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.
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.
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.
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.
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.
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.
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.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
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.
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.
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.
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.
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.
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.
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 $E_*={1 \\over 4}[|V_2|-(1/4+V_1)]$.
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.
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.
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.
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.
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...
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.
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.
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...
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 ...
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.
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.
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.
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 $\
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.
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.
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.
Invisibility in PT-symmetric complex crystals
Energy Technology Data Exchange (ETDEWEB)
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)
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.
Revisiting the Optical PT-Symmetric Dimer
Directory of Open Access Journals (Sweden)
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.
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.
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.
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.
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.
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...
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.
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...
$\\mathcal{PT}$-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.
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.
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?
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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.
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.
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").
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.
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.
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
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 ...
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...
$\\mathcal{PT}$-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.
EXCEPTIONAL POINTS IN OPEN AND PT-SYMMETRIC SYSTEMS
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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
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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.
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...
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...
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.
Bright Solitons in a PT-Symmetric Chain of Dimers
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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.
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.
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 ...
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...
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 $\
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.
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.
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’.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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...
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.
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.
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.
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.
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.
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.
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...
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 ...
Symmetric Morse potential is exactly solvable
Sasaki, Ryu
2016-01-01
Morse potential $V_M(x)= g^2\\exp (2x)-g(2h+1)\\exp(x)$ is defined on the full line, $-\\infty
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 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.
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.
Generalized Collective Inference with Symmetric Clique Potentials
Gupta, Rahul; Dewan, Ajit A
2009-01-01
Collective graphical models exploit inter-instance associative dependence to output more accurate labelings. However existing models support very limited kind of associativity which restricts accuracy gains. This paper makes two major contributions. First, we propose a general collective inference framework that biases data instances to agree on a set of {\\em properties} of their labelings. Agreement is encouraged through symmetric clique potentials. We show that rich properties leads to bigger gains, and present a systematic inference procedure for a large class of such properties. The procedure performs message passing on the cluster graph, where property-aware messages are computed with cluster specific algorithms. This provides an inference-only solution for domain adaptation. Our experiments on bibliographic information extraction illustrate significant test error reduction over unseen domains. Our second major contribution consists of algorithms for computing outgoing messages from clique clusters with ...
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.
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.
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.
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 ...
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Crossing symmetric potential model of pion-nucleon scattering
Blankleider, B; Skawronski, T
2010-01-01
A crossing symmetric $\\pi N$ scattering amplitude is constructed through a complete attachment of two external pions to the dressed nucleon propagator of an underlying $\\pi N$ potential model. Our formulation automatically provides expressions also for the crossing symmetric and gauge invariant pion photoproduction and Compton scattering amplitudes. We show that our amplitudes are unitary if they coincide on-shell with the amplitudes obtained by attaching one pion to the dressed $\\pi NN$ vertex of the same potential model.
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.
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.
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 ...
SUSY formalism for the symmetric double well potential
Indian Academy of Sciences (India)
Pinaki Patra; Abhijit Dutta; Jyoti Prasad Saha
2013-01-01
Using first- and second-order supersymmetric Darboüx formalism and starting with symmetric double well potential barrier we have obtained a class of exactly solvable potentials subject to moving boundary condition. The eigenstates are also obtained by the same technique.
Bound states for non-symmetric evolution Schroedinger potentials
Energy Technology Data Exchange (ETDEWEB)
Corona, Gulmaro Corona [Area de Analisis Matematico y sus Aplicaciones, Universidad Autonoma Metropolitana-Azcapotalco, Atzcapotzalco, DF (Mexico)). E-mail: ccg@correo.azc.uam.mx
2001-09-14
We consider the spectral problem associated with the evolution Schroedinger equation, (D{sup 2}+ k{sup 2}){phi}=u{phi}, where u is a matrix-square-valued function, with entries in the Schwartz class defined on the real line. The solution {phi}, called the wavefunction, consists of a function of one real variable, matrix-square-valued with entries in the Schwartz class. This problem has been dealt for symmetric potentials u. We found for the present case that the bound states are localized similarly to the scalar and symmetric cases, but by the zeroes of an analytic matrix-valued function. If we add an extra condition to the potential u, we can determine these states by an analytic scalar function. We do this by generalizing the scalar and symmetric cases but without using the fact that the Wronskian of a pair of wavefunction is constant. (author)
Vibrational motion in a symmetric, double minimum potential
DEFF Research Database (Denmark)
Spanget-Larsen, Jens
2015-01-01
Molecular vibrational motion in a symmetric, double minimum potential is treated by means of a quartic model potential, by reference to the tables published by Jaan Laane and the results of harmonic analyses for the stationary points. The inversion vibration of ammonia is treated in detail. - Not...... on the harmonic approximation for polyatomic molecules are appended. - Presented at a NORFA Workshop in Hirtshals, Denmark, August 1997....
Charge optimized many body (COMB) potentials for Pt and Au
Antony, A. C.; Akhade, S. A.; Lu, Z.; Liang, T.; Janik, M. J.; Phillpot, S. R.; Sinnott, S. B.
2017-06-01
Interatomic potentials for Pt and Au are developed within the third generation charge optimized many-body (COMB3) formalism. The potentials are capable of reproducing phase order, lattice constants, and elastic constants of Pt and Au systems as experimentally measured or calculated by density functional theory. We also fit defect formation energies, surface energies and stacking fault energies for Pt and Au metals. The resulting potentials are used to map a 2D contour of the gamma surface and simulate the tensile test of 16-grain polycrystalline Pt and Au structures at 300 K. The stress-strain behaviour is investigated and the primary slip systems {1 1 1} are identified. In addition, we perform high temperature (1800 K for Au and 2300 K for Pt) molecular dynamics simulations of 30 nm Pt and Au truncated octahedron nanoparticles and examine morphological changes of each particle. We further calculate the activation energy barrier for surface diffusion during simulations of several nanoseconds and report energies of 0.62+/- 0.16 eV for Pt and 1.44+/- 0.06 eV for Au. This initial parameterization and application of the Pt and Au potentials demonstrates a starting point for the extension of these potentials to multicomponent systems within the COMB3 framework.
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.
Potential electrode materials for symmetrical Solid Oxide Fuel Cells
Directory of Open Access Journals (Sweden)
Ruiz Morales, J. C.
2008-08-01
Full Text Available Chromites, titanates and Pt-YSZ-CeO_{2} cermets have been investigated as potential electrode materials for an alternative concept of Solid Oxide Fuel Cell (SOFC, the symmetrical SOFCs (SFC. In this configuration, the same electrode material is used simultaneously as anode and cathode. Interconnector materials, such as chromites, could be considered as potential SFC electrodes, at least under pure hydrogen-fed at relatively high temperatures, as they do not exhibit significant catalytic activity towards hydrocarbon oxidation. This may be overcome by partially substituting Cr in the perovskite B-sites by other transition metal cations such as Mn. La_{0.75}Sr_{0.25}Cr_{0.5}Mn_{0.5}O_{3-δ} (LSCM is a good candidate for such SFCs, rendering fuel cell performances in excess of 500 and 300mW/cm^{2} using pure H_{2} and CH_{4} as fuel, at 950 ^{o}C. Similarly, typical n-type electronic conductors traditionally regarded as anode materials, such as strontium titanates, may also operate under oxidising conditions as cathodes by substituting some Ti content for Fe to introduce p-type conductivity. Preliminary electrochemical experiments on La_{4}Sr_{8}Ti_{12-x}Fe_{x}O_{38-δ}-based SFCs show that they perform reasonably well under humidified H_{2}, at high temperatures. A third group of materials is the support material of any typical cermet anode, i.e. YSZ, CeO_{2} plus a current collector. It has been found that this combination could be optimised to operate as SFC electrodes, rendering performances of 400mW/cm^{2} under humidified pure H_{2} at 950^{o}C.
Cromitas, titanatos y cermets de Pt-YSZ-CeO_{2} han sido investigados como potenciales materiales de electrodo para un concepto alternativo de Pilas de Combustible de Óxidos Sólidos (SOFC, las pilas SOFC simétricas (SFC. En
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 ...
Invariant currents and scattering off locally symmetric potential landscapes
Kalozoumis, P. A.; Morfonios, C. V.; Diakonos, F. K.; Schmelcher, P.
2015-11-01
We study the effect of discrete symmetry breaking in inhomogeneous scattering media within the framework of generic wave propagation. Our focus is on one-dimensional scattering potentials exhibiting local symmetries. We find a class of spatially invariant nonlocal currents, emerging when the corresponding generalized potential exhibits symmetries in arbitrary spatial domains. These invariants characterize the wave propagation and provide a spatial mapping of the wave function between any symmetry related domains. This generalizes the Bloch and parity theorems for broken reflection and translational symmetries, respectively. Their nonvanishing values indicate the symmetry breaking, whereas a zero value denotes the restoration of the global symmetry where the well-known forms of the two theorems are recovered. These invariants allow for a systematic treatment of systems with any local symmetry combination, providing a tool for the investigation of the scattering properties of aperiodic but locally symmetric systems. To this aim we express the transfer matrix of a locally symmetric potential unit via the corresponding invariants and derive quantities characterizing the complete scattering device which serve as key elements for the investigation of transmission spectra and particularly of perfect transmission resonances.
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.
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 ...
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...
Maximum tunneling velocities in symmetric double well potentials
Energy Technology Data Exchange (ETDEWEB)
Manz, Jörn [State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, 92, Wucheng Road, Taiyuan 030006 (China); Institut für Chemie und Biochemie, Freie Universität Berlin, Takustr. 3, 14195 Berlin (Germany); Schild, Axel [Institut für Chemie und Biochemie, Freie Universität Berlin, Takustr. 3, 14195 Berlin (Germany); Schmidt, Burkhard, E-mail: burkhard.schmidt@fu-berlin.de [Institut für Mathematik, Freie Universität Berlin, Arnimallee 6, 14195 Berlin (Germany); Yang, Yonggang, E-mail: ygyang@sxu.edu.cn [State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, 92, Wucheng Road, Taiyuan 030006 (China)
2014-10-17
Highlights: • Coherent tunneling in one-dimensional symmetric double well potentials. • Potentials for analytical estimates in the deep tunneling regime. • Maximum velocities scale as the square root of the ratio of barrier height and mass. • In chemical physics maximum tunneling velocities are in the order of a few km/s. - Abstract: 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 several prototypical molecular models of non-cyclic and cyclic tunneling, including ammonia inversion, Cope rearrangement of semibullvalene, torsions of molecular fragments, and rotational tunneling in strong laser fields. Typical maximum velocities and angular velocities are in the order of a few km/s and from 10 to 100 THz for our non-cyclic and cyclic systems, respectively, much faster than time-averaged velocities. Even for the more extreme case of an electron tunneling through a barrier of height of one Hartree, the velocity is only about one percent of the speed of light. Estimates of the corresponding time scales for
Novel C3-symmetric molecular scaffolds with potential facial differentiation.
Hennrich, Gunther; Lynch, Vincent M; Anslyn, Eric V
2002-05-17
The conversion of 1,3,5-substituted benzene and mesitylene by electrophilic aromatic substitution and Sonogashira cross-coupling, respectively, furnished the C3-symmetric, hexasubstituted benzene derivatives 1 and 2 with an alternating substitution pattern. Based on the molecular scaffolds obtained, the two systems serve as model compounds for novel receptor molecules with distinct geometric features. X-ray structures have been obtained for 1 and 2, which are discussed in regard to their aptitude as receptor platforms or supramolecular building blocks. By looking at the rotational barriers for the functional groups placed around the molecular scaffolds by variable temperature 1H NMR spectroscopy, 1 and 2 turn out to exist in rapidly interconverting conformations. The alignment of these potential binding groups around the molecular scaffolds should be strongly biased by specific interactions with suitable guest molecules.
Isospectral partners for a complex PT-invariant potential
Sinha, A K; Sinha, Anjana; Roychoudhury, Rajkumar
2002-01-01
We construct isospectral partner potentials of a complex PT-invariant potential, viz., V(x) = V_1 sech ^2 x - i V_2 sech x tanh x using Darboux's method. Oneset of isospectral potentials are obatined which can be termed 'Satellite potentials', in the sense that they are pf the same form as the original potential. In a particular case, the supersymmetric partner potential has the same spectrum, including the zero energy ground state, a fact which cannot occur in conventional supersymmetric quantum mechanics with real potential. An explicit example of a non-trivial set of isospectral potential is also obtained.
Rovibrational states of Wigner molecules in spherically symmetric confining potentials
Cioslowski, Jerzy
2016-08-01
The strong-localization limit of three-dimensional Wigner molecules, in which repulsively interacting particles are confined by a weak spherically symmetric potential, is investigated. An explicit prescription for computation of rovibrational wavefunctions and energies that are asymptotically exact at this limit is presented. The prescription is valid for systems with arbitrary angularly-independent interparticle and confining potentials, including those involving Coulombic and screened (i.e., Yukawa/Debye) interactions. The necessary derivations are greatly simplified by explicit constructions of the Eckart frame and the parity-adapted primitive wavefunctions. The performance of the new formalism is illustrated with the three- and four-electron harmonium atoms at their strong-correlation limits. In particular, the involvement of vibrational modes with the E symmetry is readily pinpointed as the origin of the "anomalous" weak-confinement behavior of the 1S+ state of the four-electron species that is absent in its 1D+ companion of the strong-confinement regime.
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.
Stable Event-Driven Particle Dynamics: Spherically Symmetric Potentials
Bannerman, Marcus N
2012-01-01
Event-Driven Particle Dynamics is a fast and precise method to simulate particulate systems of all scales. These advantages arise from the analytical solution of the dynamics required by the discrete-potential models used. Despite the high precision solution, the finite calculation-precision of computers will still cause the simulation to enter invalid states which, if left unchecked, can lead to unresolvable errors. In this work, the treatment of these marginal invalid-states is discussed and a general event-detection algorithm is proposed which stably handles these situations. This requires a definition of the dynamics of invalid states and leads to improved algorithms for event-detection in spherically symmetric systems, including the well-established hard-sphere and square-well models. Finally, the Event-Driven Particle Dynamics technique is extended to allow the study of systems with complex spherical-mesh boundary conditions and distance constraints as a demonstration of the generality of the proposed a...
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.
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.
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 .
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.
Modeling the local potential at Pt nanoparticles in polymer electrolyte membranes.
Eslamibidgoli, Mohammad Javad; Melchy, Pierre-Éric Alix; Eikerling, Michael H
2015-04-21
We present a physical-analytical model for the potential distribution at Pt nanodeposits in a polymer electrolyte membrane (PEM). Experimental studies have shown that solid deposits of Pt in PEM play a dual role in radical-initiated membrane degradation. Surface reactions at Pt particles could facilitate the formation as well as the scavenging of ionomer-attacking radical species. The net radical balance depends on local equilibrium conditions at Pt nanodeposits in the PEM, specifically, their equivalent local electrode potential. Our approach utilizes a continuum description of crossover fluxes of reactant gases, coupled with the kinetics of electrochemical surface reactions at Pt nanodeposits to calculate the potential distribution. The local potential is a function of the PEM structure and composition, which is determined by PEM thickness, concentrations of H2 and O2, as well as the size and density distribution of Pt particles. Model results compare well with experimental data for the potential distribution in PEMs.
Chaotic motion in axially symmetric potentials with oblate quadrupole deformation
Energy Technology Data Exchange (ETDEWEB)
Letelier, Patricio S. [Departamento de Matematica Aplicada, IMECC, Universidade Estadual de Campinas, 13083-859, Campinas, SP (Brazil); Ramos-Caro, Javier, E-mail: javier@ime.unicamp.br [Departamento de Matematica Aplicada, IMECC, Universidade Estadual de Campinas, 13083-859, Campinas, SP (Brazil); Lopez-Suspes, Framsol, E-mail: framsol@gmail.com [Facultad de Telecomunicaciones, Universidad Santo Tomas and Escuela de Fisica, Universidad Industrial de Santander, Bucaramanga (Colombia)
2011-10-03
By computing the Poincare's surfaces of section and Lyapunov exponents, we study the effect of introducing an oblate quadrupole in the dynamics associated with two generic spherical potentials of physical interest: the central monopole and the isotropic harmonic oscillator. In the former case we find saddle points in the effective potential, in contrast to the statements presented by Gueron and Letelier in [E. Gueron, P.S. Letelier, Phys. Rev. E 63 (2001) 035201]. The results we show in the second case have application in nuclear or atomic physics. In particular, we find values of oblate deformation leading to a disappearance of shell structure in the single-particle spectrum. -- Highlights: → We find chaotic motion around a monopole with oblate quadrupole deformation. → This corrects the statements introduced in [E. Gueron, P.S. Letelier, Phys. Rev. E 63 (2001) 035201]. → We present an alternative model for the potential due to an oblate deformed nuclei. → This leads to stochastic regions in the phase space of classical orbits. → It suggests that the shell structure of single-particle spectrum tends to disappear.
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.
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...
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.
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.
Quantum-Carnot engine for particle confined to 2D symmetric potential well
Belfaqih, Idrus Husin; Sutantyo, Trengginas Eka Putra; Prayitno, T. B.; Sulaksono, Anto
2015-09-01
Carnot model of heat engine is the most efficient cycle consisting of isothermal and adiabatic processes which are reversible. Although ideal gas usually used as a working fluid in the Carnot engine, Bender used quantum particle confined in 1D potential well as a working fluid. In this paper, by following Bender we generalize the situation to 2D symmetric potential well. The efficiency is express as the ratio of the initial length of the system to the final length of the compressed system. The result then is shown that for the same ratio, 2D potential well is more efficient than 1D potential well.
Quantum-Carnot engine for particle confined to 2D symmetric potential well
Energy Technology Data Exchange (ETDEWEB)
Belfaqih, Idrus Husin, E-mail: idrushusin21@gmail.com; Sutantyo, Trengginas Eka Putra, E-mail: trengginas.eka@gmail.com; Prayitno, T. B., E-mail: teguh-budi@unj.ac.id [Department of Physics, Universitas Negeri Jakarta, Jl. Pemuda Rawamangun, Jakarta Timur, 13220 (Indonesia); Sulaksono, Anto, E-mail: anto.sulaksono@sci.ui.ac.id [Department of Physics, Universitas Indonesia, Depok, Jawa Barat, 164242 (Indonesia)
2015-09-30
Carnot model of heat engine is the most efficient cycle consisting of isothermal and adiabatic processes which are reversible. Although ideal gas usually used as a working fluid in the Carnot engine, Bender used quantum particle confined in 1D potential well as a working fluid. In this paper, by following Bender we generalize the situation to 2D symmetric potential well. The efficiency is express as the ratio of the initial length of the system to the final length of the compressed system. The result then is shown that for the same ratio, 2D potential well is more efficient than 1D potential well.
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.
Unified treatment of a class of spherically symmetric potentials: quasi-exact solution
Panahi, Hossein
2016-01-01
In this paper, we investigate the Schr\\"odinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all models give rise to the same basic differential equation, which is expressible as an element of the universal enveloping algebra of sl(2). Then, we obtain the general exact solutions of the problem by employing the representation theory of sl(2) Lie algebra.
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.
Directory of Open Access Journals (Sweden)
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.
Fantauzzi, Donato; Bandlow, Jochen; Sabo, Lehel; Mueller, Jonathan E; van Duin, Adri C T; Jacob, Timo
2014-11-14
ReaxFF force field parameters describing Pt-Pt and Pt-O interactions have been developed and tested. The Pt-Pt parameters are shown to accurately account for the chemical nature, atomic structures and other materials properties of bulk platinum phases, low and high-index platinum surfaces and nanoclusters. The Pt-O parameters reliably describe bulk platinum oxides, as well as oxygen adsorption and oxide formation on Pt(111) terraces and the {111} and {100} steps connecting them. Good agreement between the force field and both density functional theory (DFT) calculations and experimental observations is demonstrated in the relative surface free energies of high symmetry Pt-O surface phases as a function of the oxygen chemical potential, making ReaxFF an ideal tool for more detailed investigations of more complex Pt-O surface structures. Validation for its application to studies of the kinetics and dynamics of surface oxide formation in the context of either molecular dynamics (MD) or Monte Carlo simulations are provided in part by a two-part investigation of oxygen diffusion on Pt(111), in which nudged elastic band (NEB) calculations and MD simulations are used to characterize diffusion processes and to determine the relevant diffusion coefficients and barriers. Finally, the power of the ReaxFF reactive force field approach in addressing surface structures well beyond the reach of routine DFT calculations is exhibited in a brief proof-of-concept study of oxygen adsorbate displacement within ordered overlayers.
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.
Energy eigenvalues of spherical symmetric potentials with relativistic corrections: analytic results
Energy Technology Data Exchange (ETDEWEB)
Dineykhan, M; Zhaugasheva, S A [Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna (Russian Federation); Toinbaeva, N Sh [al-Farabi Kazak National University, Almaty (Kazakhstan)
2010-01-14
Based on the investigation of the asymptotic behaviour of the polarization loop function for charged n scalar particles in an external gauge field, we determine the interaction Hamiltonian including the relativistic corrections. The energy eigenvalues of spherical symmetric potentials for two-particle bound state systems with relativistic corrections are analytically derived. The energy spectra of linear and funnel potentials with orbital and radial excitations are determined. The energy spectrum of a superposition of Coulomb and Yukawa potentials is also determined. Our result shows that the energy spectrum with the relativistic corrections for the linear, harmonic oscillator and funnel potentials is smaller than the upper boundaries for the energy spectrum established in the framework of the spinless Salpeter equation for the orbital and radial excited states. The relativistic corrections to the energy spectrum of a superposition of the attractive Coulomb potential and the Yukawa (exponentially screened Coulomb) potentials are very small.
Directory of Open Access Journals (Sweden)
Jelena D. Lović
2017-01-01
Full Text Available Following earlier works from our laboratory, further experiments on electrochemical behavior in formic acid oxidation at electrodeposited Pt(Bi/GC and Pt/GC electrode were performed in order to examine the effect of successive increase of the forward potential scan limit. Correlation between formic acid oxidation and oxide species on Pt(Bi/GC electrode with increases of forward potential scan limit is based on the dependency of the backward peak potential from backward peak current. The obtained dependency reveals Bi influence for the scan limits up to 0.8 V. Since the Pt(Bi/GC electrode is composed of Bi core occluded by Pt and Bi-oxide surface layer, the observed behavior is explained through the influence of surface metal oxide on easier formation of OHad species. Nevertheless, the influence of electronic modification of Pt surface atoms by underlying Bi is present and leads to the stronger adsorption of OH on Pt. At higher forward potential scan limits (from 0.8 V, Pt has a dominant role in HCOOH oxidation.
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.
Coherent control for the spherical symmetric box potential in short and intensive XUV laser fields
Barna, I F
2007-01-01
Coherent control calculations are presented for a spherically symmetric box potential for non-resonant two photon transition probabilities. With the help of a genetic algorithm (GA) the population of the excited states are maximized and minimized. The external driving field is a superposition of three intensive extreme ultraviolet (XUV) linearly polarized laser pulses with different frequencies in the femtosecond duration range. We solved the quantum mechanical problem within the dipole approximation. Our investigation clearly shows that the dynamics of the electron current has a strong correlation with the optimized and neutralizing pulse shape.
Yuan, Jian-Hui; Chen, Ni; Mo, Hua; Zhang, Yan; Zhang, Zhi-Hai
2015-12-01
A detailed investigation of the second harmonic generation in symmetrical and asymmetrical Gaussian potential quantum wells under the influence of applied electric field by using the compact-density-matrix approach and the finite difference method. The results show that the second-harmonic generation susceptibility obtained in two cases can reach the magnitude of 10-4 m/V, which depend dramatically on the applied electric field and the structural parameters. Finally, the resonant peak and its corresponding to the resonant energy are also taken into account.
Unified Treatment of a Class of Spherically Symmetric Potentials: Quasi-Exact Solution
Directory of Open Access Journals (Sweden)
H. Panahi
2016-01-01
Full Text Available We investigate the Schrödinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all models give rise to the same basic differential equation, which is expressible as an element of the universal enveloping algebra of sl(2. Then, we obtain the general exact solutions of the problem by employing the representation theory of sl(2 Lie algebra.
Braneworld Inflation in Supergravity with a Shift Symmetric K$\\"{a}$hler Potential
Indian Academy of Sciences (India)
Z. Mounzi; M. Ferricha-Alami; A. Safsafi; M. Bennai
2016-06-01
We propose a new solution to the $\\eta$-problem in supergravity using a shift symmetric K\\"{a}hler potential in the context of the Randall–Sundrum type II model. We focus on a F-term supergravity inflation with a minimal K\\"{a}hler potential taking into account the radiative corrections. The slow-roll conditions are ensured by the shift symmetry where a very small value of $\\eta$ $(\\eta \\ll 1)$ is obtained. In this context, we derive all known spectrum inflationary parameters which are widely consistent with Planck 2015 data for a particular choice of brane tension and coupling constant values. A suitable observational central value of $n_{s}=0.96$ is also obtained in the case of minimal K$\\"{a}$hler potential.
Directory of Open Access Journals (Sweden)
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.
A Simple General Solution of the Radial Schrodinger Equation for Spherically Symmetric Potentials
Erbil, H H
2003-01-01
By using a simple procedure the general solution of the time-independent radial Schrodinger Equation for spherical symmetric potentials was made without making any approximation. The wave functions are always periodic. It appears two diffucilties: one of them is the solution of the equation E= U(r), where E and U(r) are the total an effective potential energies, respectively, and the other is the calculation of the integral of the square root of U(r). If analytical calculations are not possible, one must apply numerical methods. To find the energy wave function of the ground state, there is no need for the calculation of this integral, it is sufficient to find the classical turning points, that is to solve the equation E=U(r).
Iso-chemical potential trajectories in the P-T plane for He II
Maytal, B.; Nissen, J. A.; Van Sciver, S. W.
1990-01-01
Trajectories of constant chemical potential in the P-T plane serve as an integral formulation of London's equation. The trajectories are useful for analysis and synthesis of fountain effect pump performance. A family of trajectories is generated from available numerical codes.
Iso-chemical potential trajectories in the P-T plane for He II
Maytal, B.; Nissen, J. A.; Van Sciver, S. W.
1990-01-01
Trajectories of constant chemical potential in the P-T plane serve as an integral formulation of London's equation. The trajectories are useful for analysis and synthesis of fountain effect pump performance. A family of trajectories is generated from available numerical codes.
PT symmetry breaking and exceptional points for a class of inhomogeneous complex potentials
Energy Technology Data Exchange (ETDEWEB)
Dorey, Patrick; Lishman, Anna [Department of Mathematical Sciences, University of Durham, Durham DH1 3LE (United Kingdom); Dunning, Clare [SMSAS, University of Kent, Canterbury, UK CT2 7NF (United Kingdom); Tateo, Roberto [Dip. di Fisica Teorica and INFN, Universita di Torino, Via P. Giuria 1, 10125 Torino (Italy)], E-mail: p.e.dorey@durham.ac.uk, E-mail: t.c.dunning@kent.ac.uk, E-mail: AnnaLishman@dunelm.org.uk, E-mail: tateo@to.infn.it
2009-11-20
We study a three-parameter family of PT-symmetric Hamiltonians, related via the ODE/IM correspondence to the Perk-Schultz models. We show that real eigenvalues merge and become complex at quadratic and cubic exceptional points, and explore the corresponding Jordan block structures by exploiting the quasi-exact solvability of a subset of the models. The mapping of the phase diagram is completed using a combination of numerical, analytical and perturbative approaches. Among other things this reveals some novel properties of the Bender-Dunne polynomials, and gives new insight into a phase transition to infinitely many complex eigenvalues that was first observed by Bender and Boettcher. A new exactly solvable limit, the inhomogeneous complex square well, is also identified.
Thermodynamic Properties of a Nucleon under the Generalized Symmetric Woods-Saxon Potential
Lütfüoğlu, B C
2016-01-01
The exact analytical solution of the Schr\\"{o}dinger equation for a generalized symmetrical Woods-Saxon potential are examined for a nucleon in an atomic nucleus for bound and quasi-bound states in one dimension. Examining the wave functions, it is observed that the nucleon is completely confined within the nucleus, i.e., no decay probability for bound states, while tunneling probabilities arise for quasi-bound states. We have calculated the temperature dependent Helmholtz free energies, the internal energies, the entropies and the specific heat capacities of the system. It is shown that, when the quasi-bound states are included, the internal energy and entropy increase, while the Helmholtz energy decreases at high temperatures. The internal energy has an inflection point at the first excited state, at which the specific heat capacity passes through a maximum.
A second eigenvalue bound for the Dirichlet Schrodinger equation wtih a radially symmetric potential
Directory of Open Access Journals (Sweden)
Craig Haile
2000-01-01
Full Text Available We study the time-independent Schrodinger equation with radially symmetric potential $k|x|^alpha$, $k ge 0$, $k in mathbb{R}, alpha ge 2$ on a bounded domain $Omega$ in $mathbb{R}^n$, $(n ge 2$ with Dirichlet boundary conditions. In particular, we compare the eigenvalue $lambda_2(Omega$ of the operator $-Delta + k |x|^alpha $ on $Omega$ with the eigenvalue $lambda_2(S_1$ of the same operator $-Delta +kr^alpha$ on a ball $S_1$, where $S_1$ has radius such that the first eigenvalues are the same ($lambda_1(Omega = lambda_1(S_1$. The main result is to show $lambda_2(Omega le lambda_2(S_1$. We also give an extension of the main result to the case of a more general elliptic eigenvalue problem on a bounded domain $Omega$ with Dirichlet boundary conditions.
Potential oscillations in a proton exchange membrane fuel cell with a Pd-Pt/C anode
Lopes, Pietro P.; Ticianelli, Edson A.; Varela, Hamilton
We report in this paper the occurrence of potential oscillations in a proton exchange membrane fuel cell (PEMFC) with a Pd-Pt/C anode, fed with H 2/100 ppm CO, and operated at 30 °C. We demonstrate that the use of Pd-Pt/C anode enables the emergence of dynamic instabilities in a PEMFC. Oscillations are characterized by the presence of very high oscillation amplitude, ca. 0.8 V, which is almost twice that observed in a PEMFC with a Pt-Ru/C anode under similar conditions. The effects of the H 2/CO flow rate and cell current density on the oscillatory dynamics were investigated and the mechanism rationalized in terms of the CO oxidation and adsorption processes. We also discuss the fundamental aspects concerning the operation of a PEMFC under oscillatory regime in terms of the benefit resulting from the higher average power output.
Simulation of symmetric nuclei and the role of Pauli potential in binding energies
Energy Technology Data Exchange (ETDEWEB)
M. Angeles Perez-Garcia, K. Tsushima, A. Valcarce
2009-05-01
It is shown that the use of a density dependent effective Pauli potential together with a nucleon-nucleon interaction potential plays a crucial role to reproduce not only the binding energies but also the matter root mean square radii of medium mass range spin-isospin saturated nuclei. This study is performed with a semiclassical Monte Carlo many-body simulation within the context of a simplified nucleon-nucleon interaction to focus on the effect of the genuine correlations due to the fermionic nature of nucleons. The procedure obtained is rather robust and it does not depend on the detailed features of the nucleon-nucleon interaction. For nuclei below saturation the density dependence may be represented in terms either of the nucleon number, $A$, or the associated Fermi momenta. When testing the simulation procedure for idealized "infinite" symmetric nuclear matter within the corresponding range of densities, it turns out that finite size effects affect the Pauli potential strength parametrization in systems up to about 120 particles while remaining approximately stable for larger systems.
New potential structure for jewelry application. Does it exist in Pt-Mo, Pt-Hf, or other systems?
Gilmartin, Erin; Corbitt, Jacqueline; Hart, Gus
2009-10-01
The only known intermetallic structure with an 8:1 stoichiometry is that of Pt8Ti. It is intriguing that an ordered phase would occur at such low concentrations of the minority atom, but this structure occurs in about a dozen binary intermetallic systems. The formation of an ordered phase in an alloy can significantly enhance the performance of the material, particularly the hardness. We have taken a broad look at possible systems where this phase forms. Using first-principles, we calculated the stability of this structure relative to experimentally known phases for more than 70 Pt/Pd binary systems. We find the Pt8Ti structure is a possible ground state in more than 20 cases. Our experimental collaborators have verified our prediction in Pt-Mo and observed order-hardening in Pt-Hf. We discuss the discovery of new ground states via the cluster expansion that are likely to be verified experimentally and their impact on Pt- and Pd-based jewelry and catalysts.
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...
New quasi-exactly solvable Hermitian as well as non-Hermitian $\\mathcal{PT}$ -invariant potentials
Indian Academy of Sciences (India)
Avinash Khare; Bhabani Prasad Mandal
2009-08-01
We start with quasi-exactly solvable (QES) Hermitian (and hence real) as well as complex $\\mathcal{PT}$ -invariant, double sinh-Gordon potential and show that even after adding perturbation terms, the resulting potentials, in both cases, are still QES potentials. Further, by using anti-isospectral transformations, we obtain Hermitian as well as $\\mathcal{PT}$ - invariant complex QES periodic potentials. We study in detail the various properties of the corresponding Bender–Dunne polynomials.
Symmetric linear potential and imperfect Brownian ratchet in molecular motor function
Institute of Scientific and Technical Information of China (English)
Li Fang-Zhen; Hu Kuang-Hu; Su Wan-Fang; Chen Yi-Chen
2005-01-01
Biomolecular motors are tiny engines that transport materials at the microscopic level within biological cells. In recent years, Elston and Peskin et al have investigated the effect of the elastic properties of the tether that connects the motor to its cargo at the speed of the motor. In this paper we extend their work and present a tether in the form of symmetric linear potential. Our results show that when the driving mechanism is an imperfect Brownian ratchet, the average speed decreases as the stiffness of the tether increases in the limit of large motor diffusion coefficient, which is similar to the results of Elston and Peskin. However, a threshold for the stiffness of the tether connecting the motor to its cargo is found in our model. Only when the tether is stiffer than the threshold can the motor and its cargo function co-operatively, otherwise, the motor and its cargo depart from each other. This result is more realistic than that of the spring model of Elston and Peskin.
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.
Spherically symmetric potential in noncommutative spacetime with a compactified extra dimensions
Energy Technology Data Exchange (ETDEWEB)
Guedezounme, Secloka Lazare [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); Kanfon, Antonin Danvide [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); University of d' Abomey-Calavi, Faculte des Sciences et Techniques, Cotonou (Benin); Samary, Dine Ousmane [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); University of d' Abomey-Calavi, Faculte des Sciences et Techniques, Cotonou (Benin); Albert Einstein Institute, Max Planck Institute for Gravitational Physics, Potsdam (Germany)
2016-09-15
The Schroedinger equation of the spherically symmetrical quantum models such as the hydrogen atom problem seems to be analytically non-solvable in higher dimensions. When we try compactifying one or several dimensions this question can maybe solved. This paper presents a study of the spherically symmetrical quantum models on noncommutative spacetime with compactified extra dimensions. We provide analytically the resulting spectrum of the hydrogen atom and Yukawa problem in 4 + 1 dimensional noncommutative spacetime in the first order approximation of the noncommutative parameter. The case of higher dimensions D ≥ 4 is also discussed. (orig.)
Directory of Open Access Journals (Sweden)
Demetrios G. Eliopoulos
2014-03-01
Full Text Available Porphyry Cu–Au–Pd±Pt deposits are significant Au resources, but their Pd and Pt potential is still unknown. Elevated Pd, Pt (hundreds of ppb and Au contents are associated with typical stockwork magnetite-bornite-chalcopyrite assemblages, at the central parts of certain porphyry deposits. Unexpected high grade Cu–(Pd+Pt (up to 6 ppm mineralization with high Pd/Pt ratios at the Elatsite porphyry deposit, which is found in a spatial association with the Chelopech epithermal deposit (Bulgaria and the Skouries porphyry deposit, may have formed during late stages of an evolved hydrothermal system. Estimated Pd, Pt and Au potential for porphyry deposits is consistent with literature model calculations demonstrating the capacity of aqueous vapor and brine to scavenge sufficient quantities of Pt and Pd, and could contribute to the global platinum-group element (PGE production. Critical requirements controlling potential of porphyry deposits may be from the metals contained in magma (metasomatized asthenospheric mantle wedge as indicated by significant Cr, Co, Ni and Re contents. The Cr content may be an indicator for the mantle input.
Paz-Borbón, Lauro Oliver; Mortimer-Jones, Thomas V; Johnston, Roy L; Posada-Amarillas, Alvaro; Barcaro, Giovanni; Fortunelli, Alessandro
2007-10-14
The energetics of 98 atom bimetallic Pd-Pt clusters are studied using a combination of: a genetic algorithm technique (to explore vast areas of the configurational space); a basin-hopping atom-exchange routine (to search for lowest-energy homotops at fixed composition); and a shell optimisation approach (to search for high symmetry isomers). The interatomic interactions between Pd and Pt are modelled by the Gupta many-body empirical potential. For most compositions, the putative global minima are found to have structures based on defective Marks decahedra, but in the composition range from Pd46Pt52 to Pd63Pt35, the Leary tetrahedron (LT)--a structure previously identified for 98 atom Lennard-Jones clusters--is consistently found as the most stable structure. Based on the excess energy stability criterion, Pd56Pt42 represents the most stable cluster across the entire composition range. This structure, a Td-symmetry LT, exhibits multi-layer segregation with an innermost core of Pd atoms, an intermediate layer of Pt atoms and an outermost Pd surface shell (Pd-Pt-Pd). The stability of the Leary tetrahedron is compared against other low-energy competing structural motifs: the Marks decahedron (Dh-M), a "quasi" tetrahedron (a closed-packed structure) and two other closed-packed structures. The stability of LT structures is rationalized in terms of their spherical shape and the large number of nearest neighbours.
Indian Academy of Sciences (India)
B Bagchi; C Quesne; R Roychoudhury
2009-08-01
We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. $\\mathcal{PT}$ symmetry may facilitate reconciling our approach to the requirement that the rationally extended potentials be singularity free. Some examples are shown.
The use of symmetrized valence and relative motion coordinates for crystal potentials
DEFF Research Database (Denmark)
McMurry, H. L.; Hansen, Flemming Yssing
1980-01-01
Symmetrized valence coordinates are linear combinations of conventional valence coordinates which display the symmetry of a set of atoms bound by the valence bonds. Relative motion coordinates are relative translations, or relative rotations, of two or more strongly bonded groups of atoms among...... which relatively weak forces act. They are useful for expressing interactions between molecules in molecular crystals and should be chosen, also, to reflect the symmetry of the interacting groups. Since coordinates defined by these procedures possess elements of symmetry in common with the bonding...... interaction constants coupling coordinates of unlike symmetry with regard to the crystal point group are necessarily zero. They may be small, also, for coordinates which belong to different representations of the local symmetry when this is not the same as for the crystal. Procedures are given for defining...
Sinha, Debdeep; Ghosh, Pijush K.
2017-01-01
A two component nonlocal vector nonlinear Schrödinger equation (VNLSE) is considered with a self-induced parity-time-symmetric potential. It is shown that the system possess a Lax pair and an infinite number of conserved quantities and hence integrable. Some of the conserved quantities like number operator, Hamiltonian etc. are found to be real-valued, in spite of the corresponding charge densities being complex. The soliton solution for the same equation is obtained through the method of inverse scattering transformation and the condition of reduction from nonlocal to local case is mentioned.
Lütfüoğlu, B C
2016-01-01
The energy eigenvalues and the wave functions of an $\\alpha$ particle in a Bohrium $270$ nucleus were calculated by solving Schr\\"odinger equation for Generalized Symmetric Woods-Saxon potential. Using the energy spectrum by excluding and including the quasi-bound eigenvalues, entropy, internal energy, Helmholtz energy, and specific heat, as functions of reduced temperature were calculated. Stability and emission characteristics are interpreted in terms of the wave and thermodynamic functions. The kinetic energy of a decayed $\\alpha$ particle was calculated using the quasi-bound states, which is found close to the experimental value.
Directory of Open Access Journals (Sweden)
Bekir Can LÜTFÜOĞLU
2017-04-01
Full Text Available The energy eigenvalues and the wave functions of an α particle in a Bohrium 270 nucleus have been calculated by solving Schrödinger equation for Generalized Symmetric Woods-Saxon potential. Using the energy spectrum by excluding and including the quasi-bound eigenvalues, entropy, internal energy, Helmholtz energy, and specific heat, as functions of reduced temperature have been calculated. Stability and emission characteristics have been interpreted in terms of the wave and thermodynamic functions. The kinetic energy of a decayed α particle was calculated using the quasi-bound states, which has been found close to the experimental value.
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.
Exact Solutions of Klein-Gordon Equation with Scalar and Vector Rosen-Morse-Type Poten-tials
Institute of Scientific and Technical Information of China (English)
A. Soylu; O. Bayrak; I. Boztosun
2008-01-01
@@ We obtain an exact analytical solution of the Klein-Gordon equation for the equal vector and scalar Rosen-Morse and Eckart potentials as well as the parity-time (PT) symmetric version of the these potentials by using the asymptotic iteration method. Although these PT symmetric potentials are non-Hermitian, the corresponding eigenvalues are real as a result of the PT symmetry.
Complexification of three potential models – II
Indian Academy of Sciences (India)
Sanjib Meyur; S Dednath
2009-10-01
A new kind of $\\mathcal{PT}$ and non-$\\mathcal{PT}$-symmetric complex potentials are constructed from a group theoretical viewpoint of the sl(2, ) potential algebras. The real eigenvalues and the corresponding regular eigenfunctions are also obtained. The results are compared with the ones obtained before.
Lanthanum chromite materials as potential symmetrical electrodes for Solid Oxide Fuel Cells
Directory of Open Access Journals (Sweden)
Ruiz-Morales, J. C.
2007-08-01
Full Text Available A commonly used interconnector material has been tested as electrode for a new concept of Solid Oxide Fuel Cell, where the same material could be used, simultaneously, as interconnector, anode and cathode. We have found that a typical substituted chromite, such as La0.7Ca0.3CrO3-δ (LCC can be considered a good candidate for such configuration, due to its high electronic conductivity in both reducing and oxidising conditions, and moderate catalytic properties for oxygen reduction and hydrogen oxidation. The symmetrical design renders performances of 100 mWcm-2 at 950ºC, using O2 and H2 as oxidant and fuel respectively. Performances exceeding 300 mWcm-2 can be predicted for a 100μm-thick YSZ electrolyte.
Un material comúnmente utilizado como interconector ha sido probado como electrodo para un nuevo concepto de Pila de Combustible de Óxidos Sólido, en el cual el mismo material se utiliza, simultáneamente, como interconector, ánodo y cátodo. Hemos encontrado que una cromita típica como La0.7Ca0.3CrO3-δ (LCC puede ser considerada una buena candidata para dicha configuración, debido a sus altas conductividades eléctricas tanto en condiciones reductoras como oxidantes y una aceptable actividad catalítica para la reducción del oxígeno y la oxidación del hidrógeno. El diseño simétrico permite obtener rendimientos del orden de 100mWcm-2 a 950ºC, utilizando O2 e H2 como oxidante y combustible, respectivamente. Rendimientos que superan los 300mWcm-2 pueden predecirse para pilas con electrolitos de YSZ de 100 μm de grosor.
Zygridou, S.; Barton, C. W.; Nutter, P. W.; Thomson, T.
2017-07-01
Lowering the temperature at which the desirable L10 phase forms in FePt thin films is a key requirement in the development of next generation high-density data storage media and spintronic devices. Remote plasma sputtering offers a higher degree of control over the sputtering parameters, allowing the properties of films to be tailored, and potentially can affect the ordering kinetics of the L10 phase of FePt. Here, we report a comprehensive study of FePt thin films deposited under a range of temperatures and sputtering conditions. X-ray diffraction and magnetometry investigations show that whilst FePt thin films ordered in the L10 phase with high perpendicular anisotropy can be produced using this technique, there is no significant reduction in the required ordering temperature compared with films produced using conventional DC sputtering. Optimally ordered L10 FePt films were fabricated when the film was deposited at a substrate temperature of 200 °C, followed by post annealing at 750 °C.
Influence of angular momentum in axially symmetric potentials with octupole deformation
Institute of Scientific and Technical Information of China (English)
JIN Hua; SUN Zhen-Wu; ZHENG Ren-Rong
2009-01-01
The chaotic classical single-particle motion in an oblate octupole deformed potential with a non-zero z-component of angular momentum Lz is investigated. The stability analysis of the trajectories shows that with increasing rotation of the system, the unstable negative curvature regions of the effective potential surface decrease, which converts the chaotic motion of the system into a regular one.
Potential High-Temperature Shape-Memory Alloys Identified in the Ti(Ni,Pt) System
Noebe, Ronald D.; Biles, Tiffany A.; Garg, Anita; Nathal, Michael V.
2004-01-01
"Shape memory" is a unique property of certain alloys that, when deformed (within certain strain limits) at low temperatures, will remember and recover to their original predeformed shape upon heating. It occurs when an alloy is deformed in the low-temperature martensitic phase and is then heated above its transformation temperature back to an austenitic state. As the material passes through this solid-state phase transformation on heating, it also recovers its original shape. This behavior is widely exploited, near room temperature, in commercially available NiTi alloys for connectors, couplings, valves, actuators, stents, and other medical and dental devices. In addition, there are limitless applications in the aerospace, automotive, chemical processing, and many other industries for materials that exhibit this type of shape-memory behavior at higher temperatures. But for high temperatures, there are currently no commercial shape-memory alloys. Although there are significant challenges to the development of high-temperature shape-memory alloys, at the NASA Glenn Research Center we have identified a series of alloy compositions in the Ti-Ni-Pt system that show great promise as potential high-temperature shape-memory materials.
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...
Gazeau-Klauder coherent states for the partner potentials of the trigonometric symmetric scarf type
Fakhri, H.; Kianfar, A.; Sayyah-Fard, M.
2016-02-01
The supersymmetric partner Schrödinger equations for the superpotential -Atanθ with A as non-negative integers are solved by using the Darboux factorization method on the associated Romanovski differential equation. The bound states correspond to a particle which is trapped on the bounded interval -π/2≤θ≤ +π/2 and their number is infinite. Its partner Hamiltonians are iso-spectral except for the ground state which, in turn, leads us to associate different Gazeau-Klauder coherent states for each of the partner potentials with different positive definite measures to realize the resolution of identity condition. It is shown that the time evolution does not change the form of the Gazeau-Klauder coherent states. Furthermore, it is discussed that the weight distribution functions of each of the coherent states obey the sub-Poissonian statistics. Finally, Gazeau-Klauder cat states are introduced for one of the partner potentials.
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.
Wagner, Monica; Shafer, Valerie L.; Martin, Brett; Steinschneider, Mitchell
2012-01-01
The effect of exposure to the contextual features of the /pt/ cluster was investigated in native-English and native-Polish listeners using behavioral and event-related potential (ERP) methodology. Both groups experience the /pt/ cluster in their languages, but only the Polish group experiences the cluster in the context of word onset examined in…
Wagner, Monica; Shafer, Valerie L.; Martin, Brett; Steinschneider, Mitchell
2012-01-01
The effect of exposure to the contextual features of the /pt/ cluster was investigated in native-English and native-Polish listeners using behavioral and event-related potential (ERP) methodology. Both groups experience the /pt/ cluster in their languages, but only the Polish group experiences the cluster in the context of word onset examined in…
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.
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.
Institute of Scientific and Technical Information of China (English)
CHEN Chien-Tien; CHOU Y-Chen; KAO Jin-Y; LI Tai-Wei; LIU Chia-Cheng; LI Ying-Chieh; CHANG I-Hsin; LIN Jin-Sheng; YEN Chia-Wen
2001-01-01
@@ Three C2-symmetric (10R,11R)-diethyl substituted dibenzosuberane (DBS)-based helicenes with varying steric and conjugation demands of their bottom fragments were synthesized. Only the helicene-7a[with the bottom part derived from tetralone was found photo-switchable in reasonable time scale. Photoisomerization of the diastereomerically pure (10R,11R,P)-helicene (7a) at 280 nm led to virtually exclusive formation of the opposite M form-diastereomer 7a′ (7a′/7a = 99.6/0.4). The preferential return of 7a′ to 7a can be effected upon irradiation at 254 nm (7a′/7a = 3G/67) or thermally at 130 7a′/7a = 0/100). The photo-induced switching process amounts to a 133% difference in d.e. (from 99.2% to-34%). The concomitant change of helicene chirality between these two diastereomeric photostationary states augurs well for their potential application as an optical switch in LC materials. To our knowledge, our system serves as the best chirochromic optical switch as compared to the examples possessing similar photochromic properties.
Institute of Scientific and Technical Information of China (English)
CHEN; Chien-Tien
2001-01-01
Three C2-symmetric (10R,11R)-diethyl substituted dibenzosuberane (DBS)-based helicenes with varying steric and conjugation demands of their bottom fragments were synthesized. Only the helicene-7a[with the bottom part derived from tetralone was found photo-switchable in reasonable time scale. Photoisomerization of the diastereomerically pure (10R,11R,P)-helicene (7a) at 280 nm led to virtually exclusive formation of the opposite M form-diastereomer 7a′ (7a′/7a = 99.6/0.4). The preferential return of 7a′ to 7a can be effected upon irradiation at 254 nm (7a′/7a = 3G/67) or thermally at 130 7a′/7a = 0/100). The photo-induced switching process amounts to a 133% difference in d.e. (from 99.2% to-34%). The concomitant change of helicene chirality between these two diastereomeric photostationary states augurs well for their potential application as an optical switch in LC materials. To our knowledge, our system serves as the best chirochromic optical switch as compared to the examples possessing similar photochromic properties.……
Rondelli, Manuel
2017-05-10
The use of physicochemical preparation techniques of metal clusters in the ultrahigh vacuum (UHV) allows for high control of cluster nuclearity and size distribution for fundamental studies in catalysis. Surprisingly, the potential of these systems as catalysts for organic chemistry transformations in solution has not been explored. To this end, single Pt atoms and Pt clusters with two narrow size distributions were prepared in the UHV and applied for the hydrogenation of p-chloronitrobenzene to p-chloroaniline in ethanol. Following the observation of very high catalytic turnovers (approaching the million molecules of p-nitroaniline formed per Pt cluster) and of size-dependent activity, this work addresses fundamental questions with respect to the suitability of these systems as heterogeneous catalysts for the conversion of solution-phase reagents. For this purpose, we employ scanning transmission electron microscopy (STEM) and X-ray photoelectron spectroscopy (XPS) characterization before and after reaction to assess the stability of the clusters on the support and the question of heterogeneity versus homogeneity in the catalytic process.
Dong, Hao; Shu, Xiaolin; Wang, Rongming
2011-08-01
The point defects and their related physical properties in L10 FePt are investigated by molecular dynamics simulations based on an analytic bond-order potential. The calculated results agree well with the experimental value, indicating that the analytic bond-order potential is suitable to describe the structural properties and surface energies of the FePt alloy in the L10 phase. However, the calculated vacancy formation energy of an Fe atom is higher than that of a Pt atom, which disagrees with some other previously calculated results. This result indicates that the analytic bond-order potential is unable to describe the related point defect properties. The analytic bond-order potential needs to be modified in order to study these defect properties of an FePt alloy.
Chang, Cheng-Hsun-Tony; Kuo, Wei-Hsu; Chang, Yu-Chieh; Tsay, Jyh-Shen; Yau, Shueh-Lin
2017-03-01
A combination of a solution process and the control of the electric potential for magnetism represents a new approach to operating spintronic devices with a highly controlled efficiency and lower power consumption with reduced production cost. As a paradigmatic example, we investigated Co/Pt(111) in the Bloch-wall regime. The depression in coercive force was detected by applying a negative electric potential in an electrolytic solution. The reversible control of coercive force by varying the electric potential within few hundred millivolts is demonstrated. By changing the electric potential in ferromagnetic layers with smaller thicknesses, the efficiency for controlling the tunable coercive force becomes higher. Assuming that the pinning domains are independent of the applied electric potential, an electric potential tuning-magnetic anisotropy energy model was derived and provided insights into our knowledge of the relation between the electric potential tuning coercive force and the thickness of the ferromagnetic layer. Based on the fact that the coercive force can be tuned by changing the electric potential using a solution process, we developed a novel concept of electric-potential-tuned magnetic recording, resulting in a stable recording media with a high degree of writing ability.
$\\mathcal{PT}$ 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.
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...
Zajac, Juraj; Kostrhunova, Hana; Novohradsky, Vojtech; Vrana, Oldrich; Raveendran, Raji; Gibson, Dan; Kasparkova, Jana; Brabec, Viktor
2016-03-01
The molecular and cellular mechanisms of enhanced toxic effects in tumor cells of the Pt(IV) derivatives of antitumor oxaliplatin containing axial dichloroacetate (DCA) ligands were investigated. DCA ligands were chosen because DCA has shown great potential as an apoptosis sensitizer and anticancer agent reverting the Wartburg effect. In addition, DCA reverses mitochondrial changes in a wide range of cancers, promoting tumor cell apoptosis in a mitochondrial-dependent pathway. We demonstrate that (i) the transformation of oxaliplatin to its Pt(IV) derivatives containing axial DCA ligands markedly enhances toxicity in cancer cells and helps overcome inherent and acquired resistance to cisplatin and oxaliplatin; (ii) a significant fraction of the intact molecules of DCA conjugates with Pt(IV) derivative of oxaliplatin accumulates in cancer cells where it releases free DCA; (iii) mechanism of biological action of the Pt(IV) derivatives of oxaliplatin containing DCA ligands is connected with the effects of DCA released in cancer cells from the Pt(IV) prodrugs on mitochondria and metabolism of glucose; (iv) treatments with the Pt(IV) derivatives of oxaliplatin containing DCA ligands activate an autophagic response in human colorectal cancer cells; (v) the toxic effects in cancer cells of the Pt(IV) derivatives of oxaliplatin containing DCA ligands can be potentiated if cells are treated with these prodrugs in combination with 5-fluorouracil. These properties of the Pt(IV) derivatives of oxaliplatin containing DCA ligands provide opportunities for further development of new platinum-based agents with the capability of killing cancer cells resistant to conventional antitumor platinum drugs used in the clinic.
Potential-dependent water orientation on Pt(1 1 1) stepped surfaces from laser-pulsed experiments
Energy Technology Data Exchange (ETDEWEB)
Garcia-Araez, Nuria [Instituto de Electroquimica, Universidad de Alicante, Ap. 99, E-03080 Alicante (Spain); Climent, Victor [Instituto de Electroquimica, Universidad de Alicante, Ap. 99, E-03080 Alicante (Spain)], E-mail: victor.climent@ua.es; Feliu, Juan M. [Instituto de Electroquimica, Universidad de Alicante, Ap. 99, E-03080 Alicante (Spain)
2009-01-01
Coulostatic potential transients induced by nanosecond pulsed laser irradiation on Pt(1 1 1) stepped surfaces in perchloric acid solutions are analyzed here. The results provide unique information on the effect of the structure of the metal surface on the potential-dependent water reorientation at the electrified interphase. The most significant information is obtained from the sign and shape of the laser-induced transients. The existence of two potentials where the transient is zero can be related to the local properties of the surface, i.e. the existence of two local potentials of zero free charge, corresponding to the step and terrace sites. The dependency of these quantities with the step density is studied in detail. In addition, it is found that the presence of steps significantly slows down the coulostatic response at potentials in the double-layer region, which has been interpreted as a decrease in the velocity of water reorganization. The corresponding relaxation time is estimated and its dependency with the step density is also analyzed.
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.
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.
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.
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.
Chrzan, A.; Woźniak, Ł.; Szymczewska, D.; Jasiński, P.
2016-11-01
Many types of yttria-stabilized zirconia (YSZ) based gas sensors have been explored extensively in recent years. Great attention have been directed to mixed-potential-type gas sensors. It is due to growing concerns with environmental issues. Not without a significance is the fact of very attractive performance of this type of sensor allowing to detect low concentration of pollutant gases. In this paper two types of YSZ based mixed-potential planar sensors were investigated, with platinum electrode painted using commercial paste and with spin coated platinum layer. Both types had second electrode in the form of porous gold. Measurements were performed at 400 °C in synthetic air and different concentrations of SO2. Gas flow was set to 100 cm3min-1 and the concentration of 50 ppm SO2 was tested. During this measurements the sensor was sintered in-situ at increasing temperatures. Sensor with 100 nm spin-coated platinum layer sintered at 700 °C was shown to exhibit two times smaller response than sensor with 5 μm porous electrode, while consisting of over 20 times smaller amount of Pt. The influence of sintering temperature on electrical conductivity of platinum films was also examined. Moreover, the platinum microstructure was investigated using SEM microscopy.
Remmert, Sarah M; Banks, Simon T; Clary, David C
2009-04-23
The symmetric title reaction CH(3) + CH(4) --> CH(4) + CH(3) is studied using quantum scattering theory. Quantum dynamics calculations are performed in hyperspherical coordinates with a two-dimensional effective potential energy surface consisting of an analytical 18-parameter double Morse function fit to ab initio data at the CCSD(T)/cc-pVTZ//MP2/cc-pVTZ level of theory. Spectator modes are treated adiabatically by inclusion of projected zero-point energy corrections in the effective potential. The close-coupled equations are solved via R-matrix propagation. Energy and J-shifted thermal rate constants are compared to experimental data and highlight the importance of quantum tunneling. Oscillating reactivity and metastable bound state resonances are observed in the cumulative and state-to-state reaction probabilities. State-to-state differential and initial state-selected integral cross sections are presented and discussed. Primary and secondary kinetic isotope effects for two symmetric deuterated variants of the title reaction are also presented.
Level crossings in complex two-dimensional potentials
Indian Academy of Sciences (India)
Qing-Hai Wang
2009-08-01
Two-dimensional $\\mathcal{PT}$-symmetric quantum-mechanical systems with the complex cubic potential 12 = 2 + 2 + 2 and the complex Hénon–Heiles potential HH = 2 + 2 + (2 − 3/3) are investigated. Using numerical and perturbative methods, energy spectra are obtained to high levels. Although both potentials respect the $\\mathcal{PT}$ symmetry, the complex energy eigenvalues appear when level crossing happens between same parity eigenstates.
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.
Szeto, Kai C; Kongshaug, Kjell Ove; Jakobsen, Søren; Tilset, Mats; Lillerud, Karl Petter
2008-04-21
The heterobimetallic metal-organic framework {[(BPDC)PtCl(2)](3)(Gd(H(2)O)(3))(2)}.5H(2)O (BPDC = 2,2'-bipyridine-5,5'-dicarboxylate) has been designed and synthesized by hydrothermal methods. The new coordination polymer contains subunits of (BPDC)PtCl(2) (1) where both N atoms of the BPDC ligand are attached to a square-planar Pt(II) center. The two remaining cis coordination sites at Pt(II) are occupied by chloride ions. The final structure (2) of the polymeric network is obtained when Gd(III) ions link together the (BPDC)PtCl(2) units, which are organized in sheets, into larger blocks. These blocks are stacked along the crystallographic [010] direction and are held together by a hydrogen bonding scheme that involves carboxylate oxygen atoms and water molecules in the coordination sphere of Gd. The coordination polymer 2 can be obtained in a single-step reaction or in a two-step synthesis where the corresponding Pt complex (1) was first synthesized followed by reacting 1 with Gd(NO(3))(3).6H(2)O. In situ high temperature powder X-ray diffraction shows that the crystalline coordination polymer transforms into an anhydrous modification at 100 degrees C. This modification is stable to 350 degrees C, at which temperature the structure starts to decompose. The coordination sphere around platinum in the polymer closely resembles organometallic Pt complexes that have been previously found to catalytically or stoichiometrically activate and functionalize hydrocarbon C-H bonds in homogeneous systems.
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.
Kizhakevariam, Naushad; Villegas, Ignacio; Weaver, Michael J.
1995-08-01
The influence of various solvents upon the interfacial-potential profile on Pt(111) has been investigated by means of work-function changes and infrared frequency Stark shifts attending sequential-molecular dosing in ultra-high vacuum (UHV) at a suitably low temperature (ca. 100 K) with the primary objective of assessing the role of surface solvation in related electrochemical systems. The solvents examined — dichloromethane, benzene, acetone, acetonitrile, methanol, and ammonia — span a range of polarity and other solvating properties. These species were dosed onto both clean and CO-saturated Pt(111), the Stark shifts being evaluated for the CO stretching mode of terminally co-ordinated carbon monoxide. Marked decreases (≥ 1 eV) in the work function, Φ, and hence in the surface potential, φ, are observed on the addition of most solvents onto clean Pt(111). Milder yet still substantial Φ decreases are also observed for solvent dosage upon CO-saturated Pt(111). These latter Φ changes correlate approximately with the observed vCO frequency downshifts, suggesting that the latter property is also sensitive to the solvent-induced electrostatic interfacial field. The functional form of both the Φ decreases and the corresponding vCO frequency downshifts induced by solvent dosage provide insight into the dosage-dependent potential profile and its relationship to both the monolayer and multilayer solvent structure. The present findings are also briefly compared with corresponding vtCO - Φ data obtained for potassium atom dosing, where the surface potential is altered instead by varying the surface electronic charge in the presence of a given solvent. The underlying factors responsible for the surprisingly large solvent-induced surface potential shifts are discussed in detail, and the likely importance of the surface electronic charge distribution as well as solvent dipole orientation and adsorbate-metal charge sharing is pointed out.
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.
Sinha, Debdeep; Ghosh, Pijush K
2015-04-01
A class of nonlocal nonlinear Schrödinger equations (NLSEs) is considered in an external potential with a space-time modulated coefficient of the nonlinear interaction term as well as confining and/or loss-gain terms. This is a generalization of a recently introduced integrable nonlocal NLSE with self-induced potential that is parity-time-symmetric in the corresponding stationary problem. Exact soliton solutions are obtained for the inhomogeneous and/or nonautonomous nonlocal NLSE by using similarity transformation, and the method is illustrated with a few examples. It is found that only those transformations are allowed for which the transformed spatial coordinate is odd under the parity transformation of the original one. It is shown that the nonlocal NLSE without the external potential and a (d+1)-dimensional generalization of it admits all the symmetries of the (d+1)-dimensional Schrödinger group. The conserved Noether charges associated with the time translation, dilatation, and special conformal transformation are shown to be real-valued in spite of being non-Hermitian. Finally, the dynamics of different moments are studied with an exact description of the time evolution of the "pseudowidth" of the wave packet for the special case in which the system admits a O(2,1) conformal symmetry.
Sinha, Debdeep; Ghosh, Pijush K.
2015-04-01
A class of nonlocal nonlinear Schrödinger equations (NLSEs) is considered in an external potential with a space-time modulated coefficient of the nonlinear interaction term as well as confining and/or loss-gain terms. This is a generalization of a recently introduced integrable nonlocal NLSE with self-induced potential that is parity-time-symmetric in the corresponding stationary problem. Exact soliton solutions are obtained for the inhomogeneous and/or nonautonomous nonlocal NLSE by using similarity transformation, and the method is illustrated with a few examples. It is found that only those transformations are allowed for which the transformed spatial coordinate is odd under the parity transformation of the original one. It is shown that the nonlocal NLSE without the external potential and a (d +1 )-dimensional generalization of it admits all the symmetries of the (d +1 )-dimensional Schrödinger group. The conserved Noether charges associated with the time translation, dilatation, and special conformal transformation are shown to be real-valued in spite of being non-Hermitian. Finally, the dynamics of different moments are studied with an exact description of the time evolution of the "pseudowidth" of the wave packet for the special case in which the system admits a O (2 ,1 ) conformal symmetry.
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 ...
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.
Silva, Tânia Magalhães; Andersson, Sara; Sukumaran, Sunil Kumar; Marques, Maria Paula; Persson, Lo; Oredsson, Stina
2013-01-01
New strategies are needed for breast cancer treatment and one initial step is to test new chemotherapeutic drugs in breast cancer cell lines, to choose candidates for further studies towards clinical use. The cytotoxic effects of a biogenic polyamine analogue - norspermidine - and its trinuclear Pd(II) and Pt(II) complexes - Pd(3)NSpd(2) and Pt(3)NSpd(2), respectively - were investigated in one immortalized normal-like and three breast cancer cell lines. The normal-like MCF-10A cells were least sensitive to the compounds, while growth inhibition and cell death was observed in the cancer cell lines. Norspermidine and its Pd(II) complex were generally shown to have stronger antiproliferative effects than the corresponding Pt(II) complex. Moreover, both norspermidine and the Pd(II) complex reduced the cellular activity of the growth-related enzyme, ornithine decarboxylase (ODC) to a lower level than the Pt(II) complex in most of the cell lines examined. Treatment with norspermidine or the Pd(II) complex reduced the number of colonies formed in a soft agar assay performed with the breast cancer cell lines, indicating that these compounds reduced the malignancy of the breast cancer cells. The effect of norspermidine or the Pd(II) complex on colony formation was much stronger than that observed for the Pt(II) complex. The results from a new mammalian genotoxicity screen together with those of a single cell gel electrophoresis assay indicated that none of the drugs were genotoxic at a 25 µM concentration. Overall, norspermidine and its Pd(II) complex were shown to have strong antiproliferative effects. In comparison, the effects obtained with the Pd(II) complex were much stronger than that of the Pt(II) complex. The results obtained in the present study demonstrate that the trinuclear Pd(II) complex of norspermidine (Pd(3)NSpd(2)) may be regarded as a potential new metal-based drug against breast cancer, coupling a significant efficiency to a low toxicity.
Liu, Chenze; Qi, Weihong; Ouyang, Bin; Wang, Xing; Huang, Baiyun
2013-02-01
The cohesive energy (CE) of CoPt nanoparticles (NPs) with different sizes and shapes have been calculated by embedded-atom-method (EAM) potential. It is shown that CE of NPs with order or disorder structures decreases with the decrease of particle size, while the shape effects become obvious only at small size. The CE difference per atom between order and disorder structures decreases with the decrease of particle size, indicating that the possibility of order-disorder transition in small size becomes larger compared with these in large size. Significantly, the CE difference varies in proportion to order-disorder transition temperature (T(c)), which suggests that one can predict order-disorder transition of NPs by calculation the cohesive energy. The present calculated T(c) of CoPt NPs is consistent with recent experiments, simulation and theoretical predictions, and the method can also be applied to study the order-disorder transition of FePt, FePd, and so on.
Law, Richard; Waters, Dave; Morgan, Sven; Stahr, Don; Francsis, Matthew; Ashley, Kyle; Kronenberg, Andreas; Thomas, Jay; Mazza, Sarah; Heaverlo, Nicholas
2013-04-01
The quartz c-axis fabric opening-angle thermometer proposed by Kruhl (1998) offers a potential analytical technique for estimating deformation temperatures in rocks deformed by crystal plastic flow. However, in addition to deformation temperature, opening-angle is also sensitive to other variables such as strain rate, degree of hydrolytic weakening, and 3D strain type. Unless the influence of these individual variables can be quantified, use of fabric opening-angle as a deformation thermometer remains problematic and controversial. Over the last decade close correlations between: a) deformation temperatures indicated by fabric opening-angles and, b) temperatures of metamorphism indicated by trace element and mineral phase equilibria analyses, have been reported from a range of different tectonic settings, thereby arguably giving support to the use of opening-angles as a deformation thermometer. However, it needs to be demonstrated that the similar temperatures estimated by the different methods are related to the same geologic event, and therefore occupy at least a similar position on the PTt path - something that is in practice difficult to achieve for an individual rock sample. In cases where temperatures indicated by opening angles and mineral assemblages are markedly different, these differences could, for example, be explained by penetrative deformation and mineral growth/diffusion occurring at different times. Alternatively, when apparent deformation temperatures based on quartz fabrics are significantly greater than temperatures indicated by synchronous metamorphic mineral assemblages, this might be due to extreme hydrolytic weakening of quartz. We illustrate this talk on the pros and cons of using fabric opening-angles as a deformation thermometer with examples from: a) Aureoles of forcibly emplaced plutons in the White-Inyo Range of eastern California where crystal-plastic deformation and recrystallization was short-lived and synchronous with contact
Jedidi, Abdesslem; Li, Rui; Fornasiero, Paolo; Cavallo, Luigi; Carbonniere, Philippe
2015-12-03
Vibrational fingerprints of small Pt(n)P(2n) (n = 1-5) clusters were computed from their low-lying structures located from a global exploration of their DFT potential energy surfaces with the GSAM code. Five DFT methods were assessed from the CCSD(T) wavenumbers of PtP2 species and CCSD relative energies of Pt2P4 structures. The eight first Pt(n)P(2n) isomers found are reported. The vibrational computations reveal (i) the absence of clear signatures made by overtone or combination bands due to very weak mechanical and electrical anharmonicities and (ii) some significant and recurrent vibrational fingerprints in correlation with the different PP bonding situations in the Pt(n)P(2n) structures.
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.
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...
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.
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
Stebner, Aaron; Padula, Santo A.; Noebe, Ronald D.
2008-01-01
Shape memory alloys (SMAs) have been used as actuators in many different industries since the discovery of the shape memory effect, but the use of SMAs as actuation devices in aeronautics has been limited due to the temperature constraints of commercially available materials. Consequently, work is being done at NASA's Glenn Research Center to develop new SMAs capable of being used in high temperature environments. One of the more promising high-temperature shape memory alloys (HTSMAs) is Ni19.5Ti50.5Pd25Pt5. Recent work has shown that this material is capable of being used in operating environments of up to 250 C. This material has been shown to have very useful actuation capabilities, demonstrating repeatable strain recoveries up to 2.5% in the presence of an externally applied load. Based on these findings, further work has been initiated to explore potential applications and alternative forms of this alloy, such as springs. Thus, characterization of Ni19.5Ti50.5Pd25Pt5 springs, including their mechanical response and how variations in this response correlate to changes in geometric parameters, are discussed. The effects of loading history, or training, on spring behavior were also investigated. A comparison of the springs with wire actuators is made and the benefits of using one actuator form as opposed to the other discussed. These findings are used to discuss design considerations for a surge-control mechanism that could be used in the centrifugal compressor of a T-700 helicopter engine.
Stebner, Aaron; Padula, Santo A.; Noebe, Ronald D.
2008-01-01
Shape memory alloys (SMAs) have been used as actuators in many different industries since the discovery of the shape memory effect, but the use of SMAs as actuation devices in aeronautics has been limited due to the temperature constraints of commercially available materials. Consequently, work is being done at NASA's Glenn Research Center to develop new SMAs capable of being used in high temperature environments. One of the more promising high-temperature shape memory alloys (HTSMAs) is Ni19.5Ti50.5Pd25Pt5. Recent work has shown that this material is capable of being used in operating environments of up to 250 C. This material has been shown to have very useful actuation capabilities, demonstrating repeatable strain recoveries up to 2.5% in the presence of an externally applied load. Based on these findings, further work has been initiated to explore potential applications and alternative forms of this alloy, such as springs. Thus, characterization of Ni19.5Ti50.5Pd25Pt5 springs, including their mechanical response and how variations in this response correlate to changes in geometric parameters, are discussed. The effects of loading history, or training, on spring behavior were also investigated. A comparison of the springs with wire actuators is made and the benefits of using one actuator form as opposed to the other discussed. These findings are used to discuss design considerations for a surge-control mechanism that could be used in the centrifugal compressor of a T-700 helicopter engine.
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.
High pressure CO hydrogenation over bimetallic Pt-Co catalysts
DEFF Research Database (Denmark)
Christensen, Jakob Munkholt; Medford, Andrew James; Studt, Felix
2014-01-01
The potential of bimetallic Pt-Co catalysts for production of higher alcohols in high pressure CO hydrogenation has been assessed. Two catalysts (Pt3Co/SiO2 and PtCo/SiO2) were tested, and the existing literature on CO hydrogenation over Pt-Co catalysts was reviewed. It is found that the catalyst...
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
Baraket, Zina; Zaghdoudi, Jihene; Kanzari, Mounir
2017-02-01
Based on the Transfer Matrix Method (TMM) and the two fluid model for a superconductor and by taking account of the thermal expansion effect and thermo optical effects, we theoretically investigates the transmittance spectra of a one dimensional superconductor -dielectric photonic crystal (PC) designed as ((HLS)5/(SLH)5) made up of a BiGeO12(H), SiO2(L) and YaBO2CuO7 (S). The transmittance spectra shows that the system realizes a tunable filter which depends on a nonlinear relation with temperature. It's found that the symmetrical application of a linear deformation d(m) = d0+(m-1).δd(m) where d0 is the initial thickness of the layer m, δd(m) is the elementary added thickness at each layer. This linear gradation of the thickness permits to improve the temperature sensitivity of the system which acts as an optimized low temperature sensor.
Directory of Open Access Journals (Sweden)
Iwan Hilwan
2012-12-01
Full Text Available A management unit (MU of a forest concession holder implementing the sustainable forest management (SFM principles, could be involved in reducing Emmission from Reforestation and Forest Degradation (REDD+ and carbon trading project. The fact the strategic in implementing the REDD+ and carbon trading in MU level is still lack of pilot project and methodology. Therefore, some scenarios must be developed and tested to find out the best potential of carbon credit in MU level. The objectives of the research were: to calculate carbon credit in some SFM scenarios, to analyze of carbon trading project feasibility, and to determine carbon stock recovery period of logged over area (LOA. The result revealed that carbon stock and carbon credit of LOA was affected by timber cutting intensity. The 6th scenario with lowest annual allowable cutting (AAC obtained greater carbon credit and profit coming from timber harvesting income and carbon trading. In other hand, this scenario has shortest duration of carbon stock recovery period (27 years and shorter than its cutting cycle. In this case, the MU has to recalculate and to decrease its AAC to have highest benefits from carbon trading in the same cutting cycle period. It will provide double benefits from carbon trading, those are contribution in achieving the SFM purposes (production, ecology, social and climate change mitigation.Keywords: sustainable forest management, AAC, carbon stocks, recovery period, carbon trading
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...
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.
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
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...
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.
Indian Academy of Sciences (India)
Sourov Ghosh; C Retna Raj
2015-05-01
Synthesis of highly efficient functional electrocatalyst that favours the electrochemical oxidation of formic acid via CO-free dehydrogenation pathway is required for direct formic acid fuel cells. Traditional catalysts favour the dehydration pathway involving the generation of poisonous CO. Herein we demonstrate the superior electrocatalytic performance of Pt-Pd bimetallic nanoelectrocatalyst of ultralow Pt content and tuning the reaction pathway by controlling the Pt content. Bimetallic nanoparticles of Pt4Pd96, Pt7Pd93 and Pt47Pd53 compositions are synthesized by electrochemical co-deposition method in aqueous solution. The nanoparticles of ultralow Pt content, Pt4Pd96, favour the CO-free dehydrogenation pathway for formic acid oxidation with an onset potential of 0 V (SHE) whereas the Pt47Pd53 nanoparticles favour the dehydration pathway involving the formation of CO at high positive potential. The Pt content of the bimetallic nanoparticles actually controls the oxidation peak potential and catalytic activity. Significant negative shift (∼350 mV) in the oxidation peak potential and remarkable enhancement in the current density (2.6 times) are observed for Pt4Pd96 nanoparticles with respect to Pt47Pd53. The absence of three adjacent Pt and Pd atoms could be the reason for the suppression of CO pathway. The electrochemical impedance measurements indirectly support the CO-free pathway for the formic acid oxidation on Pt4Pd96 nanoparticles.
Fu, Tao; Huang, Jianxing; Lai, Shaobo; Zhang, Size; Fang, Jun; Zhao, Jinbao
2017-10-01
The catalytic activity and stability of electrocatalyst is critical for the commercialization of fuel cells, and recent reports reveal the great potential of the hollow structures with Pt skin coat for developing high-powered electrocatalysts due to their highly efficient utilization of the Pt atoms. Here, we provide a novel strategy to prepare the Pt skin coated hollow Ag-Pt structure (Ag-Pt@Pt) of ∼8 nm size at room temperature. As loaded on the graphene, the Ag-Pt@Pt exhibits a remarkable mass activity of 0.864 A/mgPt (at 0.9 V, vs. reversible hydrogen electrode (RHE)) towards oxygen reduction reaction (ORR), which is 5.30 times of the commercial Pt/C catalyst, and the Ag-Pt@Pt also shows a better stability during the ORR catalytic process. The mechanism of this significant enhancement can be attributed to the higher Pt utilization and the unique Pt on Ag-Pt surface structure, which is confirmed by the density functional theory (DFT) calculations and other characterization methods. In conclusion, this original work offers a low-cost and environment-friendly method to prepare a high active electrocatalyst with cheaper price, and this work also discloses the correlation between surface structures and ORR catalytic activity for the hollow structures with Pt skin coat, which can be instructive for designing novel advanced electrocatalysts for fuel cells.
Altarawneh, Rakan M.; Pickup, Peter G.
2017-10-01
Polarization curves, product distributions, and reaction stoichiometries have been measured for the oxidation of ethanol at anodes consisting of Pt and PtRu bilayers and a homogeneous mixture of the two catalysts. These anode structures all show synergies between the two catalysts that can be attributed to the oxidation of acetaldehyde produced at the PtRu catalyst by the Pt catalyst. The use of a PtRu layer over a Pt layer produces the strongest effect, with higher currents than a Pt on PtRu bilayer, mixed layer, or either catalyst alone, except for Pt at high potentials. Reaction stoichiometries (average number of electrons transferred per ethanol molecule) were closer to the values for Pt alone for both of the bilayer configurations but much lower for PtRu and mixed anodes. Although Pt alone would provide the highest overall fuel cell efficiency at low power densities, the PtRu on Pt bilayer would provide higher power densities without a significant loss of efficiency. The origin of the synergy between the Pt and PtRu catalysts was elucidated by separation of the total current into the individual components for generation of carbon dioxide and the acetaldehyde and acetic acid byproducts.
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.
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.
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...
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 ( ...
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.
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.
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.
Ma, Yong-Tao; Zeng, Tao; Li, Hui
2014-06-07
Four-dimensional ab initio intermolecular potential energy surfaces (PESs) for CH3F-He that explicitly incorporates dependence on the Q3 stretching normal mode of the CH3F molecule and are parametrically dependent on the other averaged intramolecular coordinates have been calculated. Analytical three-dimensional PESs for v3(CH3F) = 0 and 1 are obtained by least-squares fitting the vibrationally averaged potentials to the Morse/Long-Range potential function form. With the 3D PESs, we employ Lanczos algorithm to calculate rovibrational levels of the dimer system. Following some re-assignments, the predicted transition frequencies are in good agreement with experimental microwave data for ortho-CH3F, with the root-mean-square deviation of 0.042 cm(-1). We then provide the first prediction of the infrared and microwave spectra for the para-CH3F-He dimer. The calculated infrared band origin shifts associated with the ν3 fundamental of CH3F are 0.039 and 0.069 cm(-1) for para-CH3F-He and ortho-CH3F-He, respectively.
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.
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.
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...
Dynamics of the YSZ-Pt Interface
DEFF Research Database (Denmark)
Bay, Lasse; Jacobsen, Torben
1997-01-01
Yttria stabilized zirconia (YSZ)-Pt point electrodes were examined by linear potential sweep, potential step and impedance measurements at 1000 degrees C in air. Inductive loops and hysteresis phenomena with long relaxation times were found. Atomic force microscopy showed changes of the interface...... between Pt and YSZ induced by the current passage. These changes involve transport of solid and are slow enough to explain the large time constants. The low frequency capacitance and inductive loop forming an entire circle indicate the presence of gas reservoirs at the YSZ-Pt interface....
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.
Insights on the SO2 Poisoning of Pt3Co/VC and Pt/VC Fuel Cell Catalysts
2010-01-01
stripping voltammetry and underpotential deposition (upd) of copper adatoms. Then the performance of PEMFC cathodes employing 30wt.% Pt3Co/VC and 50wt.% Pt/VC...atoms (Pt and Cu atomic radii are 0.139 and 0.128nm, respectively [15]) makes copper underpotential deposition a perfect tool for evaluating the plat...the surface area of Pt3Co/VC catalyst is rigorously characterized by hydrogen adsorption,CO stripping voltammetry and under potential deposition (upd
Brunner, T.; Mueller, A. R.; O'Sullivan, K.; Simon, M. C.; Kossick, M.; Ettenauer, S.; Gallant, A. T.; Mané, E.; Bishop, D.; Good, M.; Gratta, G.; Dilling, J.
2012-01-01
Bradbury Nielsen gates are well known devices used to switch ion beams and are typically applied in mass or mobility spectrometers for separating beam constituents by their different flight or drift times. A Bradbury Nielsen gate consists of two interleaved sets of electrodes. If two voltages of the same amplitude but opposite polarity are applied the gate is closed, and for identical (zero) potential the gate is open. Whereas former realizations of the device employ actual wires resulting in difficulties with winding, fixing and tensioning them, our approach is to use two grids photo-etched from a metallic foil. This design allows for simplified construction of gates covering large beam sizes up to at least 900\\,mm$^2$ with variable wire spacing down to 250\\,\\textmu m. By changing the grids the wire spacing can be varied easily. A gate of this design was installed and systematically tested at TRIUMF's ion trap facility, TITAN, for use with radioactive beams to separate ions with different mass-to-charge ratios by their time-of-flight.
Mesoporous Pt and Pt/Ru alloy electrocatalysts for methanol oxidation
Energy Technology Data Exchange (ETDEWEB)
Franceschini, Esteban A. [Grupo de Celdas de Combustible, Departamento de Fisica de la Materia Condensada, Centro Atomico Constituyentes, CNEA. Av. General Paz 1499 (1650), San Martin, Buenos Aires (Argentina); Planes, Gabriel A. [Departamento de Quimica, Facultad de Ciencias Exactas, Fisicoquimicas y Naturales, Universidad Nacional de Rio Cuarto, Agencia Postal No 3, 5800, Rio Cuarto (Argentina); Williams, Federico J. [Departamento de Quimica Inorganica, Analitica y Quimica-Fisica, INQUIMAE CONICET, Facultad Ciencias Exactas y Naturales, Pabellon 2, Ciudad Universitaria, Buenos Aires (Argentina); Soler-Illia, Galo J.A.A. [Gerencia de Quimica, Centro Atomico Constituyentes, CNEA. Av. General Paz 1499 (1650), San Martin, Buenos Aires (Argentina); Corti, Horacio R. [Grupo de Celdas de Combustible, Departamento de Fisica de la Materia Condensada, Centro Atomico Constituyentes, CNEA. Av. General Paz 1499 (1650), San Martin, Buenos Aires (Argentina); Departamento de Quimica Inorganica, Analitica y Quimica-Fisica, INQUIMAE CONICET, Facultad Ciencias Exactas y Naturales, Pabellon 2, Ciudad Universitaria, Buenos Aires (Argentina)
2011-02-15
Mesoporous Pt and Pt/Ru catalysts with 2D-hexagonal mesostructure were synthesized using a triblock poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) copolymer (Pluronic F127 {sup registered}) template, on a gold support. Large electrochemical surface areas were observed for the catalysts prepared at high overpotentials. Compared to the Pt catalyst, the Pt/Ru alloy containing 3 at% of Ru exhibited lower onset potential and more than three times the limit mass activity for methanol oxidation. This behavior is assigned to the larger pore size of the mesoporous Pt and Pt/Ru catalysts obtained with this template that seems to improve the methanol accessibility to the active sites compared to those obtained using lyotropic liquid crystals. (author)
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.
Chirally symmetric but confined hadrons at finite density
Glozman, L Ya
2008-01-01
At a critical finite chemical potential and low temperature QCD undergoes the chiral restoration phase transition. The folklore tradition is that simultaneously hadrons are deconfined and there appears the quark matter. We demonstrate that it is possible to have confined but chirally symmetric hadrons at a finite chemical potential and hence beyond the chiral restoration point at a finite chemical potential and low temperature there could exist a chirally symmetric matter consisting of chirally symmetric but confined hadrons. If it does happen in QCD, then the QCD phase diagram should be reconsidered with obvious implications for heavy ion programs and astrophysics.
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.
Electrochemical quartz crystal microbalance study of the electrodeposition of Co, Pt and Pt-Co alloy
Energy Technology Data Exchange (ETDEWEB)
Martin, A.J.; Chaparro, A.M. [CIEMAT, Avda. Complutense, 22, 28040 Madrid (Spain); Daza, L. [CIEMAT, Avda. Complutense, 22, 28040 Madrid (Spain); Instituto de Catalisis y Petroleoquimica (CSIC), C/Marie Curie 2, Campus Cantoblanco, 28049 Madrid (Spain)
2007-06-10
The electrochemical deposition of Co, Pt and Pt-Co alloy are studied with the electrochemical quartz crystal microbalance (EQCM) on a gold substrate. Co is deposited from acidic sulphate bath containing boric acid. Different processes are identified in this bath. Electrodeposition of Co on Au substrate is observed at potentials above redox potential, underpotential deposition, most probably due to formation of a Co-Au alloy. At more cathodic potentials, below -0.5 V, metallic Co is formed. The film is completely dissolved at positive potentials during the anodic scan, probably mediated by Co(OH){sub 2}. The electrodeposition of platinum from acidic PtCl{sub 6}{sup 2-} bath occurs below the thermodynamic potential (0.74 V) with almost 100% efficiency. At potentials negative from 0.0 V the efficiency decreases due to parallel water reduction. The codeposition of Co and Pt is also studied in acidic bath. Here, the decrease of pH due to water reduction on Pt deposits gives rise to precipitation of Co(OH){sub 2}, together with the deposition of metallic Pt and Co. The films contain as major component the Pt{sub 3}Co alloy. (author)
Electrochemical quartz crystal microbalance study of the electrodeposition of Co, Pt and Pt-Co alloy
Martín, A. J.; Chaparro, A. M.; Daza, L.
The electrochemical deposition of Co, Pt and Pt-Co alloy are studied with the electrochemical quartz crystal microbalance (EQCM) on a gold substrate. Co is deposited from acidic sulphate bath containing boric acid. Different processes are identified in this bath. Electrodeposition of Co on Au substrate is observed at potentials above redox potential, underpotential deposition, most probably due to formation of a Co-Au alloy. At more cathodic potentials, below -0.5 V, metallic Co is formed. The film is completely dissolved at positive potentials during the anodic scan, probably mediated by Co(OH) 2. The electrodeposition of platinum from acidic PtCl 6 2- bath occurs below the thermodynamic potential (0.74 V) with almost 100% efficiency. At potentials negative from 0.0 V the efficiency decreases due to parallel water reduction. The codeposition of Co and Pt is also studied in acidic bath. Here, the decrease of pH due to water reduction on Pt deposits gives rise to precipitation of Co(OH) 2, together with the deposition of metallic Pt and Co. The films contain as major component the Pt 3Co alloy.
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
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.
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.
Doverbratt, Isa; Ponou, Siméon; Lidin, Sven; Fredrickson, Daniel C
2012-11-05
Two new phases Ca(10)Pt(7)Tt(3) (with Tt = Si, Ge) were obtained by reacting stoichiometric mixtures of the elements at high temperature. Their structures were refined from single crystal X-ray diffraction data. They are isostructural and crystallize in the Ba(10)Al(3)Ge(7) type structure, space group P6(3)/mcm (No. 193) with a = b = 8.7735(3) Å, c = 13.8260(5) Å, V = 921.66(6) Å(3), Z = 2 for Tt = Si, and a = b = 8.7995(6) Å, c = 13.9217(14) Å, V = 933.56(16) Å(3) for Tt = Ge phase. The most interesting structural features in these phases are the propeller shape {Pt(7)Tt(3)} (Tt = Si, Ge) intermetalloid clusters in a D(3h) local symmetry. LMTO electronic structure calculations and COHP analyses reveal that both Ca(10)Pt(7)Tt(3) (Tt = Si, Ge) phases are charge optimized, which is not predicted by the classical Zintl concept and the octet or Wade-Mingo's rules, but rather by a more complex bonding model based on the unprecedented electron-rich 4c-6e multicenter bonding. The clusters are best described as three-condensed trigonal planar [TtPt(3)](8-) units, resulting in a central Pt atom also with a trigonal planar coordination of three symmetrical equivalent Si/Ge atoms that are further connected to two terminal Pt atoms each. The "trefoil" electron-rich multicenter bonding is proposed here for the first time, and may be viewed as a unique bonding feature with potential relevance for the catalytic properties of the noble metal platinum.
Energy Technology Data Exchange (ETDEWEB)
FEIBELMAN,PETER J.; HAMMER,B.; NORSHOV,J.K.; WAGNER,F.; SCHEFFLER,M.; STUMPF,R.; DUMESIC,J.; WATWE,R.
2000-07-12
Notwithstanding half a dozen theoretical publications, well-converged density-functional calculations, whether based on a local or generalized-gradient exchange-correlation potential, whether all-electron or employing pseudopotentials underestimate CO's preference for low-coordination binding sites on Pt(111) and vicinals to it. For example, they imply that CO should prefer hollow- to atop-site adsorption on Pt(111), in apparent contradiction to a host of low temperature experimental studies.
Directory of Open Access Journals (Sweden)
Bibian A Hoyos
2007-01-01
Full Text Available En este trabajo se evalúa el efecto de la temperatura en el desempeño de celdas de combustible de membrana de intercambio protónico alimentadas con metano y propano, utilizando oxígeno como alimentación en el cátodo. Para la oxidación de los combustibles en los ánodos, se probaron cinco catalizadores soportados en carbón: Pt, Pt85Ru15, Pt50Ru50, Pt90Ir10 y Pt50Ir50. Como catalizador en el cátodo se usó platino puro soportado en carbón. El desempeño de las celdas de combustible fue evaluado mediante curvas de polarización obtenidas a partir de los datos corriente-potencial. Los resultados indican que la oxidación de metano se ve favorecida a altas temperaturas sobre los catalizadores Pt90/Ir10, Pt50/Ir50 y Pt50/Ru50. A bajas temperaturas los mejores catalizadores resultaron ser Pt y Pt85/Ru15. La mezcla bimetálica Pt85/Ru15 fue la que presentó mejor desempeño para llevar a cabo la oxidación de propano a 30 °C.In this paper, the effect of temperature in the performance of proton exchange membrane fuel cells feed with methane and propane, using oxygen as feed to the cathode, is presented. For the fuel oxidation in the anodes, five carbon supported catalysts were tested: Pt, Pt85/Ru15, Pt50/Ru50, Pt90/Ir10, and Pt50/Ir50. Carbon-supported pure platinum was used as catalysts in the cathode side. The performance of the fuel cells was evaluated by polarization curves obtained from the current-potential data. Results indicate that methane oxidation is favoured at high temperatures on the Pt90/Ir10, Pt50/Ir50 and Pt50/Ru50 catalysts. At low temperatures the best catalysts were Pt and Pt85/Ru15. The Pt85/Ru15 bimetallic mixture showed the best performance to carry out propane oxidation at 30 °C.
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.
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)
Morales-Acosta, D.; Arriaga, L.G. [Centro de Investigacion y Desarrollo Tecnologico en Electroquimica, Parque Tecnologico Queretaro, Sanfandila, Pedro Escobedo, C.P. 76703 Queretaro (Mexico); Alvarez-Contreras, L. [Centro de Investigacion en Materiales Avanzados S.C., Complejo Industrial Chihuahua, C. P. 31109, Chihuahua, Chih. (Mexico); Luna, S. Fraire; Varela, F.J. Rodriguez [Cinvestav Unidad Saltillo, Carr. Saltillo-Monterrey Km. 13.5, Ramos Arizpe, Coahuila, C.P. 25900 (Mexico)
2009-07-15
Pt-Pd/MWCNT with Pt:Pd atomic ratio 40:60 and Pt/MWCNT electrocatalyst were synthesized and evaluated as oxygen reduction reaction (ORR) cathodes for Direct Ethylene Glycol Fuel Cells (DEGFC) applications. As reference, a commercial Pt/C material was also tested. We found that Pt-Pd/MWCNT has high tolerance capability to EG and higher selectivity for the ORR compared to the Pt-alone materials. As a result, the shift in onset potential for the ORR, E{sub onset}, at Pt-Pd/MWCNT was considerably smaller than the shift at Pt/MWCNT or Pt/C. The average particle size (from XRD) was 3.5 and 4 nm for Pt/MWCNT and Pt-Pd/MWCNT, respectively. A moderate degree of alloying was determined for the Pt-Pd material. An advantageous application of Pt-Pd electrocatalysts should be in DEGFCs. (author)
Microwave sinthesys and characterization of Pt and Pt-Rh-Sn electrocatalysts for ethanol oxidation
Directory of Open Access Journals (Sweden)
Jovanović Vladislava M.
2011-01-01
Full Text Available Carbon supported Pt and Pt-Rh-Sn catalysts were synthesized by microwave-polyol method in ethylene glycol solution and investigated for the ethanol electro-oxidation reaction. The catalysts were characterized in terms of structure, morphology and composition by employing XRD, STM and EDX techniques. STM analysis indicated rather uniform particles and particle size of below 2 nm for both catalysts. XRD analysis of the Pt/C catalyst revealed two phases, one with the main characteristic peaks of face centered cubic crystal structure (fcc of platinum and another related to graphite like structure of carbon support Vulcan XC-72R. However, in XRD pattern of the Pt-Rh-Sn/C catalyst diffraction peaks for Pt, Rh or Sn cannot be resolved, indicating an extremely low crystallinity. The small particle sizes and homogeneous size distributions of both catalysts should be attributed to the advantages of microwave assisted modified polyol process in ethylene glycol solution. Pt-Rh- Sn/C catalyst is highly active for the ethanol oxidation with the onset potential shifted for more than 150 mV to negative values and with currents nearly 5 times higher in comparison to Pt/C catalyst. The stability tests of the catalysts, as studied by the chronoamperometric experiments, reveal that the Pt-Rh-Sn/C catalyst is evidently less poisoned then Pt/C catalyst. The increased activity of Pt-Rh-Sn/C in comparison to Pt/C catalyst is most probably promoted by bifunctional mechanism and the electronic effect of alloyed metals.
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
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.
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.
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.
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.
Zhao, Meng; Anderson, Alfred B
2016-02-18
It has been shown recently that when reactants and products are well modeled within a comprehensive self-consistent theory for the electrochemical interface, accurate predictions are possible for reversible potentials, Urev, in acid electrolyte for reactions such as reduction of H(+)(aq) to form under potential deposited H(ads) and oxidation of an OH bond of H2O(ads) to deposit OH(ads). Predictions are based on calculated Gibbs energies for the reactant and product being equal at the reversible potential, which is the potential at the crossing point for reaction and product Gibbs energies, plotted as functions of electrode potential. In this Letter, it is demonstrated that the same capability holds for these reactions in basic electrolyte. This demonstration opens up the opportunity for predictions of reversible potentials and mechanisms for other electrocatalytic reactions in base.
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.
Schwarz, J H; Schwarz, John H.; Sen, Ashoke
1994-01-01
It is frequently useful to construct dual descriptions of theories containing antisymmetric tensor fields by introducing a new potential whose curl gives the dual field strength, thereby interchanging field equations with Bianchi identities. We describe a general procedure for constructing actions containing both potentials at the same time, such that the dual relationship of the field strengths arises as an equation of motion. The price for doing this is the sacrifice of manifest Lorentz invariance or general coordinate invariance, though both symmetries can be realized nonetheless. There are various examples of global symmetries that have been realized as symmetries of field equations but not actions. These can be elevated to symmetries of the action by our method. The main example that we focus on is the low-energy effective action description of the heterotic string theory compactified on a six-torus to four dimensions. We show that the SL(2,R) symmetry, whose SL(2,Z) subgroup has been conjectured to be a...
Extended symmetrical classical electrodynamics.
Fedorov, A V; Kalashnikov, E G
2008-03-01
In this paper, we discuss a modification of classical electrodynamics in which "ordinary" point charges are absent. The modified equations contain additional terms describing the induced charges and currents. The densities of the induced charges and currents depend on the vector k and the vectors of the electromagnetic field, E and B . It is shown that the vectors E and B can be defined in terms of two four-potentials and the components of k are the components of a four-tensor of the third rank. The Lagrangian of the modified electrodynamics is defined. The conditions are derived at which only one four-potential determines the behavior of the electromagnetic field. It is also shown that static modified electrodynamics can describe the electromagnetic field in the inner region of an electric monopole. In the outer region of the electric monopole the electric field is governed by the Maxwell equations. It follows from boundary conditions at the interface between the inner and outer regions of the monopole that the vector k has a discrete spectrum. The electric and magnetic fields, energy, and angular momentum of the monopole are found for different eigenvalues of k .
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.
Symmetric sensorimotor somatotopy.
Directory of Open Access Journals (Sweden)
Simon A Overduin
Full Text Available BACKGROUND: Functional imaging has recently been used to investigate detailed somatosensory organization in human cortex. Such studies frequently assume that human cortical areas are only identifiable insofar as they resemble those measured invasively in monkeys. This is true despite the electrophysiological basis of the latter recordings, which are typically extracellular recordings of action potentials from a restricted sample of cells. METHODOLOGY/PRINCIPAL FINDINGS: Using high-resolution functional magnetic resonance imaging in human subjects, we found a widely distributed cortical response in both primary somatosensory and motor cortex upon pneumatic stimulation of the hairless surface of the thumb, index and ring fingers. Though not organized in a discrete somatotopic fashion, the population activity in response to thumb and index finger stimulation indicated a disproportionate response to fingertip stimulation, and one that was modulated by stimulation direction. Furthermore, the activation was structured with a line of symmetry through the central sulcus reflecting inputs both to primary somatosensory cortex and, precentrally, to primary motor cortex. CONCLUSIONS/SIGNIFICANCE: In considering functional activation that is not somatotopically or anatomically restricted as in monkey electrophysiology studies, our methodology reveals finger-related activation that is not organized in a simple somatotopic manner but is nevertheless as structured as it is widespread. Our findings suggest a striking functional mirroring in cortical areas conventionally ascribed either an input or an output somatotopic function.
Institute of Scientific and Technical Information of China (English)
J.R.Rodriguez; R.M.F´elix; E.A.Reynoso; Y.Gochi-Ponce; Y.Verde Gómez; S.Fuentes Moyado; G.Alonso-N ´uñez
2014-01-01
This work reports a feasible synthesis of highly-dispersed Pt and Pt-Fe nanoparticles supported on multiwall carbon nanotubes (MWCNTs) without Fe and multiwall carbon nanotubes with iron (MWCNTs-Fe) which applied as electrocatalysts for methanol electrooxidation. A Pt coordination complex salt was synthesized in an aqueous solution and it was used as precursor to prepare Pt/MWCNTs, Pt/MWCNTs-Fe, and Pt-Fe/MWCNTs using FeCl2·4H2O as iron source which were named S1, S2 and S3, respectively. The coordination complex of platinum (TOA)2PtCl6 was obtained by the chemical reaction between (NH4)2PtCl6 with tetraoctylammonium bromide (TOAB) and it was characterized by FT-IR and TGA. The materials were characterized by Raman spectroscopy, SEM, EDS, XRD, TEM and TGA. The electrocatalytic activity of Pt-based supported on MWCNTs in the methanol oxidation was investigated by cyclic voltammetry (CV) and chronoamperometry (CA). Pt-Fe/MWCNTs electrocatalysts showed the highest electrocatalytic activity and stability among the tested electrocatalysts due to that the addition of”Fe”promotes the OH species adsorption on the electrocatalyst surface at low potentials, thus, enhancing the activity toward the methanol oxidation reaction (MOR).
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.
Institute of Scientific and Technical Information of China (English)
YE ZI-YAN; ZHANG QING-YU
2001-01-01
We have studied the influence of incident atoms with low energy on the Pt(100) surface by molecular dynamics simulation. The interaction potential obtained by the embedded atom method (EAM) was used in the simulation. The incident energy changes from 0.leV to 200eV, and the target temperature ranges from 100 to 500 K. The target scales are 6×6×4 and 8×8×4 fcc cells for lower and higher incident energies, respectively. The adatom, sputtering, vacancy and backscattering yields are calculated. It was found that there is a sputtering threshold for the incident energy. When the incident energy is higher than the sputtering threshold, the sputtering yield increases with the increase of incident energy, and the sputtering shows a symmetrical pattern. We found that the adatom and vacancy yields increase as the incident energy increases. The vacancy yields are much higher than those obtained by Monte Carlo simulation. The dependence of the adatom and sputtering yields on the incident energy and the relative atomistic mechanisms are discussed.
Recent Advances in FePt Nanoparticles for Biomedicine
Directory of Open Access Journals (Sweden)
Yujuan Shi
2015-01-01
Full Text Available FePt nanoparticles have great potential for biomedical applications due to their superior characteristics, including superparamagnetism, resistance to oxidation, and high chemical stability. The present paper reviews the methods used to prepare FePt nanoparticles, surface modifications, and their applications in the biomedical field, such as biosensing, magnetic resonance imaging (MRI, targeted drug delivery, and therapy.
Adhesion and bonding of Pt/Ni and Pt/Co overlayers: Density functional calculations
Cabeza, Gabriela F.; Castellani, Norberto J.; Légaré, Pierre
2006-04-01
The electronic and energetic properties of bimetallic surfaces Pt/Ni(111) and Pt/Co(111) are examined using the FP-LAPW (Full-PotentialLinearized Augmented Plane Wave) method by means of spin-polarized and non-polarized calculations. We present both the results of the shifts in the d-band centers when one metal (Pt) is pseudomorfically deposited on another with smaller lattice constant (Ni, Co) and those corresponding to the surface and adhesion energies. The surface is modeled by a seven layer slab separated in z direction by a vacuum region of six substrate layers. The results obtained for pure Ni, Co and Pt surfaces are presented in order to compare with experimental and theoretical data reported in the literature
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.
Facile Synthesis of Nanoporous Pt-Y alloy with Enhanced Electrocatalytic Activity and Durability
Cui, Rongjing; Mei, Ling; Han, Guangjie; Chen, Jiyun; Zhang, Genhua; Quan, Ying; Gu, Ning; Zhang, Lei; Fang, Yong; Qian, Bin; Jiang, Xuefan; Han, Zhida
2017-02-01
Recently, Pt-Y alloy has displayed an excellent electrocatalytic activity for oxygen reduction reaction (ORR), and is regarded as a promising cathode catalyst for fuel cells. However, the bulk production of nanoscaled Pt-Y alloy with outstanding catalytic performance remains a great challenge. Here, we address the challenge through a simple dealloying method to synthesize nanoporous Pt-Y alloy (NP-PtY) with a typical ligament size of ~5 nm. By combining the intrinsic superior electrocatalytic activity of Pt-Y alloy with the special nanoporous structure, the NP-PtY bimetallic catalyst presents higher activity for ORR and ethanol oxidation reaction, and better electrocatalytic stability than the commercial Pt/C catalyst and nanoporous Pt alloy. The as-made NP-PtY holds great application potential as a promising electrocatalyst in proton exchange membrane fuel cells due to the advantages of facile preparation and excellent catalytic performance.
Energy Technology Data Exchange (ETDEWEB)
Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Pogosyan, G.S. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics]|[Guadalajara Univ., Jalisco (Mexico). Dept. de Matematicas CUCEI; Sissakian, A.N. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics
2006-07-15
In this paper the Feynman path integral technique is applied for superintegrable potentials on two-dimensional spaces of non-constant curvature: these spaces are Darboux spaces D{sub I} and D{sub II}, respectively. On D{sub I} there are three and on D{sub II} foru such potentials, respectively. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is either determined by a transcendental equation involving parabolic cylinder functions (Darboux space I), or by a higher order polynomial equation. The solutions on D{sub I} in particular show that superintegrable systems are not necessarily degenerate. We can also show how the limiting cases of flat space (Constant curvature zero) and the two-dimensional hyperboloid (constant negative curvature) emerge. (Orig.)
Directory of Open Access Journals (Sweden)
AMALIJA V. TRIPKOVIC
2003-11-01
Full Text Available The oxidation of formic acid was studied at supported Pt catalyst (47.5 wt%. Pt and a low-index single crystal electrodes in sulfuric acid. The supported Pt catalyst was characterized by the TEM and HRTEM techniques. The mean Pt particle diameter, calculated from electrochemical measurements, fits well with Pt particle size distribution determined by HRTEM. For the mean particle diameter the surface averaged distribution of low-index single crystal facets was established. Comparison of the activities obtained at Pt supported catalyst and low-index Pt single crystal electrodes revealed that Pt(111 plane is the most active in the potential region relevant for fuel cell applications.
Energy Technology Data Exchange (ETDEWEB)
Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Pogosyan, G.S. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics]|[Guadalajara Univ., Jalisco (Mexico). Dept. de Matematicas CUCEI; Sissakian, A.N. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics
2006-08-15
This is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze in the spaces D{sub III} and D{sub IV} five respectively four superintegrable potentials, which were first given by Kalnins et al. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is determined by a higher order polynomial equation. We show that also the free motion in Darboux space of type III can contain bound states, provided the boundary conditions are appropriate. We state the energy spectrum and the wave-functions, respectively. (orig.)
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.
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...
Modeling the electro-oxidation of CO and H2/CO on Pt, Ru, PtRu and Pt3Sn
DEFF Research Database (Denmark)
Liu, Ping; Logadottir, Ashildur; Nørskov, Jens Kehlet
2003-01-01
is developed to describe the electro-oxidation of CO and H-2 at conditions relevant to the anode of a PEM fuel cell. The model is very simple and allows us to express the kinetics of a promoted anode surface relative to the activity of pure Pt directly from the calculated adsorption energy differences...... geometry is the same. This ligand effect is ascribed to changes in the electronic structure of the surface atoms due to interactions with the surroundings, and the physical origin of the effect is discussed. The calculated adsorption energetics is used as input into a simple kinetic model, which....... In agreement with experiments, the model shows Ru, PtRu and Pt3Sn to start oxidizing CO at lower potentials than Pt. In addition, the model shows PtRu to have a considerably lower overpotential for H-2 oxidation in the presence of CO than Pt. Pt3Sn is even better than PtRu, while Ru is found to be considerably...
Modification of Pt/Co/Pt film properties by ion irradiation
Avchaciov, K. A.; Ren, W.; Djurabekova, F.; Nordlund, K.; Sveklo, I.; Maziewski, A.
2015-09-01
We studied the structural modifications of a Pt/Co/Pt trilayer epitaxial film under Ga+ 30-keV ion irradiation by means of classical molecular dynamics and Monte Carlo simulations. The semiclassical tight-binding second-moment approximation potential was adjusted to reproduce the enthalpies of formation, the lattice constants, and the order-disorder transition temperatures for Co-Pt alloys. We found that during irradiation, the sandwich-type Pt(fcc)/Co(hcp)/Pt(fcc) film structure underwent a transition to the new solid solution α -Co /Pt (fcc ) phase. Our analysis of the short-range order indicates the formation, within a nanosecond time scale, of a homogeneous chemically disordered solution. The longer time-scale simulations employing a Monte Carlo algorithm demonstrated that the transition from the disordered phase to the ordered L 10 and L 12 phases was also possible but not significant for the changes in perpendicular magnetic anisotropy (PMA) observed experimentally. The strain analysis showed that the Co layer was under tensile strain in the lateral direction at the fluences of 1.5 ×1014-3.5 ×1014ionscm -2 ; this range of fluences corresponds to the appearance of PMA. This strain was induced in the initially relaxed hcp Co layer due to its partial transformation to the fcc phase and to the influence of atomic layers with larger lattice constants at upper/lower interfaces.
An evaluation of Pt sulfite acid (PSA) as precursor for supported Pt catalysts
Energy Technology Data Exchange (ETDEWEB)
Regalbuto, J.R.; Ansel, O.; Miller, J.T. (BP Res. Cntr.); (UIC)
2010-11-12
As a catalyst precursor, platinum sulfite acid (PSA) is easy to use and not relatively expensive, and is a potentially attractive precursor for many types of supported catalysts. The ultimate usefulness for many catalyst applications will depend on the extent that Pt can be dispersed and sulfur eliminated. To our knowledge, there exists no detailed characterization in the catalysis literature of PSA and the nanoparticulate Pt phases derived from it during catalyst pretreatment. To this end a series of supports including alumina, silica, magnesia, niobia, titania, magnesia and carbon were contacted with PSA solutions and subsequently analyzed with extended x-ray absorption fine structure (EXAFS) and x-ray absorption near edge structure (XANES) analysis, and x-ray photoelectron spectroscopy (XPS) to characterize the Pt species formed upon impregnation, calcination, and reduction. While all catalysts show retention of some S, reasonably small particle sizes with relatively little Pt-S can in some instances be produced using PSA. The amount of retained sulfur appears to decrease with decreasing surface acidity, although even the most acidic supports (niobia and silica) display some storage of S even while only Pt-O bands are observed after calcination or reoxidation. More sulfur was eliminated by high temperature calcinations followed by reduction in hydrogen, at the expense of increasing Pt particle size.
Surface Structures of Cubo-octahedral Pt-Mo Catalyst Nanoparticles from Monte Carlo Simulations
Energy Technology Data Exchange (ETDEWEB)
Wang, Guofeng; Van Hove, M.A.; Ross, P.N.; Baskes, M.I.
2005-03-31
The surface structures of cubo-octahedral Pt-Mo nanoparticles have been investigated using the Monte Carlo method and modified embedded atom method potentials that we developed for Pt-Mo alloys. The cubo-octahedral Pt-Mo nanoparticles are constructed with disordered fcc configurations, with sizes from 2.5 to 5.0 nm, and with Pt concentrations from 60 to 90 at. percent. The equilibrium Pt-Mo nanoparticle configurations were generated through Monte Carlo simulations allowing both atomic displacements and element exchanges at 600 K. We predict that the Pt atoms weakly segregate to the surfaces of such nanoparticles. The Pt concentrations in the surface are calculated to be 5 to 14 at. percent higher than the Pt concentrations of the nanoparticles. Moreover, the Pt atoms preferentially segregate to the facet sites of the surface, while the Pt and Mo atoms tend to alternate along the edges and vertices of these nanoparticles. We found that decreasing the size or increasing the Pt concentration leads to higher Pt concentrations but fewer Pt-Mo pairs in the Pt-Mo nanoparticle surfaces.
Huang, Minghua; Jin, Yongdong; Jiang, Heqing; Sun, Xuping; Chen, Hongjun; Liu, Baifeng; Wang, Erkang; Dong, Shaojun
2005-08-18
Multiple-deposited Pt overlayer modified Pt nanoparticle (MD-Pt overlayer/PtNPs) films were deliberately constructed on glassy carbon electrodes through alternately multiple underpotential deposition (UPD) of Ag followed redox replacement reaction by Pt (II) cations. The linear and regular growth of the films characterized by cyclic voltammetry was observed. Atomic force spectroscopy (AFM) provides the surface morphology of the nanostructured Pt films. Rotating disk electrode (RDE) voltammetry and rotating ring-disk electrode (RRDE) voltammetry demonstrate that the MD-Pt overlayer/PtNPs films can catalyze an almost four-electron reduction of O(2) to H(2)O in air-saturated 0.1 M H(2)SO(4). Thus-prepared Pt films behave as novel nanostructured electrocatalysts for dioxygen reduction and hydrogen evolution reaction (HER) with enhanced electrocatalytic activities, in terms of both reduction peak potential and peak current, when compared to that of the bulk polycrystalline Pt electrode. Additionally, it is noted that after multiple replacement cycles, the electrocatalytic activities improved remarkably, although the increased amount of Pt is very low in comparison to that of pre-modified PtNPs due to the intrinsic feature of the UPD-redox replacement technique. In other words, the electrocatalytic activities could be improved markedly without using very much Pt by the technique of tailoring the catalytic surface. These features may provide an interesting way to produce Pt catalysts with a reliable catalytic performance as well as a reduction in cost.
Sharma, Sudhanshu; Hegde, M S
2009-03-21
Pt ions-CeO(2) interaction in Ce(1-x)Pt(x)O(2-delta) (x=0.02) has been studied for the first time by electrochemical method combined with x-ray diffraction and x-ray photoelectron spectroscopy. Working electrodes made of CeO(2) and Ce(0.98)Pt(0.02)O(2-delta) mixed with 30% carbon are treated electrochemically between 0.0-1.2 V in potentiostatic (chronoamperometry) and potentiodynamic (cyclic voltametry) mode with reference to saturated calomel electrode. Reversible oxidation of Pt(0) to Pt(2+) and Pt(4+) state due to the applied positive potential is coupled to simultaneous reversible reduction of Ce(4+) to Ce(3+) state. CeO(2) reduces to CeO(2-y) (y=0.35) after applying 1.2 V, which is not reversible; Ce(0.98)Pt(0.02)O(2-delta) reaches a steady state with Pt(2+):Pt(4+) in the ratio of 0.60:0.40 and Ce(4+):Ce(3+) in the ratio of 0.55:0.45 giving a composition Ce(0.98)Pt(0.02)O(1.74) at 1.2 V, which is reversible. Composition of Pt ion substituted compound is reversible between Ce(0.98)Pt(0.02)O(1.95) to Ce(0.98)Pt(0.02)O(1.74) within the potential range of 0.0-1.2 V. Thus, Ce(0.98)Pt(0.02)O(2-delta) forms a stable electrode for oxidation of H(2)O to O(2) unlike CeO(2). A linear relation between oxidation of Pt(2+) to Pt(4+) with simultaneous reduction in Ce(4+) to Ce(3+) is observed demonstrating Pt-CeO(2) metal support interaction is due to reversible Pt(0)/Pt(2+)/Pt(4+) interaction with Ce(4+)/Ce(3+) redox couple.
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.
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.
Monte carlo simulations of segregation in Pt-Re catalyst nanoparticles
Energy Technology Data Exchange (ETDEWEB)
Wang, Guofeng; Van Hove, M.A.; Ross, P.N.; Baskes, M.I.
2004-04-01
We have investigated the segregation of Pt atoms to the surfaces of Pt-Re nanoparticles using the Monte Carlo method and Modified Embedded Atom Method potentials that we have developed for Pt-Re alloys. The Pt75Re25 nanoparticles (containing from 586 to 4033 atoms) are assumed to have disordered fcc configurations and cubo-octahedral shapes (terminated by {l_brace}111{r_brace} and {l_brace}100{r_brace} facets), while the Pt50Re50 and Pt25Re75 nanoparticles (containing from 587 to 4061 atoms) are assumed to have disordered hcp configurations and truncated hexagonal bipyramidal shapes (terminated by {l_brace}0001{r_brace} and {l_brace}101 {bar 1}{r_brace} facets). We predict that due to the segregation process the equilibrium Pt-Re nanoparticles would achieve a core-shell structure, with a Pt-enriched shell surrounding a Pt-deficient core. For fcc cubo-octahedral Pt75Re25 nanoparticles, the shells consist of almost 100 at. percent of Pt atoms. Even in the shells of hcp truncated hexagonal bipyramidal Pt50Re50 nanoparticles, the concentrations of Pt atoms exceed 85 at. percent (35 at. percent higher than the overall concentration of Pt atoms in these nanoparticles). Most prominently, all Pt atoms will segregate to the surfaces in the hcp truncated hexagonal bipyramidal Pt25Re75 nanoparticles containing less than 1000 atoms. We also find that the Pt atoms segregate preferentially to the vertex sites, less to edge sites, and least to facet sites on the shell of Pt-Re nanoparticles.
Directory of Open Access Journals (Sweden)
Athanasios ePapaderakis
2014-06-01
Full Text Available Ternary Pt-Ru-Ni deposits on glassy carbon substrates, Pt-Ru(Ni/GC, have been formed by initial electrodeposition of Ni layers onto glassy carbon electrodes, followed by their partial exchange for Pt and Ru, upon their immersion into equimolar solutions containing complex ions of the precious metals. The overall morphology and composition of the deposits has been studied by SEM microscopy and EDS spectroscopy. Continuous but nodular films have been confirmed, with a Pt÷Ru÷Ni % bulk atomic composition ratio of 37÷12÷51 (and for binary Pt-Ni control systems of 47÷53. Fine topographical details as well as film thickness have been directly recorded using AFM microscopy. The composition of the outer layers as well as the interactions of the three metals present have been studied by XPS spectroscopy and a Pt÷Ru÷Ni % surface atomic composition ratio of 61÷12÷27 (and for binary Pt-Ni control systems of 85÷15 has been found, indicating the enrichment of the outer layers in Pt; a shift of the Pt binding energy peaks to higher values was only observed in the presence of Ru and points to an electronic effect of Ru on Pt. The surface electrochemistry of the thus prepared Pt-Ru(Ni/GC and Pt(Ni/GC electrodes in deaerated acid solutions (studied by cyclic voltammetry proves the existence of a shell consisting exclusively of Pt-Ru or Pt. The activity of the Pt-Ru(Ni deposits towards methanol oxidation (studied by slow potential sweep voltammetry is higher from that of the Pt(Ni deposit and of pure Pt; this enhancement is attributed both to the well-known Ru synergistic effect due to the presence of its oxides but also (based on the XPS findings to a modification effect of Pt electronic properties.
Institute of Scientific and Technical Information of China (English)
洪祖培; 刘蕙菁
1982-01-01
@@用碱性光电化学池观察到异常的Pt/TiO2I-V特性，可能是Pt-TiO2之间的相互作用对表面态的影响所致，和无金属的TiO2比较，Au/TiO2改变了阳极曲线的起始电位，有利于光阳极的析氧性能的改善，而Ru/TiO2，Pt/TiO2有助于阴极极化的减少。
National Research Council Canada - National Science Library
Sergey V. Buldyrev; Pradeep Kumar; Pablo G. Debenedetti; Peter J. Rossky; H. Eugene Stanley
2007-01-01
We examine by molecular dynamics simulation the solubility of small apolar solutes in a solvent whose particles interact via the Jagla potential, a spherically symmetric ramp potential with two characteristic lengths...
Institute of Scientific and Technical Information of China (English)
Javad Hosseini; Mehdi Abdolmaleki; Hamid Reza Pouretedal; Mohammad Hossein Keshavarz
2015-01-01
An electrochemical approach to fabricate a nanostructured Fe/Pt-Fe catalyst through electrodepo-sition followed by galvanic replacement is presented. An Fe/Pt-Fe nanostructured electrode was prepared by deposition of Fe-Zn onto a Fe electrode surface, followed by replacement of the Zn by Pt at open-circuit potential in a Pt-containing alkaline solution. Scanning electron microscopy and energy-dispersive X-ray techniques reveal that the Fe/Pt-Fe electrode is porous and contains Pt. The electrocatalytic activity of the Fe/Pt-Fe electrode for oxidation of methanol was examined by cyclic voltammetry and chronoamperometry. The electrooxidation current on the Fe/Pt-Fe catalyst is much higher than that on flat Pt and smooth Fe catalysts. The onset potential and peak potential on the Fe/Pt-Fe catalyst are more negative than those on flat Pt and smooth Fe electrodes for methanol electrooxidation. All results show that this nanostructured Fe/Pt-Fe electrode is very attractive for integrated fuel cell applications in alkaline media.
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.
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...
Lagrangian formulation of symmetric space sine-Gordon models
Bakas, Ioannis; Shin, H J; Park, Q Han
1996-01-01
The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim \\sigma-models, and they are integrable exhibiting a black-hole type metric in target space. We provide a Lagrangian formulation of these systems by considering a triplet of Lie groups F \\supset G \\supset H. We show that for every symmetric space F/G, the generalized sine-Gordon models can be derived from the G/H WZW action, plus a potential term that is algebraically specified. Thus, the symmetric space sine-Gordon models describe certain integrable perturbations of coset conformal field theories at the classical level. We also briefly discuss their vacuum structure, Backlund transformations, and soliton solutions.
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.
Liu, Rui; Hu, Jinyang; Zhu, Senqiang; Lu, Jiapeng; Zhu, Hongjun
2017-09-12
Recently, graphene-based materials have become well-known nonlinear optical materials for the potential application of laser protection. Two new graphene oxide-platinum complex (GO-Pt) hybrid materials (GO-Pt-1, GO-Pt-2) have been fabricated through covalent modification and electrostatic adsorption of different Pt complexes with GO. The structural and photophysical properties of the resultant hybrid materials were studied. The nonlinear optical properties and optical power limiting (OPL) performance of Pt complexes, GO, and GO-Pt hybrid materials were investigated by using Z-scan measurements at 532 nm. At the same transmittance, the results illustrate that functionalization of GO makes GO-Pt hybrid materials possess better nonlinear optical properties and OPL performance than individual Pt complexes and GO due to a combination of nonlinear scattering, nonlinear absorption, and photoinduced electron and energy transfer between GO and Pt complex moieties. Furthermore, the nonlinear optics and OPL performance of GO-Pt-2 are better than those of GO-Pt-1, due to not only the excellent optical limiting of Pt-2 and more molecules per area of GO but also the way of combination of Pt-2 and GO.
Electro-oxidation of ethanol on ternary non-alloyed Pt-Sn-Pr/C catalysts
Corradini, Patricia G.; Antolini, Ermete; Perez, Joelma
2015-02-01
Ternary Pt-Sn-Pr/C (70:10:20), (70:15:15) and (45:45:10) electro-catalysts were prepared by a modified formic acid method, and their activity for the ethanol oxidation reaction (EOR) was compared with that of Pt-Pr/C catalysts prepared by the same methods and that of commercial Pt-Sn/C (75:25) and Pt/C catalysts. Among all the catalysts, the Pt-Sn-Pr/C (45:45:10) catalyst presented both the highest mass activity and the highest specific activity. The steady state electrochemical stability of ternary Pt-Sn-Pr catalysts increased with the surface Sn/Pt atomic ratio. Following repetitive potential cycling (RPC), the activity for ethanol oxidation of Pt-Sn-Pr/C catalysts with high surface Sn/Pt atomic ratio was considerably higher than that of the corresponding as-prepared catalysts, and increased with increasing the Sn/Pt ratio. The increase of the EOR mass activity following RPC was ascribed to the increase of either the specific activity (for the Pt-Sn-Pr/C (70:15:15) catalyst) or the electrochemically active surface area (for the Pt-Sn-Pr/C (45:45:10) catalyst). Dissolution of Sn and Pr oxides from Pt-Sn-Pr/C catalyst surface was observed following RPC.
Synthesis and Characterization of Pt-loaded carbon nanostructures derived from polyaniline nanotubes
Energy Technology Data Exchange (ETDEWEB)
Xu, Gong Da; Kim, Pil; Lee, Youn Sik [Div. of Chemical Engineering, Nanomaterials Processing Research Center, Chonbuk NationalUniversity, Jeonju (Korea, Republic of)
2017-03-15
Proton exchange membrane fuel cells (PEMFC) are one of the most advanced fuel cells for future energy, owing to their high conversion efficiency, quick start-up, rapid response to variable loading, and relatively low operating temperature, compared with of her conventional energy conversion devices. PANTs were synthesized to have various aspect ratios and inner diameters. As the aniline concentration increased, the PANTs’ inner diameter greatly decreased, but their outer diameters only slightly increased, leading to a decrease in their aspect ratios. Carbonization of PANTs resulted in the formation of corresponding CNSs. Pt nanoparticles were successfully formed on the CNSs under N{sub 2} or N{sub 2}/NH{sub 3} flow. The Pt nanoparticles of the Pt- CNS-N{sub 2} /NH{sub 3} catalysts were smaller in size, less aggregated, and more uniformly dispersed than those of the Pt- CNS-N{sub 2} catalysts. The ECSA values of Pt-CNS-N{sub 2} /NH{sub 3} were larger than those of Pt-CNS-N{sub 2} and Pt/C. The half wave potentials of the Pt-CNS-N{sub 2} catalysts were lower than those of the Pt-CNS-N{sub 2} /NH{sub 3} , and close to those of the Pt/C. The Pt-CNS-N{sub 2} /NH{sub 3} catalysts exhibited better kinetic performance than the Pt-CNS -N{sub 2} catalysts and Pt/C.
Influence of bi modification of pt anode catalyst in direct formic acid fuel cells.
Kang, Sungjin; Lee, Jaeyoung; Lee, Jae Kwang; Chung, Seung-Young; Tak, Yongsug
2006-04-13
The influence of Bi modification of Pt anode catalyst on the performance of direct formic acid fuel cells was investigated. Compared with the unmodified Pt anode, the Bi modified Pt (PtBi(m)) electrode prepared by under-potential deposition (UPD) caused faster electrocatalytic oxidation of formic acid at the same value of the overpotential, and thus, PtBi(m) resulted in an increase in the power performance of direct formic acid fuel cells. Electrochemical impedance spectra helped to explain the difference of performance between the unmodified Pt and Bi modified Pt electrodes. Solution conductivity and dehydration phenomena occurring in highly concentrated formic acid solutions can also explain the higher power performance of PtBi(m).
Symmetric instability in the Gulf Stream
Thomas, Leif N.; Taylor, John R.; Ferrari, Raffaele; Joyce, Terrence M.
2013-07-01
Analyses of wintertime surveys of the Gulf Stream (GS) conducted as part of the CLIvar MOde water Dynamic Experiment (CLIMODE) reveal that water with negative potential vorticity (PV) is commonly found within the surface boundary layer (SBL) of the current. The lowest values of PV are found within the North Wall of the GS on the isopycnal layer occupied by Eighteen Degree Water, suggesting that processes within the GS may contribute to the formation of this low-PV water mass. In spite of large heat loss, the generation of negative PV was primarily attributable to cross-front advection of dense water over light by Ekman flow driven by winds with a down-front component. Beneath a critical depth, the SBL was stably stratified yet the PV remained negative due to the strong baroclinicity of the current, suggesting that the flow was symmetrically unstable. A large eddy simulation configured with forcing and flow parameters based on the observations confirms that the observed structure of the SBL is consistent with the dynamics of symmetric instability (SI) forced by wind and surface cooling. The simulation shows that both strong turbulence and vertical gradients in density, momentum, and tracers coexist in the SBL of symmetrically unstable fronts. SI is a shear instability that draws its energy from geostrophic flows. A parameterization for the rate of kinetic energy (KE) extraction by SI applied to the observations suggests that SI could result in a net dissipation of 33 mW m-2 and 1 mW m-2 for surveys with strong and weak fronts, respectively. The surveys also showed signs of baroclinic instability (BCI) in the SBL, namely thermally direct vertical circulations that advect biomass and PV. The vertical circulation was inferred using the omega equation and used to estimate the rate of release of available potential energy (APE) by BCI. The rate of APE release was found to be comparable in magnitude to the net dissipation associated with SI. This result points to an
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.
Ethanol Oxidation Reaction on Tandem Pt/Rh/SnOx Catalyst
Directory of Open Access Journals (Sweden)
Phuong Tu Mai
2017-08-01
Full Text Available To elucidate the atomic arrangement of a Pt-Rh-Sn ternary catalyst with a high catalytic activity for ethanol oxidation reaction (EOR and high CO2 selectivity, we prepared a tandem Pt/Rh/SnOx, in which a Rh adlayer was deposited on a Pt substrate (Rh coverage: 0.28, followed by depositing several layers of SnOx only on the Rh surface (Sn coverage: 0.07. For reference, Sn was randomly deposited on the Rh-modified Pt (Pt/Rh electrode whose Rh and Sn coverages were 0.22 and 0.36 (random Pt/Rh/SnOx. X-ray photoelectron spectroscopy demonstrated that Pt and Rh were metallic, and Sn was largely oxidized. Both Pt/Rh/SnOx electrodes were less positive in onset potential of EOR current density and higher in EOR current density than Pt and Rh/Pt electrodes. In situ infrared reflection-absorption spectroscopy demonstrated that the tandem Pt/Rh/SnOx electrode did not produce acetic acid, but produced CO2 in contrast to the random Pt/Rh/SnOx, suggesting that a tandem arrangement of Pt, Rh and SnOx, in which the Pt and SnOx sites were separated by the Rh sites, was effective for selective CO2 production. In the electrostatic electrolysis at 0.5 V vs. RHE, the tandem Pt/Rh/SnOx electrode exhibited higher EOR current density than the Pt and Pt/Rh electrodes after 1.5 h.
Oxygen Reduction Reaction Activity and Durability of Pt Catalysts Supported on Titanium Carbide
Directory of Open Access Journals (Sweden)
Morio Chiwata
2015-06-01
Full Text Available We have prepared Pt nanoparticles supported on titanium carbide (TiC (Pt/TiC as an alternative cathode catalyst with high durability at high potentials for polymer electrolyte fuel cells. The Pt/TiC catalysts with and without heat treatment were characterized by X-ray diffraction (XRD, X-ray photoelectron spectroscopy (XPS, and transmission electron microscopy (TEM. Hemispherical Pt nanocrystals were found to be dispersed uniformly on the TiC support after heat treatment at 600 °C in 1% H2/N2 (Pt/TiC-600 °C. The electrochemical properties (cyclic voltammetry, electrochemically active area (ECA, and oxygen reduction reaction (ORR activity of Pt/TiC-600 °C and a commercial Pt/carbon black (c-Pt/CB were evaluated by the rotating disk electrode (RDE technique in 0.1 M HClO4 solution at 25 °C. It was found that the kinetically controlled mass activity for the ORR on Pt/TiC-600 °C at 0.85 V (507 A g−1 was comparable to that of c-Pt/CB (527 A g−1. Moreover, the durability of Pt/TiC-600 °C examined by a standard potential step protocol (E = 0.9 V↔1.3 V vs. RHE, holding 30 s at each E was much higher than that for c-Pt/CB.
Dynamical systems and spherically symmetric cosmological models
He, Yanjing
2006-06-01
In this thesis we present a study of the timelike self-similar spherically symmetric cosmological models with two scalar fields with exponential potentials. We first define precisely the timelike self-similar spherically symmetric (TSS) spacetimes. We write the TSS metric in a conformally isometric form in a coordinate system adapted to the geometry of the spacetime manifold. In this coordinate system, both the metric functions of the TSS spacetimes and the potential functions of the scalar fields can be simplified to four undetermined functions of a single coordinate. As a result, the Einstein field equations reduce to an autonomous system of first-order ODEs and polynomial constraints in terms of these undetermined functions. By introducing new bounded variables as well as a new independent variable and solving the constraints, we are able to apply the theory of dynamical systems to study the properties of the TSS solutions. By finding invariant sets and associated monotonic functions, by applying the LaSalle Invariance Principle and the Monotonicity Principle, by applying the [straight phi] t -connected property of a limit set, and using other theorems, we prove that all of the TSS trajectories are heteroclinic trajectories. In addition, we conduct numerical simulations to confirm and support the qualitative analysis. We obtain all possible types of TSS solutions, by analyzing the qualitative behavior of the original system of ODES from those of the reduced one. We obtain asymptotic expressions for the TSS solutions (e.g., the asymptotic expressions for the metric functions, the source functions and the Ricci scalar). In particular, self-similar flat Friedmann-Robertson-Walker spacetimes are examined in order to obtain insights into the issues related to the null surface in general TSS spacetimes in these coordinates. A discussion of the divergence of the spacetime Ricci scalar and the possible extension of the TSS solutions across the null boundary is presented
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.
The Pt(111)/Electrolyte Interface under Oxygen Reduction Reaction Conditions
DEFF Research Database (Denmark)
Bondarenko, A.S.; Stephens, Ifan; Hansen, Heine Anton;
2011-01-01
between the adsorbate and Pt surface atoms (0.45−1.15 V vs RHE). An equivalent electric circuit is proposed to model the Pt(111)/electrolyte interface under ORR conditions within the selected potential window. This equivalent circuit reflects three processes with different time constants, which occur...... simultaneously during the ORR at Pt(111). Density functional theory (DFT) calculations were used to correlate and interpret the results of the measurements. The calculations indicate that the coadsorption of ClO4* and Cl* with OH* is unlikely. Our analysis suggests that the two-dimensional (2D) structures formed...
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.
DEFF Research Database (Denmark)
Abrikosov, I. A.; Skriver, Hans Lomholt
1993-01-01
energies and work functions for three fcc-based alloys (Cu-Ni, Ag-Pd, and Au-Pt) over the complete concentration range. The calculated mixing enthalpies for the Ag-Pd and Au-Pt systems agrees with experimental values, and the calculated concentration dependence of the lattice parameters agrees...... with experiment for all three systems. We find that the calculated surface energies and work functions in the unsegregated case exhibit a small positive deviation from a linear concentration dependence. Finally, we performed a segregation analysis based on the calculated surface energies by means of a simple...
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.
Absence of anomalous Nernst effect in spin Seebeck effect of Pt/YIG
Miao, B. F.; Huang, S. Y.; Qu, D.; Chien, C. L.
2016-01-01
The Pt/YIG structure has been widely used to study spin Seebeck effect (SSE), inverse spin Hall effect, and other pure spin current phenomena. However, the magnetic proximity effect in Pt when in contact with YIG, and the potential anomalous Nernst effect (ANE) may compromise the spin current phenomena in Pt/YIG. By inserting a Cu layer of various thicknesses between Pt and YIG, we have separated the signals from the SSE and that of the ANE. It is demonstrated that the thermal voltage in Pt/YIG mainly comes from spin current due to the longitudinal SSE with negligible contribution from the ANE.
Absence of anomalous Nernst effect in spin Seebeck effect of Pt/YIG
Energy Technology Data Exchange (ETDEWEB)
Miao, B. F., E-mail: bfmiao@nju.edu.cn [National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093 (China); Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 (United States); Huang, S. Y. [Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 (United States); Department of Physics, National Taiwan University, Taipei 10617, Taiwan (China); Qu, D.; Chien, C. L., E-mail: clchien@jhu.edu [Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 (United States)
2016-01-15
The Pt/YIG structure has been widely used to study spin Seebeck effect (SSE), inverse spin Hall effect, and other pure spin current phenomena. However, the magnetic proximity effect in Pt when in contact with YIG, and the potential anomalous Nernst effect (ANE) may compromise the spin current phenomena in Pt/YIG. By inserting a Cu layer of various thicknesses between Pt and YIG, we have separated the signals from the SSE and that of the ANE. It is demonstrated that the thermal voltage in Pt/YIG mainly comes from spin current due to the longitudinal SSE with negligible contribution from the ANE.
Absence of anomalous Nernst effect in spin Seebeck effect of Pt/YIG
Directory of Open Access Journals (Sweden)
B. F. Miao
2016-01-01
Full Text Available The Pt/YIG structure has been widely used to study spin Seebeck effect (SSE, inverse spin Hall effect, and other pure spin current phenomena. However, the magnetic proximity effect in Pt when in contact with YIG, and the potential anomalous Nernst effect (ANE may compromise the spin current phenomena in Pt/YIG. By inserting a Cu layer of various thicknesses between Pt and YIG, we have separated the signals from the SSE and that of the ANE. It is demonstrated that the thermal voltage in Pt/YIG mainly comes from spin current due to the longitudinal SSE with negligible contribution from the ANE.
Directory of Open Access Journals (Sweden)
Griselda Caballero-Manrique
2015-04-01
Full Text Available The synthesis of core-shell Pt(Cu and Pt-Ru(Cu electrocatalysts allows for a reduction in the amount of precious metal and, as was previously shown, a better CO oxidation performance can be achieved when compared to the nanoparticulated Pt and Pt-Ru ones. In this paper, the carbon black used as the support was previously submitted to electrochemical oxidation and characterized by XPS. The new catalysts thus prepared were characterized by HRTEM, FFT, EDX, and electrochemical techniques. Cu nanoparticles were generated by electrodeposition and were further transformed into Pt(Cu and Pt-Ru(Cu core-shell nanoparticles by successive galvanic exchange with Pt and spontaneous deposition of Ru species, the smallest ones being 3.3 nm in mean size. The onset potential for CO oxidation was as good as that obtained for the untreated carbon, with CO stripping peak potentials about 0.1 and 0.2 V more negative than those corresponding to Pt/C and Ru-decorated Pt/C, respectively. Carbon oxidation yielded an additional improvement in the catalyst performance, because the ECSA values for hydrogen adsorption/desorption were much higher than those obtained for the non-oxidized carbon. This suggested a higher accessibility of the Pt sites in spite of having the same nanoparticle structure and mean size.
Plasma Control in Symmetric Mirror Machines
Horton, W.; Rowan, W. L.; Alvarado, Igor; Fu, X. R.; Beklemishev, A. D.
2014-10-01
Plasma confinement in the symmetric rotating mirror plasma at the Budker Institute shows enhanced confinement with high electron temperatures with end plates biasing. Improved confinement is achieved by biasing end plate cells in the expansion tanks so as to achieve an inward pointing radial electric field. The negative potential well produces vortex plasma rotation similar to that in the negative potential well of Ohmic heated tokamaks. This plasma state has similarity with the lower turbulence level regimes documented in the Helimak where negative biasing of the end plates produces an inward radial electric field. To understand this vortex confinement we carry out 3D simulations with nonlinear partial differential equations for the electric potential and density in plasmas with an axially localized region of unfavorable and favorable magnetic curvature. The simulations show that the plasma density rapidly adjusts to be higher in the region of favorable curvature regions and remains relatively well confined while rapidly rotating. The results support the concept of using plasma-biasing electrodes in large expander tanks to achieve enhanced mirror plasma confinement. Supported by US-DoE grant to UT, LANL and the Budker Institute for Nuclear Physics.
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.
PT-invariant one-dimensional Coulomb problem
Sinha, A K; Sinha, Anjana; Roychoudhury, Rajkumar
2002-01-01
The one-dimensional Coulomb-like potential with a real coupling constant beta, and a centrifugal-like core of strength G = alpha^2 - {1/4}, viz. V(x) = {alpha^2 - (1/4)}/{(x-ic)^2} + beta/|x-ic|, is discussed in the framework of PT-symmetry. The PT-invariant exactly solvable model so formed, is found to admit a double set of real and discrete energies, numbered by a quasi-parity q = +/- 1.
Institute of Scientific and Technical Information of China (English)
杜鑫鑫; 王晓霞; 贺阳; 王健农
2016-01-01
采用催化裂解法制备了多孔碳，将其作为催化剂载体，利用液相还原和真空热处理工艺制备出PtIrFe/C三元合金催化剂。采用 X射线衍射、透射电子显微镜等手段对样品的结构形貌进行表征。使用电化学测试手段研究了不同热处理温度对其催化性能的影响。实验结果表明，热处理带来的合金化作用使催化剂的催化活性和耐久性得到了极大的提高。经过700℃热处理的样品，其面积比活性和质量比活性分别是传统商业 Pt/C 催化剂的3~4倍。%Using a mesoporous carbon (prepared via catalyzed pyrolysis)as a support material,PtIrFe/C alloy catalysts were synthesized by a liquid reduction and heat treatment method,and characterized by transmission electron microscopy and powder X-ray diffraction to explore and study the morphologies and crystallization properties.The an-nealing of the as prepared catalysts was performed at different temperatures,tested by electrochemical measurements, and proved to be of great importance for the improvement of the catalyst′s activity and durability due to the alloying effect.The catalysts annealed at 700 ℃ exhibited the highest area-specific activity and mass-specific activity which were 3-4 times higher than those of a commercial Pt/C catalyst.
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
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...
On solving the Schrödinger equation for a complex deictic potential in one dimension
Indian Academy of Sciences (India)
Ram Mehar Singh
2014-09-01
Making use of an ansatz for the eigenfunction, we investigate closed-form solutions of the Schrödinger equation for an even power complex deictic potential and its variant in one dimension. For this purpose, extended complex phase-space approach is utilized and nature of the eigenvalue and the corresponding eigenfunction is determined by the analyticity property of the eigenfunction. The imaginary part of the energy eigenvalue exists only if the potential parameters are complex, whereas it reduces to zero for real coupling parameters and the result coincides with those derived from the invariance of Hamiltonian under $\\mathcal{PT}$ operations. Thus, a non-Hermitian Hamiltonian possesses real eigenvalue, if it is $\\mathcal{PT}$-symmetric.
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...
Tilting mutation of weakly symmetric algebras and stable equivalence
Dugas, Alex
2011-01-01
We consider tilting mutations of a weakly symmetric algebra at a subset of simple modules, as recently introduced by T. Aihara. These mutations are defined as the endomorphism rings of certain tilting complexes of length 1. Starting from a weakly symmetric algebra A, presented by a quiver with relations, we give a detailed description of the quiver and relations of the algebra obtained by mutating at a single loopless vertex of the quiver of A. In this form the mutation procedure appears similar to, although significantly more complicated than, the mutation procedure of Derksen, Weyman and Zelevinsky for quivers with potentials. By definition, weakly symmetric algebras connected by a sequence of tilting mutations are derived equivalent, and hence stably equivalent. The second aim of this article is to describe explicitly the images of the simple modules under such a stable equivalence. As an application we answer a question of Asashiba on the derived Picard groups of a class of symmetric algebras of finite re...
General description of circularly symmetric Bessel beams of arbitrary order
Wang, Jia Jie; Wriedt, Thomas; Lock, James A.; Mädler, Lutz
2016-11-01
A general description of circularly symmetric Bessel beams of arbitrary order is derived in this paper. This is achieved by analyzing the relationship between different descriptions of polarized Bessel beams obtained using different approaches. It is shown that a class of circularly symmetric Davis Bessel beams derived using the Hertz vector potentials possesses the same general functional dependence as the aplanatic Bessel beams generated using the angular spectrum representation (ASR). This result bridges the gap between different descriptions of Bessel beams and leads to a general description of circularly symmetric Bessel beams, such that the Davis Bessel beams and the aplanatic Bessel beams are merely the two simplest cases of an infinite number of possible circularly symmetric Bessel beams. Additionally, magnitude profiles of the electric and magnetic fields, the energy density and the Poynting vector are displayed for Bessel beams in both paraxial and nonparaxial cases. The results presented in this paper provide a fresh perspective on the description of Bessel beams and cast some insights into the light scattering and light-matter interactions problems in practice.
Miniature Fuel Cell With Monolithically Fabricated Si Electrodes - Au-Pd-Pt Multilayer Catalyst -
Shirai, Ryo; Vasiljevic, N.; Hayase, Masanori
2016-11-01
A novel catalyst layer structure is proposed for our miniature fuel cells. In our fuel cells, conventionally porous Pt was used as a catalyst layer. In order to reduce the Pt amount, instead of porous Pt, porous Pd was formed on a Si chip and Pt was deposited atomically on the Pd by UPD-SLRR(Under Potential Deposition - Surface Limited Redox Replacement). The Pd- Pt catalyst showed satisfying performance, besides high CO tolerance was observed. Though the Pd-Pt catalyst is quite promising, Pd is also a rare metal and reduction of Pd amount is necessary. In this study, a novel Au-Pd-Pt catalyst formation strategy is proposed by UPD-SLRR, and the layered structure is preliminary fabricated.
Explorations on size limit of L10-FePt nanoparticles for practical magnetic storage
Directory of Open Access Journals (Sweden)
Tao Huang
2016-11-01
Full Text Available With the advance of HAMR technology, the storage potential of L10-FePt nanoparticles with practical considerations are of great significance. We present an L10-FePt nanoparticle model based on atomistic spin model with Langevin thermodynamics to simulate the magnetic behaviors of L10-FePt nanoparticles at Curie temperature and room temperature to explore their practical design margins. Given specific composites, the Curie temperatures of L10-FePt nanoparticles decrease with their volume sizes decrease starting from 8 nm, meaning no more laser power increment needed for smaller L10-FePt nanoparticles. However, L10-FePt nanoparticles get unstable more easily while their volume sizes decrease at room temperature within 10 years. Above all, a reasonable size of L10-FePt nanoparticles for stable information retaining should not be less than 8 nm at a certain aspect ratio.
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Pt nanoparticles were prepared by the chemical reduction method. The average diameter of Pt nanoparticles was determined to be 2.5 nm by TEM. The electrochemical properties of Pt nanoparticles were studied by cyclic voltammetry. In comparison with massive Pt, the oxidation current peak of CO adsorbed on Pt nanoparticles is broader. Twin adsorbates of CO on Pt nanoparticles were determined by in situ FTIRS for the first time. It has revealed that the linear and twin-bonded CO can be converted into bridge-bonded CO with the variation of electrode potential. A series of special properties of Pt nanoparticles, such as enhanced IR absorption of CO adsorbates, were also observed.
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.
Energy Technology Data Exchange (ETDEWEB)
Caillard, A.; Brault, P.; Mathias, J. [Groupe de Recherche sur l' Energetique des Milieux Ionises, UMR6606 Universite d' Orleans, CNRS, Polytech' Orleans BP6744, F-45067 Orleans Cedex 2 (France); Coutanceau, C.; Leger, J.-M. [Laboratoire de Catalyse en Chimie Organique, UMR6503 Universite de Poitiers, CNRS, F-86022 Poitiers (France)
2006-11-08
Plasma sputtering process was used to deposit Pt and PtRu on conductive carbon diffusion layer. Low metal loading catalysts for methanol electrooxidation were prepared and characterized by TEM and XRD. The main result is that codeposition of Pt and Ru leads to alloy phase, whereas multi-layers deposition leads to no-alloyed structure. The electrochemical performance of sputtered Pt/C electrodes was compared with that of standard electrodes, and was found lower. However, the specific activity was much higher, indicating that the catalyst utilization efficiency was higher than that obtained with a standard electrode. Then, different bimetallic PtRu/C electrodes were prepared by plasma sputtering, leading to different catalyst structures (Pt and Ru multilayer deposition or simultaneous deposition of Pt and Ru) and composition (from 100:0 to 50:50 Pt/Ru atomic ratios). At last, the different PtRu electrodes were compared in term of DMFC electrical performance. The best efficiency of the DMFC was reached when both metals Pt and Ru are simultaneously deposited (alloyed) with a ruthenium atomic ratio of 30% or 40 % Ru depending of the working potentials of the cell. (author)
Energy Technology Data Exchange (ETDEWEB)
Vidal-Iglesias, F.J.; Solla-Gullon, J.; Montiel, V.; Feliu, J.M.; Aldaz, A. [Instituto de Electroquimica, Universidad de Alicante, Apartado 99, 03080 Alicante (Spain)
2007-09-27
Ammonia has attracted attention as a possible fuel for direct fuel cells since it is easy to handle and to transport as liquid or as concentrated aqueous solution. However, on noble metal electrodes ammonia oxidation is a sluggish reaction and the electrocatalyst needs to be improved for developing efficient ammonia fuel cells. In this work, ammonia electrooxidation reaction on 3-4-nm bimetallic PtMe (Ir, Rh, Pd, Ru) and on preferentially oriented Pt(1 0 0) nanoparticles is reported. PtMe nanoparticles have been prepared by using water-in-oil microemulsions to obtain a narrow size distribution whereas preferentially oriented Pt nanoparticles have been prepared through colloidal routes. Among all the bimetallic samples tested, only Pt{sub 75}Ir{sub 25} and Pt{sub 75}Rh{sub 25} nanoparticles show, at the low potential range, an enhancement of the oxidation density current with respect to the behaviour found for pure platinum nanoparticles prepared by the same method. In addition, two Pt(1 0 0) preferentially oriented nanoparticles of different particle size (4 and 9 nm) have been also studied. These oriented nanoparticles show higher current densities than polycrystalline Pt nanoparticles due to the sensitivity of ammonia oxidation toward the presence of surface sites with square symmetry. The reactivity of the different 4-nm nanoparticles parallels well with that expected from bulk PtMe alloys and Pt single crystal electrodes. (author)
Critical behavior of spherically symmetric domain wall collapse
Ikeda, Taishi
2016-01-01
Critical collapse of a spherically symmetric domain wall is investigated. The domain wall is made of a minimally coupled scalar field with a double well potential. We consider a sequence of the initial data which describe a momentarily static domain wall characterized by its initial radius. The time evolution is performed by a full general relativistic numerical code for spherically symmetric systems. In this paper, we use the maximal slice gauge condition, in which spacelike time slices may penetrate the black hole horizon differently from other widely used procedures. In this paper, we consider two specific shapes of the double well potential, and observe the Type II critical behavior in both cases. The mass scaling, sub-critical curvature scaling, and those fine structures are confirmed. The index of the scaling behavior agrees with the massless scalar case.
Platinum Migration at the Pt/YSZ Interface
DEFF Research Database (Denmark)
Nielsen, Jimmi; Jacobsen, Torben
2006-01-01
by potential sweep, step and impedance techniques. As expected, inductive behaviour and activation during step polarization is confirmed, but furthermore, a very accentuated noise pattern is seen during cathodic step polarization. Investigation of the YSZ and Pt surfaces afterwards reveals the growth......Electrode activation, inductive hysteresis and non-linearity are well known phenomena on Pt-YSZ electrodes, and recently also regular fluctuation patterns have been reported. The oxygen electrode on YSZ surfaces is studied at Pt micro-electrodes prepared by electrochemical etching of platinum wire...... of dendrite like Pt structures from the TPB. The formation of these may explain the observed noise and contribute to the explanation of the activation mechanism taking place at the platinum-YSZ interface....
Strong Spin Hall effect in PtMn
Ou, Yongxi; Shi, Shengjie; Ralph, Daniel; Buhrman, Robert
Recent reports indicate that certain metallic antiferromagnets (AFM) can exhibit a significant spin Hall effect. Here we report a large damping-like spin torque efficiency (ξDL) in PtMn/ferromagnet(FM) bilayer structures, determined from both FM-thickness-dependent spin-torque ferromagnetic resonance (ST-FMR), and harmonic response (HR) measurements of layers with perpendicular magnetic anisotropy (PMA). We find that ξDL can vary from 0.15, depending on the thickness of PtMn, the stacking order of the samples, and the choice of the FM material. The field-like spin torque efficiency (ξFL) is also quite variable, 0phase diagram. These results indicate that AFM PtMn has significant potential both for advancing the understanding the physics of the spin Hall effect in Pt alloys, and for enabling new spintronics functionality.
$\\mathcal{PT}$-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.
Energy Technology Data Exchange (ETDEWEB)
Morales-Acosta, D.; Arriaga, L.G. [Centro de Investigacion y Desarrollo Tecnologico en Electroquimica, Pedro Escobedo, Queretaro (Mexico)]. E-mail: dmorales@cideteq.mx; Alvarez-Contreras, L. [Centro de Investigacion en Materiales Avanzados S. C., Chihuahua, Chihuahua (Mexico); Fraire Luna, S.; Rodriguez Varela, F.J. [Cinvestav, Unidad Saltillo, Ramos Arizpe, Coahuila, (Mexico)
2009-09-15
Pt-Pd/MWCNTs (atomic ratio Pt:Pd 43:57) and Pt/MWCNTs electrocatalysts were synthesized and evaluated as cathodes for oxygen reduction reaction (ORR) with the application of direct ethylene glycol fuel cells (DEGFC). A commercial PtC material was also evaluated as a reference. It was found that Pt-Pd/MWCNT has a capability for high tolerance to ethylene glycol (EG) and higher selectivity for ORR compared to a single Pt- cathode. As a result, the change in onset potential of the ORR, Eonset, in Pt-Pd/MWCNTs was considerably less than the change in Pt/MWCNTs or Pt/C. The average particle size (XRD) was 3.5nm and 4nm for Pt/MWCNTs and Pt-Pd/MWCNTs, respectively. A moderate degree of alloying was determined for the material. The application of Pt-Pd electrocatalysts in DEGFCs should be advantageous. [Spanish] Electrocatalizadores Pt-Pd/MWCNTs (relacion atomic Pt:Pd 43:57) y Pt/MWCNTs fueron sintetizados y evaluados como catodos para la reaccion de reduccion del oxigeno (ORR) con aplicacion del celdas de consumo directo de etilenglicol (Direct Ethylene Glycol Fuel Cells, o DEGFC). Como referencia, un material comercial tipo Pt/C fue tambien evaluado. Se encontro que Pt-Pd/MWCNTs tiene una alta capacidad de tolerancia al etilenglicol (EG) y una selectividad mayor hacia la ORR comparado con el catodo basado en Pt-solo. Como resultado, el cambio en potencial de inicio de la ORR, Eonset, en Pt-Pd/MWCNTs fue considerablemente menor que el cambio en Pt/MWCNTs o Pt/C. La talla de particula promedio (de XRD) fue 3.5 nm y 4 nm para Pt/MWCNTs y Pt-Pd/MWCNTs, respectivamente. Un moderado grado de aleacion fue determinado para el material. Una aplicacion ventajosa para electrocatalizadores tipo Pt-Pd debe ser en DEGFCs.
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.
Relativistic electromagnetic mass models in spherically symmetric spacetime
Maurya, S K; Ray, Saibal; Chatterjee, Vikram
2015-01-01
Under the static spherically symmetric Einstein-Maxwell spacetime of embedding class one we explore possibility of electromagnetic mass model where mass and other physical parameters have purely electromagnetic origin (Tiwari 1984, Gautreau 1985, Gron 1985). This work is in continuation of our earlier investigation (Maurya 2015a) where we developed an algorithm and found out three new solutions of electromagnetic mass models. In the present letter we consider different metric potentials $\
Electroweak Phase Transitions in left-right symmetric models
Barenboim, G; Barenboim, Gabriela; Rius, Nuria
1998-01-01
We study the finite-temperature effective potential of minimal left-right symmetric models containing a bidoublet and two triplets in the scalar sector. We perform a numerical analysis of the parameter space compatible We perform a numerical analysis of the parameter space compatible with the requirement that baryon asymmetry is not washed out by sphaleron processes after the electroweak phase transition. We find that the spectrum of scalar particles for these acceptable cases is consistent with present experimental bounds.
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.
Electrocatalytic activity of PtAu/C catalysts for glycerol oxidation.
Jin, Changchun; Sun, Chao; Dong, Rulin; Chen, Zhidong
2012-01-01
The electrocatalytic oxidation of glycerol on PtAu/C catalysts has been investigated by cyclic voltammetry. PtAu bimetallic nanoparticles are prepared by chemical reduction. Carbon-supported PtAu catalysts are found to exhibit high electrocatalytic activity for the oxidation of glycerol in alkaline solution in terms of oxidation potential and current density as well as stability, and PtAu/C catalysts with different Pt:Au composition ratios show no much difference in catalytic activity. In acidic solution, PtAu/C catalysts exhibit similar to Pt/C catalysts in activity, but the advantage of the PtAu/C catalysts in terms of per unit mass of platinum is still obvious. The PtAu/C catalysts, in a wide Pt:Au ratio range, show a remarkable enhancement in the mass specific activity of platinum with decreasing platinum content in both alkaline and acidic solutions. This is of significance for reducing the usage of platinum and indicates that though platinum acts as main active sites, gold also plays an important role in the function of PtAu/C catalysts.
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.
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.
Physics counterpart of the PT non-hermitian tight-binding chain
Jin, L
2010-01-01
We explore an alternative way of finding the link between a PT non-Hermitian Hamiltonian and a Hermitian one. Based on the analysis of the scattering problem for an imaginary potential and its time reversal process, it is shown that any real-energy eigenstate of a PT tight-binding lattice with on-site imaginary potentials shares the same wave function with a resonant transmission state of the corresponding Hermitian lattice embedded in a chain. It indicates that the PT eigenstate of a PT non-Hermitian Hamiltonian has connection to the resonance transmission state of the extended Hermitian Hamiltonian.
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.
Integrable systems and symmetric products of curves
Vanhaecke, P
1994-01-01
show how there is associated to each non-constant polynomial F(x,y) a completely integrable system with polynomial invariants on \\Rd and on \\C{2d} for each d\\geq1; in fact the invariants are not only in involution for one Poisson bracket, but for a large class of polynomial Poisson brackets, indexed by the family of polynomials in two variables. We show that the complex invariant manifolds are isomorphic to affine parts of d-fold symmetric products of a deformation of the algebraic curve F(x,y)=0, and derive the structure of the real invariant manifolds from it. We also exhibit Lax equations for the hyperelliptic case (i.e., when F(x,y) is of the form y^2+f(x)) and we show that in this case the invariant manifolds are affine parts of distinguished (non-linear) subvarieties of the Jacobians of the curves. As an application the geometry of the H\\'enon-Heiles hierarchy --- a family of superimposable integrable polynomial potentials on the plane --- is revealed and Lax equations for the hierarchy are given.
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.
Ou, Li-Hui
2015-11-01
The effects of alloying Pt with transition metal Ni on oxygen reduction reaction (ORR) mechanisms was investigated based on a systematic density functional theory (DFT) calculation explored in the present work. New insights into the ORR mechanisms were reported at the atomic level on Pt-segregated Pt3Ni(111). Only one molecular chemisorption state with the end-on OOH configuration was identified through geometry optimization and minimum energy path (MEP) analysis; top-bridge-top configuration as observed on pure Pt(111) was not identified on Pt-segregated Pt3Ni(111), indicating that alloying Pt with Ni influences the intermediates of ORR, and leads to only the dissociation mechanism of chemisorption state OOH species being involved in acid medium on Pt-segregated Pt3Ni(111). By contrast, the dissociation mechanisms of chemisorbed O2 molecule with top-bridge-top configuration and OOH species both were involved on pure Pt(111). The rds of the entire four-electron ORR was changed after Pt alloying with Ni. The rds of the entire ORR is the proton and electron transfer to O2 to form OOH on Pt-segregated Pt3Ni(111), whereas it is the reaction of O atom protonation to form OH species on pure Pt(111), indicating that sublayer Ni strongly influences the rds of ORR. The comparison of the ORR mechanisms explained that Pt3Ni alloy enhanced the ORR electrocatalytic activity more than pure Pt. The effect of electrode potential on ORR pathway on the pure Pt and Pt3Ni alloy was considered to obtain further insights into the electrochemical reduction of O2. Results showed that the proton and electron transfer becomes difficult at high potential. The ORR can easily proceed when the electrode potential lowers. For pure Pt- and Pt-based alloys, this phenomenon may imply the origin of the overpotential.
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.
Energy Technology Data Exchange (ETDEWEB)
Blanco, Raquel; Orts, Jose Manuel [Departamento de Quimica Fisica e Instituto Universitario de Electroquimica, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-11-01
A density functional theory (DFT) study of the adsorption of a water molecule on Pt(1 1 1), Pt(1 0 0) and Pt(1 1 0) surfaces has been carried out using cluster models, at the B3LYP/LANL2DZ,6-311++G(d,p) level. The water molecule binds preferentially at the top site on Pt(1 1 1) and Pt(1 0 0) with adsorption energy around -27 kJ mol{sup -1}, and is oriented with the molecular plane nearly parallel to the metal surface and the H atoms pointing away from it. On Pt(1 1 0) a hollow site is preferred, with adsorption energy of -32 kJ mol{sup -1}. Potential energy barriers for the rotation around an axis normal to the surface have been estimated to be below 1 kJ mol{sup -1} for Pt(1 1 1) and Pt(1 0 0) when water is adsorbed on top. Upon application of an external electric field (inducing positive charge density on the metal) adsorbed water is additionally stabilized on the three surfaces, especially at the top adsorption site, and adsorption on Pt(1 1 1) and Pt(1 0 0) becomes more favoured than on Pt(1 1 0). Good agreement has been found between harmonic vibrational frequencies calculated at the B3LYP/LANL2DZ,6-311++G(d,p) level and experimental frequencies for adsorbed water monomers on Pt(h k l) surfaces. (author)
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.
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.
PMN-PT/PVDF Nanocomposite for High Output Nanogenerator Applications
Directory of Open Access Journals (Sweden)
Chuan Li
2016-04-01
Full Text Available The 0.7Pb(Mg1/3Nb2/3O3-0.3PbTiO3(0.7PMN-0.3PT nanorods were obtained via hydrothermal method with high yield (over 78%. Then, new piezoelectric nanocomposites based on (1−xPb(Mg1/3Nb2/3O3-xPbTiO3 (PMN-PT nanorods were fabricated by dispersing the 0.7PMN-0.3PT nanorods into piezoelectric poly(vinylidene fluoride (PVDF polymer. The mechanical behaviors of the nanocomposites were investigated. The voltage and current generation of PMN-PT/PVDF nanocomposites were also measured. The results showed that the tensile strength, yield strength, and Young’s modulus of nanocomposites were enhanced as compared to that of the pure PVDF. The largest Young’s modulus of 1.71 GPa was found in the samples with 20 wt % nanorod content. The maximum output voltage of 10.3 V and output current of 46 nA were obtained in the samples with 20 wt % nanorod content, which was able to provide a 13-fold larger output voltage and a 4.5-fold larger output current than that of pure PVDF piezoelectric polymer. The current density of PMN-PT/PVDF nanocomposites is 20 nA/cm2. The PMN-PT/PVDF nanocomposites exhibited great potential for flexible self-powered sensing applications.
PMN-PT/PVDF Nanocomposite for High Output Nanogenerator Applications.
Li, Chuan; Luo, Wenbo; Liu, Xingzhao; Xu, Dong; He, Kai
2016-04-11
The 0.7Pb(Mg1/3Nb2/3)O₃-0.3PbTiO₃(0.7PMN-0.3PT) nanorods were obtained via hydrothermal method with high yield (over 78%). Then, new piezoelectric nanocomposites based on (1-x)Pb(Mg1/3Nb2/3)O₃-xPbTiO₃ (PMN-PT) nanorods were fabricated by dispersing the 0.7PMN-0.3PT nanorods into piezoelectric poly(vinylidene fluoride) (PVDF) polymer. The mechanical behaviors of the nanocomposites were investigated. The voltage and current generation of PMN-PT/PVDF nanocomposites were also measured. The results showed that the tensile strength, yield strength, and Young's modulus of nanocomposites were enhanced as compared to that of the pure PVDF. The largest Young's modulus of 1.71 GPa was found in the samples with 20 wt % nanorod content. The maximum output voltage of 10.3 V and output current of 46 nA were obtained in the samples with 20 wt % nanorod content, which was able to provide a 13-fold larger output voltage and a 4.5-fold larger output current than that of pure PVDF piezoelectric polymer. The current density of PMN-PT/PVDF nanocomposites is 20 nA/cm². The PMN-PT/PVDF nanocomposites exhibited great potential for flexible self-powered sensing applications.
Exotic high activity surface patterns in PtAu nanoclusters
Mokkath, Junais Habeeb
2013-05-09
The structure and chemical ordering of PtAu nanoclusters of 79, 135, and 201 atoms are studied via a combination of a basin hopping atom-exchange technique (to locate the lowest energy homotops at fixed composition), a symmetry orbit technique (to find the high symmetry isomers), and density functional theory local reoptimization (for determining the most stable homotop). The interatomic interactions between Pt and Au are derived from the empirical Gupta potential. The lowest energy structures show a marked tendency toward PtcoreAushell chemical ordering by enrichment of the more cohesive Pt in the core region and of Au in the shell region. We observe a preferential segregation of Pt atoms to (111) facets and Au atoms to (100) facets of the truncated octahedron cluster motif. Exotic surface patterns are obtained particularly for Pt-rich compositions, where Pt atoms are being surrounded by Au atoms. These surface arrangements boost the catalytic activity by creating a large number of active sites. © 2013 American Chemical Society.
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.
Control of Wind Turbines during Symmetrical and Asymmetrical Grid Faults
DEFF Research Database (Denmark)
Göksu, Ömer
As installed capacity of the wind power plants (WPPs) in power system of certain countries increases, stability of the power system becomes more critical. In order to sustain stable power system operation with high share of wind power, system operators of some countries are enforcing more stringent...... studies before. It is shown that when reactive current injection is performed during severe symmetrical faults, where the grid voltage is dropping down close to zero, the wind turbines can lose the synchronism with the grid fundamental frequency, which potentially creates risk of instability...... and reactive current references, which provide stable operation of the WTs and result in improved grid support. In summary, the response of the WTs to symmetrical and asymmetrical faults is improved by means of the proposed control solutions, which provide compliance with stringent grid codes, improved grid...
Bilaterally Symmetrical Lower Extremity Compartment Syndrome following Massive Transfusion.
Karaoren, Gulsah; Bakan, Nurten; Tomruk, Senay Goksu; Topaç, Zelin; Kurtulmuş, Tuhan; Irkören, Saime
2016-01-01
Compartment syndrome is a serious condition characterized by raised intracompartmental pressure, which develops following trauma. Well leg compartment syndrome (WLCS) is a term reserved for compartment syndrome in a nontraumatic setting, usually resulting from prolonged lithotomy position during surgery. In literature, 8 cases have been reported regarding well leg compartment syndrome in a supine position and bilateral symmetrical involvement was observed in only 2 cases. In WLCS etiology, lengthy surgery, lengthy hypotension, and extremity malpositioning have been held responsible but one of the factors with a role in the etiology may have been the tissue oedema and impaired microcirculation formed from the effect of vasoactive mediators expressed into the circulation associated with the massive blood transfusion. The case is presented here regarding symmetrical lower extremity compartment syndrome after surgery in which massive transfusion was made for gross haemorrhage from an abdominal injury. In conclusion, blood transfusion applied at the required time is life-saving but potential risks must always be considered.
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.
Okazaki, Tomohisa; Seino, Satoshi; Matsuura, Yoshiyuki; Otake, Hiroaki; Kugai, Junichiro; Ohkubo, Yuji; Nitani, Hiroaki; Nakagawa, Takashi; Yamamoto, Takao A.
2017-04-01
The process of nanoparticle formation by radiation chemical synthesis in a heterogeneous system has been investigated. Carbon-supported Pt-based bimetallic nanoparticles were synthesized using a high-energy electron beam. Rh, Cu, Ru, and Sn were used as counterpart metals. The nanoparticles were characterized by inductively coupled plasma atomic emission spectrometry, transmission electron microscopy, X-ray diffraction, and X-ray absorption spectroscopy. PtRh formed a uniform random alloy nanoparticle, while Cu partially formed an alloy with Pt and the remaining Cu existed as CuO. PtRu formed an alloy structure with a composition distribution of a Pt-rich core and Ru-rich shell. No alloying was observed in PtSn, which had a Pt-SnO2 structure. The alloy and oxide formation mechanisms are discussed considering the redox potentials, the standard enthalpy of oxide formation, and the solid solubilities of Pt and the counterpart metals.
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.
Electrochemical oxidation of methanol on Pt/(RuxSn1-xO2 nanocatalyst
Directory of Open Access Journals (Sweden)
Krstajić Mila N.
2013-01-01
Full Text Available The Ru-doped SnO2 powder, (RuxSn1-xO2, with the Sn:Ru atomic ratio of 9:1 was synthesized and used as a support for Pt nanoparticles (30 mass% loading. The (RuxSn1-xO2 support and Pt/(RuxSn1-xO2 catalyst were characterized by X-ray diffraction, energy dispersive X-ray spectroscopy and transmission electron microscopy (TEM. (RuxSn1-xO2 was found to be two-phase material consisting of probably solid solution of RuO2 in SnO2 and pure RuO2. The average Pt particle size determined by TEM was 5.3 nm. Cyclic voltammetry of Pt/(RuxSn1-xO2 indicated good conductivity of the sup-port and displayed usual features of Pt. The results of the electrochemical oxidation of COads and methanol on Pt/(RuxSn1-xO2 were compared with those on commercial Pt/C and PtRu/C catalysts. Oxidation of COads on Pt/(RuxSn1-xO2 starts at less positive potentials than on PtRu/C and Pt/C. Potentiodynamic polarization curves and chronoamperometric curves of methanol oxidation indicated higher initial activity of Pt/(RuxSn1-xO2 catalyst compared to PtRu/C, but also a greater loss in the current density over time. Potentiodynamic stability test of the catalysts revealed that deactivation of the Pt/(RuxSn1-xO2 and Pt/C was primarily caused by the poisoning of Pt surface by the methanol oxidation residues, which mostly occurred during the first potential cycle. In the case of PtRu/C the poisoning of the surface was minor and deactivation was caused by the PtRu surface area loss. [Projekat Ministarstva nauke Republike Srbije, br. ON-172054
Yang, Jian; Kwon, Youngkook; Duca, Matteo; Koper, Marc T M
2013-08-20
To overcome the shortcomings of electroanalytical methods in analyzing the ionic reaction products that are either electrochemically inert or lack distinct electrochemical/spectroscopic fingerprints, we suggest combining voltammetry with ion chromatography by applying online sample collection to the electrochemical cell and offline ion chromatographic analysis. This combination allows a quantitative analysis including the potential dependence of the product distribution in a straightforward way. As a proof-of-concept example, we discuss the formation of ionic reaction products from nitrate reduction on Pt and Sn-modified Pt electrode in acid. On the Pt electrode, ammonia was the only identifiable product. After Sn modification of the Pt electrode, a change in selectivity was observed to hydroxylamine as the dominant product. Moreover, the rate determining step of nitrate reduction (reduction to nitrite) was enhanced by Sn modification of the Pt electrode, and a significant concentration of nitrite was evidenced on a Pt electrode with a high coverage of Sn species. The suggested combination of voltammetry and online ion chromatography hence proves very useful in the quantitative elucidation of electrocatalytic reactions with different ionic products.
Loukrakpam, Rameshwori; Yuan, Qiuyi; Petkov, Valeri; Gan, Lin; Rudi, Stefan; Yang, Ruizhi; Huang, Yunhui; Brankovic, Stanko R; Strasser, Peter
2014-09-21
Efficient catalytic C-C bond splitting coupled with complete 12-electron oxidation of the ethanol molecule to CO2 is reported on nanoscale electrocatalysts comprised of a Pt monolayer (ML) and sub-monolayer (sML) deposited on Au nanoparticles (Au@Pt ML/sML). The Au@Pt electrocatalysts were synthesized using surface limited redox replacement (SLRR) of an underpotentially deposited (UPD) Cu monolayer in an electrochemical cell reactor. Au@Pt ML showed improved catalytic activity for ethanol oxidation reaction (EOR) and, unlike their Pt bulk and Pt sML counterparts, was able to generate CO2 at very low electrode potentials owing to efficient C-C bond splitting. To explain this, we explore the hypothesis that competing strain effects due to the Pt layer coverage/morphology (compressive) and the Pt-Au lattice mismatch (tensile) control surface chemisorption and overall activity. Control experiments on well-defined model Pt monolayer systems are carried out involving a wide array of methods such as high-energy X-ray diffraction, pair-distribution function (PDF) analysis, in situ electrochemical FTIR spectroscopy, and in situ scanning tunneling microscopy. The vibrational fingerprints of adsorbed CO provide compelling evidence on the relation between surface bond strength, layer strain and morphology, and catalytic activity.
高温热电偶材料PtRh40/PtRh20合金性能研究%Prorerties of PtRh40/PtRh20 High-temperature Thermocouple Wires
Institute of Scientific and Technical Information of China (English)
吴保安; 刘庆宾; 陈德茂; 汪建胜; 唐会毅; 陈小军
2013-01-01
The long-term using temperature of PtRh40/PtRh20 high-temperature thermocouple wire is 1750℃. PtRh40/PtRh20 is belong to non-standard thermocouple, and mainly applies to measure the aircraft efflux plasma temperature. The influences of annealing temperature on the tensile strength and resistivity of PtRh40 and PtRh20 alloy wires, and the influences of the cold working on tensile strength and vickers hardness of the wires were studied. The results indicated that the tensile strengths increased with the increase of annealing temperature at first, then decreased sharply, finally it is stable forming a platform. The resistivities were increased with the annealing temperature, and the tensile strength and hardness were increased with the cold working. The errors of matching thermoelectric potential of PtRh40- PtRh20 relative to ASTM E1751-2000 standard thermoelectric power is 1℃ at 1200℃, 2℃ at 1500℃, and 1℃ at 1700℃.% PtRh40/PtRh20高温热电偶长期使用温度为1750℃，主要用于飞机尾焰高温测量，属于非标热电偶，目前国内主要依靠进口。研究了 PtRh40、PtRh20退火温度与合金电阻率、抗拉强度及加工率与抗拉强度、硬度的关系，并测试了PtRh40/PtRh20热电偶热电性能。结果表明：抗拉强度随退火温度的升高先升高再急剧下降，最后稳定在一个平台，两者大约在900℃时抗拉强度降至最低；电阻率均随退火温度升高而升高；抗拉强度与硬度均随加工率的增加而提高；PtRh40/PtRh20配对热电势相对ASTM E1751-2000标准热电势测试结果为在1200℃时误差为1℃，在1500℃时误差2℃，在1700℃时误差1℃。
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)
Methanol Electro-Oxidation on Pt-Ru Alloy Nanoparticles Supported on Carbon Nanotubes
Directory of Open Access Journals (Sweden)
Yangchuan Xing
2009-09-01
Full Text Available Carbon nanotubes (CNTs have been investigated in recent years as a catalyst support for proton exchange membrane fuel cells. Improved catalyst activities were observed and attributed to metal-support interactions. We report a study on the kinetics of methanol electro-oxidation on CNT supported Pt-Ru alloy nanoparticles. Alloy catalysts with different compositions, Pt53Ru47/CNT, Pt69Ru31/CNT and Pt77Ru23/CNT, were prepared and investigated in detail. Experiments were conducted at various temperatures, electrode potentials, and methanol concentrations. It was found that the reaction order of methanol electro-oxidation on the PtRu/CNT catalysts was consistent with what has been reported for PtRu alloys with a value of 0.5 in methanol concentrations. However, the electro-oxidation reaction on the PtRu/CNT catalysts displayed much lower activation energies than that on the Pt-Ru alloy catalysts unsupported or supported on carbon black (PtRu/CB. This study provides an overall kinetic evaluation of the PtRu/CNT catalysts and further demonstrates the beneficial role of CNTs.
Electrocatalytic properties of Pt-Bi electrodes towards the electrooxidation of formic acid
Directory of Open Access Journals (Sweden)
Lović Jelena D.
2013-01-01
Full Text Available Formic acid oxidation was studied on two Pt-Bi catalysts, Pt2Bi and polycrystalline Pt modified by irreversible adsorbed Bi (Pt/Biirr in order to establish the difference between the effects of Biirr and Bi in alloyed state. The results were compared to pure Pt. It was found that both bimetallic catalysts were more active than Pt with the onset potentials shifted to more negative values and the currents at 0.0 V vs. SCE (under steady state conditions improved up to two order of magnitude. The origin of Pt2Bi high activity and stability is increased selectivity toward formic acid dehydrogenation caused by the ensemble and electronic effect and suppression of Bi leaching from the surface during formic acid oxidation. However, although Pt/Biirr also shows remarkable initial activity compared to pure Pt, dissolution of Bi is not suppressed and the poisoning of the electrode surface induced by dehydration path is observed. Comparison of the initial quasi-steady state and potentiodynamic results obtained for these two Pt-Bi catalysts revealed that the electronic effect, existing only in the alloy, contributes earlier start of the reaction, while the maximum current density is determined by the ensemble effect. [Projekat Ministarstva nauke Republike Srbije, br. H-172060
Zhang, Geng; Lu, Wangting; Cao, Longsheng; Qin, Xiaoping; Ding, Fei; Tang, Shun; Shao, Zhi-Gang; Yi, Baolian
2016-09-01
The reduction of Pt content together with the improvement of the durability of the catalyst for oxygen reduction reaction (ORR) is required to the large-scale commercialization of proton exchange membrane fuel cells. In this work, a novel ORR catalyst consisting of large Pd nanocrystal as the core with small Pt nanoparticles supported on the Pd core is prepared by a facile one-step synthesis method. The Pd substrate is presented in the form of well-defined cuboctahedrons and icosahedrons. The type of metal precursors and Pt/Pd molar ratio are important factors to obtain this Pd-supporting-Pt structure. The Pd2-s-Pt1 catalyst with a nominal Pt/Pd atomic ratio at 1/2 shows improved ORR activity: its mass specific activity and area specific activity is 2.5 and 3.5 times that of commercial Pt/C, respectively. More importantly, the Pd2-s-Pt1 catalyst demonstrates outstanding durability against potential cycling which can be ascribed to the slow dissolution of Pd core and the structure transformation from Pd@Pt to hollow PdPt alloyed nanocages. This exciting result provides a new pathway to the design of ORR catalyst with excellent durability.
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.
Directory of Open Access Journals (Sweden)
Altuğ Arda
2017-01-01
Full Text Available We find the exact bound state solutions and normalization constant for the Dirac equation with scalar-vector-pseudoscalar interaction terms for the generalized Hulthén potential in the case where we have a particular mass function m(x. We also search the solutions for the constant mass where the obtained results correspond to the ones when the Dirac equation has spin and pseudospin symmetry, respectively. After giving the obtained results for the nonrelativistic case, we search then the energy spectra and corresponding upper and lower components of Dirac spinor for the case of PT-symmetric forms of the present potential.
Monte Carlo Simulations of Segregation in Pt-Ni Catalyst Nanoparticles
Energy Technology Data Exchange (ETDEWEB)
Wang, Guofeng; Van Hove, Michel A.; Ross, Philip N.; Baskes, M.I.
2004-04-01
We have investigated the segregation of Pt atoms in the surfaces of Pt-Ni nanoparticles, using Modified Embedded Atom Model potentials and the Monte Carlo method. The nanoparticles are assumed to have disordered fcc configurations at two fixed overall concentrations (50 at. percent Pt and 75 at. percent Pt). We use four kinds of nanoparticle shapes [cube, tetrahedron, octahedron, and cubo-octahedron] terminated by {l_brace}111{r_brace} and {l_brace}100{r_brace} facets to examine the extent of the Pt segregation to the nanoparticle surfaces and determine the equilibrium structures of Pt-Ni nanoparticles at T=600 K. The model particles contain between 560 and 4631 atoms (particle size ranging from 2.5 to 5 nm). Our results imply that a complete (100)-facet reconstruction could make the cubo-octahendral Pt-Ni nanoparticles most energetically favorable, consistent with experimental observations. We predict that at 600 K due to segregation the equilibrium Pt50Ni50 nanoparticles with fewer than 2000 atoms and Pt75Ni25 nano particles with fewer than 4000 atoms would achieve a surface-sandwich structure, in which the Pt atoms are enriched in the outermost and third atomic shells while the Ni atoms are enriched in the second atomic shell. We also find that due to an order-disorder transition the Pt50Ni50 cubo-octahedral nanoparticles containing more than 2000 atoms would form a core-shell structure with a Pt-enriched surface and a Pt-deficient homogeneous core.
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.
One-pot synthesis of FePt/CNTs nanocomposites for efficient cellular imaging and cancer therapy
Energy Technology Data Exchange (ETDEWEB)
Chen, Weihong; Zheng, Xiuwen, E-mail: xwzheng1976@163.com [Linyi University, School of Chemistry & Chemical Engineering, Shandong Provincial Key Laboratory of Detection Technology for Tumor Makers (China); Li, Shulian [Linyi Tumor Hospital (China); Zhang, Wei; Wen, Xin [Linyi University, School of Chemistry & Chemical Engineering, Shandong Provincial Key Laboratory of Detection Technology for Tumor Makers (China); Yue, Ludan [Shandong Normal University (China); Wang, Jinlong [Shandong University of Technology (China)
2015-11-15
Here, we developed a facile route to synthesize carbon nanotube-based FePt nanocomposites (FePt/CNTs) as a potential theranostic platform in the cancer treatment. FePt/CNTs were firstly synthesized via one-pot polyol route, and then functionalized with 6-arm-polyethylene glycol-amine polymer. The average size of FePt nanoparticles (NPs) is 3–4 nm, which is dispersed on the CNT surface (ca.50–150 nm). The as-prepared FePt NPs display high cytotoxicity by highly reactive oxygen species in cancer cells. Folic acid and fluorescein isothiocyanate are assembled onto the surface of FePt/CNTs for effective targeting of folate receptor-positive cancer cells and simultaneously for the visualization of cellular uptake. Therefore, the FePt/CNTs NPs capability of simultaneously performing diagnosis, therapy, and targeting is, therefore, promising for future potential widespread application in biomedicine.
Structure, chemical ordering and thermal stability of Pt-Ni alloy nanoclusters.
Cheng, Daojian; Yuan, Shuai; Ferrando, Riccardo
2013-09-01
Equilibrium structures, chemical ordering and thermal properties of Pt-Ni nanoalloys are investigated by using basin hopping-based global optimization, Monte Carlo (MC) and molecular dynamics (MD) methods, based on the second-moment approximation of the tight-binding potentials (TB-SMA). The TB-SMA potential parameters for Pt-Ni nanoalloys are fitted to reproduce the results of density functional theory calculations for small clusters. The chemical ordering in cuboctahedral (CO) Pt-Ni nanoalloys with 561 and 923 atoms is obtained from the so called semi-grand-canonical ensemble MC simulation at 100 K. Two ordered phases of L12 (PtNi3) and L10 (PtNi) are found for the CO561 and CO923 Pt-Ni nanoalloys, which is in good agreement with the experimental phase diagram of the Pt-Ni bulk alloy. In addition, the order-disorder transition and thermal properties of these nanoalloys are studied by using MC and MD methods, respectively. It is shown that the typical perfect L10 PtNi structure is relatively stable, showing high order-disorder transition temperature and melting point among these CO561 and CO923 Pt-Ni nanoalloys.
Kim, Young Gwon; Kang, Hee Kyoung; Kwon, Kee-Deok; Seo, Chang Ho; Lee, Hyang Burm; Park, Yoonkyung
2015-12-09
Bacillus species have recently drawn attention due to their potential use in the biological control of fungal diseases. This paper reports on the antifungal activity of novel peptides isolated from Bacillus amyloliquefaciens PT14. Reverse-phase high-performance liquid chromatography revealed that B. amyloliquefaciens PT14 produces five peptides (PT14-1, -2, -3, -4a, and -4b) that exhibit antifungal activity but are inactive against bacterial strains. In particular, PT14-3 and PT14-4a showed broad-spectrum antifungal activity against Fusarium solani and Fusarium oxysporum. The PT14-4a N-terminal amino acid sequence was identified through Edman degradation, and a BLAST homology analysis showed it not to be identical to any other protein or peptide. PT14-4a displayed strong fungicidal activity with minimal inhibitory concentrations of 3.12 mg/L (F. solani) and 6.25 mg/L (F. oxysporum), inducing severe morphological deformation in the conidia and hyphae. On the other hand, PT14-4a had no detectable hemolytic activity. This suggests PT14-4a has the potential to serve as an antifungal agent in clinical therapeutic and crop-protection applications.
Pt、Rh及Pt-Rh合金电极上氢的吸附%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 (wRh = 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 alloys.
Dynamics of Surface Exchange Reactions Between Au and Pt for HER and HOR
DEFF Research Database (Denmark)
Abrams, Billie; Vesborg, Peter Christian Kjærgaard; Bonde, Jacob Lindner;
2009-01-01
Cyclic voltammetric analysis of the Pt-on-Au system for hydrogen evolution and oxidation reactions (HER/HOR) indicates that dynamic surface exchange reactions occur between Pt and Au. HER/HOR activities depend on the dominant surface species present, which is controllable by the potential applied...
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 $\\gamma$.
Directory of Open Access Journals (Sweden)
Xiaoting Chen
2015-06-01
Full Text Available We have prepared a multi-component nanoporous PtRuCuW (np-PtRuCuW electrocatalyst via a combined chemical dealloying and mechanical alloying process. The X-ray diffraction (XRD, transmission electron microscopy (TEM and electrochemical measurements have been applied to characterize the microstructure and electrocatalytic activities of the np-PtRuCuW. The np-PtRuCuW catalyst has a unique three-dimensional bi-continuous ligament structure and the length scale is 2.0 ± 0.3 nm. The np-PtRuCuW catalyst shows a relatively high level of activity normalized to mass (467.1 mA mgPt−1 and electrochemically active surface area (1.8 mA cm−2 compared to the state-of-the-art commercial PtC and PtRu catalyst at anode. Although the CO stripping peak of np-PtRuCuW 0.47 V (vs. saturated calomel electrode, SCE is more positive than PtRu, there is a 200 mV negative shift compared to PtC (0.67 V vs. SCE. In addition, the half-wave potential and specific activity towards oxygen reduction of np-PtRuCuW are 0.877 V (vs. reversible hydrogen electrode, RHE and 0.26 mA cm−2, indicating a great enhancement towards oxygen reduction than the commercial PtC.