and the periodic complex potential $Q_{1}(x)=\\tfrac{1}{4}h^2{\\rm e}^{-4ix}+2h^2\\cos2x$ are studied using their realizations in two-dimensional conformal field theory (2dCFT). It is shown that for the weak coupling (small) $h\\in\\mathbb{R}$ and non-integer Floquet parameter $\
Ge, Li
2016-01-01
The CPA-laser is a coexisting state of coherent perfect absorption and lasing that was proposed in parity-time ($\\cal PT$) symmetric photonic systems. In this work we show that the spectral signature of a CPA-laser displayed by the singular value spectrum of the scattering matrix ($S$) can be orders of magnitude wider than that displayed by the eigenvalue spectrum of $S$. Since the former reflects how strongly light can be absorbed or amplified and the latter announces the spontaneous symmetry breaking of $S$, these contrasting spectral signatures indicate that near perfect absorption and extremely strong amplification can be achieved even in the $\\cal PT$-symmetric phase of $S$, which is known for and defined by its flux-conserving eigenstates. We also show that these contrasting spectral signatures are accompanied by strikingly different sensitivities to disorder and imperfection, suggesting that the eigenvalue spectrum is potentially suitable for sensing and the singular value spectrum for robust switching...
Joglekar, Yogesh N
2010-01-01
We study the properties of a parity- and time-reversal- (PT) symmetric tight-binding chain of size N with position-dependent hopping amplitude. In contrast to the fragile PT-symmetric phase of a chain with constant hopping and imaginary impurity potentials, we show that, under very general conditions, our model is {\\it always} in the PT-symmetric phase. We numerically obtain the energy spectrum and the density of states of such a chain, and show that they are widely tunable. By studying the size-dependence of inverse participation ratios, we show that although the chain is not translationally invariant, most of its eigenstates are extended. Our results indicate that tight-binding models with non-Hermitian PT-symmetric hopping have a robust PT-symmetric phase and rich dynamics.
PT-Symmetric Quantum Electrodynamics
Bender, C M; Milton, K A; Shajesh, K V; Bender, Carl M.; Cavero-Pelaez, Ines; Milton, Kimball A.
2005-01-01
The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge $e$ is taken to be imaginary. However, if one also specifies that the potential $A^\\mu$ in such a theory transforms as a pseudovector rather than a vector, then the Hamiltonian becomes PT symmetric. The resulting non-Hermitian theory of electrodynamics is the analog of a spinless quantum field theory in which a pseudoscalar field $\\phi$ has a cubic self-interaction of the form $i\\phi^3$. The Hamiltonian for this cubic scalar field theory has a positive spectrum, and it has recently been demonstrated that the time evolution of this theory is unitary. The proof of unitarity requires the construction of a new operator called C, which is then used to define an inner product with respect to which the Hamiltonian is self-adjoint. In this paper the corresponding C operator for non-Hermitian quantum electrodynamics is constructed perturbatively. This construction demonstrates the unitarity of the theory. Non-Hermit...
PT-Symmetric Quantum Field Theory
Milton, K A
2003-01-01
In the context of the PT-symmetric version of quantum electrodynamics, it is argued that the C operator introduced in order to define a unitary inner product has nothing to do with charge conjugation.
Scattering properties of PT-symmetric objects
Miri, Mohammad-Ali; Facao, Margarida; Abouraddy, Ayman F; Bakry, Ahmed; Razvi, Mir A N; Alshahrie, Ahmed; Alù, Andrea; Christodoulides, Demetrios N
2016-01-01
We investigate the scattering response of parity-time (PT) symmetric structures. We show that, due to the local flow of energy between gain and loss regions, such systems can deflect light in unusual ways, as a function of the gain/loss contrast. Such structures are highly anisotropic and their scattering patterns can drastically change as a function of the angle of incidence. In addition, we derive a modified optical theorem for PT-symmetric scattering systems, and discuss its ramifications.
PT-Symmetric Optomechanically-Induced Transparency
Jing, H; Özdemir, S K; Zhang, J; Lü, X -Y; Peng, B; Yang, L; Nori, F
2014-01-01
Optomechanically-induced transparency (OMIT) and the associated slow-light propagation provide the basis for storing photons in nanofabricated phononic devices. Here we study OMIT in parity-time (PT)-symmetric microresonators with a tunable gain-to-loss ratio. This system features a reversed, non-amplifying transparency: inverted-OMIT. When the gain-to-loss ratio is steered, the system exhibits a transition from the PT-symmetric phase to the broken-PT-symmetric phase. We show that by tuning the pump power at fixed gain-to-loss ratio or the gain-to-loss ratio at fixed pump power, one can switch from slow to fast light and vice versa. Moreover, the presence of PT-phase transition results in the reversal of the pump and gain dependence of transmission rates. These features provide new tools for controlling light propagation using optomechanical devices.
PT -symmetric model of immune response
Bender, Carl M.; Ghatak, Ananya; Gianfreda, Mariagiovanna
2017-01-01
The study of PT -symmetric physical systems began in 1998 as a complex generalization of conventional quantum mechanics, but beginning in 2007 experiments began to be published in which the predicted PT phase transition was clearly observed in classical rather than in quantum-mechanical systems. This paper examines the classical PT phase transition in dynamical-system models that are moderately accurate representations of antigen-antibody systems. A surprising conclusion that can be drawn from these models is that it might be possible treat a serious disease in which the antigen concentration grows out of bounds (and the host dies) by injecting a small dose of a second (different) antigen. In this case a PT -symmetric analysis shows there are two possible favorable outcomes. In the unbroken-PT -symmetric phase the disease becomes chronic and is no longer lethal, while in the appropriate broken-PT -symmetric phase the concentration of lethal antigen goes to zero and the disease is completely cured.
Nonreciprocal Scattering by PT-symmetric stack of the layers
Shramkova, Oksana
2015-01-01
The nonreciprocal wave propagation in PT-symmetric periodic stack of binary dielectric layers characterised by balances loss and gain is analysed. The main mechanisms and resonant properties of the scattered plane waves are illustrated by the simulation results, and the effects of the periodicity and individual layer parameters on the stack nonreciprocal response are discussed. Gaussian beam dynamics in this type of structure is examined. The beam splitting in PT-symmetric periodic structure is observed. It is demonstrated that for slant beam incidence the break of the symmetry of field distribution takes place.
Revisiting the Optical PT-Symmetric Dimer
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José Delfino Huerta Morales
2016-08-01
Full Text Available Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of PT -symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical PT -symmetric dimer, a two-waveguide coupler where the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry-based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar N-waveguide couplers that are the optical realization of the Lorentz group in 2 + 1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of the Ehrenfest theorem.
Revisiting the optical $PT$-symmetric dimer
Morales, J D Huerta; López-Aguayo, S; Rodríguez-Lara, B M
2016-01-01
Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of $\\mathcal{PT}$-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical $\\mathcal{PT}$-symmetric dimer, a two-waveguide coupler were the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar $N$-waveguide couplers that are the optical realization of Lorentz group in 2+1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of Ehrenfest theorem.
Stability of solitons in PT-symmetric couplers
Driben, Rodislav
2011-01-01
Families of analytical solutions are found for symmetric and antisymmetric solitons in the dual-core system with the Kerr nonlinearity and PT-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the "supersymmetric" case, with equal coefficients of the gain, loss and inter-core coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching ("management").
Experimental demonstration of PT-symmetric stripe lasers
Gu, Zhiyuan; Lyu, Quan; Li, Meng; Xiao, Shumin; Song, Qinghai
2015-01-01
Recently, the coexistence of parity-time (PT) symmetric laser and absorber has gained tremendous research attention. While the PT symmetric absorber has been observed in microwave metamaterials, the experimental demonstration of PT symmetric laser is still absent. Here we experimentally study PT-symmetric laser absorber in stripe waveguide. Using the concept of PT symmetry to exploit the light amplification and absorption, PT-symmetric laser absorbers have been successfully obtained. Different from the single-mode PT symmetric lasers, the PT-symmetric stripe lasers have been experimentally confirmed by comparing the relative wavelength positions and mode spacing under different pumping conditions. When the waveguide is half pumped, the mode spacing is doubled and the lasing wavelengths shift to the center of every two initial lasing modes. All these observations are consistent with the theoretical predictions and confirm the PT-symmetry breaking well.
Stability analysis for solitons in PT-symmetric optical lattices
Nixon, Sean; Yang, Jianke
2012-01-01
Stability of solitons in parity-time (PT)-symmetric periodic potentials (optical lattices) is analyzed in both one- and two-dimensional systems. First we show analytically that when the strength of the gain-loss component in the PT lattice rises above a certain threshold (phase-transition point), an infinite number of linear Bloch bands turn complex simultaneously. Second, we show that while stable families of solitons can exist in PT lattices, increasing the gain-loss component has an overall destabilizing effect on soliton propagation. Specifically, when the gain-loss component increases, the parameter range of stable solitons shrinks as new regions of instability appear. Thirdly, we investigate the nonlinear evolution of unstable PT solitons under perturbations, and show that the energy of perturbed solitons can grow unbounded even though the PT lattice is below the phase transition point.
PT-symmetric deformations of integrable models.
Fring, Andreas
2013-04-28
We review recent results on new physical models constructed as PT-symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of Calogero-Moser-Sutherland type and nonlinear integrable field equations of Korteweg-de Vries type. The quantum spin chain discussed is related to the first example in the series of the non-unitary models of minimal conformal field theories. For the Calogero-Moser-Sutherland models, we provide three alternative deformations: a complex extension for models related to all types of Coxeter/Weyl groups; models describing the evolution of poles in constrained real-valued field equations of nonlinear integrable systems; and genuine deformations based on antilinearly invariant deformed root systems. Deformations of complex nonlinear integrable field equations of Korteweg-de Vries type are studied with regard to different kinds of PT-symmetrical scenarios. A reduction to simple complex quantum mechanical models currently under discussion is presented.
Nonlinear waves in $\\cal PT$-symmetric systems
Konotop, Vladimir V.; Yang, Jianke; Zezyulin, Dmitry A.
2016-01-01
Recent progress on nonlinear properties of parity-time ($\\cal PT$-) symmetric systems is comprehensively reviewed in this article. $\\cal PT$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\\cal PT$ symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a $\\cal PT$-symmetric system. The nat...
Invisibility in PT-symmetric complex crystals
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Longhi, Stefano, E-mail: longhi@fisi.polimi.it [Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci 32, I-20133 Milano (Italy)
2011-12-02
Bragg scattering in sinusoidal PT-symmetric complex crystals of finite thickness is theoretically investigated by the derivation of exact analytical expressions for reflection and transmission coefficients in terms of modified Bessel functions of first kind. The analytical results indicate that unidirectional invisibility, recently predicted for such crystals by coupled-mode theory (Z Lin et al 2011 Phys. Rev. Lett. http://dx.doi.org/10.1103/PhysRevLett.106.213901), breaks down for crystals containing a large number of unit cells. In particular, for a given modulation depth in a shallow sinusoidal potential, three regimes are encountered as the crystal thickness is increased. At short lengths the crystal is reflectionless and invisible when probed from one side (unidirectional invisibility), whereas at intermediate lengths the crystal remains reflectionless but not invisible; for longer crystals both unidirectional reflectionless and invisibility properties are broken. (paper)
Metrology with PT-Symmetric Cavities: Enhanced Sensitivity near the PT-Phase Transition.
Liu, Zhong-Peng; Zhang, Jing; Özdemir, Şahin Kaya; Peng, Bo; Jing, Hui; Lü, Xin-You; Li, Chun-Wen; Yang, Lan; Nori, Franco; Liu, Yu-Xi
2016-09-09
We propose and analyze a new approach based on parity-time (PT) symmetric microcavities with balanced gain and loss to enhance the performance of cavity-assisted metrology. We identify the conditions under which PT-symmetric microcavities allow us to improve sensitivity beyond what is achievable in loss-only systems. We discuss the application of PT-symmetric microcavities to the detection of mechanical motion, and show that the sensitivity is significantly enhanced near the transition point from unbroken- to broken-PT regimes. Our results open a new direction for PT-symmetric physical systems and it may find use in ultrahigh precision metrology and sensing.
Topological states in partially-PT-symmetric azimuthal potentials
Kartashov, Yaroslav V; Torner, Lluis
2015-01-01
We introduce partially-parity-time-symmetric (pPT-symmetric) azimuthal potentials composed from individual PT-symmetric cells located on a ring, where two azimuthal directions are nonequivalent in a sense that in such potentials excitations carrying topological dislo-cations exhibit different dynamics for different directions of energy circulation in the initial field distribution. Such non-conservative ratchet-like structures support rich families of stable vortex solitons in cubic nonlinear media, whose properties depend on the sign of the topological charge due to the nonequivalence of azimuthal directions. In contrast, oppositely charged vortex solitons remain equivalent in similar fully PT-symmetric potentials. The vortex solitons in the pPT- and PT-symmetric potentials are shown to feature qualitatively different internal current distributions, which are described by different discrete rotation symmetries of the intensity profiles.
Nonlinear waves in $\\cal PT$-symmetric systems
Konotop, Vladimir V; Zezyulin, Dmitry A
2016-01-01
Recent progress on nonlinear properties of parity-time ($\\cal PT$-) symmetric systems is comprehensively reviewed in this article. $\\cal PT$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\\cal PT$ symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a $\\cal PT$-symmetric system. The natural inclusion of nonlinearity into these $\\cal PT$ systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above $\\cal PT$-symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear $\\cal PT$-symmetric systems arising from various physical disciplines ...
PT-symmetric $\\varphi^4$ theory in d=0 dimensions
Bender, Carl M; Messina, Emanuele
2015-01-01
A detailed study of a PT-symmetric zero-dimensional quartic theory is presented and a comparison between the properties of this theory and those of a conventional quartic theory is given. It is shown that the PT-symmetric quartic theory evades the consequences of the Mermin-Wagner-Coleman theorem regarding the absence of symmetry breaking in d<2 dimensions. Furthermore, the PT-symmetric theory does not satisfy the usual Bogoliubov limit for the construction of the Green's functions because one obtains different results for the $h\\to0^-$ and the $h\\to0^+$ limits.
Anomalous doublets of states in a PT symmetric quantum model
Znojil, M; Roy, P; Roychoudhury, R; Znojil, Miloslav; Levai, Geza; Roy, Pinaki; Roychoudhury, Rajkumar
2001-01-01
A PT symmetric complexification of a conditionally exactly solvable potential in one dimension leads to a paradox. The set of its normalizable solutions proves larger than one would expect on the basis of its point canonical transformation analysis.
Cliffordized NAC supersymmetry and PT-symmetric Hamiltonians
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Toppan, Francesco [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: toppan@cbpf.br
2007-07-01
It is shown that non-anti commutative supersymmetry can be described through a Cliffordization of the superspace fermionic coordinates. A NAC supersymmetric quantum mechanical model is shown to be a PT-symmetric Hamiltonian. (author)
Nonlinear switching and solitons in PT-symmetric photonic systems
Suchkov, Sergey V; Huang, Jiahao; Dmitriev, Sergey V; Lee, Chaohong; Kivshar, Yuri S
2015-01-01
One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested Parity-Time (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT-symmetric photonic systems with an intensity-dependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly-induced PT-symmetry breaking, and all-optical switching. Nonl...
Complex {PT}-symmetric extensions of the nonlinear ultra-short light pulse model
Yan, Zhenya
2012-11-01
The short pulse equation u_{xt}=u+\\frac{1}{2}(u^2u_x)_x is PT symmetric, which arises in nonlinear optics for the ultra-short pulse case. We present a family of new complex PT-symmetric extensions of the short pulse equation, i[(iu_x)^{\\sigma }]_t=au+bu^m+ic[u^n(iu_x)^{\\epsilon }]_x \\,\\, (\\sigma ,\\, \\epsilon ,\\,a,\\,b,\\,c,\\,m,\\,n \\in {R}), based on the complex PT-symmetric extension principle. Some properties of these equations with some chosen parameters are studied including the Hamiltonian structures and exact solutions such as solitary wave solutions, doubly periodic wave solutions and compacton solutions. Our results may be useful to understand complex PT-symmetric nonlinear physical models. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
$\\mathcal{PT}$-symmetric mode-locking
Longhi, Stefano
2016-01-01
Parity-time ($\\mathcal{PT}$) symmetry is one of the most important accomplishments in optics over the past decade. Here the concept of $\\mathcal{PT}$ mode-locking of a laser is introduced, in which active phase locking of cavity axial modes is realized by asymmetric mode coupling in a complex time crystal. $\\mathcal{PT}$ mode-locking shows a transition from single to double pulse emission as the $\\mathcal{PT}$ symmetry breaking point is crossed. The transition can show a turbulent behavior, depending on a dimensionless modulation parameter that plays the same role as the Reynolds number in hydrodynamic flows.
Floquet control of the gain and loss in a PT-symmetric optical coupler
Wu, Yi; Zhu, Bo; Hu, Shu-Fang; Zhou, Zheng; Zhong, Hong-Hua
2017-02-01
Controlling the balanced gain and loss in a PT-symmetric system is a rather challenging task. Utilizing Floquet theory, we explore the constructive role of periodic modulation in controlling the gain and loss of a PT-symmetric optical coupler. It is found that the gain and loss of the system can be manipulated by applying a periodic modulation. Further, such an original non-Hermitian system can even be modulated into an effective Hermitian system derived by the high-frequency Floquet method. Therefore, compared with other PT symmetry control schemes, our protocol can modulate the unbroken PT-symmetric range to a wider parameter region. Our results provide a promising approach for controlling the gain and loss of a realistic system.
Remarks on the PT-pseudo-norm in PT-symmetric quantum mechanics
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Duc Tai Trinh [Department of Mathematics, Teacher Training College of Dalat, 29 Yersin, Dalat (Viet Nam)]|[Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Trieste 34014 (Italy)
2005-04-22
This paper presents an underlying analytical relationship between the PT-pseudo-norm associated with the PT-symmetric Hamiltonian H = p{sup 2} + V(q) and the Stokes multiplier of the differential equation corresponding to this Hamiltonian. We show that the sign alternation of the PT-pseudo-norm, which has been observed as a generic feature of the PT-inner product, is essentially controlled by the derivative of a Stokes multiplier with respect to the eigenparameter.
Spectral Singularity in confined PT symmetric optical potential
Sinha, Anjana
2013-01-01
We present an analytical study for the scattering amplitudes (Reflection |R| and Transmission |T|), of the periodic PT symmetric optical potential V(x) = W_0 cos^2 x + i W_0 V_0 sin 2x confined within the region 0 0.5) scattering is found to be anomalous (|T|^2, |R|^2 not necessarily \\leq 1). Additionally, in this parameter regime of V_0, one observes infinite number of spectral singularities E_{SS} at different values of V_0. Furthermore, for L = 2n \\pi, the transition point V_0 = 0.5 shows unidirectional invisibility with zero reflection when the beam is incident from the absorptive side (Im[V(x)] 0), transmission being identically unity in both cases.
PT-symmetric quantum electrodynamics and unitarity.
Milton, Kimball A; Abalo, E K; Parashar, Prachi; Pourtolami, Nima; Wagner, J
2013-04-28
More than 15 years ago, a new approach to quantum mechanics was suggested, in which Hermiticity of the Hamiltonian was to be replaced by invariance under a discrete symmetry, the product of parity and time-reversal symmetry, PT. It was shown that, if PT is unbroken, energies were, in fact, positive, and unitarity was satisfied. Since quantum mechanics is quantum field theory in one dimension--time--it was natural to extend this idea to higher-dimensional field theory, and in fact an apparently viable version of PT-invariant quantum electrodynamics (QED) was proposed. However, it has proved difficult to establish that the unitarity of the scattering matrix, for example, the Källén spectral representation for the photon propagator, can be maintained in this theory. This has led to questions of whether, in fact, even quantum mechanical systems are consistent with probability conservation when Green's functions are examined, since the latter have to possess physical requirements of analyticity. The status of PT QED will be reviewed in this paper, as well as the general issue of unitarity.
IS PT -SYMMETRIC QUANTUM THEORY FALSE AS A FUNDAMENTAL THEORY?
Directory of Open Access Journals (Sweden)
Miloslav Znojil
2016-06-01
Full Text Available Yi-Chan Lee et al. claim (cf. Phys. Rev. Lett. 112, 130404 (2014 that the “recent extension of quantum theory to non-Hermitian Hamiltonians” (which is widely known under the nickname of “PT-symmetric quantum theory” is “likely false as a fundamental theory”. By their opinion their results “essentially kill any hope of PT-symmetric quantum theory as a fundamental theory of nature”. In our present text we explain that their toy-model-based considerations are misleading and that they do not imply any similar conclusions.
On the integrability of PT-symmetric dimers
Pickton, J
2013-01-01
The coupled discrete linear and Kerr nonlinear Schrodinger equations with gain and loss describing transport on dimers with parity-time (PT) symmetric potentials are considered. The model is relevant among others to experiments in optical couplers and proposals on Bose-Einstein condensates in PT symmetric double-well potentials. It is shown that the models are integrable. A pendulum equation with a linear potential and a constant force for the phase-difference between the fields is obtained, which explains the presence of unbounded solutions above a critical threshold parameter.
Anomalies in PT-Symmetric Quantum Field Theory
Milton, K A
2004-01-01
It is shown that a version of PT-symmetric electrodynamics based on an axial-vector current coupling massless fermions to the photon possesses anomalies and so is rendered nonrenormalizable. An alternative theory is proposed based on the conventional vector current constructed from massive Dirac fields, but in which the PT transformation properties of electromagnetic fields are reversed. Such a theory seems to possess many attractive features.
Super Bloch Oscillation in a PT symmetric system
Turker, Z
2016-01-01
Wannier-Stark ladder in a PT symmetric system is generally complex that leads to amplified/damped Bloch oscillation. We show that a non-amplified wave packet oscillation with very large amplitude can be realized in a non-Hermitian tight binding lattice if certain conditions are satisfied. We show that pseudo PT symmetry guarantees the reality of the quasi energy spectrum in our system.
PT-Symmetric Quantum Electrodynamics and Unitarity
Milton, Kimball A; Parashar, Prachi; Pourtolami, Nima; Wagner, J
2012-01-01
More than 15 years ago, a new approach to quantum mechanics was suggested, in which Hermiticity of the Hamiltonian was to be replaced by invariance under a discrete symmetry, the product of parity and time-reversal symmetry, $\\mathcal{PT}$. It was shown that if $\\mathcal{PT}$ is unbroken, energies were, in fact, positive, and unitarity was satisifed. Since quantum mechanics is quantum field theory in 1 dimension, time, it was natural to extend this idea to higher-dimensional field theory, and in fact an apparently viable version of $\\mathcal{PT}$-invariant quantum electrodynamics was proposed. However, it has proved difficult to establish that the unitarity of the scattering matrix, for example, the K\\"all\\'en spectral representation for the photon propagator, can be maintained in this theory. This has led to questions of whether, in fact, even quantum mechanical systems are consistent with probability conservation when Green's functions are examined, since the latter have to possess physical requirements of ...
$\\mathcal{PT}$-symmetric microring laser-absorber
Longhi, Stefano
2014-01-01
The lasing and coherent perfect absorption (CPA) properties of $\\mathcal{PT}$-symmetric microrings with mixed index and gain gratings, externally coupled to a bus waveguide, are theoretically investigated. For a complex grating at the $\\mathcal{PT}$ symmetry breaking point, perfect unidirectional (either clockwise or counterclockwise) laser emission can be realized, however the grating does not discriminate longitudinal modes and CPA can not be simultaneously achieved. Above the grating $\\mathcal{PT}$ symmetry breaking point, single mode emission and simultaneous CPA can be obtained, with unbalanced and controllable excitation of clockwise and counterclockwise modes in the ring.
Scattering off PT-symmetric upside-down potentials
Bender, Carl M
2016-01-01
The upside-down $-x^4$, $-x^6$, and $-x^8$ potentials with appropriate PT-symmetric boundary conditions have real, positive, and discrete quantum-mechanical spectra. This paper proposes a straightforward macroscopic quantum-mechanical scattering experiment in which one can observe and measure these bound-state energies directly.
EXCEPTIONAL POINTS IN OPEN AND PT-SYMMETRIC SYSTEMS
Directory of Open Access Journals (Sweden)
Hichem Eleuch
2014-04-01
Full Text Available Exceptional points (EPs determine the dynamics of open quantum systems and cause also PT symmetry breaking in PT symmetric systems. From a mathematical point of view, this is caused by the fact that the phases of the wavefunctions (eigenfunctions of a non-Hermitian Hamiltonian relative to one another are not rigid when an EP is approached. The system is therefore able to align with the environment to which it is coupled and, consequently, rigorous changes of the system properties may occur. We compare analytically as well as numerically the eigenvalues and eigenfunctions of a 2 × 2 matrix that is characteristic either of open quantum systems at high level density or of PT symmetric optical lattices. In both cases, the results show clearly the influence of the environment on the system in the neighborhood of EPs. Although the systems are very different from one another, the eigenvalues and eigenfunctions indicate the same characteristic features.
PT -symmetric spectral singularity and negative-frequency resonance
Pendharker, Sarang; Guo, Yu; Khosravi, Farhad; Jacob, Zubin
2017-03-01
Vacuum consists of a bath of balanced and symmetric positive- and negative-frequency fluctuations. Media in relative motion or accelerated observers can break this symmetry and preferentially amplify negative-frequency modes as in quantum Cherenkov radiation and Unruh radiation. Here, we show the existence of a universal negative-frequency-momentum mirror symmetry in the relativistic Lorentzian transformation for electromagnetic waves. We show the connection of our discovered symmetry to parity-time (PT ) symmetry in moving media and the resulting spectral singularity in vacuum fluctuation-related effects. We prove that this spectral singularity can occur in the case of two metallic plates in relative motion interacting through positive- and negative-frequency plasmonic fluctuations (negative-frequency resonance). Our work paves the way for understanding the role of PT -symmetric spectral singularities in amplifying fluctuations and motivates the search for PT symmetry in novel photonic systems.
Bounded dynamics in finite PT-symmetric magnetic metamaterials.
Molina, Mario I
2014-03-01
We examine the PT-symmetry-breaking transition for a magnetic metamaterial of a finite extent, modeled as an array of coupled split-ring resonators in the equivalent circuit model approximation. Small-size arrays are solved completely in closed form, while for arrays larger than N=5 results were computed numerically for several gain and loss spatial distributions. In all cases, it is found that the parameter stability window decreases rapidly with the size of the array, until at N=20 approximately it is not possible to support a stable PT-symmetric phase.
PT-symmetric quantum oscillator in an optical cavity
Longhi, Stefano
2016-01-01
The quantum harmonic oscillator with parity-time ($\\mathcal{PT}$) symmetry, obtained from the ordinary (Hermitian) quantum harmonic oscillator by an imaginary displacement of the spatial coordinate, provides an important and exactly-solvable model to investigate non-Hermitian extension of the Ehrenfest theorem. Here it is shown that transverse light dynamics in an optical resonator with off-axis longitudinal pumping can emulate a $\\mathcal{PT}$-symmetric quantum harmonic oscillator, providing an experimentally accessible system to investigate non-Hermitian coherent state propagation.
PT-symmetric ladders with a scattering core
Energy Technology Data Exchange (ETDEWEB)
D' Ambroise, J. [Department of Mathematics, Amherst College, Amherst, MA 01002-5000 (United States); Lepri, S. [CNR – Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del piano 10, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Malomed, B.A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Kevrekidis, P.G. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-9305 (United States)
2014-08-01
We consider a PT-symmetric chain (ladder-shaped) system governed by the discrete nonlinear Schrödinger equation where the cubic nonlinearity is carried solely by two central “rungs” of the ladder. Two branches of scattering solutions for incident plane waves are found. We systematically construct these solutions, analyze their stability, and discuss non-reciprocity of the transmission associated with them. To relate the results to finite-size wavepacket dynamics, we also perform direct simulations of the evolution of the wavepackets, which confirm that the transmission is indeed asymmetric in this nonlinear system with the mutually balanced gain and loss. - Highlights: • We model a PT-symmetric ladder system with cubic nonlinearity on two central rungs. • We examine non-reciprocity and stability of incident plane waves. • Simulations of wavepackets confirm our results.
PT-symmetric phase in kagome photonic lattices
Chern, Gia-Wei
2015-01-01
Kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Here we propose a complex photonic lattice by placing $\\mathcal{PT}$-symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gain and loss on individual dimers, the system exhibits a $\\mathcal{PT}$-symmetric phase for finite gain/loss parameter up to a critical value. The beam evolution in this complex kagome waveguide array exhibits a novel oscillatory rotation of optical power along the propagation distance. Long-lived local chiral structures originating from the nearly flat bands of the kagome structure are observed when the lattice is subject to a narrow beam excitation.
PT-symmetric phase in kagome-based photonic lattices.
Chern, Gia-Wei; Saxena, Avadh
2015-12-15
The kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Here we propose a complex photonic lattice by placing PT-symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gain and loss on individual dimers, the system exhibits a PT-symmetric phase for finite gain/loss parameter up to a critical value. The beam evolution in this complex kagome waveguide array exhibits a novel oscillatory rotation of optical power along the propagation distance. Long-lived local chiral structures originating from the nearly flat bands of the kagome structure are observed when the lattice is subject to a narrow beam excitation.
PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model
Mostafazadeh, A
2004-01-01
We perform a perturbative calculation of the physical observables, in particular pseudo-Hermitian position and momentum operators, the equivalent Hermitian Hamiltonian operator, and the classical Hamiltonian for the PT-symmetric cubic anharmonic oscillator, $ H=p^1/(2m)+\\mu^2x^2/2+i\\epsilon x^3 $. Ignoring terms of order $ \\epsilon^4 $ and higher, we show that this system describes an ordinary quartic anharmonic oscillator with a position-dependent mass and real and positive coupling constants. This observation elucidates the classical origin of the reality and positivity of the energy spectrum. We also discuss the quantum-classical correspondence for this PT-symmetric system, compute the associated conserved probability density, and comment on the issue of factor-ordering in the pseudo-Hermitian canonical quantization of the underlying classical system.
PT-symmetric phase in kagome photonic lattices
Chern, Gia-Wei; Saxena, Avadh
2015-01-01
Kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Here we propose a complex photonic lattice by placing $\\mathcal{PT}$-symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gai...
Engineering wavefront caustics trajectories in ${\\cal PT}$-symmetric lattices
Bender, Nicholas; Kottos, Tsampikos
2015-01-01
We utilize caustic theory in ${\\cal PT}-$symmetric lattices to design focusing and curved beam dynamics. We show that the gain and loss parameter in these systems provides an addition degree of freedom which allows for the design of the same caustics trajectories with different intensity distribution in the individual waveguides. Moreover we can create aberration-free focal points at any paraxial distance $z_f$, with anomalously large focal intensity.
Non-Hermitian supersymmetry and singular PT symmetrized oscillators
Znojil, M
2002-01-01
SUSY partnership between singular potentials often breaks down. Via regularization it can be restored on certain ad hoc subspaces of Hilbert space [Das and Pernice, Nucl. Phys. B 561 (1999) 357]. Within the naturally complexified (so called PT symmetric) quantum mechanics we show how SUSY between strongly singular harmonic oscillators can completely be re-established. Our recipe leads to a new form of the bosonic creation and annihilation operators and proves continuous near the usual regular (i.e., linear harmonic) limit.
Bright solitons in a PT-symmetric chain of dimers
Kirikchi, Omar B; Susanto, Hadi
2016-01-01
We study the existence and stability of fundamental bright discrete solitons in a parity-time (PT)-symmetric coupler composed by a chain of dimers, that is modelled by linearly coupled discrete nonlinear Schrodinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anti-continuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, on the contrary of the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quart...
PT symmetry breaking in the presence of random, periodic, long-range hopping
Harter, Andrew K.; Onanga, Franck Assogba; Joglekar, Yogesh N.
2016-09-01
Over the past five years, open systems with balanced gain and loss have been investigated for extraordinary properties that are not shared by their closed counterparts. Non-Hermitian, Parity-Time (PT ) symmetric Hamiltonians faithfully model such systems. Such a Hamiltonian typically consists of a reflection-symmetric, Hermitian, nearest-neighbor hopping profile and a PT-symmetric, non-Hermitian, gain and loss potential, and has a robust PT -symmetric phase. Here we investigate the robustness of this phase in the presence of long-range hopping disorder that is not PT-symmetric, but is periodic. We find that the PT-symmetric phase remains robust in the presence of such disorder, and characterize the configurations where that happens. Our results are found using a tight-binding model, and we validate our predictions through the beam-propagation method.
Spectral singularity in confined PT symmetric optical potential
Energy Technology Data Exchange (ETDEWEB)
Sinha, Anjana [Department of Instrumentation Science, Jadavpur University, Kolkata - 700 032 (India); Roychoudhury, R. [Department of Mathematics, Bethune College, Kolkata - 700 006, India and Advanced Centre for Nonlinear and Complex Phenomena, 1175 Survey Park, Kolkata - 700075 (India)
2013-11-15
We present an analytical study for the scattering amplitudes (Reflection ‖R‖ and Transmission ‖T‖), of the periodic PT symmetric optical potential V(x)=W{sub 0}cos{sup 2}x+iV{sub 0}sin2x confined within the region 0 ⩽x⩽L, embedded in a homogeneous medium having uniform potential W{sub 0}. The confining length L is considered to be some integral multiple of the period π. We give some new and interesting results. Scattering is observed to be normal (‖T‖{sup 2}⩽ 1, ‖R‖{sup 2}⩽ 1) for V{sub 0}⩽ 0.5, when the above potential can be mapped to a Hermitian potential by a similarity transformation. Beyond this point (V{sub 0} > 0.5) scattering is found to be anomalous (‖T‖{sup 2}, ‖R‖{sup 2} not necessarily ⩽1). Additionally, in this parameter regime of V{sub 0}, one observes infinite number of spectral singularities E{sub SS} at different values of V{sub 0}. Furthermore, for L= 2nπ, the transition point V{sub 0}= 0.5 shows unidirectional invisibility with zero reflection when the beam is incident from the absorptive side (Im[V(x)] < 0) but with finite reflection when the beam is incident from the emissive side (Im[V(x)] > 0), transmission being identically unity in both cases. Finally, the scattering coefficients ‖R‖{sup 2} and ‖T‖{sup 2} always obey the generalized unitarity relation : ‖T|{sup 2}−1|=√(|R{sub R}|{sup 2}|R{sub L}|{sup 2}), where subscripts R and L stand for right and left incidence, respectively.
Three-dimensional topological solitons in PT-symmetric optical lattices
Kartashov, Yaroslav V; Huang, Guoxiang; Torner, Lluis
2016-01-01
We address the properties of fully three-dimensional solitons in complex parity-time (PT)-symmetric periodic lattices with focusing Kerr nonlinearity, and uncover that such lattices can stabilize both, fundamental and vortex-carrying soliton states. The imaginary part of the lattice induces internal currents in the solitons that strongly affect their domains of existence and stability. The domain of stability for fundamental solitons can extend nearly up to the PT-symmetry breaking point, where the linear lattice spectrum becomes complex. Vortex solitons feature spatially asymmetric profiles in the PT-symmetric lattices, but they are found to still exist as stable states within narrow regions. Our results provide the first example of continuous families of stable three-dimensional propagating solitons supported by complex potentials.
PT-Symmetric Nonlinear Metamaterials and Zero-Dimensional Systems
Tsironis, G P
2013-01-01
A one dimensional, parity-time (${\\cal PT}$)-symmetric magnetic metamaterial comprising split-ring resonators having both gain and loss is investigated. In the linear regime, the transition from the exact to the broken ${\\cal PT}$-phase is determined through the calculation of the eigenfrequency spectrum for two different configurations; the one with equidistant split-rings and the other with the split-rings forming a binary pattern (${\\cal PT}$ dimer chain). The latter system features a two-band, gapped spectrum with its shape determined by the gain/loss coefficient as well as the inter-element coupling. In the presense of nonlinearity, the ${\\cal PT}$ dimer chain with balanced gain and loss supports nonlinear localized modes in the form of novel discrete breathers below the lower branch of the linear spectrum. These breathers, that can be excited from a weak applied magnetic field by frequency chirping, can be subsequently driven solely by the gain for very long times. The effect of a small imbalance betwee...
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase transition point
Nixon, Sean; Yang, Jianke
2012-01-01
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase-transition point are analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of novel phenomena known to exist in this envelope equation are shown to also exist in the full equation including wave blowup, periodic bound states and solitary wave solutions.
Bright Solitons in a PT-Symmetric Chain of Dimers
Directory of Open Access Journals (Sweden)
Omar B. Kirikchi
2016-01-01
Full Text Available We study the existence and stability of fundamental bright discrete solitons in a parity-time- (PT- symmetric coupler composed by a chain of dimers that is modelled by linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anticontinuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, in contrast to the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quartet of complex eigenvalues. In general, the gain-loss term can be considered parasitic as it reduces the stability region of the onsite solitons. Additionally, we analyse the dynamic behaviour of the onsite and intersite solitons when unstable, where typically it is either in the form of travelling solitons or soliton blow-ups.
Kartashov, Yaroslav V; Konotop, Vladimir V; Torner, Lluis
2016-01-01
We address the propagation of light beams in longitudinally modulated PT-symmetric lattices, built as arrays of couplers with periodically varying separation between their channels, and show a number of possibilities for efficient diffraction control available in such non-conservative structures. The dynamics of light in such lattices crucially depends on the ratio of the switching length for the straight segments of each coupler and the longitudinal lattice period. Depending on the longitudinal period, one can achieve either beam rectification, when the input light propagates at a fixed angle across the structure without diffractive broadening, or dynamic localization, when the initial intensity distribution is periodically restored after each longitudinal period. Importantly, the transition between these two different propagation regimes can be achieved by tuning only gain and losses acting in the system, provided that the PT-symmetry remains unbroken. The impact of Kerr nonlinearity is also discussed.
Light propagation through a PT-symmetric photonic-crystal.
Konotop, Vladimir V; Mantsyzov, Boris I
2016-11-14
Light propagation through a finite-width periodically modulated layer obeying parity-time (PT) symmetry is considered. We consider the configuration when the resonant conditions of mode coupling by the grating are satisfied. It is shown that the dependence of the transmission and reflection coefficients on the slab width has resonant character featuring strong amplification of reflected and transmitted waves with negative angles. The dependence of the scattering data on the gain-and-loss intensity also feature strong resonances near the PT-symmetry breaking point, when the slab strongly amplifies waves reflected and transmitted with negative angles, provided the incident wave has a positive angle of incidence.
Jamming anomaly in $\\mathcal{PT}$-symmetric systems
Barashenkov, I V; Konotop, Vladimir V
2016-01-01
The Schr\\"odinger equation with a $\\mathcal{PT}$-symmetric potential is used to model an optical structure consisting of an element with gain coupled to an element with loss. At low gain-loss amplitudes $\\gamma$, raising the amplitude results in the energy flux from the active to the leaky element being boosted. We study the anomalous behaviour occurring for larger $\\gamma$, where the increase of the amplitude produces a drop of the flux across the gain-loss interface. We show that this jamming anomaly is either a precursor of the exceptional point, where two real eigenvalues coalesce and acquire imaginary parts, or precedes the eigenvalue's immersion in the continuous spectrum.
Phase transition in PT symmetric active plasmonic systems
Mattheakis, M; Molina, M I; Tsironis, G P
2015-01-01
Surface plasmon polaritons (SPPs) are coherent electromagnetic surface waves trapped on an insulator-conductor interface. The SPPs decay exponentially along the propagation due to conductor losses, restricting the SPPs propagation length to few microns. Gain materials can be used to counterbalance the aforementioned losses. We provide an exact expression for the gain, in terms of the optical properties of the interface, for which the losses are eliminated. In addition, we show that systems characterized by lossless SPP propagation are related to PT symmetric systems. Furthermore, we derive an analytical critical value of the gain describing a phase transition between lossless and prohibited SPPs propagation. The regime of the aforementioned propagation can be directed by the optical properties of the system under scrutiny. Finally, we perform COMSOL simulations verifying the theoretical findings.
PT-Symmetric Versus Hermitian Formulations of Quantum Mechanics
Bender, C M; Milton, K A; Bender, Carl M.; Chen, Jun-Hua; Milton, Kimball A.
2006-01-01
A non-Hermitian Hamiltonian that has an unbroken PT symmetry can be converted by means of a similarity transformation to a physically equivalent Hermitian Hamiltonian. This raises the following question: In which form of the quantum theory, the non-Hermitian or the Hermitian one, is it easier to perform calculations? This paper compares both forms of a non-Hermitian $ix^3$ quantum-mechanical Hamiltonian and demonstrates that it is much harder to perform calculations in the Hermitian theory because the perturbation series for the Hermitian Hamiltonian is constructed from divergent Feynman graphs. For the Hermitian version of the theory, dimensional continuation is used to regulate the divergent graphs that contribute to the ground-state energy and the one-point Green's function. The results that are obtained are identical to those found much more simply and without divergences in the non-Hermitian PT-symmetric Hamiltonian. The $\\mathcal{O}(g^4)$ contribution to the ground-state energy of the Hermitian version ...
Analytic Results for a PT-symmetric Optical Structure
Jones, H F
2011-01-01
Propagation of light through media with a complex refractive index in which gain and loss are engineered to be $PT$ symmetric has many remarkable features. In particular the usual unitarity relations are not satisfied, so that the reflection coefficients can be greater than one, and in general are not the same for left or right incidence. Within the class of optical potentials of the form $v(x)=v_1\\cos(2\\beta x)+iv_2\\sin(2\\beta x)$ the case $v_2=v_1$ is of particular interest, as it lies on the boundary of $PT$-symmetry breaking. It has been shown in a recent paper by Lin et al. that in this case one has the property of "unidirectional invisibility", while for propagation in the other direction there is a greatly enhanced reflection coefficient proportional to $L^2$, where $L$ is the length of the medium in the direction of propagation. For this potential we show how analytic expressions can be obtained for the various transmission and reflection coefficients, which are expressed in a very succinct form in te...
Tailoring Spectral Properties of Binary PT-Symmetric Gratings by Duty-Cycle Methods
DEFF Research Database (Denmark)
Lupu, Anatole T.; Benisty, Henri; Lavrinenko, Andrei
2016-01-01
We explore the frequency selective functionalities of a nonuniform PT-symmetric Bragg grating with modulated complex index profile. We start by assessing the possibility to achieve an efficient apodization of the PT-symmetric Bragg grating spectral response by using direct adaptations of the conv...
Scarcity of real discrete eigenvalues in non-analytic complex $\\mathcal{PT}$-symmetric potentials
Indian Academy of Sciences (India)
Zafar Ahmed
2009-08-01
We find that a non-differentiability occurring whether in real or imaginary part of a complex $\\mathcal{PT}$-symmetric potential causes a scarcity of the real discrete eigenvalues despite the real part alone possessing an infinite spectrum. We demonstrate this by perturbing the real potentials 2 and || by imaginary $\\mathcal{PT}$ -symmetric potentials || and , respectively.
Sublattice signatures of transitions in a $\\mathcal{PT}$-symmetric dimer lattice
Harter, Andrew K
2016-01-01
Lattice models with non-hermitian, parity and time-reversal ($\\mathcal{PT}$) symmetric Hamiltonians, realized most readily in coupled optical systems, have been intensely studied in the past few years. A $\\mathcal{PT}$-symmetric dimer lattice consists of dimers with intra-dimer coupling $\
Kulishov, Mykola; Kress, Bernard
2015-01-01
We study the diffraction produced by a slab of purely reflective PT-symmetric volume Bragg grating that combines modulations of refractive index and gain/loss of the same periodicity with a quarter-period shift between them. Such a complex grating has a directional coupling between the different diffraction orders, which allows us to find an analytic solution for the first three orders of the full Maxwell equations without resorting to the paraxial approximation. This is important, because only with the full equations can the boundary conditions, allowing for the reflections, be properly implemented. Using our solution we analyze unidirectional invisibility of such a grating in a wide variety of configurations.
Robust PT-symmetric chain and properties of its Hermitian counterpart
Joglekar, Yogesh N.; Saxena, Avadh
2011-05-01
We study the properties of a parity- and time-reversal- (PT) symmetric tight-binding chain of size N with position-dependent hopping amplitude. In contrast to the fragile PT-symmetric phase of a chain with constant hopping and imaginary impurity potentials, we show that, under very general conditions, our model is always in the PT-symmetric phase. We numerically obtain the energy spectrum and the density of states of such a chain, and show that they are widely tunable. By studying the size dependence of inverse participation ratios, we show that although the chain is not translationally invariant, most of its eigenstates are extended. Our results indicate that tight-binding models with non-Hermitian, PT-symmetric hopping have a robust PT-symmetric phase and rich dynamics which may be explored in coupled waveguides.
Quantum mechanics of $PT$ and non-$PT$ -symmetric potentials in three dimensions
Indian Academy of Sciences (India)
BHARDWAJ S B; SINGH RAM MEHAR; MISHRA S C
2016-07-01
With a view of exploring new vistas with regard to the nature of complex eigenspectra of a non-Hermitian Hamiltonian, the quasi-exact solutions of the Schrödinger equation are investigated for a shifted harmonic potential under the framework of extended complex phase-space approach. Analyticity property ofthe eigenfunction alone is found sufficient to throw light on the nature of the eigenvalues and eigenfunctions of a system. Explicit expressions of eigenvalues and eigenfunctions for the ground state as well as excited state including their $PT$-symmetric version are worked out.
PT-symmetric dimer of coupled nonlinear oscillators
Indian Academy of Sciences (India)
Avinash Khare
2015-11-01
We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry, i.e., one of them has gain and the other an equal and opposite amount of loss. We first discuss various symmetries of the model. We show that both the linear system as well as a special case of the nonlinear system can be derived from a Hamiltonian, whose structure is similar to the Pais–Uhlenbeck Hamiltonian. Exact solutions are obtained in a few special cases. We show that the system is a superintegrable system within the rotating wave approximation (RWA). We also obtain several exact solutions of these RWA equations. Further, we point out a novel superposition in the context of periodic solutions in terms of Jacobi elliptic functions that we obtain in this problem. Finally, we briefly mention numerical results about the stability of some of the solutions.
Compactons in $\\mathcal{PT}$-symmetric generalized Korteweg–de Vries equations
Indian Academy of Sciences (India)
Carl M Bender; Fred Cooper; Avinash Khare; Bogdan Mihaila; Avadh Saxena
2009-08-01
This paper considers the $\\mathcal{PT}$-symmetric extensions of the equations examined by Cooper, Shepard and Sodano. From the scaling properties of the $\\mathcal{PT}$-symmetric equations a general theorem relating the energy, momentum and velocity of any solitary-wave solution of the generalized KdV equation is derived. We also discuss the stability of the compacton solution as a function of the parameters affecting the nonlinearities.
Controllable Akhmediev breather and Kuznetsov-Ma soliton trains in PT-symmetric coupled waveguides.
Dai, Chaoqing; Wang, Yueyue; Zhang, Xiaofei
2014-12-01
The PT-symmetric and PT-antisymmetric Akhmediev breather (AB) and Kuznetsov-Ma (KM) soliton train solutions of a (2+1)-dimensional variable-coefficient coupled nonlinear Schrödinger equation in PT-symmetric coupled waveguides with gain and loss are derived via the Darboux transformation method. From these analytical solutions, we investigate the controllable behaviors of AB and KM soliton trains in a diffraction decreasing system with exponential profile. By adjusting the relation between the maximum Zm of effective propagation distance and the peak locations Zi of AB and KM soliton trains, we can control the restraint, maintenance and postpone excitations of AB and KM soliton trains.
Observation of Bloch oscillations in complex PT-symmetric photonic lattices.
Wimmer, Martin; Miri, Mohammed-Ali; Christodoulides, Demetrios; Peschel, Ulf
2015-12-07
Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals exhibit unusual properties like secondary emissions and resonant restoration of PT symmetry. In addition, we present a versatile method for reconstructing the real and imaginary components of the band structure by directly monitoring the light evolution during a cycle of these oscillations.
Phase-coupled optical diode based on PT symmetric system
Gao, Yong-Pan; Cao, Cong; Zhang, Yong; Wang, Tie-Jun; Wang, Chuan
2017-01-01
Here we investigate a phase-coupled parity-time symmetric plasmonic system, and theoretically achieved the all optical on-chip plasmonic diode using the coupled mode theory. The proposed symmetrical system consists of one loss cavity and one gain cavity each coupled with the waveguide, and we find that the controllable amplification of the input field can be achieved by changing the power coupling fraction between the resonators and the waveguide. Moreover, this loss-gain symmetric system could work as a frequency comb filter, and the operation on the device could be controlled by tuning the coupling strength between the two plasmonic cavities by tuning the coupling distance between the cavities and the waveguide.
Nonlinear wave dynamics near phase transition in $\\mathcal{PT}$-symmetric localized potentials
Nixon, Sean
2015-01-01
Nonlinear wave propagation in parity-time ($\\mathcal{PT}$) symmetric localized potentials is investigated analytically near a phase-transition point where a pair of real eigenvalues of the potential coalesce and bifurcate into the complex plane. Necessary conditions for phase transition to occur are derived based on a generalization of the Krein signature. Using multi-scale perturbation analysis, a reduced nonlinear ODE model is derived for the amplitude of localized solutions near phase transition. Above phase transition, this ODE model predicts a family of stable solitons not bifurcating from linear (infinitesimal) modes under a certain sign of nonlinearity. In addition, it predicts periodically-oscillating nonlinear modes away from solitons. Under the opposite sign of nonlinearity, it predicts unbounded growth of solutions. Below phase transition, solution dynamics is predicted as well. All analytical results are compared to direct computations of the full system and good agreement is observed.
From $\\mathcal{PT}$ -symmetric quantum mechanics to conformal field theory
Indian Academy of Sciences (India)
Patrick Dorey; Clare Dunning; Roberto Tateo
2009-08-01
One of the simplest examples of a $\\mathcal{PT}$-symmetric quantum system is the scaling Yang–Lee model, a quantum field theory with cubic interaction and purely imaginary coupling. We give a historical review of some facts about this model in ≤ 2 dimensions, from its original definition in connection with phase transitions in the Ising model and its relevance to polymer physics, to the role it has played in studies of integrable quantum field theory and $\\mathcal{PT}$-symmetric quantum mechanics. We also discuss some more general results on $\\mathcal{PT}$-symmetric quantum mechanics and the ODE/IM correspondence, and mention applications to magnetic systems and cold atom physics.
Controlling electric, magnetic, and chiral dipolar emission with PT-symmetric potentials
Energy Technology Data Exchange (ETDEWEB)
Alaeian, Hadiseh; Dionne, Jennifer A.
2015-06-01
We investigate the effect of parity-time (PT) symmetric optical potentials on the radiation of achiral and chiral dipole sources. Two properties unique to PT-symmetric potentials are observed. First, the dipole can be tuned to behave as a strong optical emitter or absorber based on the non-Hermiticity parameter and the dipole location. Second, exceptional points give rise to new system resonances that lead to orders-of-magnitude enhancements in the dipolar emitted or absorbed power. Utilizing these properties, we show that enantiomers of chiral molecules near PT-symmetric metamaterials exhibit a 4.5-fold difference in their emitted power and decay rate. The results of this work could enable new atom-cavity interactions for quantum optics, as well as all-optical enantioselective separation.
Symmetric Periodic Solutions of the Anisotropic Manev Problem
Santoprete, Manuele
2002-01-01
We consider the Manev Potential in an anisotropic space, i.e., such that the force acts differently in each direction. Using a generalization of the Poincare' continuation method we study the existence of periodic solutions for weak anisotropy. In particular we find that the symmetric periodic orbits of the Manev system are perturbed to periodic orbits in the anisotropic problem.
Compactons in PT-symmetric generalized Korteweg-de Vries equations
Energy Technology Data Exchange (ETDEWEB)
Saxena, Avadh B [Los Alamos National Laboratory; Mihaila, Bogdan [Los Alamos National Laboratory; Bender, Carl M [WASHINGTON UNIV; Cooper, Fred [SANTA FE INSTITUTE; Khare, Avinash [INSTITUTE OF PHYSICS
2008-01-01
In an earlier paper Cooper, Shepard, and Sodano introduced a generalized KdV equation that can exhibit the kinds of compacton solitary waves that were first seen in equations studied by Rosenau and Hyman. This paper considers the PT-symmetric extensions of the equations examined by Cooper, Shepard, and Sodano. From the scaling properties of the PT-symmetric equations a general theorem relating the energy, momentum, and velocity of any solitary-wave solution of the generalized KdV equation is derived, and it is shown that the velocity of the solitons is determined by their amplitude, width, and momentum.
Compactons in PT-symmetric generalized Korteweg-de Vries equations
Energy Technology Data Exchange (ETDEWEB)
Saxena, Avadh B [Los Alamos National Laboratory; Mihaila, Bogdan [Los Alamos National Laboratory; Bender, Carl M [WASHINGTON UNIV; Cooper, Fred [SANTA FE INSTITUTE; Khare, Avinash [INSTITUTE OF PHYSICS
2008-01-01
In an earlier paper Cooper, Shepard, and Sodano introduced a generalized KdV equation that can exhibit the kinds of compacton solitary waves that were first seen in equations studied by Rosenau and Hyman. This paper considers the PT-symmetric extensions of the equations examined by Cooper, Shepard, and Sodano. From the scaling properties of the PT-symmetric equations a general theorem relating the energy, momentum, and velocity of any solitary-wave solution of the generalized KdV equation is derived, and it is shown that the velocity of the solitons is determined by their amplitude, width, and momentum.
Anomalous Light Scattering by Topological PT-symmetric Particle Arrays
Ling, C. W.; Choi, Ka Hei; Mok, T. C.; Zhang, Zhao-Qing; Fung, Kin Hung
2016-12-01
Robust topological edge modes may evolve into complex-frequency modes when a physical system becomes non-Hermitian. We show that, while having negligible forward optical extinction cross section, a conjugate pair of such complex topological edge modes in a non-Hermitian -symmetric system can give rise to an anomalous sideway scattering when they are simultaneously excited by a plane wave. We propose a realization of such scattering state in a linear array of subwavelength resonators coated with gain media. The prediction is based on an analytical two-band model and verified by rigorous numerical simulation using multiple-multipole scattering theory. The result suggests an extreme situation where leakage of classical information is unnoticeable to the transmitter and the receiver when such a -symmetric unit is inserted into the communication channel.
Dynamics of higher-order solitons in regular and PT-symmetric nonlinear couplers
Driben, R
2012-01-01
Dynamics of symmetric and antisymmetric 2-solitons and 3-solitons is studied in the model of the nonlinear dual-core coupler and its PT-symmetric version. Regions of the convergence of the injected perturbed symmetric and antisymmetric N-solitons into symmetric and asymmetric quasi-solitons are found. In the PT-symmetric system, with the balanced gain and loss acting in the two cores, borders of the stability against the blowup are identified. Notably, in all the cases the stability regions are larger for antisymmetric 2-soliton inputs than for their symmetric counterparts, on the contrary to previously known results for fundamental solitons (N=1). Dynamical regimes (switching) are also studied for the 2-soliton injected into a single core of the coupler. In particular, a region of splitting of the input into a pair of symmetric solitons is found, which is explained as a manifestation of the resonance between the vibrations of the 2-soliton and oscillations of energy between the two cores in the coupler.
PT-symmetric coupler with a coupling defect: soliton interaction with exceptional point
Bludov, Yuli V; Huang, Guoxiang; Konotop, Vladimir V
2014-01-01
We study interaction of a soliton in a parity-time (PT) symmetric coupler which has local perturbation of the coupling constant. Such a defect does not change the PT-symmetry of the system, but locally can achieve the exceptional point. We found that the symmetric solitons after interaction with the defect either transform into breathers or blow up. The dynamics of anti-symmetric solitons is more complex, showing domains of successive broadening of the beam and of the beam splitting in two outwards propagating solitons, in addition to the single breather generation and blow up. All the effects are preserved when the coupling strength in the center of the defect deviates from the exceptional point. If the coupling is strong enough the only observable outcome of the soliton-defect interaction is the generation of the breather.
Green's Function of a General PT-Symmetric Non-Hermitian Non-central Potential
Mourya, Brijesh Kumar
2016-01-01
We study the path integral solution of a system of particle moving in certain class of PT symmetric non-Hermitian and non-central potential. The Hamil- tonian of the system is converted to a separable Hamiltonian of Liouville type in parabolic coordinates and is further mapped into a Hamiltonian corresponding to two 2-dimensional simple harmonic oscillators (SHOs). Thus the explicit Green's functions for a general non-central PT symmetric non hermitian potential are cal- culated in terms of that of 2d SHOs. The entire spectrum for this three dimensional system is shown to be always real leading to the fact that the system remains in unbroken PT phase all the time.
Non-Hermitian Neutrino Oscillations in Matter with PT Symmetric Hamiltonians
Ohlsson, Tommy
2015-01-01
We introduce and develop a novel approach to extend the ordinary two-flavor neutrino oscillation formalism in matter using a non-Hermitian PT symmetric effective Hamiltonian. The condition of PT symmetry is weaker and less mathematical than that of Hermicity, but more physical, and such an extension of the formalism can give rise to sub-leading effects in neutrino flavor transitions similar to the effects by so-called non-standard neutrino interactions. We derive the necessary conditions for the spectrum of the effective Hamiltonian to be real as well as the mappings between the fundamental and effective parameters including the corresponding two-flavor neutrino transition probability. We find that the effective leptonic mixing must always be maximal and that the real spectrum of the effective Hamiltonian will depend on all new fundamental parameters introduced in the non-Hermitian PT symmetric extension of the usual neutrino oscillation formalism.
A selection rule for transitions in PT-symmetric quantum theory
Mead, Lawrence R
2016-01-01
Carl Bender and collaborators have developed a quantum theory governed by Hamiltonians that are PT-symmetric rather than Hermitian. To implement this theory, the inner product was redefined to guarantee positive norms of eigenstates of the Hamiltonian. In the general case, which includes arbitrary time-dependence in the Hamiltonian, a modification of the Schrodinger equation is necessary as shown by Gong and Wang to conserve probability. In this paper, we derive the following selection rule: transitions induced by time dependence in a PT-symmetric Hamiltonian cannot occur between normalized states of differing PT-norm. We show three examples of this selection rule in action: two matrix models and one in the continuum.
Ge, Li
2016-01-01
The scattering matrix $S$ obeys the unitary relation $S^\\dagger S=1$ in a Hermitian system and the symmetry property ${\\cal PT}S{\\cal PT}=S^{-1}$ in a Parity-Time (${\\cal PT}$) symmetric system. Here we report a different symmetry relation of the $S$ matrix in a one-dimensional heterostructure, which is given by the amplitude ratio of the incident waves in the scattering eigenstates. It originates from the optical reciprocity and holds independent of the Hermiticity or $\\cal PT$ symmetry of the system. Using this symmetry relation, we probe a quasi-transition that is reminiscent of the spontaneous symmetry breaking of a $\\cal PT$-symmetric $S$ matrix, now with unbalanced gain and loss and even in the absence of gain. We show that the additional symmetry relation provides a clear evidence of an exceptional point, even when all other signatures of the $\\cal PT$ symmetry breaking are completely erased. We also discuss the existence of a final exceptional point in this correspondence, which is attributed to asymm...
From particle in a box to PT -symmetric systems via isospectral deformation
Cherian, Philip; Panigrahi, P K
2011-01-01
A family of PT -symmetric complex potentials are obtained which is isospectral to free particle in an infinite complex box in one dimension (1-D). These are generalizations to the cosec2(x) potential, isospectral to particle in a real infinite box. In the complex plane, the infinite box is extended parallel to the real axis having a real width, which is found to be an integral multiple of a constant quantum factor, arising due to boundary conditions necessary for maintaining the PT -symmetry of the superpartner. As the spectra of the particle in a box is still real, it necessarily picks out the unbroken PT -sector of its superpartner, thereby invoking a close relation between PT -symmetry and SUSY for this case.
The Horizons of Observability in PT-symmetric Four-site Quantum Lattices
Directory of Open Access Journals (Sweden)
M. Znojil
2011-01-01
Full Text Available One of the key merits of PT-symmetric (i.e., parity times time reversal symmetric quantum Hamiltonians H lies in the existence of a horizon of the stability of the system. Mathematically speaking, this horizon is formed by the boundary of the domain D(H ⊂ RD of the (real coupling strengths for which the spectrum of energies is real and non-degenerate, i.e., in principle, observable. It is shown here that even in the elementary circular four-site quantum lattices with D = 2 or D = 3 the domain of hidden Hermiticity D(H proves multiply connected, i.e., topologically nontrivial.
Controlling electric, magnetic, and chiral dipolar emission with PT-symmetric potentials
Alaeian, Hadiseh
2014-01-01
We investigate the effect of parity-time (PT)-symmetric optical potentials on the radiation of achiral and chiral emitters. Mode coalescence and the appearance of exceptional points lead to orders-of-magnitude enhancements in the emitted dipole power. Further, the emitter can be tuned to behave as a strong optical source or absorber based on the non-Hermiticity parameter. Chiral enantiomers radiating near PT metamaterials exhibit a 4.5-fold difference in their decay rate. The results of this work could enable new atom-cavity interactions for quantum optics, as well as all- optical enantio-specific separation.
Nonlinear localized modes in PT-symmetric Rosen-Morse potential well
Midya, Bikashkali
2013-01-01
We report the existence and properties of localized modes described by nonlinear Schroedinger equation with complex PT-symmetric Rosen-Morse potential well. Exact analytical expressions of the localized modes are found in both one dimensional and two-dimensional geometry with self-focusing and self-defocusing Kerr nonlinearity. Linear stability analysis reveals that these localized modes are unstable for all real values of the potential parameters although corresponding linear Schroedinger eigenvalue problem possesses unbroken PT-symmetry. This result has been verified by the direct numerical simulation of the governing equation. The transverse power flow density associated with these localized modes has also been examined.
Anomalous Light Scattering by Topological ${\\mathcal{PT}}$-symmetric Particle Arrays
Ling, C W; Mok, T C; Zhang, Z Q; Fung, Kin Hung
2016-01-01
Robust topological edge modes may evolve into complex-frequency modes when a physical system becomes non-Hermitian. We show that, while having negligible forward optical extinction cross section, a conjugate pair of such complex topological edge modes in a non-Hermitian $\\mathcal{PT}$-symmetric system can give rise to an anomalous sideway scattering when they are simultaneously excited by a plane wave. We propose a realization of such scattering state in a linear array of subwavelength resonators coated with gain media. The prediction is based on an analytical two-band model and verified by rigorous numerical simulation using multiple-multipole scattering theory. The result suggests an extreme situation where leakage of classical information is unnoticeable to the transmitter and the receiver when such a $\\mathcal{PT}$-symmetric unit is inserted into the communication channel.
Modulational instability in a PT-symmetric vector nonlinear Schrödinger system
Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.
2016-12-01
A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.
Eigenvalue spectra of a $\\mathcal{PT}$ -symmetric coupled quartic potential in two dimensions
Indian Academy of Sciences (India)
Fakir Chand; Savita; S C Mishra
2010-10-01
The Schrödinger equation was solved for a generalized $\\mathcal{PT}$-symmetric quartic potential in two dimensions. It was found that, under a suitable ansatz for the wave function, the system possessed real and discrete energy eigenvalues. Analytic expressions for the energy eigenvalues and the eigenfunctions for the first four states were obtained. Some constraining relations among the wave function parameters rendered the problem quasi-solvable.
Various scattering properties of a new PT-symmetric non-Hermitian potential
Energy Technology Data Exchange (ETDEWEB)
Ghatak, Ananya, E-mail: gananya04@gmail.com [Department of Physics, Banaras Hindu University, Varanasi-221005 (India); Mandal, Raka Dona Ray, E-mail: rakad.ray@gmail.com [Department of Physics, Rajghat Besant School, Varanasi-221001 (India); Mandal, Bhabani Prasad, E-mail: bhabani.mandal@gmail.com [Department of Physics, Banaras Hindu University, Varanasi-221005 (India)
2013-09-15
We complexify a 1-d potential V(x)=V{sub 0}cosh{sup 2}μ(tanh[(x−μd)/d]+tanh(μ)){sup 2} which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters (μ,d) becomes imaginary. For the case of μ→iμ, we have an entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this potential becomes invisible from the left (or right) at certain discrete energies. The penetrating states in the other case (d→id) are always reciprocal even though it is PT-invariant and no spectral singularity (SS) is present in this case. The presence of MSS and reflectionlessness is also discussed for the free states in the later case. -- Highlights: •Existence of multiple spectral singularities (MSS) in PT-symmetric non-Hermitian system is shown. •Reciprocity is restored at discrete positive energies even for parity non-invariant complex system. •Co-existence of MSS with deep energy minima of transitivity is obtained. •Possibilities of both unidirectional and bidirectional invisibility are explored for a non-Hermitian system. •Penetrating states are shown to be reciprocal for all energies for PT-symmetric system.
Modulation theory in PT-Symmetric Magnetic Metamaterial Arrays in the continuum limit
Wang, Danhua
2013-01-01
We present results on the dynamics of split-ring dimers having both gain and loss in one dimensional nonlinear parity-time- (PT-)symmetric magnetic metamaterials. For the longwave (continuum) limit approximation and in the weakly nonlinear limit, we show analytic results on the existence of gap soliton solutions and on symmetry breaking phenomenon at a critical value of the gain/loss term.
Controlling of blow-up responses by nonlinear PT -symmetric coupling
Karthiga, S.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2017-03-01
We investigate the dynamics of a coupled waveguide system with competing linear and nonlinear loss-gain profiles which can facilitate power saturation. We show the usefulness of the model in achieving unidirectional beam propagation. In this regard, the considered type of coupled waveguide system has two drawbacks: (i) difficulty in achieving perfect isolation of light in a waveguide and (ii) existence of blow-up-type behavior for certain input power situations. We here show a nonlinear PT -symmetric coupling that helps to overcome these two drawbacks. Such a nonlinear coupling has close connection with the phenomenon of stimulated Raman scattering. In particular, we have elucidated the role of this nonlinear coupling using an integrable PT -symmetric situation. In particular, using the integrals of motion, we have reduced this coupled waveguide problem to the problem of dynamics of a particle in a potential. With the latter picture, we have clearly illustrated the role of the considered nonlinear coupling. The above PT -symmetric case corresponds to a limiting form of a general equation describing the phenomenon of stimulated Raman scattering. We also point out the ability to transport light unidirectionally even in this general case.
Nonlinear modal interactions in parity-time (${\\cal PT}$) symmetric lasers
Ge, Li
2016-01-01
Parity-time ($\\cal PT$) symmetric lasers have attracted considerable attention lately due to their promising applications and intriguing properties, such as free spectral range doubling and single-mode lasing. In this work we discuss nonlinear modal interactions in these laser systems under steady state conditions, and we demonstrate that several gain clamping scenarios can occur for lasing operation in the $\\cal PT$-symmetric and $\\cal PT$-broken phases. In particular, we show that, depending on the system's design and the external pump profile, its operation in the nonlinear regime falls into two different categories: in one the system is frozen in the $\\cal PT$ phase space as the applied gain increases, while in the other the system is pulled towards its exceptional point. These features are first illustrated by a coupled mode formalism and later verified by employing the Steady-state Ab-initio Laser Theory (SALT). Our findings shine light on the robustness of single-mode operation in these lasers against ...
Indian Academy of Sciences (India)
E Caliceti; S Graffi
2009-08-01
We generalize some recently established criteria for the reality and non-reality of the spectrum of some classes of $\\mathcal{PT}$-symmetric Schrödinger operators. The criteria include cases of discrete spectra and continuous ones.
Continuation of periodic orbits in symmetric Hamiltonian and conservative systems
Galan-Vioque, J.; Almaraz, F. J. M.; Macías, E. F.
2014-12-01
We present and review results on the continuation and bifurcation of periodic solutions in conservative, reversible and Hamiltonian systems in the presence of symmetries. In particular we show how two-point boundary value problem continuation software can be used to compute families of periodic solutions of symmetric Hamiltonian systems. The technique is introduced with a very simple model example (the mathematical pendulum), justified with a theoretical continuation result and then applied to two non trivial examples: the non integrable spring pendulum and the continuation of the figure eight solution of the three body problem.
Non-Hermitian neutrino oscillations in matter with PT symmetric Hamiltonians
Ohlsson, Tommy
2016-03-01
We introduce and develop a novel approach to extend the ordinary two-flavor neutrino oscillation formalism in matter using a non-Hermitian PT symmetric effective Hamiltonian. The condition of PT symmetry is weaker and less mathematical than that of hermicity, but more physical, and such an extension of the formalism can give rise to sub-leading effects in neutrino flavor transitions similar to the effects by so-called non-standard neutrino interactions. We derive the necessary conditions for the spectrum of the effective Hamiltonian to be real as well as the mappings between the fundamental and effective parameters. We find that the real spectrum of the effective Hamiltonian will depend on all new fundamental parameters introduced in the non-Hermitian PT symmetric extension of the usual neutrino oscillation formalism and that either i) the spectrum is exact and the effective leptonic mixing must always be maximal or ii) the spectrum is approximate and all new fundamental parameters must be small.
Directed transport of coupled systems in symmetric periodic potentials
Institute of Scientific and Technical Information of China (English)
郑志刚; 刘凤芝; 高建
2003-01-01
In this paper, we discuss the damped unidirectional motions of a coupled lattice in a periodic potential. Each particle in the lattice is subject to a time-periodic ac force. Our studies reveal that a directed transport process can be observed when the ac forces acting on the coupled lattice have a phase shift (mismatch). This directed motion is a collaboration of the coupling, the substrate potential, and the periodic force, which are all.symmetric. The absence of any one of these three factors will not give rise to a directed current. We discuss the complex relations between the directed current and parameters in the system. Results in this paper can be accomplished in experiments. Moreover,our results can be generalized to the studies of directed transport processes in more complicated spatially extended systems.
Non-reciprocal mu-near-zero mode in PT-symmetric magnetic domains
Wang, Jin; Ling, Chi Wai; Chan, C T; Fung, Kin Hung
2014-01-01
We find that a new type of non-reciprocal modes exist at an interface between two \\emph{parity-time} ($\\mathcal{PT}$) symmetric magnetic domains (MDs) near the frequency of zero effective permeability. The new mode is non-propagating and purely magnetic when the two MDs are semi-infinite while it becomes propagating in the finite case. In particular, two pronounced nonreciprocal responses could be observed via the excitation of this mode: one-way optical tunneling for oblique incidence and unidirectional beam shift at normal incidence. When the two MDs system becomes finite in size, it is found that perfect-transmission mode could be achieved if $\\mathcal{PT}$-symmetry is maintained. The unique properties of such an unusual mode are investigated by analytical modal calculation as well as numerical simulations. The results suggest a new approach to the design of compact optical isolator.
Nonreciprocal μ -near-zero mode in PT -symmetric magnetic domains
Wang, Jin; Dong, Hui Yuan; Ling, Chi Wai; Chan, C. T.; Fung, Kin Hung
2015-06-01
We find that a new type of nonreciprocal modes exists at an interface between two parity-time- (PT -) symmetric magnetic domains (MDs) near the frequency of zero effective permeability. This mode is nonpropagating and purely magnetic when the two MDs are semi-infinite, while it becomes propagating in the finite case. In particular, two pronounced nonreciprocal responses could be observed via the excitation of this mode: one-way optical tunneling for oblique incidence and unidirectional beam shift at normal incidence. When the two MDs system becomes finite in size, it is found that perfect-transmission mode could be achieved if PT symmetry is maintained. The unique properties of such an unusual mode are investigated by analytical modal calculation as well as numerical simulations. The results suggest a different approach to the design of compact optical isolator.
PT-symmetric microring lasers: Self-adapting broadband mode-selective resonators
Hodaei, Hossein; Heinrich, Matthias; Christodoulides, Demetrios N; Khajavikhan, Mercedeh
2014-01-01
We demonstrate experimentally that stable single longitudinal mode operation can be readily achieved in PT-symmetric arrangements of coupled microring resonators. Whereas any active resonator is in principle capable of displaying single-wavelength operation, selective breaking of PT-symmetry can be utilized to systematically enhance the maximum achievable gain of this mode, even if a large number of competing longitudinal or transverse resonator modes fall within the amplification bandwidth of the inhomogeneously broadened active medium. This concept is robust with respect to fabrication tolerances, and its mode selectivity is established without the need for additional components or specifically designed filters. Our results may pave the way for a new generation of versatile cavities lasing at a desired longitudinal resonance. Along these lines, traditionally highly multi-moded microring resonator configurations can be fashioned to suppress all but one longitudinal mode.
All-optical $\\mathcal{PT}$-symmetric amplitude to phase modulator
Gutiérrez, Oscar Ignacio Zaragoza; Rodríguez-Lara, B M
2015-01-01
We study electromagnetic field propagation through a planar three-waveguide coupler with linear gain and loss, in a configuration that is the optical analog of a quantum $\\mathcal{PT}$-symmetric system, and provide its closed-form analytic propagator. At an specific propagation length, we show that the device provides all-optical amplitude to phase modulation with a $\\pi$ modulation range, if an extra binary phase is allowed in the reference signal, as well as phase to amplitude modulation, with an amplitude modulation range that depends linearly on the gain-to-coupling ratio of the system.
Zero width resonance (spectral singularity) in a complex PT-symmetric potential
Ahmed, Zafar
2009-01-01
We show that the complex PT-Symmetric potential, $V(x)=-V_1 {sech}^2x + iV_2 {sech}x ~\\tanh x, $, entails a single zero-width resonance (spectral singularity) when $V_1+|V_2|=4n^2+4n+{3\\over 4}(n=1,2,3.., |V_2|>|V_1|+ {{sgn}(V_1) \\over 4})$ and the positive resonant energy is given as $E_*={1 \\over 4}[|V_2|-(1/4+V_1)]$.
Families of particles with different masses in PT-symmetric quantum field theory.
Bender, Carl M; Klevansky, S P
2010-07-16
An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the Dyson-Schwinger equations derived from a Lagrangian can have many different but equally valid solutions. Nonunique solutions to the Dyson-Schwinger equations arise when the functional integral for the Green's functions of the quantum field theory converges in different pairs of Stokes' wedges in complex-field space, and the solutions are physically viable if the pairs of Stokes' wedges are PT symmetric.
Floquet Topological Phases Driven by $\\mathcal{PT}$ Symmetric Nonunitary Time Evolution
Kim, Dakyeong; Kawakami, Norio; Obuse, Hideaki
2016-01-01
We study Floquet topological phases driven by $\\mathcal{PT}$ symmetric nonunitary time evolution in one dimension, based on an experimental setup of discrete-time quantum walks. We develop, for nonunitary time-evolution operators, a procedure to calculate topological invariants for Floquet topological phases and find that the bulk-edge correspondence gives correct predictions of the emergent edge states. These edge states make exponential growth of wavefunction amplitudes at specific positions with time controllable. Hereby, we propose that these phenomena inherent in open quantum systems are feasibly observed by present experiments of quantum walks in both classical and quantum regimes.
Generation of families of spectra in PT-symmetric quantum mechanics and scalar bosonic field theory.
Schmidt, Steffen; Klevansky, S P
2013-04-28
This paper explains the systematics of the generation of families of spectra for the -symmetric quantum-mechanical Hamiltonians H=p(2)+x(2)(ix)(ε), H=p(2)+(x(2))(δ) and H=p(2)-(x(2))(μ). In addition, it contrasts the results obtained with those found for a bosonic scalar field theory, in particular in one dimension, highlighting the similarities to and differences from the quantum-mechanical case. It is shown that the number of families of spectra can be deduced from the number of non-contiguous pairs of Stokes wedges that display PT symmetry. To do so, simple arguments that use the Wentzel-Kramers-Brillouin approximation are used, and these imply that the eigenvalues are real. However, definitive results are in most cases presently only obtainable numerically, and not all eigenvalues in each family may be real. Within the approximations used, it is illustrated that the difference between the quantum-mechanical and the field-theoretical cases lies in the number of accessible regions in which the eigenfunctions decay exponentially. This paper reviews and implements well-known techniques in complex analysis and PT-symmetric quantum theory.
Non-Hermitian ${\\cal PT}$-symmetric relativistic quantum theory in an intensive magnetic field
Rodionov, V N
2016-01-01
We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of physical parameters. This condition not only guarantees the reality of the eigenvalues of Hamiltonian operators, but also implies the preservation of the probabilities of the considered quantum processes. However as it was shown relatively recently (Bender, Boettcher 1998), Hermiticity is a sufficient but it is not a necessary condition. It turned out that among non-Hermitian Hamiltonians it is possible to allocate a number of such which have real energy spectra and can ensure the development of systems over time with preserving unitarity. This type of Hamiltonians includes so-called parity-time (${\\cal PT}$) symmetric models which is already used in various fields of modern physics. The most developed in this respect are models, which used in the field of ${\\cal PT}$-symmetric op...
A possible method for non-Hermitian and Non-PT-symmetric Hamiltonian systems.
Li, Jun-Qing; Miao, Yan-Gang; Xue, Zhao
2014-01-01
A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator η+ and defining the annihilation and creation operators to be η+ -pseudo-Hermitian adjoint to each other. The operator η+ represents the η+ -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator η+ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-PT-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution) are found not to be altered by the noncommutativity.
A possible method for non-Hermitian and Non-PT-symmetric Hamiltonian systems.
Directory of Open Access Journals (Sweden)
Jun-Qing Li
Full Text Available A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator η+ and defining the annihilation and creation operators to be η+ -pseudo-Hermitian adjoint to each other. The operator η+ represents the η+ -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator η+ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-PT-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution are found not to be altered by the noncommutativity.
Institute of Scientific and Technical Information of China (English)
ZHANG DuanZhi
2014-01-01
We study some monotonicity and iteration inequality of the Maslov-type index i-1of linear Hamiltonian systems.As an application we prove the existence of symmetric periodic solutions with prescribed minimal period for first order nonlinear autonomous Hamiltonian systems which are semipositive,even,and superquadratic at zero and infinity.This result gives a positive answer to Rabinowitz’s minimal period conjecture in this case without strictly convex assumption.We also give a different proof of the existence of symmetric periodic solutions with prescribed minimal period for classical Hamiltonian systems which are semipositive,even,and superquadratic at zero and infinity which was proved by Fei,Kim and Wang in 2001.
Observation of Bloch oscillations in complex PT-symmetric photonic lattices
Wimmer, Martin; Christodoulides, Demetrios; Peschel, Ulf
2016-01-01
Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals ...
Singular Mapping for a $PT$-Symmetric Sinusoidal Optical Lattice at the Symmetry-Breaking Threshold
Jones, H F
2014-01-01
A popular $PT$-symmetric optical potential (variation of the refractive index) that supports a variety of interesting and unusual phenomena is the imaginary exponential, the limiting case of the potential $V_0[\\cos(2\\pi x/a)+i\\lambda\\sin(2\\pi x/a)]$ as $\\lambda \\to 1$, the symmetry-breaking point. For $\\lambda<1$, when the spectrum is entirely real, there is a well-known mapping by a similarity transformation to an equivalent Hermitian potential. However, as $\\lambda \\to 1$, the spectrum, while remaining real, contains Jordan blocks in which eigenvalues and the corresponding eigenfunctions coincide. In this limit the similarity transformation becomes singular. Nonetheless, we show that the mapping from the original potential to its Hermitian counterpart can still be implemented; however, the inverse mapping breaks down. We also illuminate the role of Jordan associated functions in the original problem, showing that they map onto eigenfunctions in the associated Hermitian problem.
Optical solitons in PT-symmetric nonlinear couplers with gain and loss
Alexeeva, N. V.; Barashenkov, I. V.; Sukhorukov, Andrey A.; Kivshar, Yuri S.
2012-06-01
We study spatial and temporal solitons in the PT symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single combination of the soliton's amplitude and the gain-loss coefficient of the waveguides. The unstable perturbations of the high-frequency soliton break the symmetry between its active and lossy components which results in a blowup of the soliton or a formation of a long-lived breather state. The unstable perturbations of the low-frequency soliton separate its two components in space, thereby blocking the power drainage of the active component and cutting the power supply to the lossy one. Eventually this also leads to the blowup or breathing.
Optical solitons in $\\mathcal{PT}$-symmetric nonlinear couplers with gain and loss
Alexeeva, N V; Sukhorukov, Andrey A; Kivshar, Yuri S
2012-01-01
We study spatial and temporal solitons in the $\\mathcal{PT}$ symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single combination of the soliton's amplitude and the gain/loss coefficient of the waveguides. The unstable perturbations of the high-frequency soliton break the symmetry between its active and lossy components which results in a blowup of the soliton or a formation of a long-lived breather state. The unstable perturbations of the low-frequency soliton separate its two components in space blocking the power drainage of the active component and cutting the power supply to the lossy one. Eventually this also leads to the blowup or breathing.
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Energy Technology Data Exchange (ETDEWEB)
Midya, Bikashkali, E-mail: bikash.midya@gmail.com [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India); Roychoudhury, Rajkumar, E-mail: rroychoudhury123@gmail.com [Advanced Center for Nonlinear and Complex Phenomena, Kolkata 700075 (India)
2014-02-15
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expression of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effects of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined. -- Highlights: • Existence of localized modes is investigated in PT-symmetric complex potentials. • Exact analytical expression of the localized modes is obtained. • Effect of gain/loss profile on the stability of these localized modes is discussed. • Localized modes in 2D and associated transverse power-flow density are also examined.
Discrete solitons in self-defocusing systems with $\\mathcal{PT}$-symmetric defects
Chen, Zhiqiang; Chai, Jinglei; Zhang, Xiangyu; Li, Yongyao; Malomed, Boris A
2015-01-01
We construct families of discrete solitons (DSs) in an array of self-defocusing waveguides with an embedded $\\mathcal{PT}$ (parity-time)-symmetric dimer, which is represented by a pair of waveguides carrying mutually balanced gain and loss. Four types of states attached to the embedded defect are found, namely, staggered and unstaggered bright localized modes and gray or anti-gray DSs. Their existence and stability regions expand with the increase of the strength of the coupling between the dimer-forming sites. The existence of the gray and staggered bright DSs is qualitatively explained by dint of the continuum limit. All the gray and anti-gray DSs are stable (some of them are unstable if the dimer carries the nonlinear $\\mathcal{PT}$ symmetry, represented by balanced nonlinear gain and loss; in that case, the instability does not lead to a blowup, but rather creates oscillatory dynamical states). The boundary between the gray and anti-gray DSs is predicted in an approximate analytical form.
Is the Periodic Table all right ("PT OK")?
Pyykkö, Pekka
2016-12-01
The history of the Periodic Table and its predecessors spans almost 200 years. The present IUPAC PT for Z = 1-118 is still adequate. The remarkable measurement for the Lr atom does not change the chemistry. The extensions up to Z = 172 are discussed and compared. New data for ions are presented. The "Madelung rule" is found to be surprisingly good even in that range.
Is the Periodic Table all right (“PT OK”?
Directory of Open Access Journals (Sweden)
Pyykkö Pekka
2016-01-01
Full Text Available The history of the Periodic Table and its predecessors spans almost 200 years. The present IUPAC PT for Z = 1−118 is still adequate. The remarkable measurement for the Lr atom does not change the chemistry. The extensions up to Z = 172 are discussed and compared. New data for ions are presented. The “Madelung rule” is found to be surprisingly good even in that range.
STABILITY OF BOSE-EINSTEIN CONDENSATES IN A PT-SYMMETRIC DOUBLE-δ POTENTIAL CLOSE TO BRANCH POINTS
Directory of Open Access Journals (Sweden)
Andreas Löhle
2014-04-01
Full Text Available A Bose-Einstein condensate trapped in a double-well potential, where atoms are incoupled to one side and extracted from the other, can in the mean-field limit be described by the nonlinear Gross-Pitaevskii equation (GPE with a PT symmetric external potential. If the strength of the in- and outcoupling is increased two PT broken states bifurcate from the PT symmetric ground state. At this bifurcation point a stability change of the ground state is expected. However, it is observed that this stability change does not occur exactly at the bifurcation but at a slightly different strength of the in-/outcoupling effect. We investigate a Bose-Einstein condensate in a PT symmetric double-δ potential and calculate the stationary states. The ground state’s stability is analysed by means of the Bogoliubov-de Gennes equations and it is shown that the difference in the strength of the in-/outcoupling between the bifurcation and the stability change can be completely explained by the norm-dependency of the nonlinear term in the Gross-Pitaevskii equation.
Perturbation Theory for PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold
Jones, H F
2011-01-01
The $PT$ symmetric potential $V_0[\\cos(2\\pi x/a)+i\\lambda\\sin(2\\pi x/a)]$ has a completely real spectrum for $\\lambda\\le 1$, and begins to develop complex eigenvalues for $\\lambda>1$. At the symmetry-breaking threshold $\\lambda=1$ some of the eigenvectors become degenerate, giving rise to a Jordan-block structure for each degenerate eigenvector. In general this is expected to give rise to a secular growth in the amplitude of the wave. However, it has been shown in a recent paper by Longhi, by numerical simulation and by the use of perturbation theory, that for an initial wave packet this growth is suppressed, giving instead a constant maximum amplitude. We revisit this problem by developing the perturbation theory further. We verify that the results found by Longhi persist to second order, and with different input wave packets we are able to see the seeds in perturbation theory of the phenomenon of birefringence first discovered by El-Ganainy et al.
Nonlinear wave dynamics near phase transition in PT-symmetric localized potentials
Nixon, Sean; Yang, Jianke
2016-09-01
Nonlinear wave propagation in parity-time symmetric localized potentials is investigated analytically near a phase-transition point where a pair of real eigenvalues of the potential coalesce and bifurcate into the complex plane. Necessary conditions for a phase transition to occur are derived based on a generalization of the Krein signature. Using the multi-scale perturbation analysis, a reduced nonlinear ordinary differential equation (ODE) is derived for the amplitude of localized solutions near phase transition. Above the phase transition, this ODE predicts a family of stable solitons not bifurcating from linear (infinitesimal) modes under a certain sign of nonlinearity. In addition, it predicts periodically-oscillating nonlinear modes away from solitons. Under the opposite sign of nonlinearity, it predicts unbounded growth of solutions. Below the phase transition, solution dynamics is predicted as well. All analytical results are compared to direct computations of the full system and good agreement is observed.
A periodic table of symmetric tandem mismatches in RNA.
Wu, M; McDowell, J A; Turner, D H
1995-03-14
The stabilities and structures of a series of RNA octamers containing symmetric tandem mismatches were studied by UV melting and imino proton NMR. The free energy increments for tandem mismatch formation are found to depend upon both mismatch sequence and adjacent base pairs. The observed sequence dependence of tandem mismatch stability is UGGU > GUUG > GAAG > or = AGGA > UUUU > CAAC > or = CUUC approximately UCCU approximately CCCC approximately ACCA approximately AAAA, and the closing base pair dependence is 5'G3'C > 5'C3'G > 5'U3'A approximately 5'A3'U. These results differ from expectations based on models used in RNA folding algorithms and from the sequence dependence observed for folding of RNA hairpins. Imino proton NMR results indicate the sequence dependence is partially due to hydrogen bonding within mismatches.
Emergence of quasiperiodicity in symmetrically coupled, identical period-doubling systems
DEFF Research Database (Denmark)
Reick, Christian; Mosekilde, Erik
1995-01-01
When two Identical period-doubling systems are coupled symmetrically, the period-doubling transition to chaos may be replaced by a quasiperiodic transition. The reason for this is that at an early stage of the period-doubling cascade, a Hopf bifurcation instead of a period-doubling bifurcation...... occurs. Our main result is that the emergence of this Hopf bifurcation is a generic phenomenon in symmetrically coupled, identical period-doubling systems. The whole phenomenon is stable against small nonsymmetric perturbations. Our results cover maps and differential equations of arbitrary dimension...
Indian Academy of Sciences (India)
Fakir Chand; S C Mishra; Ram Mehar Singh
2009-08-01
We investigate the quasi-exact solutions of an analogous Schrödinger wave equation for two-dimensional non-Hermitian complex Hamiltonian systems within the framework of an extended complex phase space characterized by = 1 + 3, = 2 + 4, = 1 + 3, = 2 + 4. Explicit expressions for the energy eigenvalues and eigenfunctions for ground and first excited states of a two-dimensional $\\mathcal{PT}$-symmetric sextic potential and some of its variants are obtained. The eigenvalue spectra are found to be real within some parametric domains.
Hang, Chao; Gabadadze, Gregory; Huang, Guoxiang
2017-02-01
We present a physical setup for realizing all-real-spectrum optical potentials with arbitrary gain-and-loss distributions in a coherent medium consisting of a cold three-level atomic gas driven by control and probe laser fields. We show that by the interference of Raman resonances and the Stark shift induced by a far-detuned laser field, tunable, non-parity-time (non-PT )-symmetric optical potentials with all-real spectra proposed recently by Nixon and Yang [Phys. Rev. A 93, 031802(R) (2016), 10.1103/PhysRevA.93.031802] can be actualized physically. We also show that when the real parts of the non-PT -symmetric optical potentials are tuned cross certain thresholds, phase transitions—where the eigenspectrum of the system changes from all real to complex—may occur and hence the stability of the probe-field propagation is altered. Our scheme can also be extended to high dimensions and to a nonlinear propagation regime, where stable optical solitons with power of the order of nano-Watts may be generated in the system.
Directory of Open Access Journals (Sweden)
Nkongho Ayuketang Arreyndip
2015-01-01
Full Text Available We consider a particle in a spatial symmetric/asymmetric potential driven by time periodic bichromatic AC fields of ratchet type. The associated time-dependent Schrödinger equation is conveniently tackled with the Floquet theory. We next proceed to investigate the ratchet effect induced by the driver, comparing the symmetric with the asymmetric cases. It turns out that the current in the asymmetric case is stronger than that of the symmetric one. Besides, we also investigate the case where the driver is a delta kicked acting on our spatial potential with more emphasis on its chaotic behaviour. Here we check that the current emerges as the phase space is mixed and that the system with asymmetric spatial potential becomes more chaotic than the symmetric one at low kicking strength.
Stabilizing and destabilizing perturbations of PT-symmetric indefinitely damped systems.
Kirillov, O N
2013-04-28
Eigenvalues of a potential dynamical system with damping forces that are described by an indefinite real symmetric matrix can behave as those of a Hamiltonian system when gain and loss are in a perfect balance. This happens when the indefinitely damped system obeys parity-time ( ) symmetry. How do pure imaginary eigenvalues of a stable -symmetric indefinitely damped system behave when variation in the damping and potential forces destroys the symmetry? We establish that it is essentially the tangent cone to the stability domain at the exceptional point corresponding to the Whitney umbrella singularity on the stability boundary that manages transfer of instability between modes.
Rodionov, V N
2013-01-01
The modified Dirac equations for the massive particles with the replacement of the physical mass $m$ with the help of the relation $m\\rightarrow m_1+ \\gamma_5 m_2$ are investigated. It is shown that for a fermion theory with a $\\gamma_5$-mass term, the limiting of the mass specter by the value $ m_{max}= {m_1}^2/2m_2$ takes place. In this case the different regions of the unbroken $\\cal PT$ symmetry may be expressed by means of the restriction of the physical mass $m\\leq m_{max}$. It should be noted that in the approach which was developed by C.Bender et al. for the $\\cal PT$-symmetric version of the massive Thirring model with $\\gamma_5$-mass term, the region of the unbroken $\\cal PT$-symmetry was found in the form $m_1\\geq m_2$ \\cite{ft12}. However on the basis of the mass limitation $m\\leq m_{max}$ we obtain that the domain $m_1\\geq m_2$ consists of two different parametric sectors: i) $0\\leq m_2 \\leq m_1/\\sqrt{2}$ -this values of mass parameters $m_1,m_2$ correspond to the traditional particles for which ...
Biased Motion in a Symmetric Periodic Potential by Breaking Temporal Symmetry
Institute of Scientific and Technical Information of China (English)
ZHENG Zhi-Gang; LI Xiao-Wen
2001-01-01
Unidirectional transport of a particle in a spatially periodic and symmetric potential under a periodic force with broken temporal symmetry is studied. With a collaboration of the potential field and the asymmetric ac force, a dc current can be observed. Resonant current steps are found for a finite period of the ac force. A phase diagram of these resonant steps is given. Stochastic-resonance-like directional transport induced by thermal noises is revealed.
Minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems
Liu, Chungen
2009-01-01
In this paper, we consider the minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems. We prove that if the Hamiltonian function $H\\in C^2(\\Bbb R^{2n}, \\Bbb R)$ is super-quadratic and convex, for every number $\\tau>0$, there exists at least one $\\tau$-periodic brake orbit $(\\tau,x)$ with minimal period $\\tau$ or $\\tau/2$ provided $H(Nx)=H(x)$.
Directory of Open Access Journals (Sweden)
Holger Cartarius
2013-01-01
Full Text Available We investigate the Gross-Pitaevskii equation for a Bose-Einstein condensate in a PT symmetric double-well potential by means of the time-dependent variational principle and numerically exact solutions. A one-dimensional and a fully three-dimensional setup are used. Stationary states are determined and the propagation of wave function is investigated using the time-dependent Gross-Pitaevskii equation. Due to the nonlinearity of the Gross-Pitaevskii equation the potential dependson the wave function and its solutions decide whether or not the Hamiltonian itself is PT symmetric. Stationary solutions with real energy eigenvalues fulfilling exact PT symmetry are found as well as PT broken eigenstates with complex energies. The latter describe decaying or growing probability amplitudes and are not true stationary solutions of the time-dependent Gross-Pitaevskii equation. However, they still provide qualitative information about the time evolution of the wave functions.
The Limiting Spectral Measure for the Ensemble of Symmetric Period m--Circulant Matrices
Kologlu, Murat; Miller, Steven J
2010-01-01
Given an ensemble of N x N random matrices, the first question to ask is whether or not the empirical spectral measures of typical matrices converge to a limiting spectral measure as N tends to infinity. While this has been proved in many thin patterned ensembles sitting inside all real symmetric matrices, frequently there is no nice closed form expression for the limiting measure. Further, current theorems provide few pictures of transitions between ensembles. We consider the ensemble of symmetric period m--circulant matrices with entries i.i.d.r.v. These matrices have toroidal diagonals periodic of period m. We view m as a ``dial'' we can ``turn'' from the highly structured symmetric circulant matrices, whose limiting eigenvalue density is a Gaussian, to the ensemble of all real symmetric matrices, whose limiting eigenvalue density is a semi-circle. The limiting eigenvalue densities f_m show a visually stunning convergence to the semi-circle as m tends to infinity, which we prove. In contrast to most studie...
Particles versus fields in $\\mathcal{PT}$-symmetrically deformed integrable systems
Indian Academy of Sciences (India)
Andreas Fring
2009-08-01
We review some recent results on how $\\mathcal{PT}$ symmetry, that is a simultaneous time-reversal and parity transformation, can be used to construct new integrable models. Some complex valued multi-particle systems, such as deformations of the Calogero–Moser– Sutherland models, are shown to arise naturally from real valued field equations of non-linear integrable systems. Deformations of complex non-linear integrable field equations, some of them even allowing for compacton solutions, are also investigated. The integrabilty of various systems is established by means of the Painlevé test.
One- and two-dimensional solitons in PT-symmetric systems emulating the spin-orbit coupling
Sakaguchi, Hidetsugu
2016-01-01
We introduce a two-dimensional (2D) system, which can be implemented in dual-core planar optical couplers with the Kerr nonlinearity in its cores, making it possible to blend effects of the PT symmetry, represented by the balanced linear gain and loss in the two cores, and spin-orbit coupling (SOC), emulated by a spatially biased coupling between the cores. Families of 1D and 2D solitons and their stability boundaries are identified. In the 1D setting, the addition of the SOC terms leads, at first, to shrinkage of the stability area for PT-symmetric solitons, which is followed by its rapid expansion. 2D solitons have their stability region too, in spite of the simultaneous action of two major destabilizing factors, viz., the collapse driven by the Kerr nonlinearity, and a trend towards spontaneous breakup of the gain-loss balance. In the limit of the SOC terms dominating over the intrinsic diffraction, the 1D system gives rise to a new model for gap solitons, which admits exact analytical solutions.
Four-wave mixing in a parity-time (PT)-symmetric coupler.
Wasak, T; Szańkowski, P; Konotop, V V; Trippenbach, M
2015-11-15
Parity-time (PT) symmetry allows for implementing controllable matching conditions for the four-wave mixing in 1D coupled waveguides. Different types of the process involving energy transition between slow and fast modes are established. In the case of defocusing Kerr media, the degenerated four-wave mixing is studied in detail. It is shown that unbroken PT symmetry supports the process existing in the conservative limit and, at the same time, originates new types of matching conditions, which cannot exist in the conservative system. In the former case, a slow beam splits into two fast beams, with nearly conserved total power, while in the latter case, one slow beam and one fast beam are generated. In the last process, the energy of the input primary slow beam is not changed and growth of the energy of the generated slow beam varies due to gain and loss of the medium. The appreciable generation of the fifth mode, i.e., the effect of the secondary resonant interactions, is observed.
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Midya, Bikashkali
2014-01-01
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expressions of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effect of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined.
Asymmetric soliton mobility in competing linear-nonlinear PT-symmetric lattices
Kartashov, Yaroslav V; Torner, Lluis
2016-01-01
We address the transverse mobility of spatial solitons in competing parity-time-symmetric linear and nonlinear lattices. The competition between out-of-phase linear and nonlinear lattices results in a drastic mobility enhancement within a range of soliton energies. We show that within such range, the addition of even a small imaginary part in the linear potential makes soliton mobility strongly asymmetric. The minimal phase tilt required for setting solitons into radiationless motion across the lattice in the direction opposite to that of the internal current drops to nearly zero, while the minimal phase tilt required for motion in the opposite direction notably increases. For a given initial phase tilt, the velocity of soliton motion grows with an increase of the balanced gain/losses. In this regime of enhanced mobility, tilted solitons can efficiently drag other solitons that were initially at rest, to form moving soliton pairs.
Directory of Open Access Journals (Sweden)
Yi-Xiang Chen
Full Text Available Two families of Gaussian-type soliton solutions of the (n+1-dimensional Schrödinger equation with cubic and power-law nonlinearities in PT-symmetric potentials are analytically derived. As an example, we discuss some dynamical behaviors of two dimensional soliton solutions. Their phase switches, powers and transverse power-flow densities are discussed. Results imply that the powers flow and exchange from the gain toward the loss regions in the PT cell. Moreover, the linear stability analysis and the direct numerical simulation are carried out, which indicates that spatial Gaussian-type soliton solutions are stable below some thresholds for the imaginary part of PT-symmetric potentials in the defocusing cubic and focusing power-law nonlinear medium, while they are always unstable for all parameters in other media.
Periodic Orbits of Radially Symmetric Keplerian-Like Systems with a Singularity
Directory of Open Access Journals (Sweden)
Shengjun Li
2016-01-01
Full Text Available We study planar radially symmetric Keplerian-like systems with repulsive singularities near the origin and with some semilinear growth near infinity. By the use of topological degree theory, we prove the existence of two distinct families of periodic orbits; one rotates around the origin with small angular momentum, and the other one rotates around the origin with both large angular momentum and large amplitude.
On the Special Role of Symmetric Periodic Orbits in a Chaotic System
Bénet, L; Papenbrock, T; Seligman, T H
1998-01-01
After early work of Henon it has become folk knowledge that symmetric periodic orbits are of particular importance. We reinforce this belief by additional studies and we further find that invariant closed symplectic submanifolds caused by discrete symmetries prove to be an important complement to the long known role of the orbits. The latter have particular importance in semi-classics. Based on the structural stability of hyperbolic horseshoes we give an argument that opens an avenue to the understanding of these facts.
Komar, Paulina; Chávez-Ángel, Emigdio; Euler, Christoph; Balke, Benjamin; Kolb, Ute; Müller, Mathis M.; Kleebe, Hans-Joachim; Fecher, Gerhard H.; Jakob, Gerhard
2016-10-01
Thermoelectric modules based on half-Heusler compounds offer a cheap and clean way to create eco-friendly electrical energy from waste heat. Here we study the impact of the period composition on the electrical and thermal properties in non-symmetric superlattices, where the ratio of components varies according to (TiNiSn)n:(HfNiSn)6-n, and 0 ⩽ n ⩽ 6 unit cells. The thermal conductivity (κ) showed a strong dependence on the material content achieving a minimum value for n = 3, whereas the highest value of the figure of merit ZT was achieved for n = 4. The measured κ can be well modeled using non-symmetric strain relaxation applied to the model of the series of thermal resistances.
She, M.; Jiang, L. P.
2014-12-01
In this paper, an oscillating dark energy model is presented in an isotropic but inhomogeneous plane symmetric space-time by considering a time periodic varying deceleration parameter. We find three different types of new solutions which describe different scenarios of oscillating universe. The first two solutions show an oscillating universe with singularities. For the third one, the universe is singularity-free during the whole evolution. Moreover, the Hubble parameter oscillates and keeps positive which explores an interesting possibility to unify the early inflation and late time acceleration of the universe.
A new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem
Institute of Scientific and Technical Information of China (English)
XU XingBo; FU YanNing
2009-01-01
We show that there exists a new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem.In such a solution,the infinitesimal body is confined to the vicinity of a primary and moves on a nearly circular orbit.This orbit is almost perpendicular to the orbital plane of the pri-maries,where the line of symmetry of the orbit lies.The existence is shown by applying a corollary of Arenstorf's fixed point theorem to s periodicity equation system of the problem.And this existence doesn't require any restriction on the mass ratio of the primaries,nor on the eccentricity of their rela-tive elliptic orbit.Potential relevance of this new class of periodic solutions to real celestial body sys-tems and the follow-up studies in this respect are also discussed.
A new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
We show that there exists a new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem. In such a solution, the infinitesimal body is confined to the vicinity of a primary and moves on a nearly circular orbit. This orbit is almost perpendicular to the orbital plane of the primaries, where the line of symmetry of the orbit lies. The existence is shown by applying a corollary of Arenstorf’s fixed point theorem to a periodicity equation system of the problem. And this existence doesn’t require any restriction on the mass ratio of the primaries, nor on the eccentricity of their relative elliptic orbit. Potential relevance of this new class of periodic solutions to real celestial body systems and the follow-up studies in this respect are also discussed.
Dirichlet spectra of the paradigm model of complex PT-symmetric potential: V(x) = -(ix) N
Ahmed, Zafar; Kumar, Sachin; Sharma, Dhruv
2017-08-01
So far the spectra En(N) of the paradigm model of complex PT(Parity-Time)-symmetric potential VBB(x , N) = -(ix) N is known to be analytically continued for N > 4. Consequently, the well known eigenvalues of the Hermitian cases (N = 6 , 10) cannot be recovered. Here, we illustrate Kato's theorem that even if a Hamiltonian H(λ) is an analytic function of a real parameter λ, its eigenvalues En(λ) may not be analytic at finite number of Isolated Points (IPs). In this light, we present the Dirichlet spectra En(N) of VBB(x , N) for 2 ≤ N < 12 using the numerical integration of Schrödinger equation with ψ(x = ± ∞) = 0 and the diagonalization of H =p2 / 2 μ +VBB(x , N) in the harmonic oscillator basis. We show that these real discrete spectra are consistent with the most simple two-turning point CWKB (C refers to complex turning points) method provided we choose the maximal turning points (MxTP) [ - a + ib , a + ib , a , b ∈ R] such that | a | is the largest for a given energy among all (multiple) turning points. We find that En(N) are continuous function of N but non-analytic (their first derivative is discontinuous) at IPs N = 4 , 8; where the Dirichlet spectrum is null (as VBB becomes a Hermitian flat-top potential barrier). At N = 6 and 10, VBB(x , N) becomes a Hermitian well and we recover its well known eigenvalues.
Silicon waveguide filter based on cladding modulated anti-symmetric long-period grating.
Liu, Qing; Gu, Zhonghua; Kee, Jack Sheng; Park, Mi Kyoung
2014-12-01
In this paper, we demonstrate an optical filter using cladding modulated anti-symmetric long-period grating in a two-mode silicon waveguide. The filter consists of a two-mode waveguide connected with an input and output single-mode waveguide through two linear tapers. The anti-symmetric grating is formed by placing two periodic arrays of silicon squares offset by half of a grating pitch along the two-mode waveguide. Light coupling occurs between two co-propagating modes at the coupling wavelength through the grating and results in a rejection band at the output. The grating pitch, coupling coefficient, transmission spectrum and 3-dB bandwidth of the grating are investigated with the coupled-mode theory. By using a cladding modulated grating, the grating coupling strength can be controlled over a wide range by the two-mode waveguide width or separation distance between the grating and waveguide. Band-rejection filters are experimentally demonstrated in 1-μm, 0.8-μm and 0.7-μm wide two-mode silicon waveguides and rejection bands with different bandwidths and maximal attenuation contrasts larger than 15 dB (~97% coupling efficiency) have been achieved.
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Smarandache F.
2010-04-01
Full Text Available In this article, we find out some analytical and numerical solutions to the problem of barrier tunneling for cluster deuterium, in particular using Langevin method to solve the time-independent Schroedinger equation.
A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x
Midya, Bikashkali; Roychoudhury, Rajkumar
2010-01-01
It is shown that the PT symmetric Hamiltonian with the periodic potential V(x) = 4 cos^2 x + 4 i V_0 sin 2x can be mapped into a Hermitian Hamiltonian for $V_0<0.5$, by a similarity transformation. It is also shown that there exist a second critical point of the potential V(x), apart from the known critical point $V_0=0.5$, for $V_0^c ~ .888437$ after which no part of the eigenvalues and the band structure remains real. Relevant physical consequence of this finding has been pointed out.
Zhang, Zhao; Sahoo, Sharmistha; Teo, Jeffrey
We mimic the massless surface Majorana's of topological superconductors by coupled wire models in two spatial dimensions, and introduce many-body gapping interactions that preserve time reversal symmetry. Coupling with a Z2 gauge theory, the symmetric gapped surface generically carries a non-trivial GN topological order, where N is the number of Majorana species and GN is some SO(r)1 or SO(3)3 -like topological state. These form a 32-fold periodic class GN ≅GN + 32 , and a Z32 relative tensor product structure GN1⊗bGN2 ≅GN1 +N2 by anyon condensation. We present the anyon structures of these topological states, and understand the topological orders through bulk-boundary correspondence and the Wilson structures on a torus geometry.
Nguyen, Ba Phi
2016-01-01
We study numerically the transport and localization properties of waves in ordered and disordered ladder-shaped lattices with local $\\mathcal{PT}$ symmetry. Using a transfer matrix method, we calculate the transmittance and the reflectance for the individual channels and the Lyapunov exponent for the whole system. In the absence of disorder, we find that when the gain/loss parameter $\\rho$ is smaller than the interchain coupling parameter $t_{v}$, the transmittance and the reflectance are periodic functions of the system size, whereas when $\\rho$ is larger than $t_{v}$, the transmittance is found to be an exponentially-decaying function while the reflectance attains a saturation value in the thermodynamic limit. For a fixed system size, there appear perfect transmission resonances in each individual channel at several values of the gain/loss strength smaller than $t_{v}$. A singular behavior of the transmittance is also found to appear at various values of $\\rho$ for a given system size. When disorder is inse...
Mostafazadeh, Ali
2016-01-01
Among the interesting outcomes of the study of the physical applications of spectral singularities in PT-symmetric optical systems is the discovery of CPA-lasers. These are devices that act both as a threshold laser and a coherent perfect absorber (CPA) for the same values of their physical parameters. Unlike a homogeneous slab that is made to act as a CPA, a slab CPA-laser would absorb the incident waves coming from the left and right of the device provided that they have appropriate intensity and phase contrasts. We provide a comprehensive study of one of the simplest experimentally accessible examples of a CPA-laser, namely a PT-symmetric optical slab system consisting of a balanced pair of adjacent or separated gain and loss components. In particular, we give a closed form expression describing the spectral singularities of the system which correspond to its CPA-laser configurations. We determine the intensity and phase contrasts for the TE and TM waves that are emitted (absorbed) whenever the slab acts a...
Symmetrical periods used as matching layers in multilayer thin film design
Institute of Scientific and Technical Information of China (English)
Dan Wang; Zhengxiu Fan; Jianbing Huang; Jun Bi; Yingjian Wang
2006-01-01
Properties of symmetrical layers as matching layers in multilayer thin film design were analyzed. Acalculation method was presented to derive parameters of desired equivalent refractive index. A harmonicbeam splitter was designed and fabricated to test this matching method.
Mostafazadeh, Ali; Sarısaman, Mustafa
2016-12-01
Among the interesting outcomes of the study of the physical applications of spectral singularities in PT-symmetric optical systems is the discovery of CPA-lasers. These are devices that act both as a threshold laser and a coherent perfect absorber (CPA) for the same values of their physical parameters. Unlike a homogeneous slab that is made to act as a CPA, a slab CPA-laser would absorb the incident waves coming from the left and right of the device provided that they have appropriate intensity and phase contrasts. We provide a comprehensive study of one of the simplest experimentally accessible examples of a CPA-laser, namely a PT-symmetric optical slab system consisting of a balanced pair of adjacent or separated gain and loss components. In particular, we give a closed form expression describing the spectral singularities of the system which correspond to its CPA-laser configurations. We determine the intensity and phase contrasts for the TE and TM waves that are emitted (absorbed) whenever the slab acts as a laser (CPA). We also investigate the behavior of the time-averaged energy density and Poynting vector for these waves. This is necessary for determining the optimal values of the physical parameters of the system that make it act as a CPA-laser. These turn out to correspond to situations where the separation distance s between the gain and loss layers is an odd multiple of a characteristic length scale s0. A curious by-product of our study is that, except for the cases where s is an even integer multiple of s0, there is a critical angle of polarization beyond which the energy of the waves emitted from the lossy layer can be larger than the energy of those emitted from the gain layer.
Znojil, Miloslav
2017-07-01
The phenomenon of the birth of an isolated quantum bound state at the lower edge of the continuum is studied for a particle moving along a discrete real line of coordinates x ∈Z . The motion is controlled by a weakly nonlocal 2 J -parametric external potential V which is non-Hermitian but P T symmetric. The model is found exactly solvable. The bound states are interpreted as Sturmians. Their closed-form definitions are presented and discussed up to J =7 .
Petrashov, Victor; Shaikhaidarov, R S; Sosnin, I. A.; DELSING, P; Claeson, T; Volkov, A.
1998-01-01
The conductance (G) of mirror-symmetric, disordered normal (N) metal mesoscopic structures with two interfaces to superconductors (S) has been studied experimentally with applied condensate phase differences Delta phi between the N/S interfaces. At Delta phi = 2n pi(n = 0,1,2,3,...) the conductance showed reentrance to the normal state below the temperature corresponding to the Thouless energy. The current-voltage characteristics were found to be: strongly nonlinear even at distances between ...
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Engelwati Gani
2012-11-01
Full Text Available The study was conducted at PT. Unilever Indonesia, Tbk, which aims to determine the level of working capital management and corporate productivity. Quantitative analysis methods used and data analysis techniques used are the working capital analysis, financial ratio analysis and the analysis of the productivity ratio. Research results obtained from the results that a decrease in working capital at PT. Unilever Indonesia, Tbk. from the year 2006-2010 which decreases the amount of current assets while current liabilities increased. PT levels of liquidity. Unilever Indonesia, Tbk. is also quite low and has decreased every year. Expected PT. Unilever Indonesia, Tbk. able to increase the amount of current assets to cash and cash equivalents productivity is not compromised. Productivity ratio of PT. Unilever Indonesia, Tbk in 2010 has increased due to production cost savings and increased sales obtained. This suggests a tight working capital management is carried out by PT. Unilever Indonesia, Tbk. can increase company productivity.
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Daniel Haag
2014-04-01
Full Text Available We consider the linear and nonlinear Schrödinger equation for a Bose-Einstein condensate in a harmonic trap with PT-symmetric double-delta function loss and gain terms. We verify that the conditions for the applicability of a recent proposition by Mityagin and Siegl on singular perturbations of harmonic oscillator type self-adjoint operators are fulfilled. In both the linear and nonlinear case we calculate numerically the shifts of the unperturbed levels with quantum numbers n of up to 89 in dependence on the strength of the non-Hermiticity and compare with rigorous estimates derived by those authors. We confirm that the predicted 1/n1/2 estimate provides a valid upper bound on the shrink rate of the numerical eigenvalues. Moreover, we find that a more recent estimate of log(n/n3/2 is in excellent agreement with the numerical results. With nonlinearity the shrink rates are found to be smaller than without nonlinearity, and the rigorous estimates, derived only for the linear case, are no longer applicable.
DEFF Research Database (Denmark)
Gadegaard, N.; Almdal, K.; Larsen, N.B.
1999-01-01
experimental results are compared to theoretical predictions on the scaling behavior of the lamella period as a function of temperature. The morphology of the surface was investigated by atomic force microscopy. Holes were found around defects in the films. The cross-section of the holes revealed the lamellar...... structure with a periodicity comparable to what was found by neutron reflectivity. (C) 1999 Elsevier Science B.V. All rights reserved....
Particle dynamics in a symmetrically driven underdamped inhomogeneous periodic potential system
Kharkongor, D.; Reenbohn, W. L.; Mahato, Mangal C.
2016-08-01
We numerically solve the underdamped Langevin equation to obtain the trajectories of a particle in a sinusoidal potential driven by a temporally sinusoidal force in a medium with coefficient of friction periodic in space as the potential but with a phase difference. With the appropriate choice of system parameters, like the mean friction coefficient and the period of the applied field, only two kinds of periodic trajectories are obtained for all possible initial conditions at low noise strengths: one with a large amplitude and a large phase lag with respect to the applied field and the other with a small amplitude and a small phase lag. Thus, the periodic potential system is effectively mapped dynamically into a bistable system. Though the directional asymmetry, brought about only by the frictional inhomogeneity, is weak we find both the phenomena of stochastic resonance, with ready explanation in terms of the two dynamical states of trajectories, and ratchet effect simultaneously in the same parameter space. We analyze the results in detail attempting to find plausible explanations for each.
Uji Efektivitas Sponsorship Produk Bearing Racing pada PT. SKF Indonesia Periode 2008 - 2012
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Septian Willy Yanto
2013-05-01
Full Text Available The highest achievement of marketing is sales transaction, so the marketing strategy should have impacts on sales. Promotion in the form of sponsorship has just been conducted by PT. SKF Indonesia since 2010-2011. This study aims to analyze the development of bearing products in PT. SKF Indonesia and to test the effectiveness of promotional strategies in the form of motor racing team sponsorship based on average sales of the bearing racing products data. Anova test results showed that the average sales prior to sponsorship were smaller than the average sales after sponsorship. Thus, sponsorship strategy is efective to raise the average of bearing racing product sales in SKF Indonesia with α = 0.05 and 0.01.
ANALISIS TINGKAT KESEHATAN PT. BANK BRISYARIAH PERIODE 2011-2014 DENGAN MENGGUNAKAN METODE CAMEL
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Ari Kristin Prasetyoningrum
2017-01-01
Full Text Available The rapid development of banking as well as high levels of complexity influence the performance and increase the risk of a bank. Therefore, it is important for banks to maintain the trust because of activities related to public confidence. This study aims to determine the health level of PT. Bank BRISyariah in 2011-2014 by using CAMEL. This research used quantitative descriptive analysis aims to analyze the soundness of PT. Bank BRISyariah in 2011-2014 using the CAMEL factors include capital, asset quality, management, earnings and liquidity. Data used in this study a BRISyariah Annual Report 2011 to 2014 taken from www.brisyariah.co.id. and Quarterly Financial Report Bank BRISyariah published by Bank Indonesia was taken from www.bi.go.id. Based on the analysis of the Bank’s soundness BRISyariah using CAMEL ratio in 2011-2014 can be said that in general PT. Bank BRISyariah in conditions HEALTHY, the the first rank in the CAR, PPAP, ROA, NPM, and CR; The second rank in the KAP; BOPO ranked third; and LDR in the fourth.
PT Symmetry as a Generalization of Hermiticity
Wang, Qing-hai; Zhang, Jie-hong
2010-01-01
The Hilbert space in PT-symmetric quantum mechanics is formulated as a linear vector space with a dynamic weight function in the inner product. The most general PT-symmetric matrix Hamiltonians are constructed for 2*2 and 3*3 cases. In the former case, the PT-symmetric Hamiltonian represents the most general matrix Hamiltonian with a real spectrum. In both cases, the Hermitian matrix is shown to be a special case of PT-symmetric matrices. This finding confirms and strengthens the early belief that the PT-symmetric quantum mechanics is a generalization of the conventional Hermitian quantum mechanics.
Pengaruh Buy Back Saham PT Telkom terhadap Dividen Periode 2005 - 2008
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Natasya Rusbandi
2010-04-01
Full Text Available Micro and macroeconomic condition has negative and positive effect for the financial market and also the investment. Based on that condition, many companies had to do some corporate action which mean investors and also shareholders had to adjust their portfolio for getting their objective. Investors and shareholder will see this corporate action. It includes the investor who wants to buy the companys stock. This attention had always related with the dividend payment which will get by the investor, because for the long term investor, or the shareholders, the information about dividend payment is very important for them. When global financial crises happened in 2008, some of the emiten in Indonesia capital market, had donne their corporate action which is the buy back or repurchase stock of their outstanding shares. Some of them is the state owned enterprise, PT TELKOM. Some important thing which related with the buy back is the stock price and also dividend price. With this buy back strategy, it can be seen that PT TELKOM had tried to eliminate any threat with their stock price at that time, or to prevent their stock price become undervalued. Especially in the third quarter in 2008. This strategy had shown succeed because when the global financial crisis happened, TELKOM performance had indicated succeed based on their financial report and also the EPS and DPS every year did not show significance different result.
Pengaruh Buy Back Saham PT Telkom terhadap Dividen Periode 2005 - 2008
Directory of Open Access Journals (Sweden)
Natasya Rusbandi
2010-05-01
Full Text Available Micro and macro economic condition has negative and positive effect for the financial market and also the investment. Based on that condition, many companies had to do some corporate action which mean investors and also shareholders had to adjust their portfolio for getting their objective. Investors and shareholder will see this corporate action. It includes the investor who wants to buy the company’s stock. This attention had always related with the dividend payment which will get by the investor, because for the long term investor, or the shareholders, the information about dividend payment is very important for them. When global financial crises happened in 2008, some of the emiten in Indonesia capital market, had donne their corporate action which is the buy back or repurchase stock of their outstanding shares. Some of them is the state owned enterprise, PT TELKOM. Some important thing which related with the buy back is the stock price and also dividend price. With this buy back strategy, it can be seen that PT TELKOM had tried to eliminate any threat with their stock price at that time, or to prevent their stock price become undervalued. Especially in the third quarter in 2008. This strategy had shown succeed because when the global financial crisis happened, TELKOM performance had indicated succeed based on their financial report and also the EPS and DPS every year did not show significance different result.
Chen, Yong; Yan, Zhenya; Mihalache, Dumitru; Malomed, Boris A
2017-04-28
Since the parity-time-([Formula: see text]-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with [Formula: see text]-symmetric potentials have been investigated. However, previous studies of [Formula: see text]-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized [Formula: see text]-symmetric Scarf-II potentials. The broken linear [Formula: see text] symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than [Formula: see text]-symmetric ones, but feature similar properties. Our results may suggest new experiments for [Formula: see text]-symmetric nonlinear waves in nonlinear nonuniform optical media.
Photometric study of Pluto near perihelion. Pt. 2. Refined rotation period. Color indices
Energy Technology Data Exchange (ETDEWEB)
Lyutyj, V.M.; Tarashchuk, V.P. (Moskovskij Gosudarstvennyj Univ. (USSR). Gosudarstvennyj Astronomicheskij Inst. ' ' GAISh' '
1984-07-01
Results of UBV photometry of Pluto during 1982-1983 are reported. Using all photoelectric observations of 1953-1983 a more accurate period is calculated. The significant reddening at maximum light (phases 0.6-0.7) is revealed. The secular variations of the mean brightness of Pluto does not contradict a 124-year periodicity.
Exceptional contours and band structure design in parity-time symmetric photonic crystals
Cerjan, Alexander; Fan, Shanhui
2016-01-01
We investigate the properties of multidimensional parity-time symmetric periodic systems whose non-Hermitian periodicity is an integer multiple of the underlying Hermitian system's periodicity. This creates a natural set of degeneracies which can undergo thresholdless $\\mathcal{PT}$ transitions. We derive a $\\mathbf{k} \\cdot \\mathbf{p}$ perturbation theory suited to the continuous eigenvalues of such systems in terms of the modes of the underlying Hermitian system. In photonic crystals, such thresholdless $\\mathcal{PT}$ transitions are shown to yield significant control over the band structure of the system, and can result in all-angle supercollimation, a $\\mathcal{PT}$-superprism effect, and unidirectional behavior.
Exceptional Contours and Band Structure Design in Parity-Time Symmetric Photonic Crystals.
Cerjan, Alexander; Raman, Aaswath; Fan, Shanhui
2016-05-20
We investigate the properties of two-dimensional parity-time symmetric periodic systems whose non-Hermitian periodicity is an integer multiple of the underlying Hermitian system's periodicity. This creates a natural set of degeneracies that can undergo thresholdless PT transitions. We derive a k·p perturbation theory suited to the continuous eigenvalues of such systems in terms of the modes of the underlying Hermitian system. In photonic crystals, such thresholdless PT transitions are shown to yield significant control over the band structure of the system, and can result in all-angle supercollimation, a PT-superprism effect, and unidirectional behavior.
MOSTAFAZADEH, Ali
2013-01-01
PHYSICAL REVIEW A 87, 012103 (2013) Invisibility and PT symmetry Ali Mostafazadeh* Department of Mathematics, Koc¸ University, Sarıyer 34450, Istanbul, Turkey (Received 9 July 2012; published 3 January 2013) For a general complex scattering potential defined on a real line, we show that the equations governing invisibility of the potential are invariant under the combined action of parity and time-reversal (PT ) transformation. We determine the PT -symmetric as well as no...
Aghajamali, Alireza; Barati, Mahmood; Wu, Chien-Jang
2014-01-01
In this paper the characteristic matrix method is used to study the propagation of electromagnetic waves through one-dimensional lossy photonic crystals composed of negative and positive refractive index material layers with symmetric and asymmetric geometric structures with a defect layer at the center of the structure. First, the positive index material defect layer is considered, and the effects of the polarization and the angle of incidence on the defect mode in the transmission spectra of the both structures are investigated. The results show that the number of the defect modes in the transmission spectra depends on the geometry (symmetric or asymmetric) of the structure. In addition, it is shown that the defect mode frequency increases as the angle of incidence increases. This property is independent of the geometry of the structure. Then, for normal incidence, the negative index material defect layer is considered, and the properties of defect modes for both structures are investigated. The results can...
Canteaut, Anne; Videau, Marion
2005-01-01
http://www.ieee.org/; We present an extensive study of symmetric Boolean functions, especially of their cryptographic properties. Our main result establishes the link between the periodicity of the simplified value vector of a symmetric Boolean function and its degree. Besides the reduction of the amount of memory required for representing a symmetric function, this property has some consequences from a cryptographic point of view. For instance, it leads to a new general bound on the order of...
Light propagation in periodically modulated complex waveguides
Nixon, Sean
2014-01-01
Light propagation in optical waveguides with periodically modulated index of refraction and alternating gain and loss are investigated for linear and nonlinear systems. Based on a multiscale perturbation analysis, it is shown that for many non-parity-time ($\\mathcal{PT}$) symmetric waveguides, their linear spectrum is partially complex, thus light exponentially grows or decays upon propagation, and this growth or delay is not altered by nonlinearity. However, several classes of non-$\\mathcal{PT}$-symmetric waveguides are also identified to possess all-real linear spectrum. In the nonlinear regime longitudinally periodic and transversely quasi-localized modes are found for $\\mathcal{PT}$-symmetric waveguides both above and below phase transition. These nonlinear modes are stable under evolution and can develop from initially weak initial conditions.
Control of Power in Parity-Time -Symmetric Lattices
Kozlov, Maksim
2015-01-01
We investigate wave transport properties of Parity-Time (PT) symmetric lattices that are periodically modulated along the direction of propagation. We demonstrate that in the regime of unbroken PT-symmetry the system Floquet-Bloch modes may interfere constructively leading to either controlled oscillations or linear power absorption and amplification occurring exactly at the phase transition point. The differential power response is effected by the overlap of the gain and loss system distribution with wave intensity pattern that is formed through Rabi oscillations engaging the coupled Floquet-Bloch modes.
Energy Technology Data Exchange (ETDEWEB)
Zotov, N. [Forschungszentrum CAESAR, Ludwig-Erhard-Allee 2, D-53175 Bonn (Germany)]. E-mail: zotov@caesar.de; Feydt, J. [Forschungszentrum CAESAR, Ludwig-Erhard-Allee 2, D-53175 Bonn (Germany); Walther, T. [Forschungszentrum CAESAR, Ludwig-Erhard-Allee 2, D-53175 Bonn (Germany); Ludwig, A. [Forschungszentrum CAESAR, Ludwig-Erhard-Allee 2, D-53175 Bonn (Germany); Institut fuer Werkstoffe, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany)
2006-10-31
Double-period [(Pt 1.7 nm/Fe 0.9 nm){sub 5}Fe(t {sub Fe2})]{sub 8} and [(Pt 1.8 nm/Fe 0.6 nm){sub 5}Fe(t {sub Fe2})]{sub 8} multilayers with different thickness t {sub Fe2} (between 0.23 and 4.32 nm) of the additional Fe layers, prepared by combinatorial sputter deposition, show differences in the mosaic spread and the vertical interfacial roughness when deposited on native or thermally oxidised Si wafers. Simulations of the wide-angle X-ray scattering intensities revealed the presence of interdiffusion in the (Pt/Fe){sub 5} bilayers and systematic variations of the grain sizes, perpendicular to the film surface, as well as the rms variations of the two superlattice periods with the total film thickness. A comparison of {omega}-rocking scans shows an increase of the correlated vertical roughness of the (Pt/Fe){sub 5} multilayers with the total multilayer thickness.
Directory of Open Access Journals (Sweden)
J. H. Duke
2010-05-01
Full Text Available A sporadic phenomenon of internal tide resonance (ITR in the western equatorial Pacific thermocline is shown to precede 11 of 12 major upturns in the Niño 3.4 index between 1992 and 2008. Observed ITR has up to 9 °C semidiurnal temperature excursions indicating thermocline heave, but is invisible in time resolution longer than one day. It is independent of westerly wind bursts (WWB. A hypothesis is advanced that (1 ITR dissipates vorticity, leading to Pacific countercurrent consolidation (PCC by reducing the vortex stretching term in Sverdrup balance. The consequence of lost vorticity survives ephemeral ITR events; (2 The specific surface area of countercurrents is reduced by PCC, which reduces frictional opposition to zonal gradient pressure, which triggers eastward advection at El Niño onset; (3 PCC also accelerates transfer of potential energy to the "pycnostad" below the Equatorial Undercurrent. This shoals the equatorial thermocline, leading to a distinct mode of equatorially symmetric La Niña (ESLN characterized by a winter monsoon cell above a "cold eye" that is separated from the South American continent, as in 1998; (4 Precessional southward intertropical convergence zone migration (ITCZ is an alternate PCC trigger, but its effect is modulated by obliquity; and (5 ESLN causes global cooling in all timescales by (a reduced Hadley cell water vapor production when its rising branch is above the cold eye, (b equatorward shift in southern circumpolar westerlies due to Hadley cell constriction, (c possible CO_{2} sequestration by increased EUC iron fertilized export production on the equator, and (d possible adjacent cloud seeding by biogenic dimethyl sulphide. Surprising coincidences of WWB with perigean eclipses suggest a parallel atmospheric tide influence. Proposed PCC-ESLN forcing operates in multiple timescales, beginning where the annual cycle of strong equinoctial tides coincides with the minimum perigee cycle. This
A periodic point-based method for the analysis of Nash equilibria in 2 x 2 symmetric quantum games
Energy Technology Data Exchange (ETDEWEB)
Schneider, David, E-mail: schneide@tandar.cnea.gov.ar [Departamento de Fisica, Comision Nacional de EnergIa Atomica. Av. del Libertador 8250, 1429 Buenos Aires (Argentina)
2011-03-04
We present a novel method of looking at Nash equilibria in 2 x 2 quantum games. Our method is based on a mathematical connection between the problem of identifying Nash equilibria in game theory, and the topological problem of the periodic points in nonlinear maps. To adapt our method to the original protocol designed by Eisert et al (1999 Phys. Rev. Lett. 83 3077-80) to study quantum games, we are forced to extend the space of strategies from the initial proposal. We apply our method to the extended strategy space version of the quantum Prisoner's dilemma and find that a new set of Nash equilibria emerge in a natural way. Nash equilibria in this set are optimal as Eisert's solution of the quantum Prisoner's dilemma and include this solution as a limit case.
Bender, Carl M; DeKieviet, Maarten; Klevansky, S P
2013-04-28
PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics.
Dunajewski, Adam; Dusza, Jacek J.; Rosado Muñoz, Alfredo
2014-11-01
The article presents a proposal for the description of human gait as a periodic and symmetric process. Firstly, the data for researches was obtained in the Laboratory of Group SATI in the School of Engineering of University of Valencia. Then, the periodical model - Mean Double Step (MDS) was made. Finally, on the basis of MDS, the symmetrical models - Left Mean Double Step and Right Mean Double Step (LMDS and RMDS) could be created. The method of various functional extensions was used. Symmetrical gait models can be used to calculate the coefficients of asymmetry at any time or phase of the gait. In this way it is possible to create asymmetry, function which better describes human gait dysfunction. The paper also describes an algorithm for calculating symmetric models, and shows exemplary results based on the experimental data.
Nonlinear behaviors of parity-time-symmetric lasers
Yang, Jianke
2016-01-01
We propose a time-dependent partial differential equation model to investigate the dynamical behavior of the parity-time (PT) symmetric laser during the nonlinear stage of its operation. This model incorporates physical effects such as the refractive index distribution, dispersion, material loss, nonlinear gain saturation and self-phase modulation. We show that when the loss is weak, multiple stable steady states and time-periodic states of light exist above the lasing threshold, rendering the laser multi-mode. However, when the loss is strong, only a single stable steady state of broken PT symmetry exists for a wide range of the gain amplitude, rendering the laser single-mode. These results reveal the important role the loss plays in maintaining the single-mode operation of PT lasers.
Locally parity-time-symmetric and globally parity-symmetric systems
Ahmed, W. W.; Herrero, R.; Botey, M.; Staliunas, K.
2016-11-01
We introduce a class of systems holding parity-time (PT ) symmetry locally, whereas being globally P symmetric. The potential, U =U (|r |) , fulfills PT symmetry with respect to periodically distributed points r0:U (| r0+r |) =U*(| r0-r |) being r0≠0 . We show that such systems hold unusual properties arising from the merging of the two different symmetries, leading to a strong field localization and enhancement at the double-symmetry center, r =0 , when the coupling of outward to inward propagating waves is favored. We explore such general potentials in one and two dimensions, which could have actual realizations combining gain-loss and index modulations in nanophotonic structures. In particular, we show how to render a broad aperture vertical-cavity surface-emitting laser into a bright and narrow beam source, as a direct application.
Znojil, M
2002-01-01
A re-formulated, non-Hermitian version of the Witten's supersymmetric quantum mechanics is presented. Its use of pseudo-Hermitian (so called PT symmetric) Hamiltonians is reviewed and illustrated via several forms of an innovated supersymmetric partnership between strongly singular ("spiked") harmonic oscillators.
Nonlinearity-induced PT-symmetry without material gain
Miri, Mohammad-Ali; Alù, Andrea
2016-06-01
Parity-time symmetry has raised a great deal of attention in optics in recent years, yet its application has been so far hindered by the stringent requirements on coherent gain balanced with loss. In this paper, we show that the conditions to enable parity and time symmetry can be simultaneously satisfied for a pair of modes with mixed frequencies interacting in a nonlinear medium, without requiring the presence of material gain. First, we consider a guided wave structure with second order nonlinearity and we derive the PT-symmetric Hamiltonian that governs the interaction of two waves of mixed frequencies when accompanied by a high intensity pump beam at the sum frequency. We also extend the results to an array of coupled nonlinear waveguide channels. It is shown that the evolution dynamics of the low-frequency waves is associated with a periodic PT-symmetric lattice while the phase of the pump beams can be utilized as a control parameter to modify the gain and loss distribution, thus realizing different PT lattices by design. Our results suggest that nonlinear wave mixing processes can form a rich platform to realize PT-symmetric Hamiltonians of arbitrary dimensions in optical systems, without requiring material gain.
Directory of Open Access Journals (Sweden)
Christianto V.
2010-07-01
Full Text Available In this article, we find out some analytical and numerical solutions to the problem of barrier tunneling for cluster deuterium, in particular using Langevin method to solve the time-independent Schrödinger equation.
$\\mathcal{PT}$ symmetry in a fractional Schr\\"odinger equation
Zhang, Yiqi; Belić, Milivoj R; Zhu, Yi; Zhong, Weiping; Zhang, Yanpeng; Christodoulides, Demetrios N; Xiao, Min
2016-01-01
We investigate the fractional Schr\\"odinger equation with a periodic $\\mathcal{PT}$-symmetric potential. In the inverse space, the problem transfers into a first-order nonlocal frequency-delay partial differential equation. We show that at a critical point, the band structure becomes linear and symmetric in the one-dimensional case, which results in a nondiffracting propagation and conical diffraction of input beams. If only one channel in the periodic potential is excited, adjacent channels become uniformly excited along the propagation direction, which can be used to generate laser beams of high power and narrow width. In the two-dimensional case, there appears conical diffraction that depends on the competition between the fractional Laplacian operator and the $\\mathcal{PT}$-symmetric potential. This investigation may find applications in novel on-chip optical devices.
Progressive symmetric erythrokeratoderma
Directory of Open Access Journals (Sweden)
Gharpuray Mohan
1990-01-01
Full Text Available Four patients had symmetrically distributed hyperkeratotic plaques on the trunk and extremities; The lesions in all of them had appeared during infancy, and after a brief period of progression, had remained static, All of them had no family history of similar skin lesions. They responded well to topical applications of 6% salicylic acid in 50% propylene glycol. Unusual features in these cases of progressive symmetric erythrokeratoderma were the sparing of palms and soles, involvement of the trunk and absence of erythema.
Vasiljević, Gorazd
2014-01-01
This BSc thesis deals with certain topics from graph theory. When we talk about studying graphs, we usually mean studying their structure and their structural properties. By doing that, we are often interested in automorphisms of a graph (symmetries), which are permutations of its vertex set, preserving adjacency. There exist graphs, which are symmetric enough, so that automorhism group acts transitively on their vertex set. This means that for any pair of vertices of the graph, there is an a...
Topologically protected bound states in photonic parity-time-symmetric crystals.
Weimann, S; Kremer, M; Plotnik, Y; Lumer, Y; Nolte, S; Makris, K G; Segev, M; Rechtsman, M C; Szameit, A
2017-04-01
Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.
Accessing the exceptional points of parity-time symmetric acoustics
Shi, Chengzhi; Dubois, Marc; Chen, Yun; Cheng, Lei; Ramezani, Hamidreza; Wang, Yuan; Zhang, Xiang
2016-03-01
Parity-time (PT) symmetric systems experience phase transition between PT exact and broken phases at exceptional point. These PT phase transitions contribute significantly to the design of single mode lasers, coherent perfect absorbers, isolators, and diodes. However, such exceptional points are extremely difficult to access in practice because of the dispersive behaviour of most loss and gain materials required in PT symmetric systems. Here we introduce a method to systematically tame these exceptional points and control PT phases. Our experimental demonstration hinges on an active acoustic element that realizes a complex-valued potential and simultaneously controls the multiple interference in the structure. The manipulation of exceptional points offers new routes to broaden applications for PT symmetric physics in acoustics, optics, microwaves and electronics, which are essential for sensing, communication and imaging.
PT-Symmetry Quantum Electrodynamics--PTQED
Milton, Kimball A; Parashar, Prachi; Shajesh, K V; Wagner, Jef
2007-01-01
The construction of $\\mathcal{PT}$-symmetric quantum electrodynamics is reviewed. In particular, the massless version of the theory in 1+1 dimensions (the Schwinger model) is solved. Difficulties with unitarity of the $S$-matrix are discussed.
Chen, Yong; Yan, Zhenya
2017-01-01
The effect of derivative nonlinearity and parity-time-symmetric (PT -symmetric) potentials on the wave propagation dynamics is explored in the derivative nonlinear Schrödinger equation, where the physically interesting Scarf-II and harmonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken and broken linear PT -symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT -symmetric phases are broken. The semielastic interactions between particular bright solitons and exotic incident waves are illustrated such that we find that particular nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT -symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT -symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT -symmetric phase.
Dissipation-Induced Super Scattering and Lasing PT-Spaser
Feng, Simin
2015-01-01
Giant transmission and reflection of a finite bandwidth are shown to occur at the same wavelength when the electromagnetic wave is incident on a periodic array of PT-symmetric dimers embedded in a metallic film. Remarkably, we found that this phenomenon vanishes if the metallic substrate is lossless while keeping other parameters unchanged. When the metafilm is adjusted to the vicinity of a spectral singularity, tuning substrate dissipation to a critical value can lead to supper scattering in stark contrast to what would be expected in conventional systems. The PT-synthetic plasmonic metafilm acts as a lasing PT-spaser, a planar source of coherent radiation. The metallic dissipation provides a mean to couple light out of the dark modes of the PT- spaser. Above a critical gain-loss coupling, the metafilm behaves as a meta-gain medium with the meta-gain atoms made from the PT-plasmonic dimers. This phenomenon implies that super radiation is possible from a cavity having gain elements by tuning the cavity dissip...
Harter, Andrew K; Joglekar, Yogesh N
2016-01-01
Open, non-equilibrium systems with balanced gain and loss, known as parity-time ($\\mathcal{PT}$)-symmetric systems, exhibit properties that are absent in closed, isolated systems. A key property is the $\\mathcal{PT}$-symmetry breaking transition, which occurs when the gain-loss strength, a measure of the openness of the system, exceeds the intrinsic energy-scale of the system. We analyze the fate of this transition in disordered lattices with non-Hermitian gain and loss potentials $\\pm i\\gamma$ at reflection-symmetric sites. Contrary to the popular belief, we show that the $\\mathcal{PT}$-symmetric phase is protected in the presence of a correlated (periodic) disorder which leads to a positive $\\mathcal{PT}$-symmetry breaking threshold. We uncover a veiled symmetry of such disordered systems that is instrumental for the said protection, and show that this symmetry leads to new localization behavior across the $\\mathcal{PT}$-symmetry breaking transition. We elucidate the interplay between such localization and ...
Perpendicular magnetic anisotropy of Co85Cr15/Pt multilayers
Institute of Scientific and Technical Information of China (English)
Pol Hwang; Baohe Li; Tao Yang; Zhonghai Zhai; Fengwu Zhu
2004-01-01
The CoCr/Pt bilayers and (CoCr/Pt)20 multilayers with Pt underlayer were prepared by DC magnetron sputtering. The effects of prepared condition on perpendicular magnetic anisotropy were investigated. The results show that the thickness of Pt underlayer has a great effect on the microstructure and perpendicular magnetic anisotropy of CoCr/Pt bilayers and (CoCr/Pt)20 multilayers.When the thickness of Pt underlayer increases, Pt(111) and CoCr(002) peaks of both CoCr/Pt bilayers and (CoCr/Pt)20 multilayers increase and the bilayer periodicity of the multilayers is improved. The effective magnetic anisotropy of (CoCr/Pt)20 multilayers with Pt underlayer was much larger than that of CoCr/Pt bilayers. The (CoCr/Pt)20 multilayers has a stronger perpendicular magnetic anisotropy than that of CoCr/Pt bilayers. This is ascribed to the interface magnetic anisotropy of the multilayers.
Exact control of parity-time symmetry in periodically modulated nonlinear optical couplers
Yang, Baiyuan; Hu, QiangLin; Yu, XiaoGuang
2016-01-01
We propose a mechanism for realization of exact control of parity-time (PT) symmetry by using a periodically modulated nonlinear optical coupler with balanced gain and loss. It is shown that for certain appropriately chosen values of the modulation parameters, we can construct a family of exact analytical solutions for the two-mode equations describing the dynamics of such nonlinear couplers. These exact solutions give explicit examples that allow us to precisely manipulate the system from nonlinearity-induced symmetry breaking to PT symmetry, thus providing an analytical approach to the all-optical signal control in nonlinear PT-symmetric structures.
Taming the Exceptional Points of Parity-Time Symmetric Acoustics
Dubois, Marc; Shi, Chengzhi; Chen, Yun; Cheng, Lei; Ramezani, Hamidreza; Wang, Yuan; Zhang, Xiang
Parity-time (PT) symmetric concept and development lead to a wide range of applications including coherent perfect absorbers, single mode lasers, unidirectional cloaking and sensing, and optical isolators. These new applications and devices emerge from the existence of a phase transition in PT symmetric complex-valued potential obtained by balancing gain and loss materials. However, the systematic extension of such devices is adjourned by the key challenge in the management of the complex scattering process within the structure in order to engineer PT phase and exceptional points. Here, based on active acoustic elements, we experimentally demonstrate the simultaneous control of complex-valued potentials and multiple interference inside the structure at any given frequency. This method broadens the scope of applications for PT symmetric devices in many fields including optics, microwaves, electronics, which are crucial for sensing, imaging, cloaking, lasing, absorbing, etc.
Symmetric Powers of Symmetric Bilinear Forms
Institute of Scientific and Technical Information of China (English)
Se(a)n McGarraghy
2005-01-01
We study symmetric powers of classes of symmetric bilinear forms in the Witt-Grothendieck ring of a field of characteristic not equal to 2, and derive their basic properties and compute their classical invariants. We relate these to earlier results on exterior powers of such forms.
Jiang, Haiyong
2016-04-11
We present an automatic algorithm for symmetrizing facade layouts. Our method symmetrizes a given facade layout while minimally modifying the original layout. Based on the principles of symmetry in urban design, we formulate the problem of facade layout symmetrization as an optimization problem. Our system further enhances the regularity of the final layout by redistributing and aligning boxes in the layout. We demonstrate that the proposed solution can generate symmetric facade layouts efficiently. © 2015 IEEE.
Symmetrization of Facade Layouts
Jiang, Haiyong
2016-02-26
We present an automatic approach for symmetrizing urban facade layouts. Our method can generate a symmetric layout through minimally modifying the original input layout. Based on the principles of symmetry in urban design, we formulate facade layout symmetrization as an optimization problem. Our method further enhances the regularity of the final layout by redistributing and aligning elements in the layout. We demonstrate that the proposed solution can effectively generate symmetric facade layouts.
Chambler, A F; Chapman-Sheath, P J; Pearse, M F; Hollingdale, J
1997-10-01
Chronic recurrent multifocal osteomyelitis is often confused with symmetrical Brodie's abscess as it has a similar pathogenesis. We report an otherwise healthy 17-year-old boy presenting with a true symmetrical Brodie's abscess. We conclude that a symmetrical Brodie's abscess presenting in an otherwise healthy patient is a separate clinical condition with a different management protocol.
Directory of Open Access Journals (Sweden)
Mohamad Heykal
2011-05-01
Full Text Available The fourth quarter in 2008 is the peak of Global Monetary Crisis, which is the decreasing of liquidity in companies around the world. The crisis also affected towards fluctuation of world petroleum price. Automotive industry in Indonesia was also affected towards cost of foreign exchange fluctuation and petroleum price due to the crisis. PT Astra International, Tbk. is assumed to represent automotive industry in Indonesia. The research is done through literature research and financial and sales report analysis in 2000-2008. The performance reduction is directly connected by the decreasing of earnings, especially in motor vehicle and parts sale in those years and also the increasing of cost of production, due to the increasing of import fee and transportation cost. Foreign exchange fluctuation and petroleum price directly affects the work performance of PT Astra Internasional.
Pakpahan, Yuliantri Solideo
2015-01-01
Methods Z-score Altman models, Springate models and Zmijewski models are the method of analysis to determine whether the financial performance at PT. Indonesia Asahan Aluminium (Persero) leads to bankruptcy or not to obtain data to support and assist in responding to problems that occur in the company and to determine the development of the company's financial performance in 2010-2014. Economic Value Added (EVA) as a method that takes into account the cost of capital as a substitute for th...
Mohamad Heykal; Theresa Febrona; Hidayatullah
2011-01-01
The fourth quarter in 2008 is the peak of Global Monetary Crisis, which is the decreasing of liquidity in companies around the world. The crisis also affected towards fluctuation of world petroleum price. Automotive industry in Indonesia was also affected towards cost of foreign exchange fluctuation and petroleum price due to the crisis. PT Astra International, Tbk. is assumed to represent automotive industry in Indonesia. The research is done through literature research and financial and sal...
DÍaz, R.; Rivas, M.
2010-01-01
In order to study Boolean algebras in the category of vector spaces we introduce a prop whose algebras in set are Boolean algebras. A probabilistic logical interpretation for linear Boolean algebras is provided. An advantage of defining Boolean algebras in the linear category is that we are able to study its symmetric powers. We give explicit formulae for products in symmetric and cyclic Boolean algebras of various dimensions and formulate symmetric forms of the inclusion-exclusion principle.
Baum, Brian; Dionne, Jennifer; Alaeian, Hadiseh; Jankovic, Vladan; Lawrence, Mark
2016-09-01
Metasurfaces offer exotic optical properties, which often originate from carefully designed material geometries. With locked geometries, these metasurfaces are difficult or impossible to change post-fabrication. Here, we theoretically explore a nano-scale coaxial structure capable of adjustably manipulating the polarization, phase, and spatial distribution of light through the introduction of parity-time (PT) symmetric perturbations. Coaxial waveguides possess degenerate modes, corresponding to different orbital angular momentum (OAM) states. The degeneracy of OAM modes can be lifted through the introduction of any non-zero amount of gain and loss into the structure in a way that matches the azimuthal periodicity of the degenerate mode pair. New hybrid complex conjugate modes are created which lose their pure OAM nature and are either amplifying or lossy. We confirm this behavior using both a Hamiltonian formulation and degenerate perturbation theory, and propose this selective excitation and absorption scheme as a new method of filtering for mode division multiplexing in on-chip nanophotonic systems. In addition to the creation of new hybrid modes, we show that these PT-symmetric perturbations in coaxial apertures are capable of converting incident circularly polarized light into linearly polarized light with unity efficiency. Further, due to the localization of field intensity within the gain sections, it is possible to rotate linear polarization and induce up to a pi-phase shift. We describe how our PT-symmetric coaxial aperture could function as a reconfigurable meta-atom for phase, amplitude, and polarization controlled meta-surfaces, and discuss routes toward unity-efficiency, reconfigurable holography.
PT Symmetry in Classical and Quantum Statistical Mechanics
Meisinger, Peter N
2012-01-01
PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside of the conventional equilibrium statistical mechanics of Hermitian systems. PT-symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviors than Hermitian systems, displaying sinusoidally-modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with PT symmetry include Z(N) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbor Ising (ANNNI) model. Quantum many-body problems with a non-zero chemical potential have a natural PT-symmetric representation related to the sign problem. Two-dimensional QCD with heavy quarks at non-zero chemical potential can be solved by diagona...
Inverse Symmetric Inflationary Attractors
Odintsov, S D
2016-01-01
We present a class of inflationary potentials which are invariant under a special symmetry, which depends on the parameters of the models. As we show, in certain limiting cases, the inverse symmetric potentials are qualitatively similar to the $\\alpha$-attractors models, since the resulting observational indices are identical. However, there are some quantitative differences which we discuss in some detail. As we show, some inverse symmetric models always yield results compatible with observations, but this strongly depends on the asymptotic form of the potential at large $e$-folding numbers. In fact when the limiting functional form is identical to the one corresponding to the $\\alpha$-attractors models, the compatibility with the observations is guaranteed. Also we find the relation of the inverse symmetric models with the Starobinsky model and we highlight the differences. In addition, an alternative inverse symmetric model is studied and as we show, not all the inverse symmetric models are viable. Moreove...
Symmetric cryptographic protocols
Ramkumar, Mahalingam
2014-01-01
This book focuses on protocols and constructions that make good use of symmetric pseudo random functions (PRF) like block ciphers and hash functions - the building blocks for symmetric cryptography. Readers will benefit from detailed discussion of several strategies for utilizing symmetric PRFs. Coverage includes various key distribution strategies for unicast, broadcast and multicast security, and strategies for constructing efficient digests of dynamic databases using binary hash trees. • Provides detailed coverage of symmetric key protocols • Describes various applications of symmetric building blocks • Includes strategies for constructing compact and efficient digests of dynamic databases
PT phase transition in multidimensional quantum systems
Bender, Carl M
2012-01-01
Non-Hermitian PT-symmetric quantum-mechanical Hamiltonians generally exhibit a phase transition that separates two parametric regions, (i) a region of unbroken PT symmetry in which the eigenvalues are all real, and (ii) a region of broken PT symmetry in which some of the eigenvalues are complex. This transition has recently been observed experimentally in a variety of physical systems. Until now, theoretical studies of the PT phase transition have generally been limited to one-dimensional models. Here, four nontrivial coupled PT-symmetric Hamiltonians, $H=p^2/2+x^2/2+q^2/2+y^2/2+igx^2y$, $H=p^2/2+x^2/2+q^2/2+y^2+igx^2y$, $H=p^2/2+x^2/2+q^2/2+y^2/2+r^2/2+z^2/2+igxyz$, and $H=p^2/2+x^2/2+q^2/2+y^2+r^2/2+3z^2/2+igxyz$ are examined. Based on extensive numerical studies, this paper conjectures that all four models exhibit a phase transition. The transitions are found to occur at $g\\approx 0.1$, $g\\approx 0.04$, $g\\approx 0.1$, and $g\\approx 0.05$. These results suggest that the PT phase transition is a robust phen...
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J.
1977-08-01
Causally symmetric spacetimes are spacetimes with J/sup +/(S) isometric to J/sup -/(S) for some set S. We discuss certain properties of these spacetimes, showing for example that, if S is a maximal Cauchy surface with matter everywhere on S, then the spacetime has singularities in both J/sup +/(S) and J/sup -/(S). We also consider totally vicious spacetimes, a class of causally symmetric spacetimes for which I/sup +/(p) =I/sup -/(p) = M for any point p in M. Two different notions of stability in general relativity are discussed, using various types of causally symmetric spacetimes as starting points for perturbations.
Symmetrization and Applications
Kesavan, S
2006-01-01
The study of isoperimetric inequalities involves a fascinating interplay of analysis, geometry and the theory of partial differential equations. Several conjectures have been made and while many have been resolved, a large number still remain open.One of the principal tools in the study of isoperimetric problems, especially when spherical symmetry is involved, is Schwarz symmetrization, which is also known as the spherically symmetric and decreasing rearrangement of functions. The aim of this book is to give an introduction to the theory of Schwarz symmetrization and study some of its applicat
Twofold Transition in PT-symmetric Coupled Oscillators
2013-12-26
2Dipartimento di Matematica e Fisica Ennio De Giorgi, Università del Salento and I. N. F. N. Sezione di Lecce, Via Arnesano, I-73100 Lecce, Italy...supermode, as shown in Fig. 6, instead of two pairs of real frequencies. B. Unbalanced loss and gain Let us consider the general case (2) in which μ = ν...correspond to the eigenfunctions ψm,n(x,y). The eigenfunctions have the general form ψm,n(x,y) = e−(2axy+bx2+cy2)/2Pm,n(x,y), (12) where b = c∗ = 2(a
Superior long-term activity for a Pt-Re alloy compared to Pt in methanol oxidation reactions
Duke, Audrey S.; Xie, Kangmin; Monnier, John R.; Chen, Donna A.
2017-03-01
Pt-Re bimetallic catalysts have shown enhanced activity compared to pure Pt for reactions involving oxidation, but the origins of this improved activity are not fully understood. Methanol oxidation on a Pt-Re alloy surface and pure Pt foil was studied in a microreactor coupled to an ultrahigh vacuum chamber. For reaction at 60 °C, the Pt-Re alloy surface exhibits superior long-term activity over a 24 h reaction period compared to pure Pt. The initial activity of Pt is 10-15% higher than on Pt-Re; however, the Pt surface gradually loses activity after 10 h online, whereas the activity of Pt-Re does not diminish. Post-reaction XPS shows that more carbon accumulates on the Pt than on Pt-Re, and the improved long-term activity is attributed to a greater ability of Pt-Re to oxidize the carbonaceous intermediates that eventually poison active sites. Both Pt and Pt-Re surfaces have almost no activity for methanol oxidation until a minimum coverage of oxygen is achieved from O2 dissociation. A comparison with methanol oxidation studies on Pt and Pt-Re in a pressure regime that is 150 times lower than in this work demonstrates that more carbon and less oxygen accumulate on the surfaces during reaction at the lower pressures.
N>=2 symmetric superpolynomials
Alarie-Vézina, L; Mathieu, P
2015-01-01
The theory of symmetric functions has been extended to the case where each variable is paired with an anticommuting one. The resulting expressions, dubbed superpolynomials, provide the natural N=1 supersymmetric version of the classical bases of symmetric functions. Here we consider the case where two independent anticommuting variables are attached to each ordinary variable. The N=2 super-version of the monomial, elementary, homogeneous symmetric functions, as well as the power sums, are then constructed systematically (using an exterior-differential formalism for the multiplicative bases), these functions being now indexed by a novel type of superpartitions. Moreover, the scalar product of power sums turns out to have a natural N=2 generalization which preserves the duality between the monomial and homogeneous bases. All these results are then generalized to an arbitrary value of N. Finally, for N=2, the scalar product and the homogenous functions are shown to have a one-parameter deformation, a result that...
Counting with symmetric functions
Mendes, Anthony
2015-01-01
This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enu...
Symmetric tensor decomposition
Brachat, Jerome; Mourrain, Bernard; Tsigaridas, Elias
2009-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables of total degree d as a sum of powers of linear forms (Waring's problem), incidence properties on secant varieties of the Veronese Variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester's approach from the dual point of view. Exploiting this duality, we propose necessary and sufficient conditions for the existence of such a decomposition of a given rank, using the properties of Hankel (and quasi-Hankel) matrices, derived from multivariate polynomials and normal form computations. This leads to the resolution of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on th...
Multiparty Symmetric Sum Types
DEFF Research Database (Denmark)
Nielsen, Lasse; Yoshida, Nobuko; Honda, Kohei
2010-01-01
This paper introduces a new theory of multiparty session types based on symmetric sum types, by which we can type non-deterministic orchestration choice behaviours. While the original branching type in session types can represent a choice made by a single participant and accepted by others...... determining how the session proceeds, the symmetric sum type represents a choice made by agreement among all the participants of a session. Such behaviour can be found in many practical systems, including collaborative workflow in healthcare systems for clinical practice guidelines (CPGs). Processes...... with the symmetric sums can be embedded into the original branching types using conductor processes. We show that this type-driven embedding preserves typability, satisfies semantic soundness and completeness, and meets the encodability criteria adapted to the typed setting. The theory leads to an efficient...
Directory of Open Access Journals (Sweden)
MADE GEDE WIRAKUSUMA
2011-07-01
Full Text Available The usefulness of financial report would decrease if it is not timely reported. The purpose of this study is to examine the impact of profitability, solvency, auditor reputation, company size, earnings content, and industry type on late publication of financial report on Indonesia Stock Market during period of 2007-2009. The hypotheses are tested using multiple regression technique. The results show that auditor reputation and company size significantly affect the late publication of financial reports of companies listed on Indonesia Stock Market during 2007-2009. Other variables, i.e profitability, solvency, and earnings information content do not affect the late publication. The control variable, industry type, also does not have any impact on the late financial report publication of the listed companies.
Symmetric Spaces in Supergravity
Ferrara, Sergio
2008-01-01
We exploit the relation among irreducible Riemannian globally symmetric spaces (IRGS) and supergravity theories in 3, 4 and 5 space-time dimensions. IRGS appear as scalar manifolds of the theories, as well as moduli spaces of the various classes of solutions to the classical extremal black hole Attractor Equations. Relations with Jordan algebras of degree three and four are also outlined.
Distributed Searchable Symmetric Encryption
Bösch, Christoph; Peter, Andreas; Leenders, Bram; Lim, Hoon Wei; Tang, Qiang; Wang, Huaxiong; Hartel, Pieter; Jonker, Willem
2014-01-01
Searchable Symmetric Encryption (SSE) allows a client to store encrypted data on a storage provider in such a way, that the client is able to search and retrieve the data selectively without the storage provider learning the contents of the data or the words being searched for. Practical SSE schemes
Energy Technology Data Exchange (ETDEWEB)
Schmahl, W.
1983-07-01
Autoradiographic studies were conducted at the cerebral hemispheres of mouse embryos X-irradiated on day 12 of gestation and of normal litter mates during the subsequent developmental period. By counting the percentage of labeled mitoses the generation time, the potential doubling time, the growth fraction, as well as the length of the individual cell cycle stages of the neuroblast cells were determined. A continuous increase of generation time was found in the normal brains, concomitant with a latero-medial gradient in telencephalic wall differentiation progress. After X-irradiation this normal differentiation pattern still prevails, but with some marked topographical pecularities. The most important finding was a significant lengthening of the generation time at the medially situated rudiments of the ventricular zone and, similarly at the heterotopic cell islets located within the intermediary zone. Concomitant with this effect, which was seen mainly on days 15 and 17 of gestation, there was a marked increase of mitotic time of these special neuroblasts. The latter finding was regarded as a random event only, which has no causal relationship to the pathogenesis of the heterotopic islets or similar overgrowth anomalies after X-irradiation. In spite of the long generation time of these histological pecularities, they make a considerable contribution to the regeneration of the injured telencephalic wall: up to day 15 gestation the heterotopias had a growth fraction of nearly 1.0(=100 %), whereas the percentage of proliferating cells within the orthotopic remainders of the ventricular zone was only 44%.
PT Symmetry and QCD: Finite Temperature and Density
Directory of Open Access Journals (Sweden)
Michael C. Ogilvie
2009-04-01
Full Text Available The relevance of PT symmetry to quantum chromodynamics (QCD, the gauge theory of the strong interactions, is explored in the context of finite temperature and density. Two significant problems in QCD are studied: the sign problem of finite-density QCD, and the problem of confinement. It is proven that the effective action for heavy quarks at finite density is PT-symmetric. For the case of 1+1 dimensions, the PT-symmetric Hamiltonian, although not Hermitian, has real eigenvalues for a range of values of the chemical potential μ, solving the sign problem for this model. The effective action for heavy quarks is part of a potentially large class of generalized sine-Gordon models which are non-Hermitian but are PT-symmetric. Generalized sine-Gordon models also occur naturally in gauge theories in which magnetic monopoles lead to confinement. We explore gauge theories where monopoles cause confinement at arbitrarily high temperatures. Several different classes of monopole gases exist, with each class leading to different string tension scaling laws. For one class of monopole gas models, the PT-symmetric affine Toda field theory emerges naturally as the effective theory. This in turn leads to sine-law scaling for string tensions, a behavior consistent with lattice simulations.
PT symmetry in classical and quantum statistical mechanics.
Meisinger, Peter N; Ogilvie, Michael C
2013-04-28
PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside the conventional equilibrium statistical mechanics of Hermitian systems. PT-symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviours than Hermitian systems, displaying sinusoidally modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with PT-symmetry include Z(N) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbour Ising model. Quantum many-body problems with a non-zero chemical potential have a natural PT-symmetric representation related to the sign problem. Two-dimensional quantum chromodynamics with heavy quarks at non-zero chemical potential can be solved by diagonalizing an appropriate PT-symmetric Hamiltonian.
Feijoo, David; Konotop, Vladimir V
2016-01-01
We analyze a system of three two-dimensional nonlinear Schr\\"odinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time ($\\mathcal{PT}$) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the $\\mathcal{PT}$-symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and $\\mathcal{PT}$-symmetric cases. Interactions and collisions between the conservative and $\\mathcal{PT}$-symmetric solitons are briefly investigated, as well.
Generating functions for symmetric and shifted symmetric functions
Jing, Naihuan; Rozhkovskaya, Natasha
2016-01-01
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to treat various families of symmetric functions and their shifted analogues.
Generating functions for symmetric and shifted symmetric functions
Jing, Naihuan; Rozhkovskaya, Natasha
2016-01-01
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to treat various families of symmetric functions and their shifted analogues.
EQUIFOCAL HYPERSURFACES IN SYMMETRIC SPACES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This note investigates the multiplicity problem of principal curvatures of equifocal hyper surfaces in simply connected rank 1 symmetric spaces. Using Clifford representation theory, and the author also constructs infinitely many equifocal hypersurfaces in the symmetric spaces.
Homogenous finitary symmetric groups
Directory of Open Access Journals (Sweden)
Otto. H. Kegel
2015-03-01
Full Text Available We characterize strictly diagonal type of embeddings of finitary symmetric groups in terms of cardinality and the characteristic. Namely, we prove the following. Let kappa be an infinite cardinal. If G=underseti=1stackrelinftybigcupG i , where G i =FSym(kappan i , (H=underseti=1stackrelinftybigcupH i , where H i =Alt(kappan i , is a group of strictly diagonal type and xi=(p 1 ,p 2 ,ldots is an infinite sequence of primes, then G is isomorphic to the homogenous finitary symmetric group FSym(kappa(xi (H is isomorphic to the homogenous alternating group Alt(kappa(xi , where n 0 =1,n i =p 1 p 2 ldotsp i .
Chen, Yan; Feng, Huijuan; Ma, Jiayao; Peng, Rui; You, Zhong
2016-06-01
The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.
Symmetric Extended Ockham Algebras
Institute of Scientific and Technical Information of China (English)
T.S. Blyth; Jie Fang
2003-01-01
The variety eO of extended Ockham algebras consists of those algealgebra with an additional endomorphism k such that the unary operations f and k commute. Here, we consider the cO-algebras which have a property of symmetry. We show that there are thirty two non-isomorphic subdirectly irreducible symmetric extended MS-algebras and give a complete description of them.2000 Mathematics Subject Classification: 06D15, 06D30
Symmetrization Selection Rules, 1
Page, P R
1996-01-01
We introduce a category of strong and electromagnetic interaction selection rules for the two-body connected decay and production of exotic J^{PC} = 0^{+-}, 1^{-+}, 2^{+-}, 3^{-+}, ... hybrid and four-quark mesons. The rules arise from symmetrization in states in addition to Bose symmetry and CP invariance. Examples include various decays to \\eta'\\eta, \\eta\\pi, \\eta'\\pi and four-quark interpretations of a 1^{-+} signal.
Symmetrization Selection Rules, 2
Page, P R
1996-01-01
We introduce strong interaction selection rules for the two-body decay and production of hybrid and conventional mesons coupling to two S-wave hybrid or conventional mesons. The rules arise from symmetrization in states in the limit of non-relativistically moving quarks. The conditions under which hybrid coupling to S-wave states is suppressed are determined by the rules, and the nature of their breaking is indicated.
PT; Pro-time; Anticoagulant-prothrombin time; Clotting time: protime; INR; International normalized ratio ... PT is measured in seconds. Most of the time, results are given as what is called INR ( ...
Lu, Guojin
Pt and Pt-based alloy catalysts were synthesized by electrodeposition on HOPG. The nucleation and growth, morphology, composition and crystal structure, and electrocatalytic activity (towards relevant reactions in the frame of PEMFCs and DMFCs) of these model electrodes were systematically investigated. The presence of chlorides inhibits the Pt reduction processes. There is a transition from progressive to instantaneous nucleation with increasing overpotential for the deposition from 1 mM H2PtCl6 electrolytes. The possibility of instantaneous nucleation at large overpotential by using electrolytes with large chloride concentration is advantageous for the growth of small, well dispersed nanoparticles. The electrochemical data were confirmed by AFM and SEM imaging studies. Relatively narrow size distributed nanoparticles can be obtained from the current system. While MOR activity decreases with decreasing particle size, the HER and HOR activity of deposited Pt particles increases with decreasing deposition period. The ORR activity first increases then decreases with increasing deposition time. Interactions between Pt and Ru, or Ni or Co are observed and they form solid solution as verified by XRD. Underpotential deposition occurs for Pt-Ni or Pt-Co co-electrodeposition. Pt-Ru deposition can be described as progressive nucleation at low overpotential and instantaneous nucleation at high overpotentials. Through direct morphological observations, the Pt-Ni or Pt-Co nucleation can be approximately described as progressive. Pt-Ru deposits are superior to Pt towards MOR. The optimum Ru content is about 50 at.%. Pt-Ni and Pt-Co deposits are more active than Pt for ORR. The optimum content is about 30 at.% Ni or 50 at.% Co. Dealloying of Pt-Ru and Pt-Ni or Pt-Co electrodeposit is observed after electrochemical characterization. The extent of dealloying increases with the content of the alloying element.
Spontaneous breakdown of $\\mathcal{PT}$ symmetry in the complex Coulomb potential
Indian Academy of Sciences (India)
G Lévai
2009-08-01
The $\\mathcal{PT}$ symmetry of the Coulomb potential and its solutions are studied along trajectories satisfying the $\\mathcal{PT}$ symmetry requirement. It is shown that with appropriate normalization constant the general solutions can be chosen $\\mathcal{PT}$ -symmetric if the parameter that corresponds to angular momentum in the Hermitian case is real. $\\mathcal{PT}$ symmetry is spontaneously broken, however, for complex values of the form $L = − \\dfrac{1}{2} + i$. In this case the potential remains $\\mathcal{PT}$ -symmetric, while the two independent solutions are transformed to each other by the $\\mathcal{PT}$ operation and at the same time, the two series of discrete energy eigenvalues turn into each other’s complex conjugate.
Yang, Jianke
2016-01-01
Stability of soliton families in one-dimensional nonlinear Schroedinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of parameter values both below and above phase transition. In addition, a pseudo-Hamiltonian-Hopf bifurcation is revealed, where pairs of purely-imaginary eigenvalues in the linear-stability spectra of solitons collide and bifurcate off the imaginary axis, creating oscillatory instability, which resembles Hamiltonian-Hopf bifurcations of solitons in Hamiltonian systems even though the present system is dissipative and non-Hamiltonian. The most important numerical finding is that, eigenvalues of linear-stability operators of these solitons appear in quartets $(\\lambda, -\\lambda, \\lambda^*, -\\lambda^*)$, similar to conservative systems and PT-symmetric systems. This quartet eigenvalue symmetry is very surprising for non-PT-symmetric systems, and it has far-reaching consequences ...
Towards nanoscale multiplexing with parity-time symmetric plasmonic coaxial waveguides
Alaeian, Hadiseh; Jankovic, Vladan; Lawrence, Mark; Dionne, Jennifer A
2016-01-01
We theoretically investigate a nanoscale mode-division multiplexing scheme based on parity-time (PT) symmetric coaxial plasmonic waveguides. Coaxial waveguides support paired degenerate modes corresponding to distinct orbital angular momentum states. PT symmetric inclusions of gain and loss break the degeneracy of the paired modes and create new hybrid modes without orbital angular momentum. This process can be made thresholdless by matching the mode order with the number of gain and loss sections within the coaxial ring. Using both a Hamiltonian formulation and degenerate perturbation theory, we show how the wavevectors and fields evolve with increased loss/gain and derive sufficient conditions for thresholdless transitions. As a multiplexing filter, this PT symmetric coaxial waveguide could help double density rates in on-chip nanophotonic networks.
Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides
Nixon, Sean
2016-01-01
Many classes of non-parity-time (PT) symmetric waveguides with arbitrary gain and loss distributions still possess all-real linear spectrum or exhibit phase transition. In this article, nonlinear light behaviors in these complex waveguides are probed analytically near a phase transition. Using multi-scale perturbation methods, a nonlinear ordinary differential equation (ODE) is derived for the light's amplitude evolution. This ODE predicts that the first class of these non-PT-symmetric waveguides support continuous families of solitons and robust amplitude-oscillating solutions both above and below phase transition, in close analogy with PT-symmetric systems. For the other classes of waveguides, the light's intensity always amplifies under the effect of nonlinearity even if the waveguide is below phase transition. These analytical predictions are confirmed by direct computations of the full system.
Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of total degree d as a sum of powers of linear forms (Waring’s problem), incidence properties on secant varieties of the Veronese variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester’s approach from the dual point of view...
Symmetrically Constrained Compositions
Beck, Matthias; Lee, Sunyoung; Savage, Carla D
2009-01-01
Given integers $a_1, a_2, ..., a_n$, with $a_1 + a_2 + ... + a_n \\geq 1$, a symmetrically constrained composition $\\lambda_1 + lambda_2 + ... + lambda_n = M$ of $M$ into $n$ nonnegative parts is one that satisfies each of the the $n!$ constraints ${\\sum_{i=1}^n a_i \\lambda_{\\pi(i)} \\geq 0 : \\pi \\in S_n}$. We show how to compute the generating function of these compositions, combining methods from partition theory, permutation statistics, and lattice-point enumeration.
Holographic Spherically Symmetric Metrics
Petri, Michael
The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.
Sirsi, Swarnamala; Hegde, Subramanya
2011-01-01
Quantum computation on qubits can be carried out by an operation generated by a Hamiltonian such as application of a pulse as in NMR, NQR. Quantum circuits form an integral part of quan- tum computation. We investigate the nonlocal operations generated by a given Hamiltonian. We construct and study the properties of perfect entanglers, that is, the two-qubit operations that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power. Our work addresses the problem of analyzing the quantum evolution in the special case of two qubit symmetric states. Such a symmetric space can be considered to be spanned by the angular momentum states {|j = 1,m>;m = +1, 0,-1}. Our technique relies on the decomposition of a Hamiltonian in terms of newly defined Hermitian operators Mk's (k= 0.....8) which are constructed out of angular momentum operators Jx, Jy, Jz. These operators constitute a linearly independent set of traceless matrices (except for M0). Further...
Directory of Open Access Journals (Sweden)
Giuseppe Di Maio
2008-04-01
Full Text Available The subject of hyperspace topologies on closed or closed and compact subsets of a topological space X began in the early part of the last century with the discoveries of Hausdorff metric and Vietoris hit-and-miss topology. In course of time, several hyperspace topologies were discovered either for solving some problems in Applied or Pure Mathematics or as natural generalizations of the existing ones. Each hyperspace topology can be split into a lower and an upper part. In the upper part the original set inclusion of Vietoris was generalized to proximal set inclusion. Then the topologization of the Wijsman topology led to the upper Bombay topology which involves two proximities. In all these developments the lower topology, involving intersection of finitely many open sets, was generalized to locally finite families but intersection was left unchanged. Recently the authors studied symmetric proximal topology in which proximity was used for the first time in the lower part replacing intersection with its generalization: nearness. In this paper we use two proximities also in the lower part and we obtain the lower Bombay hypertopology. Consequently, a new hypertopology arises in a natural way: the symmetric Bombay topology which is the join of a lower and an upper Bombay topology.
The Symmetricity of Normal Modes in Symmetric Complexes
Song, Guang
2016-01-01
In this work, we look at the symmetry of normal modes in symmetric structures, particularly structures with cyclic symmetry. We show that normal modes of symmetric structures have different levels of symmetry, or symmetricity. One novel theoretical result of this work is that, for a ring structure with $m$ subunits, the symmetricity of the normal modes falls into $m$ groups of equal size, with normal modes in each group having the same symmetricity. The normal modes in each group can be computed separately, using a much smaller amount of memory and time (up to $m^3$ less), thus making it applicable to larger complexes. We show that normal modes with perfect symmetry or anti-symmetry have no degeneracy while the rest of the modes have a degeneracy of two. We show also how symmetry in normal modes correlates with symmetry in structure. While a broken symmetry in structure generally leads to a loss of symmetricity in symmetric normal modes, the symmetricity of some symmetric normal modes is preserved even when s...
RT-Symmetric Laplace Operators on Star Graphs: Real Spectrum and Self-Adjointness
Directory of Open Access Journals (Sweden)
Maria Astudillo
2015-01-01
Full Text Available How ideas of PT-symmetric quantum mechanics can be applied to quantum graphs is analyzed, in particular to the star graph. The class of rotationally symmetric vertex conditions is analyzed. It is shown that all such conditions can effectively be described by circulant matrices: real in the case of odd number of edges and complex having particular block structure in the even case. Spectral properties of the corresponding operators are discussed.
Plane symmetric cosmological models
Yadav, Anil Kumar; Ray, Saibal; Mallick, A
2016-01-01
In this work, we perform the Lie symmetry analysis on the Einstein-Maxwell field equations in plane symmetric spacetime. Here Lie point symmetries and optimal system of one dimensional subalgebras are determined. The similarity reductions and exact solutions are obtained in connection to the evolution of universe. The present study deals with the electromagnetic energy of inhomogeneous universe where $F_{12}$ is the non-vanishing component of electromagnetic field tensor. To get a deterministic solution, it is assumed that the free gravitational field is Petrov type-II non-degenerate. The electromagnetic field tensor $F_{12}$ is found to be positive and increasing function of time. As a special case, to validate the solution set, we discuss some physical and geometric properties of a specific sub-model.
Institute of Scientific and Technical Information of China (English)
傅育熙
1998-01-01
An alternative presentation of the π－calculus is given.This version of the π-calculus is symmetric in the sense that communications are symmetric and there is no difference between input and output prefixes.The point of the symmetric π-calculus is that it has no abstract names.The set of closed names is therefore homogeneous.The π－calculus can be fully embedded into the symmetric π-calculus.The symmetry changes the emphasis of the communication mechanism of the π-calculus and opens up possibility for further variations.
Density functional theory studies of the adsorption of ethylene and oxygen on Pt(111) and Pt3Sn(111)
DEFF Research Database (Denmark)
Watwe, R.M.; Cortright, R.D.; Mavrikakis, Manos
2001-01-01
of pi -bonded ethylene, di-sigma -bonded ethylene, and ethylidyne species are weaker on Pt3Sn(111) than on Pt(111) by 21, 31, and 50 kJ/mol, respectively. Hence, the electronic effect of Sn on the adsorption of ethylene depends on the type of adsorption site, with adsorption on three-fold site weakened......Density functional theory, employing periodic slab calculations, was used to investigate the interactions of ethylene and oxygen with Pt(111) and Pt3Sn(111). The predicted energetics and structures of adsorbed species on Pt(111) are in good agreement with experimental data. The binding energies...
Representation of Fuzzy Symmetric Relations
1986-03-19
Std Z39-18 REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. Valverde Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda...REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. "Valverde* Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda. Diagonal, 649
Parallel Symmetric Eigenvalue Problem Solvers
2015-05-01
Plemmons G. Golub and A. Sameh. High-speed computing : scientific appli- cations and algorithm design. University of Illinois Press, Champaign, Illinois , 1988...16. SECURITY CLASSIFICATION OF: Sparse symmetric eigenvalue problems arise in many computational science and engineering applications such as...Eigenvalue Problem Solvers Report Title Sparse symmetric eigenvalue problems arise in many computational science and engineering applications such as
MINIMIZATION PROBLEM FOR SYMMETRIC ORTHOGONAL ANTI-SYMMETRIC MATRICES
Institute of Scientific and Technical Information of China (English)
Yuan Lei; Anping Liao; Lei Zhang
2007-01-01
By applying the generalized singular value decomposition and the canonical correlation decomposition simultaneously, we derive an analytical expression of the optimal approximate solution (X), which is both a least-squares symmetric orthogonal anti-symmetric solution of the matrix equation ATXA ＝ B and a best approximation to a given matrix X*.Moreover, a numerical algorithm for finding this optimal approximate solution is described in detail, and a numerical example is presented to show the validity of our algorithm.
Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
Peng, Bo; Lei, Fuchuan; Monifi, Faraz; Gianfreda, Mariagiovanna; Long, Gui Lu; Fan, Shanhui; Nori, Franco; Bender, Carl M; Yang, Lan
2013-01-01
Optical systems combining balanced loss and gain profiles provide a unique platform to implement classical analogues of quantum systems described by non-Hermitian parity-time- (PT-) symmetric Hamiltonians and to originate new synthetic materials with novel properties. To date, experimental works on PT-symmetric optical systems have been limited to waveguides in which resonances do not play a role. Here we report the first demonstration of PT-symmetry breaking in optical resonator systems by using two directly coupled on-chip optical whispering-gallery-mode (WGM) microtoroid silica resonators. Gain in one of the resonators is provided by optically pumping Erbium (Er3+) ions embedded in the silica matrix; the other resonator exhibits passive loss. The coupling strength between the resonators is adjusted by using nanopositioning stages to tune their distance. We have observed reciprocal behavior of the PT-symmetric system in the linear regime, as well as a transition to nonreciprocity in the PT symmetry-breaking...
Energy Technology Data Exchange (ETDEWEB)
Hasan, Mohammad, E-mail: mohammadhasan786@gmail.com [ISRO Satellite Centre (ISAC), Bangalore-560017 (India); Ghatak, Ananya, E-mail: gananya04@gmail.com [Department of Physics, Banaras Hindu University, Varanasi-221005 (India); Mandal, Bhabani Prasad, E-mail: bhabani.mandal@gmail.com [Department of Physics, Banaras Hindu University, Varanasi-221005 (India)
2014-05-15
We consider a non-Hermitian medium with a gain and loss symmetric, exponentially damped potential distribution to demonstrate different scattering features analytically. The condition for critical coupling (CC) for unidirectional wave and coherent perfect absorption (CPA) for bidirectional waves are obtained analytically for this system. The energy points at which total absorption occurs are shown to be the spectral singular points for the time reversed system. The possible energies at which CC occurs for left and right incidence are different. We further obtain periodic intervals with increasing periodicity of energy for CC and CPA to occur in this system. -- Highlights: •Energy ranges for CC and CPA are obtained explicitly for complex WS potential. •Analytical conditions for CC and CPA for PT symmetric WS potential are obtained. •Conditions for left and right CC are shown to be different. •Conditions for CC and CPA are shown to be that of SS for the time reversed system. •Our model shows the great flexibility of frequencies for CC and CPA.
Half-spectral unidirectional invisibility in non-Hermitian periodic optical structures
Longhi, Stefano
2015-01-01
The phenomenon of half-spectral unidirectional invisibility is introduced for one-dimensional periodic optical structures with tailored real and imaginary refractive index distributions in a non-$\\mathcal{PT}$-symmetric configuration. The effect refers to the property that the optical medium appears to be invisible, both in reflection and transmission, below the Bragg frequency when probed from one side, and above the Bragg frequency when probed from the opposite side. Half-spectral invisibility is obtained by a combination of in-phase index and gain gratings whose spatial amplitudes are related each other by a Hilbert transform.
PT-symmetry and kagome lattices (Conference Presentation)
Saxena, Avadh; Chern, Gia-Wei
2016-09-01
We consider a complex photonic lattice by placing PT-symmetric dimers at the Kagome lattice points. This lattice is a two-dimensional network of corner-sharing triangles. Each dimer represents a pair of strongly coupled waveguides. The frustrated coupling between waveguide modes results in a dispersionless flat band comprising spatially localized modes. For a balanced arrangement of gain and loss on each dimer, up to a critical value of the gain/loss parameter the system exhibits a PT-symmetric phase. The beam evolution in the waveguide array leads to an oscillatory rotation of the optical power. We observe local chiral structures with a narrow beam excitation. We also study nonlinearity and disorder in this set up.
Pseudo-Hermitian Systems with PT-Symmetry: Degeneracy and Krein Space
Choutri, B.; Cherbal, O.; Ighezou, F. Z.; Drir, M.
2017-02-01
We show in the present paper that pseudo-Hermitian Hamiltonian systems with even PT-symmetry (P2=1,T2=1) admit a degeneracy structure. This kind of degeneracy is expected traditionally in the odd PT-symmetric systems (P2=1,T2=-1) which is appropriate to the fermions (Scolarici and Solombrino, Phys. Lett. A 303, 239 2002; Jones-Smith and Mathur, Phys. Rev. A 82, 042101 2010). We establish that the pseudo-Hermitian Hamiltonians with even PT-symmetry admit a degeneracy structure if the operator PT anticommutes with the metric operator η σ which is necessarily indefinite. We also show that the Krein space formulation of the Hilbert space is the convenient framework for the implementation of unbroken PT-symmetry. These general results are illustrated with great details for four-level pseudo-Hermitian Hamiltonian with even PT -symmetry.
PT-symmetry breaking with divergent potentials: lattice and continuum cases
Joglekar, Yogesh N; Saxena, Avadh
2014-01-01
We investigate the parity- and time-reversal ($\\mathcal{PT}$)-symmetry breaking in lattice models in the presence of long-ranged, non-hermitian, $\\mathcal{PT}$-symmetric potentials that remain finite or become divergent in the continuum limit. By scaling analysis of the fragile $\\mathcal{PT}$ threshold for an open finite lattice, we show that continuum loss-gain potentials $V_\\alpha(x)\\propto i |x|^\\alpha \\mathrm{sign}(x)$ have a positive $\\mathcal{PT}$-breaking threshold for $\\alpha>-2$, and a zero threshold for $\\alpha\\leq -2$. When $\\alpha<0$ localized states with complex (conjugate) energies in the continuum energy-band occur at higher loss-gain strengths. We investigate the signatures of $\\mathcal{PT}$-symmetry breaking in coupled waveguides, and show that the emergence of localized states dramatically shortens the relevant time-scale in the $\\mathcal{PT}$-symmetry broken region.
Jet quenching and high-pt azimuthal asymmetry
Lokhtin, Igor P; Vitev, I
2002-01-01
The azimuthal anisotropy of high-pt particle production in non-central heavy ion collisions is among the most promising observables of partonic energy loss in an azimuthally non-symmetric volume of quark-gluon plasma. We discuss the implications of nuclear geometry for the models of partonic energy loss in the context of recent RHIC data and consequences for observation of jet quenching at the LHC.
Particle-vortex symmetric liquid
Mulligan, Michael
2016-01-01
We introduce an effective theory with manifest particle-vortex symmetry for disordered thin films undergoing a magnetic field-tuned superconductor-insulator transition. The theory may enable one to access both the critical properties of the strong-disorder limit, which has recently been confirmed [Breznay et al., PNAS 113, 280 (2016)] to exhibit particle-vortex symmetric electrical response, and the metallic phase discovered earlier [Mason and Kapitulnik, Phys. Rev. Lett. 82, 5341 (1999)] in less disordered samples. Within the effective theory, the Cooper-pair and field-induced vortex degrees of freedom are simultaneously incorporated into an electrically-neutral Dirac fermion minimally coupled to an (emergent) Chern-Simons gauge field. A derivation of the theory follows upon mapping the superconductor-insulator transition to the integer quantum Hall plateau transition and the subsequent use of Son's particle-hole symmetric composite Fermi liquid. Remarkably, particle-vortex symmetric response does not requir...
Harmonic analysis on symmetric spaces
Terras, Audrey
This text explores the geometry and analysis of higher rank analogues of the symmetric spaces introduced in volume one. To illuminate both the parallels and differences of the higher rank theory, the space of positive matrices is treated in a manner mirroring that of the upper-half space in volume one. This concrete example furnishes motivation for the general theory of noncompact symmetric spaces, which is outlined in the final chapter. The book emphasizes motivation and comprehensibility, concrete examples and explicit computations (by pen and paper, and by computer), history, and, above all, applications in mathematics, statistics, physics, and engineering. The second edition includes new sections on Donald St. P. Richards’s central limit theorem for O(n)-invariant random variables on the symmetric space of GL(n, R), on random matrix theory, and on advances in the theory of automorphic forms on arithmetic groups.
Symmetric autocompensating quantum key distribution
Walton, Zachary D.; Sergienko, Alexander V.; Levitin, Lev B.; Saleh, Bahaa E. A.; Teich, Malvin C.
2004-08-01
We present quantum key distribution schemes which are autocompensating (require no alignment) and symmetric (Alice and Bob receive photons from a central source) for both polarization and time-bin qubits. The primary benefit of the symmetric configuration is that both Alice and Bob may have passive setups (neither Alice nor Bob is required to make active changes for each run of the protocol). We show that both the polarization and the time-bin schemes may be implemented with existing technology. The new schemes are related to previously described schemes by the concept of advanced waves.
Axially Symmetric, Spatially Homothetic Spacetimes
Wagh, S M; Wagh, Sanjay M.; Govinder, Keshlan S.
2002-01-01
We show that the existence of appropriate spatial homothetic Killing vectors is directly related to the separability of the metric functions for axially symmetric spacetimes. The density profile for such spacetimes is (spatially) arbitrary and admits any equation of state for the matter in the spacetime. When used for studying axisymmetric gravitational collapse, such solutions do not result in a locally naked singularity.
Shearfree Spherically Symmetric Fluid Models
Sharif, M
2013-01-01
We try to find some exact analytical models of spherically symmetric spacetime of collapsing fluid under shearfree condition. We consider two types of solutions: one is to impose a condition on the mass function while the other is to restrict the pressure. We obtain totally of five exact models, and some of them satisfy the Darmois conditions.
Particle-vortex symmetric liquid
Mulligan, Michael
2017-01-01
We introduce an effective theory with manifest particle-vortex symmetry for disordered thin films undergoing a magnetic field-tuned superconductor-insulator transition. The theory may enable one to access both the critical properties of the strong-disorder limit, which has recently been confirmed by Breznay et al. [Proc. Natl. Acad. Sci. USA 113, 280 (2016), 10.1073/pnas.1522435113] to exhibit particle-vortex symmetric electrical response, and the nearby metallic phase discovered earlier by Mason and Kapitulnik [Phys. Rev. Lett. 82, 5341 (1999), 10.1103/PhysRevLett.82.5341] in less disordered samples. Within the effective theory, the Cooper-pair and field-induced vortex degrees of freedom are simultaneously incorporated into an electrically neutral Dirac fermion minimally coupled to a (emergent) Chern-Simons gauge field. A derivation of the theory follows upon mapping the superconductor-insulator transition to the integer quantum Hall plateau transition and the subsequent use of Son's particle-hole symmetric composite Fermi liquid. Remarkably, particle-vortex symmetric response does not require the introduction of disorder; rather, it results when the Dirac fermions exhibit vanishing Hall effect. The theory predicts approximately equal (diagonal) thermopower and Nernst signal with a deviation parameterized by the measured electrical Hall response at the symmetric point.
Symmetric relations of finite negativity
Kaltenbaeck, M.; Winkler, H.; Woracek, H.; Forster, KH; Jonas, P; Langer, H
2006-01-01
We construct and investigate a space which is related to a symmetric linear relation S of finite negativity on an almost Pontryagin space. This space is the indefinite generalization of the completion of dom S with respect to (S.,.) for a strictly positive S on a Hilbert space.
Vassiliev Invariants from Symmetric Spaces
DEFF Research Database (Denmark)
Biswas, Indranil; Gammelgaard, Niels Leth
We construct a natural framed weight system on chord diagrams from the curvature tensor of any pseudo-Riemannian symmetric space. These weight systems are of Lie algebra type and realized by the action of the holonomy Lie algebra on a tangent space. Among the Lie algebra weight systems, they are ......, they are exactly characterized by having the symmetries of the Riemann curvature tensor....
Thermophoresis of Axially Symmetric Bodies
2007-11-02
Sweden Abstract. Thermophoresis of axially symmetric bodies is investigated to first order in the Knudsen-mimber, Kn. The study is made in the limit...derived. Asymptotic solutions are studied. INTRODUCTION Thermophoresis as a phenomenon has been known for a long time, and several authors have approached
Axiomatizations of symmetrically weighted solutions
Kleppe, John; Reijnierse, Hans; Sudhölter, P.
2013-01-01
If the excesses of the coalitions in a transferable utility game are weighted, then we show that the arising weighted modifications of the well-known (pre)nucleolus and (pre)kernel satisfy the equal treatment property if and only if the weight system is symmetric in the sense that the weight of a su
Computationally Efficient Searchable Symmetric Encryption
Liesdonk, van Peter; Sedghi, Saeed; Doumen, Jeroen; Hartel, Pieter; Jonker, Willem; Jonker, Willem; Petkovic, Milan
2010-01-01
Searchable encryption is a technique that allows a client to store documents on a server in encrypted form. Stored documents can be retrieved selectively while revealing as little information as possible to the server. In the symmetric searchable encryption domain, the storage and the retrieval are
Symmetrical progressive erythro-keratoderma
Directory of Open Access Journals (Sweden)
Sunil Gupta
1999-01-01
Full Text Available A 13-year-old male child had gradually progressive, bilaterall, symmetrical, erythematous hyperkeratotic plaques over knees, elbows, natal cleft, dorsa of hands and feet with palmoplantar keratoderma. High arched palate, fissured tongue and sternal depression (pectus-excavatum were unusual associations.
Bott periodicity of inclusions
Mare, Augustin-Liviu
2011-01-01
When looking at Bott's original proof of his periodicity theorem for the stable homotopy groups of the orthogonal and unitary groups, one sees in the background a differential geometric periodicity phenomenon. We show that this geometric phenomenon extends to the standard inclusion of the orthogonal group into the unitary group. This explains the periodicity of the group homomorphisms between stable homotopy groups which are induced by the inclusion map. Standard inclusions between other classical Riemannian symmetric spaces are also discussed.
Understanding symmetrical components for power system modeling
Das, J C
2017-01-01
This book utilizes symmetrical components for analyzing unbalanced three-phase electrical systems, by applying single-phase analysis tools. The author covers two approaches for studying symmetrical components; the physical approach, avoiding many mathematical matrix algebra equations, and a mathematical approach, using matrix theory. Divided into seven sections, topics include: symmetrical components using matrix methods, fundamental concepts of symmetrical components, symmetrical components –transmission lines and cables, sequence components of rotating equipment and static load, three-phase models of transformers and conductors, unsymmetrical fault calculations, and some limitations of symmetrical components.
Electrically tunable coalescence of exceptional points in parity-time symmetric waveguides
Wang, Jin; Wu, Raymond P H; Mok, T C; Fung, Kin Hung
2016-01-01
We demonstrate theoretically the high electric tunability of the emergence and coalescence of exceptional points in PT-symmetric waveguides bounded by imperfect conductive layers. Owing to the competition effect of multimode interaction, multiple exceptional points and PT phase transitions could be attained in such a simple system and, meanwhile, their occurrences are strongly dependent on the boundary conductive layers. When the conductive layers become very thin, it is found that the sideway transmittance and reflectance of the same system can be tuned between zero and one by a small change in carrier density. The results may provide an effective method for fast tuning and modulation of optical signals through electrical gating.
Rapid thermal annealing of FePt and FePt/Cu thin films
Energy Technology Data Exchange (ETDEWEB)
Brombacher, Christoph
2011-01-10
Chemically ordered FePt is one of the most promising materials to reach the ultimate limitations in storage density of future magnetic recording devices due to its high uniaxial magnetocrystalline anisotropy and a corrosion resistance superior to rare-earth based magnets. In this study, FePt and FePt/Cu bilayers have been sputter deposited at room temperature onto thermally oxidized silicon wafers, glass substrates and self-assembled arrays of spherical SiO{sub 2} particles with diameters down to 10 nm. Millisecond flash lamp annealing, as well as conventional rapid thermal annealing was employed to induce the phase transformation from the chemically disordered A1 phase into the chemically ordered L1{sub 0} phase. The influence of the annealing temperature, annealing time and the film thickness on the ordering transformation and (001) texture evolution of FePt films with near equiatomic composition was studied. Whereas flash lamp annealed FePt films exhibit a polycrystalline morphology with high chemical L1{sub 0} order, rapid thermal annealing can lead to the formation of chemically ordered FePt films with (001) texture on amorphous SiO{sub 2}/Si substrates. The resultant high perpendicular magnetic anisotropy and large coercivities up to 40 kOe are demonstrated. Simultaneously to the ordering transformation, rapid thermal annealing to temperatures exceeding 600 C leads to a break up of the continuous FePt film into separated islands. This dewetting behavior was utilized to create regular arrays of FePt nanostructures on SiO{sub 2} particle templates with periods down to 50 nm. The addition of Cu improves the (001) texture formation and chemical ordering for annealing temperatures T{sub a} {<=}600 C. In addition, the magnetic anisotropy and the coercivity of the ternary FePtCu alloy can be effectively tailored by adjusting the Cu content. The prospects of FePtCu based exchange spring media, as well as the magnetic properties of FePtCu nanostructures fabricated
The antipodal sets of compact symmetric spaces
National Research Council Canada - National Science Library
Liu, Xingda; Deng, Shaoqiang
2014-01-01
We study the antipodal set of a point in a compact Riemannian symmetric space. It turns out that we can give an explicit description of the antipodal set of a point in any connected simply connected compact Riemannian symmetric space...
Symmetric normalisation for intuitionistic logic
DEFF Research Database (Denmark)
Guenot, Nicolas; Straßburger, Lutz
2014-01-01
, but using a non-local rewriting. The second system is the symmetric completion of the first, as normally given in deep inference for logics with a DeMorgan duality: all inference rules have duals, as cut is dual to the identity axiom. We prove a generalisation of cut elimination, that we call symmetric...... normalisation, where all rules dual to standard ones are permuted up in the derivation. The result is a decomposition theorem having cut elimination and interpolation as corollaries.......We present two proof systems for implication-only intuitionistic logic in the calculus of structures. The first is a direct adaptation of the standard sequent calculus to the deep inference setting, and we describe a procedure for cut elimination, similar to the one from the sequent calculus...
Symmetric two-coordinate photodiode
Directory of Open Access Journals (Sweden)
Dobrovolskiy Yu. G.
2008-12-01
Full Text Available The two-coordinate photodiode is developed and explored on the longitudinal photoeffect, which allows to get the coordinate descriptions symmetric on the steepness and longitudinal resistance great exactness. It was shown, that the best type of the coordinate description is observed in the case of scanning by the optical probe on the central part of the photosensitive element. The ways of improvement of steepness and linear of its coordinate description were analyzed.
Rotationally symmetric viscous gas flows
Weigant, W.; Plotnikov, P. I.
2017-03-01
The Dirichlet boundary value problem for the Navier-Stokes equations of a barotropic viscous compressible fluid is considered. The flow region and the data of the problem are assumed to be invariant under rotations about a fixed axis. The existence of rotationally symmetric weak solutions for all adiabatic exponents from the interval (γ*,∞) with a critical exponent γ* < 4/3 is proved.
Indian Academy of Sciences (India)
XIE QIONGTAO; YAN LINA; WANG LINMAO; FU JUN
2016-05-01
We investigate both the non-Hermitian parity–time-(PT-)symmetric and Hermitianasymmetric volcano potentials, and present the analytical solution in terms of the confluent Heun function. Under certain special conditions, the confluent Heun function can be terminated as a polynomial, thereby leading to certain exact analytical results. It is found that the non-Hermitian PTsymmetric volcano potentials support the normalizable and non-normalizable reflectionless stateswith real energies. The Hermitian asymmetric volcano potentials allow normalizable reflectionless states with complex energies.
Antisymmetric PT-photonic structures with balanced positive and negative index materials
Ge, Li
2012-01-01
In this Letter we study a new class of synthetic materials in which the refractive index satisfies a special symmetry, n(-x)=-n^*(x), which we term antisymmetric parity-time (APT) systems. Unlike PT-symmetric systems which require balanced gain and loss, i.e. n(-x)=n^*(x), APT systems consist of balanced positive and negative index materials (NIMs). Despite the seemingly PT-symmetric optical potential $V(x)\\equiv n(x)^2\\omega^2/c^2$, such systems are not invariant under combined PT operation due to the discontinuity of the spatial derivative of the wavefunction. We show that APT systems display intriguing properties such as spontaneous phase transition of the scattering matrix, bidirectional invisibility, and a continuous lasing spectrum.
Symmetric products of mixed Hodge modules
Maxim, Laurentiu; Schuermann, Joerg
2010-01-01
Generalizing a theorem of Macdonald, we show a formula for the mixed Hodge structure on the cohomology of the symmetric products of bounded complexes of mixed Hodge modules by showing the existence of the canonical action of the symmetric group on the multiple external self-products of complexes of mixed Hodge modules. We also generalize a theorem of Hirzebruch and Zagier on the signature of the symmetric products of manifolds to the case of the symmetric products of symmetric parings on bounded complexes with constructible cohomology sheaves where the pairing is not assumed to be non-degenerate.
Singular Value Decomposition for Unitary Symmetric Matrix
Institute of Scientific and Technical Information of China (English)
ZOUHongxing; WANGDianjun; DAIQionghai; LIYanda
2003-01-01
A special architecture called unitary sym-metric matrix which embodies orthogonal, Givens, House-holder, permutation, and row (or column) symmetric ma-trices as its special cases, is proposed, and a precise corre-spondence of singular values and singular vectors between the unitary symmetric matrix and its mother matrix is de-rived. As an illustration of potential, it is shown that, for a class of unitary symmetric matrices, the singular value decomposition (SVD) using the mother matrix rather than the unitary symmetric matrix per se can save dramatically the CPU time and memory without loss of any numerical precision.
Discrete Torsion and Symmetric Products
Dijkgraaf, R
1999-01-01
In this note we point out that a symmetric product orbifold CFT can be twisted by a unique nontrivial two-cocycle of the permutation group. This discrete torsion changes the spins and statistics of corresponding second-quantized string theory making it essentially ``supersymmetric.'' The long strings of even length become fermionic (or ghosts), those of odd length bosonic. The partition function and elliptic genus can be described by a sum over stringy spin structures. The usual cubic interaction vertex is odd and nilpotent, so this construction gives rise to a DLCQ string theory with a leading quartic interaction.
A charged spherically symmetric solution
Indian Academy of Sciences (India)
K Moodley; S D Maharaj; K S Govinder
2003-09-01
We ﬁnd a solution of the Einstein–Maxwell system of ﬁeld equations for a class of accelerating, expanding and shearing spherically symmetric metrics. This solution depends on a particular ansatz for the line element. The radial behaviour of the solution is fully speciﬁed while the temporal behaviour is given in terms of a quadrature. By setting the charge contribution to zero we regain an (uncharged) perfect ﬂuid solution found previously with the equation of state =+ constant, which is a generalisation of a stiff equation of state. Our class of charged shearing solutions is characterised geometrically by a conformal Killing vector.
Spherically symmetric scalar field collapse
Indian Academy of Sciences (India)
Koyel Ganguly; Narayan Banerjee
2013-03-01
It is shown that a scalar field, minimally coupled to gravity, may have collapsing modes even when the energy condition is violated, that is, for ( + 3) < 0. This result may be useful in the investigation of the possible clustering of dark energy. All the examples dealt with have apparent horizons formed before the formation of singularity. The singularities formed are shell focussing in nature. The density of the scalar field distribution is seen to diverge at singularity. The Ricci scalar also diverges at the singularity. The interior spherically symmetric metric is matched with exterior Vaidya metric at the hypersurface and the appropriate junction conditions are obtained.
Immanant Conversion on Symmetric Matrices
Directory of Open Access Journals (Sweden)
Purificação Coelho M.
2014-01-01
Full Text Available Letr Σn(C denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C -> Σn (C satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB = dχ·(Φ(Α + αΦ(Β for all matrices A,В ε Σ„(С and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С.
Stability Analysis of Fixed points in a Parity-time symmetric coupler with Kerr nonlinearity
Deka, Jyoti Prasad
2016-01-01
We report our study on nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. In the linear regime, the differential equations governing the dynamics of the coupler, under some parametric changes, can be solved exactly. But with the inclusion of nonlinearity, analytical solution of the system is a rather complicated job. And the sensitiveness of the system on the initial conditions is yet another critical issue. To circumvent the situation, we have employed the mathematical framework of nonlinear dynamics. Considering the parity-time threshold of the linear PT-coupler as the reference point, we find that in nonlinear coupler the parity-time symmetric threshold governs the existence of fixed points. We have found that the stability of the ground state undergoes a phase transition when the gain/loss coefficient is increased from zero to beyond the PT threshold. In the unbroken PT regime, we find that the instabilities in the initial launch conditions can trigger an exponential growth and dec...
Characterization of FePt nanoparticles in FePt/C multilayers
Energy Technology Data Exchange (ETDEWEB)
Barradas, N.P. E-mail: nunoni@itn.mces.pt; Alves, E.; Babonneau, D
2004-06-01
The areal density growth of recording media is expected to reach 100 Gbit/in.{sup 2} within a few years. Such high densities require magnetic grain sizes of 10 nm or less, which is close to the superparamagnetic limit of current media. Therefore, in order to retain thermal stability, it is essential to use a magnetic material with high anisotropy energy. Ordered metallic phases such as FePt and CoPt, which have very large magnetocrystalline anisotropy, are regarded as attractive candidates. We have deposited at different temperatures by ion beam sputtering C/(FePt/C){sub x20} multilayers, with nominal thickness t{sub C}=4 nm and t{sub FePt}=1 nm. The FePt consists of nanoparticles embedded in the C matrix. Using Rutherford backscattering at grazing angles of incidence, we determined the stoichiometry of the nanoparticles, the multilayer periodicity and the nanoparticle height. We compare the results with X-ray reflectivity, grazing incidence small-angle X-ray scattering, and transmission electron microscopy results.
Characterization of azo dyes on Pt and Pt/polyaniline/dispersed Pt electrodes
Energy Technology Data Exchange (ETDEWEB)
Molina, J.; Fernandez, J.; Rio, A.I. del; Bonastre, J. [Departamento de Ingenieria Textil y Papelera, EPS de Alcoy, Universitat Politecnica de Valencia, Plaza Ferrandiz y Carbonell s/n, 03801 Alcoy (Spain); Cases, F., E-mail: fjcases@txp.upv.es [Departamento de Ingenieria Textil y Papelera, EPS de Alcoy, Universitat Politecnica de Valencia, Plaza Ferrandiz y Carbonell s/n, 03801 Alcoy (Spain)
2012-06-15
The electrochemical characterization of two organic dyes (amaranth and procion orange MX-2R) has been performed on Pt electrodes and Pt electrodes coated with polyaniline and dispersed Pt. Electrodes with different Pt loads have been synthesized and characterized obtaining that a load of 300 {mu}g cm{sup -2} was the optimum one. Scanning electron microscopy (SEM) and atomic force microscopy (AFM) was employed to observe the distribution and morphology of the Pt nanoparticles. The electroactivity of the electrodes has also been characterized by means of scanning electrochemical microscopy (SECM). The chemical characterization of Pt dispersed Pani coated Pt electrodes (Pt-Pani-Pt) was performed by means of X-ray photoelectron spectroscopy (XPS). The electrochemical characterization of the dyes has been performed by means of cyclic voltammetry. Voltammograms have shown that the presence of the dyes diminishes characteristic Pt oxidation and reduction peaks. However, redox processes due to the dyes, appeared in the voltammograms. The different species responsible of these redox processes were generated in the vicinity of the electrode and were not adsorbed on the electrode surface since after stirring, the different redox processes disappeared. Characterization with different scan rates showed that redox processes of both dyes were controlled by diffusion.
Schwarz Methods: To Symmetrize or Not to Symmetrize
Holst, Michael
2010-01-01
A preconditioning theory is presented which establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition and multigrid. It is illustrated why symmetrizing may be a bad idea for linear methods. It is conjectured that enforcing minimal symmetry achieves the best results when combined with conjugate gradient acceleration. Also, it is shown that absence of symmetry in the linear preconditioner is advantageous when the linear method is accelerated by using the Bi-CGstab method. Numerical examples are presented for two test problems which illustrate the theory and conjectures.
Institute of Scientific and Technical Information of China (English)
张臻蓉; 刘洪; 韩宝善
2002-01-01
The domain structure of (PtCoPt)/Si multilayers in the dc demagnetized state has been investigated by magnetic force microscopy. The domain structure is found to change dramatically as the thickness of the non-magnetic Si sublayer(tsi) increases. Together with the analysis of magnetic properties, the variation of the domain period indicates that the domain wall energy decreases. Using the model developed by Draaisma and de Jonge, the domain wall energy is obtained.
Optical waveguide arrays: quantum effects and PT symmetry breaking
Joglekar, Yogesh N; Scott, Derek D; Vemuri, Gautam
2013-01-01
Over the last two decades, advances in fabrication have led to significant progress in creating patterned heterostructures that support either carriers, such as electrons or holes, with specific band structure or electromagnetic waves with a given mode structure and dispersion. In this article, we review the properties of light in coupled optical waveguides that support specific energy spectra, with or without the effects of disorder, that are well-described by a Hermitian tight-binding model. We show that with a judicious choice of the initial wave packet, this system displays the characteristics of a quantum particle, including transverse photonic transport and localization, and that of a classical particle. We extend the analysis to non-Hermitian, parity and time-reversal ($\\mathcal{PT}$) symmetric Hamiltonians which physically represent waveguide arrays with spatially separated, balanced absorption or amplification. We show that coupled waveguides are an ideal candidate to simulate $\\mathcal{PT}$-symmetri...
Fine Spectra of Symmetric Toeplitz Operators
Directory of Open Access Journals (Sweden)
Muhammed Altun
2012-01-01
Full Text Available The fine spectra of 2-banded and 3-banded infinite Toeplitz matrices were examined by several authors. The fine spectra of n-banded triangular Toeplitz matrices and tridiagonal symmetric matrices were computed in the following papers: Altun, “On the fine spectra of triangular toeplitz operators” (2011 and Altun, “Fine spectra of tridiagonal symmetric matrices” (2011. Here, we generalize those results to the (2+1-banded symmetric Toeplitz matrix operators for arbitrary positive integer .
Lee, Ja Bin; An, Gwang Guk; Yang, Seung Mo; Hong, Jin Pyo
2014-11-01
We report the structural and magnetic properties of a [Co/Pt] multilayer matrix as a function of Pt thickness. Increasing Pt thickness allows for the formation of a well-aligned fcc (111) CoPt3 structure in a [Co/Pt]n multilayer geometry, where the clear appearance of main (111) peak of CoPt3 measured using the X-ray diffraction patterns was confirmed. High-resolution transmission electron microscopy images, along with the corresponding fast Fourier transform patterns displayed the ordered structure with clear 6-fold symmetric diffraction spots. The c/a lattice constant ratio of 0.949 was calculated by utilizing the XRD and, demonstrating the presence of a well-aligned CoPt3 structure. The Pt thickness-dependent saturation magnetization (M(s)) values for the in- and out-of-plane M-H hysteresis loops obtained by vibrating sample magnetometer measurements showed distinctly opposite trends. The increase in the out-of-plane M(s) value with increasing Pt thickness seems to originate from the enhanced perpendicular orbital moment of the proper CoPt3 structure.
Classification of symmetric toroidal orbifolds
Energy Technology Data Exchange (ETDEWEB)
Fischer, Maximilian; Ratz, Michael; Torrado, Jesus [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-09-15
We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N{>=}1 supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six dimensions. We find in total 520 inequivalent toroidal orbifolds, 162 of them with Abelian point groups such as Z{sub 3}, Z{sub 4}, Z{sub 6}-I etc. and 358 with non-Abelian point groups such as S{sub 3}, D{sub 4}, A{sub 4} etc. We also briefly explore the properties of some orbifolds with Abelian point groups and N=1, i.e. specify the Hodge numbers and comment on the possible mechanisms (local or non-local) of gauge symmetry breaking.
Classification of symmetric toroidal orbifolds
Energy Technology Data Exchange (ETDEWEB)
Fischer, Maximilian; Ratz, Michael; Torrado, Jesus [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-09-15
We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N{>=}1 supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six dimensions. We find in total 520 inequivalent toroidal orbifolds, 162 of them with Abelian point groups such as Z{sub 3}, Z{sub 4}, Z{sub 6}-I etc. and 358 with non-Abelian point groups such as S{sub 3}, D{sub 4}, A{sub 4} etc. We also briefly explore the properties of some orbifolds with Abelian point groups and N=1, i.e. specify the Hodge numbers and comment on the possible mechanisms (local or non-local) of gauge symmetry breaking.
Symmetric functions and Hall polynomials
MacDonald, Ian Grant
1998-01-01
This reissued classic text is the acclaimed second edition of Professor Ian Macdonald's groundbreaking monograph on symmetric functions and Hall polynomials. The first edition was published in 1979, before being significantly expanded into the present edition in 1995. This text is widely regarded as the best source of information on Hall polynomials and what have come to be known as Macdonald polynomials, central to a number of key developments in mathematics and mathematical physics in the 21st century Macdonald polynomials gave rise to the subject of double affine Hecke algebras (or Cherednik algebras) important in representation theory. String theorists use Macdonald polynomials to attack the so-called AGT conjectures. Macdonald polynomials have been recently used to construct knot invariants. They are also a central tool for a theory of integrable stochastic models that have found a number of applications in probability, such as random matrices, directed polymers in random media, driven lattice gases, and...
A Minimally Symmetric Higgs Boson
Low, Ian
2014-01-01
Models addressing the naturalness of a light Higgs boson typically employ symmetries, either bosonic or fermionic, to stabilize the Higgs mass. We consider a setup with the minimal amount of symmetries: four shift symmetries acting on the four components of the Higgs doublet, subject to the constraints of linearly realized SU(2)xU(1) electroweak symmetry. Up to terms that explicitly violate the shift symmetries, the effective lagrangian can be derived, irrespective of the spontaneously broken group G in the ultraviolet, and is universal in all models where the Higgs arises as a pseudo-Nambu-Goldstone boson (PNGB). Very high energy scatterings of vector bosons could provide smoking gun signals of a minimally symmetric Higgs boson.
Computing symmetric colorings of the dihedral group
Zelenyuk, Yuliya
2016-06-01
A symmetry on a group G is a mapping G ∋ x ↦ gx-1 g ∈ G, where g ∈ G. A subset A ⊆ G is symmetric if it is invariant under some symmetry, that is, A = gA-1g. The notion of symmetry has interesting relations to enumerative combinatorics. A coloring is symmetric if χ(gx-1g) = χ(x) for some g ∈ G. We discuss an approach how to compute the number of symmetric r-colorings for any finite group. Using this approach we derive the formula for the number of symmetric r-colorings of the dihedral group D3.
NMR Study of Layered Transition Metal Ditelluride (Ir,Pt)Te2
Magishi, K.; Saito, T.; Koyama, K.; Matsumoto, N.; Nagata, S.
2012-12-01
We report the results of 125Te and 195Pt NMR measurements on (Ir,Pt)Te2 in order to elucidate the characteristic electronic states. For PtTe2, the NMR spectrum exhibits a sharp line, which shows the uniaxially symmetric powder pattern due to the anisotropic Knight shift. The Knight shift is almost independent of temperature and is larger than that for IrTe2. Also, the nuclear spin-lattice relaxation rate 1/T1 of PtTe2 is proportional to the temperature in a wide temperature range, that is, obeys the Korringa relation as expected for simple metallic systems. From the analyses of the Knight shift and 1/T1, it is suggested that the antiferromagnetic correlations slightly exist.
Gyroid phase of fluids with spherically symmetric competing interactions.
Edelmann, Markus; Roth, Roland
2016-06-01
We study the phase diagram of a fluid with spherically symmetric competing pair interactions that consist of a short-ranged attraction and a longer-ranged repulsion in addition to a hard core. To this end we perform free minimizations of three-dimensional triple periodic structures within the framework of classical density functional theory. We compare our results to those from Landau theory. Our main finding is that the double gyroid phase can exist as a thermodynamically stable phase.
$\\mathcal{PT}$-Symmetry-Breaking Chaos in Optomechanics
Lü, Xin-You; Ma, Jin-Yong; Wu, Ying
2015-01-01
We demonstrate a $\\mathcal{PT}$-symmetry-breaking chaos in optomechanical system (OMS), which features an ultralow driving threshold. In principle, this chaos will emerge once a driving laser is applied to the cavity mode and lasts for a period of time. The driving strength is inversely proportional to the starting time of chaos. This originally comes from the dynamical enhancement of nonlinearity by field localization in $\\mathcal{PT}$-symmetry-breaking phase ($\\mathcal{PT}$BP). Moreover, this chaos is switchable by tuning the system parameters so that a $\\mathcal{PT}$-symmetry phase transition occurs. This work may fundamentally broaden the regimes of cavity optomechanics and nonlinear optics. It offers the prospect of exploring ultralow-power-laser triggered chaos and its potential applications in secret communication.
Automorphism groups of causal symmetric spaces of Cayley type and bounded symmetric domains
Institute of Scientific and Technical Information of China (English)
Soji; Kaneyuki
2005-01-01
Symmetric spaces of Cayley type are a higher dimensional analogue of a onesheeted hyperboloid in R3. They form an important class of causal symmetric spaces. To a symmetric space of Cayley type M, one can associate a bounded symmetric domain of tube type D. We determine the full causal automorphism group of M. This clarifies the relation between the causal automorphism group and the holomorphic automorphism group of D.
Partially locally rotationally symmetric perfect fluid cosmologies
Mustapha, N; Van Elst, H; Marklund, M; Mustapha, Nazeem; Ellis, George F R; Elst, Henk van; Marklund, Mattias
2000-01-01
We show that there are no new consistent perfect fluid cosmologies with the kinematic variables and the electric and magnetic parts of the Weyl curvature all rotationally symmetric about a common axis in an open neighbourhood ${\\cal U}$ of an event. The consistent solutions of this kind are either locally rotationally symmetric, or are subcases of the Szekeres model.
CANONICAL EXTENSIONS OF SYMMETRIC LINEAR RELATIONS
Sandovici, Adrian; Davidson, KR; Gaspar, D; Stratila, S; Timotin, D; Vasilescu, FH
2006-01-01
The concept of canonical extension of Hermitian operators has been recently introduced by A. Kuzhel. This paper deals with a generalization of this notion to the case of symmetric linear relations. Namely, canonical regular extensions of symmetric linear relations in Hilbert spaces are studied. The
Symmetric products, permutation orbifolds and discrete torsion
Bántay, P
2000-01-01
Symmetric product orbifolds, i.e. permutation orbifolds of the full symmetric group S_{n} are considered by applying the general techniques of permutation orbifolds. Generating functions for various quantities, e.g. the torus partition functions and the Klein-bottle amplitudes are presented, as well as a simple expression for the discrete torsion coefficients.
Inversion-symmetric topological insulators
Hughes, Taylor L.; Prodan, Emil; Bernevig, B. Andrei
2011-06-01
We analyze translationally invariant insulators with inversion symmetry that fall outside the current established classification of topological insulators. These insulators exhibit no edge or surface modes in the energy spectrum and hence they are not edge metals when the Fermi level is in the bulk gap. However, they do exhibit protected modes in the entanglement spectrum localized on the cut between two entangled regions. Their entanglement entropy cannot be made to vanish adiabatically, and hence the insulators can be called topological. There is a direct connection between the inversion eigenvalues of the Hamiltonian band structure and the midgap states in the entanglement spectrum. The classification of protected entanglement levels is given by an integer N, which is the difference between the negative inversion eigenvalues at inversion symmetric points in the Brillouin zone, taken in sets of 2. When the Hamiltonian describes a Chern insulator or a nontrivial time-reversal invariant topological insulator, the entirety of the entanglement spectrum exhibits spectral flow. If the Chern number is zero for the former, or time reversal is broken in the latter, the entanglement spectrum does not have spectral flow, but, depending on the inversion eigenvalues, can still exhibit protected midgap bands similar to impurity bands in normal semiconductors. Although spectral flow is broken (implying the absence of real edge or surface modes in the original Hamiltonian), the midgap entanglement bands cannot be adiabatically removed, and the insulator is “topological.” We analyze the linear response of these insulators and provide proofs and examples of when the inversion eigenvalues determine a nontrivial charge polarization, a quantum Hall effect, an anisotropic three-dimensional (3D) quantum Hall effect, or a magnetoelectric polarization. In one dimension, we establish a link between the product of the inversion eigenvalues of all occupied bands at all inversion
Effect of annealing on phase sequence and their composition in the Pt-coated Mo system
Energy Technology Data Exchange (ETDEWEB)
Khumalo, Z.M., E-mail: zakhele@tlabs.ac.za [Department of Physics, University of Cape Town, Private Bag X3, Rondebosch 7701 (South Africa); Materials Research Department, National Research Foundation, iThemba LABS, P.O. Box 722, Somerset West (South Africa); Topić, M. [Materials Research Department, National Research Foundation, iThemba LABS, P.O. Box 722, Somerset West (South Africa); Comrie, C.M. [Department of Physics, University of Cape Town, Private Bag X3, Rondebosch 7701 (South Africa); Materials Research Department, National Research Foundation, iThemba LABS, P.O. Box 722, Somerset West (South Africa); Blumenthal, M. [Department of Physics, University of Cape Town, Private Bag X3, Rondebosch 7701 (South Africa); Pineda-Vargas, C.A.; Bucher, R. [Materials Research Department, National Research Foundation, iThemba LABS, P.O. Box 722, Somerset West (South Africa); Kisslinger, K. [Center for Functional Nanomaterials, Brookhaven National Laboratory, P.O. Box 5000, Upton, NY USA (United States)
2014-11-01
Highlights: • Platinum coatings were prepared using electron beam evaporator. • The phase analysis revealed the presence of the MoPt{sub 2} and MoPt. • At low annealing time, the MoPt{sub 2} phase appeared to have more Pt content. • The MoPt{sub 2} phase disappeared as the annealing time increases. • It is believed that the MoPt phase was growing at the expense of the MoPt{sub 2}. - Abstract: The phase formation sequence and the composition of phases induced by thermal annealing in a platinum (Pt) coated molybdenum (Mo) system were investigated by X-ray diffraction (XRD), Rutherford backscattering spectrometry (RBS) and transmission electron microscopy (TEM). The X-ray diffraction study of a 0.2 μm thick platinum layer deposited on a Mo substrate and annealed at temperatures between 800 °C and 900 °C for different periods of time shows the formation of MoPt{sub 2} and MoPt phases. It was also found that these phases nucleate sequentially and the MoPt{sub 2} phase becomes unstable at 900 °C after a longer annealing time of 8 h. Rutherford backscattering spectroscopy and transmission electron microscopy showed that the coating thickness approximately doubled after thermal annealing, from 0.22 μm to 0.46 μm, due to the formation of the Pt–Mo phases.
Classification of Entanglement in Symmetric States
Aulbach, Martin
2011-01-01
Quantum states that are symmetric with respect to permutations of their subsystems appear in a wide range of physical settings, and they have a variety of promising applications in quantum information science. In this thesis the entanglement of symmetric multipartite states is categorised, with a particular focus on the pure multi-qubit case and the geometric measure of entanglement. An essential tool for this analysis is the Majorana representation, a generalisation of the single-qubit Bloch sphere representation, which allows for a unique representation of symmetric n qubit states by n points on the surface of a sphere. Here this representation is employed to search for the maximally entangled symmetric states of up to 12 qubits in terms of the geometric measure, and an intuitive visual understanding of the upper bound on the maximal symmetric entanglement is given. Furthermore, it will be seen that the Majorana representation facilitates the characterisation of entanglement equivalence classes such as Stoc...
Baryon symmetric big bang cosmology
Stecker, F. W.
1978-01-01
Both the quantum theory and Einsteins theory of special relativity lead to the supposition that matter and antimatter were produced in equal quantities during the big bang. It is noted that local matter/antimatter asymmetries may be reconciled with universal symmetry by assuming (1) a slight imbalance of matter over antimatter in the early universe, annihilation, and a subsequent remainder of matter; (2) localized regions of excess for one or the other type of matter as an initial condition; and (3) an extremely dense, high temperature state with zero net baryon number; i.e., matter/antimatter symmetry. Attention is given to the third assumption, which is the simplest and the most in keeping with current knowledge of the cosmos, especially as pertains the universality of 3 K background radiation. Mechanisms of galaxy formation are discussed, whereby matter and antimatter might have collided and annihilated each other, or have coexisted (and continue to coexist) at vast distances. It is pointed out that baryon symmetric big bang cosmology could probably be proved if an antinucleus could be detected in cosmic radiation.
Symmetric Structure in Logic Programming
Institute of Scientific and Technical Information of China (English)
Jin-Zhao Wu; Harald Fecher
2004-01-01
It is argued that some symmetric structure in logic programs could be taken into account when implementing semantics in logic programming. This may enhance the declarative ability or expressive power of the semantics. The work presented here may be seen as representative examples along this line. The focus is on the derivation of negative information and some other classic semantic issues. We first define a permutation group associated with a given logic program. Since usually the canonical models used to reflect the common sense or intended meaning are minimal or completed models of the program, we expose the relationships between minimal models and completed models of the original program and its so-called G-reduced form newly-derived via the permutation group defined. By means of this G-reduced form, we introduce a rule to assume negative information termed G-CWA, which is actually a generalization of the GCWA. We also develop the notions of G-definite, G-hierarchical and G-stratified logic programs, which are more general than definite, hierarchical and stratified programs, and extend some well-known declarative and procedural semantics to them, respectively.
Substring-Searchable Symmetric Encryption
Directory of Open Access Journals (Sweden)
Chase Melissa
2015-06-01
Full Text Available In this paper, we consider a setting where a client wants to outsource storage of a large amount of private data and then perform substring search queries on the data – given a data string s and a search string p, find all occurrences of p as a substring of s. First, we formalize an encryption paradigm that we call queryable encryption, which generalizes searchable symmetric encryption (SSE and structured encryption. Then, we construct a queryable encryption scheme for substring queries. Our construction uses suffix trees and achieves asymptotic efficiency comparable to that of unencrypted suffix trees. Encryption of a string of length n takes O(λn time and produces a ciphertext of size O(λn, and querying for a substring of length m that occurs k times takes O(λm+k time and three rounds of communication. Our security definition guarantees correctness of query results and privacy of data and queries against a malicious adversary. Following the line of work started by Curtmola et al. (ACM CCS 2006, in order to construct more efficient schemes we allow the query protocol to leak some limited information that is captured precisely in the definition. We prove security of our substring-searchable encryption scheme against malicious adversaries, where the query protocol leaks limited information about memory access patterns through the suffix tree of the encrypted string.
DEFF Research Database (Denmark)
Shao, Jing; Kammer Hansen, Kent
2013-01-01
/CGO electrode by selectively trapping NO2 in the form of nitrate over the BaO sites and provided availability for a direct reduction of the stored nitrate. The BaO-Pt-Al2O3 layer enhanced the NOx adsorption and promoted the formation of NO2 due to the NO oxidation ability of the Pt catalyst, but hindered......This study uses electrochemical impedance spectroscopy (EIS) to characterize an LSM/CGO symmetric cell modified by NOx adsorbents for the application of electrochemical NOx reduction. Three cells were prepared and tested: a blank cell, a cell impregnated with BaO, and a cell coated with a Ba...
PT symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras
Guenther, Uwe
2010-01-01
Gauged PT quantum mechanics (PTQM) and corresponding Krein space setups are studied. For models with constant non-Abelian gauge potentials and extended parity inversions compact and noncompact Lie group components are analyzed via Cartan decompositions. A Lie triple structure is found and an interpretation as PT-symmetrically generalized Jaynes-Cummings model is possible with close relation to recently studied cavity QED setups with transmon states in multilevel artificial atoms. For models with Abelian gauge potentials a hidden Clifford algebra structure is found and used to obtain the fundamental symmetry of Krein space related J-selfadjoint extensions for PTQM setups with ultra-localized potentials.
Identification of {sup 166}Pt and {sup 167}Pt
Energy Technology Data Exchange (ETDEWEB)
Bingham, C.R.; Toth, K.S.; Batchelder, J.C.; Blumenthal, D.J.; Brown, L.T.; Busse, B.C.; Conticchio, L.F.; Davids, C.N.; Davinson, T.; Henderson, D.J.; Irvine, R.J.; Seweryniak, D.; Walters, W.B.; Woods, P.J.; Zimmerman, B.E. [The University of Tennessee, Knoxville, Tennessee 37996 (United States)]|[Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States)]|[Louisiana State University, Baton Rouge, Louisiana 70803 (United States)]|[Argonne National Laboratory, Argonne, Illinois 60439 (United States)]|[Vanderbilt University, Nashville, Tennessee 37235 (United States)]|[Oregon State University, Corvallis, Oregon 97331 (United States)]|[University of Maryland, College Park, Maryland 20742 (United States)]|[Edinburgh University, Edinburgh, EH9 3JZ (United Kingdom)
1996-07-01
In a series of {sup 78}Kr bombardments of {sup 92}Mo the new isotopes {sup 166}Pt and {sup 167}Pt were identified via their {alpha}-decay properties. The {alpha}-decay energies and half-lives of these two nuclides are as follows. (1) {sup 166}Pt, {ital E}{sub {alpha}} = 7110(15) keV, {ital T}{sub 1/2} = 0.3(1) ms, and (2) {sup 167}Pt, {ital E}{sub {alpha}} = 6988(10) keV, {ital T}{sub 1/2} = 0.7(2) ms. Also, the half-life of {sup 168}Pt, which was previously unknown, was determined to be 2.0(4) ms. In a separate but concurrent experiment involving {sup 78}Kr + {sup 96}Ru reactions, {sup 170}Pt was made and a half-life of 14.7(5) ms was measured for it; the one published value is 6{sub {minus}2}{sup +5} ms. Results for {sup 162{minus}164}Os contained in the same data sets were also analyzed and by using mother-daughter correlations, the {alpha} branches of {sup 162,163,164}Os were established to be near 100{percent}. {copyright} {ital 1996 The American Physical Society.}
Symmetric Partial Derivatives%对称偏导数
Institute of Scientific and Technical Information of China (English)
徐永平
2001-01-01
In this paper, symmetric partial derivatives and symmetric total differential of a function of several variables are defined. The relationship between partial derivative and the symmetric partial derivative, the total differential and the symmetric total derivative are discussed. By means of the concept of symmetric partial derivatives, the existence theorem of the total differential of a function of several is obtained.
Coscheduling Technique for Symmetric Multiprocessor Clusters
Energy Technology Data Exchange (ETDEWEB)
Yoo, A B; Jette, M A
2000-09-18
Coscheduling is essential for obtaining good performance in a time-shared symmetric multiprocessor (SMP) cluster environment. However, the most common technique, gang scheduling, has limitations such as poor scalability and vulnerability to faults mainly due to explicit synchronization between its components. A decentralized approach called dynamic coscheduling (DCS) has been shown to be effective for network of workstations (NOW), but this technique is not suitable for the workloads on a very large SMP-cluster with thousands of processors. Furthermore, its implementation can be prohibitively expensive for such a large-scale machine. IN this paper, they propose a novel coscheduling technique based on the DCS approach which can achieve coscheduling on very large SMP-clusters in a scalable, efficient, and cost-effective way. In the proposed technique, each local scheduler achieves coscheduling based upon message traffic between the components of parallel jobs. Message trapping is carried out at the user-level, eliminating the need for unsupported hardware or device-level programming. A sending process attaches its status to outgoing messages so local schedulers on remote nodes can make more intelligent scheduling decisions. Once scheduled, processes are guaranteed some minimum period of time to execute. This provides an opportunity to synchronize the parallel job's components across all nodes and achieve good program performance. The results from a performance study reveal that the proposed technique is a promising approach that can reduce response time significantly over uncoordinated time-sharing and batch scheduling.
The symmetric extendibility of quantum states
Nowakowski, Marcin L.
2016-09-01
Studies on the symmetric extendibility of quantum states have become particularly important in the context of the analysis of one-way quantum measures of entanglement, and the distillability and security of quantum protocols. In this paper we analyze composite systems containing a symmetric extendible part, with particular attention devoted to the one-way security of such systems. Further, we introduce a new one-way entanglement monotone based on the best symmetric approximation of a quantum state and the extendible number of a quantum state. We underpin these results with geometric observations about the structures of multi-party settings which posses substantial symmetric extendible components in their subspaces. The impossibility of reducing the maximal symmetric extendibility by means of the one-way local operations and classical communication method is pointed out on multiple copies. Finally, we state a conjecture linking symmetric extendibility with the one-way distillability and security of all quantum states, analyzing the behavior of a private key in the neighborhood of symmetric extendible states.
Random matrix theory and symmetric spaces
Energy Technology Data Exchange (ETDEWEB)
Caselle, M.; Magnea, U
2004-05-01
In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing the ensembles are in strict correspondence with symmetric spaces and the intrinsic characteristics of their restricted root lattices. Several important results can be obtained from this identification. In particular the Cartan classification of triplets of symmetric spaces with positive, zero and negative curvature gives rise to a new classification of random matrix ensembles. The review is organized into two main parts. In Part I the theory of symmetric spaces is reviewed with particular emphasis on the ideas relevant for appreciating the correspondence with random matrix theories. In Part II we discuss various applications of symmetric spaces to random matrix theories and in particular the new classification of disordered systems derived from the classification of symmetric spaces. We also review how the mapping from integrable Calogero-Sutherland models to symmetric spaces can be used in the theory of random matrices, with particular consequences for quantum transport problems. We conclude indicating some interesting new directions of research based on these identifications.
Problem of the coexistence of several non-Hermitian observables in PT -symmetric quantum mechanics
Znojil, Miloslav; Semorádová, Iveta; RÅ¯žička, František; Moulla, Hafida; Leghrib, Ilhem
2017-04-01
During recent developments in quantum theory it has been clarified that observable quantities (such as energy and position) may be represented by operators Λ (with real spectra) that are manifestly non-Hermitian in a preselected friendly Hilbert space H(F ). The consistency of these models is known to require an upgrade of the inner product, i.e., mathematically speaking, a transition H(F )→H(S ) to another, standard, Hilbert space. We prove that whenever we are given more than one candidate for an observable (i.e., say, two operators Λ0 and Λ1) in advance, such an upgrade need not exist in general.
A class of symmetric controlled quantum operations
Vaccaro, J A; Huelga, S F; Vaccaro, John A.
2001-01-01
Certain quantum gates, such as the controlled-NOT gate, are symmetric in terms of the operation of the control system upon the target system and vice versa. However, no operational criteria yet exist for establishing whether or not a given quantum gate is symmetrical in this sense. We consider a restricted, yet broad, class of two-party controlled gate operations for which the gate transforms a reference state of the target into one of an orthogonal set of states. We show that for this class of gates it is possible to establish a simple necessary and sufficient condition for the gate operation to be symmetric.
A class of symmetric controlled quantum operations
Energy Technology Data Exchange (ETDEWEB)
Vaccaro, John A.; Steuernagel, O.; Huelga, S.F. [Division of Physics and Astronomy, Department of Physical Sciences, University of Hertfordshire, Hatfield (United Kingdom)
2001-09-07
Certain quantum gates, such as the controlled-NOT gate, are symmetric in terms of the operation of the control system upon the target system and vice versa. However, no operational criteria yet exist for establishing whether or not a given quantum gate is symmetrical in this sense. We consider a restricted, yet broad, class of two-party controlled gate operations for which the gate transforms a reference state of the target into one of an orthogonal set of states. We show that for this class of gates it is possible to establish a simple necessary and sufficient condition for the gate operation to be symmetric. (author)
Nilpotent orbits in real symmetric pairs
Dietrich, Heiko; Ruggeri, Daniele; Trigiante, Mario
2016-01-01
In the classification of stationary solutions in extended supergravities with symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play an important role. In this paper we discuss two approaches to determining the nilpotent orbits of a real symmetric pair. We apply our methods to an explicit example, and thereby classify the nilpotent orbits of SL_2(R)^4 acting on the fourth tensor power of the natural 2-dimensional SL_2(R)-module. This makes it possible to classify all stationary solutions of the so-called STU-supergravity model.
Harter, Andrew K.; Lee, Tony E.; Joglekar, Yogesh N.
2016-06-01
Aubry-André-Harper lattice models, characterized by a reflection-asymmetric sinusoidally varying nearest-neighbor tunneling profile, are well known for their topological properties. We consider the fate of such models in the presence of balanced gain and loss potentials ±i γ located at reflection-symmetric sites. We predict that these models have a finite PT -breaking threshold only for specific locations of the gain-loss potential and uncover a hidden symmetry that is instrumental to the finite threshold strength. We also show that the topological edge states remain robust in the PT -symmetry-broken phase. Our predictions substantially broaden the possible experimental realizations of a PT -symmetric system.
Pt/C Fuel Cell Catalyst Degradation
DEFF Research Database (Denmark)
Zana, Alessandro
This thesis investigates the degradation behavior of Pt/C catalysts under simulated automotive conditions. By using the “tool box” synthesis method the Pt loading has been changed from low to high Pt loadings, therefore permitting to study the role of Pt on the degradation of high surface area (H...
Pt/C Fuel Cell Catalyst Degradation
DEFF Research Database (Denmark)
Zana, Alessandro
This thesis investigates the degradation behavior of Pt/C catalysts under simulated automotive conditions. By using the “tool box” synthesis method the Pt loading has been changed from low to high Pt loadings, therefore permitting to study the role of Pt on the degradation of high surface area (H...
Resonant mode conversion in the waveguides with an unbroken and broken PT-symmetry
Vysloukh, Victor A
2014-01-01
We study resonant mode conversion in the PT-symmetric multimode waveguides, where symmetry breaking manifests itself in sequential destabilization (appearance of the complex eigenvalues) of the pairs of adjacent guided modes. We show that the efficient mode conversion is possible even in the presence of the resonant longitudinal modulation of the complex refractive index. The distinguishing feature of the resonant mode conversion in the PT-symmetric structure is a drastic growth of the width of the resonance curve when the gain/losses coefficient approaches a critical value, at which symmetry breaking occurs. We found that in the system with broken symmetry the resonant coupling between exponentially growing mode with stable higher-order one effectively stabilizes dynamically coupled pair of modes and remarkably diminishes the average rate of the total power growth.
Study on the preparation of Pt nanocapsules
Zhang, Yi-fan; Ji, Zhen; Chen, Ke; Liu, Bo-wen; Jia, Cheng-chang; Yang, Shan-wu
2017-01-01
Ag@Pt core-shell nanoparticles (Ag@Pt NPs) were prepared by a co-reduction method. Pt nanocapsules with diameters of less than 10 nm were obtained by an electrochemical method. Cyclic voltammetry (CV) scanning was used to cavitate the Ag@Pt NPs, and the morphology, structure, and cavitation conditions were studied. The results indicate that the effective cavitation conditions to obtain Pt nanoparticles from Ag@Pt NPs are a scanning voltage of 0 to 0.8 V and continuous CV scanning over 2 h. This cavitation method is also applicable for the syntheses of Ir, Ru, and Ru-Pt nanocapsules.
Selective synthesis of secondary amines from nitriles using Pt nanowires as a catalyst.
Lu, Shuanglong; Wang, Jiaqing; Cao, Xueqin; Li, Xinming; Gu, Hongwei
2014-04-04
A new one-pot method has been developed for the selective synthesis of secondary amines via reductive amination of the corresponding nitriles using Pt nanowires as a catalyst. This method allows for the synthesis of both unsymmetrical and symmetrical secondary amines in excellent yields (up to 95%) in the presence or absence of additional amines, respectively. Furthermore, the reaction proceeds under mild conditions and is environmentally benign.
Symmetric centres of braided monoidal categories
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper introduces the concept of‘symmetric centres' of braided monoidal categories. Let H be a Hopf algebra with bijective antipode over a field k. We address the symmetric centre of the Yetter-Drinfel'd module category HH(yD) and show that a left Yetter-Drinfel'd module M belongs to the symmetric centre of HH(yD) if and only if M is trivial. We also study the symmetric centres of categories of representations of quasitriangular Hopf algebras and give a sufficient and necessary condition for the braid of H(M) to induce the braid of (H(H)(A),(○)A,A,φ,l,r), or equivalently, the braid of (A#H(H),(○)A,A,φ,l,r), where A is a quantum commutative H-module algebra.
Martingale Rosenthal inequalities in symmetric spaces
Energy Technology Data Exchange (ETDEWEB)
Astashkin, S V [Samara State University, Samara (Russian Federation)
2014-12-31
We establish inequalities similar to the classical Rosenthal inequalities for sequences of martingale differences in general symmetric spaces; a central role is played here by the predictable quadratic characteristic of a martingale. Bibliography: 26 titles.
Resistor Networks based on Symmetrical Polytopes
National Research Council Canada - National Science Library
Moody, Jeremy; Aravind, P.K
2015-01-01
This paper shows how a method developed by Van Steenwijk can be generalized to calculate the resistance between any two vertices of a symmetrical polytope all of whose edges are identical resistors...
Spherically symmetric brane spacetime with bulk gravity
Chakraborty, Sumanta; SenGupta, Soumitra
2015-01-01
Introducing term in the five-dimensional bulk action we derive effective Einstein's equation on the brane using Gauss-Codazzi equation. This effective equation is then solved for different conditions on dark radiation and dark pressure to obtain various spherically symmetric solutions. Some of these static spherically symmetric solutions correspond to black hole solutions, with parameters induced from the bulk. Specially, the dark pressure and dark radiation terms (electric part of Weyl curvature) affect the brane spherically symmetric solutions significantly. We have solved for one parameter group of conformal motions where the dark radiation and dark pressure terms are exactly obtained exploiting the corresponding Lie symmetry. Various thermodynamic features of these spherically symmetric space-times are studied, showing existence of second order phase transition. This phenomenon has its origin in the higher curvature term with gravity in the bulk.
Symmetric states: Their nonlocality and entanglement
Energy Technology Data Exchange (ETDEWEB)
Wang, Zizhu; Markham, Damian [CNRS LTCI, Département Informatique et Réseaux, Telecom ParisTech, 23 avenue d' Italie, CS 51327, 75214 Paris CEDEX 13 (France)
2014-12-04
The nonlocality of permutation symmetric states of qubits is shown via an extension of the Hardy paradox and the extension of the associated inequality. This is achieved by using the Majorana representation, which is also a powerful tool in the study of entanglement properties of symmetric states. Through the Majorana representation, different nonlocal properties can be linked to different entanglement properties of a state, which is useful in determining the usefulness of different states in different quantum information processing tasks.
Success and decisiveness on proper symmetric games
Freixas Bosch, Josep; Pons Vallès, Montserrat
2015-01-01
The final publication is available at Springer via http://dx.doi.org/10.1007/s10100-013-0332-5 This paper provides a complete study for the possible rankings of success and decisiveness for individuals in symmetric voting systems, assuming anonymous and independent probability distributions. It is proved that for any pair of symmetric voting systems it is always possible to rank success and decisiveness in opposite order whenever the common probability of voting for “acceptance...
Institute of Scientific and Technical Information of China (English)
Jian WANG
2009-01-01
The study of symmetric property in the L2-sense for the non-positive definite operator is motivated by the theory of probability and analysis. This paper presents some sufficient conditions for the existence of symmetric measure for Lévy type operator. Some new examples are illustrated. The present study is an important step for considering various ergodic properties and functional inequalities of Lévy type operator.
Parity-time symmetric quantum critical phenomena
Ashida, Yuto; Ueda, Masahito
2016-01-01
Symmetry plays a central role in the theory of phase transitions. Parity-time (PT) symmetry is an emergent notion in synthetic nonconservative systems, where the gain-loss balance creates a threshold for spontaneous symmetry breaking across which spectral singularity emerges. Considerable studies on PT symmetry have been conducted in optics and weakly interacting open quantum systems. Here by extending the idea of PT symmetry to strongly correlated many-body systems, we discover unconventional quantum critical phenomena, where spectral singularity and quantum criticality conspire to yield an exotic universality class which has no counterpart in known critical phenomena. Moreover, we find that superfluid correlation is anomalously enhanced owing to winding renormalization group flows in a PT-symmetry-broken quantum critical phase. Our findings can experimentally be tested in ultracold atoms.
Mirror-Symmetric Matrices and Their Application
Institute of Scientific and Technical Information of China (English)
李国林; 冯正和
2002-01-01
The well-known centrosymmetric matrices correctly reflect mirror-symmetry with no component or only one component on the mirror plane. Mirror-symmetric matrices defined in this paper can represent mirror-symmetric structures with various components on the mirror plane. Some basic properties of mirror-symmetric matrices were studied and applied to interconnection analysis. A generalized odd/even-mode decomposition scheme was developed based on the mirror reflection relationship for mirror-symmetric multiconductor transmission lines (MTLs). The per-unit-length (PUL) impedance matrix Z and admittance matrix Y can be divided into odd-mode and even-mode PUL matrices. Thus the order of the MTL system is reduced from n to k and k+p, where p(≥0)is the conductor number on the mirror plane. The analysis of mirror-symmetric matrices is related to the theory of symmetric group, which is the most effective tool for the study of symmetry.
Bender, N; Ellis, F M; Kottos, T
2015-01-01
We propose a family of {\\it local} $\\cal{PT}$-symmetric photonic lattices with transverse index gradient $\\omega$, where the emergence of {\\it stable} Bloch-Zener oscillations are controlled by the degree of non-Hermiticity $\\gamma$ of the lattice. In the exact $\\cal{PT}$-symmetric phase we identify a condition between $\\omega$ and $\\gamma$ for which a wavepacket self -imaging together with a cascade of splittings and giant recombinations occurs at various propagation distances. The giant wavepacket recombination is further enhanced by introducing local impurities.
Pt···Pt vs Pt···S contacts between Pt-containing heterobimetallic lantern complexes.
Baddour, Frederick G; Fiedler, Stephanie R; Shores, Matthew P; Bacon, Jeffrey W; Golen, James A; Rheingold, Arnold L; Doerrer, Linda H
2013-12-01
A trio of Pt-based heterobimetallic lantern complexes of the form [(py)PtM(SAc)4(py)] (M = Co, 1; Ni, 2; Zn, 3) with unusual octahedral coordination of Pt(II) was prepared from a reaction of [PtM(SAc)4] with excess pyridine. These dipyridine lantern complexes could be converted to monopyridine derivatives with gentle heat to give the series [PtM(SAc)4(py)] (M = Co, 4; Ni, 5; Zn, 6). An additional family of the form [PtM(SAc)4(pyNH2)] (M = Co, 7; Ni, 8; Zn, 9) was synthesized from reaction of [PtM(SAc)4(OH2)] or [PtM(SAc)4] with 4-aminopyridine. Dimethylsulfoxide and N,N-dimethylformamide were also determined to react with [PtM(SAc)4] (M = Co, Ni), respectively, to give [PtCo(SAc)4(DMSO)](DMSO), 10, and [PtNi(SAc)4(DMF)](DMF), 11. Structural and magnetic data for these compounds and those for two other previously published families, [PtM(tba)4(OH2)] and [PtM(SAc)4(L)], L = OH2, pyNO2, are used to divide the structures among three distinct categories based on Pt···Pt and Pt···S distances. In general, the weaker donors H2O and pyNO2 seem to favor metallophilicity and antiferromagnetic coupling between 3d metal centers. When Pt···S interactions are favored over Pt···Pt ones, no coupling is observed and the pKa of the pyridine donor correlates with the interlantern S···S distance. UV-vis-NIR electronic and (1)H NMR spectra provide complementary characterization as well.
Premature temporal theta (PT theta).
Hughes, J R; Fino, J J; Hart, L A
1987-07-01
A distinctive pattern called premature temporal theta (PT theta) was studied in 436 infants, ranging in age from 24 to 46 weeks. The pattern is seen in early prematurity, maximizes at 29-31 weeks and then diminishes and disappears near term. Usually the pattern is found independently on both temporal areas, but with a right-sided preference. Patients without PT theta or with a significantly low amount had either neurological or non-neurological (medical) conditions. With age there is a tendency for an increase in frequency and a decrease in amplitude. Five different peaks in the amount of this pattern are seen at approximately every month. Unilateral PT theta tends to be seen in older babies, more often on the right side and with an abnormal EEG. An abnormal EEG is usually associated with a delay in both the appearance and disappearance of this wave form. PT theta is also associated mainly with REM or active sleep. A polynomial rather than an exponential or power function best describes these data with changes of age. PT theta may arise from the inferior temporal gyrus and/or especially the transverse gyrus.
Effect of Pt coverage in Pt-deposited Pd nanostructure electrodes on electrochemical properties
Energy Technology Data Exchange (ETDEWEB)
Park, Ah-Reum; Lee, Young-Woo; Kwak, Da-Hee; Park, Kyung-Won [Soongsil University, Seoul (Korea, Republic of)
2015-06-15
We have fabricated Pt-deposited Pd electrodes via a two-gun sputtering deposition system by separately operating Pd and Pt target as a function of sputtering time of Pt target. For Pt-deposited Pd electrodes (Pd/Pt-X), Pd were first deposited on the substrates at 20 W for 5min, followed by depositing Pt on the Pd-only electrodes as a function of sputtering time (X=1, 3, 5, 7, and 10min) at 20W on the Pt target. As the sputtering time of Pt target increased, the portion of Pt on the Pd electrodes increased, representing an increased coverage of Pt on the Pd electrodes. The Pd/Pt-7 electrode having an optimized Pt coverage exhibits an excellent electrocatalytic activity for methanol oxidation reaction.
Electron transport in a Pt-CO-Pt nanocontact: Density functional theory calculations
DEFF Research Database (Denmark)
Strange, Mikkel; Thygesen, Kristian Sommer; Jacobsen, Karsten Wedel
2006-01-01
We have performed first-principles calculations for the mechanic and electric properties of pure Pt nanocontacts and a Pt contact with a single CO molecule adsorbed. For the pure Pt contacts we see a clear difference between point contacts and short chains in good agreement with experiments. We i...... of the transmission function for the Pt-CO-Pt contact, and show that the conductance is largely determined by the local d band at the Pt apex atoms....
Xiao, Pingping; Wang, Xianping; Sun, Jingjing; Huang, Meizhen; Chen, Xianfeng; Cao, Zhuangqi
2012-06-18
A new scheme is proposed to measure the electro-optical (EO) and converse-piezoelectric (CPE) coefficients of the PMN-PT ceramics simultaneously, in which the PMN-PT ceramics acts as the guiding layer of a symmetrical metal-cladding waveguide. As the applied electric field exerts on the waveguide, the effective refractive index (RI) (or synchronous angle) can be effectively tuned from a selected mode to another adjacent mode owing to the high sensitivity and the small spacing of the ultra-high order modes. Subsequently, a correlation between EO and CPE coefficients is established. With this correlation and the measurement of the effective RI change to the applied voltage, the quadratic EO and CPE coefficients of PMN-PT ceramics are obtained simultaneously. The obtained results are further checked by fitting the variations of effective RI to a quadratic function. Our measurement method can be extended to a wide range of other materials.
Directory of Open Access Journals (Sweden)
Carsten Strohmann
2012-03-01
Full Text Available The title compound, [FePt(C9H9NO2S(C18H15P(C25H22P2(CO3], represents a rare example of an isonitrile-bridged heterobimetallic complex (here Pt and Fe and is an interesting precursor for the preparation of heterodinuclear μ-aminocarbyne complexes, since the basic imine-type N atom of the μ2-C=N–R ligand readily undergoes addition with various electrophiles to afford iminium-like salts. In the crystal, the almost symmetrically bridging μ2-C=N-R ligand (neglecting the different atomic radii of Fe and Pt is strongly bent towards the Fe(CO3 fragment, with a C=N-R angle of only 121.1 (4°.
Performance of plasma sputtered fuel cell electrodes with ultra-low Pt loadings
Energy Technology Data Exchange (ETDEWEB)
Cavarroc, M.; Ennadjaoui, A. [MID Dreux Innovation, CAdD, 4 Rue Albert Caquot-28500 Vernouillet (France); Mougenot, M.; Brault, P.; Escalier, R.; Tessier, Y. [Groupe de Recherches sur l' Energetique des Milieux Ionises, CNRS Universite d' Orleans, BP6744, 14 rue d' Issoudun, 45067 Orleans (France); Durand, J.; Roualdes, S. [Institut Europeen des Membranes, ENSCM, UM2, CNRS, Universite Montpellier 2, CC047, Place Eugene Bataillon, 34095 Montpellier cedex 5 (France); Sauvage, T. [Conditions Extremes et Materiaux, Haute Temperature et Irradiation, UPR3079 CNRS, Site Cyclotron, 3A rue de la Ferollerie, 45071 Orleans Cedex 2 (France); Coutanceau, C. [Laboratoire de Catalyse en Chimie Organique, UMR6503 Universite de Poitiers, CNRS, 86022, Poitiers (France)
2009-04-15
Ultra-low Pt content PEMFC electrodes have been manufactured using magnetron co-sputtering of carbon and platinum on a commercial E-Tek {sup registered} uncatalyzed gas diffusion layer in plasma fuel cell deposition devices. Pt loadings of 0.16 and 0.01 mg cm{sup -2} have been realized. The Pt catalyst is dispersed as small clusters with size less than 2 nm over a depth of 500 nm. PEMFC test with symmetric electrodes loaded with 10 {mu}g cm{sup -2} led to maximum reproducible power densities as high as 0.4 and 0.17 W cm{sup -2} with Nafion {sup registered} 212 and Nafion {sup registered} 115 membranes, respectively. (author)
Hongyan Wu; Zhengbin Gu; Shantao Zhang; G. Hussain
2015-01-01
The CVD-grown graphene as a middle layer was introduced between Pt cylinders and SiO2/Si to extend the application of graphene for improving the wear performance of microelectromechanical systems. Periodic arrays of Pt cylinders were prepared on the graphene/SiO2/Si (Pt/graphene) and SiO2/Si substrate (Pt/SiO2) using the magnetron sputtering technique. To characterize Pt/graphene and Pt/SiO2, nanoindentation and macrotribological tests were performed. The results showed that the friction coef...
Solitonlike solutions of magnetostatic equilibria: Plane-symmetric case
Yoshino, Hirotaka
2008-01-01
We present the plane-symmetric solitonlike solutions of magnetostatic equilibria by solving the nonlinear Grad-Shafranov (GS) equation numerically. The solutions have solitonlike and periodic structures in the $x$ and $y$ directions, respectively, and $z$ is the direction of plane symmetry. Although such solutions are unstable against the numerical iteration, we give the procedure to realize the sufficient convergence. Our result provides the definite answer for the existence of the solitonlike solutions that was questioned in recent years. The method developed in this paper will make it possible to study the axisymmetric solitonlike solutions of the nonlinear GS equation, which could model astrophysical jets with knotty structures.
Directory of Open Access Journals (Sweden)
Hongyan Wu
2015-01-01
Full Text Available The CVD-grown graphene as a middle layer was introduced between Pt cylinders and SiO2/Si to extend the application of graphene for improving the wear performance of microelectromechanical systems. Periodic arrays of Pt cylinders were prepared on the graphene/SiO2/Si (Pt/graphene and SiO2/Si substrate (Pt/SiO2 using the magnetron sputtering technique. To characterize Pt/graphene and Pt/SiO2, nanoindentation and macrotribological tests were performed. The results showed that the friction coefficient was lower and the wear lifetime of Pt/graphene was longer than those of Pt/SiO2. Graphene, as a middle layer, was not only observed to have significant influence on the mechanical properties (i.e., microhardness and elastic modulus, but also found to improve the adhesive strength between SiO2/Si and Pt cylinders.
Electrodeposited CoPt and FePt alloys nanowires
Energy Technology Data Exchange (ETDEWEB)
Cagnon, L. [Laboratoire de Cristallographie, CNRS, BP 166, 38042 Grenoble cedex 9 (France)]. E-mail: laurent.cagnon@grenoble.cnrs.fr; Dahmane, Y. [Laboratoire Louis Neel, CNRS, BP 166, 38042 Grenoble cedex 9 (France); Laboratoire de Materiaux, Electrochimie et Corrosion, BP 17, 15000 Tizi-Ouzou (Algeria); Voiron, J. [Laboratoire Louis Neel, CNRS, BP 166, 38042 Grenoble cedex 9 (France); Pairis, S. [Laboratoire de Cristallographie, CNRS, BP 166, 38042 Grenoble cedex 9 (France); Bacia, M. [Laboratoire de Cristallographie, CNRS, BP 166, 38042 Grenoble cedex 9 (France); Ortega, L. [Laboratoire de Cristallographie, CNRS, BP 166, 38042 Grenoble cedex 9 (France); Benbrahim, N. [Laboratoire de Materiaux, Electrochimie et Corrosion, BP 17, 15000 Tizi-Ouzou (Algeria); Kadri, A. [Laboratoire de Materiaux, Electrochimie et Corrosion, BP 17, 15000 Tizi-Ouzou (Algeria)
2007-03-15
We have investigated CoPt and FePt alloys with the face centered tetragonal phase L10, which present very large magnetocrystalline anisotropy. Equiatomic CoPt nanowires exhibiting large coercive fields up to 1.1 T have been successfully prepared by electrodeposition into nanopores of commercial and home-made alumina membranes from a very simple electrolyte. The as-deposited material has the FCC structure with soft magnetic properties. An annealing treatment at 700 deg. C is crucial to transform this phase into the L1{sub 0} phase, which presents hard magnetic properties. Nanowires of annealed samples consist of small grains around 20 nm, with their c axes randomly distributed. The coercivity does not depend on the morphology and porosity of the two types of membranes but only on the deposited material elaborated with the appropriate thermal annealing process. Our preliminary results with FePt alloy indicate a more complicated system since the as-deposited material shows no magnetization. Magnetism appears only after annealing at 700-750 deg. C. Coercivity up to 0.85 T has been obtained at room temperature but with inhomogeneous phase composition. To achieve a single hard phase L1{sub 0}, it is essential to get for the as-deposited sample the equiatomic composition and then to employ the suitable annealing parameters (temperature and time) to change the whole FCC phase into the FCT ordered L1{sub 0} phase.
Liu, Mingfeng; Hao, Liang; Jin, Tianli; Cao, Jiangwei; Bai, Jianmin; Wu, Dongping; Wang, Ying; Wei, Fulin
2015-06-01
The effect of electric field (E-field) on the magnetism of FePt thin films in FePt/0.7Pb(Mg1/3Nb2/3)O3-0.3PbTiO3 (PMN-PT) heterostructures was investigated by anomalous Hall effect measurement. For FePt films of different thicknesses, the coercivity vs E-field curves show a typical butterfly-like loop behavior. Further results indicate that the coercivity variation is composed of the volatile symmetrical butterfly-like loop and nonvolatile hysteresis loop-like parts, which originate from the volatile and nonvolatile strains induced by the E-field in the PMN-PT(001) substrate, respectively. No significant difference has been observed after inserting a 2 nm W interlayer, suggesting that the charge-mediated coercivity variation is negligible in FePt/PMN-PT heterostructures.
On the quantum levels of isolated spherically symmetric gravitational systems
Kastrup, H A
1996-01-01
The known canonical quantum theory of a spherically symmetric pure (Schwarzschild) gravitational system describes isolated black holes by plane waves exp(-iMc^2\\tau/\\hbar) with respect to their continuous masses M and the proper time \\tau of observers at spatial infinity. On the other hand Bekenstein and Mukhanov postulated discrete mass levels for such black holes in the spirit of the Bohr- Sommerfeld quantisation in atomic physics. The two approaches can be related by postulating periodic boundary conditions in time for the plane waves and by iden- tifying the period \\Delta in real time with the period \\Delta_H = 8\\pi GM/c^3 in Euclidean time. This yields the mass spectrum M_n = (1/2)\\sqrt{n}m_P, n=1,2,...
Ab-initio study of the coadsorption of Li and H on Pt(001), Pt(110) and Pt(111) surfaces
Energy Technology Data Exchange (ETDEWEB)
Saad, Farida [Laboratoire de Physique et Chimie Quantique, Faculte des Sciences, Universite Mouloud Mammeri, 15000 Tizi-Ouzou (Algeria); Zemirli, Mourad, E-mail: zemirlimourad@mail.ummto.dz [Laboratoire de Physique et Chimie Quantique, Faculte des Sciences, Universite Mouloud Mammeri, 15000 Tizi-Ouzou (Algeria); Benakki, Mouloud; Bouarab, Said [Laboratoire de Physique et Chimie Quantique, Faculte des Sciences, Universite Mouloud Mammeri, 15000 Tizi-Ouzou (Algeria)
2012-02-15
The coadsorption of Li and H atoms on Pt(001), Pt(110) and Pt(111) surfaces is studied using density functional theory with generalised gradient approximation. In all calculations Li, H and the two topmost layers of the metal were allowed to relax. At coverage of 0.25 mono-layer in a p(2 Multiplication-Sign 2) unit cell, lithium adsorption at the hollow site for the three surfaces is favoured over top and bridge sites. The most favoured adsorption sites for H atom on the Pt(001) and Pt(110) surfaces are the top and bridge sites, while on Pt(111) surface the fcc site appears to be slightly favoured over the hcp site. The coadsorption of Li and atomic hydrogen shows that the interaction between the two adsorbates is stabilising when they are far from each other. The analysis of Li, H and Pt local density of states shows that Li strongly interacts with the Pt surfaces.
Insight into the Reaction Mechanisms of Methanol on PtRu/Pt(111): A Density Functional Study
Ding, Qiuyue; Xu, Wenbin; Sang, Pengpeng; Xu, Jing; Zhao, Lianming; He, Xiaoli; Guo, Wenyue
2016-04-01
Periodic DFT calculations have been performed to systematically investigate the mechanisms of methanol decomposition and oxidation on the PtRu/Pt(111) surface. Geometries and energies for the primary species involved are analyzed and the reaction network has been mapped out. The calculation shows that among three initial Csbnd H, Osbnd H, and Csbnd O bond scissions of methanol, the Osbnd H bond scission is found to be the most favorable and bears a lower energy barrier than the desorption of methanol. The decomposition of CH3O occurs via the path CH3O → CH2O → CHO → CO with the limiting step of the first dehydrogenation. Although the oxidation of CO is hindered by a high barrier, the CHO oxidation to CHOOH could occur facilely. Further decomposition of formic acid to CO2 and/or CO could occur via four possible pathways, that is, initial Csbnd H, Osbnd H, and Csbnd O bond activations as well as simultaneous activation of Csbnd H and Csbnd O bonds, where the first pathway, HCOOH → COOH → CO2, is the most favorable from a kinetic point of view. Compared to that on Pt(111), methanol on PtRu/Pt(111) prefers to decomposition rather than desorption and then oxidation via the favorable non-CO path with a lower rate-determining energy barrier of CH3O → CH2O for the whole reaction, which indicates that PtRu alloy can improved tolerance toward CO poisoning compared with pure Pt.
Predicting Pt-195 NMR chemical shift using new relativistic all-electron basis set.
Paschoal, D; Guerra, C Fonseca; de Oliveira, M A L; Ramalho, T C; Dos Santos, H F
2016-10-01
Predicting NMR properties is a valuable tool to assist the experimentalists in the characterization of molecular structure. For heavy metals, such as Pt-195, only a few computational protocols are available. In the present contribution, all-electron Gaussian basis sets, suitable to calculate the Pt-195 NMR chemical shift, are presented for Pt and all elements commonly found as Pt-ligands. The new basis sets identified as NMR-DKH were partially contracted as a triple-zeta doubly polarized scheme with all coefficients obtained from a Douglas-Kroll-Hess (DKH) second-order scalar relativistic calculation. The Pt-195 chemical shift was predicted through empirical models fitted to reproduce experimental data for a set of 183 Pt(II) complexes which NMR sign ranges from -1000 to -6000 ppm. Furthermore, the models were validated using a new set of 75 Pt(II) complexes, not included in the descriptive set. The models were constructed using non-relativistic Hamiltonian at density functional theory (DFT-PBEPBE) level with NMR-DKH basis set for all atoms. For the best model, the mean absolute deviation (MAD) and the mean relative deviation (MRD) were 150 ppm and 6%, respectively, for the validation set (75 Pt-complexes) and 168 ppm (MAD) and 5% (MRD) for all 258 Pt(II) complexes. These results were comparable with relativistic DFT calculation, 200 ppm (MAD) and 6% (MRD). © 2016 Wiley Periodicals, Inc.
Symmetric cryptographic protocols for extended millionaires' problem
Institute of Scientific and Technical Information of China (English)
LI ShunDong; WANG DaoShun; DAI YiQi
2009-01-01
Yao's millionaires' problem is a fundamental problem in secure multiparty computation, and its solutions have become building blocks of many secure multiparty computation solutions. Unfortunately,most protocols for millionaires' problem are constructed based on public cryptography, and thus are inefficient. Furthermore, all protocols are designed to solve the basic millionaires' problem, that is,to privately determine which of two natural numbers is greater. If the numbers are real, existing solutions do not directly work. These features limit the extensive application of the existing protocols. This study introduces and refines the first symmetric cryptographic protocol for the basic millionaires' problem, and then extends the symmetric cryptographic protocol to privately determining which of two real numbers is greater, which are called the extended millionaires' problem, and proposes corresponding Constructed based on symmetric cryptography, these protocols are very efficient.
Chiral light by symmetric optical antennas
Mekonnen, Addis; Zubritskaya, Irina; Jönsson, Gustav Edman; Dmitriev, Alexandre
2014-01-01
Chirality is at the origin of life and is ubiquitous in nature. An object is deemed chiral if it is non-superimposable with its own mirror image. This relates to how circularly polarized light interacts with such object, a circular dichroism, the differential absorption of right and left circularly polarized light. According to the common understanding in biology, chemistry and physics, the circular dichroism results from an internal chiral structure or external symmetry breaking by illumination. We show that circular dichroism is possible with simple symmetric optical nanoantennas at symmetric illumination. We experimentally and theoretically demonstrate that two electromagnetic dipole-like modes with a phase lag, in principle, suffice to produce circular dichroism in achiral structure. Examples of the latter are all visible spectrum optical nanoantennas, symmetric nanoellipses and nanodimers. The simplicity and generality of this finding reveal a whole new significance of the electromagnetic design at a nan...
The Robust Assembly of Small Symmetric Nanoshells.
Wagner, Jef; Zandi, Roya
2015-09-01
Highly symmetric nanoshells are found in many biological systems, such as clathrin cages and viral shells. Many studies have shown that symmetric shells appear in nature as a result of the free-energy minimization of a generic interaction between their constituent subunits. We examine the physical basis for the formation of symmetric shells, and by using a minimal model, demonstrate that these structures can readily grow from the irreversible addition of identical subunits. Our model of nanoshell assembly shows that the spontaneous curvature regulates the size of the shell while the mechanical properties of the subunit determine the symmetry of the assembled structure. Understanding the minimum requirements for the formation of closed nanoshells is a necessary step toward engineering of nanocontainers, which will have far-reaching impact in both material science and medicine.
INERTIA SETS OF SYMMETRIC SIGN PATTERN MATRICES
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A sign pattern matrix is a matrixwhose entries are from the set {+ ,- ,0}. The symmetric sign pattern matrices that require unique inertia have recently been characterized. The purpose of this paper is to more generally investigate the inertia sets of symmetric sign pattern matrices. In particular, nonnegative fri-diagonal sign patterns and the square sign pattern with all + entries are examined. An algorithm is given for generating nonnegative real symmetric Toeplitz matrices with zero diagonal of orders n≥3 which have exactly two negative eigenvalues. The inertia set of the square pattern with all + off-diagonal entries and zero diagonal entries is then analyzed. The types of inertias which can be in the inertia set of any sign pattern are also obtained in the paper. Specifically, certain compatibility and consecutiveness properties are established.
Symmetric States on the Octonionic Bloch Ball
Graydon, Matthew
2012-02-01
Finite-dimensional homogeneous self-dual cones arise as natural candidates for convex sets of states and effects in a variety of approaches towards understanding the foundations of quantum theory in terms of information-theoretic concepts. The positive cone of the ten-dimensional Jordan-algebraic spin factor is one particular instantiation of such a convex set in generalized frameworks for quantum theory. We consider a projection of the regular 9-simplex onto the octonionic projective line to form a highly symmetric structure of ten octonionic quantum states on the surface of the octonionic Bloch ball. A uniform subnormalization of these ten symmetric states yields a symmetric informationally complete octonionic quantum measurement. We discuss a Quantum Bayesian reformulation of octonionic quantum formalism for the description of two-dimensional physical systems. We also describe a canonical embedding of the octonionic Bloch ball into an ambient space for states in usual complex quantum theory.
Local neighborliness of the symmetric moment curve
Lee, Seung Jin
2011-01-01
A centrally symmetric analogue of the cyclic polytope, the bicyclic polytope, was defined in [BN08]. The bicyclic polytope is defined by the convex hull of finitely many points on the symmetric moment curve where the set of points has a symmetry about the origin. In this paper, we study the Barvinok-Novik orbitope, the convex hull of the symmetric moment curve. It was proven in [BN08] that the orbitope is locally $k$-neighborly, that is, the convex hull of any set of $k$ distinct points on an arc of length not exceeding $\\phi_k$ in $\\mathbb{S}^1$ is a $(k-1)$-dimensional face of the orbitope for some positive constant $\\phi_k$. We prove that we can choose $\\phi_k $ bigger than $\\gamma k^{-3/2} $ for some positive constant $\\gamma$.
Radiative corrections in symmetrized classical electrodynamics
Van Meter JR; Kerman; Chen; Hartemann
2000-12-01
The physics of radiation reaction for a point charge is discussed within the context of classical electrodynamics. The fundamental equations of classical electrodynamics are first symmetrized to include magnetic charges: a double four-potential formalism is introduced, in terms of which the field tensor and its dual are employed to symmetrize Maxwell's equations and the Lorentz force equation in covariant form. Within this framework, the symmetrized Dirac-Lorentz equation is derived, including radiation reaction (self-force) for a particle possessing both electric and magnetic charge. The connection with electromagnetic duality is outlined, and an in-depth discussion of nonlocal four-momentum conservation for the wave-particle system is given.
Symmetry theorems via the continuous steiner symmetrization
Directory of Open Access Journals (Sweden)
L. Ragoub
2000-06-01
Full Text Available Using a new approach due to F. Brock called the Steiner symmetrization, we show first that if $u$ is a solution of an overdetermined problem in the divergence form satisfying the Neumann and non-constant Dirichlet boundary conditions, then $Omega$ is an N-ball. In addition, we show that we can relax the condition on the value of the Dirichlet boundary condition in the case of superharmonicity. Finally, we give an application to positive solutions of some semilinear elliptic problems in symmetric domains for the divergence case.
Synthesis of cyclically symmetric five-ports
DEFF Research Database (Denmark)
Guldbrandsen, Tom
1994-01-01
A class of matched, symmetric five-ports have been synthesized by solving the circular cylindrical wave equation. Among the solutions are chosen those for which the match condition is fulfilled over the broadest bandwidth. Bandwidths up to +/-20% have been found......A class of matched, symmetric five-ports have been synthesized by solving the circular cylindrical wave equation. Among the solutions are chosen those for which the match condition is fulfilled over the broadest bandwidth. Bandwidths up to +/-20% have been found...
Active Sound Localization in a Symmetric Environment
Directory of Open Access Journals (Sweden)
Jordan Brindza
2013-07-01
Full Text Available Localization for humanoid robots becomes difficult when events that disrupt robot positioning information occur. This holds especially true in symmetric environments because landmark data may not be sufficient to determine orientation. We propose a system of localizing humanoid robots in a known, symmetric environment using a Rao-Blackwellized particle filter and a sound localization system. This system was used in the RoboCup Standard Platform League, and has been found to reduce the amount of own-goals scored as compared with the previously used localization system without sound.
Time-Symmetric Approach to Gravity
Chu, S Y
1998-01-01
Quantization of the time symmetric system of interacting strings requires that gravity, just as electromagnetism in Wheeler-Feynman's time symmetric electro- dynamics, also be an "adjunct field" instead of an independent entity. The "adjunct field" emerges, at a scale large compared to that of the strings, as a "statistic" that summarizes how the string positions in the underlying space- time are "compactified" into those in Minkowski space. We are able to show, WITHOUT adding a scalar curvature term to the string action, that the "adjunct gravitational field" satisfies Einstein's equation with no cosmological term.
Benign symmetric lipomatosis of the knees
Institute of Scientific and Technical Information of China (English)
Zhiqiang Yin; Di Wu; Yixin Ge; Meihua Zhang; Zhigang Bi; Dan Luo
2008-01-01
Benign symmetric lipomatosis(BSL) is a rare disease characterized by the presence of multiple, symmetric and nonencapsulated fat masses in the face, neck and other areas. It is commonly seen in middle-aged Caucasian Mediterranean males, while its etiology is still not clear. The majority of the patients with BSL have a history of alcohol abuse and hepatopathy. BSL of the limbs is very rare. This article reports a unique case of a 60-year-old Chinese woman with involvement of the knees confirmed by the results of magnetic resonance imaging(MRI) and histopathology, which was not described previously in published literatures.
Inflation in spherically symmetric inhomogeneous models
Energy Technology Data Exchange (ETDEWEB)
Stein-Schabes, J.A.
1986-11-01
Exact analytical solutions of Einstein's equations are found for a spherically symmetric inhomogeneous metric in the presence of a massless scalar field with a flat potential. The process of isotropization and homogenization is studied in detail. It is found that the time dependence of the metric becomes de Sitter for large times. Two cases are studied. The first deals with a homogeneous scalar field, while the second with a spherically symmetric inhomogeneous scalar field. In the former case the metric is of the Robertson-Walker form, while the latter is intrinsically inhomogeneous. 16 refs.
Solitons in a chain of PT-invariant dimers
Suchkov, Sergey V; Dmitriev, Sergey V; Kivshar, Yuri S
2011-01-01
Dynamics of a chain of interacting parity-time invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of the discrete nonlinear Schrodinger (DNLS) equation is demonstrated. Approximate solutions for solitons whose width is large in comparison to the lattice spacing are derived, using a continuum counterpart of the discrete equations. These solitons are mobile, featuring nearly elastic collisions. Stationary solutions for narrow solitons, which are immobile due to the pinning by the effective Peierls-Nabarro potential, are constructed numerically, starting from the anti-continuum limit. The solitons with the amplitude exceeding a certain critical value suffer an instability leading to blowup, which is a specific feature of the nonlinear PT-symmetric chain, making it dynamically different from DNLS lattices. A qualitative explanation of this feature is proposed. The instability...
Results of the Proficiency Test, PT1 and PT2, 2012
DEFF Research Database (Denmark)
Vendramin, Niccolò; Nicolajsen, Nicole; Christophersen, Maj-Britt
A comparative test of diagnostic procedures was provided by the European Union Reference Laboratory (EURL) for Fish Diseases. The test was divided into proficiency test 1 (PT1) and proficiency test 2 (PT2). The number of National Reference Laboratories (NRLs) participating in PT1 and PT2 was 43...
Oxygen reduction activity of Pt and Pt-alloys in acid electrolyte
Energy Technology Data Exchange (ETDEWEB)
Paulus, Ursula A. [Paul Scherrer Inst., CH-5232 Villigen PSI (Switzerland); Schmidt, Thomas J.; Stamenkovic, Vojislav R.; Markovic, Nenad M.; Ross, Philip N. [Material Science Division, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720 (United States)
2001-07-01
The oxygen reduction reaction (ORR) has been studied on polycrystalline (pc) Pt, Pt{sub 3}Ni and Pt{sub 3}Co bulk alloy electrodes and on carbon supported Pt, PtNi and PtCo alloy catalysts. Base voltammetry measurements as well as complementary Auger Electron Spectroscopy (AES) and Low Energy Ion Scattering (LEIS) on bulk electrodes and High Resolution Transmission Electron Microscopy (HRTEM)-analysis on the supported catalysts allow an estimation of the surface composition. By using the rotating ring-disk electrode (RRDE) technique both the kinetic analysis of the ORR and in parallel the detection and quantification of the amount of peroxide produced during the ORR are possible. The activity for the ORR increases in the order Pt < Pt{sub 3}Ni < Pt{sub 3}Co for equally prepared bulk alloys and Pt < Pt{sub 3}Ni {approx} Pt{sub 3}CO < PtCo for the carbon supported catalysts, respectively. It was proposed that the mechanism for the ORR is the same on pure Pt and the PtNi and PtCo alloys. (author)
Hydrogen Adsorption on Pt, Rh and Pt-Rh Electrodes
Institute of Scientific and Technical Information of China (English)
贾梦秋; A.M.Meretskyi
2005-01-01
The hydrogen adsorption on Pt-Rh alloys in sulfuric acid aqueous solutions was studied by the method of cathode pulses. Hydrogen adsorption on the electrode with all ratio of alloy components (ωRh = 0-100%) is well described by the Temkin logarithmic isotherm. The surface coverage by adsorbed hydrogen at the same potential is decreased with increasing content of rhodium in the system. A linear dependence of adsorption peak potential on the alloy compositions in the case of weakly bonded adsorbed hydrogen is established. Hydrogen adsorption heat as a function of surface coverage for Pt-Rh-electrodes was obtained. The shape of the current-potential curve and position of the weakly bonded hydrogen adsorption on the potential scale are all related to alloy compositions, thus can serve as the basis for the determination surface composition of allovs.
Surface termination of CePt5/Pt (111 ): The key to chemical inertness
Praetorius, C.; Zinner, M.; Held, G.; Fauth, K.
2015-11-01
The surface termination of CePt5/Pt (111 ) is determined experimentally by LEED-IV. In accordance with recent theoretical predictions, a dense Pt terminated surface is being found. Whereas the CePt5 volume lattice comprises Pt kagome layers, additional Pt atoms occupy the associated hole positions at the surface. This finding provides a natural explanation for the remarkable inertness of the CePt5 intermetallic. Implications of the structural relaxations determined by LEED-IV analysis are discussed with regard to observations by scanning tunneling microscopy and electron spectroscopies.
Studies of surface processes of electrocatalytic reduction of CO2 on Pt(210), Pt(310) and Pt(510)
Institute of Scientific and Technical Information of China (English)
FAN; ChunJie; FAN; YouJun; ZHEN; ChunHua; ZHENG; QingWei; SUN; ShiGang
2007-01-01
Surface processes of CO2 reduction on Pt(210), Pt(310), and Pt(510) electrodes were studied by cyclic voltammetry. Different surface structures of these platinum single crystal electrodes were obtained by various treatment conditions. The experimental results illustrated that the electrocatalytic activity of Pt single crystal electrodes towards CO2 reduction is decreased in an order of Pt(210)＞Pt(310)＞Pt(510), i.e., with the decrease of (110) step density on well-defined surfaces. When the surfaces were reconstructed due to oxygen adsorption, the catalytic activity of all the three electrodes has been enhanced to a certain extent. Although the activity order remains unchanged, the electrocatalytic activity has been enhanced more significantly as the density of (110) step sites is more intensive on the Pt single crystal surface. It has revealed that the more open the surface structure is, the more active the Pt single crystal electrode will be, and the easier for the electrode to be transformed into a surface structure that exhibits higher activity under external inductions. However, the relatively ordered surfaces of Pt single crystal electrode are comparatively stable under the same external inductions. The present study has gained knowledge on the interaction between CO2 and Pt single crystal electrode surfaces at a microscopic level, and thrown new insight into understanding the surface processes of electrocatalytic reduction of CO2.
Highly active Pt3Pb and core-shell Pt3Pb-Pt electrocatalysts for formic acid oxidation.
Kang, Yijin; Qi, Liang; Li, Meng; Diaz, Rosa E; Su, Dong; Adzic, Radoslav R; Stach, Eric; Li, Ju; Murray, Christopher B
2012-03-27
Formic acid is a promising chemical fuel for fuel cell applications. However, due to the dominance of the indirect reaction pathway and strong poisoning effects, the development of direct formic acid fuel cells has been impeded by the low activity of existing electrocatalysts at desirable operating voltage. We report the first synthesis of Pt(3)Pb nanocrystals through solution phase synthesis and show they are highly efficient formic acid oxidation electrocatalysts. The activity can be further improved by manipulating the Pt(3)Pb-Pt core-shell structure. Combined experimental and theoretical studies suggest that the high activity from Pt(3)Pb and the Pt-Pb core-shell nanocrystals results from the elimination of CO poisoning and decreased barriers for the dehydrogenation steps. Therefore, the Pt(3)Pb and Pt-Pb core-shell nanocrystals can improve the performance of direct formic acid fuel cells at desired operating voltage to enable their practical application. © 2012 American Chemical Society
Fields, Strings, Matrices and Symmetric Products
Dijkgraaf, R.
1999-01-01
In these notes we review the role played by the quantum mechanics and sigma models of symmetric product spaces in the light-cone quantization of quantum field theories, string theory and matrix theory. Lectures given at the Institute for Theoretical Physics, UC Santa Barbara, January 1998 and the Spring School on String Theory and Mathematics, Harvard University, May 1998.
How Symmetrical Assumptions Advance Strategic Management Research
DEFF Research Database (Denmark)
Foss, Nicolai Juul; Hallberg, Hallberg
2014-01-01
We develop the case for symmetrical assumptions in strategic management theory. Assumptional symmetry obtains when assumptions made about certain actors and their interactions in one of the application domains of a theory are also made about this set of actors and their interactions in other appl...
Noncommutative spherically symmetric spacetimes at semiclassical order
Fritz, Christopher
2016-01-01
Working within the recent formalism of Poisson-Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order $O(\\lambda)$. Here $\\lambda$ is the deformation parameter, plausibly the Planck scale. We find that $r,t,dr,dt$ are all forced to be central, i.e. undeformed at order $\\lambda$, while for each value of $r,t$ we are forced to have a fuzzy sphere of radius $r$ with a unique differential calculus which is necessarily nonassociative at order $\\lambda^2$. We give the spherically symmetric quantisation of the FLRW cosmology in detail and also recover a previous analysis for the Schwarzschild black hole, now showing that the quantum Ricci tensor for the latter vanishes at order $\\lambda$. The quantum Laplace-Beltrami operator for spherically symmetric models turns out to be undeformed at order $\\lambda$ whi...
efficient and convenient synthesis of symmetrical carboxylic ...
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An efficient and convenient procedure for the synthesis of symmetrical .... solution was stirred for 16 h at 35 °C followed by filtration and washing with ... obtained hydrous zirconia sample was ground to fine powder and immersed in 1 M H2SO4 ..... Ullmann's Encyclopedia of Industrial Chemistry, Wiley-VCH: Weinheim; 2002.
Designing new symmetrical facial oligothiophene amphiphiles
Janeliunas, Dainius; Eelkema, Rienk; Nieto-Ortega, Belén; Ramírez Aguilar, Francisco J; López Navarrete, Juan T; van der Mee, Lars; Stuart, Marc C A; Casado, Juan; van Esch, Jan H
2013-01-01
In this study we designed a new class of symmetrical facial oligothiophene amphiphiles, which could be obtained in fewer steps than for previously reported analogues, but still possess the specific substituent sequence to control their backbone curvature. This novel design allows the late-stage intr
Tautological Integrals on Symmetric Products of Curves
Institute of Scientific and Technical Information of China (English)
Zhi Lan WANG
2016-01-01
We propose a conjecture on the generating series of Chern numbers of tautological bundles on symmetric products of curves and establish the rank 1 and rank −1 case of this conjecture. Thus we compute explicitly the generating series of integrals of Segre classes of tautological bundles of line bundles on curves, which has a similar structure as Lehn’s conjecture for surfaces.
Jordan algebraic approach to symmetric optimization
Vieira, M.V.C.
2007-01-01
In this thesis we present a generalization of interior-point methods for linear optimization based on kernel functions to symmetric optimization. It covers the three standard cases of conic optimization: linear optimization, second-order cone optimization and semi-definite optimization. We give an
Symmetrized solutions for nonlinear stochastic differential equations
Directory of Open Access Journals (Sweden)
G. Adomian
1981-01-01
Full Text Available Solutions of nonlinear stochastic differential equations in series form can be put into convenient symmetrized forms which are easily calculable. This paper investigates such forms for polynomial nonlinearities, i.e., equations of the form Ly+ym=x where x is a stochastic process and L is a linear stochastic operator.
Spectrum generating algebra of the symmetric top
Energy Technology Data Exchange (ETDEWEB)
Bijker, R. [Universidad Nacional Autonoma de Mexico, Mexico City (Mexico). Inst. de Ciencias Nucleares; Leviatan, A. [Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel)
1998-03-02
We consider an algebraic treatment of a three-body system. We develop the formalism for a system of three identical objects and show that it provides a simultaneous description of the vibrational and rotational excitations of an oblate symmetric top. (orig.) 8 refs.
Spectrum generating algebra of the symmetric top
Bijker, R
1997-01-01
We consider an algebraic treatment of a three-body system. We develop the formalism for a system of three identical objects and show that it provides a simultaneous description of the vibrational and rotational excitations of an oblate symmetric top.
Fourier inversion on a reductive symmetric space
Ban, E.P. van den
2001-01-01
Let X be a semisimple symmetric space. In previous papers, [8] and [9], we have dened an explicit Fourier transform for X and shown that this transform is injective on the space C 1 c (X) ofcompactly supported smooth functions on X. In the present paper, which is a continuation of these papers, we e
The Symmetric Rudin-Shapiro Transform
DEFF Research Database (Denmark)
Harbo, Anders La-Cour
2003-01-01
A method for constructing spread spectrum sequences is presented. The method is based on a linear, orthogonal, symmetric transform, the Rudin-Shapiro transform (RST), which is in many respects quite similar to the Haar wavelet packet transform. The RST provides the means for generating large sets...
The Symmetric Rudin-Shapiro Transform
DEFF Research Database (Denmark)
Harbo, Anders La-Cour
2003-01-01
A method for constructing spread spectrum sequences is presented. The method is based on a linear, orthogonal, and symmetric transform given as the Rudin-Shapiro transform (RST), which is in many respects quite similar to the Haar wavelet packet transform. The RST provides the means for generating...
Unary self-verifying symmetric difference automata
CSIR Research Space (South Africa)
Marais, Laurette
2016-07-01
Full Text Available We investigate self-verifying nondeterministic finite automata, in the case of unary symmetric difference nondeterministic finite automata (SV-XNFA). We show that there is a family of languages Ln=2 which can always be represented non...
Exterior Powers of Symmetric Bilinear Forms
Institute of Scientific and Technical Information of China (English)
Seán McGarraghy
2002-01-01
We study exterior powers of classes of symmetric bilinear forms in the Witt-Grothendieck ring of a field of characteristic not equal to 2, and derive their basic properties. The exterior powers are used to obtain annihilating polynomials for quadratic forms in the Witt ring.
Realizability of stationary spherically symmetric transonic accretion
Ray, A K; Ray, Arnab K.
2002-01-01
The spherically symmetric stationary transonic (Bondi) flow is considered a classic example of an accretion flow. This flow, however, is along a separatrix, which is usually not physically realizable. We demonstrate, using a pedagogical example, that it is the dynamics which selects the transonic flow.
Adaptively Secure Computationally Efficient Searchable Symmetric Encryption
Sedghi, S.; Liesdonk, van P.; Doumen, J.M.; Hartel, P.H.; Jonker, W.
2009-01-01
Searchable encryption is a technique that allows a client to store documents on a server in encrypted form. Stored documents can be retrieved selectively while revealing as little information as possible to the server. In the symmetric searchable encryption domain, the storage and the retrieval are
On balanced truncation for symmetric nonlinear systems
Fujimoto, K.; Scherpen, Jacqueline M.A.
2014-01-01
This paper is concerned with model order reduction based on balanced realization for symmetric nonlinear systems. A new notion of symmetry for nonlinear systems was characterized recently. It plays an important role in linear systems theory and is expected to provide new insights to nonlinear system
Fundamental group of locally symmetric varieties
Sankaran, G K
1995-01-01
Take a bounded symmetric domain D and an arithmetic subgroup \\Gamma of {\\rm Aut}(D). Take the quotient D/\\Gamma, compactify and resolve the singularities. We study the fundamental group of the compact complex manifolds that result from this procedure, and in particular the case of Siegel modular threefolds.
Qp-spaces on bounded symmetric domains
Directory of Open Access Journals (Sweden)
Jonathan Arazy
2008-01-01
Full Text Available We generalize the theory of Qp spaces, introduced on the unit disc in 1995 by Aulaskari, Xiao and Zhao, to bounded symmetric domains in Cd, as well as to analogous Moebius-invariant function spaces and Bloch spaces defined using higher order derivatives; the latter generalization contains new results even in the original context of the unit disc.
Onthe static and spherically symmetric gravitational field
Gottlieb, Ioan; Maftei, Gheorghe; Mociutchi, Cleopatra
Starting from a generalization of Einstein 's theory of gravitation, proposed by one of the authors (Cleopatra Mociutchi), the authors study a particular spherical symmetric case. Among other one obtain the compatibility conditions for the existence of the static and spherically symmetruic gravitational filed in the case of extended Einstein equation.
Some aspects of symmetric Gamma process mixtures
Naulet, Zacharie; Barat, Eric
2015-01-01
In this article, we present some specific aspects of symmetric Gamma process mixtures for use in regression models. We propose a new Gibbs sampler for simulating the posterior and we establish adaptive posterior rates of convergence related to the Gaussian mean regression problem.
Super-symmetric informationally complete measurements
Energy Technology Data Exchange (ETDEWEB)
Zhu, Huangjun, E-mail: hzhu@pitp.ca
2015-11-15
Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is intimately connected with the geometry of the quantum state space and also has profound implications for foundational studies. Here we explore those SICs that are most symmetric according to a natural criterion and show that all of them are covariant with respect to the Heisenberg–Weyl groups, which are characterized by the discrete analog of the canonical commutation relation. Moreover, their symmetry groups are subgroups of the Clifford groups. In particular, we prove that the SIC in dimension 2, the Hesse SIC in dimension 3, and the set of Hoggar lines in dimension 8 are the only three SICs up to unitary equivalence whose symmetry groups act transitively on pairs of SIC projectors. Our work not only provides valuable insight about SICs, Heisenberg–Weyl groups, and Clifford groups, but also offers a new approach and perspective for studying many other discrete symmetric structures behind finite state quantum mechanics, such as mutually unbiased bases and discrete Wigner functions.
Convexity and symmetrization in relativistic theories
Ruggeri, T.
1990-09-01
There is a strong motivation for the desire to have symmetric hyperbolic field equations in thermodynamics, because they guarantee well-posedness of Cauchy problems. A generic quasi-linear first order system of balance laws — in the non-relativistic case — can be shown to be symmetric hyperbolic, if the entropy density is concave with respect to the variables. In relativistic thermodynamics this is not so. This paper shows that there exists a scalar quantity in relativistic thermodynamics whose concavity guarantees a symmetric hyperbolic system. But that quantity — we call it —bar h — is not the entropy, although it is closely related to it. It is formed by contracting the entropy flux vector — ha with a privileged time-like congruencebar ξ _α . It is also shown that the convexity of h plus the requirement that all speeds be smaller than the speed of light c provide symmetric hyperbolic field equations for all choices of the direction of time. At this level of generality the physical meaning of —h is unknown. However, in many circumstances it is equal to the entropy. This is so, of course, in the non-relativistic limit but also in the non-dissipative relativistic fluid and even in relativistic extended thermodynamics for a non-degenerate gas.
Maximum tunneling velocities in symmetric double well potentials
Manz, Jörn; Schmidt, Burkhard; Yang, Yonggang
2014-01-01
We consider coherent tunneling of one-dimensional model systems in non-cyclic or cyclic symmetric double well potentials. Generic potentials are constructed which allow for analytical estimates of the quantum dynamics in the non-relativistic deep tunneling regime, in terms of the tunneling distance, barrier height and mass (or moment of inertia). For cyclic systems, the results may be scaled to agree well with periodic potentials for which semi-analytical results in terms of Mathieu functions exist. Starting from a wavepacket which is initially localized in one of the potential wells, the subsequent periodic tunneling is associated with tunneling velocities. These velocities (or angular velocities) are evaluated as the ratio of the flux densities versus the probability densities. The maximum velocities are found under the top of the barrier where they scale as the square root of the ratio of barrier height and mass (or moment of inertia), independent of the tunneling distance. They are applied exemplarily to ...
Cu-capped surface alloys of Pt/Cu left brace 100 right brace
Alshamaileh, E; Wander, A
2003-01-01
The room-temperature deposition of 0.5 monolayer (ML) Pt on Cu left brace 100 right brace followed by annealing to 525 K results in a sharp c(2 x 2) low-energy electron diffraction (LEED) pattern. The structure of this surface alloy is investigated by means of symmetrized automated tensor low-energy electron diffraction (SATLEED) analysis and ab initio plane wave density functional calculations. The results are then compared with those for the similar system 0.5 ML Pd/Cu left brace 100 right brace. SATLEED results for the Pt/Cu left brace 100 right brace show that it consists of an ordered c(2 x 2) Cu-Pt second layer alloy capped with a pure Cu first layer. The first and second interlayer spacings are found to be expanded by +5.1 +- 1.7 and +3.5 +- 1.7% respectively (relative to the bulk Cu interlayer spacing of 1.807 A) due to the insertion of the 8% larger Pt atoms into the second layer. The ordered mixed layer is found to be rippled by 0.08 +- 0.06 A with Pt atoms rippled outwards towards the solid-vacuum ...
Symmetric key structural residues in symmetric proteins with beta-trefoil fold.
Directory of Open Access Journals (Sweden)
Jianhui Feng
Full Text Available To understand how symmetric structures of many proteins are formed from asymmetric sequences, the proteins with two repeated beta-trefoil domains in Plant Cytotoxin B-chain family and all presently known beta-trefoil proteins are analyzed by structure-based multi-sequence alignments. The results show that all these proteins have similar key structural residues that are distributed symmetrically in their structures. These symmetric key structural residues are further analyzed in terms of inter-residues interaction numbers and B-factors. It is found that they can be distinguished from other residues and have significant propensities for structural framework. This indicates that these key structural residues may conduct the formation of symmetric structures although the sequences are asymmetric.
The limiting form of symmetric instability in geophysical flows
Griffiths, Stephen
2017-04-01
The stability of parallel flow with vertical shear, density stratification and background rotation is of fundamental importance in geophysical fluid dynamics. For a flow with vertical shear Uz and buoyancy frequency N, the dominant instability is typically a symmetric instability (sometimes known as slantwise convection) when 1/4 linear stability problem has been well studied for the case of constant Uz and N, and has some interesting mathematical properties (e.g., non-separable governing PDE, an absence of normal mode solutions in rectangular domains). Here, for the first time, a general theory of symmetric instability is given when Ri varies smoothly with height, thinking of the more realistic case where an unstable layer with Ri 1. The mathematical theory is developed for horizontally periodic disturbances to a basic state with arbitrary smooth N(z), but constant Uz. An asymptotic analysis is used to derive expressions for the most unstable mode, which occurs in the limit of large cross-isentropic wavenumber and takes the form of solutions trapped within the unstable layer; the same result is derived using an interesting generalised parcel dynamics argument, which explicitly shows how the trapping is linked to vertical variations of the potential vorticity. A separate asymptotic analysis is given for the small wavenumber limit, where only one such trapped mode may exist, as expected from the spectral theory of the Schrödinger equation. These two limiting results are shown to be consistent with an exact solution of the linear stability problem that can be obtained for a special choice of N(z). The asymptotic analysis can be extended to allow for weak diffusion at arbitrary Prandtl number, yielding an explicit diffusive scale selection at large wavenumber. Numerical simulations show that these weakly diffusive modes dominate the early stages of the nonlinear evolution of the symmetric instability.
Electrochemical NOx reduction on an LSM/CGO symmetric cell modified by NOx adsorbents
DEFF Research Database (Denmark)
Shao, Jing; Kammer Hansen, Kent
2013-01-01
nitrate reduction. The cell with the BaO/Pt/Al2O3 layer exhibited a preferable performance at low temperatures (350 and 400 °C) and low voltages (1.5 to 2 V) due to the NO oxidation ability of the Pt catalyst, although its performance was relatively poor at elevated temperatures and voltages due......This study investigated the effect of modifying a (La0.85Sr0.15)0.99MnO3 (LSM)/Ce0.9Gd0.1O1.95 (CGO) symmetric cell by NOx adsorbents on the electrochemical reduction of NOx under O2-rich conditions. The modification was based on a full ceramic cell structure without any noble metals. Three cells...... were prepared and tested: a blank cell, a cell impregnated with BaO, and a cell coated with a BaO/Pt/Al2O3 layer. The electrochemical reduction of NOx on the three cells was studied by conversion measurement, degradation testing, and microstructure characterization. The modification, either...
Quasi-symmetric Conjugacy of Blaschke Products on the unit Circle
DEFF Research Database (Denmark)
Petersen, Carsten Lunde
2007-01-01
Let B be a Blaschke product for which the restriction to the unit circle 1 is a degree d > 1 covering. We prove that B is quasi-symmetrically conjugate to z zd on 1, if all its periodic points in 1 are repelling and if 1 does not intersect the -limit set of any recurrent critical point for B....
Symmetric miniaturized heating system for active microelectronic devices
McCracken, Michael; Mayer, Michael; Jourard, Isaac; Moon, Jeong-Tak; Persic, John
2010-07-01
To qualify interconnect technologies such as microelectronic fine wire bonds for mass production of integrated circuit (IC) packages, it is necessary to perform accelerated aging tests, e.g., to age a device at an elevated temperature or to subject the device to thermal cycling and measure the decrease of interconnect quality. There are downsides to using conventional ovens for this as they are relatively large and have relatively slow temperature change rates, and if electrical connections are required between monitoring equipment and the device being heated, they must be located inside the oven and may be aged by the high temperatures. Addressing these downsides, a miniaturized heating system (minioven) is presented, which can heat individual IC packages containing the interconnects to be tested. The core of this system is a piece of copper cut from a square shaped tube with high resistance heating wire looped around it. Ceramic dual in-line packages are clamped against either open end of the core. One package contains a Pt100 temperature sensor and the other package contains the device to be aged placed in symmetry to the temperature sensor. According to the temperature detected by the Pt100, a proportional-integral-derivative controller adjusts the power supplied to the heating wire. The system maintains a dynamic temperature balance with the core hot and the two symmetric sides with electrical connections to the device under test at a cooler temperature. Only the face of the package containing the device is heated, while the socket holding it remains below 75 °C when the oven operates at 200 °C. The minioven can heat packages from room temperature up to 200 °C in less than 5 min and maintain this temperature at 28 W power. During long term aging, a temperature of 200 °C was maintained for 1120 h with negligible resistance change of the heating wires after 900 h (heating wire resistance increased 0.2% over the final 220 h). The device is also subjected to
Symmetric miniaturized heating system for active microelectronic devices.
McCracken, Michael; Mayer, Michael; Jourard, Isaac; Moon, Jeong-Tak; Persic, John
2010-07-01
To qualify interconnect technologies such as microelectronic fine wire bonds for mass production of integrated circuit (IC) packages, it is necessary to perform accelerated aging tests, e.g., to age a device at an elevated temperature or to subject the device to thermal cycling and measure the decrease of interconnect quality. There are downsides to using conventional ovens for this as they are relatively large and have relatively slow temperature change rates, and if electrical connections are required between monitoring equipment and the device being heated, they must be located inside the oven and may be aged by the high temperatures. Addressing these downsides, a miniaturized heating system (minioven) is presented, which can heat individual IC packages containing the interconnects to be tested. The core of this system is a piece of copper cut from a square shaped tube with high resistance heating wire looped around it. Ceramic dual in-line packages are clamped against either open end of the core. One package contains a Pt100 temperature sensor and the other package contains the device to be aged placed in symmetry to the temperature sensor. According to the temperature detected by the Pt100, a proportional-integral-derivative controller adjusts the power supplied to the heating wire. The system maintains a dynamic temperature balance with the core hot and the two symmetric sides with electrical connections to the device under test at a cooler temperature. Only the face of the package containing the device is heated, while the socket holding it remains below 75 degrees C when the oven operates at 200 degrees C. The minioven can heat packages from room temperature up to 200 degrees C in less than 5 min and maintain this temperature at 28 W power. During long term aging, a temperature of 200 degrees C was maintained for 1120 h with negligible resistance change of the heating wires after 900 h (heating wire resistance increased 0.2% over the final 220 h). The
Energy Technology Data Exchange (ETDEWEB)
Ferreiro, J.E.; Arguelles, D.J.; Rams, H. Jr.
1986-01-01
A case of thyrotoxic periodic paralysis is reported in a Hispanic man with an unusual recurrence six weeks after radioactive iodine treatment. Thyrotoxic periodic paralysis has now been well characterized in the literature: it occurs primarily in Orientals with an overwhelming male preponderance and a higher association of specific HLA antigens. Clinical manifestations include onset after high carbohydrate ingestion or heavy exertion, with progressive symmetric weakness leading to flaccid paralysis of the extremities and other muscle groups, lasting several hours. If hypokalemia is present, potassium administration may help abort the attack. Although propranolol can be efficacious in preventing further episodes, the only definitive treatment is establishing a euthyroid state. The pathophysiology is still controversial, but reflects altered potassium and calcium dynamics as well as certain morphologic characteristics within the muscle unit itself.
PT AND PT/NI "NEEDLE" ELETROCATALYSTS ON CARBON NANOTUBES WITH HIGH ACTIVITY FOR THE ORR
Energy Technology Data Exchange (ETDEWEB)
Colon-Mercado, H.
2011-11-10
Platinum and platinum/nickel alloy electrocatalysts supported on graphitized (gCNT) or nitrogen doped carbon nanotubes (nCNT) are prepared and characterized. Pt deposition onto carbon nanotubes results in Pt 'needle' formations that are 3.5 nm in diameter and {approx}100 nm in length. Subsequent Ni deposition and heat treatment results in PtNi 'needles' with an increased diameter. All Pt and Pt/Ni materials were tested as electrocatalysts for the oxygen reduction reaction (ORR). The Pt and Pt/Ni catalysts showed excellent performance for the ORR, with the heat treated PtNi/gCNT (1.06 mA/cm{sup 2}) and PtNi/nCNT (0.664 mA/cm{sup 2}) showing the highest activity.
Goto, Tomoyo; Itoh, Toshio; Akamatsu, Takafumi; Shin, Woosuck
2015-12-15
The CO sensing properties of a micro thermoelectric gas sensor (micro-TGS) with a double AuPtPd/SnO₂ and Pt/α-Al₂O₃ catalyst were investigated. While several nanometer sized Pt and Pd particles were uniformly dispersed on SnO₂, the Au particles were aggregated as particles measuring >10 nm in diameter. In situ diffuse reflectance Fourier transform Infrared spectroscopy (DRIFT) analysis of the catalyst showed a CO adsorption peak on Pt and Pd, but no clear peak corresponding to the interaction between CO and Au was detected. Up to 200 °C, CO combustion was more temperature dependent than that of H₂, while H₂ combustion was activated by repeated exposure to H₂ gas during the periodic gas test. Selective CO sensing of the micro-TGS against H₂ was attempted using a double catalyst structure with 0.3-30 wt% Pt/α-Al₂O₃ as a counterpart combustion catalyst. The sensor output of the micro-TGS decreased with increasing Pt content in the Pt/α-Al₂O₃ catalyst, by cancelling out the combustion heat from the AuPtPd/SnO₂ catalyst. In addition, the AuPtPd/SnO₂ and 0.3 wt% Pt/α-Al₂O₃ double catalyst sensor showed good and selective CO detection. We therefore demonstrated that our micro-TGS with double catalyst structure is useful for controlling the gas selectivity of CO against H₂.
... Too Tall or Too Short All About Puberty Period Cramps KidsHealth > For Kids > Period Cramps Print A ... re a girl who gets them. What Are Period Cramps? Lots of girls experience cramps before or ...
REPRESENTATION OF SYMMETRIC SUPER-MARTINGALE MULTIPLICATIVE FUNCTIONALS
Institute of Scientific and Technical Information of China (English)
金蒙为; 应坚刚
2002-01-01
The authors introduce concepts of even and odd additive functionals and prove that an even martingale continuous additive functional of a symmetric Markov process vanishes identically.A representation for symmetric super-martingale multiplicative functionals are also given.
The Symmetric Solutions of Affiliated Value Model
Institute of Scientific and Technical Information of China (English)
Che Ka-jia; Li Zhi-chen
2004-01-01
In a symmetric affiliated value model, this paper analyses High-Technology industrial firms' competitive strategy in research and development (R&D). We obtain the symmetric Bayesian Nash Equilibrium functions with or without government's prize:b1(x)=v(x,x)Fn-1(x|x)-∫x0Fn-1(y|y)dv(y,y), b2(x)=∫x0[v(y,y)+v0]dFn-1(y|y), and b3(x)=∫x0v(y,y)(fn-1(y|y))/(1-Fn-1(y|y))dy. We find the firm's investment level will increase in prize, only when the constant prize v0≥v(y,y)(Fn-1(y|y))/(1-Fn-1(y|y)), does the firm invest more aggressively with constant prize than with variable prize.
Representations of the infinite symmetric group
Borodin, Alexei
2016-01-01
Representation theory of big groups is an important and quickly developing part of modern mathematics, giving rise to a variety of important applications in probability and mathematical physics. This book provides the first concise and self-contained introduction to the theory on the simplest yet very nontrivial example of the infinite symmetric group, focusing on its deep connections to probability, mathematical physics, and algebraic combinatorics. Following a discussion of the classical Thoma's theorem which describes the characters of the infinite symmetric group, the authors describe explicit constructions of an important class of representations, including both the irreducible and generalized ones. Complete with detailed proofs, as well as numerous examples and exercises which help to summarize recent developments in the field, this book will enable graduates to enhance their understanding of the topic, while also aiding lecturers and researchers in related areas.
Four-qubit PPT entangled symmetric states
Tura, J; Hyllus, P; Kuś, M; Samsonowicz, J; Lewenstein, M
2012-01-01
We solve an open question of the existence of four-qubit entangled symmetric states with positive partial transpositions (PPT states). We reach this goal with two different approaches. First, we propose a half-analytical-half-numerical method that allows to construct multipartite PPT entangled symmetric states (PPTESS) from the qubit-qudit PPT entangled states. Second, we adapt the algorithm allowing to search for extremal elements in the convex set of bipartite PPT states [J. M. Leinaas, J. Myrheim, and E. Ovrum, Phys. Rev. A 76, 034304 (2007)] to the multipartite scenario. With its aid we search for extremal four-qubit PPTESS and show that generically they have ranks (5,7,8). Finally, we provide an exhaustive characterization of these states with respect to their separability properties.
Nonlinear electrodynamics as a symmetric hyperbolic system
Abalos, Fernando; Goulart, Érico; Reula, Oscar
2015-01-01
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the point-wise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that, the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a non-empty intersection. Namely that there exist families of symmetrizers in the sense of Geroch which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well-posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet and Euler-Heisenberg.
Replica symmetric spin glass field theory
Energy Technology Data Exchange (ETDEWEB)
Temesvari, T. [Research Group for Theoretical Physics of the Hungarian Academy of Sciences, Eoetvoes University, Pazmany Peter setany 1/A, H-1117 Budapest (Hungary)]. E-mail: temtam@helios.elte.hu
2007-06-18
A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v). Exact symmetry arguments are used to prove that its extremum is proportional to the inverse spin glass susceptibility. By the idea of independent droplet excitations a scaling form for g(v) can be derived, whereas it can be exactly computed in the mean field Sherrington-Kirkpatrick model. It is shown by a first order perturbative treatment that the replica symmetric phase is unstable down to dimensions d < or approx. 6, and the mean field scaling function proves to be very robust. Although replica symmetry breaking is escalating for decreasing dimensionality, a mechanism caused by the infrared divergent replicon propagator may destroy the mean field picture at some low enough dimension.
Replica symmetric spin glass field theory
Temesvári, T.
2007-06-01
A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v). Exact symmetry arguments are used to prove that its extremum is proportional to the inverse spin glass susceptibility. By the idea of independent droplet excitations a scaling form for g(v) can be derived, whereas it can be exactly computed in the mean field Sherrington-Kirkpatrick model. It is shown by a first order perturbative treatment that the replica symmetric phase is unstable down to dimensions d≲6, and the mean field scaling function proves to be very robust. Although replica symmetry breaking is escalating for decreasing dimensionality, a mechanism caused by the infrared divergent replicon propagator may destroy the mean field picture at some low enough dimension.
Leptogenesis in left-right symmetric theories
Joshipura, A S; Rodejohann, W
2001-01-01
The masses and mixing of the light left-handed neutrinos can be related to those of the heavy right-handed neutrinos in left-right symmetric theories. Properties of the light neutrinos are measured in terrestrial experiments and the CP-violating decays of their heavy counterparts produce a baryon asymmetry via the well-known leptogenesis mechanism. The left-handed Higgs triplet, present in left-right symmetric theories, modifies the usual see-saw formula. It is possible to relate the lepton asymmetry to the light neutrino parameters when the triplet and the top quark through the usual see-saw mechanism give dominant contribution to the neutrino mass matrix. We find that in this situation the small angle MSW and vacuum solutions produce reasonable asymmetry, whereas the large angle MSW case requires extreme fine-tuning of the three phases in the mixing matrix.
Polymer-based symmetric electrochromic devices
Energy Technology Data Exchange (ETDEWEB)
Arbizzani, Catia; Cerroni, Maria Grazia [Department of Chemistry `G. Ciamician`, University of Bologna, via Selmi 2, 40126 Bologna (Italy); Mastragostino, Marina [Department of Physical Chemistry, University of Palermo, via Archirafi 26, 20123 Palermo (Italy)
1998-12-30
The fact that conjugated polymers repeatedly undergo electrochemical doping/undoping processes, which are accompanied by color changes, makes these materials very attractive, and much effort has been devoted to their use in advanced devices. There is renewed interest in electroactive polymers that reversibly undergo both p- and n-doping because of their potential application in symmetric electrochemical devices. We employed fused molecules, dithienothiophenes, as monomers to obtain polymers with a narrow band gap suitable for n- and p-doping. The performance results of two symmetric electrochromic devices having as electrodes both poly(dithieno[3,4-b:3`,4`-d]thiophene) (pDTT1) and poly(dithieno[3,4-b:2`,3`-d]thiophene) (pDTT3) are reported and discussed
Matrix calculus for axially symmetric polarized beam.
Matsuo, Shigeki
2011-06-20
The Jones calculus is a well known method for analyzing the polarization of a fully polarized beam. It deals with a beam having spatially homogeneous polarization. In recent years, axially symmetric polarized beams, where the polarization is not homogeneous in its cross section, have attracted great interest. In the present article, we show the formula for the rotation of beams and optical elements on the angularly variant term-added Jones calculus, which is required for analyzing axially symmetric beams. In addition, we introduce an extension of the Jones calculus: use of the polar coordinate basis. With this calculus, the representation of some angularly variant beams and optical elements are simplified and become intuitive. We show definitions, examples, and conversion formulas between different notations.
Factored Facade Acquisition using Symmetric Line Arrangements
Ceylan, Duygu
2012-05-01
We introduce a novel framework for image-based 3D reconstruction of urban buildings based on symmetry priors. Starting from image-level edges, we generate a sparse and approximate set of consistent 3D lines. These lines are then used to simultaneously detect symmetric line arrangements while refining the estimated 3D model. Operating both on 2D image data and intermediate 3D feature representations, we perform iterative feature consolidation and effective outlier pruning, thus eliminating reconstruction artifacts arising from ambiguous or wrong stereo matches. We exploit non-local coherence of symmetric elements to generate precise model reconstructions, even in the presence of a significant amount of outlier image-edges arising from reflections, shadows, outlier objects, etc. We evaluate our algorithm on several challenging test scenarios, both synthetic and real. Beyond reconstruction, the extracted symmetry patterns are useful towards interactive and intuitive model manipulations.
Maximally Symmetric Spacetimes emerging from thermodynamic fluctuations
Bravetti, A; Quevedo, H
2015-01-01
In this work we prove that the maximally symmetric vacuum solutions of General Relativity emerge from the geometric structure of statistical mechanics and thermodynamic fluctuation theory. To present our argument, we begin by showing that the pseudo-Riemannian structure of the Thermodynamic Phase Space is a solution to the vacuum Einstein-Gauss-Bonnet theory of gravity with a cosmological constant. Then, we use the geometry of equilibrium thermodynamics to demonstrate that the maximally symmetric vacuum solutions of Einstein's Field Equations -- Minkowski, de-Sitter and Anti-de-Sitter spacetimes -- correspond to thermodynamic fluctuations. Moreover, we argue that these might be the only possible solutions that can be derived in this manner. Thus, the results presented here are the first concrete examples of spacetimes effectively emerging from the thermodynamic limit over an unspecified microscopic theory without any further assumptions.
Leptogenesis in left-right symmetric theories
Energy Technology Data Exchange (ETDEWEB)
Joshipura, Anjan S. E-mail: anjan@prl.ernet.in; Paschos, Emmanuel A. E-mail: paschos@physik.uni-dortmund.de; Rodejohann, Werner E-mail: rodejoha@xena.physik.uni-dortmund.de
2001-09-17
The masses and mixing of the light left-handed neutrinos can be related to those of the heavy right-handed neutrinos in left-right symmetric theories. Properties of the light neutrinos are measured in terrestrial experiments and the CP-violating decays of their heavy counterparts produce a baryon asymmetry via the well-known leptogenesis mechanism. The left-handed Higgs triplet, present in left-right symmetric theories, modifies the usual see-saw formula. It is possible to relate the lepton asymmetry to the light neutrino parameters when the triplet and the top quark through the usual see-saw mechanism give the dominant contribution to the neutrino mass matrix. We find that in this situation the small angle MSW and vacuum solutions produce reasonable asymmetry, whereas the large angle MSW case requires extreme fine-tuning of the three phases in the mixing matrix.
Chirally symmetric strong and electroweak interactions
Rajpoot, Subhash
1988-07-01
Strong and electroweak interactions may be a relic of the spontaneous breakdown of a chirally symmetric colour-flavour gauge group. The minimum possibility of such a structure that is symmetric between left and right is SU(3) L×SU(3) R×SU(2) L×SU(2) R×U(1) B- L where quantum chromodynamics originates in the chiral colour group SU(3) L×SU(3) R and the electroweak interaction originates in the ambidextrous electroweak interaction group SU L×SU(2) R×U(1) B- L. The chiral anomalies are cancelled by adding a set of fermions that transform as singlets under the weak interaction group SU(2) L×SU(2) R. This model requires only three Higgs representations to break the proposed gauge symmetry to SU(3) C×U(1) em and give masses to all the quarks and leptons of the theory. All fermion masses are “see-saw” masses.
Cusped Wilson lines in symmetric representations
Correa, Diego H; Trancanelli, Diego
2015-01-01
We study the cusped Wilson line operators and Bremsstrahlung functions associated to particles transforming in the rank-$k$ symmetric representation of the gauge group $U(N)$ for ${\\cal N} = 4$ super Yang-Mills. We find the holographic D3-brane description for Wilson loops with internal cusps in two different limits: small cusp angle and $k\\sqrt{\\lambda}\\gg N$. This allows for a non-trivial check of a conjectured relation between the Bremsstrahlung function and the expectation value of the 1/2 BPS circular loop in the case of a representation other than the fundamental. Moreover, we observe that in the limit of $k\\gg N$, the cusped Wilson line expectation value is simply given by the exponential of the 1-loop diagram. Using group theory arguments, this eikonal exponentiation is conjectured to take place for all Wilson loop operators in symmetric representations with large $k$, independently of the contour on which they are supported.
The quantum capacity with symmetric side channels
Smith, G; Winter, A; Smith, Graeme; Smolin, John A.; Winter, Andreas
2006-01-01
We present an upper bound for the quantum channel capacity that is both additive and convex. Our bound can be interpreted as the capacity of a channel for high-fidelity communication when assisted by the family of all channels mapping symmetrically to their output and environment. The bound seems to be quite tight, and for degradable quantum channels it coincides with the unassisted channel capacity. Using this symmetric side channel capacity, we find new upper bounds on the capacity of the depolarizing channel. We also briefly indicate an analogous notion for distilling entanglement using the same class of (one-way) channels, yielding one of the few genuinely 1-LOCC monotonic entanglement measures.
Static spherically symmetric wormholes with isotropic pressure
Cataldo, Mauricio; Rodríguez, Pablo
2016-01-01
In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there is no spherically symmetric traversable wormholes sustained by sources with a linear equation of state $p=\\omega \\rho$ for the isotropic pressure, independently of the form of the redshift function $\\phi(r)$. We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic fluids, and show that it also may describe wormhole spacetimes with a power-law redshift function, which leads to a polynomial shape function, generalizing a power-law shape function, and inducing a solid angle deficit.
Laser weldability of Pt and Ti alloys
Energy Technology Data Exchange (ETDEWEB)
Noolu, N.J. [Center for Advanced Materials Joining, University of Waterloo, Waterloo (Canada)]. E-mail: nnoolu@mecheng1.uwaterloo.ca; Kerr, H.W. [Center for Advanced Materials Joining, University of Waterloo, Waterloo (Canada); Zhou, Y. [Center for Advanced Materials Joining, University of Waterloo, Waterloo (Canada); Xie, J. [Cardiac Rhythm Management Division, Street Jude Medical Inc., Sylmar, CA (United States)
2005-04-25
Crack susceptibility of laser spot welds between Pt and Ti alloys was studied by characterizing the surface and the cross-sections of the welds produced at different pulse energies. Increase in laser pulse energy increased the dilution by the Ti alloy, giving rise to the evolution of microstructures with varying Ti contents across the entire fusion zone. Hardness results showed that regions with 66-75% Ti, i.e. consisting of primary Ti{sub 3}Pt and/or Ti{sub 3}Pt + TiPt eutectic, have a hardness higher than 700 Vickers hardness numbers (VHN), while regions with 42-66% Ti, i.e. consisting of primary TiPt, possessed hardness between 400 and 700 VHN. The extent of cracking increased with the increase in pulse energy and the cracked regions consisted of Ti contents between 50 and 75%. Brittle cracking in microstructures consisting of Ti{sub 3}Pt and TiPt phases suggested that one or both of the constituent phases are susceptible to cracking. However, crack arrest in microstructures predominantly consisting of TiPt showed that Ti{sub 3}Pt is the most susceptible phase to cracking in Pt-Ti alloy welds.
16×10Gb/s symmetric WDM-FOFDM-PON realization with colorless ONUs.
Lei, Cheng; Chen, Hongwei; Chen, Minghua; Xie, Shizhong
2011-08-01
A novel symmetric WDM-PON scheme with colorless ONU is proposed. The baseband 4-ASK Fast-OFDM signal is upconverted by an intermediate frequency carrier, reserving a frequency gap between the FOFDM signal and the optical carrier. After distributing different wavelengths to corresponding ONU by AWG, periodic BPFs are employed to extract the optical carriers for upstream transmission, achieving colorless ONUs. A WDM-PON system with 16 colorless ONUs is established, and 10-Gb/s symmetric transmission for each ONU is also realized. Experiment shows that the system tolerance to the intrachannel crosstalk is greatly improved when the crosstalk signal locates at relatively higher frequency band.
Symmetric sequence processing in a recurrent neural network model with a synchronous dynamics
Energy Technology Data Exchange (ETDEWEB)
Metz, F L; Theumann, W K [Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 Porto Alegre (Brazil)], E-mail: fernando@itf.fys.kuleuven.be, E-mail: theumann@if.ufrgs.br
2009-09-25
The synchronous dynamics and the stationary states of a recurrent attractor neural network model with competing synapses between symmetric sequence processing and Hebbian pattern reconstruction are studied in this work allowing for the presence of a self-interaction for each unit. Phase diagrams of stationary states are obtained exhibiting phases of retrieval, symmetric and period-two cyclic states as well as correlated and frozen-in states, in the absence of noise. The frozen-in states are destabilized by synaptic noise and well-separated regions of correlated and cyclic states are obtained. Excitatory or inhibitory self-interactions yield enlarged phases of fixed-point or cyclic behaviour.
Spherically Symmetric, Self-Similar Spacetimes
Wagh, S M; Wagh, Sanjay M.; Govinder, Keshlan S.
2001-01-01
Self-similar spacetimes are of importance to cosmology and to gravitational collapse problems. We show that self-similarity or the existence of a homothetic Killing vector field for spherically symmetric spacetimes implies the separability of the spacetime metric in terms of the co-moving coordinates and that the metric is, uniquely, the one recently reported in [cqg1]. The spacetime, in general, has non-vanishing energy-flux and shear. The spacetime admits matter with any equation of state.
Expansion-free Cylindrically Symmetric Models
Sharif, M
2013-01-01
This paper investigates cylindrically symmetric distribution of an-isotropic fluid under the expansion-free condition, which requires the existence of vacuum cavity within the fluid distribution. We have discussed two family of solutions which further provide two exact models in each family. Some of these solutions satisfy Darmois junction condition while some show the presence of thin shell on both boundary surfaces. We also formulate a relation between the Weyl tensor and energy density.
Irreducible complexity of iterated symmetric bimodal maps
Directory of Open Access Journals (Sweden)
J. P. Lampreia
2005-01-01
Full Text Available We introduce a tree structure for the iterates of symmetric bimodal maps and identify a subset which we prove to be isomorphic to the family of unimodal maps. This subset is used as a second factor for a ∗-product that we define in the space of bimodal kneading sequences. Finally, we give some properties for this product and study the ∗-product induced on the associated Markov shifts.
Quantum unharmonic symmetrical oscillators using elliptic functions
Energy Technology Data Exchange (ETDEWEB)
Sanchez, A.M.; Bejarano, J.d.
1986-04-21
The authors study in the JWKB approximation the energy levels of the symmetric anharmonic oscillators V(x) Ax/sup 2/ + Bx/sup 4/ for different signs and values of A and B. Comparisons are made with published results for specific cases and with numerical calculations. An additional example is given of exact value, to add to the very rare catalogue of known examples.
Resistor Networks based on Symmetrical Polytopes
Directory of Open Access Journals (Sweden)
Jeremy Moody
2015-03-01
Full Text Available This paper shows how a method developed by Van Steenwijk can be generalized to calculate the resistance between any two vertices of a symmetrical polytope all of whose edges are identical resistors. The method is applied to a number of cases that have not been studied earlier such as the Archimedean polyhedra and their duals in three dimensions, the regular polytopes in four dimensions and the hypercube in any number of dimensions.
Symmetrical peripheral gangrene associated with peripartum cardiomyopathy
Directory of Open Access Journals (Sweden)
Ajay Jaryal
2013-01-01
Full Text Available Symmetrical peripheral gangrene (SPG is a rare clinical entity. It was first described in late 19 th century and since then has been reported with array of medical conditions mainly those complicated with shock, sepsis, and disseminated intravascular coagulation (DIC. Here in, we describe a parturient with peripartum cardiomyopathy (PPCM and SPG. Clinicians should be aware of this entity as early recognition can help in reducing morbidity and mortality.
On integrability of strings on symmetric spaces
Energy Technology Data Exchange (ETDEWEB)
Wulff, Linus [Blackett Laboratory, Imperial College,London SW7 2AZ (United Kingdom)
2015-09-17
In the absence of NSNS three-form flux the bosonic string on a symmetric space is described by a symmetric space coset sigma-model. Such models are known to be classically integrable. We show that the integrability extends also to cases with non-zero NSNS flux (respecting the isometries) provided that the flux satisfies a condition of the form H{sub abc}H{sup cde}∼R{sub ab}{sup de}. We then turn our attention to the type II Green-Schwarz superstring on a symmetric space. We prove that if the space preserves some supersymmetry there exists a truncation of the full superspace to a supercoset space and derive the general form of the superisometry algebra. In the case of vanishing NSNS flux the corresponding supercoset sigma-model for the string is known to be integrable. We prove that the integrability extends to the full string by augmenting the supercoset Lax connection with terms involving the fermions which are not captured by the supercoset model. The construction is carried out to quadratic order in these fermions. This proves the integrability of strings on symmetric spaces supported by RR flux which preserve any non-zero amount of supersymmetry. Finally we also construct Lax connections for some supercoset models with non-zero NSNS flux describing strings in AdS{sub 2,3}×S{sup 2,3}×S{sup 2,3}×T{sup 2,3,4} backgrounds preserving eight supersymmetries.
Coefficients of symmetric square L-functions
Institute of Scientific and Technical Information of China (English)
LAU; Yuk-Kam
2010-01-01
Let λsym2f(n) be the n-th coefficient in the Dirichlet series of the symmetric square L-function associated with a holomorphic primitive cusp form f.We prove Ω± results for λsym2f(n) and evaluate the number of positive(resp.,negative) λsym2f(n) in some intervals.
Time-symmetric electrodynamics and quantum measurement
Pegg, D. T.
The application of the Wheeler-Feynman theory of time-symmetric electrodynamics to obtain definite answers to questions concerning the objective existence of quantum states in an optical EPR type of experiment is discussed. This theory allows the influence of the detector on the system being studied to be taken into account. The result is an entirely fresh understanding of experiments of the Kocher-Commins type.
Symmetric Wilson Loops beyond leading order
Chen-Lin, Xinyi
2016-01-01
We study the circular Wilson loop in the symmetric representation of U(N) in $\\mathcal{N} = 4$ super-Yang-Mills (SYM). In the large N limit, we computed the exponentially-suppressed corrections for strong coupling, which suggests non-perturbative physics in the dual holographic theory. We also computed the next-to-leading order term in 1/N, and the result matches with the exact result from the k-fundamental representation.
Symmetric categorial grammar: residuation and Galois connections
Moortgat, Michael
2010-01-01
The Lambek-Grishin calculus is a symmetric extension of the Lambek calculus: in addition to the residuated family of product, left and right division operations of Lambek's original calculus, one also considers a family of coproduct, right and left difference operations, related to the former by an arrow-reversing duality. Communication between the two families is implemented in terms of linear distributivity principles. The aim of this paper is to complement the symmetry between (dual) resid...
Entropy, subentropy and the elementary symmetric functions
Jozsa, Richard; Mitchison, Graeme
2013-01-01
We use complex contour integral techniques to study the entropy H and subentropy Q as functions of the elementary symmetric polynomials, revealing a series of striking properties. In particular for these variables, derivatives of -Q are equal to derivatives of H of one higher order and the first derivatives of H and Q are seen to be completely monotone functions. It then follows that exp (-H) and exp(-Q) are Laplace transforms of infinitely divisible probability distributions.
Compensator configurations for load currents' symmetrization
Rusinaru, D.; Manescu, L. G.; Dinu, R. C.
2016-02-01
This paper approaches aspects regarding the mitigation effects of asymmetries in 3-phase 3-wire networks. The measure consisting in connecting of load current symmetrization devices at the load coupling point is presented. A time-variation of compensators parameters is determined as a function of the time-recorded electrical values. The general sizing principle of the load current symmetrization reactive components is based on a simple equivalent model of the unbalanced 3-phase loads. By using these compensators a certain control of the power components transits is ensured in the network. The control is based on the variations laws of the compensators parameters as functions of the recorded electrical values: [B] = [T]·[M]. The link between compensator parameters and measured values is ensured by a transformation matrix [T] for each operation conditions of the supply network. Additional conditions for improving of energy and efficiency performance of the compensator are considered: i.e. reactive power compensation. The compensator sizing algorithm was implemented into a MATLAB environment software, which generate the time-evolution of the parameters of load current symmetrization device. The input data of application takes into account time-recording of the electrical values. By using the compensator sizing software, some results were achieved for the case of a consumer connected at 20 kV busbar of a distribution substation, during 24 hours measurement session. Even the sizing of the compensators aimed some additional network operation aspects (power factor correction) correlated with the total or major load symmetrizations, the harmonics aspects of the network values were neglected.
Classification Models for Symmetric Key Cryptosystem Identification
Directory of Open Access Journals (Sweden)
Shri Kant
2012-01-01
Full Text Available The present paper deals with the basic principle and theory behind prevalent classification models and their judicious application for symmetric key cryptosystem identification. These techniques have been implemented and verified on varieties of known and simulated data sets. After establishing the techniques the problems of cryptosystem identification have been addressed.Defence Science Journal, 2012, 62(1, pp.38-45, DOI:http://dx.doi.org/10.14429/dsj.62.1440
SVD row or column symmetric matrix
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A new architecture for row or column symmetric matrix called extended matrix is defined, and a precise correspondence of the singular values and singular vectors between the extended matrix and its original (namely, the mother matrix) is derived. As an illustration of potential, we show that, for a class of extended matrices, the singular value decomposition using the mother matrix rather than the extended matrix per se can save the CPU time and memory without loss of numerical precision.
Low Pt content direct methanol fuel cell anode catalyst: nanophase PtRuNiZr
Narayanan, Sekharipuram R. (Inventor); Whitacre, Jay F. (Inventor)
2010-01-01
A method for the preparation of a metallic material having catalytic activity that includes synthesizing a material composition comprising a metal content with a lower Pt content than a binary alloy containing Pt but that displays at least a comparable catalytic activity on a per mole Pt basis as the binary alloy containing Pt; and evaluating a representative sample of the material composition to ensure that the material composition displays a property of at least a comparable catalytic activity on a per mole Pt basis as a representative binary alloy containing Pt. Furthermore, metallic compositions are disclosed that possess substantial resistance to corrosive acids.
QR factorization for row or column symmetric matrix
Institute of Scientific and Technical Information of China (English)
ZOU; Hongxing(邹红星); WANG; Dianjun(王殿军); DAI; Qionghai(戴琼海); LI; Yanda(李衍达)
2003-01-01
The problem of fast computing the QR factorization of row or column symmetric matrix isconsidered. We address two new algorithms based on a correspondence of Q and R matrices between the rowor column symmetric matrix and its mother matrix. Theoretical analysis and numerical evidence show that, fora class of row or column symmetric matrices, the QR factorization using the mother matrix rather than therow or column symmetric matrix per se can save dramatically the CPU time and memory without loss of anynumerical precision.
Direct Determination of the Ionization Energies of PtC, PtO, and PtO2 with VUVRadiation
Energy Technology Data Exchange (ETDEWEB)
Citir, Murat; Metz, Ricardo B.; Belau, Leonid; Ahmed, Musahid
2008-07-21
Photoionization efficiency curves were measured for gas-phase PtC, PtO, and PtO2 using tunable vacuum ultraviolet (VUV) radiation at the Advanced Light Source. The molecules were prepared by laser ablation of a platinum tube, followed by reaction with CH4 or N2O and supersonic expansion. These measurements providethe first directly measured ionization energy for PtC, IE(PtC) = 9.45 +- 0.05 eV. The direct measurement also gives greatly improved ionization energies for the platinum oxides, IE(PtO) = 10.0 +- 0.1 eV and IE(PtO2) = 11.35 +- 0.05 eV. The ionization energy connects the dissociation energies of the neutral and cation, leading to greatly improved 0 K bond dissociation energies for the neutrals: D0(Pt-C) = 5.95 +- 0.07 eV, D0(Pt-O)= 4.30 +- 0.12 eV, and D0(OPt-O) = 4.41 +- 0.13 eV, as well as enthalpies of formation for the gas-phase molecules Delta H0 f,0(PtC(g)) = 701 +- 7 kJ/mol, Delta H0f,0(PtO(g)) = 396 +- 12 kJ/mol, and Delta H0f,0(PtO2(g)) = 218 +- 11 kJ/mol. Much of the error in previous Knudsen cell measurements of platinum oxide bond dissociation energies is due to the use of thermodynamic second law extrapolations. Third law values calculated using statistical mechanical thermodynamic functions are in much better agreement with values obtained from ionization energies and ion energetics. These experiments demonstrate that laser ablation production with direct VUV ionization measurements is a versatile tool to measure ionization energies and bond dissociation energies for catalytically interesting species such as metal oxides and carbides.
Distal symmetrical polyneuropathy: definition for clinical research.
England, J D; Gronseth, G S; Franklin, G; Miller, R G; Asbury, A K; Carter, G T; Cohen, J A; Fisher, M A; Howard, J F; Kinsella, L J; Latov, N; Lewis, R A; Low, P A; Sumner, A J
2005-01-01
The objective of this report was to develop a case definition of "distal symmetrical polyneuropathy" to standardize and facilitate clinical research and epidemiological studies. A formalized consensus process was employed to reach agreement after a systematic review and classification of evidence from the literature. The literature indicates that symptoms alone have relatively poor diagnostic accuracy in predicting the presence of polyneuropathy; signs are better predictors of polyneuropathy than symptoms; and single abnormalities on examination are less sensitive than multiple abnormalities in predicting the presence of polyneuropathy. The combination of neuropathic symptoms, signs, and electrodiagnostic findings provides the most accurate diagnosis of distal symmetrical polyneuropathy. A set of case definitions was rank ordered by likelihood of disease. The highest likelihood of polyneuropathy (useful for clinical trials) occurs with a combination of multiple symptoms, multiple signs, and abnormal electrodiagnostic studies. A modest likelihood of polyneuropathy (useful for field or epidemiological studies) occurs with a combination of multiple symptoms and multiple signs when the results of electrodiagnostic studies are not available. A lower likelihood of polyneuropathy occurs when electrodiagnostic studies and signs are discordant. For research purposes, the best approach for defining distal symmetrical polyneuropathy is a set of case definitions rank ordered by estimated likelihood of disease. The inclusion of this formalized case definition in clinical and epidemiological research studies will ensure greater consistency of case selection.
Neutrino Mass Matrix Predicted From Symmetric Texture
Bando, M; Bando, Masako; Obara, Midori
2003-01-01
Within the framework of grand unified theories, we make full analysis of symmetric texture to see if such texture can reproduce large neutrino mixings, which have recently been confirmed by the observed solar and atmospheric neutrino oscillation experiments. It is found that so-called symmetric texture with anomalous U(1) family symmetry with Froggatt-Nielsen mechanism does not provide a natural explanation of two large mixing angles. On the contrary we should adopt "zero texture" which have been extensively studied by many authors and only this scenario can reproduce two large mixing angles naturally. Under such "zero texture" with minimal symmetric Majorana matrix, all the neutrino masses and mixing angles, 6 quantities, are expressed in terms of up-quark masses, $m_t,m_c,m_u$ with two adjustable parameters. This provides interesting relations among neutrio mixing angles, $\\tan^2 2\\theta_{12} \\simeq \\frac{144m_c}{m_t} \\tan^2 2\\theta_{23} \\cos^2 \\theta_{23}, \\quad \\sin^2 \\theta_{13} \\simeq \\frac{4m_c}{m_t}\\s...
The Exponent Set of Central Symmetric Primitive Matrices
Institute of Scientific and Technical Information of China (English)
陈佘喜; 胡亚辉
2004-01-01
This paper first establishes a distance inequality of the associated diagraph of a central symmetric primitive matrix, then characters the exponent set of central symmetric primitive matrices, and proves that the exponent set of central symmetric primitive matrices of order n is {1, 2,… ,n-1}. There is no gap in it.
Kashiwara-Vergne-Rouviere methods for symmetric spaces
Torossian, Charles
2002-01-01
This article follows our previous work on Campbell-Hausdorff formula. We study the case of symmetric spaces. We recover, by using a Kontsevich's deformation of the Baker-Campbell-Hausdorff formula, Rouviere's results on the convolution of invariant distributions, for solvable symmetric spaces and "very symmetric spaces".
Kashiwara-Vergne-Rouviere methods for symmetric spaces
Torossian, Charles
2002-01-01
This article follows our previous work on Campbell-Hausdorff formula. We study the case of symmetric spaces. We recover, by using a Kontsevich's deformation of the Baker-Campbell-Hausdorff formula, Rouviere's results on the convolution of invariant distributions, for solvable symmetric spaces and "very symmetric spaces".
Comparative study of ethanol oxidation at Pt: Based nanoalloys and UPD modified Pt nanoparticles
Directory of Open Access Journals (Sweden)
Tripković Amalija V.
2010-01-01
Full Text Available The activity of two alloys, Pt3Sn/C and Pt3Ru2/C, was compared with the activity of Pt/C modified with corresponding amounts of SnUPD (≈25 % and RuUPD (≈40 % in oxidation of ethanol. Pt3Sn/C, Pt3Ru2/C and Pt/C catalysts were characterized by XRD. To establish the activity and stability of the catalysts, potentiodynamic, quasi steady-state and chronoamperometric measurements were performed. Both alloys are more active than SnUPD or RuUPD modified Pt/C catalysts. Electronic effect determining dominantly the activity of Pt3Sn/C is the main reason for its higher activity compared to Pt3Ru2/C. Since SnUPD and RuUPD do not provoke any significant modification of electronic environment, both modified Pt/C catalysts are less active than corresponding alloys. More pronounced difference in activity between Pt3Sn/C and SnUPD modified Pt/C than between Pt3Ru2/C and RuUPD modified Pt/C is caused by electronic effect in Pt3Sn/C. High activity of Pt3Sn/C modified with small amount of SnUPD (≈10% can be explained by combining the electronic effect, causing less strongly bonded adsorbate on Pt sites and easier mobility of SnUPD, with enhanced amount of oxygen-containing species on Sn sites resulting finally in reinforcement of bifunctional mechanism.
Electrodeposited Pt and Pt-Sn nanoparticles on Ti as anodes for direct methanol fuel cells
Institute of Scientific and Technical Information of China (English)
Hanaa B HASSAN
2009-01-01
Electro-oxidation of methanol was studied on titanium supported nanocrystallite Pt and Ptx-Sny catalysts prepared by electrodeposition techniques. Their electro-catalytic activities were studied in 0.5mol/L H2SO4 and compared to those of a smooth Pt, Pt/Pt and Pt-Sn/Pt electrodes. Platinum was deposited on Ti by galvanostatic and potentiostatic techniques. X-ray diffractometer (XRD) and energy dispersive X-ray (EDX) techniques were applied in order to investigate the chemical composition and the phase structure of the modified electrodes. Scanning electron microscopy (SEM) was used to characterize the surface morphology and to correlate the results obtained from the two electrochemical deposition methods. Results show that modified Pt/Ti electrodes prepared by the two methods have comparable performance and enhanced catalytic activity towards methanol electro-oxidation compared to Pt/Pt and smooth Pt electrodes. Steady state Tafel plots experiments show a higher rate of methanol oxidation on a Pt/Ti catalyst than that on a smooth Pt. Introduction of a small amount of Sn deposited with Pt improves the catalytic activity and the stability of prepared electrode with time as indicated from the cyclic votlammetry and the chronoamperometric experiments. The effect of variations in the composition for binary catalysts of the type Ptx-Sny/Ti towards the methanol oxidation reaction is reported. Consequently, the Ptx-Sny/Ti (x∶y (8∶1), molar ratio) catalyst is a very promising one for methanol oxidation.
Molecular dynamics simulation study of the melting of Pd-Pt nanoclusters
Sankaranarayanan, Subramanian K. R. S.; Bhethanabotla, Venkat R.; Joseph, Babu
2005-05-01
Bimetallic nanoclusters are of interest because of their utility in catalysis and sensors. The thermal characteristics of bimetallic Pt-Pd nanoclusters of different sizes and compositions were investigated through molecular dynamics simulations using quantum Sutton-Chen (QSC) many-body potentials. Monte Carlo simulations employing the bond order simulation model were used to generate minimum energy configurations, which were utilized as the starting point for molecular dynamics simulations. The calculated initial configurations of the Pt-Pd system consisted of surface segregated Pd atoms and a Pt-rich core. Melting characteristics were studied by following the changes in potential energy and heat capacity as functions of temperature. Structural changes accompanying the thermal evolution were studied by the bond order parameter method. The Pt-Pd clusters exhibited a two-stage melting: surface melting of the external Pd atoms followed by homogeneous melting of the Pt core. These transitions were found to depend on the composition and size of the nanocluster. Melting temperatures of the nanoclusters were found to be much lower than those of bulk Pt and Pd. Bulk melting temperatures of Pd and Pt simulated using periodic boundary conditions compare well with experimental values, thus providing justification for the use of QSC potentials in these simulations. Deformation parameters were calculated to characterize the structural evolution resulting from diffusion of Pd and Pt atoms. The results indicate that in Pd-Pt clusters, Pd atoms prefer to remain at the surface even after melting. In addition, Pt also tends to diffuse to the surface after melting due to reduction of its surface energy with temperature. This mixing pattern is different from those reported in some of the earlier studies on melting of bimetallics.
D4-symmetric Maps with Hidden Euclidean Symmetry
Crawford, J D
1993-01-01
Bifurcation problems in which periodic boundary conditions (PBC) or Neumann boundary conditions (NBC) are imposed often involve partial differential equations that have Euclidean symmetry. In this case posing the bifurcation problem with either PBC or NBC on a finite domain can lead to a symmetric bifurcation problem for which the manifest symmetries of the domain do not completely characterize the constraints due to symmetry on the bifurcation equations. Additional constraints due to the Euclidean symmetry of the equations can have a crucial influence on the structure of the bifurcation equations. An example is the bifurcation of standing waves on the surface of fluid layer. The Euclidean symmetry of an infinite fluid layer constrains the bifurcation of surface waves in a finite container with square cross section because the waves satisfying PBC or NBC can be shown to lie in certain finite-dimensional fixed point subspaces of the infinite-dimensional problem. These constraints are studied by analyzing the f...
High-performance core-shell PdPt@Pt/C catalysts via decorating PdPt alloy cores with Pt
Wu, Yan-Ni; Liao, Shi-Jun; Liang, Zhen-Xing; Yang, Li-Jun; Wang, Rong-Fang
A core-shell structured low-Pt catalyst, PdPt@Pt/C, with high performance towards both methanol anodic oxidation and oxygen cathodic reduction, as well as in a single hydrogen/air fuel cell, is prepared by a novel two-step colloidal approach. For the anodic oxidation of methanol, the catalyst shows three times higher activity than commercial Tanaka 50 wt% Pt/C catalyst; furthermore, the ratio of forward current I f to backward current I b is high up to 1.04, whereas for general platinum catalysts the ratio is only ca. 0.70, indicating that this PdPt@Pt/C catalyst has high activity towards methanol anodic oxidation and good tolerance to the intermediates of methanol oxidation. The catalyst is characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), and X-ray photoelectron spectroscopy (XPS). The core-shell structure of the catalyst is revealed by XRD and TEM, and is also supported by underpotential deposition of hydrogen (UPDH). The high performance of the PdPt@Pt/C catalyst may make it a promising and competitive low-Pt catalyst for hydrogen fueled polymer electrolyte membrane fuel cell (PEMFC) or direct methanol fuel cell (DMFC) applications.
The dynamics of a symmetric coupling of three modified quadratic maps
Institute of Scientific and Technical Information of China (English)
Paulo C.Rech
2013-01-01
We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms,and identify various interesting features as a function of two control parameters.In particular,we investigate the emergence of quasiperiodic states arising from Naimark-Sacker bifurcations of stable period-1,period-2,and period-3 orbits.We also investigate the multistability in the same coupling.Lyapunov exponents,parameter planes,phase space portraits,and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states,from quasiperiodic to mode-locked states and to chaotic states,and from chaotic to hyperchaotic states.
Liu, Jie; Fan, Xiayue; Liu, Xiaorui; Song, Zhishuang; Deng, Yida; Han, Xiaopeng; Hu, Wenbin; Zhong, Cheng
2017-06-07
A new approach has been developed for in situ preparing cubic-shaped Pt particles with (100) preferential orientation on the surface of the conductive support by using a quick, one-step, and clean electrochemical method with periodic square-wave potential. The whole electrochemical deposition process is very quick (only 6 min is required to produce cubic Pt particles), without the use of particular capping agents. The shape and the surface structure of deposited Pt particles can be controlled by the lower and upper potential limits of the square-wave potential. For a frequency of 5 Hz and an upper potential limit of 1.0 V (vs saturated calomel electrode), as the lower potential limit decreases to the H adsorption potential region, the Pt deposits are changed from nearly spherical particles to cubic-shaped (100)-oriented Pt particles. High-resolution transmission electron microscopy and selected-area electron diffraction reveal that the formed cubic Pt particles are single-crystalline and enclosed by (100) facets. Cubic Pt particles exhibit characteristic H adsorption/desorption peaks corresponding to the (100) preferential orientation. Ge irreversible adsorption indicates that the fraction of wide Pt(100) surface domains is 47.8%. The electrocatalytic activities of different Pt particles are investigated by ammonia electro-oxidation, which is particularly sensitive to the amount of Pt(100) sites, especially larger (100) domains. The specific activity of cubic Pt particles is 3.6 times as high as that of polycrystalline spherical Pt particles, again confirming the (100) preferential orientation of Pt cubes. The formation of cubic-shaped Pt particles is related with the preferential electrochemical deposition and dissolution processes of Pt, which are coupled with the periodic desorption and adsorption processes of O-containing species and H adatoms.
Comparison of winding-number sequences for symmetric and asymmetric oscillatory systems.
Englisch, Volker; Parlitz, Ulrich; Lauterborn, Werner
2015-08-01
The bifurcation sets of symmetric and asymmetric periodically driven oscillators are investigated and classified by means of winding numbers. It is shown that periodic windows within chaotic regions are forming winding-number sequences on different levels. These sequences can be described by a simple formula that makes it possible to predict winding numbers at bifurcation points. Symmetric and asymmetric systems follow similar rules for the development of winding numbers within different sequences and these sequences can be combined into a single general rule. The role of the two distinct period-doubling cascades is investigated in the light of the winding-number sequences discovered. Examples are taken from the double-well Duffing oscillator, a special two-parameter Duffing oscillator, and a bubble oscillator.
Spontaneous PT-Symmetry Breaking for Systems of Noncommutative Euclidean Lie Algebraic Type
Dey, Sanjib; Fring, Andreas; Mathanaranjan, Thilagarajah
2015-11-01
We propose a noncommutative version of the Euclidean Lie algebra E 2. Several types of non-Hermitian Hamiltonian systems expressed in terms of generic combinations of the generators of this algebra are investigated. Using the breakdown of the explicitly constructed Dyson maps as a criterium, we identify the domains in the parameter space in which the Hamiltonians have real energy spectra and determine the exceptional points signifying the crossover into the different types of spontaneously broken PT-symmetric regions with pairs of complex conjugate eigenvalues. We find exceptional points which remain invariant under the deformation as well as exceptional points becoming dependent on the deformation parameter of the algebra.
Symmetric Euler orientation representations for orientational averaging.
Mayerhöfer, Thomas G
2005-09-01
A new kind of orientation representation called symmetric Euler orientation representation (SEOR) is presented. It is based on a combination of the conventional Euler orientation representations (Euler angles) and Hamilton's quaternions. The properties of the SEORs concerning orientational averaging are explored and compared to those of averaging schemes that are based on conventional Euler orientation representations. To that aim, the reflectance of a hypothetical polycrystalline material with orthorhombic crystal symmetry was calculated. The calculation was carried out according to the average refractive index theory (ARIT [T.G. Mayerhöfer, Appl. Spectrosc. 56 (2002) 1194]). It is shown that the use of averaging schemes based on conventional Euler orientation representations leads to a dependence of the result from the specific Euler orientation representation that was utilized and from the initial position of the crystal. The latter problem can be overcome partly by the introduction of a weighing factor, but only for two-axes-type Euler orientation representations. In case of a numerical evaluation of the average, a residual difference remains also if a two-axes type Euler orientation representation is used despite of the utilization of a weighing factor. In contrast, this problem does not occur if a symmetric Euler orientation representation is used as a matter of principle, while the result of the averaging for both types of orientation representations converges with increasing number of orientations considered in the numerical evaluation. Additionally, the use of a weighing factor and/or non-equally spaced steps in the numerical evaluation of the average is not necessary. The symmetrical Euler orientation representations are therefore ideally suited for the use in orientational averaging procedures.
Communities and classes in symmetric fractals
Krawczyk, M J
2014-01-01
Two aspects of fractal networks are considered: the community structure and the class structure, where classes of nodes appear as a consequence of a local symmetry of nodes. The analysed systems are the networks constructed for two selected symmetric fractals: the Sierpinski triangle and the Koch curve. Communities are searched for by means of a set of differential equations. Overlapping nodes which belong to two different communities are identified by adding some noise to the initial connectivity matrix. Then, a node can be characterized by a spectrum of probabilities of belonging to different communities. Our main goal is that the overlapping nodes with the same spectra belong to the same class.
Quantum asymmetric cryptography with symmetric keys
Gao, Fei; Wen, Qiaoyan; Qin, Sujuan; Zhu, Fuchen
2009-12-01
Based on quantum encryption, we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use symmetric keys in such a scheme, which is quite different from that in conventional public-key cryptography. The security of our scheme is analyzed and some features are discussed. Furthermore, the state-estimation attack to a prior QPKC scheme is demonstrated.
Quantum asymmetric cryptography with symmetric keys
Gao, Fei; Wen, Qiao-Yan; Qin, Su-Juan; Zhu, Fu-Chen
2008-01-01
Based on quantum encryption, we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use symmetric keys in such a scheme, which is quite different from that in conventional public-key cryptography. The security of our scheme is analyzed and some features are discussed. Furthermore, the state-estimation attack to a prior QPKC scheme is demonstr...
Quantum asymmetric cryptography with symmetric keys
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Based on quantum encryption,we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use symmetric keys in such a scheme,which is quite different from that in conventional public-key cryptography. The security of our scheme is analyzed and some features are discussed. Furthermore,the state-estimation attack to a prior QPKC scheme is demonstrated.
Congruence Permutable Symmetric Extended de Morgan Algebras
Institute of Scientific and Technical Information of China (English)
Jie FANG
2006-01-01
An algebra A is said to be congruence permutable if any two congruences on it are per-mutable. This property has been investigated in several varieties of algebras, for example, de Morgan algebras, p-algebras, Kn,o-algebras. In this paper, we study the class of symmetric extended de Morgan algebras that are congruence permutable. In particular we consider the case where A is finite, and show that A is congruence permutable if and only if it is isomorphic to a direct product of finitely many simple algebras.
Quantum asymmetric cryptography with symmetric keys
Institute of Scientific and Technical Information of China (English)
GAO Fei; WEN QiaoYan; QIN SuJuan; ZHU FuChen
2009-01-01
Based on quantum encryption, we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use symmetric keys in such a scheme, which is quite different from that in conventional public-key cryptography. The security of our scheme is analyzed and some features are discussed. Furthermore, the state-estimation attack to a prior QPKC scheme is demonstrated.
Stability of Reflection Symmetric Collapsing Structures
Sharif, M
2015-01-01
In this paper, we explore instability regions of non-static axial reflection symmetric spacetime with anisotropic source in the interior. We impose linear perturbation on the Einstein field equations and dynamical equations to establish the collapse equation. The effects of different physical factors like energy density and anisotropic stresses on the instability regions are studied under Newtonian and post-Newtonian limits. We conclude that stiffness parameter has a significant role in this analysis while the reflection terms increase instability ranges of non-static axial collapse.
Design of spherical symmetric gradient index lenses
Miñano, Juan C.; Grabovičkić, Dejan; Benítez, Pablo; González, Juan C.; Santamaría, Asunción
2012-10-01
Spherical symmetric refractive index distributions also known as Gradient Index lenses such as the Maxwell-Fish-Eye (MFE), the Luneburg or the Eaton lenses have always played an important role in Optics. The recent development of the technique called Transformation Optics has renewed the interest in these gradient index lenses. For instance, Perfect Imaging within the Wave Optics framework has recently been proved using the MFE distribution. We review here the design problem of these lenses, classify them in two groups (Luneburg moveable-limits and fixed-limits type), and establish a new design techniques for each type of problem.
Degenerate Neutrinos in Left Right Symmetric Theory
Joshipura, Anjan S.
1994-01-01
Various hints on the neutrino masses namely, ({\\em i}) the solar neutrino deficit ({\\em ii}) the atmospheric neutrino deficit ({\\em iii}) the need for the dark matter and/or ({\\em iv}) the non-zero neutrinoless double beta decay collectively imply that all the three neutrinos must be nearlty degenerate. This feature can be understood in the left right symmetric theory. We present a model based on the group $SU(2)_{L}\\times SU(2)_R\\times U(1)_{B-L}\\times SU(2)_H$ which can explain the required...
Symmetric Structure of Induction Motor Systems
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
In this paper, symmetric structure of induction motor system in stationary αβ0 coordinates is studied bythe geometric approach. The results show that the system possesses symmetry (G, θ, Ф) and infinitesimal symme-try. Under certain conditions, the system can be transformed into a form possessing state-space symmetry (G, Ф)and infinitesimal state-space symmetry by means of state feedback and input coordinate base transform. The resultscan be extended to the fifth order induction motor system fed by hysteresis-band current-controlled PWM inverter.
Specialization of Quadratic and Symmetric Bilinear Forms
Knebusch, Manfred
2010-01-01
The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970's. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory. This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed for fields of characteristic different from 2, are explored here without this restriction. In addition to chapters on specialization theory, generic splitting t
Jackson's Theorem on Bounded Symmetric Domains
Institute of Scientific and Technical Information of China (English)
Ming Zhi WANG; Guang Bin REN
2007-01-01
Polynomial approximation is studied on bounded symmetric domain Ω in C n for holo-morphic function spaces X ,such as Bloch-type spaces,Bergman-type spaces,Hardy spaces,Ω algebra and Lipschitz space.We extend the classical Jackson ’s theorem to several complex variables:E k f,X ) ω (1 /k,f,X ),where E k f,X )is the deviation of the best approximation of f ∈X by polynomials of degree at mostk with respect to the X -metric and ω (1/k,f,X )is the corresponding modulus of continuity.
SU(2) Invariants of Symmetric Qubit States
Sirsi, Swarnamala
2011-01-01
Density matrix for N-qubit symmetric state or spin-j state (j = N/2) is expressed in terms of the well known Fano statistical tensor parameters. Employing the multiaxial representation [1], wherein a spin-j density matrix is shown to be characterized by j(2j+1) axes and 2j real scalars, we enumerate the number of invariants constructed out of these axes and scalars. These invariants are explicitly calculated in the particular case of pure as well as mixed spin-1 state.
Synthesis of controllers for symmetric systems
Ameur Abid, Chiheb; Zouari, Belhassen
2010-11-01
This article deals with supervisory control problem for coloured Petri (CP) nets. Considering a CP-net, we build a condensed version of the ordinary state-space, namely the symbolic reachability graph (SRG). This latter graph allows to cope with state-space explosion problem for symmetric systems. The control specification can be expressed in terms of either forbidden states or forbidden sequences of transitions. According to these specifications, we derive the controller by applying the theory of regions on the basis of the SRG. Thanks to expressiveness power of CP-nets, the obtained controller to be connected to the plant model is reduced to one single place.
Scalar Resonances in Axially Symmetric Spacetimes
Ranea-Sandoval, Ignacio F
2015-01-01
We study properties of resonant solutions to the scalar wave equation in several axially symmetric spacetimes. We prove that non-axial resonant modes do not exist neither in the Lanczos dust cylinder, the $(2+1)$ extreme BTZ spacetime nor in a class of simple rotating wormhole solutions. Moreover, we find unstable solutions to the wave equation in the Lanczos dust cylinder and in the $r^2 <0$ region of the extreme $(2+1)$ BTZ spacetime, two solutions that possess closed timelike curves. Similarities with previous results obtained for the Kerr spacetime are explored.
Nanotribology of Symmetric and Asymmetric Liquid Lubricants
Directory of Open Access Journals (Sweden)
Shinji Yamada
2010-03-01
Full Text Available When liquid molecules are confined in a narrow gap between smooth surfaces, their dynamic properties are completely different from those of the bulk. The molecular motions are highly restricted and the system exhibits solid-like responses when sheared slowly. This solidification behavior is very dependent on the molecular geometry (shape of liquids because the solidification is induced by the packing of molecules into ordered structures in confinement. This paper reviews the measurements of confined structures and friction of symmetric and asymmetric liquid lubricants using the surface forces apparatus. The results show subtle and complex friction mechanisms at the molecular scale.
Effect of resistance to sintering on Pt/PPy-MWCNT catalysts for PEM fuel cells
Energy Technology Data Exchange (ETDEWEB)
Kim, K. [Yonsei Univ., Seoul (Korea, Republic of). Specialized Graduate School of Hydrogen and Fuel Cell; Kim, H. [Yonsei Univ., Seoul (Korea, Republic of). Dept. of Chemical and Biomolecular Engineering
2010-07-01
Recent studies have suggested that platinum (Pt) growth contributes to the degradation of fuel cell performance, as the electrochemical surface area of Pt is decreased when the particles increase in size. This study investigated the effect of inhibition to the sintering effect and uniform dispersion of Pt in a polypyrrole(Pp) multiwalled carbon nanotube (MWCNT) composite supported Pt catalyst. The sintering effect was investigated under half-cell conditions using a 0.5M sulfuric acid (H{sub 2}SO{sub 4}) electrolyte with cyclic voltammetry ranging from 0 to 1.2 V with a 5 mV per second sweep rate. The hydrogen desorption peak was carried out from the charge under the electrochemically active surface area at 4000 cycle periods. The study showed that coating the MWCNT with Ppy showed higher Pt distribution and a lower Pt sintering effect. The results were attributed to the rough surface characteristics obtained using the Ppy. Results also indicated that the catalytic activity for the oxygen reduction reaction increased by improving the interaction and stability of the Pt. 1 ref.
Guan, Guoqing; Zapf, Ralf; Kolb, Gunther; Men, Yong; Hessel, Volker; Loewe, Holger; Ye, Jianhui; Zentel, Rudolf
2007-01-21
A novel Pt-based catalyst with highly regular, periodic inverse opal microstructure was fabricated in a microchannel reactor, and catalytic testing revealed excellent conversion and stable activity for propane combustion at low temperatures.
Room-temperature formation of Pt$_3$Si/Pt$_2$Si films on poly-Si substrates
Dubkov, V P; Chizh, K V; Yuryev, V A
2016-01-01
We propose a way of formation of thin bilayer Pt$_3$Si/Pt$_2$Si films at room temperature on poly-Si substrates by Pt magnetron sputtering and wet etching, obtain such film, investigate its structure and phase composition and estimate the thickness of its layers. We verify by direct x-ray photoelectron-spectroscopic measurements our previous observation of the Pt$_2$Si layer formaton between Pt and poly-Si films as a result of Pt magnetron sputtering at room temperature. This layer likely appears due to high enough temperature of Pt ions in the magnetron plasma sufficient for chemical reaction of the silicide film formation on the Si surface. The Pt$_3$Si layer likely forms from the Pt--Pt$_3$Si layer (Pt$_{95}$Si$_5$), which arises under Pt film during the magnetron sputtering, as a result of Pt removal by wet etching.
A comparative study of Pt and Pt-Pd core-shell nanocatalysts
Energy Technology Data Exchange (ETDEWEB)
Long, Nguyen Viet, E-mail: nguyenviet_long@yahoo.com [Department of Materials Science and Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555 (Japan); Posts and Telecommunications Institute of Technology, km 10 Nguyen Trai, Thanh Xuan, Ha Dong, Hanoi (Viet Nam); Laboratory for Nanotechnology, Vietnam National University, Ho Chi Minh, Linh Trung, Thu Duc, Ho Chi Minh (Viet Nam); Department of Molecular and Material Sciences, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasugakouen, Kasuga, Fukuoka 816-8580 (Japan); Ohtaki, Michitaka [Department of Molecular and Material Sciences, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasugakouen, Kasuga, Fukuoka 816-8580 (Japan); Hien, Tong Duy [Laboratory for Nanotechnology, Vietnam National University, Ho Chi Minh, Linh Trung, Thu Duc, Ho Chi Minh (Viet Nam); Randy, Jalem [Department of Materials Science and Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555 (Japan); Nogami, Masayuki, E-mail: nogami@nitech.ac.jp [Department of Materials Science and Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555 (Japan)
2011-10-30
Highlights: > The syntheses of Pt (4-8 nm) and Pt-Pd core-shell nanoparticles (15-25 nm) are showed. > Pt-Pd core-shell catalysts possess catalytic property much better than Pt catalysts. > Pt-Pd core-shell catalysts exhibit fast and highly stable catalytic activity. > Fascinatingly, size effect is not as really important as nanostructuring effect. > Fast, stable, sensitive hydrogen adsorption is very crucial for fuel cells. - Abstract: This comparative study characterizes two types of metallic and core-shell bimetallic nanoparticles prepared with our modified polyol method. These nanoparticles consist of Pt and Pt-Pd core-shell nanocatalysts exhibiting polyhedral morphologies. The controlled syntheses of Pt metallic nanoparticles in the 10-nm regime (4-8 nm) and Pt-Pd bimetallic core-shell nanoparticles in the 30-nm regime (15-25 nm) are presented. To realize our ultimate research goals for proton exchange membrane fuel cells (PEMFCs) and direct methanol fuel cells (DMFCs), we thoroughly investigate the dependence of the electrocatalytic properties of the nanoparticles on the structure, size and morphology. Significant differences in the electrocatalysis are also explained in experimental evidences of both Pt and Pt-Pd nanocatalysts. We suggested that the core-shell controlled morphologies and nanostructures of the Pd nanoshell as the Pd atomic monolayers will not only play an important role in producing inexpensive, novel Pt- and Pd-based nanocatalysts but also in designing more efficient Pt- and Pd-based nanocatalysts for practical use in DMFC technology. Our comparative results show that Pt-Pd nanocatalysts with Pd nanoshells exhibited much better electrocatalytic activity and stabilization compared to Pt nanocatalysts. Interestingly, we found that the size effect is not as strong as the nanostructuring effect on the catalytic properties of the researched nanoparticles. A nanostructure effect of the core-shell bimetallic nanoparticles was identified.
AN ANIMAL MODEL OF PLATINUM (PT) HYPERSENSITIVITY
Exposure to Pt salts has been associated with occupational asthma. Pt, the most active component and widely used metal in catalytic converters, is released in automobile exhaust and is a proposed diesel fuel additive. Thus, with the potential for widespread environmental distrib...
Electroweak Baryogenesis in R-symmetric Supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Fok, R.; Kribs, Graham D.; Martin, Adam; Tsai, Yuhsin
2013-03-01
We demonstrate that electroweak baryogenesis can occur in a supersymmetric model with an exact R-symmetry. The minimal R-symmetric supersymmetric model contains chiral superfields in the adjoint representation, giving Dirac gaugino masses, and an additional set of "R-partner" Higgs superfields, giving R-symmetric \\mu-terms. New superpotential couplings between the adjoints and the Higgs fields can simultaneously increase the strength of the electroweak phase transition and provide additional tree-level contributions to the lightest Higgs mass. Notably, no light stop is present in this framework, and in fact, we require both stops to be above a few TeV to provide sufficient radiative corrections to the lightest Higgs mass to bring it up to 125 GeV. Large CP-violating phases in the gaugino/higgsino sector allow us to match the baryon asymmetry of the Universe with no constraints from electric dipole moments due to R-symmetry. We briefly discuss some of the more interesting phenomenology, particularly of the of the lightest CP-odd scalar.
Symmetric-key cryptosystem with DNA technology
Institute of Scientific and Technical Information of China (English)
LU MingXin; LAI XueJia; XIAO GuoZhen; QIN Lei
2007-01-01
DNA cryptography is a new field which has emerged with progress in the research of DNA computing. In our study, a symmetric-key cryptosystem was designed by applying a modern DNA biotechnology, microarray, into cryptographic technologies. This is referred to as DNA symmetric-key cryptosystem (DNASC). In DNASC,both encryption and decryption keys are formed by DNA probes, while its ciphertext is embedded in a specially designed DNA chip (microarray). The security of this system is mainly rooted in difficult biology processes and problems, rather than conventional computing technology, thus it is unaffected by changes from the attack of the coming quantum computer. The encryption process is a fabrication of a specially designed DNA chip and the decryption process is the DNA hybridization.In DNASC, billions of DNA probes are hybridized and identified at the same time,thus the decryption process is conducted in a massive, parallel way. The great potential in vast parallelism computation and the extraordinary information density of DNA are displayed in DNASC to some degree.
Analysis of non-symmetrical flapping airfoils
Tay, W. B.; Lim, K. B.
2009-08-01
Simulations have been done to assess the lift, thrust and propulsive efficiency of different types of non-symmetrical airfoils under different flapping configurations. The variables involved are reduced frequency, Strouhal number, pitch amplitude and phase angle. In order to analyze the variables more efficiently, the design of experiments using the response surface methodology is applied. Results show that both the variables and shape of the airfoil have a profound effect on the lift, thrust, and efficiency. By using non-symmetrical airfoils, average lift coefficient as high as 2.23 can be obtained. The average thrust coefficient and efficiency also reach high values of 2.53 and 0.61, respectively. The lift production is highly dependent on the airfoil’s shape while thrust production is influenced more heavily by the variables. Efficiency falls somewhere in between. Two-factor interactions are found to exist among the variables. This shows that it is not sufficient to analyze each variable individually. Vorticity diagrams are analyzed to explain the results obtained. Overall, the S1020 airfoil is able to provide relatively good efficiency and at the same time generate high thrust and lift force. These results aid in the design of a better ornithopter’s wing.
Chirally symmetric strong and electroweak interactions
Energy Technology Data Exchange (ETDEWEB)
Rajpoot, S.
1988-07-21
Strong and electroweak interactions may be a relic of the spontaneous breakdown of a chirally symmetric colour-flavour gauge group. The minimum possibility of such a structure that is symmetric between left and right is SU(3)/sub L/xSU(3)/sub R/xSU(2)/sub L/xSU(2)/sub R/xU(1)/sub B-L/ where quantum chromodynamics originates in the chiral colour group SU(3)/sub L/xSU(3)/sub R/ and the electroweak interaction originates in the ambidextrous electroweak interaction group SU(2)/sub L/xSU(2)/sub R/xU(1)/sub B-L/. The chiral anomalies are cancelled by adding a set of fermions that transform as singlets under the weak interaction group SU(2)/sub L/xSU(2)/sub R/. This model requires only three Higgs representations to break the proposed gauge symmetry to SU(3)/sup C/xU(1)/sub em/ and give masses to all the quarks and leptons of the theory. All fermion masses are 'see-saw' masses.
Electrochemical study of the Pt and Pt-Ni upon multiwalled carbon nanotubes
Mohammed, Norani Muti; Mumtaz, Asad; Ansari, Muhammad Shahid; Ahmad, Riaz
2016-11-01
Direct methanol fuel cells have attracted great interest in the recent development of portable devices. New routes are being developed for synthesizing the catalysts used in the methanol oxidation. In this work, the electrochemical behavior of the Pt and Pt-Ni upon multiwalled carbon nanotubes, synthesized via a new modified route, has been studied. The results showed that Pt-Ni 10% has the comparable current density to the Pt 20%-loading which is nearly 3 times greater than 10% Pt loading. The transfer of the polarization curve of Pt-Ni 10% towards lower polarization region following the catalyst with 20% Pt loading indicates the higher activity of the nano-electro-catalysts in the alkaline media. Also the long term efficiency and activity of the Pt-Ni with 10% loading is nearly reaching the 20% Pt-loading which is almost 10 folds greater than the 10% Pt loading. The study revealed that Ni in Pt-based nanoalloy impart not only an enhanced activity but also better durability of catalyst in direct methanol fuel cell applications.