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Sample records for boson-fermion degeneracy symmetry

  1. Orbifold symmetry reductions of massive boson-fermion degeneracy

    NASA Astrophysics Data System (ADS)

    Florakis, Ioannis; Kounnas, Costas

    2009-10-01

    We investigate the existence of string vacua with Massive Spectrum Degeneracy Symmetry ( MSDS) in Heterotic and Type II orbifold constructions. We present a classification of all possible Z2N-orbifolds with MSDS symmetry that can be constructed in the formalism of the 2d free fermionic construction. We explicitly construct several two-dimensional models whose Reduced Massive Spectrum Degeneracy Symmetry ( RMSDS) is due to a set of Z-orbifold projections induced naturally in the framework of the free fermionic construction. In all proposed models the massive boson and fermion degrees of freedom exhibit Massive Spectrum Degeneracy Symmetry while the number of massless bosons n(b) and massless fermions n(f) are different; n(b)≠n(f). This property distinguishes the MSDSZ-twisted theories from ordinary supersymmetric ones. Some comments are stated concerning the large marginal JJ¯-deformations of the proposed models connecting them to higher-dimensional gauged-supergravity theories with non-trivial geometrical fluxes.

  2. Marginal deformations of vacua with massive boson-fermion degeneracy symmetry

    NASA Astrophysics Data System (ADS)

    Florakis, Ioannis; Kounnas, Costas; Toumbas, Nicolaos

    2010-07-01

    Two-dimensional string vacua with Massive Spectrum boson-fermion Degeneracy Symmetry, [, are explicitly constructed in Type II and Heterotic superstring theories. The study of their moduli space indicates the existence of large marginal deformations that connect continuously the initial [ vacua to higher-dimensional conventional superstring vacua, where spacetime supersymmetry is spontaneously broken by geometrical fluxes. We find that the maximally symmetric, [, Type II vacuum, is in correspondence with the maximal, N=8, d=4 "gauged supergravity", where the supergravity gauging is induced by the fluxes. This correspondence is extended to less symmetric cases where the initial MSDS symmetry is reduced by orbifolds: [:MSDS]d=2 ↔ [. We also exhibit and analyse thermal interpretations of some Euclidean versions of the models and identify classes of MSDS vacua that remain tachyon-free under arbitrary marginal deformations about the extended symmetry point. The connection between the two-dimensional MSDS vacua and the resulting four-dimensional effective supergravities arises naturally within the context of an adiabatic cosmological evolution, where the very early Universe is conjectured to be described by an MSDS vacuum, while at late cosmological times it is described by an effective N=1 supergravity theory with spontaneously broken supersymmetry.

  3. Particle-hole symmetry in generalized seniority, microscopic interacting boson (fermion) model, nucleon-pair approximation, and other models

    NASA Astrophysics Data System (ADS)

    Jia, L. Y.

    2016-06-01

    The particle-hole symmetry (equivalence) of the full shell-model Hilbert space is straightforward and routinely used in practical calculations. In this work I show that this symmetry is preserved in the subspace truncated up to a certain generalized seniority and give the explicit transformation between the states in the two types (particle and hole) of representations. Based on the results, I study particle-hole symmetry in popular theories that could be regarded as further truncations on top of the generalized seniority, including the microscopic interacting boson (fermion) model, the nucleon-pair approximation, and other models.

  4. Critical-Point Symmetries in Boson-Fermion Systems: The Case of Shape Transitions in Odd Nuclei in a Multiorbit Model

    SciTech Connect

    Alonso, C. E.; Arias, J. M.; Vitturi, A.

    2007-02-02

    We investigate phase transitions in boson-fermion systems. We propose an analytically solvable model [E(5/12)] to describe odd nuclei at the critical point in the transition from the spherical to {gamma}-unstable behavior. In the model, a boson core described within the Bohr Hamiltonian interacts with an unpaired particle assumed to be moving in the three single-particle orbitals j=1/2, 3/2, 5/2. Energy spectra and electromagnetic transitions at the critical point compare well with the results obtained within the interacting boson-fermion model, with a boson-fermion Hamiltonian that describes the same physical situation.

  5. Critical-point symmetries in boson-fermion systems: the case of shape transitions in odd nuclei in a multiorbit model.

    PubMed

    Alonso, C E; Arias, J M; Vitturi, A

    2007-02-02

    We investigate phase transitions in boson-fermion systems. We propose an analytically solvable model [E(5/12)] to describe odd nuclei at the critical point in the transition from the spherical to gamma-unstable behavior. In the model, a boson core described within the Bohr Hamiltonian interacts with an unpaired particle assumed to be moving in the three single-particle orbitals j=1/2, 3/2, 5/2. Energy spectra and electromagnetic transitions at the critical point compare well with the results obtained within the interacting boson-fermion model, with a boson-fermion Hamiltonian that describes the same physical situation.

  6. Boson/Fermion Janus Particles

    NASA Astrophysics Data System (ADS)

    Tsekov, R.

    2017-04-01

    Thermodynamically, bosons and fermions differ by their statistics only. A general entropy functional is proposed by superposition of entropic terms, typical for different quantum gases. The statistical properties of the corresponding Janus particles are derived by variation of the weight of the boson/fermion fraction. It is shown that di-bosons and anti-fermions separate in gas and liquid phases, while three-phase equilibrium appears for poly-boson/fermion Janus particles.

  7. Complete Boson-Fermion Model of Superconductivity

    NASA Astrophysics Data System (ADS)

    de Llano, Manuel

    2003-03-01

    The unification of the 1957 BCS theory with that of Bose-Einstein condensation (BEC) that gives roughly good first-principles transition temperature Tc predictions in either 2D or 3D for all of the ``Uemura plot'' ``exotic'' or conventional superconductors without abandoning the much-maligned phonon interaction mechanism has recently been achieved [1]-[3]. The same dynamical mechanism also allows for room-temperature superconductivity. The only condition is that one depart moderately from the perfect electron (e)-/hole (h)-Cooper-pair (CP) symmetry to which BCS (and indeed also the somewhat more general BCS-Bose crossover) theory are restricted by construction. It now becomes feasible to explain, among other things, why largely all superconductors empirically have substantially higher T_c's if their normal-state charge carriers are holes rather than electrons. A complete (in the sense that 2h-CPs are not ignored) boson-fermion model (CBFM) has been developed that reduces in the appropriate special cases to: a) ordinary BCS theory for weak boson-fermion coupling; b) the BCS-Bose ``crossover'' theory dating back to 1967; and, for no 2h-CPs to: c) the 1989 boson-fermion (BF) BEC model by T.D. Lee et al. of superconductors which without 2h-CPs is unrelated to BCS theory; d) an ideal BF binary-gas model [4] predicting nonzero BEC T_c's even in 2D; and finally to e) ordinary BEC (1925). The CBFM is a BF statistical model similar to those developed in the mid-50's by Schafroth, Blatt & Butler but which now includes 2h-CPs on an equal footing with 2e-CPs, and which unlike these models also contains the empirically well-established fermionic energy gap. [1] V.V. Tolmachev, Phys. Lett. A 266, 400 (2000). [2] M. Fortes, M.A. Solis, M. de Llano & V.V. Tolmachev, Physica C 364, 95 (2001). [3] M. de Llano & V.V. Tolmachev, Physica A 317, 546 (2003). [4] M. Casas, N.J. Davidson, M. de Llano, T.A. Mamedov, A. Puente, R.M. Quick, A. Rigo & M.A. Solis, Physica A 295, 146 (2001

  8. General form of the boson-fermion interaction in the interacting boson-fermion model-2

    NASA Astrophysics Data System (ADS)

    Matus, F. A.; Barea, J.

    2017-03-01

    The boson-fermion interaction in the interacting boson-fermion model-2 (IBFM-2) is derived in a systematic and general form from a quadrupole-quadrupole force using several nondegenerate levels. The boson-fermion quadrupole operator employed is obtained from the boson-fermion image of the one nucleon transfer operator which in turn can be calculated following two alternative schemes: the Otsuka-Arima-Iachello and generalized Holstein-Primakoff schemes. Four different terms (two quadrupole and two exchange) were obtained. Application of the new expressions to a single-j model is studied and analyzed.

  9. Evolution of boson-fermion stars

    NASA Astrophysics Data System (ADS)

    Valdez-Alvarado, Susana; Palenzuela, Carlos; Alic, Daniela; Ureña-López, L. Arturo; Becerril, Ricardo

    2012-08-01

    The boson-fermion stars can be modeled with a complex scalar field coupled minimally to a perfect fluid (i.e., without viscosity and non-dissipative). We present a study of these solutions and their dynamical evolution by solving numerically the Einstein-Klein-Gordon-Hydrodynamic (EKGHD) system. It is shown that stable configurations exist, but stability of general configurations depends finely upon the number of bosons and fermions.

  10. Symmetry and degeneracy manifolds in Jahn-Teller molecules

    NASA Astrophysics Data System (ADS)

    Mead, C. A.

    2013-04-01

    We consider problems in dealing with molecular systems of n identical nuclei. One problem is that of finding suitable internal coordinates. For n <= 4, these can be simply the internuclear distances. For n > 4, it is shown that, with perhaps one exception, there is no internal coordinate system that treats all nuclei equivalently. We also consder the properties of conical intersections between two Born-Oppenheimer electronic energy surfaces, in particular the problem of identifying the two coordinates that remove the degeneracy to first order in the near neighborhoods of symmetry manifolds.

  11. Plethystic vertex operators and boson-fermion correspondences

    NASA Astrophysics Data System (ADS)

    Fauser, Bertfried; Jarvis, Peter D.; King, Ronald C.

    2016-10-01

    We study the algebraic properties of plethystic vertex operators, introduced in (2010 J. Phys. A: Math. Theor. 43 405202), underlying the structure of symmetric functions associated with certain generalized universal character rings of subgroups of the general linear group, defined to stabilize tensors of Young symmetry type characterized by a partition of arbitrary shape π. Here we establish an extension of the well-known boson-fermion correspondence involving Schur functions and their associated (Bernstein) vertex operators: for each π, the modes generated by the plethystic vertex operators and their suitably constructed duals, satisfy the anticommutation relations of a complex Clifford algebra. The combinatorial manipulations underlying the results involve exchange identities exploiting the Hopf-algebraic structure of certain symmetric function series and their plethysms.

  12. Plaquette boson-fermion model of cuprates

    NASA Astrophysics Data System (ADS)

    Altman, Ehud; Auerbach, Assa

    2002-03-01

    The strongly interacting Hubbard model on the square lattice is reduced to the low energy plaquette boson fermion model (PBFM). The four bosons (an antiferromagnon triplet and a d-wave hole pair), and the fermions are defined by the lowest plaquette eigenstates. We apply the contractor renormalization method of Morningstar and Weinstein to compute the boson effective interactions. The range-3 truncation error is found to be very small, signaling short hole-pair and magnon coherence lengths. The pair-hopping and magnon interactions are comparable, which explains the rapid destruction of antiferromagnetic order with emergence of superconductivity, and validates a key assumption of the projected SO(5) theory. A vacuum crossing at larger doping marks a transition into the overdoped regime. With hole fermions occupying small Fermi pockets and Andreev coupled to hole pair bosons, the PBFM yields several testable predictions for photoemission, tunneling asymmetry, and entropy measurements.

  13. Bosons, fermions and anyons in the plane, and supersymmetry

    SciTech Connect

    Horvathy, Peter A.; Plyushchay, Mikhail S.; Valenzuela, Mauricio

    2010-09-15

    Universal vector wave equations allowing for a unified description of anyons, and also of usual bosons and fermions in the plane are proposed. The existence of two essentially different types of anyons, based on unitary and also on non-unitary infinite-dimensional half-bounded representations of the (2 + 1)D Lorentz algebra is revealed. Those associated with non-unitary representations interpolate between bosons and fermions. The extended formulation of the theory includes the previously known Jackiw-Nair (JN) and Majorana-Dirac (MD) descriptions of anyons as particular cases, and allows us to compose bosons and fermions from entangled anyons. The theory admits a simple supersymmetric generalization, in which the JN and MD systems are unified in N = 1 and N = 2 supermultiplets. Two different non-relativistic limits of the theory are investigated. The usual one generalizes Levy-Leblond's spin 1/2 theory to arbitrary spin, as well as to anyons. The second, 'Jackiw-Nair' limit (that corresponds to Inoenue-Wigner contraction with both anyon spin and light velocity going to infinity), is generalized to boson/fermion fields and interpolating anyons. The resulting exotic Galilei symmetry is studied in both the non-supersymmetric and supersymmetric cases.

  14. Symmetry and Degeneracy in Quantum Mechanics. Self-Duality in Finite Spin Systems

    ERIC Educational Resources Information Center

    Osacar, C.; Pacheco, A. F.

    2009-01-01

    The symmetry of self-duality (Savit 1980 "Rev. Mod. Phys. 52" 453) of some models of statistical mechanics and quantum field theory is discussed for finite spin blocks of the Ising chain in a transverse magnetic field. The existence of this symmetry in a specific type of these blocks, and not in others, is manifest by the degeneracy of their…

  15. Symmetry and Degeneracy in Quantum Mechanics. Self-Duality in Finite Spin Systems

    ERIC Educational Resources Information Center

    Osacar, C.; Pacheco, A. F.

    2009-01-01

    The symmetry of self-duality (Savit 1980 "Rev. Mod. Phys. 52" 453) of some models of statistical mechanics and quantum field theory is discussed for finite spin blocks of the Ising chain in a transverse magnetic field. The existence of this symmetry in a specific type of these blocks, and not in others, is manifest by the degeneracy of their…

  16. Pseudo-Hermitian Systems with PT-Symmetry: Degeneracy and Krein Space

    NASA Astrophysics Data System (ADS)

    Choutri, B.; Cherbal, O.; Ighezou, F. Z.; Drir, M.

    2017-05-01

    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.

  17. Pseudo-Hermitian Systems with PT-Symmetry: Degeneracy and Krein Space

    NASA Astrophysics Data System (ADS)

    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.

  18. Single Nodal Loop of Accidental Degeneracies in Minimal Symmetry: Triclinic CaAs3

    NASA Astrophysics Data System (ADS)

    Quan, Y.; Yin, Z. P.; Pickett, W. E.

    2017-04-01

    The existence of closed loops of degeneracies in crystals has been intimately connected with associated crystal symmetries, raising the following question: What is the minimum symmetry required for topological character, and can one find an example? Triclinic CaAs3 , in the space group P 1 ¯ with only a center of inversion, has been found to display, without need for tuning, a nodal loop of accidental degeneracies with topological character, centered on one face of the Brillouin zone that is otherwise fully gapped. The small loop is very flat in energy, yet is cut four times by the Fermi energy, a condition that results in an intricate repeated touching of inversion related pairs of Fermi surfaces at Weyl points. Spin-orbit coupling lifts the fourfold degeneracy along the loop, leaving trivial Kramers pairs. With its single nodal loop that emerges without protection from any point group symmetry, CaAs3 represents the primal "hydrogen atom" of nodal loop systems.

  19. A rationale for the symmetries by base substitutions of degeneracy in the genetic code.

    PubMed

    Jestin, Jean-Luc

    2010-01-01

    The first symmetry by base substitutions of degeneracy in the genetic code was described by Rumer (1966) and the other symmetries were identified later by Jestin (2006) and Jestin and Soulé (2007). Here, a rationale accounting for these symmetries is reported. The number of non-synonymous substitutions over the replicated coding sequence is written as a function of the substitution matrix, whose elements are the number of substitutions from any codon to any other codon. The p-adic distance used as a similarity measure and applied to this matrix is shown to be biologically relevant. The rationale indicates that symmetries by base substitutions of degeneracy in the genetic code are symmetries of the measures of the number of non-synonymous substitutions for sets of synonymous codons.

  20. Twisted vertex algebras, bicharacter construction and boson-fermion correspondences

    NASA Astrophysics Data System (ADS)

    Anguelova, Iana I.

    2013-12-01

    The boson-fermion correspondences are an important phenomena on the intersection of several areas in mathematical physics: representation theory, vertex algebras and conformal field theory, integrable systems, number theory, cohomology. Two such correspondences are well known: the types A and B (and their super extensions). As a main result of this paper we present a new boson-fermion correspondence of type D-A. Further, we define a new concept of twisted vertex algebra of order N, which generalizes super vertex algebra. We develop the bicharacter construction which we use for constructing classes of examples of twisted vertex algebras, as well as for deriving formulas for the operator product expansions, analytic continuations, and normal ordered products. By using the underlying Hopf algebra structure we prove general bicharacter formulas for the vacuum expectation values for two important groups of examples. We show that the correspondences of types B, C, and D-A are isomorphisms of twisted vertex algebras.

  1. Twisted vertex algebras, bicharacter construction and boson-fermion correspondences

    SciTech Connect

    Anguelova, Iana I.

    2013-12-15

    The boson-fermion correspondences are an important phenomena on the intersection of several areas in mathematical physics: representation theory, vertex algebras and conformal field theory, integrable systems, number theory, cohomology. Two such correspondences are well known: the types A and B (and their super extensions). As a main result of this paper we present a new boson-fermion correspondence of type D-A. Further, we define a new concept of twisted vertex algebra of order N, which generalizes super vertex algebra. We develop the bicharacter construction which we use for constructing classes of examples of twisted vertex algebras, as well as for deriving formulas for the operator product expansions, analytic continuations, and normal ordered products. By using the underlying Hopf algebra structure we prove general bicharacter formulas for the vacuum expectation values for two important groups of examples. We show that the correspondences of types B, C, and D-A are isomorphisms of twisted vertex algebras.

  2. Study of {beta}-Decay in the Proton-Neutron Interacting Boson-Fermion Model

    SciTech Connect

    Zuffi, L.; Brant, S.; Yoshida, N.

    2006-04-26

    We study {beta}-decay in odd-A nuclei together with the energy levels and other properties in the proton-neutron interacting-boson-fermion model. We also report on the preliminary results in the odd-odd nuclei in the proton-neutron interacting boson-fermion-fermion model.

  3. Exceptional points of degeneracy and P T symmetry in photonic coupled chains of scatterers

    NASA Astrophysics Data System (ADS)

    Othman, Mohamed A. K.; Galdi, Vincenzo; Capolino, Filippo

    2017-03-01

    We demonstrate the existence of exceptional points of degeneracy (EPDs) of periodic eigenstates in non-Hermitian coupled chains of dipolar scatterers. Guided modes supported by these structures can exhibit an EPD in their dispersion diagram at which two or more Bloch eigenstates coalesce, in both their eigenvectors and eigenvalues. We show the emergence of a second-order modal EPD associated with the parity-time (P T ) symmetry condition, at which each particle pair in the double chain exhibits balanced gain and loss. Furthermore, we also demonstrate a fourth-order EPD occurring at the band edge. Such a degeneracy condition was previously referred to as a degenerate band edge in lossless anisotropic photonic crystals. Here, we rigorously show it under the occurrence of gain and loss balance for a discrete guiding system. We identify a more general regime of gain and loss balance showing that P T symmetry is not necessary to attain EPDs. Moreover, we investigate the degree of detuning of the EPD when the geometrical symmetry or balanced condition is broken. Furthermore, we demonstrate a realistic implementation of the EPD in a coupled chain made of pairs of plasmonic nanospheres and active core-shell nanospheres at optical frequencies. These findings open avenues toward superior light localization and transport with application to high-Q resonators utilized in sensors, filters, low-threshold switching and lasing.

  4. Conformal symmetry algebra of the quark potential and degeneracies in the hadron spectra

    NASA Astrophysics Data System (ADS)

    Kirchbach, M.

    2012-10-01

    The essence of the potential algebra concept [Y. Alhassid, F. Gürsey, F. Yachello. Phys. Rev. Lett. 50 (1983)] is that quantum mechanical free motions of scalar particles on curved surfaces of given isometry algebras can be mapped on 1D Schrödinger equations with particular potentials. As long as the Laplace-Beltrami operator on a curved surface is proportional to one of the Casimir invariants of the isometry algebra, free motion on the surface is described by means of the eigenvalue problem of that very Casimir operator. In effect, the excitation modes considered are classified according to the irreducible representations of the algebra of interest and are characterized by typical degeneracies. In consequence, also the spectra of the equivalent Schrödinger operators are classified according to the same irreducible representations and carry the same typical degeneracies. A subtle point concerns the representation of the algebra elements which may or may not be unitarily equivalent to the standard one generating classical groups like SO(n), SO(p,q), etc. To be specific, any similarity transformations of an algebra that underlies, say, an orthogonal group, always conserve the commutators among the elements, but a non-unitarily transformed algebra must not generate same group. One can then consider the parameters of the non-unitary similarity transformation as group symmetry breaking scales and seek to identify them with physical observables. We here use the potential algebra concept as a guidance in the search for an interaction describing conformal degeneracies. For this purpose we subject the so(4) ⊂ so(2,4) isometry algebra of the S3 ball to a particular non-unitary similarity transformation and obtain a deformed isometry copy to S3 such that free motion on the copy is equivalent to a cotangent perturbed motion on S3, and to the 1D Schrödinger operator with the trigonometric Rosen-Morse potential as well. The latter presents itself especially well suited for

  5. Localized modes in arrays of boson-fermion mixtures

    SciTech Connect

    Bludov, Yu. V.; Konotop, V. V.

    2006-10-15

    It is shown that the mean-field description of a boson-fermion mixture with a dominating fermionic component, loaded in a one-dimensional optical lattice, is reduced to the nonlinear Schroedinger equation with a periodic potential and periodic nonlinearity. In such a system there exist localized modes having peculiar properties. In particular, for some regions of parameters there exists a lower bound for a number of bosons necessary for creation of a mode, while for other domains small amplitude gap solitons are not available in the vicinity of either of the gap edges. We found that the lowest branch of the symmetric solution either does not exist or exists only for a restricted range of energies in a gap, unlike in pure bosonic condensates. The simplest bifurcations of the modes are shown and stability of the modes is verified numerically.

  6. The boson fermion resonance model in one dimension

    NASA Astrophysics Data System (ADS)

    Citro, R.; Orignac, E.

    2006-05-01

    We discuss the phase transitions of fermions in one dimension with a narrow Feshbach resonance described by the boson-fermion resonance model. By means of the bosonization technique, we derive a low-energy Hamiltonian of the system and show that a strongly correlated state exists, where the order parameters of the Bose condensation and superfluidity decay with the same critical exponent. We also show that density fluctuations near the Fermi wavevector are strongly suppressed as a consequence of a spin gap and a gap against the formation of phase slips. We find a Luther-Emery point where the phase slips and the spin excitations can be described in terms of pseudofermions, providing closed form expressions of the density-density correlations and the spectral functions. The relevance of our results for experiments with ultracold atomic gases subject to one-dimensional confinement is also discussed.

  7. d -wave superconductivity in boson+fermion dimer models

    NASA Astrophysics Data System (ADS)

    Goldstein, Garry; Chamon, Claudio; Castelnovo, Claudio

    2017-05-01

    We present a slave-particle mean-field study of the mixed boson+fermion quantum dimer model introduced by Punk et al. [Proc. Natl. Acad. Sci. USA 112, 9552 (2015), 10.1073/pnas.1512206112] to describe the physics of the pseudogap phase in cuprate superconductors. Our analysis naturally leads to four charge e fermion pockets whose total area is equal to the hole doping p for a range of parameters consistent with the t -J model for high-temperature superconductivity. Here we find that the dimers are unstable to d -wave superconductivity at low temperatures. The region of the phase diagram with d -wave rather than s -wave superconductivity matches well with the appearance of the four fermion pockets. In the superconducting regime, the dispersion contains eight Dirac cones along the diagonals of the Brillouin zone.

  8. Collapse in boson-fermion mixtures with all-repulsive interactions

    SciTech Connect

    Prytula, Vladyslav I.; Konotop, Vladimir V.; Perez-Garcia, Victor M.; Vekslerchik, Vadym E.

    2007-10-15

    We describe the collapse of the bosonic component in a boson-fermion mixture due to the pressure exerted on it by a large fermionic component, leading to collapse in a system with all-repulsive interactions. We describe the phenomena of early collapse and superslow collapse of the mixture.

  9. Retarded boson-fermion interaction in atomic systems

    NASA Astrophysics Data System (ADS)

    Datta, Sambhu N.; Misra, Anirban

    2006-08-01

    The retarded interaction between an electron and a spin-0 nucleus is derived from electrodynamical perturbation theory. The contribution of retardation at order v2/c2 mimics the Breit interaction [Phys. Rev. 34, 553 (1929); 36, 388 (1930); 39, 616 (1932)] with the Dirac matrix α2 being replaced by p2/m2c where p2 is the linear momentum operator for the nucleus. An effective one-electron retardation operator is obtained in relative coordinates, and this can be used through all orders in perturbation theory without any problem of infinite degeneracy. A few steps of unitary transformation lead to the nonrelativistic limit. The leading terms in retardation corrections to energy are of order (me/mn)α2Z4(α2mec2). The implications for atomic systems are discussed.

  10. Lifetime measurements in 71Ge and a new interacting boson-fermion model interpretation

    NASA Astrophysics Data System (ADS)

    Ivaşcu, M.; Mărginean, N.; Bucurescu, D.; Căta-Danil, I.; Ur, C. A.; Lobach, Yu. N.

    1999-08-01

    The lifetimes of twelve low spin excited states have been measured in 71Ge using the Doppler shift attenuation method in the 71Ga(p,nγ) reaction at 3.0 and 3.5 MeV incident energy. New interacting boson-fermion model calculations for this nucleus account well for the properties of all its levels known up to about 1.5 MeV excitation.

  11. Internal parity symmetry and degeneracy of Bethe Ansatz strings in the isotropic heptagonal magnetic ring

    NASA Astrophysics Data System (ADS)

    Milewski, J.; Lulek, B.; Lulek, T.; Łabuz, M.; Stagraczyński, R.

    2014-02-01

    The exact Bethe eigenfunctions for the heptagonal ring within the isotropic XXX model exhibit a doubly degenerated energy level in the three-deviation sector at the centre of the Brillouin zone. We demonstrate an explicit construction of these eigenfunctions by use of algebraic Bethe Ansatz, and point out a relation of degeneracy to parity conservation, applied to the configuration of strings for these eigenfunctions. Namely, the internal structure of the eigenfunctions (the 2-string and the 1-string, with opposite quasimomenta) admits generation of two mutually orthogonal eigenfunctions due to the fact that the strings which differ by their length are distinguishable objects.

  12. Fermionic Symmetries: Degeneracies when T=0 Two body matrix elements are set equal to zero

    NASA Astrophysics Data System (ADS)

    Zamick, Larry; Robinson, Shadow Jq

    2001-10-01

    In shell model calculations for ^43Ti and ^44Ti not perfect but surprisingly good results are obtained when all the T=0 two body matrix elements are set equal to zero. In this model and in the single j shell approximation (j=f_7/2) many degeneracies arise. For example for the T=1/2 states in ^43Ti(^43Sc) the I=1/2_1^- and 1/32_1^- states are degenerate as are the 1/32_2^-, 1/72_1^- and 1/92_1^- T=1/2 states. In ^44Ti the T=0 states 3^+_2, 7^+_2,9^+_1, and 10^+1 are degenerate and so are the 10^+2 and 12^+1 states. Concerning the 1/2_1^- and 1/32_1^- we find that both have (J_p,J_n) configuration (4,7/2). For the 3^+_2, 7^+_2,9^+_1, and 10^+1 all four states have the configurations (4,6) and (6,4). This means that couplings to other states will vanish. This means that certain 6j and 9j symbols will vanish e.g. j & j& 4 j&1/32& 6 \\=0 and j & j& 6 j&j& 6 4 & 6 &10 \\=0. One can explain these vanishings in terms of Talmi's method of calculating coeffiecients of fractional parentage to states not allowed by the Pauli principle. For example for the T=3/2 states of ^43Ca there are no f_7/2^3 I=1/32^- states. Hence the c.f.p. to these states must vanish. One c.f.p. contains the above 6j symbol and so this 6j symbol will vanish. For the T=2 states in ^44Ca there is no f_7/2^4 state with I=10^+. One of the two particle c.f.p to this state is proportional to the above 9j symbol and so the 9j must vanish. Note that we are using arguments about T=3/2 states to explain degeneracies of T=1/2 states; and we are using arguments about T=2 states to explain degeneracies of T=0 states. When T=0 two body matrix elements are reintroduced the 9^+1 and 10^+1 are no longer degenerate and the splitting even in a full fp space calculation is due almost entirely to the T=0 matrix elements. The common thread for the T=1/2 and T=0 states that are degenerate is that they have angular momentum which in the single j shell calculation cannot occur for identical particles. For these angular momenta

  13. Transition probabilities and interacting boson-fermion model description of positive parity states in 117Sb

    NASA Astrophysics Data System (ADS)

    Lobach, Yu. N.; Bucurescu, D.

    1998-09-01

    The Doppler shift attenuation method was used to determine lifetimes in the picosecond region for excited states of 117Sb populated with the (α,2nγ) reaction at Eα=27.2 MeV. Interacting boson-fermion model calculations explain reasonably well the main features of the positive parity levels known up to about 2.5 MeV excitation. The mixing of the lowest one-quasiparticle 9/2+ state with the intruder (2p-1h) 9/2+ state, as well as the quadrupole deformation of the intruder band are also discussed.

  14. Comparisons of interacting-boson-fermion approximation and triaxial calculations for odd-mass N =80 nuclei

    SciTech Connect

    Aryaeinejad, R.; Chou, W.; McHarris, W.C. )

    1989-09-01

    The interacting-boson-fermion-approximation and triaxial models were used to calculate excitation energies and mixing ratios for the {ital N}=80 nuclei, {sup 139}Pr, {sup 141}Pm, and {sup 143}Eu. For low-lying negative- and positive-parity states both models yield roughly the same numbers, in good agreement with experimental results. For high-lying states we find that the interacting-boson-fermion-approximation model describes the level structure considerably better than the triaxial model. On the other hand, the triaxial model gives more satisfactory results in predicting the mixing ratios.

  15. Superconductivity in the boson-fermion model with short range fermion repulsion

    NASA Astrophysics Data System (ADS)

    Kostyrko, Tomasz

    1998-03-01

    We consider influence of an on-site Coulomb repulsion U between fermions on superconducting properties of a two-component system of the wide band electrons hybridized with heavy boson-like local electron pairs^1,2. Within an RPA treatment valid for U< fermion bandwidth, we show that U almost completely suppresses superconductivity as long as a boson level stays above a Fermi level (BCS limit), reducing both Tc and a range of stability of an s-wave superconducting phase at T=0 K. In a Bose region, where the chemical potential remains pinned to the boson level, superconductivity is always stable at T=0 K and suppression of Tc is relatively small, especially for finite values of a boson mass. Above results are verified with the conclusions based on an effective t-J like hamiltonian derived by means of a canonical perturbation method from the boson-fermion model in a strong U limit. We show that the on-site boson-fermion hybridization is reduced by a factor of 2t/U (t - fermion hopping) and transforms into an intersite coupling supporting an extended s-wave superconducting order in this limit. [1em] 1. J. Ranninger and Robaszkiewicz, Physica B 135, 468 (1985). 2. R. Friedberg and T.D. Lee, Phys. Rev. B 40, 423 (1989).

  16. Level Density In Interacting Boson-Fermion-Fermion Model (IBFFM) Of The Odd-Odd Nucleus 196Au

    SciTech Connect

    Kabashi, Skender; Bekteshi, Sadik

    2007-04-23

    The level density of the odd-odd nucleus 196Au is investigated in the interacting boson-fermion-fermion model (IBFFM) which accounts for collectivity and complex interaction between quasiparticle and collective modes.The IBFFM total level density is fitted by Gaussian and its tail is also fitted by Bethe formula and constant temperature Fermi gas model.

  17. Phase transitions in the interacting boson fermion model: The {gamma}-unstable case

    SciTech Connect

    Alonso, C.E.; Arias, J.M.; Fortunato, L.; Vitturi, A.

    2005-12-15

    The phase transition around the critical point in the evolution from spherical to deformed {gamma}-unstable shapes is investigated in odd nuclei within the interacting boson fermion model. We consider the particular case of an odd j=3/2 particle coupled to an even-even boson core that undergoes a transition from spherical U(5) to {gamma}-unstable O(6) situation. The particular choice of the j=3/2 orbital preserves in the odd case the condition of {gamma}-instability of the system. As a consequence, energy spectrum and electromagnetic transitions, in correspondence of the critical point, display behaviors qualitatively similar to those of the even core. The results are also in qualitative agreement with the recently proposed E(5/4) model, although few differences are present, due to the different nature of the two schemes.

  18. Composite-Particles (Boson, Fermion) Theory of Fractional Quantum Hall Effect

    NASA Astrophysics Data System (ADS)

    Fujita, Shigeji; Suzuki, Akira; Ho, Hung-Cheuk

    2017-02-01

    A theory is developed for fractional quantum Hall effect in terms of composite (c)-bosons (fermions) without useing Laughlin's results about the fractional charge. Here the c-particle (fermion, boson) is defined as a bound composite fermion (boson) containing a conduction electron and an even (odd) number of fluxons (elementary magnetic fluxes). The Bose-condensed c-bosons, each containing an electron and an odd number m of fluxons at the filling factor ν=1/ m is shown to generate the Hall conductivity plateau value m e 2/ h, where the density of c-particles, n_{φ }^{(m)}, either bosonic or fermionic, with m fluxons is given by n_{φ }^{(m)}=ne/m, n e = electron density. The only assumption is that any c-fermion carries a charge magnitude equal to the electron charge e. The quantum Hall state is shown to be more stable at ν=1/3 than at ν=1.

  19. One-loop renormalizable Wess-Zumino model on a bosonic-fermionic noncommutative superspace

    NASA Astrophysics Data System (ADS)

    Miao, Yan-Gang; Wang, Xu-Dong

    2014-08-01

    We construct a deformed Wess-Zumino model on the noncommutative superspace where the bosonic and fermionic coordinates are no longer commutative with each other. Using the background field method, we calculate the primary one-loop effective action based on the deformed action. By comparing the two actions, we find that the deformed Wess-Zumino model is not renormalizable. To obtain a renormalizable model, we combine the primary one-loop effective action with the deformed action, and then calculate the secondary one-loop effective action based on the combined action. After repeating this process a third time, we finally give the one-loop renormalizable action up to the second order of bosonic-fermionic noncommutative parameters by using our specific techniques of calculation.

  20. Mixing-demixing transition and collapse of a vortex state in a quasi-two-dimensional boson-fermion mixture

    SciTech Connect

    Adhikari, Sadhan K.; Salasnich, Luca

    2007-05-15

    We investigate the mixing-demixing transition and the collapse in a quasi-two-dimensional degenerate boson-fermion mixture (DBFM) with a bosonic vortex. We solve numerically a quantum-hydrodynamic model based on a new density functional which accurately takes into account the dimensional crossover. It is demonstrated that with the increase of interspecies repulsion, a mixed state of DBFM could turn into a demixed state. The system collapses for interspecies attraction above a critical value which depends on the vortex quantum number. For interspecies attraction just below this critical limit there is almost complete mixing of boson and fermion components. Such mixed and demixed states of a DBFM could be experimentally realized by varying an external magnetic field near a boson-fermion Feshbach resonance, which will result in a continuous variation of interspecies interaction.

  1. From the Hubbard to a Plaquette Boson-Fermion Model for Cuprates

    NASA Astrophysics Data System (ADS)

    Altman, Ehud; Auerbach, Assa

    2002-03-01

    We describe a systematic approach to connect the microscopic physics of the Hubbard model to the phenomena of underdoped High Tc cuprate superconductors. We apply the Contractor Renormalization method of Morningstar and Weinstein to reduce the strongly interacting Hubbard model on the square lattice to the low energy Plaquette Boson Fermion Model (PBFM). The four bosons (an antiferromagnon triplet and a d-wave hole pair), and the fermions are defined by the lowest plaquette eigenstates. We compute the boson effective interactions, and the range-3 truncation error is found to be very small, signaling short hole-pair and magnon coherence lengths. The pair-hopping and magnon interactions are comparable, which explains the rapid destruction of antiferromagnetic order with emergence of superconductivity, and validates a key assumption of the projected SO(5) theory. A vacuum crossing at larger doping marks a transition into the overdoped regime. The PBFM includes hole fermions occupying small Fermi pockets and Andreev coupled to hole pair bosons. In mean field theory it exhibits a pairing gap near the nodes, which grows with Tc and a pseudogap with oposite doping dependence. The PBFM yields several testable predictions for photoemmission, tunneling asymmetry and thermodynamic measurements.

  2. Depairing and Bose-Einstein-condensation temperatures in a simple boson-fermion model of superconductors

    NASA Astrophysics Data System (ADS)

    Mamedov, T. A.; de Llano, M.

    2007-03-01

    Starting from the Friedberg-TD Lee Hamiltonian describing a coexisting and dynamically interacting many-particle binary boson-fermion gas mixture with a coupling (λ) -dependent gap 2Δ(λ) in the boson dispersion relation for the s -wave Cooper or BCS model interaction, we deduce several observed characteristic features of high-temperature superconductors at the simplest level. Analytic expressions for both the unpaired-fermion and boson number densities, as well for the fermion chemical potential μ(λ,T) , all of which vary with the degree of bosonization and with temperature T , are derived in detail using two-time, finite-temperature Green function techniques. Simple implicit formulas are then obtained for both two and three dimensions for the pseudogap T* and Bose-Einstein condensation Tc temperatures in terms of μ(λ,T) and 2Δ(λ) . In particular, even at the s -wave level we find a self-consistent description of the generic phase diagram observed in cuprates, including the appearance of a pseudogap and a dome-shaped Tc vs doping behavior both of which hinge on the gapped boson spectrum.

  3. Phase transitions in the boson-fermion resonance model in one dimension

    NASA Astrophysics Data System (ADS)

    Orignac, E.; Citro, R.

    2006-06-01

    We study one-dimensional fermions with photoassociation or with a narrow Fano-Feshbach resonance described by the boson-fermion resonance model. Using the bosonization technique, we derive a low-energy Hamiltonian of the system. We show that at low energy, the order parameters for the Bose condensation and fermion superfluidity become identical, while a spin gap and a gap against the formation of phase slips are formed. As a result of these gaps, charge density wave correlations decay exponentially in contrast with the phases where only bosons or only fermions are present. We find a Luther-Emery point where the phase slips and the spin excitations can be described in terms of pseudofermions. This allows us to provide closed form expressions of the density-density correlations and the spectral functions. The spectral functions of the fermions are gapped, whereas the spectral functions of the bosons remain gapless. The application of a magnetic field results in a loss of coherence between the bosons and the fermion and the disappearance of the gap. Changing the detuning has no effect on the gap until either the fermion or the boson density is reduced to zero. Finally, we discuss the formation of a Mott insulating state in a periodic potential. The relevance of our results for experiments with ultracold atomic gases subject to one-dimensional confinement is also discussed.

  4. Specific heat of underdoped cuprate superconductors from a phenomenological layered Boson-Fermion model

    NASA Astrophysics Data System (ADS)

    Salas, P.; Fortes, M.; Solís, M. A.; Sevilla, F. J.

    2016-05-01

    We adapt the Boson-Fermion superconductivity model to include layered systems such as underdoped cuprate superconductors. These systems are represented by an infinite layered structure containing a mixture of paired and unpaired fermions. The former, which stand for the superconducting carriers, are considered as noninteracting zero spin composite-bosons with a linear energy-momentum dispersion relation in the CuO2 planes where superconduction is predominant, coexisting with the unpaired fermions in a pattern of stacked slabs. The inter-slab, penetrable, infinite planes are generated by a Dirac comb potential, while paired and unpaired electrons (or holes) are free to move parallel to the planes. Composite-bosons condense at a critical temperature at which they exhibit a jump in their specific heat. These two values are assumed to be equal to the superconducting critical temperature Tc and the specific heat jump reported for YBa2Cu3O6.80 to fix our model parameters namely, the plane impenetrability and the fraction of superconducting charge carriers. We then calculate the isochoric and isobaric electronic specific heats for temperatures lower than Tc of both, the composite-bosons and the unpaired fermions, which matches the latest experimental curves. From the latter, we extract the linear coefficient (γn) at Tc, as well as the quadratic (αT2) term for low temperatures. We also calculate the lattice specific heat from the ARPES phonon spectrum, and add it to the electronic part, reproducing the experimental total specific heat at and below Tc within a 5% error range, from which the cubic (ßT3) term for low temperatures is obtained. In addition, we show that this model reproduces the cuprates mass anisotropies.

  5. {beta} decay of odd-A As to Ge isotopes in the interacting boson-fermion model

    SciTech Connect

    Brant, S.; Yoshida, N.; Zuffi, L.

    2004-11-01

    The structure of odd-mass isotopes of As and Ge is described in the framework of the proton-neutron interacting boson-fermion model. The energy levels and the electromagnetic properties of {sup 69,71,73}As and {sup 69,71,73}Ge are calculated and compared with the experiment. The {beta}-decay rates from the As isotopes to the Ge isotopes are calculated. The calculated decays tend to be stronger than the observed ones. This may indicate a mixture of components outside the model space in the wave functions of actual nuclei. The effect of the higher-order terms in the decay operators seems small.

  6. Remove Degeneracy in Relativistic Symmetries for Manning—Rosen Plus Quasi-Hellman Potentials by Tensor Interaction

    NASA Astrophysics Data System (ADS)

    Mousavi, Mohsen; Shojaei, Mohammad Reza

    2016-11-01

    The relativistic Dirac equation under spin and pseudo-spin symmetries is investigated for Manning—Rosen plus quasi-Hellman potentials with tensor interaction. For the first time we consider the Hulthen plus Yukawa for tensor interaction. The Formula method is used to obtain the energy eigen-values and wave functions. We also discuss about the energy eigen-values and the Dirac spinors for the Manning—Rosen plus quasi-Hellman potentials for the spin and pseudo-spin symmetry with Formula method. To show the accuracy of the present model, some numerical results are shown in both pseudo-spin and spin symmetry limits.

  7. Stable Degeneracies for Ising Models

    NASA Astrophysics Data System (ADS)

    Knauf, Andreas

    2016-10-01

    We introduce and consider the notion of stable degeneracies of translation invariant energy functions, taken at spin configurations of a finite Ising model. By this term we mean the lack of injectivity that cannot be lifted by changing the interaction. We show that besides the symmetry-induced degeneracies, related to spin flip, translation and reflection, there exist additional stable degeneracies, due to more subtle symmetries. One such symmetry is the one of the Singer group of a finite projective plane. Others are described by combinatorial relations akin to trace identities. Our results resemble traits of the length spectrum for closed geodesics on a Riemannian surface of constant negative curvature. There, stable degeneracy is defined w.r.t. Teichmüller space as parameter space.

  8. Description of odd-mass nuclei within the interacting boson-fermion model based on the Gogny energy density functional

    NASA Astrophysics Data System (ADS)

    Nomura, K.; Rodríguez-Guzmán, R.; Robledo, L. M.

    2017-07-01

    Spectroscopic properties of odd-mass nuclei are studied within the framework of the interacting boson-fermion model (IBFM) with parameters based on the Hartree-Fock-Bogoliubov (HFB) approximation. The parametrization D1M of the Gogny energy density functional (EDF) was used at the mean-field level to obtain the deformation energy surfaces for the considered nuclei in terms of the quadrupole deformations (β ,γ ). In addition to the energy surfaces, both single-particle energies and occupation probabilities were used as a microscopic input for building the IBFM Hamiltonian. Only three strength parameters for the particle-boson-core coupling are fitted to experimental spectra. The IBFM Hamiltonian is then used to compute the energy spectra and electromagnetic transition rates for selected odd-mass Eu and Sm nuclei as well as for 195Pt and 195Au. A reasonable agreement with the available experimental data is obtained for the considered odd-mass nuclei.

  9. Odd-even {sup 147-153}Pm isotopes within the neutron-proton interacting boson-fermion model

    SciTech Connect

    Barea, J.; Alonso, C. E.; Arias, J. M.

    2011-02-15

    Low-lying energy states of the {sup 147-153}Pm isotopic chain are studied within the framework of the neutron-proton interacting boson-fermion model (IBFM-2). The spectra of these isotopes show a transition from a particle coupled to a vibrational core to a particle coupled to a deformed one. The calculation reproduces this behavior. In addition, reduced transition probabilities B(E2) and B(M1) and quadrupole and magnetic moments, as well as spectroscopic factors corresponding to stripping and pickup transfer reactions, are calculated. Obtained results compare well with the available experimental data, which reinforces the reliability of the wave functions obtained within the IBFM-2 model.

  10. On-chip generation of Einstein-Podolsky-Rosen states with arbitrary symmetry

    SciTech Connect

    Gräfe, Markus; Heilmann, René; Nolte, Stefan; Szameit, Alexander

    2015-05-04

    We experimentally demonstrate a method for integrated-optical generation of two-photon Einstein-Podolsky-Rosen states featuring arbitrary symmetries. In our setting, we employ detuned directional couplers to impose a freely tailorable phase between the two modes of the state. Our results allow to mimic the quantum random walk statistics of bosons, fermions, and anyons, particles with fractional exchange statistics.

  11. {beta} decay of the even-even {sup 124}Ba nucleus: A test for the interacting boson-fermion-fermion model

    SciTech Connect

    Brant, S.; Yoshida, N.; Zuffi, L.

    2006-08-15

    The interacting boson-fermion-fermion model approach to {beta} decay is applied to the decay from the even-even {sup 124}Ba to the odd-odd {sup 124}Cs nucleus. The theoretical results for energy levels, electromagnetic properties and {beta} decay rates are compared with experimental data for {sup 124}Cs. The calculated {beta}-decay rates demonstrate that the interacting boson approximation can be applied in the description of {beta} decays from even-even to odd-odd nuclei.

  12. BEC-polaron gas in a boson-fermion mixture: A many-body extension of Lee-Low-Pines theory

    NASA Astrophysics Data System (ADS)

    Nakano, Eiji; Yabu, Hiroyuki

    2016-05-01

    We investigate the ground state properties of the gaseous mixture of a single species of bosons and fermions at zero temperature, where bosons are major in population over fermions, and form the Bose-Einstein condensate (BEC). The boson-boson and boson-fermion interactions are assumed to be weakly repulsive and attractive, respectively, while the fermion-fermion interaction is absent due to the Pauli exclusion for the low energy s -wave scattering. We treat fermions as a gas of polarons dressed with Bogoliubov phonons, which is an elementary excitation of the BEC, and evaluate the ground state properties with the method developed by Lemmens, Devreese, and Brosens (LDB) originally for the electron polaron gas, and also with a general extension of the Lee-Low-Pines theory for many-body systems (eLLP), which incorporates the phonon drag effects as in the original LLP theory. The formulation of eLLP is developed and discussed in the present paper. The binding (interaction) energy of the polaron gas is calculated in these methods and shown to be finite (negative) for the dilute gas of heavy fermions with attractive boson-fermion interactions, though the suppression by the many-body effects exists.

  13. General degeneracy in density functional perturbation theory

    NASA Astrophysics Data System (ADS)

    Palenik, Mark C.; Dunlap, Brett I.

    2017-07-01

    Degenerate perturbation theory from quantum mechanics is inadequate in density functional theory (DFT) because of nonlinearity in the Kohn-Sham potential. Herein, we develop the fully general perturbation theory for open-shell, degenerate systems in Kohn-Sham DFT, without assuming the presence of symmetry or equal occupation of degenerate orbitals. To demonstrate the resulting methodology, we apply it to the iron atom in the central field approximation, perturbed by an electric quadrupole. This system was chosen because it displays both symmetry required degeneracy, between the five 3 d orbitals, as well as accidental degeneracy, between the 3 d and 4 s orbitals. The quadrupole potential couples the degenerate 3 d and 4 s states, serving as an example of the most general perturbation.

  14. Braiding statistics and link invariants of bosonic/fermionic topological quantum matter in 2+1 and 3+1 dimensions

    NASA Astrophysics Data System (ADS)

    Putrov, Pavel; Wang, Juven; Yau, Shing-Tung

    2017-09-01

    Topological Quantum Field Theories (TQFTs) pertinent to some emergent low energy phenomena of condensed matter lattice models in 2+1 and 3+1 dimensions are explored. Many of our TQFTs are highly-interacting without free quadratic analogs. Some of our bosonic TQFTs can be regarded as the continuum field theory formulation of Dijkgraaf-Witten twisted discrete gauge theories. Other bosonic TQFTs beyond the Dijkgraaf-Witten description and all fermionic TQFTs (namely the spin TQFTs) are either higher-form gauge theories where particles must have strings attached, or fermionic discrete gauge theories obtained by gauging the fermionic Symmetry-Protected Topological states (SPTs). We analytically calculate both the Abelian and non-Abelian braiding statistics data of anyonic particle and string excitations in these theories, where the statistics data can one-to-one characterize the underlying topological orders of TQFTs. Namely, we derive path integral expectation values of links formed by line and surface operators in these TQFTs. The acquired link invariants include not only the familiar Aharonov-Bohm linking number, but also Milnor triple linking number in 3 dimensions, triple and quadruple linking numbers of surfaces, and intersection number of surfaces in 4 dimensions. We also construct new spin TQFTs with the corresponding knot/link invariants of Arf(-Brown-Kervaire), Sato-Levine and others. We propose a new relation between the fermionic SPT partition function and the Rokhlin invariant. As an example, we can use these invariants and other physical observables, including ground state degeneracy, reduced modular Sxy and Txy matrices, and the partition function on RP3 manifold, to identify all ν ∈Z8 classes of 2+1 dimensional gauged Z2-Ising-symmetric Z2f -fermionic Topological Superconductors (realized by stacking ν layers of a pair of chiral and anti-chiral p-wave superconductors [ p + ip and p - ip], where boundary supports non-chiral Majorana-Weyl modes) with

  15. Semifluxon degeneracy choreography in Aharonov-Bohm billiards

    NASA Astrophysics Data System (ADS)

    Berry, M. V.; Popescu, S.

    2010-09-01

    Every energy level of a charged quantum particle confined in a region threaded by a magnetic flux line with quantum flux one-half must be degenerate for some position of the semifluxon within the boundary B. This is illustrated by computations for which B is a circle and a conformal transformation of a circle without symmetry. As the shape of B is varied, two degeneracies between the same pair of levels can collide and annihilate. Degeneracy of three levels requires three shape parameters, or the positions of three semifluxons; degeneracy of N levels can be generated by int{N(N + 1)/4} semifluxons. The force on the semifluxon is derived.

  16. Giant nonreciprocity near exceptional-point degeneracies

    NASA Astrophysics Data System (ADS)

    Thomas, Roney; Li, Huanan; Ellis, F. M.; Kottos, Tsampikos

    2016-10-01

    We show that gyrotropic structures with balanced gain and loss that respect antilinear symmetries exhibit a giant nonreciprocity at the so-called exact phase where the eigenfrequencies of the isolated non-Hermitian setup are real. The effect occurs in a parameter domain near an exceptional- point (EP) degeneracy, where mode orthogonality collapses. The theoretical predictions are confirmed numerically in the microwave domain, where a nonreciprocal transport above 90 dB is demonstrated, and are further verified using lumped-circuitry modeling. The analysis allows us to speculate the universal nature of the phenomenon for any wave system where EP and gyrotropy can coexist.

  17. The Simplicity of Perfect Atoms: Degeneracies in Supersymmetric Hydrogen

    SciTech Connect

    Rube, Tomas; Wacker, Jay G.; /SLAC /Stanford U., ITP

    2011-08-19

    Supersymmetric QED hydrogen-like bound states are remarkably similar to non-supersymmetric hydrogen, including an accidental degeneracy of the fine structure and which is broken by the Lamb shift. This article classifies the states, calculates the leading order spectrum, and illustrates the results in several limits. The relation to other non-relativistic bound states is explored. Supersymmetric bound states provide a laboratory for studying dynamics in supersymmetric theories. Bound states like hydrogen provide a framework for understanding the qualitative dynamics of QCD mesons, a supersymmetric version of QED can provide a qualitative picture for the symmetries and states of superQCD mesons. Furthermore, recent interest in dark matter as a composite state, leads to asking how supersymmetry acts upon these composite states [4-7]. This article calculates the leading order corrections to a hydrogen-like atoms in an exactly supersymmetric version of QED. Much of the degeneracy is broken by the fine structure and a seminal calculation was performed in [1] for positronium, see [2] for an N = 2 version of positronium. Supersymmetric hydrogen is a similar except for the absence of annihilation diagrams, see [3] for an independent calculation. In the heavy proton mass limit, the supersymmetric interactions of the theory become irrelevant operators, suppressed by powers of the proton mass like the magnetic moment operator in QED and the fine structure is identical to the non-supersymmetric theory. This article finds that fine structure spectrum of supersymmetric spectrum of hydrogen has an accidental degeneracy which is exactly analogous to the accidental degeneracy of the l = 0 and l = 1 levels of the n = 2; j = 1/2 state of hydrogen. The supersymmetric version of the Lamb shift lifts the residual degeneracy and this article computes the logarithmically enhanced breaking.

  18. Changing anyonic ground degeneracy with engineered gauge fields

    NASA Astrophysics Data System (ADS)

    Cobanera, Emilio; Ulrich, Jascha; Hassler, Fabian

    2016-09-01

    For systems of lattice anyons such as Majoranas and parafermions, the unconventional quantum statistics determines a set of global symmetries (e.g., fermion parity for Majoranas) admitting no relevant perturbations. Any operator that breaks these symmetries explicitly would violate locality if added to the Hamiltonian. As a consequence, the associated quasidegeneracy of topologically nontrivial phases is protected, at least partially, by locality via the symmetries singled out by quantum statistics. We show that it is possible to bypass this type of protection by way of specifically engineered gauge fields, in order to modify the topological structure of the edge of the system without destroying the topological order completely. To illustrate our ideas in a concrete setting, we focus on the Z6 parafermion chain. Starting in the topological phase of the chain (sixfold ground degeneracy), we show that a gauge field with restricted dynamics acts as a relevant perturbation, driving a transition to a phase with threefold degeneracy and Z3 parafermion edge modes. The transition from the Z3 to the topologically trivial phase occurs on a critical line in the three-state Potts universality class. We also investigate numerically the emergence of Majorana edge modes when the Z6 chain is coupled to a differently restricted gauge field.

  19. Spin degeneracy and conductance fluctuations in open quantum dots.

    PubMed

    Folk, J A; Patel, S R; Birnbaum, K M; Marcus, C M; Duruöz, C I; Harris, J S

    2001-03-05

    The dependence of conductance fluctuations on parallel magnetic field is used as a probe of spin degeneracy in open GaAs quantum dots. The variance of fluctuations at high parallel field is reduced from the low-field variance (with broken time-reversal symmetry) by factors ranging from roughly 2 in a 1 microm (2) dot to greater than 4 in 8 microm (2) dots. The factor of 2 is expected for Zeeman splitting of spin-degenerate channels. A possible explanation for the larger suppression based on field-dependent spin-orbit scattering is proposed.

  20. Higher derivative field theories: degeneracy conditions and classes

    NASA Astrophysics Data System (ADS)

    Crisostomi, Marco; Klein, Remko; Roest, Diederik

    2017-06-01

    We provide a full analysis of ghost free higher derivative field theories with coupled degrees of freedom. Assuming the absence of gauge symmetries, we derive the degeneracy conditions in order to evade the Ostrogradsky ghosts, and analyze which (non)trivial classes of solutions this allows for. It is shown explicitly how Lorentz invariance avoids the propagation of "half" degrees of freedom. Moreover, for a large class of theories, we construct the field redefinitions and/or (extended) contact transformations that put the theory in a manifestly first order form. Finally, we identify which class of theories cannot be brought to first order form by such transformations.

  1. Coexistence of orbital degeneracy lifting and superconductivity in iron-based superconductors

    NASA Astrophysics Data System (ADS)

    Miao, H.; Wang, L.-M.; Richard, P.; Wu, S.-F.; Ma, J.; Qian, T.; Xing, L.-Y.; Wang, X.-C.; Jin, C.-Q.; Chou, C.-P.; Wang, Z.; Ku, W.; Ding, H.

    2014-06-01

    We report the angle-resolved photoemission spectroscopy observation of the lifting of symmetry-protected band degeneracy, and consequently the breakdown of local tetragonal symmetry in the superconducting state of Li(Fe1-xCox)As. Supported by theoretical simulations, we analyze the doping and temperature dependences of this band splitting and demonstrate an intimate connection between ferro-orbital correlations and superconductivity.

  2. Exactly soluble model of boundary degeneracy

    NASA Astrophysics Data System (ADS)

    Ganeshan, Sriram; Gorshkov, Alexey V.; Gurarie, Victor; Galitski, Victor M.

    2017-01-01

    We investigate the topological degeneracy that can be realized in Abelian fractional quantum spin Hall states with multiply connected gapped boundaries. Such a topological degeneracy (also dubbed as "boundary degeneracy") does not require superconducting proximity effect and can be created by simply applying a depletion gate to the quantum spin Hall material and using a generic spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We construct an exactly soluble microscopic model manifesting this topological degeneracy and solve it using the recently developed technique [S. Ganeshan and M. Levin, Phys. Rev. B 93, 075118 (2016), 10.1103/PhysRevB.93.075118]. The corresponding string operators spanning this degeneracy are explicitly calculated. It is argued that the proposed scheme is experimentally reasonable.

  3. Nodal surfaces and interdimensional degeneracies

    SciTech Connect

    Loos, Pierre-François; Bressanini, Dario

    2015-06-07

    The aim of this paper is to shed light on the topology and properties of the nodes (i.e., the zeros of the wave function) in electronic systems. Using the “electrons on a sphere” model, we study the nodes of two-, three-, and four-electron systems in various ferromagnetic configurations (sp, p{sup 2}, sd, pd, p{sup 3}, sp{sup 2}, and sp{sup 3}). In some particular cases (sp, p{sup 2}, sd, pd, and p{sup 3}), we rigorously prove that the non-interacting wave function has the same nodes as the exact (yet unknown) wave function. The number of atomic and molecular systems for which the exact nodes are known analytically is very limited and we show here that this peculiar feature can be attributed to interdimensional degeneracies. Although we have not been able to prove it rigorously, we conjecture that the nodes of the non-interacting wave function for the sp{sup 3} configuration are exact.

  4. Parameter degeneracy in neutrino oscillation — Solution network and structural overview

    NASA Astrophysics Data System (ADS)

    Minakata, Hisakazu; Uchinami, Shoichi

    2010-04-01

    It is known that there is a phenomenon called “parameter degeneracy” in neutrino oscillation measurement of lepton mixing parameters; A set of the oscillation probabilities, e.g., P( ν μ → ν e ) and its CP-conjugate Pleft( {{{bar ν }_μ } to {{bar ν }_e}} right) at a particular neutrino energy does not determine uniquely the values of θ 13 and δ. With use of the approximate form of the oscillation probability á la Cervera et al., a complete analysis of the eightfold parameter degeneracy is presented. We propose a unified view of the various types of the degeneracy as invariance of the oscillation probabilities under discrete mappings of the mixing parameters. Explicit form of the mapping is obtained either by symmetry argument, or by deriving exact analytic expressions of all the degeneracy solutions for a given true solution. Due to the one-to-one mapping structure the degeneracy solutions are shown to form a network. We extend our analysis into the parameter degeneracy in T- and CPT-conjugate measurement as well as to the setup with the golden and the silver channels, P( ν e → ν μ ) and P( ν e → ν τ ). Some characteristic features of the degeneracy solutions in CP-conjugate measurement, in particular their energy dependences, are illuminated by utilizing the explicit analytic solutions.

  5. Decomposition of fractional quantum Hall model states: Product rule symmetries and approximations

    SciTech Connect

    Thomale, Ronny; Bernevig, B. Andrei; Estienne, Benoit; Regnault, Nicolas

    2011-07-15

    We provide a detailed description of a product rule structure of the monomial (Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall (FQH) states derived recently, which we now extend to spin-singlet states. We show that the Haldane-Rezayi spin-singlet state can be obtained without exact diagonalization through a differential equation method that we conjecture to be generic to other FQH model states. The product rule symmetries allow us to build approximations of FQH states that exhibit increasing overlap with the exact state (as a function of system size) even though our approximation omits more than half of the Hilbert space. We show that the product rule is valid for any FQH state that can be written as an expectation value of parafermionic operators.

  6. Angular-overlap calculation of the Jahn-Teller stabilization energie for f-orbital degeneracies

    SciTech Connect

    Warren, K.D.

    1980-03-01

    The angular-overlap model is applied to the calculation of the linear Jahn-Teller coupling constants for f-orbital degeneracies. The MX/sub 6/, O/sub h/, chromophore is treated as representative of the highest symmetry commonly occurring in the lanthanide and actinide series, and it is shown that, even when spin-orbit effects are taken into account, 5f orbital degeneracies may lead to significant Jahn-Teller stabilization energies. The operation of this effect for F/sup 1/ GAMMA/sub 8/ states is considered. 2 tables.

  7. Quantum degeneracy of mixed strontium gases

    NASA Astrophysics Data System (ADS)

    Yan, Mi; Desalvo, Brian; Mickelson, Pascal; Martinez de Escobar, Natali; Killian, Thomas

    2010-03-01

    We have attained quantum degeneracy in a mixture of ^88Sr (bosons) and ^87Sr (fermions). A Bose-Einstein condensate of ^88Sr, which has attractive interactions, is produced via sympathetic cooling using ^87Sr. Simultaneously, we have demonstrated Fermi degeneracy of ^87Sr by observing the difference in the sizes of the atom cloud, due to the Fermi pressure, between degenerate ^87Sr and ^88Sr.

  8. Degeneracies in parametrized modified gravity models

    SciTech Connect

    Hojjati, Alireza

    2013-01-01

    We study degeneracies between parameters in some of the widely used parametrized modified gravity models. We investigate how different observables from a future photometric weak lensing survey such as LSST, correlate the effects of these parameters and to what extent the degeneracies are broken. We also study the impact of other degenerate effects, namely massive neutrinos and some of the weak lensing systematics, on the correlations.

  9. Degeneracy and complexity in biological systems

    PubMed Central

    Edelman, Gerald M.; Gally, Joseph A.

    2001-01-01

    Degeneracy, the ability of elements that are structurally different to perform the same function or yield the same output, is a well known characteristic of the genetic code and immune systems. Here, we point out that degeneracy is a ubiquitous biological property and argue that it is a feature of complexity at genetic, cellular, system, and population levels. Furthermore, it is both necessary for, and an inevitable outcome of, natural selection. PMID:11698650

  10. A First Test of the E(5/4) Bose-Fermi Symmetry : 135Ba

    NASA Astrophysics Data System (ADS)

    Cakirli, R. B.; Fetea, M. S.; Casten, R. F.; Warner, D. D.; McCutchan, E. A.; Meyer, D. A.; Heinz, A.; Ai, H.; Gurdal, G.; Qian, J.; Winkler, R.

    2007-04-01

    There has been intense recent interest in equilibrium shape / phase transitions in nuclei and the concept of critical point symmetries to describe them. The first critical point symmetry for an odd-mass nucleus has been recently proposed, namely, the E(5/4) Bose-Fermi critical point symmetry, it corresponds to coupling between an odd particle in a j = 3/2 orbit and the E(5) critical point symmetry, at the transition between the O(6) gamma-soft and the U(5) vibrator symmetries. Since 134Ba is a candidate for the E(5) critical point symmetry, we carried out a β-decay experiment on 135Ba whose last neutron can occupy a 2d3/2 orbit as a first test of E(5/4). The experimental results were compared to E(5/4) and also with the Interacting Boson-Fermion Approximation Model (IBFA) and Shell Model calculations. We see fair agreement with E(5/4) for B(E2) values but not for all energies. The IBFA shows better agreement with data than E(5/4) and the Shell model shows the best agreement.

  11. Accidental degeneracies in nonlinear quantum deformed systems

    NASA Astrophysics Data System (ADS)

    Aleixo, A. N. F.; Balantekin, A. B.

    2011-09-01

    We construct a multi-parameter nonlinear deformed algebra for quantum confined systems that includes many other deformed models as particular cases. We demonstrate that such systems exhibit the property of accidental pairwise energy level degeneracies. We also study, as a special case of our multi-parameter deformation formalism, the extension of the Tamm-Dancoff cutoff deformed oscillator and the occurrence of accidental pairwise degeneracy in the energy levels of the deformed system. As an application, we discuss the case of a trigonometric Rosen-Morse potential, which is successfully used in models for quantum confined systems, ranging from electrons in quantum dots to quarks in hadrons.

  12. Approximate symmetries of Hamiltonians

    NASA Astrophysics Data System (ADS)

    Chubb, Christopher T.; Flammia, Steven T.

    2017-08-01

    We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

  13. Classification of (2+1)-dimensional topological order and symmetry-protected topological order for bosonic and fermionic systems with on-site symmetries

    NASA Astrophysics Data System (ADS)

    Lan, Tian; Kong, Liang; Wen, Xiao-Gang

    2017-06-01

    In 2+1-dimensional space-time, gapped quantum states are always gapped quantum liquids (GQL) which include both topologically ordered states (with long range entanglement) and symmetry protected topological (SPT) states (with short range entanglement). In this paper, we propose a classification of 2+1D GQLs for both bosonic and fermionic systems: 2+1D bosonic/fermionic GQLs with finite on-site symmetry are classified by nondegenerate unitary braided fusion categories over a symmetric fusion category (SFC) E , abbreviated as UMTC/E, together with their modular extensions and total chiral central charges. In our classification, SFC E describes the symmetry, which is Rep(G ) for bosonic symmetry G , or sRep(Gf) for fermionic symmetry Gf. As a special case of the above result, we find that the modular extensions of Rep(G ) classify the 2+1D bosonic SPT states of symmetry G , while the c =0 modular extensions of sRep(Gf) classify the 2+1D fermionic SPT states of symmetry Gf. Many fermionic SPT states are studied based on the constructions from free-fermion models. But free-fermion constructions cannot produce all fermionic SPT states. Our classification does not have such a drawback. We show that, for interacting 2+1D fermionic systems, there are exactly 16 superconducting phases with no symmetry and no fractional excitations (up to E8 bosonic quantum Hall states). Also, there are exactly 8 Z2×Z2f -SPT phases, 2 Z8f-SPT phases, and so on. Besides, we show that two topological orders with identical bulk excitations and central charge always differ by the stacking of the SPT states of the same symmetry.

  14. Robust topological degeneracy of classical theories

    NASA Astrophysics Data System (ADS)

    Vaezi, Mohammad-Sadegh; Ortiz, Gerardo; Nussinov, Zohar

    2016-05-01

    We challenge the hypothesis that the ground states of a physical system whose degeneracy depends on topology must necessarily realize topological quantum order and display nonlocal entanglement. To this end, we introduce and study a classical rendition of the Toric Code model embedded on Riemann surfaces of different genus numbers. We find that the minimal ground state degeneracy (and those of all levels) depends on the topology of the embedding surface alone. As the ground states of this classical system may be distinguished by local measurements, a characteristic of Landau orders, this example illustrates that topological degeneracy is not a sufficient condition for topological quantum order. This conclusion is generic and, as shown, it applies to many other models. We also demonstrate that certain lattice realizations of these models, and other theories, display a ground state entropy (and those of all levels) that is "holographic", i.e., extensive in the system boundary. We find that clock and U (1 ) gauge theories display topological (in addition to gauge) degeneracies.

  15. Non-symmorphic band degeneracy at the Fermi level in ZrSiTe

    NASA Astrophysics Data System (ADS)

    Topp, Andreas; Lippmann, Judith M.; Varykhalov, Andrei; Duppel, Viola; Lotsch, Bettina V.; Ast, Christian R.; Schoop, Leslie M.

    2016-12-01

    Non-symmorphic materials have recently been predicted to exhibit many different exotic features in their electronic structures. These originate from forced band degeneracies caused by the non-symmorphic symmetry, which not only creates the possibility to realize Dirac semimetals, but also recently resulted in the prediction of novel quasiparticles beyond the usual Dirac, Weyl or Majorana fermions, which can only exist in the solid state. Experimental realization of non-symmorphic materials that have the Fermi level located at the degenerate point is difficult, however, due to the requirement of an odd band filling. In order to investigate the effect of forced band degeneracies on the transport behavior, a material that has such a degeneracy at or close to the Fermi level is desired. Here, we show with angular resolved photoemission experiments supported by density functional calculations, that ZrSiTe hosts several fourfold degenerate Dirac crossings at the X point, resulting from non-symmorphic symmetry. These crossings form a Dirac line node along XR, which is located almost directly at the Fermi level and shows almost no dispersion in energy. ZrSiTe is thus the first real material that allows for transport measurements investigating Dirac fermions that originate from non-symmorphic symmetry.

  16. Degeneracy Breaking for K2 Microlens Parallaxes

    NASA Astrophysics Data System (ADS)

    Gould, Andrew; Yee, Jennifer; Carey, Sean

    2015-10-01

    By adding Spitzer observations to microlensing targets being observed from Kepler and Earth, we will create the first interplanetary network of microlensing observatories. This 3-observatory configuration has the unique potential to break the famous 4-fold degeneracy for space-based microlensing parallaxes. This is crucial both for the interpretation of some individual events and to rigorously validate the statistical methods that are used when (as is usually the case) this special 3-observatory configuration is not possible. The Kepler K2 C9 microlensing campaign will monitor about 4 square degrees of the Bulge from 6 Apr to 29 Jun, with the aim of measuring microlens parallaxes. Spitzer can observe this K2 field from 18 Jun to 26 Jul. The 11-day overlap between the two campaigns will allow us to break the 4-fold degeneracy of about 50 microlensing events. Some of these events will be well-covered over the peak from K2, with Spitzer observations of the falling wing providing the necessary information to break the degeneracy in the K2-Earth parallax. Others will be the reverse, with K2 observations of the rising event breaking the degeneracy in Spitzer-Earth parallaxes (i.e., for events peaking during the Spitzer campaign). Breaking this degeneracy leads to a definitive measurement of the magnitude of the microlens parallax vector, which will enable measurements of the masses and distances of the lens systems, including events with planets that contribute to the ~12 needed to make a first measurement of the Galactic distribution of planets, binaries, and many single-lens events, some of which could be black holes, brown dwarfs, or other interesting objects. The distance distribution of the ensemble of lenses can serve as a probe of Galactic structure. All lightcurves will be reduced using our customized software and then made public (for unrestricted use), within two months of the completion of observations (as we did for our 2015 observations).

  17. On dark degeneracy and interacting models

    SciTech Connect

    Carneiro, S.; Borges, H.A. E-mail: humberto@ufba.br

    2014-06-01

    Cosmological background observations cannot fix the dark energy equation of state, which is related to a degeneracy in the definition of the dark sector components. Here we show that this degeneracy can be broken at perturbation level by imposing two observational properties on dark matter. First, dark matter is defined as the clustering component we observe in large scale structures. This definition is meaningful only if dark energy is unperturbed, which is achieved if we additionally assume, as a second condition, that dark matter is cold, i.e. non-relativistic. As a consequence, dark energy models with equation-of-state parameter −1 ≤ ω < 0 are reduced to two observationally distinguishable classes with ω = −1, equally competitive when tested against observations. The first comprises the ΛCDM model with constant dark energy density. The second consists of interacting models with an energy flux from dark energy to dark matter.

  18. Scalar non-degeneracy and flavor unification

    SciTech Connect

    Kojima, Kentaro

    2008-05-13

    Grand unified models of the strong and electroweak forces generally predict some types of flavor unification. The flavor structure in unified theory is probed with superparticle mass spectrum observed in future particle experiments. It is shown that the generation dependence of sfermion mass non-degeneracy provides direct imprints of unification of the standard model matter multiplets. The implication from flavor-violating rare process is also discussed.

  19. The degeneracy of the free Dirac equation

    SciTech Connect

    Gupta, V. . School of Physics Tata Inst. of Fundamental Research, Bombay ); McKellar, B.H.J. . School of Physics); Wu, D.D. . School of Physics Institute of High Energy Physics, Beijing, BJ . Electron LINAC Dept. General Atomics, San Diego, CA )

    1991-08-01

    Parity-mixed solutions of the free Dirac equation with the same 4-momentum are considered. The first-order EM energy has an electric dipole moment term whose value depends on the mixing angle. Further implications of this degeneracy to perturbative calculations are discussed. It is argued that the properties of the Dirac equation with the Coulomb potential can be used to decide the mixing angle, which should be zero.

  20. Contact degeneracies of closed 2-forms

    SciTech Connect

    Zot'ev, Dmitrii B

    2007-04-30

    Consider a closed 2-form that is degenerate at the points of a hypersurface and is non-degenerate outside it. In the neighbourhood of a singularity (which is called contact under certain natural conditions) the limit behaviour of Hamiltonian fields is investigated and a canonical form of the 2-form is found (Darboux's theorem). Connections with regular Lie structures are established. Properties of integrable structures on Liouville tori containing contact degeneracies are studied. Bibliography: 16 titles.

  1. Dark degeneracy and interacting cosmic components

    SciTech Connect

    Aviles, Alejandro; Cervantes-Cota, Jorge L.

    2011-10-15

    We study some properties of the dark degeneracy, which is the fact that what we measure in gravitational experiments is the energy-momentum tensor of the total dark sector, and any split into components (as in dark matter and dark energy) is arbitrary. In fact, just one dark fluid is necessary to obtain exactly the same cosmological and astrophysical phenomenology as the {Lambda}CDM model. We work explicitly the first-order perturbation theory and show that beyond the linear order the dark degeneracy is preserved under some general assumptions. Then we construct the dark fluid from a collection of interacting fluids. Finally, we try to break the degeneracy with a general class of couplings to baryonic matter. Nonetheless, we show that these interactions can also be understood in the context of the {Lambda}CDM model as between dark matter and baryons. For this last investigation we choose two independent parametrizations for the interactions, one inspired by electromagnetism and the other by chameleon theories. Then, we constrain them with a joint analysis of CMB and supernovae observational data.

  2. Hidden in plain view: degeneracy in complex systems.

    PubMed

    Mason, P H; Domínguez D, J F; Winter, B; Grignolio, A

    2015-02-01

    Degeneracy is a word with two meanings. The popular usage of the word denotes deviance and decay. In scientific discourse, degeneracy refers to the idea that different pathways can lead to the same output. In the biological sciences, the concept of degeneracy has been ignored for a few key reasons. Firstly, the word "degenerate" in popular culture has negative, emotionally powerful associations that do not inspire scientists to consider its technical meaning. Secondly, the tendency of searching for single causes of natural and social phenomena means that scientists can overlook the multi-stranded relationships between cause and effect. Thirdly, degeneracy and redundancy are often confused with each other. Degeneracy refers to dissimilar structures that are functionally similar while redundancy refers to identical structures. Degeneracy can give rise to novelty in ways that redundancy cannot. From genetic codes to immunology, vaccinology and brain development, degeneracy is a crucial part of how complex systems maintain their functional integrity. This review article discusses how the scientific concept of degeneracy was imported into genetics from physics and was later introduced to immunology and neuroscience. Using examples of degeneracy in immunology, neuroscience and linguistics, we demonstrate that degeneracy is a useful way of understanding how complex systems function. Reviewing the history and theoretical scope of degeneracy allows its usefulness to be better appreciated, its coherency to be further developed, and its application to be more quickly realized. Crown Copyright © 2014. Published by Elsevier Ireland Ltd. All rights reserved.

  3. Approximate degeneracy of heavy-light mesons with the same L

    NASA Astrophysics Data System (ADS)

    Matsuki, Takayuki; Lü, Qi-Fang; Dong, Yubing; Morii, Toshiyuki

    2016-07-01

    Careful observation of the experimental spectra of heavy-light mesons tells us that heavy-light mesons with the same angular momentum L are almost degenerate. The estimate is given how much this degeneracy is broken in our relativistic potential model, and it is analytically shown that expectation values of a commutator between the lowest order Hamiltonian and L→2 are of the order of 1 /mQ with a heavy quark mass mQ. It turns out that nonrelativistic approximation of heavy quark system has a rotational symmetry and hence degeneracy among states with the same L. This feature can be tested by measuring higher orbitally and radially excited heavy-light meson spectra for D /Ds / B /Bs in LHCb and forthcoming BelleII.

  4. Hidden Degeneracies in Piecewise Smooth Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Jeffrey, Mike R.

    When a flow suffers a discontinuity in its vector field at some switching surface, the flow can cross through or slide along the surface. Sliding along the switching surface can be understood as the flow along an invariant manifold inside a switching layer. It turns out that the usual method for finding sliding modes — the Filippov convex combination or Utkin equivalent control — results in a degeneracy in the switching layer whenever the flow is tangent to the switching surface from both sides. We derive the general result and analyze the simplest case here, where the flow curves parabolically on either side of the switching surface (the so-called fold-fold or two-fold singularities). The result is a set of zeros of the fast switching flow inside the layer, which is structurally unstable to perturbation by terms nonlinear in the switching parameter, terms such as (signx)2 [where the superscript does mean “squared”]. We provide structurally stable forms, and show that in this form the layer system is equivalent to a generic singularity of a two timescale system. Finally we show that the same degeneracy arises when a discontinuity is smoothed using standard regularization methods.

  5. Breaking Degeneracy of Tautomerization-Metastability from Days to Seconds.

    PubMed

    Kügel, Jens; Sixta, Aimee; Böhme, Markus; Krönlein, Andreas; Bode, Matthias

    2016-12-27

    We present a detailed study of the tautomerization, that is, the switching of hydrogen protons, between different sites in the molecular frame of phthalocyanine (H2Pc) on a Ag(111) substrate by means of scanning tunneling microscopy (STM) and STM-based pump-and-sample techniques. Our data reveal that the symmetry mismatch between the substrate and the molecular frame lifts the energetic degeneracy of the two H2Pc tautomers. Their energy difference is so large that only one tautomer can be found in the ground state. Tip-induced tautomerization was triggered at sufficiently high bias voltages. The excited metastable H2Pc tautomer was found to exhibit a lifetime of at least several days, as derived from the fact that the molecule did not change back to the ground state within experimentally accessible time scales as long as noninvasive tunneling parameters were used to probe the state of the molecule. By the controlled removal of a hydrogen proton from the molecule, a four-level system was created. Pump-and-sample experiments reveal that the lifetime of the metastable positions amounts to seconds only. Current- and bias-dependent studies indicate that the presence of the STM tip modifies the potential barrier, thereby allowing for a controlled tuning of the metastable tautomer's lifetime.

  6. Quasi-degenerate neutrinos from an abelian family symmetry

    SciTech Connect

    Binetruy, P. |; Lavignac, S.; Petcov, S. |; Ramond, P.

    1996-12-31

    The authors show that models with an abelian family symmetry which accounts for the observed hierarchies of masses and mixings in the quark sector may also accommodate quasi-degeneracies in the neutrino mass spectrum. Such approximate degeneracies are, in this context, associated with large mixing angles. The parameters of this class of models are constrained. The authors discuss their phenomenological implications for present and foreseen neutrino experiments.

  7. New coupling limits, dynamical symmetries and microscopic operators of IBM/TQM

    NASA Astrophysics Data System (ADS)

    Paar, V.

    1985-01-01

    A new particle-core basis having approximate supersymmetric (SUSY) features associated with SU(3) dynamical symmetry is introduced. The SUSY and CO-SUSY limits of IBFM/PTQM appear for the characteristic intermediate coupling strengths Γ/δ=±(Γ/δ)SUSY. The CO-SUSY limit is a truncated analog of the Stephens rotation-aligned scheme. A paradox was found in the relation of the SUSY and truncated strong coupling (TSC) limits to the strong coupling limit of the Bohr-Mottelson model. Microscopic dyson and Holstein-Primakoff realizations of RPA collective quadrupole phonon operators are explicitly constructed. Employing this mapping procedure in conjunction with the leading RPA diagrams, various operators of IBM/TQM, IBFM/PTQM have been derived in the particle-hole channel: E2 operator, one-particle transfer operator, two-particle transfer operator etc. In addition to the standard terms, this derivation gives in the same diagrammatic order the additional terms also. A new model was introduced for the odd-odd nuclei in the framework of IBM/TQM. For the SU(3) core the truncated analog of Gallagher-Moszkowski bands appears as the approximate SUSY pattern, of the same intrinsic structure as in the odd-even system. The idea of boson-fermion dynamical symmetry and supersymmetry is extended to odd-odd nuclei and hypernuclei.

  8. Defects and degeneracies in supersymmetry protected phases

    NASA Astrophysics Data System (ADS)

    Fokkema, Thessa; Schoutens, Kareljan

    2015-08-01

    We analyse a class of 1D lattice models, known as \\text{M}k models, which are characterised by an order-k clustering of spin-less fermions and by N}=2 lattice supersymmetry. Our main result is the identification of a class of (bulk or edge) defects, that are in one-to-one correspondence with so-called spin fields in a corresponding {Z}k parafermion CFT. In the gapped regime, injecting such defects leads to ground-state degeneracies that are protected by the supersymmetry. The defects, which are closely analogous to quasi-holes over the fermonic Read-Rezayi quantum Hall states, display characteristic fusion rules, which are of Ising type for k = 2 and of Fibonacci type for k = 3.

  9. Neutrino degeneracy and cosmological nucleosynthesis, revisited

    NASA Technical Reports Server (NTRS)

    Olive, K. A.; Schramm, David N.; Thomas, D.; Walker, T. P.

    1991-01-01

    A reexamination of the effects of non-zero degeneracies on Big Bang Nucleosynthesis is made. As previously noted, non-trivial alterations of the standard model conclusions can be induced only if excess lepton numbers L sub i, comparable to photon number densities eta sub tau, are assumed (where eta sub tau is approx. 3 times 10(exp 9) eta sub b). Furthermore, the required lepton number densities (L sub i eta sub tau) must be different for upsilon sub e than for upsilon sub mu and epsilon sub tau. It is shown that this loophole in the standard model of nucleosynthesis is robust and will not vanish as abundance and reaction rate determinations improve. However, it is also argued that theoretically (L sub e) approx. (L sub mu) approx. (L sub tau) approx. eta sub b is much less than eta sub tau which would preclude this loophole in standard unified models.

  10. Interface gapless states from interfacial symmetries

    NASA Astrophysics Data System (ADS)

    Takahashi, Ryuji; Murakami, Shuichi

    2015-03-01

    Previously we have shown that at an interface between two topological insulators with opposite Dirac velocities, gapless interface states protected by mirror symmetry appear. We can calculate the interface dispersion using the Fu-Kane-Mele (FKM) tight-binding model, and it typically consists of Dirac cones. In this presentation, we report another kind of interface metallic states; the Fermi surface forms loops (``Fermi loop''), rather than isolated Dirac points, sometimes seen in the interface of the FKM models. Such a degeneracy along a loop is unexpected. This Fermi loop appears when the whole junction system preserves particle-hole symmetry, while each system breaks particle-hole symmetry. We call this symmetry ``interfacial particle-hole symmetry'' (IPHS). We discuss the IPHS in general systems and show that the Fermi loop results from a sign change of a Pfaffian of some matrix, defined only in junctions with IPHS symmetry.

  11. Breaking a dark degeneracy with gravitational waves

    SciTech Connect

    Lombriser, Lucas; Taylor, Andy E-mail: ant@roe.ac.uk

    2016-03-01

    We identify a scalar-tensor model embedded in the Horndeski action whose cosmological background and linear scalar fluctuations are degenerate with the concordance cosmology. The model admits a self-accelerated background expansion at late times that is stable against perturbations with a sound speed attributed to the new field that is equal to the speed of light. While degenerate in scalar fluctuations, self-acceleration of the model implies a present cosmological tensor mode propagation at ∼<95 % of the speed of light with a damping of the wave amplitude that is ∼>5 % less efficient than in general relativity. We show that these discrepancies are endemic to self-accelerated Horndeski theories with degenerate large-scale structure and are tested with measurements of gravitational waves emitted by events at cosmological distances. Hence, gravitational-wave cosmology breaks the dark degeneracy in observations of the large-scale structure between two fundamentally different explanations of cosmic acceleration—a cosmological constant and a scalar-tensor modification of gravity. The gravitational wave event GW150914 recently detected with the aLIGO instruments and its potential association with a weak short gamma-ray burst observed with the Fermi GBM experiment may have provided this crucial measurement.

  12. Measures of degeneracy and redundancy in biological networks

    PubMed Central

    Tononi, Giulio; Sporns, Olaf; Edelman, Gerald M.

    1999-01-01

    Degeneracy, the ability of elements that are structurally different to perform the same function, is a prominent property of many biological systems ranging from genes to neural networks to evolution itself. Because structurally different elements may produce different outputs in different contexts, degeneracy should be distinguished from redundancy, which occurs when the same function is performed by identical elements. However, because of ambiguities in the distinction between structure and function and because of the lack of a theoretical treatment, these two notions often are conflated. By using information theoretical concepts, we develop here functional measures of the degeneracy and redundancy of a system with respect to a set of outputs. These measures help to distinguish the concept of degeneracy from that of redundancy and make it operationally useful. Through computer simulations of neural systems differing in connectivity, we show that degeneracy is low both for systems in which each element affects the output independently and for redundant systems in which many elements can affect the output in a similar way but do not have independent effects. By contrast, degeneracy is high for systems in which many different elements can affect the output in a similar way and at the same time can have independent effects. We demonstrate that networks that have been selected for degeneracy have high values of complexity, a measure of the average mutual information between the subsets of a system. These measures promise to be useful in characterizing and understanding the functional robustness and adaptability of biological networks. PMID:10077671

  13. Symmetry impedes symmetry discrimination.

    PubMed

    Tjan, Bosco S; Liu, Zili

    2005-12-16

    Objects in the world, natural and artificial alike, are often bilaterally symmetric. The visual system is likely to take advantage of this regularity to encode shapes for efficient object recognition. The nature of encoding a symmetric shape, and of encoding any departure from it, is therefore an important matter in visual perception. We addressed this issue of shape encoding empirically, noting that a particular encoding scheme necessarily leads to a specific profile of sensitivity in perceptual discriminations. We studied symmetry discrimination using human faces and random dots. Each face stimulus was a frontal view of a three-dimensional (3-D) face model. The 3-D face model was a linearly weighted average (a morph) between the model of an original face and that of the corresponding mirror face. Using this morphing technique to vary the degree of asymmetry, we found that, for faces and analogously generated random-dot patterns alike, symmetry discrimination was worst when the stimuli were nearly symmetric, in apparent opposition to almost all studies in the literature. We analyzed the previous work and reconciled the old and new results using a generic model with a simple nonlinearity. By defining asymmetry as the minimal difference between the left and right halves of an object, we found that the visual system was disproportionately more sensitive to larger departures from symmetry than to smaller ones. We further demonstrated that our empirical and modeling results were consistent with Weber-Fechner's and Stevens's laws.

  14. Generalized mass ordering degeneracy in neutrino oscillation experiments

    SciTech Connect

    Coloma, Pilar; Schwetz, Thomas

    2016-09-07

    Here, we consider the impact of neutral-current (NC) nonstandard neutrino interactions (NSI) on the determination of the neutrino mass ordering. We show that in the presence of NSI there is an exact degeneracy which makes it impossible to determine the neutrino mass ordering and the octant of the solar mixing angle θ12 at oscillation experiments. The degeneracy holds at the probability level and for arbitrary matter density profiles, and hence solar, atmospheric, reactor, and accelerator neutrino experiments are affected simultaneously. The degeneracy requires order-1 corrections from NSI to the NC electron neutrino-quark interaction and can be tested in electron neutrino NC scattering experiments.

  15. Generalized mass ordering degeneracy in neutrino oscillation experiments

    SciTech Connect

    Coloma, Pilar; Schwetz, Thomas

    2016-09-07

    Here, we consider the impact of neutral-current (NC) nonstandard neutrino interactions (NSI) on the determination of the neutrino mass ordering. We show that in the presence of NSI there is an exact degeneracy which makes it impossible to determine the neutrino mass ordering and the octant of the solar mixing angle θ12 at oscillation experiments. The degeneracy holds at the probability level and for arbitrary matter density profiles, and hence solar, atmospheric, reactor, and accelerator neutrino experiments are affected simultaneously. The degeneracy requires order-1 corrections from NSI to the NC electron neutrino-quark interaction and can be tested in electron neutrino NC scattering experiments.

  16. Generalized mass ordering degeneracy in neutrino oscillation experiments

    NASA Astrophysics Data System (ADS)

    Coloma, Pilar; Schwetz, Thomas

    2016-09-01

    We consider the impact of neutral-current (NC) nonstandard neutrino interactions (NSI) on the determination of the neutrino mass ordering. We show that in the presence of NSI there is an exact degeneracy which makes it impossible to determine the neutrino mass ordering and the octant of the solar mixing angle θ12 at oscillation experiments. The degeneracy holds at the probability level and for arbitrary matter density profiles, and hence solar, atmospheric, reactor, and accelerator neutrino experiments are affected simultaneously. The degeneracy requires order-1 corrections from NSI to the NC electron neutrino-quark interaction and can be tested in electron neutrino NC scattering experiments.

  17. Analysis and resolution of the ground-state degeneracy of the two-component Bose-Hubbard model.

    PubMed

    Wang, Wei; Penna, Vittorio; Capogrosso-Sansone, Barbara

    2014-08-01

    We study the degeneracy of the ground-state energy E of the two-component Bose-Hubbard model and of the perturbative correction E(1). We show that the degeneracy properties of E and E(1) are closely related to the connectivity properties of the lattice. We determine general conditions under which E is nondegenerate. This analysis is then extended to investigate the degeneracy of E(1). In this case, in addition to the lattice structure, the degeneracy also depends on the number of particles present in the system. After identifying the cases in which E(1) is degenerate and observing that the standard (degenerate) perturbation theory is not applicable, we develop a method to determine the zeroth-order correction to the ground state by exploiting the symmetry properties of the lattice. This method is used to implement the perturbative approach to the two-component Bose-Hubbard model in the case of degenerate E(1) and is expected to be a valid tool to perturbatively study the asymmetric character of the Mott insulator to superfluid transition between the particle and hole side.

  18. Photorefractive optical fuzzy-logic processor based on grating degeneracy

    NASA Astrophysics Data System (ADS)

    Wu, Weishu; Yang, Changxi; Campbell, Scott; Yeh, Pochi

    1995-04-01

    A novel optical fuzzy-logic processor using light-induced gratings in photorefractive crystals is proposed and demonstrated. By exploiting grating degeneracy, one can easily implement parallel fuzzy-logic functions in disjunctive normal form.

  19. Tuning Spin- and Valley-Degeneracies in Multicomponent Quantum Well Transport

    NASA Astrophysics Data System (ADS)

    Prabhu-Gaunkar, Sunanda

    degeneracies can be tuned with structural parameters such as growth orientation, QW width and additional confinement such as gating along specific directions. We detail a theory to calculate the ground energy of each valley in a multi-valley system, considering the influence of growth orientation, quantum confinement and miscut angles on valley degeneracies. We first study AlAs QWs grown along the high mobility (001) facet, which has two degenerate valleys. Since valley mass is anisotropic along different directions we can perform transport experiments with orientation sensitivity on specific sample geometries which permit us to distinguish between the valleys. The mass anisotropy also gives rise to anisotropy in valley resistance, and we measure the valley anisotropy ratio at various half-filling factors. The measurement of this resistance anisotropy ratio at half-filled Landau levels is the first evidence of valley ordering of Landau levels. We also study AlAs QW grown along the lower mobility and lesser studied (111) facet with three degenerate valleys. Though they have not yet been experimentally demonstrated, on-axis AlAs (111) valleys would exhibit an SU(3)-like symmetry which is of interest due to the novelty of valley texture excitations which might arise. A small miscut angle to the principle growth axis allows us to grow defect-free (111) AlAs QWs but also breaks the degeneracy. We optimize the growth with AFM, TEM and XRD morphology characterization of the GaAs, AlGaAs and AlAs layers individually and in combination on (111) GaAs substrate. We show with numerical simulations that careful selection of miscut angle with respect to the valley orientation can exactly determine the valley degeneracy breaking in this SU(3)-like system. Furthermore, the valley degeneracies that we observe with transport characterization match with the numerical simulations. By choosing current to flow along the three valley orientations, and measuring the longitudinal resistance we can

  20. The degeneracy problem in non-canonical inflation

    SciTech Connect

    Easson, Damien A.; Powell, Brian A. E-mail: brian.powell007@gmail.com

    2013-03-01

    While attempting to connect inflationary theories to observational physics, a potential difficulty is the degeneracy problem: a single set of observables maps to a range of different inflaton potentials. Two important classes of models affected by the degeneracy problem are canonical and non-canonical models, the latter marked by the presence of a non-standard kinetic term that generates observables beyond the scalar and tensor two-point functions on CMB scales. The degeneracy problem is manifest when these distinguishing observables go undetected. We quantify the size of the resulting degeneracy in this case by studying the most well-motivated non-canonical theory having Dirac-Born-Infeld Lagrangian. Beyond the scalar and tensor two-point functions on CMB scales, we then consider the possible detection of equilateral non-Gaussianity at Planck-precision and a measurement of primordial gravitational waves from prospective space-based laser interferometers. The former detection breaks the degeneracy with canonical inflation but results in poor reconstruction prospects, while the latter measurement enables a determination of n{sub T} which, while not breaking the degeneracy, can be shown to greatly improve the non-canonical reconstruction.

  1. Massive Degeneracy and Goldstone Bosons: A Challenge for the Light Cone

    SciTech Connect

    Weinstein, Marvin; /SLAC

    2010-10-27

    Wherein it is argued that the light front formalism has problems dealing with Goldstone symmetries. It is further argued that the notion that in hadron condensates can explain Goldstone phenomena is false. This talk can be summarized as follows: (1) Exact symmetries can be realized in Wigner or Goldstone mode. (2) When a symmetry is realized in Wigner mode the states of the theory form degenerate irreducible representations of the symmetry group and the lowest energy state is unique. (3) When a symmetry is realized in Goldstone mode the lowest energy state of the theory is infinitely degenerate, the states of the theory do not form irreducible representations of the symmetry group and there are massless particles coupled by the conserved currents to any one of the possible ground states. (4) In finite volume the signal of a Goldstone realization of a symmetry is that the number of nearly degenerate states grows rapidly with increasing volume and the gap between these states shrinks exponentially with the volume. (5) The existence of a condensate such as the magnetization, for a ferromagnet, or the staggered magnetization for an anti-ferromagnet, signals a Goldstone symmetry. This is because this condensate transforms non-trivially under the symmetry transformations and so its existence implies the ground state isn't unique. (6) PCAC means that the pion, kaon and eta are would be Goldstone bosons of the theory where the quark masses are set to zero. This interpretation is overwhelmingly supported by experimental data. This means that these particles are really the wiggling of the order parameter or condensate. (7) Finally, in order for the Goldstone particle to exist there has to be something to wiggle every place where the particle can exist. This means that the condensate that is the order parameter for this Goldstone symmetry cannot be confined to the interior of hadrons. Thus, to reiterate, the challenge for the Light Front is to show how the formalism gives

  2. Ubiquitous symmetries

    NASA Astrophysics Data System (ADS)

    Nucci, M. C.

    2016-09-01

    We review some of our recent work devoted to the problem of quantization with preservation of Noether symmetries, finding hidden linearity in superintegrable systems, and showing that nonlocal symmetries are in fact local. In particular, we derive the Schrödinger equation for the isochronous Calogero goldfish model using its relation to Darwin equation. We prove the linearity of a classical superintegrable system on a plane of nonconstant curvature. We find the Lie point symmetries that correspond to the nonlocal symmetries (also reinterpreted as λ-symmetries) of the Riccati chain.

  3. On the Parity Degeneracy of Baryons

    NASA Astrophysics Data System (ADS)

    Kirchbach, M.

    The gross features of the observed baryon excitation spectrum below 2 GeV are well explained if the spectrum generating algebra of its intrinsic orbital angular momentum states is o(4) ⊗ su(2)I. The spins of the resonances are obtained through the coupling of a Lorentz bi-spinor {1/2,0} ⊕ {0,1/2} to a multiplet of the type {j,j} in its O(4)/O(3) reduction. The parities of the resonances follow from those of the O(3) members of the {j,j} multiplets. In this way relativistic SL(2,C) representations are constructed. For example, the first S11, P11, and D13 states with masses around 1500 MeV fit into the {1/2,1/2} ⊗ [{1/2,0} ⊕ {0,1/2}] representation. The observed parities of the resonances correspond to natural parities of the {1/2,1/2} states. The second P11, S11, D13 — together with the first P13, F15, D15, and (a predicted) F17-resonances, centered around 1700 MeV, are organized into the {3/2,3/2} ⊗ [{1/2,0} ⊕ {0,1/2}] representation. We argue that the members of the {3/2,3/2} multiplet carry unnatural parities and that in this region chiral symmetry is restored. In the N(939)→ N(1650) transition the chiral symmetry mode is changed, and therefore, a chiral phase transition is predicted to take place.

  4. Symmetry breaking around a wormhole

    NASA Astrophysics Data System (ADS)

    Choudhury, A. L.

    1996-11-01

    We have modified the extended version Coule and Maeda's version (D. H. Coule and Kei-ichi Maeda, Class.Quant.Grav.7,995(1990)) of the Gidding-Strominger model (S. B. Giddings and A. Strominger, Nucl.Phys. B307, 854(l988)) of the euclidean gravitational field interacting with axion. The new model has R-symmetry in contrast to the previous model. At the lowest perturbation case the model retains a wormhole solution. We assume that the scalar expands adiabatically and satisfies ideal gas law in a crude first approximation. Under the Higg's mechanism the symmetry can be broken at the tree approximation. This mechanism, we hope, can be used to introduce the degeneracy of quark masses.

  5. Symmetry algebra of a generalized anisotropic harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Castanos, O.; Lopez-Pena, R.

    1993-01-01

    It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.

  6. Exceptional points and symmetry recovery in a two-state system

    NASA Astrophysics Data System (ADS)

    Zhang, Xu-Lin; Wang, Shubo; Chen, Wen-Jie; Chan, C. T.

    2017-08-01

    We consider a two-state system consisting of a pair of coupled ferromagnetic waveguides. A monotonically increasing bias magnetic field can dynamically manipulate the system to enter a PT -symmetry-broken phase and then reenter a symmetric phase. The symmetry recovery is enabled by the presence of accidental degeneracy points when the system has no loss and each degeneracy point can spawn a pair of exceptional points when asymmetric loss is introduced. We performed microwave experiments to demonstrate the presence of the exceptional point and symmetry recovery.

  7. New Evidence for Neutrino Degeneracy in the Early Universe

    NASA Astrophysics Data System (ADS)

    Mathews, G.; Kajino, T.; Orito, M.

    2000-12-01

    We reanalyze cosmological constraints on the existence of a net universal lepton asymmetry and neutrino degeneracy in light of reanalyzed primordial nucleosynthesis and the recently reported CMB power spectra from BOOMERANG and MAXIMA-1. We explore physically plausible lepton-asymmetric models with large ν μ and ν τ degeneracies together with a moderate ν e degeneracy. We show that primordial nucleosynthesis by itself permits very large neutrino degeneracies 0. <= ξν_μ, ξν_τ <= 40, 0. <= ξνe <= 1.4 together with large baryon densities 0.1 <= Ω b h250 <= 1 as long as some destruction of primordial lithium is assumed. We also show that structure formation and the power spectrum of the cosmic microwave background allows for the possibility of an Ω = 1, Ω Λ = 0.4, cosmological model for which there is both significant lepton asymetry (| ξν_μ | = | ξν_τ | ≈ 11) and a relatively large baryon density (Ω b ≈ 0.06). The best neutrino asymmetric models naturally accommodate the observed suppression of the second acoustic peak in the CMB spectrum. Goodness of fit contours show a well developed minimum with degeneracy parameter ξ ν μ = ξ ν τ ≈ 2, ξ ν e ≈ 0.1, and Ω b h502 ≈ 0.1 for a broad range of cosmological parameters.

  8. Analytical study of mode degeneracy in non-Hermitian photonic crystals with TM-like polarization

    NASA Astrophysics Data System (ADS)

    Yin, Xuefan; Liang, Yong; Ni, Liangfu; Wang, Zhixin; Peng, Chao; Li, Zhengbin

    2017-08-01

    We present a study of the mode degeneracy in non-Hermitian photonic crystals (PC) with TM-like polarization and C4 v symmetry from the perspective of the coupled-wave theory (CWT). The CWT framework is extended to include TE-TM coupling terms which are critical for modeling the accidental triple degeneracy within non-Hermitian PC systems. We derive the analytical form of the wave function and the condition of Dirac-like-cone dispersion when radiation loss is relatively small. We find that, similar to a real Dirac cone, the Dirac-like cone in non-Hermitian PCs possesses good linearity and isotropy, even with a ring of exceptional points (EPs) inevitably existing in the vicinity of the second-order Γ point. However, the Berry phase remains zero at the Γ point, indicating the cone does not obey the Dirac equation and is only a Dirac-like cone. The topological modal interchange phenomenon and nonzero Berry phase of the EPs are also discussed.

  9. Translational Symmetry and Microscopic Constraints on Symmetry-Enriched Topological Phases: A View from the Surface

    NASA Astrophysics Data System (ADS)

    Cheng, Meng; Zaletel, Michael; Barkeshli, Maissam; Vishwanath, Ashvin; Bonderson, Parsa

    2016-10-01

    The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and a remarkably similar set of constraints at the surface of a 3D interacting topological insulator. This, combined with recent work on symmetry-enriched topological phases with on-site unitary symmetries, enables us to develop a framework for understanding the structure of symmetry-enriched topological phases with both translational and on-site unitary symmetries, including the effective theory of symmetry defects. This framework places stringent constraints on the possible types of symmetry fractionalization that can occur in 2D systems whose unit cell contains fractional spin, fractional charge, or a projective representation of the symmetry group. As a concrete application, we determine when a topological phase must possess a "spinon" excitation, even in cases when spin rotational invariance is broken down to a discrete subgroup by the crystal structure. We also describe the phenomena of "anyonic spin-orbit coupling," which may arise from the interplay of translational and on-site symmetries. These include the possibility of on-site symmetry defect branch lines carrying topological charge per unit length and lattice dislocations inducing degeneracies protected by on-site symmetry.

  10. Fundamental frequency degeneracy of standing surface acoustic waves under metallic gratings on piezoelectric substrates

    NASA Astrophysics Data System (ADS)

    Darinskii, A. N.; Biryukov, S. V.; Weihnacht, M.

    2002-11-01

    The paper studies specific features of surface acoustic waves on piezoelectric substrates under infinite periodic grating arrays. The grating is made up of identical metallic electrodes of finite thickness and has one electrode per cell. It has been shown via the analysis of numerical algorithms and the coupling-of-modes equations that one of the fundamental frequencies of the standing wave under short-circuited grating necessarily coincides with one of the fundamental frequencies corresponding to the open-circuited grating if the substrate assumes particular orientations connected with its crystallographic symmetry. The existence of degeneracy does not depend on the material constants of the substrate and the electrode, the thickness of the electrode, and the specific electrode shape provided that the electrode is uniform along the wave normal and shaped symmetrically in the same direction. The proof applies both to ordinary and leaky surface waves. copyright 2002 Acoustical Society of America.

  11. Generalized mass ordering degeneracy in neutrino oscillation experiments

    DOE PAGES

    Coloma, Pilar; Schwetz, Thomas

    2016-09-07

    Here, we consider the impact of neutral-current (NC) nonstandard neutrino interactions (NSI) on the determination of the neutrino mass ordering. We show that in the presence of NSI there is an exact degeneracy which makes it impossible to determine the neutrino mass ordering and the octant of the solar mixing angle θ12 at oscillation experiments. The degeneracy holds at the probability level and for arbitrary matter density profiles, and hence solar, atmospheric, reactor, and accelerator neutrino experiments are affected simultaneously. The degeneracy requires order-1 corrections from NSI to the NC electron neutrino-quark interaction and can be tested in electron neutrinomore » NC scattering experiments.« less

  12. Robust Topological and Holographic Degeneracies of Classical Systems

    NASA Astrophysics Data System (ADS)

    Vaezi, Seyyed Mohammad Sadegh; Nussinov, Zohar; Ortiz, Gerardo

    We challenge the hypothesis that the ground states of a physical system whose degeneracy depends on topology must necessarily realize topological quantum order and display non-local entanglement. To this end, we introduce and study a classical rendition of the Toric Code model embedded on Riemann surfaces of different genus numbers. We find that the minimal ground state degeneracy (and those of all levels) depends on the topology of the embedding surface alone. As the ground states of this classical system may be distinguished by local measurements, a characteristic of Landau orders, this example illustrates that topological degeneracy is not a sufficient condition for topological quantum order. This conclusion is generic and, as shown, it applies to many other models. We also demonstrate that in certain lattice realizations of these models, and other theories, one can find a ground state entropy that is ''holographic'', i.e., extensive in the system's boundary.

  13. Dicyclic horizontal symmetries

    NASA Astrophysics Data System (ADS)

    Kong, Otto Cho Wing

    In the very successful standard theory of particle physics, the occurrence of repeated quark and lepton flavors, and especially their peculiar mass spectrum, can be accommodated parametrically but is largely unexplained. The present dissertation is an investigation into dicyclic horizontal symmetries as a theory addressing this elusive problem of flavor, as well as some other related issues in particle physics. A horizontal symmetry is a supplement to the perspective based on the experimentally well-established standard model, and its (supersymmetric) unification theories. Dicyclic groups are a special class of discrete non- abelian groups. The most pressing part of the flavor problem in the standard model is the existence of three families of (fermionic) matter and the unnaturally large hierarchy among the parameters describing their masses and mixing. In particular, the top quark is singled out as the only fermion having a natural mass at electroweak breaking scale. While bottom and tau masses may be suppressed by the Higgs vacuum expectation value, the small masses of the other two families beg an explanation. The supersymmetric counterpart of the problem is the need for a high degree of degeneracy especially among the squarks of the lighter two families. We first analyze the phenomenologically-viable quark and squark mass matrix textures using a simple algebraic method, paying particular attention to a 2 + 1 family structure. These serve as inputs for our model building exercises. We next illustrate how the various theoretical and phenomenological constraints single out a gauged dicyclic group as the most appealing candidate for a horizontal symmetry and discuss systematically our major model building strategies. A few models obtained along this line are then presented. These include a supersymmetric SU(5) /otimes Q12 /otimes U(1) model that successfully produces a phenomenologically-viable mass matrix texture pattern for the quarks and squarks.

  14. Boson-fermion confusion: the string path to supersymmetry

    NASA Astrophysics Data System (ADS)

    Ramond, P.

    Reminiscences on the String origins of Supersymmetry are followed by a discussion of the importance of confusing bosons with fermions in building superstring theories in 9 + 1 dimensions. In eleven dimensions, the kinship between bosons and fermions is more subtle, and may involve the exceptional group F4.

  15. Ultracold superstrings in atomic boson-fermion mixtures.

    PubMed

    Snoek, Michiel; Haque, Masudul; Vandoren, S; Stoof, H T C

    2005-12-16

    We propose a setup with ultracold atomic gases that can be used to make a nonrelativistic superstring in four spacetime dimensions. In particular, we consider for the creation of the superstring a fermionic atomic gas that is trapped in the core of a vortex in a Bose-Einstein condensate. We explain the required tuning of experimental parameters to achieve supersymmetry between the fermionic atoms and the bosonic modes describing the oscillations in the vortex position. Furthermore, we discuss the experimental consequences of supersymmetry.

  16. Ultracold Superstrings in Atomic Boson-Fermion Mixtures

    SciTech Connect

    Snoek, Michiel; Haque, Masudul; Vandoren, S.; Stoof, H.T.C.

    2005-12-16

    We propose a setup with ultracold atomic gases that can be used to make a nonrelativistic superstring in four spacetime dimensions. In particular, we consider for the creation of the superstring a fermionic atomic gas that is trapped in the core of a vortex in a Bose-Einstein condensate. We explain the required tuning of experimental parameters to achieve supersymmetry between the fermionic atoms and the bosonic modes describing the oscillations in the vortex position. Furthermore, we discuss the experimental consequences of supersymmetry.

  17. Vacuum degeneracy in massive gravity: Multiplicity of fundamental scales

    NASA Astrophysics Data System (ADS)

    Arraut, Ivan; Chelabi, Kaddour

    2017-07-01

    The presence of Nambu-Goldstone bosons introduce a natural degeneracy inside the vacuum solutions of the nonlinear formulations of massive gravity in the same spirit of the σ-models. When the gravitational effects are taken into account, and the observers are located at any distance with respect to the source, this degeneracy corresponds to a multiplicity (flow) of the fundamental scales of the theory. The different values of the fundamental scales are connected to each other through the broken generators of the theory.

  18. Age-Metallicity Degeneracy at mid-UV Wavelengths

    NASA Astrophysics Data System (ADS)

    Bertone, E.; Chavez, M.; Buzzoni, A.

    2009-11-01

    The so-called age-metallicity degeneracy, which affects the optical spectral properties of stellar populations, is also present at mid-ultraviolet wavelengths. We give here the results for two reference objects: the Sun (assumed as representative of the turnoff star of a single stellar population) and M 32. Within a theoretical framework, we have explored the properties of the age-metallicity degeneracy by means of 17 spectroscopic indices from 2100 to 3100 Å: our preliminary results show a metallicity sensitivity parameter value of 1.7±1.2, which is compatible with the Worthey's value of 3/2 in the optical interval.

  19. Symmetry matters.

    PubMed

    Moubayidin, Laila; Østergaard, Lars

    2015-09-01

    985 I. 985 II. 986 III. 987 IV. 988 V. 989 989 References 989 SUMMARY: The development of multicellular organisms depends on correct establishment of symmetry both at the whole-body scale and within individual tissues and organs. Setting up planes of symmetry must rely on communication between cells that are located at a distance from each other within the organism, presumably via mobile morphogenic signals. Although symmetry in nature has fascinated scientists for centuries, it is only now that molecular data to unravel mechanisms of symmetry establishment are beginning to emerge. As an example we describe the genetic and hormonal interactions leading to an unusual bilateral-to-radial symmetry transition of an organ in order to promote reproduction.

  20. The simplicity of perfect atoms: Degeneracies in supersymmetric hydrogen

    SciTech Connect

    Rube, Tomas; Wacker, Jay G.

    2011-06-15

    Supersymmetric QED hydrogen-like bound states are remarkably similar to nonsupersymmetric hydrogen, including an accidental degeneracy of the fine structure and is broken by the Lamb shift. This article classifies the states, calculates the leading order spectrum, and illustrates the results in several limits. The relation to other nonrelativistic bound states is explored.

  1. The simplicity of perfect atoms: Degeneracies in supersymmetric hydrogen

    DOE PAGES

    Rube, Tomas; Wacker, Jay G.

    2011-06-07

    In this study, supersymmetric QED hydrogen-like bound states are remarkably similar to nonsupersymmetric hydrogen, including an accidental degeneracy of the fine structure and is broken by the Lamb shift. This article classifies the states, calculates the leading order spectrum, and illustrates the results in several limits. The relation to other nonrelativistic bound states is explored.

  2. Degeneracy of energy levels of pseudo-Gaussian oscillators

    SciTech Connect

    Iacob, Theodor-Felix; Iacob, Felix; Lute, Marina

    2015-12-07

    We study the main features of the isotropic radial pseudo-Gaussian oscillators spectral properties. This study is made upon the energy levels degeneracy with respect to orbital angular momentum quantum number. In a previous work [6] we have shown that the pseudo-Gaussian oscillators belong to the class of quasi-exactly solvable models and an exact solution has been found.

  3. Quantification of degeneracy in Hodgkin-Huxley neurons on Newman-Watts small world network.

    PubMed

    Man, Menghua; Zhang, Ya; Ma, Guilei; Friston, Karl; Liu, Shanghe

    2016-08-07

    Degeneracy is a fundamental source of biological robustness, complexity and evolvability in many biological systems. However, degeneracy is often confused with redundancy. Furthermore, the quantification of degeneracy has not been addressed for realistic neuronal networks. The objective of this paper is to characterize degeneracy in neuronal network models via quantitative mathematic measures. Firstly, we establish Hodgkin-Huxley neuronal networks with Newman-Watts small world network architectures. Secondly, in order to calculate the degeneracy, redundancy and complexity in the ensuing networks, we use information entropy to quantify the information a neuronal response carries about the stimulus - and mutual information to measure the contribution of each subset of the neuronal network. Finally, we analyze the interdependency of degeneracy, redundancy and complexity - and how these three measures depend upon network architectures. Our results suggest that degeneracy can be applied to any neuronal network as a formal measure, and degeneracy is distinct from redundancy. Qualitatively degeneracy and complexity are more highly correlated over different network architectures, in comparison to redundancy. Quantitatively, the relationship between both degeneracy and redundancy depends on network coupling strength: both degeneracy and redundancy increase with complexity for small coupling strengths; however, as coupling strength increases, redundancy decreases with complexity (in contrast to degeneracy, which is relatively invariant). These results suggest that the degeneracy is a general topologic characteristic of neuronal networks, which could be applied quantitatively in neuroscience and connectomics.

  4. Extended degeneracy and order by disorder in the square lattice J1-J2-J3 model

    NASA Astrophysics Data System (ADS)

    Danu, Bimla; Nambiar, Gautam; Ganesh, R.

    2016-09-01

    The square lattice antiferromagnet with frustrating next-nearest-neighbor coupling continues to generate tremendous interest, with an elusive quantum disordered phase in the vicinity of J2=J1/2 . At this precise value of frustration, the classical model has a very large degeneracy, which makes the problem difficult to handle. We show that introducing a ferromagnetic J3 coupling partially lifts this degeneracy. It gives rise to a four-site magnetic unit cell with the constraint that the spins on every square must add to zero. This leads to a two-parameter family of ground states and an emergent vector order parameter. We reinterpret this family of ground states as coexistence states of three spirals. Using spin wave analysis, we show that thermal and quantum fluctuations break this degeneracy differently. Thermal fluctuations break it down to a threefold degeneracy with one Néel phase and two stripe phases. This threefold symmetry is restored via a Z3 thermal transition, as we demonstrate using classical Monte Carlo simulations. On the other hand, quantum fluctuations select the Néel state. In the extreme quantum limit of spin 1 /2 , we use exact diagonalization to demonstrate Néel ordering beyond a critical J3 coupling. For weak J3, a variational approach suggests an s -wave plaquette-RVB state. Away from the J2=J1/2 line, we show that quantum fluctuations favor Néel ordering strongly enough to stabilize it within the classical stripe region. Our results shed light on the origin of the quantum disordered phase in the J1-J2 model.

  5. A torus bifurcation theorem with symmetry

    NASA Technical Reports Server (NTRS)

    Vangils, S. A.; Golubitsky, M.

    1989-01-01

    Hopf bifurcation in the presence of symmetry, in situations where the normal form equations decouple into phase/amplitude equations is described. A theorem showing that in general such degeneracies are expected to lead to secondary torus bifurcations is proved. By applying this theorem to the case of degenerate Hopf bifurcation with triangular symmetry it is proved that in codimension two there exist regions of parameter space where two branches of asymptotically stable two-tori coexist but where no stable periodic solutions are present. Although a theory was not derived for degenerate Hopf bifurcations in the presence of symmetry, examples are presented that would have to be accounted for by any such general theory.

  6. Breaking the Symmetry in Molecular Nanorings

    PubMed Central

    2016-01-01

    Because of their unique electronic properties, cyclic molecular structures ranging from benzene to natural light-harvesting complexes have received much attention. Rigid π-conjugated templated porphyrin nanorings serve as excellent model systems here because they possess well-defined structures that can readily be controlled and because they support highly delocalized excitations. In this study, we have deliberately modified a series of six-porphyrin nanorings to examine the impact of lowering the rotational symmetry on their photophysical properties. We reveal that as symmetry distortions increase in severity along the series of structures, spectral changes and an enhancement of radiative emission strength occur, which derive from a transfer of oscillator strength into the lowest (k = 0) state. We find that concomitantly, the degeneracy of the dipole-allowed first excited (k = ±1) state is lifted, leading to an ultrafast polarization switching effect in the emission from strongly symmetry-broken nanorings. PMID:26735906

  7. Coulomb analogy for non-Hermitian degeneracies near quantum phase transitions.

    PubMed

    Cejnar, Pavel; Heinze, Stefan; Macek, Michal

    2007-09-07

    Degeneracies near the real axis in a complex-extended parameter space of a Hermitian Hamiltonian are studied. We present a method to measure distributions of such degeneracies on the Riemann sheet of a selected level and apply it in classification of quantum phase transitions. The degeneracies are shown to behave similarly as complex zeros of a partition function.

  8. Noncompact dynamical symmetry of a spin-orbit-coupled oscillator

    NASA Astrophysics Data System (ADS)

    Haaker, S. M.; Bais, F. A.; Schoutens, K.

    2014-03-01

    We explain the finite as well as infinite degeneracy in the spectrum of a particular system of spin-1/2 fermions with spin-orbit coupling in three spatial dimensions. Starting from a generalized Runge-Lenz vector, we explicitly construct a complete set of symmetry operators, which span a noncompact SO(3,2) algebra. The degeneracy of the physical spectrum only involves an infinite, so-called singleton representation. In the branch where orbital and spin angular momentum are aligned, the full representation appears, constituting a three-dimensional analog of Landau levels. Antialigning the spin leads to a finite degeneracy due to a truncation of the singleton representation. We conclude the paper by constructing the spectrum generating algebra of the problem.

  9. Epigenomics and the concept of degeneracy in biological systems.

    PubMed

    Maleszka, Ryszard; Mason, Paul H; Barron, Andrew B

    2014-05-01

    Researchers in the field of epigenomics are developing more nuanced understandings of biological complexity, and exploring the multiple pathways that lead to phenotypic expression. The concept of degeneracy-referring to the multiple pathways that a system recruits to achieve functional plasticity-is an important conceptual accompaniment to the growing body of knowledge in epigenomics. Distinct from degradation, redundancy and dilapidation; degeneracy refers to the plasticity of traits whose function overlaps in some environments, but diverges in others. While a redundant system is composed of repeated identical elements performing the same function, a degenerate system is composed of different elements performing similar or overlapping functions. Here, we describe the degenerate structure of gene regulatory systems from the basic genetic code to flexible epigenomic modifications, and discuss how these structural features have contributed to organism complexity, robustness, plasticity and evolvability.

  10. Study on the degeneracy of antisense peptides using affinity chromatography.

    PubMed

    Zhao, R; Yu, X; Liu, H; Zhai, L; Xiong, S; Su, T; Liu, G

    2001-04-13

    The degeneracy of antisense peptides was studied by high-performance affinity chromatography. A model sense peptide (AAAA) and its antisense peptides (CGGG, GGGG, RGGG, SGGG) were designed and synthesized according to the degeneracy of genetic codes. An affinity column with AAAA as the ligand was prepared. The affinity chromatographic behaviors of antisense peptides on the column were evaluated. The results indicated that model antisense peptides have clear retention on the immobilized AAAA affinity column. RGGG showed the strongest affinity interaction. Similar result was obtained from another experiment that Arg-substituted antisense peptide of fusion peptide (1-11) of influenza virus A was also shown the highest affinity binding to immobilized fusion peptide.

  11. Universal Velocity-Field Characteristics for a Nanowire Arbitrary Degeneracy

    SciTech Connect

    Chek, Desmond C. Y.; Hashim, Abdul Manaf; Tan, Michael Loong Peng; Arora, Vijay K.

    2011-05-25

    The effects of electric field on the carrier motion and drift velocity in nanowire (NW) are presented in this paper. When the electric field is applied in NW, the electron is expected to move in anti-parallel direction to the electric field. This is so-called randomness motion is transformed into streamlined motion in extremely high electric field. The normalized Fermi energy and relative electron population as a function of electric field are examined for various degeneracies. It was found that the electric field has lesser influence on the relative electron population with the increased degeneracy. The drift velocity in NW is shown to increase with electric field until it reaches the saturation velocity. Two approximations have been made to simplify the theoretical equation. It is also shown in this paper that when the quantum emission is taken into account, the drift and saturation velocity degrades.

  12. Topological degeneracy of non-Abelian states for dummies

    NASA Astrophysics Data System (ADS)

    Oshikawa, Masaki; Kim, Yong Baek; Shtengel, Kirill; Nayak, Chetan; Tewari, Sumanta

    2007-06-01

    We present a physical construction of degenerate groundstates of the Moore-Read Pfaffian states, which exhibits non-Abelian statistics, on general Riemann surface with genus g. The construction is given by a generalization of the recent argument [M.O., T. Senthil, Phys. Rev. Lett. 96 (2006) 060601] which relates fractionalization and topological order. The nontrivial groundstate degeneracy obtained by Read and Green [Phys. Rev. B 61 (2000) 10267] based on differential geometry is reproduced exactly. Some restrictions on the statistics, due to the fractional charge of the quasiparticle are also discussed. Furthermore, the groundstate degeneracy of the p + i p superconductor in two dimensions, which is closely related to the Pfaffian states, is discussed with a similar construction.

  13. Black hole state degeneracy in loop quantum gravity

    SciTech Connect

    Agullo, Ivan; Diaz-Polo, Jacobo; Fernandez-Borja, Enrique

    2008-05-15

    The combinatorial problem of counting the black hole quantum states within the isolated horizon framework in loop quantum gravity is analyzed. A qualitative understanding of the origin of the band structure shown by the degeneracy spectrum, which is responsible for the black hole entropy quantization, is reached. Even when motivated by simple considerations, this picture allows to obtain analytical expressions for the most relevant quantities associated to this effect.

  14. On the degeneracy of the IMRT optimization problem.

    PubMed

    Alber, M; Meedt, G; Nüsslin, F; Reemtsen, R

    2002-11-01

    One approach to the computation of photon IMRT treatment plans is the formulation of an optimization problem with an objective function that derives from an objective density. An investigation of the second-order properties of such an objective function in a neighborhood of the minimizer opens an intuitive access to many traits of this approach. A general finding is that only a small subset of the parameter space has nonzero curvature, while the objective function is entirely flat in a neighborhood of the minimizer in most directions. The dimension of the subspace of vanishing curvature serves as a measure for the degeneracy of the solution. This finding is important both for algorithm design and evaluation of the mathematical model of clinical intuition, expressed by the objective function. The structure of the subspace of great curvature is found to be imposed on the problem by conflicts between objectives of target and critical structures. These conflicts and their corresponding modes of resolution form a common trait between all reasonable treatment plans of a given case. The high degree of degeneracy makes the use of a conjugate gradient optimization algorithm particularly favorable since the number of iterations to convergence is equivalent to the number of different eigenvalues of the curvature tensor and is hence independent from the number of optimization parameters. A high level of degeneracy of the fluence profiles implies that it should be possible to stipulate further delivery-related conditions without causing severe deterioration of the dose distribution.

  15. A backtracking algorithm that deals with particle filter degeneracy

    NASA Astrophysics Data System (ADS)

    Baarsma, Rein; Schmitz, Oliver; Karssenberg, Derek

    2016-04-01

    Particle filters are an excellent way to deal with stochastic models incorporating Bayesian data assimilation. While they are computationally demanding, the particle filter has no problem with nonlinearity and it accepts non-Gaussian observational data. In the geoscientific field it is this computational demand that creates a problem, since dynamic grid-based models are often already quite computationally demanding. As such it is of the utmost importance to keep the amount of samples in the filter as small as possible. Small sample populations often lead to filter degeneracy however, especially in models with high stochastic forcing. Filter degeneracy renders the sample population useless, as the population is no longer statistically informative. We have created an algorithm in an existing data assimilation framework that reacts to and deals with filter degeneracy based on Spiller et al. [2008]. During the Bayesian updating step of the standard particle filter, the algorithm tests the sample population for filter degeneracy. If filter degeneracy has occurred, the algorithm resets to the last time the filter did work correctly and recalculates the failed timespan of the filter with an increased sample population. The sample population is then reduced to its original size and the particle filter continues as normal. This algorithm was created in the PCRaster Python framework, an open source tool that enables spatio-temporal forward modelling in Python [Karssenberg et al., 2010] . The framework already contains several data assimilation algorithms, including a standard particle filter and a Kalman filter. The backtracking particle filter algorithm has been added to the framework, which will make it easy to implement in other research. The performance of the backtracking particle filter is tested against a standard particle filter using two models. The first is a simple nonlinear point model, and the second is a more complex geophysical model. The main testing

  16. Inherited Symmetry

    ERIC Educational Resources Information Center

    Attanucci, Frank J.; Losse, John

    2008-01-01

    In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the…

  17. Inherited Symmetry

    ERIC Educational Resources Information Center

    Attanucci, Frank J.; Losse, John

    2008-01-01

    In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the…

  18. Non-Hermitian Hamiltonians with unitary and antiunitary symmetries

    NASA Astrophysics Data System (ADS)

    Fernández, Francisco M.; Garcia, Javier

    2014-03-01

    We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary for the diagonalization of the Hamiltonian in a given basis set. We can also classify the solutions according to the irreducible representations of the point group and thus analyse their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry C2v exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit which suggests that the phenomenon is not robust. Point-group symmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry.

  19. Elementary excitations in magnetically ordered systems with orbital degeneracy

    SciTech Connect

    Joshi, A.; Ma, M. ); Mila, F. ); Shi, D.N. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Peoples Republic of ); Zhang, F.C. )

    1999-09-01

    The generalized Holstein-Primakoff transformation is used to develop a quantum flavor wave theory for spin systems with orbital degeneracy. Elementary excitations of ordered ground states consist of spin, orbital, and spin-orbital waves. Spin and spin-orbital waves couple to each other due to orbital anisotropy and Hund[close quote]s rule, resulting in modes observable by inelastic neutron scattering. In the SU(4) limit, flavor waves are dispersionless along one or more directions, and give rise to quantum fluctuations of reduced dimensionality. [copyright] [ital 1999] [ital The American Physical Society

  20. Low-dimensional relativistic degeneracy in quantum plasmas

    NASA Astrophysics Data System (ADS)

    Akbari-Moghanjoughi, M.; Esfandyari-Kalejahi, A.; Esfandyari-Kalejahi

    2013-12-01

    In this work we investigate the effect of relativistic degeneracy on different properties of low-dimensional quantum plasmas. Using the dielectric response from the conventional quantum hydrodynamic model, including the quantum diffraction effect (Bohm potential) on free electrons, we explore the existence of the Shukla-Eliasson attractive screening and possibility of the ion structure formation in low-dimensional, completely degenerate electron-ion plasmas. A generalized degeneracy pressure expression for arbitrary relativity parameter in two-dimensional case is derived, indicating that change in the polytropic index (change in the equation of state) for the two-dimensional quantum fluid takes place at the electron number-density of n 0 ~= 1.1 × 1020cm-2 whereas this is known to occur for the three-dimensional case in the electron density of n 0 ~= 5.9 × 1029cm-3. Also, a generalized dielectric function valid for all dimensionalities and densities of a degenerate electron gas is calculated, and distinct properties of electron-ion plasmas, such as static screening, structure factor and Thomson scattering, are investigated in terms of plasma dimensionality.

  1. Degeneracy, frequency response and filtering in IMRT optimization

    NASA Astrophysics Data System (ADS)

    Llacer, Jorge; Agazaryan, Nzhde; Solberg, Timothy D.; Promberger, Claus

    2004-07-01

    This paper attempts to provide an answer to some questions that remain either poorly understood, or not well documented in the literature, on basic issues related to intensity modulated radiation therapy (IMRT). The questions examined are: the relationship between degeneracy and frequency response of optimizations, effects of initial beamlet fluence assignment and stopping point, what does filtering of an optimized beamlet map actually do and how could image analysis help to obtain better optimizations? Two target functions are studied, a quadratic cost function and the log likelihood function of the dynamically penalized likelihood (DPL) algorithm. The algorithms used are the conjugate gradient, the stochastic adaptive simulated annealing and the DPL. One simple phantom is used to show the development of the analysis tools used and two clinical cases of medium and large dose matrix size (a meningioma and a prostate) are studied in detail. The conclusions reached are that the high number of iterations that is needed to avoid degeneracy is not warranted in clinical practice, as the quality of the optimizations, as judged by the DVHs and dose distributions obtained, does not improve significantly after a certain point. It is also shown that the optimum initial beamlet fluence assignment for analytical iterative algorithms is a uniform distribution, but such an assignment does not help a stochastic method of optimization. Stopping points for the studied algorithms are discussed and the deterioration of DVH characteristics with filtering is shown to be partially recoverable by the use of space-variant filtering techniques.

  2. Degeneracy, frequency response and filtering in IMRT optimization.

    PubMed

    Llacer, Jorge; Agazaryan, Nzhde; Solberg, Timothy D; Promberger, Claus

    2004-07-07

    This paper attempts to provide an answer to some questions that remain either poorly understood, or not well documented in the literature, on basic issues related to intensity modulated radiation therapy (IMRT). The questions examined are: the relationship between degeneracy and frequency response of optimizations, effects of initial beamlet fluence assignment and stopping point, what does filtering of an optimized beamlet map actually do and how could image analysis help to obtain better optimizations? Two target functions are studied, a quadratic cost function and the log likelihood function of the dynamically penalized likelihood (DPL) algorithm. The algorithms used are the conjugate gradient, the stochastic adaptive simulated annealing and the DPL. One simple phantom is used to show the development of the analysis tools used and two clinical cases of medium and large dose matrix size (a meningioma and a prostate) are studied in detail. The conclusions reached are that the high number of iterations that is needed to avoid degeneracy is not warranted in clinical practice, as the quality of the optimizations, as judged by the DVHs and dose distributions obtained, does not improve significantly after a certain point. It is also shown that the optimum initial beamlet fluence assignment for analytical iterative algorithms is a uniform distribution, but such an assignment does not help a stochastic method of optimization. Stopping points for the studied algorithms are discussed and the deterioration of DVH characteristics with filtering is shown to be partially recoverable by the use of space-variant filtering techniques.

  3. Degeneracy allows for both apparent homogeneity and diversification in populations

    PubMed Central

    Whitacre, James M.; Atamas, Sergei P.

    2013-01-01

    Trait diversity – the substrate for natural selection – is necessary for adaptation through selection, particularly in populations faced with environmental changes that diminish population fitness. In habitats that remain unchanged for many generations, stabilizing selection maximizes exploitation of resources by reducing trait diversity to a narrow optimal range. One might expect that such ostensibly homogeneous populations would have a reduced potential for heritable adaptive responses when faced with fitness-reducing environmental changes. However, field studies have documented populations that, even after long periods of evolutionary stasis, can still rapidly evolve in response to changed environmental conditions. We argue that degeneracy, the ability of diverse population elements to function similarly, can satisfy both the current need to maximize fitness and the future need for diversity. Degenerate ensembles appear functionally redundant in certain environmental contexts and functionally diverse in others. We propose that genetic variation not contributing to the observed range of phenotypes in a current population, also known as cryptic genetic variation (CGV), is a specific case of degeneracy. We argue that CGV, which gradually accumulates in static populations in stable environments, reveals hidden trait differences when environments change. By allowing CGV accumulation, static populations prepare themselves for future rapid adaptations to environmental novelty. A greater appreciation of degeneracy’s role in resolving the inherent tension between current stabilizing selection and future directional selection has implications in conservation biology and may be applied in social and technological systems to maximize current performance while strengthening the potential for future changes. PMID:22910487

  4. Degeneracy-Preserving Quantum Nondemolition Measurement of Parity-Type Observables for Cat Qubits

    NASA Astrophysics Data System (ADS)

    Cohen, Joachim; Smith, W. Clarke; Devoret, Michel H.; Mirrahimi, Mazyar

    2017-08-01

    A central requirement for any quantum error correction scheme is the ability to perform quantum nondemolition measurements of an error syndrome, corresponding to a special symmetry property of the encoding scheme. It is in particular important that such a measurement does not introduce extra error mechanisms, not included in the error model of the correction scheme. In this Letter, we ensure such a robustness by designing an interaction with a measurement device that preserves the degeneracy of the measured observable. More precisely, we propose a scheme to perform continuous and quantum nondemolition measurement of photon-number parity in a microwave cavity. This corresponds to the error syndrome in a class of error correcting codes called the cat codes, which have recently proven to be efficient and versatile for quantum information processing. In our design, we exploit the strongly nonlinear Hamiltonian of a high-impedance Josephson circuit, coupling a high-Q cavity storage cavity mode to a low-Q readout one. By driving the readout resonator at its resonance, the phase of the reflected or transmitted signal carries directly exploitable information on parity-type observables for encoded cat qubits of the high-Q mode.

  5. Mode-splitting and quasi-degeneracies in circular plate vibration problems: The example of free vibrations of the stator of a traveling wave ultrasonic motor

    NASA Astrophysics Data System (ADS)

    Kumar, Ashwin; Krousgrill, Charles M.

    2012-12-01

    In systems with rotational symmetry, bending modes occur in doubly-degenerate pairs with two independent vibration modes for each repeated natural frequency. In circular plates, the standing waves of two such degenerate bending modes can be superposed with a 1/4 period separation in time to yield a traveling wave response. This is the principle of a traveling wave ultrasonic motor (TWUM), in which a traveling bending wave in a stator drives the rotor through a friction contact. The stator contains teeth to increase the speed at the contact region, and these affect the rotational symmetry of the plate. When systems with rotational symmetry are modified either in their geometry, or by spatially varying their properties or boundary conditions, some mode-pairs split into singlet modes having distinct frequencies. In addition, coupling between some pairs of distinct unperturbed modes also causes quasi-degeneracies in the perturbed modes, which leads their frequency curves to approach and veer away in some regions of the parameter space. This paper discusses the effects of tooth geometry on the behavior of plate modes under free vibration. It investigates mode splitting and quasi-degeneracies and derives analytic expressions to predict these phenomena, using variational methods and a degenerate perturbation scheme for the solution to the plate's discrete eigenvalue problem; these expressions are confirmed by solving the discrete eigenvalue problem of the plate with teeth.

  6. The symmetric Tamm-Dancoff q-oscillator: the representation, quasi-Fibonacci nature, accidental degeneracy and coherent states

    NASA Astrophysics Data System (ADS)

    Chung, Won Sang; Gavrilik, A. M.; Kachurik, I. I.; Rebesh, A. P.

    2014-08-01

    In this paper we propose a symmetric q-deformed Tamm-Dancoff (S-TD) oscillator algebra and study its representation, coordinate realization, and main properties. In particular, the non-Fibonacci (more exactly, quasi-Fibonacci) nature of the S-TD oscillator is established, the possibility of relating it to a certain p,q-deformed oscillator family is shown, and the occurrence of pairwise accidental degeneracy is proven. We also find the coherent state for the S-TD oscillator and show that it satisfies a completeness relation. The main advantage of the S-TD model over the usual Tamm-Dancoff oscillator is that due to the q\\leftrightarrow {{q}^{-1}} symmetry, it admits not only real, but also complex (phase-like) values of the deformation parameter q.

  7. Resolving octant degeneracy at LBL experiment by combining Daya Bay reactor setup

    NASA Astrophysics Data System (ADS)

    Bora, Kalpana; Dutta, Debajyoti

    2014-03-01

    Long baseline Experiment(LBL) have promised to be a very powerful experimental setup to study various issues related to Neutrinos. Some ongoing and planned LBL and medium baseline experiments are- T2K, MINOS, NOvA, LBNE, LBNO etc. But, the long baseline experiments are crippled due to presence of some parameter degeneracies, like the Octant -degeneracy. In this work, we first show the presence of Octant degeneracy in LBL experiments and then combine it with Daya Bay Reactor experiment at different values of CP violation phase. We show that the Octant degeneracy in LBNE can be resolved completely with this proposal.

  8. Broken Symmetry

    ScienceCinema

    None

    2016-07-12

    - Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not “renormalizable”. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged “vector” particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of

  9. Broken Symmetry

    SciTech Connect

    2011-02-24

    - Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not “renormalizable”. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged “vector” particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of

  10. Non-Hermitian Hamiltonians with unitary and antiunitary symmetries

    SciTech Connect

    Fernández, Francisco M. Garcia, Javier

    2014-03-15

    We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary for the diagonalization of the Hamiltonian in a given basis set. We can also classify the solutions according to the irreducible representations of the point group and thus analyse their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry C{sub 2v} exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit which suggests that the phenomenon is not robust. Point-group symmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry. -- Highlights: •PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. •PT-symmetric multidimensional oscillators appear to show PT phase transitions. •This transition was conjectured to be a high-energy phenomenon. •We show that point group symmetry is useful for predicting broken PT symmetry in multidimensional oscillators. •PT-symmetric oscillators with C{sub 2v} symmetry exhibit phase transitions at the trivial Hermitian limit.

  11. Nonsymmorphic symmetry-required band crossings in topological semimetals

    NASA Astrophysics Data System (ADS)

    Zhao, Y. X.; Schnyder, Andreas P.

    2016-11-01

    We show that for two-band systems nonsymmorphic symmetries may enforce the existence of band crossings in the bulk, which realize Fermi surfaces of reduced dimensionality. We find that these unavoidable crossings originate from the momentum dependence of the nonsymmorphic symmetry, which puts strong restrictions on the global structure of the band configurations. Three different types of nonsymmorphic symmetries are considered: (i) a unitary nonsymmorphic symmetry, (ii) a nonsymmorphic magnetic symmetry, and (iii) a nonsymmorphic symmetry combined with inversion. For nonsymmorphic symmetries of the latter two types, the band crossings are located at high-symmetry points of the Brillouin zone, with their exact positions being determined by the algebra of the symmetry operators. To characterize these band degeneracies we introduce a global topological charge and show that it is of Z2 type, which is in contrast to the local topological charge of Fermi points in, say, Weyl semimetals. To illustrate these concepts, we discuss the π -flux state as well as the Su-Schrieffer-Heeger model at its critical point and show that these two models fit nicely into our general framework of nonsymmorphic two-band systems.

  12. Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity

    NASA Astrophysics Data System (ADS)

    Al-Hashimi, M. H.; Shalaby, A. M.; Wiese, U.-J.

    2015-11-01

    The non-relativistic hydrogen atom enjoys an accidental SO(4) symmetry, that enlarges the rotational SO(3) symmetry, by extending the angular momentum algebra with the Runge-Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson-Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius R with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter γ, in general the accidental SO(4) symmetry is lifted. However, for R =(l + 1) (l + 2) a (where a is the Bohr radius and l is the orbital angular momentum) some degeneracy remains when γ = ∞ or γ =2/R. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of R and γ.

  13. Quantum group symmetries and completeness for \\boldsymbol {A}_{\\boldsymbol {2n}}^{\\boldsymbol{(2)}} open spin chains

    NASA Astrophysics Data System (ADS)

    Ahmed, Ibrahim; Nepomechie, Rafael I.; Wang, Chunguang

    2017-07-01

    We argue that the Hamiltonians for A(2)2n open quantum spin chains corresponding to two choices of integrable boundary conditions have the symmetries Uq(Bn) and Uq(Cn) , respectively. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of each type. With the help of this formula, we verify numerically (for a generic value of the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.

  14. Symmetry-Enforced Line Nodes in Unconventional Superconductors

    NASA Astrophysics Data System (ADS)

    Micklitz, T.; Norman, M. R.

    2017-05-01

    We classify line nodes in superconductors with strong spin-orbit interactions and time-reversal symmetry, where the latter may include nonprimitive translations in the magnetic Brillouin zone to account for coexistence with antiferromagnetic order. We find four possible combinations of irreducible representations of the order parameter on high-symmetry planes, two of which allow for line nodes in pseudospin-triplet pairs and two that exclude conventional fully gapped pseudospin-singlet pairs. We show that the former can only be realized in the presence of band-sticking degeneracies, and we verify their topological stability using arguments based on Clifford algebra extensions. Our classification exhausts all possible symmetry protected line nodes in the presence of spin-orbit coupling and a (generalized) time-reversal symmetry. Implications for existing nonsymmorphic and antiferromagnetic superconductors are discussed.

  15. Gapped symmetric edges of symmetry-protected topological phases

    NASA Astrophysics Data System (ADS)

    Lu, Yuan-Ming; Lee, Dung-Hai

    2014-05-01

    Symmetry-protected topological (SPT) phases are gapped quantum phases which host symmetry-protected gapless edge excitations. On the other hand, the edge states can be gapped by spontaneously breaking symmetry. We show that topological defects on the symmetry-broken edge cannot proliferate due to their fractional statistics. A gapped symmetric boundary, however, can be achieved between an SPT phase and certain fractionalized phases by condensing the bound state of a topological defect and an anyon. We demonstrate this by two examples in two dimensions: an exactly solvable model for the boundary between a topological Ising paramagnet and the double-semion model, and a fermionic example about the quantum spin Hall edge. Such a hybrid structure containing both SPT phase and fractionalized phase generally support ground-state degeneracy on a torus.

  16. Mimicking glide symmetry dispersion with coupled slot metasurfaces

    NASA Astrophysics Data System (ADS)

    Camacho, Miguel; Mitchell-Thomas, Rhiannon C.; Hibbins, Alastair P.; Sambles, J. Roy; Quevedo-Teruel, Oscar

    2017-09-01

    In this letter, we demonstrate that the dispersion properties associated with glide symmetry can be achieved in systems that only possess reflection symmetry by balancing the influence of two sublattices. We apply this approach to a pair of coupled slots cut into an infinite perfectly conducting plane. Each slot is notched on either edge, with the complete two-slot system having only mirror symmetry. By modifying the relative size of the notches on either side of the slots, we show that a linear dispersion relation with a degeneracy with non-zero group velocity at the Brillouin zone boundary can be achieved. These properties, until now, only found in systems with glide symmetry are numerically and experimentally validated. We also show that these results can be used for the design of ultra-wideband one-dimensional leaky wave antennas in coplanar waveguide technology.

  17. Degeneracy measures for the algebraic classification of numerical spacetimes

    SciTech Connect

    Owen, Robert

    2010-06-15

    We study the issue of algebraic classification of the Weyl curvature tensor, with a particular focus on numerical relativity simulations. The spacetimes of interest in this context, binary black hole mergers, and the ringdowns that follow them, present subtleties in that they are generically, strictly speaking, type I, but in many regions approximately, in some sense, type D. To provide meaning to any claims of ''approximate'' Petrov class, one must define a measure of degeneracy on the space of null rays at a point. We will investigate such a measure, used recently to argue that certain binary black hole merger simulations ring down to the Kerr geometry, after hanging up for some time in Petrov type II. In particular, we argue that this hangup in Petrov type II is an artefact of the particular measure being used, and that a geometrically better-motivated measure shows a black hole merger produced by our group settling directly to Petrov type D.

  18. On disentangling initial mass function degeneracies in integrated light

    NASA Astrophysics Data System (ADS)

    Tang, Baitian; Worthey, Guy

    2015-11-01

    The study of extragalactic integrated light can yield partial information on stellar population ages, abundances, and the initial mass function (IMF). The power-law slope of the IMF has been studied in recent investigations with gravity-sensitive spectral indicators that hopefully measure the ratio between KM dwarfs and giants. We explore two additional effects that might mimic the effects of the IMF slope in integrated light, the low-mass cutoff (LMCO) and a variable contribution of light from the asymptotic giant branch (AGB). We show that the spectral effects of these three (IMF slope, LMCO, AGB strength) are subtle compared to age-abundance effects. We illustrate parameter degeneracies and covariances and conclude that the three effects can be disentangled, but only in the regime of very accurate observations, with enhanced effectiveness if high-precision photometry is combined with spectroscopy.

  19. Epigenomics and the concept of degeneracy in biological systems

    PubMed Central

    Mason, Paul H.; Barron, Andrew B.

    2014-01-01

    Researchers in the field of epigenomics are developing more nuanced understandings of biological complexity, and exploring the multiple pathways that lead to phenotypic expression. The concept of degeneracy—referring to the multiple pathways that a system recruits to achieve functional plasticity—is an important conceptual accompaniment to the growing body of knowledge in epigenomics. Distinct from degradation, redundancy and dilapidation; degeneracy refers to the plasticity of traits whose function overlaps in some environments, but diverges in others. While a redundant system is composed of repeated identical elements performing the same function, a degenerate system is composed of different elements performing similar or overlapping functions. Here, we describe the degenerate structure of gene regulatory systems from the basic genetic code to flexible epigenomic modifications, and discuss how these structural features have contributed to organism complexity, robustness, plasticity and evolvability. PMID:24335757

  20. Cosmological degeneracy versus cosmography: A cosmographic dark energy model

    NASA Astrophysics Data System (ADS)

    Luongo, Orlando; Pisani, Giovanni Battista; Troisi, Antonio

    In this work, we use cosmography to alleviate the degeneracy among cosmological models, proposing a way to parametrize matter and dark energy in terms of cosmokinematics quantities. The recipe of using cosmography allows to expand observable quantities in Taylor series and to directly compare those expansions with data. The strategy involves the expansions of q and j, up to the second-order around a(t) = 1. This includes additional cosmographic parameters which are fixed by current values of q0 and j0. We therefore propose a fully self-consistent parametrization of the total energy density driving the late-time universe speed up. This stratagem does not remove all the degeneracy but enables one to pass from the model-dependent couple of coefficients, ω0 and Ωm,0, to model-independent quantities determined from cosmography. Afterwards, we describe a feasible cosmographic dark energy model, in which matter is fixed whereas dark energy evolves by means of the cosmographic series. Our technique provides robust constraints on cosmokinematic parameters, permitting one to separately bound matter from dark energy densities. Our cosmographic dark energy model turns out to be one parameter only, but differently from the lambda cold dark matter (ΛCDM) paradigm, it does not contain ansatz on the dark energy form. In addition, we even determine the free parameter of our model in suitable 1σ intervals through Monte Carlo analyses based on the Metropolis algorithm. We compare our results with the standard concordance model and we find that our treatment seems to indicate that dark energy slightly evolves in time, reducing to a pure cosmological constant only as z → 0.

  1. Continuous symmetry measures for complex symmetry group.

    PubMed

    Dryzun, Chaim

    2014-04-05

    Symmetry is a fundamental property of nature, used extensively in physics, chemistry, and biology. The Continuous symmetry measures (CSM) is a method for estimating the deviation of a given system from having a certain perfect symmetry, which enables us to formulate quantitative relation between symmetry and other physical properties. Analytical procedures for calculating the CSM of all simple cyclic point groups are available for several years. Here, we present a methodology for calculating the CSM of any complex point group, including the dihedral, tetrahedral, octahedral, and icosahedral symmetry groups. We present the method and analyze its performances and errors. We also introduce an analytical method for calculating the CSM of the linear symmetry groups. As an example, we apply these methods for examining the symmetry of water, the symmetry maps of AB4 complexes, and the symmetry of several Lennard-Jones clusters.

  2. Avoiding Degeneracy in Multidimensional Unfolding by Penalizing on the Coefficient of Variation

    ERIC Educational Resources Information Center

    Busing, Frank M. T. A.; Groenen, Patrick J. K.; Heiser, Willem J.

    2005-01-01

    Multidimensional unfolding methods suffer from the degeneracy problem in almost all circumstances. Most degeneracies are easily recognized: the solutions are perfect but trivial, characterized by approximately equal distances between points from different sets. A definition of an absolutely degenerate solution is proposed, which makes clear that…

  3. Supersolid formation in a quantum gas breaking a continuous translational symmetry

    NASA Astrophysics Data System (ADS)

    Léonard, Julian; Morales, Andrea; Zupancic, Philip; Esslinger, Tilman; Donner, Tobias

    2017-03-01

    The concept of a supersolid state combines the crystallization of a many-body system with dissipationless flow of the atoms from which it is built. This quantum phase requires the breaking of two continuous symmetries: the phase invariance of a superfluid and the continuous translational invariance to form the crystal. Despite having been proposed for helium almost 50 years ago, experimental verification of supersolidity remains elusive. A variant with only discrete translational symmetry breaking on a preimposed lattice structure—the ‘lattice supersolid’—has been realized, based on self-organization of a Bose–Einstein condensate. However, lattice supersolids do not feature the continuous ground-state degeneracy that characterizes the supersolid state as originally proposed. Here we report the realization of a supersolid with continuous translational symmetry breaking along one direction in a quantum gas. The continuous symmetry that is broken emerges from two discrete spatial symmetries by symmetrically coupling a Bose–Einstein condensate to the modes of two optical cavities. We establish the phase coherence of the supersolid and find a high ground-state degeneracy by measuring the crystal position over many realizations through the light fields that leak from the cavities. These light fields are also used to monitor the position fluctuations in real time. Our concept provides a route to creating and studying glassy many-body systems with controllably lifted ground-state degeneracies, such as supersolids in the presence of disorder.

  4. Degeneracy, degree, and heavy tails in quantum annealing

    NASA Astrophysics Data System (ADS)

    King, Andrew D.; Hoskinson, Emile; Lanting, Trevor; Andriyash, Evgeny; Amin, Mohammad H.

    2016-05-01

    Both simulated quantum annealing and physical quantum annealing have shown the emergence of "heavy tails" in their performance as optimizers: The total time needed to solve a set of random input instances is dominated by a small number of very hard instances. Classical simulated annealing, in contrast, does not show such heavy tails. Here we explore the origin of these heavy tails, which appear for inputs with high local degeneracy—large isoenergetic clusters of states in Hamming space. This category includes the low-precision Chimera-structured problems studied in recent benchmarking work comparing the D-Wave Two quantum annealing processor with simulated annealing. On similar inputs designed to suppress local degeneracy, performance of a quantum annealing processor on hard instances improves by orders of magnitude at the 512-qubit scale, while classical performance remains relatively unchanged. Simulations indicate that perturbative crossings are the primary factor contributing to these heavy tails, while sensitivity to Hamiltonian misspecification error plays a less significant role in this particular setting.

  5. Dynamics versus structure: breaking the density degeneracy in star formation

    NASA Astrophysics Data System (ADS)

    Parker, Richard J.

    2014-12-01

    The initial density of individual star-forming regions (and by extension the birth environment of planetary systems) is difficult to constrain due to the `density degeneracy problem': an initially dense region expands faster than a more quiescent region due to two-body relaxation and so two regions with the same observed present-day density may have had very different initial densities. We constrain the initial densities of seven nearby star-forming regions by folding in information on their spatial structure from the {Q}-parameter and comparing the structure and present-day density to the results of N-body simulations. This in turn places strong constraints on the possible effects of dynamical interactions and radiation fields from massive stars on multiple systems and protoplanetary discs. We apply our method to constrain the initial binary population in each of these seven regions and show that the populations in only three - the Orion Nebula Cluster, ρ Oph, and Corona Australis - are consistent with having evolved from the Kroupa universal initial period distribution and a binary fraction of unity.

  6. Degeneracy estimation in interference models on wireless networks

    NASA Astrophysics Data System (ADS)

    McBride, Neal; Bulava, John; Galiotto, Carlo; Marchetti, Nicola; Macaluso, Irene; Doyle, Linda

    2017-03-01

    We present a Monte Carlo study of interference in real-world wireless networks using the Potts model. Our approach maps the Potts energy to discrete interference levels. These levels depend on the configurations of radio frequency allocation in the network. For the first time, we estimate the degeneracy of these interference levels using the Wang-Landau algorithm. The cumulative distribution function of the resulting density of states is found to increase rapidly at a critical interference value. We compare these critical values for several different real-world interference networks and Potts models. Our results show that models with a greater number of available frequency channels and less dense interference networks result in the majority of configurations having lower interference levels. Consequently, their critical interference levels occur at lower values. Furthermore, the area under the density of states increases and shifts to lower interference values. Therefore, the probability of randomly sampling low interference configurations is higher under these conditions. This result can be used to consider dynamic and distributed spectrum allocation in future wireless networks.

  7. Degeneracy: a design principle for achieving robustness and evolvability.

    PubMed

    Whitacre, James; Bender, Axel

    2010-03-07

    Robustness, the insensitivity of some of a biological system's functionalities to a set of distinct conditions, is intimately linked to fitness. Recent studies suggest that it may also play a vital role in enabling the evolution of species. Increasing robustness, so is proposed, can lead to the emergence of evolvability if evolution proceeds over a neutral network that extends far throughout the fitness landscape. Here, we show that the design principles used to achieve robustness dramatically influence whether robustness leads to evolvability. In simulation experiments, we find that purely redundant systems have remarkably low evolvability while degenerate, i.e. partially redundant, systems tend to be orders of magnitude more evolvable. Surprisingly, the magnitude of observed variation in evolvability can neither be explained by differences in the size nor the topology of the neutral networks. This suggests that degeneracy, a ubiquitous characteristic in biological systems, may be an important enabler of natural evolution. More generally, our study provides valuable new clues about the origin of innovations in complex adaptive systems. 2009 Elsevier Ltd. All rights reserved.

  8. Degeneracy-driven self-structuring dynamics in selective repertoires.

    PubMed

    Atamas, Sergei P; Bell, Jonathan

    2009-08-01

    Numerous biological interactions, such as interactions between T cell receptors or antibodies with antigens, interactions between enzymes and substrates, or interactions between predators and prey are often not strictly specific. In such less specific, or "sloppy," systems, referred to here as degenerate systems, a given unit of a diverse resource (antigens, enzymatic substrates, prey) is at risk of being recognized and consumed by multiple consumers (lymphocytes, enzymes, predators). In this study, we model generalized degenerate consumer-resource systems of Lotka-Volterra and Verhulst types. In the degenerate systems of Lotka-Volterra, there is a continuum of types of consumer and resource based on variation of a single trait (characteristic, or preference). The consumers experience competition for a continuum of resource types. This non-local interaction system is modeled with partial differential-integral equations and shows spontaneous self-structuring of the consumer population that depends on the degree of interaction degeneracy between resource and consumer, but does not mirror the distribution of resource. We also show that the classical Verhulst (i.e. logistic) single population model can be generalized to a degenerate model, which shows qualitative behavior similar to that in the degenerate Lotka-Volterra model. These results provide better insight into the dynamics of selective systems in biology, suggesting that adaptation of degenerate repertoires is not a simple "mirroring" of the environment by the "fittest" elements of population.

  9. Another stage of development: Biological degeneracy and the study of bodily ageing.

    PubMed

    Mason, Paul H; Maleszka, Ryszard; Dominguez D, Juan F

    2016-12-21

    Ageing is a poorly understood process of human development mired by a scientific approach that struggles to piece together distributed variable factors involved in ongoing transformations of living systems. Reconfiguring existing research paradigms, we review the concept of 'degeneracy', which has divergent popular and technical definitions. The technical meaning of degeneracy refers to the structural diversity underlying functional plasticity. Degeneracy is a distributed system property that can be observed within individual brains or across different brains. For example, dementias with similar behavioural anomalies can result from a diverse range of cellular "faults", which is an example of degeneracy because the symptoms are similar in spite of different underlying mechanisms. Degeneracy is a valuable epistemological tool that can transformatively enhance scientific models of bodily ageing. We propose that movement science is one of the first areas that can productively integrate degeneracy into models of bodily ageing. We also propose model organisms such as eusocial honey bees in which degeneracy can be studied at the molecular and cellular level. Developing a vocabulary for thinking about how distributed variable factors are interlinked is important if we are to understand bodily ageing not as a single entity, but as the heterogeneous construction of changing biological, social, and environmental processes.

  10. Symmetry for the nonadiabatic transition in Floquet states

    SciTech Connect

    Hijii, Keigo; Miyashita, Seiji

    2010-01-15

    The frequency of the Rabi oscillation driven by a periodic external field varies with the parameters of the external field, e.g., frequency and amplitude, and it becomes zero at some points of the parameters, which is called coherent destruction of tunneling. This phenomenon is understood as a degeneracy of the Floquet quasienergies as a function of the parameters. We prove that the time-reversal symmetry of the external field is a necessary condition of the degeneracy. We demonstrate the gap opening in the quasienergy spectrum in asymmetrically periodically driven systems. Moreover, an adiabatic transition of the Floquet states is demonstrated and analyzed in the analogy to the Landau-Zener transition.

  11. Lower bounds for the ground-state degeneracies of frustrated systems on fractal lattices

    PubMed

    Curado; Nobre

    2000-12-01

    The total number of ground states for nearest-neighbor-interaction Ising systems with frustrations, defined on hierarchical lattices, is investigated. A simple method is presented, which allows one to factorize the ground-state degeneracy, at a given hierarchy level n, in terms of contributions due to all hierarchy levels. Such a method may yield the exact ground-state degeneracy of uniformly frustrated systems, whereas it works as an approximation for randomly frustrated models. In the latter cases, it is demonstrated that such an approximation yields lower-bound estimates for the ground-state degeneracies.

  12. Detecting ground-state degeneracy in many-body systems through qubit decoherence

    NASA Astrophysics Data System (ADS)

    Cui, Hai-Tao; Yi, Xue-Xi

    2017-02-01

    By coupling with a qubit, we demonstrate that qubit decoherence can unambiguously detect the occurrence of ground-state degeneracy in many-body systems. We first demonstrate universality using the two-band model. Consequently, several exemplifications, focused on topological condensed matter systems in one, two, and three dimensions, are presented to validate our proposal. The key point is that qubit decoherence varies significantly when energy bands touch each other at the Fermi surface. In addition, it can partially reflect the degeneracy inside the band. This feature implies that qubit decoherence can be used for reliable diagnosis of ground-state degeneracy.

  13. Broken-Symmetry Quantum Hall States in Twisted Bilayer Graphene

    NASA Astrophysics Data System (ADS)

    Kim, Youngwook; Park, Jaesung; Song, Intek; Ok, Jong Mok; Jo, Younjung; Watanabe, Kenji; Taniquchi, Takashi; Choi, Hee Cheul; Lee, Dong Su; Jung, Suyong; Kim, Jun Sung

    2016-12-01

    Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley, providing eight-fold degeneracy in the low energy states. We have investigated broken-symmetry quantum Hall (QH) states and their transitions due to the interplay of the relative strength of valley, spin and layer polarizations in twisted bilayer graphene. The energy gaps of the broken-symmetry QH states show an electron-hole asymmetric behaviour, and their dependence on the induced displacement field are opposite between even and odd filling factor states. These results strongly suggest that the QH states with broken valley and spin symmetries for individual layer become hybridized via interlayer tunnelling, and the hierarchy of the QH states is sensitive to both magnetic field and displacement field due to charge imbalance between layers.

  14. Broken-Symmetry Quantum Hall States in Twisted Bilayer Graphene

    PubMed Central

    Kim, Youngwook; Park, Jaesung; Song, Intek; Ok, Jong Mok; Jo, Younjung; Watanabe, Kenji; Taniquchi, Takashi; Choi, Hee Cheul; Lee, Dong Su; Jung, Suyong; Kim, Jun Sung

    2016-01-01

    Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley, providing eight-fold degeneracy in the low energy states. We have investigated broken-symmetry quantum Hall (QH) states and their transitions due to the interplay of the relative strength of valley, spin and layer polarizations in twisted bilayer graphene. The energy gaps of the broken-symmetry QH states show an electron-hole asymmetric behaviour, and their dependence on the induced displacement field are opposite between even and odd filling factor states. These results strongly suggest that the QH states with broken valley and spin symmetries for individual layer become hybridized via interlayer tunnelling, and the hierarchy of the QH states is sensitive to both magnetic field and displacement field due to charge imbalance between layers. PMID:27905496

  15. Linear electronic transport in dense plasmas. II. Finite degeneracy contributions

    NASA Astrophysics Data System (ADS)

    Léger, D.; Deutsch, C.

    1991-06-01

    The formalism described in the first paper in this series is hereafter specialized to a thorough investigation of finite degeneracy contributions to thermoelectronic and mechanical transport coefficients, conveniently expressed as reduced quantities. Temperature corrections are systematically discussed through the analytical properties of the jellium dielectric function. The Thomas-Fermi one appears as a paradigm of regular behavior at q=2k_F while the Lindhard and its T-dependent extension head a singular class characterized by diverging derivatives. Specific methods are developed for these important cases. Results are presented in terms of analytic expansions in the degeneracy parameter α, and exact expressions for the above-mentioned corrections are derived up to order α2. Finally we display a number of numerical results pertaining to fully ionized proton-helium binary mixtures of Astrophysical interest. The connection of the present formalism and its numerical outputs with other previous treatments is also carefully examined. Le formalisme exposé et détaillé dans le premier article de cette série est ici appliqué à la détermination des contributions de dégénérescence partielle aux coefficients de transport thermoélectroniques et mécanique (viscosité), coefficients préalablement exprimés sous forme d'expressions réduites. Les corrections de température finie sont systématiquement analysées en relation avec les propriétés analytiques de la fonction diélectrique du jellium. Alors que celle de Thomas-Fermi fournit l'exemple type de fonction parfaitement régulière en q=2k_F, celle de Lindhard et sa généralisation à T finie sont au contraire caractérisées par des dérivées divergentes en ce point. Des méthodes spécifiques sont développées pour traiter correctement ces cas importants. Nos résultats sont présentés sous forme de développements analytiques en puissance du paramètre de dégénérescence α, et des expressions

  16. Relativistic Pseudospin Symmetry

    SciTech Connect

    Ginocchio, Joseph N.

    2011-05-06

    We show that the pseudospin symmetry that Akito Arima discovered many years ago (with collaborators) is a symmetry of the the Dirac Hamiltonian for which the sum of the scalar and vector potentials are a constant. In this paper we discuss some of the implications of this relativistic symmetry and the experimental data that support these predictions. In his original paper Akito also discussed pseudo-U(3) symmetry. We show that pseudo-U(3) symmetry is a symmetry of the Dirac Hamiltonian for which the sum of harmonic oscillator vector and scalar potentials are equal to a constant, and we give the generators of pseudo-U(3) symmetry. Going beyond the mean field we summarize new results on non relativistic shell model Hamiltonians that have pseudospin symmetry and pseudo-orbital angular momentum symmetry as a dynamical symmetries.

  17. Lifting degeneracies in the oscillation parameters by a neutrino factory

    NASA Astrophysics Data System (ADS)

    Aoki, Mayumi; Hagiwara, Kaoru; Okamura, Naotoshi

    2005-01-01

    We study the potential of a very long baseline neutrino oscillation experiment with a neutrino factory and a large segmented water-Čerenkov calorimeter detector in resolving the degeneracies in the neutrino oscillation parameters; the sign of the larger mass-squared difference δm132, the sign of |Uμ 3 | 2 (≡sin2θATM) - 1 / 2, and a possible two-fold ambiguity in the determination of the CP phase δMNS. We find that the above problems can be resolved even if the particle charges are not measured. The following results are obtained in our exploratory study for a neutrino factory which delivers 1021 decaying μ+ and μ- at 10 GeV and a 100 kton detector which is placed 2100 km away and is capable of measuring the event energy and distinguishing e± from μ±, but not their charges. The sign of δm132 can be determined for 4|Ue 3 | 2 (1 -|Ue 3 | 2) ≡sin2 2θRCT ≳ 0.008. That of sin2θATM - 1 / 2 can be resolved for sin2 2θATM = 0.96 when sin2 2θRCT ≳ 0.06. The CP-violating phase δMNS can be uniquely constrained for sin2 2θRCT ≳ 0.02 if its true value is around 90° or 270°, while it can be constrained for sin2 2θRCT ≳ 0.03 if its true value is around 0° or 180°.

  18. Quantum Otto engine with exchange coupling in the presence of level degeneracy

    NASA Astrophysics Data System (ADS)

    Mehta, Venu; Johal, Ramandeep S.

    2017-09-01

    We consider a quasistatic quantum Otto cycle using two effectively two-level systems with degeneracy in the excited state. The systems are coupled through isotropic exchange interaction of strength J >0 , in the presence of an external magnetic field B which is varied during the cycle. We prove the positive work condition and show that level degeneracy can act as a thermodynamic resource, so that a larger amount of work can be extracted than in the nondegenerate case, both with and without coupling. We also derive an upper bound for the efficiency of the cycle. This bound is the same as derived for a system of coupled spin-1/2 particles [G. Thomas and R. S. Johal, Phys. Rev. E 83, 031135 (2011), 10.1103/PhysRevE.83.031135], i.e., without degeneracy, and depends only on the control parameters of the Hamiltonian, being independent of the level degeneracy and the reservoir temperatures.

  19. Ground-state degeneracies leave recognizable topological scars in the electronic density.

    PubMed

    Baer, Roi

    2010-02-19

    In Kohn-Sham density functional theory (KS DFT) a fictitious system of noninteracting particles is constructed having the same ground-state (GS) density as the physical system of interest. A fundamental open question in DFT concerns the ability of an exact KS calculation to spot and characterize the GS degeneracies in the physical system. In this Letter we provide theoretical evidence suggesting that the GS density, as a function of position on a 2D manifold of parameters affecting the external potential, is "topologically scarred" in a distinct way by degeneracies. These scars are sufficiently detailed to enable determination of the positions of degeneracies and even the associated Berry phases. We conclude that an exact KS calculation can spot and characterize the degeneracies of the physical system.

  20. Dynamic symmetries and quantum nonadiabatic transitions

    DOE PAGES

    Li, Fuxiang; Sinitsyn, Nikolai A.

    2016-05-30

    Kramers degeneracy theorem is one of the basic results in quantum mechanics. According to it, the time-reversal symmetry makes each energy level of a half-integer spin system at least doubly degenerate, meaning the absence of transitions or scatterings between degenerate states if the Hamiltonian does not depend on time explicitly. Here we generalize this result to the case of explicitly time-dependent spin Hamiltonians. We prove that for a spin system with the total spin being a half integer, if its Hamiltonian and the evolution time interval are symmetric under a specifically defined time reversal operation, the scattering amplitude between anmore » arbitrary initial state and its time reversed counterpart is exactly zero. Lastly, we also discuss applications of this result to the multistate Landau–Zener (LZ) theory.« less

  1. Dynamic symmetries and quantum nonadiabatic transitions

    SciTech Connect

    Li, Fuxiang; Sinitsyn, Nikolai A.

    2016-05-30

    Kramers degeneracy theorem is one of the basic results in quantum mechanics. According to it, the time-reversal symmetry makes each energy level of a half-integer spin system at least doubly degenerate, meaning the absence of transitions or scatterings between degenerate states if the Hamiltonian does not depend on time explicitly. Here we generalize this result to the case of explicitly time-dependent spin Hamiltonians. We prove that for a spin system with the total spin being a half integer, if its Hamiltonian and the evolution time interval are symmetric under a specifically defined time reversal operation, the scattering amplitude between an arbitrary initial state and its time reversed counterpart is exactly zero. Lastly, we also discuss applications of this result to the multistate Landau–Zener (LZ) theory.

  2. Dynamic symmetries and quantum nonadiabatic transitions

    SciTech Connect

    Li, Fuxiang; Sinitsyn, Nikolai A.

    2016-05-30

    Kramers degeneracy theorem is one of the basic results in quantum mechanics. According to it, the time-reversal symmetry makes each energy level of a half-integer spin system at least doubly degenerate, meaning the absence of transitions or scatterings between degenerate states if the Hamiltonian does not depend on time explicitly. Here we generalize this result to the case of explicitly time-dependent spin Hamiltonians. We prove that for a spin system with the total spin being a half integer, if its Hamiltonian and the evolution time interval are symmetric under a specifically defined time reversal operation, the scattering amplitude between an arbitrary initial state and its time reversed counterpart is exactly zero. Lastly, we also discuss applications of this result to the multistate Landau–Zener (LZ) theory.

  3. Dynamic symmetries and quantum nonadiabatic transitions

    NASA Astrophysics Data System (ADS)

    Li, Fuxiang; Sinitsyn, Nikolai A.

    2016-12-01

    Kramers degeneracy theorem is one of the basic results in quantum mechanics. According to it, the time-reversal symmetry makes each energy level of a half-integer spin system at least doubly degenerate, meaning the absence of transitions or scatterings between degenerate states if the Hamiltonian does not depend on time explicitly. We generalize this result to the case of explicitly time-dependent spin Hamiltonians. We prove that for a spin system with the total spin being a half integer, if its Hamiltonian and the evolution time interval are symmetric under a specifically defined time reversal operation, the scattering amplitude between an arbitrary initial state and its time reversed counterpart is exactly zero. We also discuss applications of this result to the multistate Landau-Zener (LZ) theory.

  4. Quantification of Degeneracy in Biological Systems for Characterization of Functional Interactions Between Modules

    PubMed Central

    Li, Yao; Dwivedi, Gaurav; Huang, Wen; Yi, Yingfei

    2012-01-01

    There is an evolutionary advantage in having multiple components with overlapping functionality (i.e degeneracy) in organisms. While theoretical considerations of degeneracy have been well established in neural networks using information theory, the same concepts have not been developed for differential systems, which form the basis of many biochemical reaction network descriptions in systems biology. Here we establish mathematical definitions of degeneracy, complexity and robustness that allow for the quantification of these properties in a system. By exciting a dynamical system with noise, the mutual information associated with a selected observable output and the interacting subspaces of input components can be used to define both complexity and degeneracy. The calculation of degeneracy in a biological network is a useful metric for evaluating features such as the sensitivity of a biological network to environmental evolutionary pressure. Using a two-receptor signal transduction network, we find that redundant components will not yield high degeneracy whereas compensatory mechanisms established by pathway crosstalk will. This form of analysis permits interrogation of large-scale differential systems for non-identical, functionally equivalent features that have evolved to maintain homeostasis during disruption of individual components. PMID:22619750

  5. The effect of degeneracy parameter on Weibel instability in dense plasma

    SciTech Connect

    Mahdavi, M.; Khodadadi Azadboni, F.

    2013-12-15

    In this paper, the role of degeneracy parameter, in both directions parallel and perpendicular with propagation direction of the laser beam in plasma, on the growth rate of Weibel instability, is studied. Calculations show that with the temperature anisotropy, β = T{sub ∥}/T{sub ⊥} = 0.2 and a 0.75 times reduction of the degeneracy parameter, the increased rate of the the Weibel instability growth rate is 72%. The degeneracy required for minimal growth rate in interaction laser plasma with a density of 1.2 × 10{sup 32}m{sup −3}, is larger than 3. The reduction of temperature and the degeneracy parameter of plasma in parallel direction will also increase growth rate about 30% more than incrossing degeneracy parameter in transverse direction. With the minimum pressure costs of cold compression, subsequent degeneracy parameters, and the minimum value of electron quiver energy, we can expect growth rate of Weibel instability order 0.01.

  6. Searching for Radial Symmetry.

    PubMed

    Jennings, Ben J; Kingdom, Frederick A A

    2017-01-01

    Symmetry is ubiquitous in the natural world. Numerous investigations, dating back over one hundred years, have explored the visual processing of symmetry. However, these studies have been concerned with mirror symmetry, overlooking radial (or rotational) symmetry, which is also prevalent in nature. Using a visual search paradigm, which approximates the everyday task of searching for an object embedded in background clutter, we have measured how quickly and how accurately human observers detect radially symmetric dot patterns. Performance was compared with mirror symmetry. We found that with orders of radial symmetry greater than 5, radial symmetry can be detected more easily than mirror symmetry, revealing for the first time that radial symmetry is a salient property of objects for human vision.

  7. Searching for Radial Symmetry

    PubMed Central

    Kingdom, Frederick A. A.

    2017-01-01

    Symmetry is ubiquitous in the natural world. Numerous investigations, dating back over one hundred years, have explored the visual processing of symmetry. However, these studies have been concerned with mirror symmetry, overlooking radial (or rotational) symmetry, which is also prevalent in nature. Using a visual search paradigm, which approximates the everyday task of searching for an object embedded in background clutter, we have measured how quickly and how accurately human observers detect radially symmetric dot patterns. Performance was compared with mirror symmetry. We found that with orders of radial symmetry greater than 5, radial symmetry can be detected more easily than mirror symmetry, revealing for the first time that radial symmetry is a salient property of objects for human vision. PMID:28855979

  8. Chemical potential and reaction electronic flux in symmetry controlled reactions.

    PubMed

    Vogt-Geisse, Stefan; Toro-Labbé, Alejandro

    2016-07-15

    In symmetry controlled reactions, orbital degeneracies among orbitals of different symmetries can occur along a reaction coordinate. In such case Koopmans' theorem and the finite difference approximation provide a chemical potential profile with nondifferentiable points. This results in an ill-defined reaction electronic flux (REF) profile, since it is defined as the derivative of the chemical potential with respect to the reaction coordinate. To overcome this deficiency, we propose a new way for the calculation of the chemical potential based on a many orbital approach, suitable for reactions in which symmetry is preserved. This new approach gives rise to a new descriptor: symmetry adapted chemical potential (SA-CP), which is the chemical potential corresponding to a given irreducible representation of a symmetry group. A corresponding symmetry adapted reaction electronic flux (SA-REF) is also obtained. Using this approach smooth chemical potential profiles and well defined REFs are achieved. An application of SA-CP and SA-REF is presented by studying the Cs enol-keto tautomerization of thioformic acid. Two SA-REFs are obtained, JA'(ξ) and JA'' (ξ). It is found that the tautomerization proceeds via an in-plane delocalized 3-center 4-electron O-H-S hypervalent bond which is predicted to exist only in the transition state (TS) region. © 2016 Wiley Periodicals, Inc.

  9. Symmetries in Physics

    NASA Astrophysics Data System (ADS)

    Brading, Katherine; Castellani, Elena

    2010-01-01

    Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.

  10. Symmetries in Physics

    NASA Astrophysics Data System (ADS)

    Brading, Katherine; Castellani, Elena

    2003-12-01

    Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.

  11. CP as a Symmetry of Symmetries

    NASA Astrophysics Data System (ADS)

    Trautner, Andreas

    2017-07-01

    It is explained that the Standard Model combined charge conjugation and parity transformation (CP) is a simultaneous complex conjugation outer automorphism transformation of gauge and space-time symmetries. Simple examples are given for the general concept of outer automorphisms (“symmetries of symmetries”), as well as for their possible actions on physical theories. It is highlighted that complex conjugation outer automorphisms do not, in general, exist for all symmetries. Examples are given for cases in which the physical CP transformation is violated as a consequence of requiring another symmetry. A toy model is illustrated in which CP is spontaneously violated in the broken phase of a continuous gauge symmetry, while an unbroken outer automorphism protects the topological vacuum angle at θ = 0.

  12. Lifting mean field degeneracies in anisotropic spin systems

    NASA Astrophysics Data System (ADS)

    Sizyuk, Yuriy; Perkins, Natalia; Wolfle, Peter

    We propose a method for calculating the fluctuation contribution to the free energy of anisotropic spin systems with generic bilinear superexchange magnetic Hamiltonian based on the Hubbard-Stratonovich transformation. We show that this contribution splits the set of mean field degenerate states with rotational symmetry, and chooses states with the order parameter directed along lattice symmetric directions as the true ground states. We consider the simple example of Heisenberg-compass model on cubic lattice to show that depending on the relative strength of the compass and Heisenberg interactions the spontaneous magnetization is pinned to either one of the cubic directions or one of the cubic body diagonals with a intermediate phase in between where the minima and maxima of the free energy interchange. DMR-1005932, DMR-1511768, and NSF PHY11-25915.

  13. A new method to break the mass-sheet degeneracy using aperture moments

    NASA Astrophysics Data System (ADS)

    Rexroth, Markus; Natarajan, Priyamvada; Kneib, Jean-Paul

    2016-08-01

    Mass determinations from gravitational lensing shear and the higher order estimator flexion are both subject to the mass-sheet degeneracy. Mass sheet degeneracy refers to a transformation that leaves the reduced shear and flexion invariant. In general, this transformation can be approximated by the addition of a constant surface mass density sheet. We propose a new technique to break the mass-sheet degeneracy. The method uses mass moments of the shear or flexion fields in combination with convergence information derived from number counts which exploit the magnification bias. The difference between the measured mass moments provides an estimator for the magnitude of the additive constant that is the mass sheet. For demonstrating this, we derive relations that hold true in general for nth order moments and show how they can be employed effectively to break the degeneracy. We investigate the detectability of this degeneracy parameter from our method and find that the degeneracy parameter can be feasibly determined from stacked galaxy-galaxy lensing data and cluster lensing data. Furthermore, we compare the signal-to-noise ratios of convergence information from number counts with shear and flexion for singular isothermal sphere and Navarro-Frenk-White models. We find that the combination of shear and flexion performs best on galaxy and cluster scales and the convergence information can therefore be used to break the mass-sheet degeneracy without quality loss in the mass reconstruction. In summary, there is power in the combination of shear, flexion, convergence and their higher order moments. With the anticipated wealth of lensing data from upcoming and future satellite missions - EUCLID and WFIRST - this technique will be feasible.

  14. Approximate flavor symmetries

    SciTech Connect

    Rasin, A.

    1994-04-01

    We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.

  15. Neutrinos and flavor symmetries

    SciTech Connect

    Tanimoto, Morimitsu

    2015-07-15

    We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ{sub 13} and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ{sub 13} is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.

  16. Polynomial Graphs and Symmetry

    ERIC Educational Resources Information Center

    Goehle, Geoff; Kobayashi, Mitsuo

    2013-01-01

    Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…

  17. Polynomial Graphs and Symmetry

    ERIC Educational Resources Information Center

    Goehle, Geoff; Kobayashi, Mitsuo

    2013-01-01

    Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…

  18. Chiral symmetry and chiral-symmetry breaking

    SciTech Connect

    Peskin, M.E.

    1982-12-01

    These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed. (WHK)

  19. Neurobiological degeneracy: A key property for functional adaptations of perception and action to constraints.

    PubMed

    Seifert, Ludovic; Komar, John; Araújo, Duarte; Davids, Keith

    2016-10-01

    A crucial aspect of understanding human behavior relates to how perception and action sub-systems are integrated during coordinated and controlled movement in goal-directed activity. Here we discuss how a neurobiological system property, degeneracy (i.e., many coordinative structures to achieve one function), can help us understand how skilled individuals functionally adapt perception and action to interacting constraints during performance. Since most research investigating degeneracy has been conducted in neuroanatomy, genetics and theoretical neurobiology, here we clarify how degeneracy is exhibited in perceptual-motor systems. Using an ecological dynamics framework, we highlight how degeneracy underpins the functional role of movement coordination variability in performance of multi-articular tasks. Following that, we discuss how degenerate neurobiological systems are able to exploit system stability and flexibility in their movement coordination. Third, we show how better coupling of information and movement could lead individuals to explore functionally degenerate behaviors. Last, we explore how degeneracy can support pluri-potentiality (i.e., one coordinative structure for many perceptual-motor functions) as a way toward innovation or refinement in performance.

  20. Symmetry operation measures.

    PubMed

    Pinsky, Mark; Casanova, David; Alemany, Pere; Alvarez, Santiago; Avnir, David; Dryzun, Chaim; Kizner, Ziv; Sterkin, Alexander

    2008-01-30

    We introduce a new mathematical tool for quantifying the symmetry contents of molecular structures: the Symmetry Operation Measures. In this approach, we measure the minimal distance between a given structure and the structure which is obtained after applying a selected symmetry operation on it. If the given operation is a true symmetry operation for the structure, this distance is zero; otherwise it gives an indication of how different the transformed structure is from the original one. Specifically, we provide analytical solutions for measures of all the improper rotations, S n p, including mirror symmetry and inversion, as well as for all pure rotations, C n p. These measures provide information complementary to the Continuous Symmetry Measures (CSM) that evaluate the distance between a given structure and the nearest structure which belongs to a selected symmetry point-group.

  1. Composite Weyl nodes stabilized by screw symmetry with and without time-reversal invariance

    NASA Astrophysics Data System (ADS)

    Tsirkin, Stepan S.; Souza, Ivo; Vanderbilt, David

    2017-07-01

    We classify the band degeneracies in three-dimensional crystals with screw symmetry nm and broken P *T symmetry, where P stands for spatial inversion and T for time reversal. The generic degeneracies along symmetry lines are Weyl nodes: chiral contact points between pairs of bands. They can be single nodes with a chiral charge of magnitude |χ |=1 or composite nodes with |χ |=2 or 3, and the possible χ values only depend on the order n of the axis, not on the pitch m /n of the screw. Double Weyl nodes require n =4 or 6, and triple nodes require n =6 . In all cases, the bands split linearly along the axis, and for composite nodes the splitting is quadratic on the orthogonal plane. This is true for triple as well as double nodes, due to the presence in the effective two-band Hamiltonian of a nonchiral quadratic term that masks the chiral cubic dispersion. If T symmetry is present and P is broken, there may exist on some symmetry lines Weyl nodes pinned to T -invariant momenta, which in some cases are unavoidable. In the absence of other symmetries, their classification depends on n ,m , and the type of T symmetry. With spinless T such T -invariant Weyl nodes are always double nodes, while with spinful T they can be single or triple nodes. T -invariant triples nodes can occur not only on sixfold axes but also on threefold ones, and their in-plane band splitting is cubic, not quadratic as in the case of generic triple nodes. These rules are illustrated by means of first-principles calculations for hcp cobalt, a T -broken, P -invariant crystal with 63 symmetry, and for trigonal tellurium and hexagonal NbSi2, which are T -invariant, P -broken crystals with threefold and sixfold screw symmetry, respectively.

  2. Conformal symmetry and light flavor baryon spectra

    NASA Astrophysics Data System (ADS)

    Kirchbach, M.; Compean, C. B.

    2010-08-01

    The degeneracy among parity pairs systematically observed in the N and Δ spectra is interpreted to hint on a possible conformal symmetry realization in the light flavor baryon sector in line with AdS5/CFT4. The case is made by showing that all the observed N and Δ resonances with masses below 2500 MeV distribute fairly well each over the first levels of a unitary representation of the conformal group, a representation that covers the spectrum of a quark-diquark system, placed directly on a conformally compactified Minkowski spacetime, R1⊗S3, as approached from the AdS5 cone. The free geodesic motion on the S3 manifold is described by means of the scalar conformal equation there, which is of the Klein-Gordon-type. The equation is then gauged by the curved Coulomb potential that has the form of a cotangent function. Conformal symmetry is not exact, this because the gauge potential slightly modifies the conformal centrifugal barrier of the free geodesic motion. Thanks to this, the degeneracy between P11-S11 pairs from same level is relaxed, while the remaining states belonging to same level remain practically degenerate. The model describes the correct mass ordering in the P11-S11 pairs through the spectra as a combined effect of the above conformal symmetry breaking, on the one side, and a parity change of the diquark from a scalar at low masses, to a pseudoscalar at higher masses, on the other. The quality of the wave functions is illustrated by calculations of realistic mean square charge radii and electric charge form factors on the examples of the proton, and the protonic P11(1440), and S11(1535) resonances. The scheme also allows for a prediction of the dressing function of an effective instantaneous gluon propagator from the Fourier transform of the gauge potential. We find a dressing function that is finite in the infrared and tends to zero at infinity.

  3. Dispersion in a thermal plasma including arbitrary degeneracy and quantum recoil.

    PubMed

    Melrose, D B; Mushtaq, A

    2010-11-01

    The longitudinal response function for a thermal electron gas is calculated including two quantum effects exactly, degeneracy, and the quantum recoil. The Fermi-Dirac distribution is expanded in powers of a parameter that is small in the nondegenerate limit and the response function is evaluated in terms of the conventional plasma dispersion function to arbitrary order in this parameter. The infinite sum is performed in terms of polylogarithms in the long-wavelength and quasistatic limits, giving results that apply for arbitrary degeneracy. The results are applied to the dispersion relations for Langmuir waves and to screening, reproducing known results in the nondegenerate and completely degenerate limits, and generalizing them to arbitrary degeneracy.

  4. All Majorana Models with Translation Symmetry are Supersymmetric

    NASA Astrophysics Data System (ADS)

    Hsieh, Timothy H.; Halász, Gábor B.; Grover, Tarun

    2016-10-01

    We establish results similar to Kramers and Lieb-Schultz-Mattis theorems but involving only translation symmetry and for Majorana modes. In particular, we show that all states are at least doubly degenerate in any one- and two-dimensional array of Majorana modes with translation symmetry, periodic boundary conditions, and an odd number of modes per unit cell. Moreover, we show that all such systems have an underlying N =2 supersymmetry and explicitly construct the generator of the supersymmetry. Furthermore, we establish that there cannot be a unique gapped ground state in such one-dimensional systems with antiperiodic boundary conditions. These general results are fundamentally a consequence of the fact that translations for Majorana modes are represented projectively, which in turn stems from the anomalous nature of a single Majorana mode. An experimental signature of the degeneracy arising from supersymmetry is a zero-bias peak in tunneling conductance.

  5. Island of Rare Earth Nuclei with Tetrahedral and Octahedral Symmetries: Possible Experimental Evidence

    SciTech Connect

    Dudek, J.; Dubray, N.; Pangon, V.; Dobaczewski, J.; Olbratowski, P.; Schunck, N.

    2006-08-18

    Calculations using realistic mean-field methods suggest the existence of nuclear shapes with tetrahedral T{sub d} and/or octahedral O{sub h} symmetries sometimes at only a few hundreds of keV above the ground states in some rare earth nuclei around {sup 156}Gd and {sup 160}Yb. The underlying single-particle spectra manifest exotic fourfold rather than Kramers's twofold degeneracies. The associated shell gaps are very strong, leading to a new form of shape coexistence in many rare earth nuclei. We present possible experimental evidence of the new symmetries based on the published experimental results--although an unambiguous confirmation will require dedicated experiments.

  6. Quantization due to breaking the commutativity of symmetries. Wobbling oscillator and anharmonic Penning trap

    NASA Astrophysics Data System (ADS)

    Karasev, M. V.

    2016-10-01

    We discuss two examples of classical mechanical systems which can become quantum either because of degeneracy of an integral of motion or because of tuning parameters at resonance. In both examples, the commutativity of the symmetry algebra is breaking, and noncommutative symmetries arise. Over the new noncommutative algebra, the system can reveal its quantum behavior including the tunneling effect. The important role is played by the creation-annihilation regime for the perturbation or anharmonism. Activation of this regime sometimes needs in an additional resonance deformation (Cartan subalgebra breaking).

  7. Dual-Species Quantum Degeneracy of 40K and 87Rb on an Atom Chip

    SciTech Connect

    Extavour, M. H. T.; LeBlanc, L. J.; Schumm, T.; Cieslak, B.; Myrskog, S.; Stummer, A.; Aubin, S.; Thywissen, J. H.

    2006-11-07

    In this article we review our recent experiments with a 40K-87Rb mixture. We demonstrate rapid sympathetic cooling of a 40K-87Rb mixture to dual quantum degeneracy on an atom chip. We also provide details on efficient BEC production, species-selective magnetic confinement, and progress toward integration of an optical lattice with an atom chip. The efficiency of our evaporation allows us to reach dual degeneracy after just 6 s of evaporation - more rapidly than in conventional magnetic traps. When optimizing evaporative cooling for efficient evaporation of 87Rb alone we achieve BEC after just 4 s of evaporation and an 8 s total cycle time.

  8. Spitzer Observations of OGLE-2015-BLG-1212 Reveal a New Path toward Breaking Strong Microlens Degeneracies

    NASA Technical Reports Server (NTRS)

    Bozza, V.; Shvartzvald, Y.; Udalski, A.; Novati, S.Calchi; Bond, I. A.; Han, C.; Hundertmark, M.; Poleski, R.; Pawlak, M.; Szymanski, M. K.; hide

    2016-01-01

    Spitzer microlensing parallax observations of OGLE-2015-BLG-1212 decisively break a degeneracy between planetary and binary solutions that is somewhat ambiguous when only ground-based data are considered. Only eight viable models survive out of an initial set of 32 local minima in the parameter space. These models clearly indicate that the lens is a stellar binary system possibly located within the bulge of our Galaxy, ruling out the planetary alternative. We argue that several types of discrete degeneracies can be broken via such space-based parallax observations.

  9. Spitzer Observations of OGLE-2015-BLG-1212 Reveal a New Path toward Breaking Strong Microlens Degeneracies

    NASA Astrophysics Data System (ADS)

    Bozza, V.; Shvartzvald, Y.; Udalski, A.; Calchi Novati, S.; Bond, I. A.; Han, C.; Hundertmark, M.; Poleski, R.; Pawlak, M.; Szymański, M. K.; Skowron, J.; Mróz, P.; Kozłowski, S.; Wyrzykowski, Ł.; Pietrukowicz, P.; Soszyński, I.; Ulaczyk, K.; OGLE Group; and; Beichman, C.; Bryden, G.; Carey, S.; Fausnaugh, M.; Gaudi, B. S.; Gould, A.; Henderson, C. B.; Pogge, R. W.; Wibking, B.; Yee, J. C.; Zhu, W.; Spitzer Team; Abe, F.; Asakura, Y.; Barry, R. K.; Bennett, D. P.; Bhattacharya, A.; Donachie, M.; Freeman, M.; Fukui, A.; Hirao, Y.; Inayama, K.; Itow, Y.; Koshimoto, N.; Li, M. C. A.; Ling, C. H.; Masuda, K.; Matsubara, Y.; Muraki, Y.; Nagakane, M.; Nishioka, T.; Ohnishi, K.; Oyokawa, H.; Rattenbury, N.; Saito, To.; Sharan, A.; Sullivan, D. J.; Sumi, T.; Suzuki, D.; Tristram, P. J.; Wakiyama, Y.; Yonehara, A.; MOA Group; Choi, J.-Y.; Park, H.; Jung, Y. K.; Shin, I.-G.; Albrow, M. D.; Park, B.-G.; Kim, S.-L.; Lee, C.-U.; Cha, S.-M.; Kim, D.-J.; Lee, Y.; KMTNet Group; Dominik, M.; Jørgensen, U. G.; Andersen, M. I.; Bramich, D. M.; Burgdorf, M. J.; Ciceri, S.; D'Ago, G.; Evans, D. F.; Figuera Jaimes, R.; Gu, S.-H.; Hinse, T. C.; Kains, N.; Kerins, E.; Korhonen, H.; Kuffmeier, M.; Mancini, L.; Popovas, A.; Rabus, M.; Rahvar, S.; Rasmussen, R. T.; Scarpetta, G.; Skottfelt, J.; Snodgrass, C.; Southworth, J.; Surdej, J.; Unda-Sanzana, E.; von Essen, C.; Wang, Y.-B.; Wertz, O.; MiNDSTEp; Maoz, D.; Friedmann, M.; Kaspi, S.; Wise Group

    2016-03-01

    Spitzer microlensing parallax observations of OGLE-2015-BLG-1212 decisively break a degeneracy between planetary and binary solutions that is somewhat ambiguous when only ground-based data are considered. Only eight viable models survive out of an initial set of 32 local minima in the parameter space. These models clearly indicate that the lens is a stellar binary system possibly located within the bulge of our Galaxy, ruling out the planetary alternative. We argue that several types of discrete degeneracies can be broken via such space-based parallax observations.

  10. { Z}_N symmetry breaking in projected entangled pair state models

    NASA Astrophysics Data System (ADS)

    Rispler, Manuel; Duivenvoorden, Kasper; Schuch, Norbert

    2017-09-01

    We consider projected entangled pair state (PEPS) models with a global { Z}N symmetry, which are constructed from { Z}N -symmetric tensors and are thus { Z}N -invariant wavefunctions, and study the occurence of long-range order and symmetry breaking in these systems. First, we show that long-range order in those models is accompanied by a degeneracy in the so-called transfer operator of the system. We subsequently use this degeneracy to determine the nature of the symmetry broken states, i.e. those stable under arbitrary perturbations, and provide a succinct characterization in terms of the fixed points of the transfer operator (i.e. the different boundary conditions) in the individual symmetry sectors. We verify our findings numerically through the study of a { Z}3 -symmetric model, and show that the entanglement Hamiltonian derived from the symmetry broken states is quasi-local (unlike the one derived from the symmetric state), reinforcing the locality of the entanglement Hamiltonian for gapped phases.

  11. Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals

    NASA Astrophysics Data System (ADS)

    Yang, Bohm-Jung; Bojesen, Troels Arnfred; Morimoto, Takahiro; Furusaki, Akira

    2017-02-01

    Topological semimetals have energy bands near the Fermi energy sticking together at isolated points/lines/planes in the momentum space, which are often accompanied by stable surface states and intriguing bulk topological responses. Although it has been known that certain crystalline symmetries play an important role in protecting band degeneracy, a general recipe for stabilizing the degeneracy, especially in the presence of spin-orbit coupling, is still lacking. Here we show that a class of novel topological semimetals with point/line nodes can emerge in the presence of an off-centered rotation/mirror symmetry whose symmetry line/plane is displaced from the center of other symmorphic symmetries in nonsymmorphic crystals. Due to the partial translation perpendicular to the rotation axis/mirror plane, an off-centered rotation/mirror symmetry always forces two energy bands to stick together and form a doublet pair in the relevant invariant line/plane in momentum space. Such a doublet pair provides a basic building block for emerging topological semimetals with point/line nodes in systems with strong spin-orbit coupling.

  12. Symmetry-Enforced Line Nodes in Unconventional Superconductors [Nodal-Line Superconductors and Band-Sticking

    DOE PAGES

    Micklitz, T.; Norman, M. R.

    2017-05-18

    We classify line nodes in superconductors with strong spin-orbit interactions and time-reversal symmetry, where the latter may include nonprimitive translations in the magnetic Brillouin zone to account for coexistence with antiferromagnetic order. We find four possible combinations of irreducible representations of the order parameter on high-symmetry planes, two of which allow for line nodes in pseudospin-triplet pairs and two that exclude conventional fully gapped pseudospin-singlet pairs. We show that the former can only be realized in the presence of band-sticking degeneracies, and we verify their topological stability using arguments based on Clifford algebra extensions. Lastly, our classification exhausts all possiblemore » symmetry protected line nodes in the presence of spin-orbit coupling and a (generalized) time-reversal symmetry. Implications for existing nonsymmorphic and antiferromagnetic superconductors are discussed.« less

  13. From physical symmetries to emergent gauge symmetries

    NASA Astrophysics Data System (ADS)

    Barceló, Carlos; Carballo-Rubio, Raúl; Di Filippo, Francesco; Garay, Luis J.

    2016-10-01

    Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.

  14. Baryogenesis from symmetry principle

    NASA Astrophysics Data System (ADS)

    Fong, Chee Sheng

    2016-01-01

    In this work, a formalism based on symmetry which allows one to express asymmetries of all the particles in terms of conserved charges is developed. The manifestation of symmetry allows one to easily determine the viability of a baryogenesis scenario and also to identify the different roles played by the symmetry. This formalism is then applied to the standard model and its supersymmetric extension, which constitute two important foundations for constructing models of baryogenesis.

  15. On the dynamical and geometrical symmetries of Keplerian motion

    NASA Astrophysics Data System (ADS)

    Wulfman, Carl E.

    2009-05-01

    The dynamical symmetries of classical, relativistic and quantum-mechanical Kepler systems are considered to arise from geometric symmetries in PQET phase space. To establish their interconnection, the symmetries are related with the aid of a Lie-algebraic extension of Dirac's correspondence principle, a canonical transformation containing a Cunningham-Bateman inversion, and a classical limit involving a preliminary canonical transformation in ET space. The Lie-algebraic extension establishes the conditions under which the uncertainty principle allows the local dynamical symmetry of a quantum-mechanical system to be the same as the geometrical phase-space symmetry of its classical counterpart. The canonical transformation converts Poincaré-invariant free-particle systems into ISO(3,1) invariant relativistic systems whose classical limit produces Keplerian systems. Locally Cartesian relativistic PQET coordinates are converted into a set of eight conjugate position and momentum coordinates whose classical limit contains Fock projective momentum coordinates and the components of Runge-Lenz vectors. The coordinate systems developed via the transformations are those in which the evolution and degeneracy groups of the classical system are generated by Poisson-bracket operators that produce ordinary rotation, translation and hyperbolic motions in phase space. The way in which these define classical Keplerian symmetries and symmetry coordinates is detailed. It is shown that for each value of the energy of a Keplerian system, the Poisson-bracket operators determine two invariant functions of positions and momenta, which together with its regularized Hamiltonian, define the manifold in six-dimensional phase space upon which motions evolve.

  16. Symmetries in Lagrangian Dynamics

    ERIC Educational Resources Information Center

    Ferrario, Carlo; Passerini, Arianna

    2007-01-01

    In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…

  17. Symmetries in Lagrangian Dynamics

    ERIC Educational Resources Information Center

    Ferrario, Carlo; Passerini, Arianna

    2007-01-01

    In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…

  18. Symmetry and Interculturality

    ERIC Educational Resources Information Center

    Marchis, Iuliana

    2009-01-01

    Symmetry is one of the fundamental concepts in Geometry. It is a Mathematical concept, which can be very well connected with Art and Ethnography. The aim of the article is to show how to link the geometrical concept symmetry with interculturality. For this mosaics from different countries are used.

  19. Tensor network decompositions in the presence of a global symmetry

    SciTech Connect

    Singh, Sukhwinder; Pfeifer, Robert N. C.; Vidal, Guifre

    2010-11-15

    Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance in the context of tensor network algorithms as well, thus setting the stage for cross-fertilization between these two areas of research.

  20. Relationship between symmetry protected topological phases and boundary conformal field theories via the entanglement spectrum

    NASA Astrophysics Data System (ADS)

    Cho, Gil Young; Shiozaki, Ken; Ryu, Shinsei; Ludwig, Andreas W. W.

    2017-07-01

    Quantum phase transitions out of a symmetry-protected topological (SPT) phase in (1  +  1) dimensions into an adjacent, topologically distinct SPT phase protected by the same symmetry or a trivial gapped phase, are typically described by a conformal field theory (CFT). At the same time, the low-lying entanglement spectrum of a gapped phase close to such a quantum critical point is known (Cho et al arXiv:1603.04016), very generally, to be universal and described by (gapless) boundary conformal field theory. Using this connection we show that symmetry properties of the boundary conditions in boundary CFT can be used to characterize the symmetry-protected degeneracies of the entanglement spectrum, a hallmark of non-trivial symmetry-protected topological phases. Specifically, we show that the relevant boundary CFT is the orbifold of the quantum critical point with respect to the symmetry group defining the SPT, and that the boundary states of this orbifold carry a quantum anomaly that determines the topological class of the SPT. We illustrate this connection using various characteristic examples such as the time-reversal breaking ‘Kitaev chain’ superconductor (symmetry class D), the Haldane phase, and the {Z}8 classification of interacting topological superconductors in symmetry class BDI in (1  +  1) dimensions.

  1. Transition from {gamma}-rigid to {gamma}-soft dynamics in the interacting boson model: Quasicriticality and quasidynamical symmetry

    SciTech Connect

    Macek, Michal; Cejnar, Pavel; Dobes, Jan

    2009-07-15

    We study the transition from the {gamma}-rigid to {gamma}-soft collective nuclear dynamics across the Casten triangle of the interacting boson model using mean-field techniques and confront the description with the exact diagonalization. We inspect the domain of validity of the SU(3) quasidynamical symmetry inside the Casten triangle and reveal critical behavior within the low-lying excited spectrum due to a degeneracy of {beta} and {gamma} vibrations.

  2. A universal symmetry detection algorithm.

    PubMed

    Maurer, Peter M

    2015-01-01

    Research on symmetry detection focuses on identifying and detecting new types of symmetry. The paper presents an algorithm that is capable of detecting any type of permutation-based symmetry, including many types for which there are no existing algorithms. General symmetry detection is library-based, but symmetries that can be parameterized, (i.e. total, partial, rotational, and dihedral symmetry), can be detected without using libraries. In many cases it is faster than existing techniques. Furthermore, it is simpler than most existing techniques, and can easily be incorporated into existing software. The algorithm can also be used with virtually any type of matrix-based symmetry, including conjugate symmetry.

  3. Degeneracy between the dark components resulting from the fact that gravity only measures the total energy-momentum tensor

    SciTech Connect

    Kunz, Martin

    2009-12-15

    Gravity probes only the total energy-momentum tensor, which leads to a perfect degeneracy for generalized dark energy models. Because of this degeneracy, {omega}{sub m} cannot be measured. We demonstrate this explicitly by showing that the combination of cosmic microwave background and supernova data is compatible with very large and very small values of {omega}{sub m} for a specific family of dark energy models. We also show that for the same reason interacting dark energy is always equivalent to a family of noninteracting models. We argue that it is better to face this degeneracy and to parametrize the actual observables.

  4. Large enhancement in thermoelectric efficiency of quantum dot junctions due to increase of level degeneracy

    NASA Astrophysics Data System (ADS)

    Kuo, David M. T.; Chen, Chih-Chieh; Chang, Yia-Chung

    2017-02-01

    It is theoretically demonstrated that the figure of merit (Z T ) of quantum dot (QD) junctions can be significantly enhanced when the degree of degeneracy of the energy levels involved in electron transport is increased. The theory is based on the the Green-function approach in the Coulomb blockade regime by including all correlation functions resulting from electron-electron interactions associated with the degenerate levels (L ). We found that electrical conductance (Ge) as well as electron thermal conductance (κe) are highly dependent on the level degeneracy (L ), whereas the Seebeck coefficient (S ) is not. Therefore, the large enhancement of Z T is mainly attributed to the increase of Ge when the phonon thermal conductance (κp h) dominates the heat transport of the QD junction system. In the serially coupled double-QD case, we also obtain a large enhancement of Z T arising from higher L . Unlike Ge and κe, S is found almost independent on electron interdot hopping strength.

  5. Vortex degeneracy lifting and Aharonov-Bohm-like interference in deformed photonic graphene.

    PubMed

    Zhang, Peng; Gallardo, Daniel; Liu, Sheng; Gao, Yuanmei; Li, Tongcang; Wang, Yuan; Chen, Zhigang; Zhang, Xiang

    2017-03-01

    Photonic graphene, a honeycomb lattice of evanescently coupled waveguides, has provided a superior platform for investigating a host of fundamental phenomena such as unconventional edge states, synthetic magnetic fields, photonic Landau levels, Floquet topological insulators, and pseudospin effects. Here, we demonstrate both experimentally and numerically, topological vortex degeneracy lifting and Aharonov-Bohm-like interference from local deformation in a photonic honeycomb lattice. When a single valley is excited, lattice deformation leads to the generation of a vortex pair due to the lifting of degeneracy associated with pseudospin states. In the case of double-valley excitation, we observe the Aharonov-Bohm-like interference merely due to the deformation of the graphene lattice, which gives rise to an artificial gauge field. Our results may provide insight into the understanding of similar phenomena in other graphene-like materials and structures.

  6. More about the doubling degeneracy operators associated with Majorana fermions and Yang-Baxter equation

    PubMed Central

    Yu, Li-Wei; Ge, Mo-Lin

    2015-01-01

    A new realization of doubling degeneracy based on emergent Majorana operator Γ presented by Lee-Wilczek has been made. The Hamiltonian can be obtained through the new type of solution of Yang-Baxter equation, i.e. -matrix. For 2-body interaction, gives the “superconducting” chain that is the same as 1D Kitaev chain model. The 3-body Hamiltonian commuting with Γ is derived by 3-body -matrix, we thus show that the essence of the doubling degeneracy is due to . We also show that the extended Γ′-operator is an invariant of braid group BN for odd N. Moreover, with the extended Γ′-operator, we construct the high dimensional matrix representation of solution to Yang-Baxter equation and find its application in constructing 2N-qubit Greenberger-Horne-Zeilinger state for odd N. PMID:25631987

  7. More about the doubling degeneracy operators associated with Majorana fermions and Yang-Baxter equation

    NASA Astrophysics Data System (ADS)

    Yu, Li-Wei; Ge, Mo-Lin

    2015-01-01

    A new realization of doubling degeneracy based on emergent Majorana operator Γ presented by Lee-Wilczek has been made. The Hamiltonian can be obtained through the new type of solution of Yang-Baxter equation, i.e. -matrix. For 2-body interaction, gives the ``superconducting'' chain that is the same as 1D Kitaev chain model. The 3-body Hamiltonian commuting with Γ is derived by 3-body -matrix, we thus show that the essence of the doubling degeneracy is due to . We also show that the extended Γ'-operator is an invariant of braid group BN for odd N. Moreover, with the extended Γ'-operator, we construct the high dimensional matrix representation of solution to Yang-Baxter equation and find its application in constructing 2N-qubit Greenberger-Horne-Zeilinger state for odd N.

  8. Split of Chiral Degeneracy in Mechanical and Structural Properties of Oligopeptide-Polysaccharide Biomaterials

    SciTech Connect

    Taraban, Marc B.; Hyland, Laura L.; Yu, Y. Bruce

    2013-09-23

    Enantiomeric biomaterials which are mirror images of each other are characterized by chiral degeneracy—identical structural characteristics and bulk material properties. The addition of another chiral component, d-polysaccharide, has been shown to split such degeneracy and result in two distinct biomaterials. Dynamic oscillatory rheometry and small-angle X-ray scattering demonstrate that the natural biochirality combination of l-peptides and d-polysaccharides assembles faster, has higher elastic moduli (G'), and is structurally more beneficial as opposed to the alternative d-peptide and d-polysaccharide combination. Chemical modifications of the OH-groups in α-d-glucose units in d-polysaccharides weaken such splitting of chiral degeneracy. These findings form a basis to design novel biomaterials and provide additional insight on why proteins and polysaccharides have oppoiste chirality in the biological world.

  9. SPIN-PRECESSION: BREAKING THE BLACK HOLE-NEUTRON STAR DEGENERACY

    SciTech Connect

    Chatziioannou, Katerina; Cornish, Neil; Klein, Antoine; Yunes, Nicolás

    2015-01-01

    Mergers of compact stellar remnants are prime targets for the LIGO/Virgo gravitational wave detectors. The gravitational wave signals from these merger events can be used to study the mass and spin distribution of stellar remnants, and provide information about black hole horizons and the material properties of neutron stars. However, it has been suggested that degeneracies in the way that the star's mass and spin are imprinted in the waveforms may make it impossible to distinguish between black holes and neutron stars. Here we show that the precession of the orbital plane due to spin-orbit coupling breaks the mass-spin degeneracy, and allows us to distinguish between standard neutron stars and alternative possibilities, such as black holes or exotic neutron stars with large masses and spins.

  10. Degeneracy and relativistic microreversibility relations for collisional-radiative equilibrium models

    NASA Astrophysics Data System (ADS)

    Faussurier, Gérald; Blancard, Christophe

    2017-06-01

    We present the relativistic expressions of standard nonrelativistic microreversibility relations that can be used in collisional-radiative equilibrium models to calculate the transition rates including the free electron degeneracy for collisional excitation and deexcitation, collisional ionization and three-body recombination, dielectronic capture and autoionization, photoexcitation and photodeexcitation, and radiative recombination and photoionization. Semiempirical expressions or more refined calculations can be used for the cross sections of interest as long as they are calculated by taking into account either nonrelativistic, relativistic, or ultrarelativistic effects for both the bound and free electrons. The bound and the free electrons should be treated on the same footing. This is crucial for the internal consistency of the approach valid at arbitrary degeneracy and relativistic degrees.

  11. Exceptional point and degeneracy of the neutral Higgs boson system H-A

    SciTech Connect

    Felix-Beltran, O.; Gomez-Bock, M.; Hernandez, E.; Mondragon, A.; Mondragon, M.

    2009-04-20

    We analyze the masses and mixings of the isolated neutral and heavy Higgs fields H and A of the Minimal Supersymmetric Standard Model (MSSM) with CP violation, which have opposite CP parities and nearly degenerate masses. At the degeneracy point, the hypersurfaces that represent the physical masses as functions of the system parameters have a rank one algebraic branch point, and the real and imaginary parts have branch cuts, both starting at the same exceptional point but extending in opposite directions in parameter space. Associated with this singularity, the propagator for the mixed neutral Higgs system H-A has a double pole in the non-physical sheet of the squared energy complex plane s. The continuity of the transition amplitude matrix at the exact degeneracy of the masses is examined.

  12. Vacuum degeneracy of a circuit QED system in the ultrastrong coupling regime.

    PubMed

    Nataf, Pierre; Ciuti, Cristiano

    2010-01-15

    We investigate theoretically the quantum vacuum properties of a chain of N superconducting Josephson atoms inductively coupled to a transmission line resonator. We derive the quantum field Hamiltonian for such a circuit QED system, showing that, due to the type and strength of the interaction, a quantum phase transition can occur with a twice degenerate quantum vacuum above a critical coupling. In the finite-size case, the degeneracy is lifted, with an energy splitting decreasing exponentially with increasing values of g{2}N{2}, where g is the dimensionless vacuum Rabi coupling per artificial atom. We determine analytically the ultrastrong coupling asymptotic expression of the two degenerate vacua for an arbitrary number of artificial atoms and of resonator modes. In the ultrastrong coupling regime the degeneracy is protected with respect to random fluctuations of the transition energies of the Josephson elements.

  13. Dynamical symmetries for fermions

    SciTech Connect

    Guidry, M.

    1989-01-01

    An introduction is given to the Fermion Dynamical Symmetry Model (FDSM). The analytical symmetry limits of the model are then applied to the calculation of physical quantities such as ground-state masses and B(E{sub 2}) values in heavy nuclei. These comparisons with data provide strong support for a new principle of collective motion, the Dynamical Pauli Effect, and suggest that dynamical symmetries which properly account for the pauli principle are much more persistent in nuclear structure than the corresponding boson symmetries. Finally, we present an assessment of criticisms which have been voiced concerning the FDSM, and a discussion of new phenomena and exotic spectroscopy'' which may be suggested by the model. 14 refs., 8 figs., 4 tabs.

  14. Symmetries in Physics

    SciTech Connect

    Castanos, Octavio

    2010-09-10

    The purpose of this course is to study the evolution of the symmetry concept and establish its influence in the knowledge of the fundamental laws of nature. Physicist have been using the symmetry concept in two ways: to solve problems and to search for new understanding of the world around us. In quantum physics symmetry plays a key role in gaining an understanding of the physical laws governing the behavior of matter and field systems. It provides, generally, a shortcut based on geometry for discovering the secrets of the Universe. Because it is believed that the laws of physics are invariant under discrete and continuous transformation operations of the space and time, there are continuous symmetries, for example, energy and momentum together with discrete ones corresponding to charge, parity and time reversal operations.

  15. Another Broken Symmetry

    ERIC Educational Resources Information Center

    Groetsch, C. W.

    2005-01-01

    Resistance destroys symmetry. In this note, a graphical exploration serves as a guide to a rigorous elementary proof of a specific asymmetry in the trajectory of a point projectile in a medium offering linear resistance.

  16. The Symmetries of QCD

    ScienceCinema

    Sekhar Chivukula

    2016-07-12

    The symmetries of a quantum field theory can be realized in a variety of ways. Symmetries can be realized explicitly, approximately, through spontaneous symmetry breaking or, via an anomaly, quantum effects can dynamically eliminate a symmetry of the theory that was present at the classical level.  Quantum Chromodynamics (QCD), the modern theory of the strong interactions, exemplify each of these possibilities. The interplay of these effects determine the spectrum of particles that we observe and, ultimately, account for 99% of the mass of ordinary matter. 

  17. Dynamical spacetime symmetry

    NASA Astrophysics Data System (ADS)

    Lovelady, Benjamin C.; Wheeler, James T.

    2016-04-01

    According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dimensional Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected S O (n ) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an S O (n -1 ,1 ) connection on the spacetime. The principal fiber bundle character of the original S O (n ) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.

  18. Animal Gaits and Symmetry

    NASA Astrophysics Data System (ADS)

    Golubitsky, Martin

    2012-04-01

    Many gaits of four-legged animals are described by symmetry. For example, when a horse paces it moves both left legs in unison and then both right legs and so on. The motion is described by two symmetries: Interchange front and back legs, and swap left and right legs with a half-period phase shift. Biologists postulate the existence of a central pattern generator (CPG) in the neuronal system that sends periodic signals to the legs. CPGs can be thought of as electrical circuits that produce periodic signals and can be modeled by systems with symmetry. In this lecture we discuss animal gaits; use gait symmetries to construct a simplest CPG architecture that naturally produces quadrupedal gait rhythms; and make several testable predictions about gaits.

  19. Symmetries in Physics

    NASA Astrophysics Data System (ADS)

    Castaños, Octavio

    2010-09-01

    The purpose of this course is to study the evolution of the symmetry concept and establish its influence in the knowledge of the fundamental laws of nature. Physicist have been using the symmetry concept in two ways: to solve problems and to search for new understanding of the world around us. In quantum physics symmetry plays a key role in gaining an understanding of the physical laws governing the behavior of matter and field systems. It provides, generally, a shortcut based on geometry for discovering the secrets of the Universe. Because it is believed that the laws of physics are invariant under discrete and continuous transformation operations of the space and time, there are continuous symmetries, for example, energy and momentum together with discrete ones corresponding to charge, parity and time reversal operations.

  20. Gauge symmetry from decoupling

    NASA Astrophysics Data System (ADS)

    Wetterich, C.

    2017-02-01

    Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang-Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.

  1. Halogenated benzene radical cations and ground state degeneracy splitting by asymmetric substitution

    USGS Publications Warehouse

    Bondybey, V.E.; Vaughn, C.R.; Miller, T.A.; English, J.H.; Shiley, R.H.

    1981-01-01

    The absorption and laser induced fluorescence of several halogenated benzene radical cations were studied in solid Ne matrices. The spectra of 1,2,4-trifluorobenzene, l,3-dichloro-5-fluorobenzene, and l-chloro-3,5- difluorobenzene radical cations are observed and analyzed. Studies of fluorescence polarization and a photoselection technique were used to examine the splitting of the degeneracy of the benzene cation ground state by asymmetric subsitution. ?? 1981 American Institute of Physics.

  2. Degeneracy between primordial tensor modes and cosmic strings in future CMB data from the Planck satellite

    SciTech Connect

    Urrestilla, Jon; Mukherjee, Pia; Liddle, Andrew R.; Hindmarsh, Mark; Kunz, Martin; Bevis, Neil

    2008-06-15

    While observations indicate that the predominant source of cosmic inhomogeneities are adiabatic perturbations, there are a variety of candidates to provide auxiliary trace effects, including inflation-generated primordial tensors and cosmic defects which both produce B-mode cosmic microwave background polarization. We investigate whether future experiments may suffer confusion as to the true origin of such effects, focusing on the ability of Planck to distinguish tensors from cosmic strings, and show that there is no significant degeneracy.

  3. Near-degeneracy effects on the frequencies of rotationally-split mixed modes in red giants

    NASA Astrophysics Data System (ADS)

    Deheuvels, S.; Ouazzani, R. M.; Basu, S.

    2017-09-01

    Context. The Kepler space mission has made it possible to measure the rotational splittings of mixed modes in red giants, thereby providing an unprecedented opportunity to probe the internal rotation of these stars. Aims: Asymmetries have been detected in the rotational multiplets of several red giants. This is unexpected since all the red giants whose rotation profiles have been measured thus far are found to rotate slowly, and low rotation, in principle, produces symmetrical multiplets. Our aim here is to explain these asymmetries and find a way of exploiting them to probe the internal rotation of red giants. Methods: We show that in the cases where asymmetrical multiplets were detected, near-degeneracy effects are expected to occur, because of the combined effects of rotation and mode mixing. Such effects have not been taken into account so far. By using both perturbative and non-perturbative approaches, we show that near-degeneracy effects produce multiplet asymmetries that are very similar to the observations. We then propose and validate a method based on the perturbative approach to probe the internal rotation of red giants using multiplet asymmetries. Results: We successfully apply our method to the asymmetrical l = 2 multiplets of the Kepler young red giant KIC 7341231 and obtain precise estimates of its mean rotation in the core and the envelope. The observed asymmetries are reproduced with a good statistical agreement, which confirms that near-degeneracy effects are very likely the cause of the detected multiplet asymmetries. Conclusions: We expect near-degeneracy effects to be important for l = 2 mixed modes all along the red giant branch (RGB). For l = 1 modes, these effects can be neglected only at the base of the RGB. They must therefore be taken into account when interpreting rotational splittings and as shown here, they can bring valuable information about the internal rotation of red giants.

  4. Equation of state of the relativistic free electron gas at arbitrary degeneracy

    NASA Astrophysics Data System (ADS)

    Faussurier, Gérald

    2016-12-01

    We study the problem of the relativistic free electron gas at arbitrary degeneracy. The specific heat at constant volume and particle number CV and the specific heat at constant pressure and particle number CP are calculated. The question of equation of state is also studied. Non degenerate and degenerate limits are considered. We generalize the formulas obtained in the non-relativistic and ultra-relativistic regimes.

  5. Quantum Spectral Symmetries

    NASA Astrophysics Data System (ADS)

    Hamhalter, Jan; Turilova, Ekaterina

    2017-02-01

    Quantum symmetries of spectral lattices are studied. Basic properties of spectral order on A W ∗-algebras are summarized. Connection between projection and spectral automorphisms is clarified by showing that, under mild conditions, any spectral automorphism is a composition of function calculus and Jordan ∗-automorphism. Complete description of quantum spectral symmetries on Type I and Type II A W ∗-factors are completely described.

  6. The nuclear symmetry energy

    NASA Astrophysics Data System (ADS)

    Baldo, M.; Burgio, G. F.

    2016-11-01

    The nuclear symmetry energy characterizes the variation of the binding energy as the neutron to proton ratio of a nuclear system is varied. This is one of the most important features of nuclear physics in general, since it is just related to the two component nature of the nuclear systems. As such it is one of the most relevant physical parameters that affect the physics of many phenomena and nuclear processes. This review paper presents a survey of the role and relevance of the nuclear symmetry energy in different fields of research and of the accuracy of its determination from the phenomenology and from the microscopic many-body theory. In recent years, a great interest was devoted not only to the Nuclear Matter symmetry energy at saturation density but also to its whole density dependence, which is an essential ingredient for our understanding of many phenomena. We analyze the nuclear symmetry energy in different realms of nuclear physics and astrophysics. In particular we consider the nuclear symmetry energy in relation to nuclear structure, astrophysics of Neutron Stars and supernovae, and heavy ion collision experiments, trying to elucidate the connections of these different fields on the basis of the symmetry energy peculiarities. The interplay between experimental and observational data and theoretical developments is stressed. The expected future developments and improvements are schematically addressed, together with most demanded experimental and theoretical advances for the next few years.

  7. Pseudospin symmetry for modified Rosen-Morse potential including a Pekeris-type approximation to the pseudo-centrifugal term

    NASA Astrophysics Data System (ADS)

    Wei, Gao-Feng; Dong, Shi-Hai

    2010-11-01

    By applying a Pekeris-type approximation to the pseudo-centrifugal term, we study the pseudospin symmetry of a Dirac nucleon subjected to scalar and vector modified Rosen-Morse (MRM) potentials. A complicated quartic energy equation and spinor wave functions with arbitrary spin-orbit coupling quantum number k are presented. The pseudospin degeneracy is checked numerically. Pseudospin symmetry is discussed theoretically and numerically in the limit case α rightarrow 0 . It is found that the relativistic MRM potential cannot trap a Dirac nucleon in this limit.

  8. Quantum Fluctuations along Symmetry Crossover in a Kondo-Correlated Quantum Dot

    NASA Astrophysics Data System (ADS)

    Ferrier, Meydi; Arakawa, Tomonori; Hata, Tokuro; Fujiwara, Ryo; Delagrange, Raphaëlle; Deblock, Richard; Teratani, Yoshimichi; Sakano, Rui; Oguri, Akira; Kobayashi, Kensuke

    2017-05-01

    Universal properties of entangled many-body states are controlled by their symmetry and quantum fluctuations. By the magnetic-field tuning of the spin-orbital degeneracy in a Kondo-correlated quantum dot, we have modified quantum fluctuations to directly measure their influence on the many-body properties along the crossover from SU(4) to SU(2) symmetry of the ground state. High-sensitive current noise measurements combined with the nonequilibrium Fermi liquid theory clarify that the Kondo resonance and electron correlations are enhanced as the fluctuations, measured by the Wilson ratio, increase along the symmetry crossover. Our achievement demonstrates that nonlinear noise constitutes a measure of quantum fluctuations that can be used to tackle quantum phase transitions.

  9. Symmetry and electronic structure of noble-metal nanoparticles and the role of relativity.

    PubMed

    Häkkinen, Hannu; Moseler, Michael; Kostko, Oleg; Morgner, Nina; Hoffmann, Margarita Astruc; von Issendorff, Bernd

    2004-08-27

    We present high resolution UV-photoelectron spectra of cold mass selected Cun-, Agn-, and Aun- with n=53-58. The observed electron density of states is not the expected simple electron shell structure, but is strongly influenced by electron-lattice interactions. Only Cu55- and Ag55- exhibit highly degenerate states. This is a direct consequence of their icosahedral symmetry, as is confirmed by density functional theory calculations. Neighboring sizes exhibit perturbed electronic structures, as they are formed by removal or addition of atoms to the icosahedron and therefore have lower symmetries. Gold clusters in the same size range show completely different spectra with almost no degeneracy, which indicates that they have structures of much lower symmetry. This behavior is related to strong relativistic bonding effects in gold, as demonstrated by ab initio calculations for Au55-.

  10. Lowering of Boson-Fermion System Energy with a Gapped Cooper Resonant-Pair Dispersion Relation

    NASA Astrophysics Data System (ADS)

    Mamedov, T. A.; de Llano, M.

    2007-09-01

    Applying two-time Green-function techniques to the Friedberg-T.D. Lee phenomenological Hamiltonian of a many-fermion system, it is shown that positive-energy resonant bosonic pairs associated with four-fermion excitations above the Fermi sea are energetically lower in a ground-state that is a mixture of two coexisting and dynamically interacting many-particle subsystems: a) unpaired fermions and b) composite bosons. It is argued that an interaction between free fermions and bosons excited above the Fermi sea in the mixture, namely, the continuous processes of pair-formation from, and disintegration into, two unpaired electrons, results in a substantially lowering the total system energy. The positive-energy composite bosons begin to appear incoherently below a de-pairing temperature T* as their coupling- and temperature-dependent number density gradually increases from zero. This leads quite naturally to the pseudogap phenomenon observed in high-Tc cuprates

  11. Lowering of Boson-Fermion System Energy with a Gapped Cooper Resonant-Pair Dispersion Relation

    NASA Astrophysics Data System (ADS)

    Mamedov, T. A.; de Llano, M.

    Applying two-time Green-function techniques to the Friedberg-T.D. Lee phenomenological Hamiltonian of a many-fermion system, it is shown that positive-energy resonant bosonic pairs associated with four-fermion excitations above the Fermi sea are energetically lower in a ground-state that is a mixture of two coexisting and dynamically interacting many-particle subsystems: a) unpaired fermions and b) composite bosons. It is argued that an interaction between free fermions and bosons excited above the Fermi sea in the mixture, namely, the continuous processes of pair-formation from, and disintegration into, two unpaired electrons, results in a substantially lowering the total system energy. The positive-energy composite bosons begin to appear incoherently below a depairing temperature T* as their coupling- and temperature-dependent number density gradually increases from zero. This leads quite naturally to the pseudogap phenomenon observed in high-Tc cuprates.

  12. Tunneling into quantum wires: Regularization of the tunneling Hamiltonian and consistency between free and bosonized fermions

    NASA Astrophysics Data System (ADS)

    Filippone, Michele; Brouwer, Piet W.

    2016-12-01

    Tunneling between a point contact and a one-dimensional wire is usually described with the help of a tunneling Hamiltonian that contains a δ function in position space. Whereas the leading-order contribution to the tunneling current is independent of the way this δ function is regularized, higher-order corrections with respect to the tunneling amplitude are known to depend on the regularization. Instead of regularizing the δ function in the tunneling Hamiltonian, one may also obtain a finite tunneling current by invoking the ultraviolet cutoffs in a field-theoretic description of the electrons in the one-dimensional conductor, a procedure that is often used in the literature. For the latter case, we show that standard ultraviolet cutoffs lead to different results for the tunneling current in fermionic and bosonized formulations of the theory, when going beyond leading order in the tunneling amplitude. We show how to recover the standard fermionic result using the formalism of functional bosonization and revisit the tunneling current to leading order in the interacting case.

  13. Two-particle bosonic-fermionic quantum walk via integrated photonics.

    PubMed

    Sansoni, Linda; Sciarrino, Fabio; Vallone, Giuseppe; Mataloni, Paolo; Crespi, Andrea; Ramponi, Roberta; Osellame, Roberto

    2012-01-06

    Quantum walk represents one of the most promising resources for the simulation of physical quantum systems, and has also emerged as an alternative to the standard circuit model for quantum computing. Here we investigate how the particle statistics, either bosonic or fermionic, influences a two-particle discrete quantum walk. Such an experiment has been realized by exploiting polarization entanglement to simulate the bunching-antibunching feature of noninteracting bosons and fermions. To this scope a novel three-dimensional geometry for the waveguide circuit is introduced, which allows accurate polarization independent behavior, maintaining remarkable control on both phase and balancement.

  14. Transport in thin insulating films close to the Boson-Fermion Crossover

    NASA Astrophysics Data System (ADS)

    Joy, J. C.; Zhang, X.; Hollen, S. M.; Zhao, C.; Fernandes, G.; Xu, J. M.; Valles, J. M., Jr.

    2015-03-01

    In two-dimensional systems, sufficient levels of disorder are known to localize Cooper Pairs into a phase incoherent insulating state. While many theoretical and experimental works have shown this state's existence, its ubiquity close to the disorder tuned Superconductor to Insulator transition is still an open problem. Recent experiments on nanopatterned Pb0.9Bi0.1 films have suggested a crossover from Bosonic to Fermionic transport deep in the insulating phase, indicating that the Cooper Pair Insulator (CPI) only persists to a finite level of microscopic disorder. The normal state resistance at which this crossover occurs is governed by the extent coupling constant inhomogeneities on the scale of the coherence length, which allow the formation of locally phase coherent superconducting islands in the insulating state. By tuning the scale of these inhomogeneities and examining the extent of the CPI state, we argue that the disorder tuned Superconductor to Insulator transition proceeds via pair breaking and Anderson localization of fermions when the level spacing in the islands approaches the size of the mean field gap. This work was supported by the NSF through grants No. DMR-1307290 and DMR-0907357 and by the AFRL, the ONR, and the AFOSR. Currently at the Center for Emergent Materials, Ohio State University.

  15. Nuclei and Fundamental Symmetries

    NASA Astrophysics Data System (ADS)

    Haxton, Wick

    2016-09-01

    Nuclei provide marvelous laboratories for testing fundamental interactions, often enhancing weak processes through accidental degeneracies among states, and providing selection rules that can be exploited to isolate selected interactions. I will give an overview of current work, including the use of parity violation to probe unknown aspects of the hadronic weak interaction; nuclear electric dipole moment searches that may shed light on new sources of CP violation; and tests of lepton number violation made possible by the fact that many nuclei can only decay by rare second-order weak interactions. I will point to opportunities in both theory and experiment to advance the field. Based upon work supported in part by the US Department of Energy, Office of Science, Office of Nuclear Physics and SciDAC under Awards DE-SC00046548 (Berkeley), DE-AC02-05CH11231 (LBNL), and KB0301052 (LBNL).

  16. Hidden symmetries of the Higgs oscillator and the conformal algebra

    NASA Astrophysics Data System (ADS)

    Evnin, Oleg; Nivesvivat, Rongvoram

    2017-01-01

    We give a solution to the long-standing problem of constructing the generators of hidden symmetries of the quantum Higgs oscillator, a particle on a d-sphere moving in a central potential varying as the inverse cosine-squared of the polar angle. This superintegrable system is known to possess a rich algebraic structure, including a hidden SU(d) symmetry that can be deduced from classical conserved quantities and degeneracies of the quantum spectrum. The quantum generators of this SU(d) have not been constructed thus far, except at d  =  2, and naive quantization of classical conserved quantities leads to deformed Lie algebras with quadratic terms in the commutation relations. The nonlocal generators we obtain here satisfy the standard su(d) Lie algebra, and their construction relies on a recently discovered realization of the conformal algebra, which contains a complete set of raising and lowering operators for the Higgs oscillator. This operator structure has emerged from a relation between the Higgs oscillator Schrödinger equation and the Klein-Gordon equation in Anti-de Sitter spacetime. From such a point-of-view, constructing the hidden symmetry generators reduces to manipulations within the abstract conformal algebra so(d, 2).

  17. Physicochemical principle to identify spherical symmetries in the genetic code

    NASA Astrophysics Data System (ADS)

    Yang, , Prof. _, Dr.

    2004-05-01

    Based on the molecular structural regularity in nucleobases, upon analysing the atomic contents in amino acid side chains together with solid geometrically rearranging a Hamiltonian graph of the genetic code, hidden rotational symmetries inherent in the degeneracy of codons are unraveled. The internal relation of the 20 amino acids is identified to be in agreement with the spherical and polyhedral symmetry of a quasi-28-gon, i.e., icosikaioctagon, accompanied with two proposed evolutionary axes. Quasi-rotational symmetries in the distribution of both side-chain carbon atoms and side-chain skeleton atoms (carbon, nitrogen, oxygen and sulfur) within the amino acids are presented in the framework of this 28-gon organization. Additionally, we have identified that the sum of the side-chain skeleton atom (C, N, O and S) numbers from amino acids encoded by the 16 genetic code doublets is 100, which is equal to the sum of the backbone skeleton [C, N and O from NH2CHCOOH] atom numbers (5 for each amino acid) from 20 standard amino acids. All together, this study suggests that side chain carbon atomic numbers, side-chain skeleton atomic numbers and amino-acid backbone atomic numbers are balanced within the genetic code by an yet unknown physicochemical principle and non-physicochemical factors.

  18. Symmetry in Multiferroics

    NASA Astrophysics Data System (ADS)

    Cheong, Sang-Wook

    2008-03-01

    Symmetries govern Nature ubiquitously from the beauty of human faces to the local gauge invariance of quantum field theory. Magnetic order in frustrated magnets can occur without space inversion symmetry. When it relaxes to the magnetically-ordered configuration through exchange-striction, lattice can also loose inversion symmetry, leading to the presence of ferroelectric polarization. In these magnetically-driven ferroelectrics, dielectric properties turn out to be highly susceptible to applied magnetic fields. Both symmetric and antisymmetric exchange coupling can be involved in the exchange-striction. One form of symmetry often broken in Nature is the symmetry between left- and right-handedness. For example, the manner in which light propagates naturally selects one handedness, and is customarily described by a right-handed rule, depicting the relationship among the oscillating electric field, magnetic field and propagation vector of light. Chiral molecules also have a definite handedness, and given the preponderance of chiral molecules, it is not surprising that most complex proteins as well as their constituent amino acids are chiral. What is remarkable however, is that most of naturally occurring amino acids share the same chirality; only left-handedness. Such handedness, or chirality, appears to be a characteristic signature of life. In the multiferroic spinel CoCr2O4, conical magnetic order accompanies ferroelectric polarization as well as ferromagnetic moment. The relevant handedness and chirality in the multiferroic state will be also discussed.

  19. Lectures on Yangian symmetry

    NASA Astrophysics Data System (ADS)

    Loebbert, Florian

    2016-08-01

    In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang-Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross-Neveu model, the Heisenberg spin chain and { N }=4 superconformal Yang-Mills theory in four dimensions.

  20. Neutrino physics from a U(2) flavor symmetry

    SciTech Connect

    Carone, C.D.; Hall, L.J. |

    1997-10-01

    We consider the neutrino physics of models with a sequentially broken U(2) flavor symmetry. Such theories yield the observed pattern of quark and lepton masses, while maintaining sufficient degeneracies between superparticles of the first two generations to solve the supersymmetric flavor problem. Neutrino mass ratios and mixing angles in these models may differ significantly from those of the charged leptons, even though the neutrinos and charged leptons transform identically under the flavor group. A wide class of well-motivated U(2) theories yield order one {nu}{sub {mu}}- {nu}{sub {tau}} mixing, without a fine-tuning of parameters. These models provide a natural solution to the atmospheric neutrino deficit, and also have distinctive signatures at long-baseline neutrino oscillation experiments. {copyright} {ital 1997} {ital The American Physical Society}

  1. Symmetry of priapulids (Priapulida). 2. Symmetry of larvae.

    PubMed

    Adrianov, A V; Malakhov, V V

    2001-02-01

    Larvae of priapulids are characterized by radial symmetry evident from both external and internal characters of the introvert and lorica. The bilaterality appears as a result of a combination of several radial symmetries: pentaradial symmetry of the teeth, octaradial symmetry of the primary scalids, 25-radial symmetry of scalids, biradial symmetry of the neck, and biradial and decaradial symmetry of the trunk. Internal radiality is exhibited by musculature and the circumpharyngeal nerve ring. Internal bilaterality is evident from the position of the ventral nerve cord and excretory elements. Externally, the bilaterality is determined by the position of the anal tubulus and two shortened midventral rows of scalids bordering the ventral nerve cord. The lorical elements define the biradial symmetry that is missing in adult priapulids. The radial symmetry of larvae is a secondary appearance considered an evolutionary adaptation to a lifestyle within the three-dimensional environment of the benthic sediment.

  2. Symmetry in context: salience of mirror symmetry in natural patterns.

    PubMed

    Cohen, Elias H; Zaidi, Qasim

    2013-05-31

    Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits.

  3. Symmetry in context: Salience of mirror symmetry in natural patterns

    PubMed Central

    Cohen, Elias H.; Zaidi, Qasim

    2013-01-01

    Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits. PMID:23729773

  4. Seeing Science through Symmetry

    NASA Astrophysics Data System (ADS)

    Gould, L. I.

    Seeing Through Symmetry is a course that introduces non-science majors to the pervasive influence of symmetry in science. The concept of symmetry is usedboth as a link between subjects (such as physics, biology, mathematics, music, poetry, and art) and as a method within a subject. This is done through the development and use of interactive multimedia learning environments to stimulate learning. Computer-based labs enable the student to further explore the concept by being gently led from the arts to science. This talk is an update that includes some of the latest changes to the course. Explanations are given on methodology and how a variety of interactive multimedia tools contribute to both the lecture and lab portion of the course (created in 1991 and taught almost every semester since then, including one in Sweden).

  5. Baryons and chiral symmetry

    NASA Astrophysics Data System (ADS)

    Liu, Keh-Fei

    The relevance of chiral symmetry in baryons is highlighted in three examples in the nucleon spectroscopy and structure. The first one is the importance of chiral dynamics in understanding the Roper resonance. The second one is the role of chiral symmetry in the lattice calculation of πNσ term and strangeness. The third one is the role of chiral U(1) anomaly in the anomalous Ward identity in evaluating the quark spin and the quark orbital angular momentum. Finally, the chiral effective theory for baryons is discussed.

  6. Weakly broken galileon symmetry

    SciTech Connect

    Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Vernizzi, Filippo

    2015-09-01

    Effective theories of a scalar ϕ invariant under the internal galileon symmetryϕ→ϕ+b{sub μ}x{sup μ} have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of weakly broken galileon invariance, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon’s quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.

  7. BOOK REVIEW: Symmetry Breaking

    NASA Astrophysics Data System (ADS)

    Ryder, L. H.

    2005-11-01

    One of the most fruitful and enduring advances in theoretical physics during the last half century has been the development of the role played by symmetries. One needs only to consider SU(3) and the classification of elementary particles, the Yang Mills enlargement of Maxwell's electrodynamics to the symmetry group SU(2), and indeed the tremendous activity surrounding the discovery of parity violation in the weak interactions in the late 1950s. This last example is one of a broken symmetry, though the symmetry in question is a discrete one. It was clear to Gell-Mann, who first clarified the role of SU(3) in particle physics, that this symmetry was not exact. If it had been, it would have been much easier to discover; for example, the proton, neutron, Σ, Λ and Ξ particles would all have had the same mass. For many years the SU(3) symmetry breaking was assigned a mathematical form, but the importance of this formulation fell away when the quark model began to be taken seriously; the reason the SU(3) symmetry was not exact was simply that the (three, in those days) quarks had different masses. At the same time, and in a different context, symmetry breaking of a different type was being investigated. This went by the name of `spontaneous symmetry breaking' and its characteristic was that the ground state of a given system was not invariant under the symmetry transformation, though the interactions (the Hamiltonian, in effect) was. A classic example is ferromagnetism. In a ferromagnet the atomic spins are aligned in one direction only—this is the ground state of the system. It is clearly not invariant under a rotation, for that would change the ground state into a (similar but) different one, with the spins aligned in a different direction; this is the phenomenon of a degenerate vacuum. The contribution of the spin interaction, s1.s2, to the Hamiltonian, however, is actually invariant under rotations. As Coleman remarked, a little man living in a ferromagnet would

  8. Symmetry constraint for foreground extraction.

    PubMed

    Fu, Huazhu; Cao, Xiaochun; Tu, Zhuowen; Lin, Dongdai

    2014-05-01

    Symmetry as an intrinsic shape property is often observed in natural objects. In this paper, we discuss how explicitly taking into account the symmetry constraint can enhance the quality of foreground object extraction. In our method, a symmetry foreground map is used to represent the symmetry structure of the image, which includes the symmetry matching magnitude and the foreground location prior. Then, the symmetry constraint model is built by introducing this symmetry structure into the graph-based segmentation function. Finally, the segmentation result is obtained via graph cuts. Our method encourages objects with symmetric parts to be consistently extracted. Moreover, our symmetry constraint model is applicable to weak symmetric objects under the part-based framework. Quantitative and qualitative experimental results on benchmark datasets demonstrate the advantages of our approach in extracting the foreground. Our method also shows improved results in segmenting objects with weak, complex symmetry properties.

  9. Symmetry matters: photodissociation dynamics of symmetrically versus asymmetrically substituted phenols.

    PubMed

    Karsili, Tolga N V; Wenge, Andreas M; Marchetti, Barbara; Ashfold, Michael N R

    2014-01-14

    We report a combined experimental (H (Rydberg) atom photofragment translational spectroscopy) and theoretical (ab initio electronic structure and vibronic coupling calculations) study of the effects of symmetry on the photodissociation dynamics of phenols. Ultraviolet photoexcitation to the bound S1((1)ππ*) state of many phenols leads to some O-H bond fission by tunneling through the barrier under the conical intersection (CI) between the S1 and dissociative S2((1)πσ*) potential energy surfaces in the R(O-H) stretch coordinate. Careful analysis of the total kinetic energy release spectra of the resulting products shows that the radicals formed following S1 ← S0 excitation of phenol and symmetrically substituted phenols like 4-fluorophenol all carry an odd number of quanta in vibrational mode ν(16a), whereas those deriving from asymmetrically substituted systems like 3-fluorophenol or 4-methoxyphenol do not. This contrasting behavior can be traced back to symmetry. Symmetrically substituted phenols exist in two equivalent rotamers, which interconvert by tunneling through the barrier to OH torsional motion. Their states are thus best considered in the non-rigid G4 molecular symmetry group, wherein radiationless transfer from the S1 to S2 state requires a coupling mode of a2 symmetry. Of the three a2 symmetry parent modes, the out-of-plane ring puckering mode ν(16a) shows much the largest interstate coupling constant in the vicinity of the S1/S2 CI. The nuclear motions associated with ν(16a) are orthogonal to the dissociation coordinate, and are thus retained in the radical products. Introducing asymmetry (even a non-linear substituent in the 4-position) lifts the degeneracy of the rotamers, and lowers the molecular symmetry to Cs. Many more parent motions satisfy the reduced (a'') symmetry requirement to enable S1/S2 coupling, the most effective of which is OH torsion. This motion 'disappears' on O-H bond fission; symmetry thus imposes no restriction to

  10. Eccentricity Inferences in Multi-planet systems with Transit Timing: Degeneracies and Apsidal Alignment

    NASA Astrophysics Data System (ADS)

    Jontof-Hutter, Daniel; Van Laerhoven, Christa L.; Ford, Eric B.

    2016-05-01

    Hundreds of multi-transiting systems discovered by the Kepler mission show Transit Timing Variations (TTV). In cases where the TTVs are uniquely attributable to transiting planets, the TTVs enable precise measurements of planetary masses and orbital parameters. Of particular interest are the constraints on eccentricity vectors that can be inferred in systems of low-mass exoplanets.The TTVs in these systems are dominated by a signal caused by near-resonant mean motions. This causes the well-known near-degeneracy between planetary masses and orbital eccentricities. In addition, it causes a degeneracy between the eccentricities of interacting planet pairs.For many systems, the magnitude of individual eccentricities are weakly constrained, yet the data typically provide a tight constraint on the posterior joint distribution for the eccentricity vector components. This permits tight constraints on the relative eccentricity and degree of alignment of interacting planets.For a sample of two and three-planet systems with TTVs, we highlight the effects of these correlations. While the most eccentric orbital solutions for these systems show apsidal alignment, this is often due to the degeneracy that causes correlated constraints on the eccentricity vector components. We compare the likelihood of apsidal alignment for two choices of eccentricity prior: a wide prior using a Rayleigh distribution of scale length 0.1 and a narrower prior with scale length 0.02. In all cases the narrower prior decreased the fraction of samples that exhibited apsidal alignment. However, apsidal alignment persisted in the majority of cases with a narrower eccentricity prior. For a sample of our TTV solutions, we ran simulations of these systems over secular timescales, and decomposed their eccentricity eigenmodes over time, confirming that in most cases, the eccentricities were dominated by parallel eigenmodes which favor apsidal alignment.

  11. Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy.

    PubMed

    Xu, Zhongxiao; Wu, Yuelong; Tian, Long; Chen, Lirong; Zhang, Zhiying; Yan, Zhihui; Li, Shujing; Wang, Hai; Xie, Changde; Peng, Kunchi

    2013-12-13

    Long-lived and high-fidelity memory for a photonic polarization qubit (PPQ) is crucial for constructing quantum networks. We present a millisecond storage system based on electromagnetically induced transparency, in which a moderate magnetic field is applied on a cold-atom cloud to lift Zeeman degeneracy and, thus, the PPQ states are stored as two magnetic-field-insensitive spin waves. Especially, the influence of magnetic-field-sensitive spin waves on the storage performances is almost totally avoided. The measured average fidelities of the polarization states are 98.6% at 200  μs and 78.4% at 4.5 ms, respectively.

  12. Cluster-Void Degeneracy Breaking: Dark Energy, Planck, and the Largest Cluster and Void

    NASA Astrophysics Data System (ADS)

    Sahlén, Martin; Zubeldía, Íñigo; Silk, Joseph

    2016-03-01

    Combining galaxy cluster and void abundances breaks the degeneracy between mean matter density {{{Ω }}}{{m}} and power-spectrum normalization {σ }8. For the first time for voids, we constrain {{{Ω }}}{{m}}=0.21+/- 0.10 and {σ }8=0.95+/- 0.21 for a flat Λ CDM universe, using extreme-value statistics on the claimed largest cluster and void. The Planck-consistent results detect dark energy with two objects, independently of other dark energy probes. Cluster-void studies are also complementary in scale, density, and nonlinearity, and are of particular interest for testing modified-gravity models.

  13. Elimination of depth degeneracy in optical frequency-domain imaging through polarization-based optical demodulation

    PubMed Central

    Vakoc, B. J.; Yun, S. H.; Tearney, G. J.; Bouma, B. E.

    2009-01-01

    A novel optical frequency-domain imaging system is demonstrated that employs a passive optical demodulation circuit and a chirped digital acquisition clock derived from a voltage-controlled oscillator. The demodulation circuit allows the separation of signals from positive and negative depths to better than 50 dB, thereby eliminating depth degeneracy and doubling the imaging depth range. Our system design is compatible with dual-balanced and polarization-diverse detection, important techniques in the practical biomedical application of optical frequency-domain imaging. PMID:16480209

  14. Mass Hierarchy Resolution in Reactor Anti-neutrino Experiments: Parameter Degeneracies and Detector Energy Response

    SciTech Connect

    X. Qian, D. A. Dwyer, R. D. McKeown, P. Vogel, W. Wang, C. Zhang`

    2013-02-01

    Determination of the neutrino mass hierarchy using a reactor neutrino experiment at ∼60  km is analyzed. Such a measurement is challenging due to the finite detector resolution, the absolute energy scale calibration, and the degeneracies caused by current experimental uncertainty of |Δm{sub 32}{sup 2}|. The standard {chi}{sup 2} method is compared with a proposed Fourier transformation method. In addition, we show that for such a measurement to succeed, one must understand the nonlinearity of the detector energy scale at the level of a few tenths of percent.

  15. Exploring Metric Symmetry

    SciTech Connect

    Zwart, P.H.; Grosse-Kunstleve, R.W.; Adams, P.D.

    2006-07-31

    Relatively minor perturbations to a crystal structure can in some cases result in apparently large changes in symmetry. Changes in space group or even lattice can be induced by heavy metal or halide soaking (Dauter et al, 2001), flash freezing (Skrzypczak-Jankun et al, 1996), and Se-Met substitution (Poulsen et al, 2001). Relations between various space groups and lattices can provide insight in the underlying structural causes for the symmetry or lattice transformations. Furthermore, these relations can be useful in understanding twinning and how to efficiently solve two different but related crystal structures. Although (pseudo) symmetric properties of a certain combination of unit cell parameters and a space group are immediately obvious (such as a pseudo four-fold axis if a is approximately equal to b in an orthorhombic space group), other relations (e.g. Lehtio, et al, 2005) that are less obvious might be crucial to the understanding and detection of certain idiosyncrasies of experimental data. We have developed a set of tools that allows straightforward exploration of possible metric symmetry relations given unit cell parameters and a space group. The new iotbx.explore{_}metric{_}symmetry command produces an overview of the various relations between several possible point groups for a given lattice. Methods for finding relations between a pair of unit cells are also available. The tools described in this newsletter are part of the CCTBX libraries, which are included in the latest (versions July 2006 and up) PHENIX and CCI Apps distributions.

  16. Horror Vacui Symmetry.

    ERIC Educational Resources Information Center

    Crumpecker, Cheryl

    2003-01-01

    Describes an art lesson used with children in the third grade to help them learn about symmetry, as well as encouraging them to draw larger than usual. Explains that students learn about the belief called "Horror Vacui" of the Northwest American Indian tribes and create their interpretation of this belief. (CMK)

  17. Introduction to chiral symmetry

    SciTech Connect

    Koch, V.

    1996-01-08

    These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential ideas of chiral perturbation theory. Some applications to the physics of ultrarelativistic heavy ion collisions will be presented.

  18. Symmetry in Season.

    ERIC Educational Resources Information Center

    Seidel, Judith Day

    1998-01-01

    Presents activities that demonstrate how technology can help students discover the mathematics in nature. Claims that these experiences can clarify students' vision of the symmetry of beauty that fills the world beyond the computer. Concludes that the use of flexible software tools helps students explore how a shape is affected when they change…

  19. Symmetry the Trademark Way.

    ERIC Educational Resources Information Center

    Renshaw, Barbara S.

    1986-01-01

    Trademark designs provide a familiar yet innovative way for students to look at a number of mathematical concepts. How line and rotational symmetry can be presented using trademarks is the focus of this article. The emphasis is on the design of bulletin boards. (MNS)

  20. Active fluctuation symmetries

    NASA Astrophysics Data System (ADS)

    Maes, Christian; Salazar, Alberto

    2014-01-01

    In contrast with the understanding of fluctuation symmetries for entropy production, similar ideas applied to the time-symmetric fluctuation sector have been less explored. Here we give detailed derivations of time-symmetric fluctuation symmetries in boundary-driven particle systems such as the open Kawasaki lattice gas and the zero-range model. As a measure of time-symmetric dynamical activity over time T we count the difference (Nℓ - Nr)/T between the number of particle jumps in or out at the left edge and those at the right edge of the system. We show that this quantity satisfies a fluctuation symmetry from which we derive a new Green-Kubo-type relation. It will follow then that the system is more active at the edge connected to the particle reservoir with the largest chemical potential. We also apply these exact relations derived for stochastic particle models to a deterministic case, the spinning Lorentz gas, where the symmetry relation for the activity is checked numerically.

  1. Emergent spinless Weyl semimetals between the topological crystalline insulator and normal insulator phases with glide symmetry

    NASA Astrophysics Data System (ADS)

    Kim, Heejae; Murakami, Shuichi

    2016-05-01

    We construct a theory describing phase transitions between the spinless topological crystalline insulator phase with glide symmetry and a normal insulator phase. We show that a spinless Weyl semimetal phase should intervene between these two phases. Here, because all the bands are free from degeneracy in general, a gap closing between a single conduction band and a single valence band at phase transition generally gives rise to a pair creation of Weyl nodes; hence the Weyl semimetal phase naturally appears. We show the relationship between the change of the Z2 topological number when the system goes through the Weyl semimetal phase, and the trajectory of the Weyl nodes.

  2. Topological Phases on Non-orientable Surfaces: Twisting by Parity Symmetry

    NASA Astrophysics Data System (ADS)

    Chan, Pak On; Teo, Chi Yan; Ryu, Shinsei

    We discuss (2+1)D topological phases on non-orientable spatial surfaces, such as Möbius strip, real projective plane and Klein bottle, etc., which are obtained by twisting the parent topological phases by their underlying pairty symmetries through introducing parity defects. We construct the ground states on arbitrary non-orientable closed manifolds and calculate the ground state degeneracy. Such degeneracy is shown to be robust against continuous deformation of the underlying manifold. We also study the action of the mapping class group on the multiplet of ground states on the Klein bottle. The physical properties of the topological states on non-orientable surfaces are deeply related to the parity symmetric anyons which do not have a notion of orientation in their statistics. For example, the number of ground states on the projective plane equals the root of the number of distinguishable parity symmetric anyons, while the ground state degeneracy on the Klein bottle equals the total number of parity symmetric anyons; In deforming the Klein bottle, the Dehn twist encodes the topological spins whereas the Y-homeomorphism tells the particle-hole relation of the parity symmetric anyons.

  3. Degeneracies of particle and nuclear physics uncertainties in neutrinoless β β decay

    NASA Astrophysics Data System (ADS)

    Lisi, E.; Rotunno, A. M.; Šimkovic, F.

    2015-11-01

    Theoretical estimates for the half-life of neutrinoless double beta decay (0 ν β β ) in candidate nuclei are affected by both particle and nuclear physics uncertainties, which may complicate the interpretation of decay signals or limits. We study such uncertainties and their degeneracies in the following context: three 0 ν β β nuclei of great interest for large-scale experiments (Ge 76 , Te 130 , Xe 136 ), two representative particle physics mechanisms (light and heavy Majorana neutrino exchange), and a large set of nuclear matrix elements (NME), computed within the quasiparticle random phase approximation (QRPA). It turns out that the main theoretical uncertainties, associated with the effective axial coupling gA and with the nucleon-nucleon potential, can be parametrized in terms of NME rescaling factors, up to small residuals. From this parametrization, the following QRPA features emerge: (1) the NME dependence on gA is milder than quadratic, (2) in each of the two mechanisms, the relevant lepton number violating parameter is largely degenerate with the NME rescaling factors, and (3) the light and heavy neutrino exchange mechanisms are basically degenerate in the above three nuclei. We comment on the challenging theoretical and experimental improvements required to reduce such particle and nuclear physics uncertainties and their degeneracies.

  4. Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy*

    NASA Astrophysics Data System (ADS)

    Kechedzhi, Kostyantyn; Smelyanskiy, Vadim N.

    2016-04-01

    Real-life quantum computers are inevitably affected by intrinsic noise resulting in dissipative nonunitary dynamics realized by these devices. We consider an open-system quantum annealing algorithm optimized for such a realistic analog quantum device which takes advantage of noise-induced thermalization and relies on incoherent quantum tunneling at finite temperature. We theoretically analyze the performance of this algorithm considering a p -spin model that allows for a mean-field quasiclassical solution and, at the same time, demonstrates the first-order phase transition and exponential degeneracy of states, typical characteristics of spin glasses. We demonstrate that finite-temperature effects introduced by the noise are particularly important for the dynamics in the presence of the exponential degeneracy of metastable states. We determine the optimal regime of the open-system quantum annealing algorithm for this model and find that it can outperform simulated annealing in a range of parameters. Large-scale multiqubit quantum tunneling is instrumental for the quantum speedup in this model, which is possible because of the unusual nonmonotonous temperature dependence of the quantum-tunneling action in this model, where the most efficient transition rate corresponds to zero temperature. This model calculation is the first analytically tractable example where open-system quantum annealing algorithm outperforms simulated annealing, which can, in principle, be realized using an analog quantum computer.

  5. Topological degeneracy and pairing in a one-dimensional gas of spinless fermions

    NASA Astrophysics Data System (ADS)

    Ruhman, Jonathan; Altman, Ehud

    2017-08-01

    We revisit the low-energy physics of one-dimensional spinless fermion liquids, showing that with sufficiently strong interactions the conventional Luttinger liquid can give way to a strong-pairing phase. While the density fluctuations in both phases are described by a gapless Luttinger liquid, single fermion excitations are gapped only in the strong-pairing phase. Smooth spatial Interfaces between the two phases lead to topological degeneracies in the ground-state and low-energy spectrum of the density fluctuations. Using a concrete microscopic model, with both single-particle and pair hopping, we show that the strong-pairing state is established through emergence of a new low-energy fermionic mode. We characterize the two phases with numerical calculations using the density matrix renormalization group. In particular we find enhancement of the central charge from c =1 in the two Luttinger liquid phases to c =3 /2 at the critical point, which gives direct evidence for an emergent critical Majorana mode. Finally, we confirm the existence of topological degeneracies in the low-energy phonon spectrum, associated with spatial interfaces between the two phases.

  6. Structures and Symmetries in Physics

    NASA Astrophysics Data System (ADS)

    Rangacharyulu, Chary

    Symmetries play a very significant role in describing the dynamics of physical structures and phenomena. While preserved symmetries enable physicists to establish systematics and predict regularities, broken symmetries open up new avenues of research as they admit new degrees of freedom. Quite often, physicists resort to mathematical symmetries to define the patterns and use metaphors to convey meaning. A caution is warranted not to take the symbolisms too literally and to be aware of limitations while borrowing physics language into other disciplines.

  7. Dynamical Symmetries in Classical Mechanics

    ERIC Educational Resources Information Center

    Boozer, A. D.

    2012-01-01

    We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that…

  8. Dynamical Symmetries in Classical Mechanics

    ERIC Educational Resources Information Center

    Boozer, A. D.

    2012-01-01

    We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that…

  9. Reflections on Symmetry and Proof

    ERIC Educational Resources Information Center

    Merrotsy, Peter

    2008-01-01

    The concept of symmetry is fundamental to mathematics. Arguments and proofs based on symmetry are often aesthetically pleasing because they are subtle and succinct and non-standard. This article uses notions of symmetry to approach the solutions to a broad range of mathematical problems. It responds to Krutetskii's criteria for mathematical…

  10. Helical symmetry in linear systems

    SciTech Connect

    Bicak, Jiri; Schmidt, Bernd G.

    2007-11-15

    We investigate properties of solutions of the scalar wave equation and Maxwell's equations on Minkowski space with helical symmetry. Existence of local and global solutions with this symmetry is demonstrated with and without sources. The asymptotic properties of the solutions are analyzed. We show that the Newman-Penrose retarded and advanced scalars exhibit specific symmetries and generalized peeling properties.

  11. Precursors and BRST symmetry

    NASA Astrophysics Data System (ADS)

    de Boer, Jan; Freivogel, Ben; Kabir, Laurens; Lokhande, Sagar F.

    2017-07-01

    In the AdS/CFT correspondence, bulk information appears to be encoded in the CFT in a redundant way. A local bulk field corresponds to many different non-local CFT operators (precursors). We recast this ambiguity in the language of BRST symmetry, and propose that in the large N limit, the difference between two precursors is a BRST exact and ghost-free term. This definition of precursor ambiguities has the advantage that it generalizes to any gauge theory. Using the BRST formalism and working in a simple model with global symmetries, we re-derive a precursor ambiguity appearing in earlier work. Finally, we show within this model that the obtained ambiguity has the right number of parameters to explain the freedom to localize precursors within different spatial regions of the boundary order by order in the large N expansion.

  12. PSEUDOSPIN SYMMETRY IN NUCLEI, SPIN SYMMETRY IN HADRONS

    SciTech Connect

    P. PAGE; T. GOLDMAN; J. GINOCCHIO

    2000-08-01

    Ginocchio argued that chiral symmetry breaking in QCD is responsible for the relativistic pseudospin symmetry in the Dirac equation, explaining the observed approximate pseudospin symmetry in sizable nuclei. On a much smaller scale, it is known that spin-orbit splittings in hadrons are small. Specifically, new experimental data from CLEO indicate small splittings in D-mesons. For heavy-light mesons we identify a cousin of pseudospin symmetry that suppresses these splittings in the Dirac equation, known as spin symmetry. We suggest an experimental test of the implications of spin symmetry for wave functions in electron-positron annihilation. We investigate how QCD can give rise to two different dynamical symmetries on nuclear and hadronic scales.

  13. Chiral symmetry and pentaquarks

    SciTech Connect

    Dmitri Diakonov

    2004-07-01

    Spontaneous chiral symmetry breaking, mesons and baryons are illustrated in the language of the Dirac theory. Various forces acting between quarks inside baryons are discussed. I explain why the naive quark models typically overestimate pentaquark masses by some 500 MeV and why in the fully relativistic approach to baryons pentaquarks turn out to be light. I discuss briefly why it can be easier to produce pentaquarks at low than at high energies.

  14. Symmetries of spacetime

    NASA Astrophysics Data System (ADS)

    Bojowald, Martin

    2016-07-01

    The equations of Hamiltonian gravity are often considered ugly cousins of the elegant and manifestly covariant versions found in the Lagrangian theory. However, both formulations are fundamental in their own rights because they make different statements about the nature of spacetime and its symmetries. These implications, along with the history of their derivation and an introduction of recent mathematical support, are the topic of this essay.

  15. Binary-Symmetry Detection

    NASA Technical Reports Server (NTRS)

    Lopez, Hiram

    1987-01-01

    Transmission errors for zeros and ones tabulated separately. Binary-symmetry detector employs psuedo-random data pattern used as test message coming through channel. Message then modulo-2 added to locally generated and synchronized version of test data pattern in same manner found in manufactured test sets of today. Binary symmetrical channel shows nearly 50-percent ones to 50-percent zeroes correspondence. Degree of asymmetry represents imbalances due to either modulation, transmission, or demodulation processes of system when perturbed by noise.

  16. PT symmetry in optics

    NASA Astrophysics Data System (ADS)

    Christodoulides, Demetrios

    2015-03-01

    Interest in complex Hamiltonians has been rekindled after the realization that a wide class of non-Hermitian Hamiltonians can have entirely real spectra as long as they simultaneously respect parity and time reversal operators. In non-relativistic quantum mechanics, governed by the Schrödinger equation, a necessary but not sufficient condition for PT symmetry to hold is that the complex potential should involve real and imaginary parts which are even and odd functions of position respectively. As recently indicated, optics provides a fertile ground to observe and utilize notions of PT symmetry. In optics, the refractive index and gain/loss profiles play the role of the real and imaginary parts of the aforementioned complex potentials. As it has been demonstrated in several studies, PT-symmetric optical structures can exhibit peculiar properties that are otherwise unattainable in traditional Hermitian (conservative) optical settings. Among them, is the possibility for breaking this symmetry through an abrupt phase transition, band merging effects and unidirectional invisibility. Here we review recent developments in the field of -symmetric optics.

  17. Measuring the Degeneracy of Discrete Energy Levels Using a GaAs /AlGaAs Quantum Dot

    NASA Astrophysics Data System (ADS)

    Hofmann, A.; Maisi, V. F.; Gold, C.; Krähenmann, T.; Rössler, C.; Basset, J.; Märki, P.; Reichl, C.; Wegscheider, W.; Ensslin, K.; Ihn, T.

    2016-11-01

    We demonstrate an experimental method for measuring quantum state degeneracies in bound state energy spectra. The technique is based on the general principle of detailed balance and the ability to perform precise and efficient measurements of energy-dependent tunneling-in and -out rates from a reservoir. The method is realized using a GaAs /AlGaAs quantum dot allowing for the detection of time-resolved single-electron tunneling with a precision enhanced by a feedback control. It is thoroughly tested by tuning orbital and spin degeneracies with electric and magnetic fields. The technique also lends itself to studying the connection between the ground-state degeneracy and the lifetime of the excited states.

  18. Symmetries in laminated composite plates

    NASA Technical Reports Server (NTRS)

    Noor, A. K.

    1976-01-01

    The different types of symmetry exhibited by laminated anisotropic fibrous composite plates are identified and contrasted with the symmetries of isotropic and homogeneous orthotropic plates. The effects of variations in the fiber orientation and the stacking sequence of the layers on the symmetries exhibited by composite plates are discussed. Both the linear and geometrically nonlinear responses of the plates are considered. A simple procedure is presented for exploiting the symmetries in the finite element analysis. Examples are given of square, skew and polygonal plates where use of symmetry concepts can significantly reduce the scope and cost of analysis.

  19. Symmetry and Condensed Matter Physics

    NASA Astrophysics Data System (ADS)

    El-Batanouny, M.; Wooten, F.

    2008-03-01

    Preface; 1. Symmetry and physics; 2. Symmetry and group theory; 3. Group representations: concepts; 4. Group representations: formalism and methodology; 5. Dixon's method for computing group characters; 6. Group action and symmetry projection operators; 7. Construction of the irreducible representations; 8. Product groups and product representations; 9. Induced representations; 10. Crystallographic symmetry and space-groups; 11. Space groups: Irreps; 12. Time-reversal symmetry: color groups and the Onsager relations; 13. Tensors and tensor fields; 14. Electronic properties of solids; 15. Dynamical properties of molecules, solids and surfaces; 16. Experimental measurements and selection rules; 17. Landau's theory of phase transitions; 18. Incommensurate systems and quasi-crystals; References; Bibliography; Index.

  20. Symmetry methods for option pricing

    NASA Astrophysics Data System (ADS)

    Davison, A. H.; Mamba, S.

    2017-06-01

    We obtain a solution of the Black-Scholes equation with a non-smooth boundary condition using symmetry methods. The Black-Scholes equation along with its boundary condition are first transformed into the one dimensional heat equation and an initial condition respectively. We then find an appropriate general symmetry generator of the heat equation using symmetries and the fundamental solution of the heat equation. The symmetry generator is chosen such that the boundary condition is left invariant; the symmetry can be used to solve the heat equation and hence the Black-Scholes equation.

  1. Invariants of broken discrete symmetries.

    PubMed

    Kalozoumis, P A; Morfonios, C; Diakonos, F K; Schmelcher, P

    2014-08-01

    The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.

  2. Invariants of Broken Discrete Symmetries

    NASA Astrophysics Data System (ADS)

    Kalozoumis, P. A.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.

    2014-08-01

    The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.

  3. Halting the 'sad degenerationist parade': medical concerns about heredity and racial degeneracy in New Zealand psychiatry, 1853-99.

    PubMed

    Dawson, Maree

    2012-01-01

    Historians have focused on early twentieth-century positive eugenics in New Zealand In this article, I argue that the response came from a tradition of concern about heredity and white racial degeneracy, which extended beyond the British Empire. This article focuses on concerns about heredity at the Auckland Mental Hospital between 1850 and 1899, and contextualises these concerns in New Zealand mental hospital statistics from the late-nineteenth century. This article also considers Australasian, British, North and South American medical and immigration legislation history, and contrasts this with the legislation and medical discourses which formed part of a fear of heredity, racial degeneracy, immigration and mental illness in New Zealand.

  4. Chiral Potts rapidity curve descended from six-vertex model and symmetry group of rapidities

    NASA Astrophysics Data System (ADS)

    Roan, Shi-shyr

    2005-08-01

    In this paper, we present a systematical account of the descending procedure from the six-vertex model to the N-state chiral Potts model through fusion relations of τ(j)-operators, following the works of Bazhanov-Stroganov and Baxter-Bazhanov-Perk. A careful analysis of the descending process leads to the appearance of the high genus curve as the rapidity constraint for the chiral Potts models. Full symmetries of the rapidity curve are identified, as is its symmetry group structure. By normalized transfer matrices of the chiral Potts model, the τ(2)T relation can be reduced to functional equations over a hyperelliptic curve associated with rapidities, by which the degeneracy of τ(2)-eigenvalues is revealed in the case of the superintegrable chiral Potts model.

  5. Broken vertex symmetry and finite zero-point entropy in the artificial square ice ground state

    SciTech Connect

    Gliga, Sebastian; Kákay, Attila; Heyderman, Laura J.; Hertel, Riccardo; Heinonen, Olle G.

    2015-08-26

    In this paper, we study degeneracy and entropy in the ground state of artificial square ice. In theoretical models, individual nanomagnets are typically treated as single spins with only two degrees of freedom, leading to a twofold degenerate ground state with intensive entropy and thus no zero-point entropy. Here, we show that the internal degrees of freedom of the nanostructures can result, through edge bending of the magnetization and breaking of local magnetic symmetry at the vertices, in a transition to a highly degenerate ground state with finite zero-point entropy, similar to that of the pyrochlore spin ices. Finally, we find that these additional degrees of freedom have observable consequences in the resonant spectrum of the lattice, and predict the occurrence of edge “melting” above a critical temperature at which the magnetic symmetry is restored.

  6. Broken vertex symmetry and finite zero-point entropy in the artificial square ice ground state

    DOE PAGES

    Gliga, Sebastian; Kákay, Attila; Heyderman, Laura J.; ...

    2015-08-26

    In this paper, we study degeneracy and entropy in the ground state of artificial square ice. In theoretical models, individual nanomagnets are typically treated as single spins with only two degrees of freedom, leading to a twofold degenerate ground state with intensive entropy and thus no zero-point entropy. Here, we show that the internal degrees of freedom of the nanostructures can result, through edge bending of the magnetization and breaking of local magnetic symmetry at the vertices, in a transition to a highly degenerate ground state with finite zero-point entropy, similar to that of the pyrochlore spin ices. Finally, wemore » find that these additional degrees of freedom have observable consequences in the resonant spectrum of the lattice, and predict the occurrence of edge “melting” above a critical temperature at which the magnetic symmetry is restored.« less

  7. Empirical signatures of quantum phase transitions and universal properties of critical point descriptions and dynamical symmetries

    SciTech Connect

    Casten, R. F.; Bonatsos, Dennis; McCutchan, E. A.

    2009-01-28

    Recently, a new signature for quantum phase transitional regions has been discussed. This signature, based on degeneracies of yrast and intrinsic excitations, can distinguish first and second order phase transitions, and is valid not only at or near the analytic critical points described by X(5) and E(5), but along the phase transitional line connecting them as well. In addition, a study of a number of recent analytic solutions to the Bohr Hamiltonian and of the dynamical symmetries of the IBA Hamiltonian has revealed a set of extremely simple and general analytic formulas that describe the energies of 0{sup +} states. For the case of flat-bottomed geometrical potentials, the formula depends solely on the number of relevant dimensions. For the IBA (large boson number limit) a single formula describes all three dynamical symmetries.

  8. Effects of custodial symmetry breaking in the Georgi-Machacek model at high energies

    NASA Astrophysics Data System (ADS)

    Blasi, Simone; De Curtis, Stefania; Yagyu, Kei

    2017-07-01

    The model proposed by Georgi and Machacek enables the Higgs sector to involve isospin triplet scalar fields while retaining a custodial S U (2 )V symmetry in the potential and, thus, ensuring the electroweak ρ parameter to be one at tree level. This custodial symmetry, however, is explicitly broken by loop effects of the U (1 )Y hypercharge gauge interaction. In order to make the model consistent at high energies, we construct the most general form of the Higgs potential without the custodial symmetry, and then we derive the one-loop β functions for all the model parameters. Assuming the δi quantities describing the custodial symmetry breaking to be zero at low energy, we find that |δi| are typically smaller than the magnitude of the U (1 )Y gauge coupling and the other running parameters in the potential also at high energy without spoiling perturbativity and vacuum stability. We also clarify that the mass degeneracy among the S U (2 )V 5-plet and 3-plet Higgs bosons is smoothly broken by ˜0.1 % corrections. These results show that the amount of the custodial symmetry breaking is kept well under control up to energies close to the theory cutoff.

  9. Hidden pseudospin and spin symmetries and their origins in atomic nuclei

    NASA Astrophysics Data System (ADS)

    Liang, Haozhao; Meng, Jie; Zhou, Shan-Gui

    2015-03-01

    Symmetry plays a fundamental role in physics. The quasi-degeneracy between single-particle orbitals (n , l , j = l + 1 / 2) and (n - 1 , l + 2 , j = l + 3 / 2) indicates a hidden symmetry in atomic nuclei, the so-called pseudospin symmetry (PSS). Since the introduction of the concept of PSS in atomic nuclei, there have been comprehensive efforts to understand its origin. Both splittings of spin doublets and pseudospin doublets play critical roles in the evolution of magic numbers in exotic nuclei discovered by modern spectroscopic studies with radioactive ion beam facilities. Since the PSS was recognized as a relativistic symmetry in 1990s, many special features, including the spin symmetry (SS) for anti-nucleon, and many new concepts have been introduced. In the present Review, we focus on the recent progress on the PSS and SS in various systems and potentials, including extensions of the PSS study from stable to exotic nuclei, from non-confining to confining potentials, from local to non-local potentials, from central to tensor potentials, from bound to resonant states, from nucleon to anti-nucleon spectra, from nucleon to hyperon spectra, and from spherical to deformed nuclei. Open issues in this field are also discussed in detail, including the perturbative nature, the supersymmetric representation with similarity renormalization group, and the puzzle of intruder states.

  10. Screening charged impurities and lifting the orbital degeneracy in graphene by populating Landau levels.

    PubMed

    Luican-Mayer, Adina; Kharitonov, Maxim; Li, Guohong; Lu, Chih-Pin; Skachko, Ivan; Gonçalves, Alem-Mar B; Watanabe, K; Taniguchi, T; Andrei, Eva Y

    2014-01-24

    We report the observation of an isolated charged impurity in graphene and present direct evidence of the close connection between the screening properties of a 2D electron system and the influence of the impurity on its electronic environment. Using scanning tunneling microscopy and Landau level spectroscopy, we demonstrate that in the presence of a magnetic field the strength of the impurity can be tuned by controlling the occupation of Landau-level states with a gate voltage. At low occupation the impurity is screened, becoming essentially invisible. Screening diminishes as states are filled until, for fully occupied Landau levels, the unscreened impurity significantly perturbs the spectrum in its vicinity. In this regime we report the first observation of Landau-level splitting into discrete states due to lifting the orbital degeneracy.

  11. Partially ferromagnetic electromagnet for trapping and cooling neutral atoms to quantum degeneracy

    SciTech Connect

    Fauquembergue, M.; Riou, J-F.; Guerin, W.; Rangwala, S.; Moron, F.; Villing, A.; Le Coq, Y.; Bouyer, P.; Aspect, A.; Lecrivain, M.

    2005-10-15

    We have developed a compact partially ferromagnetic electromagnet to produce an Ioffe-Pritchard trap for neutral atoms. Our structure permits strong magnetic confinement with low power consumption. Compared to the previous iron-core electromagnet [B. Desruelle, V. Boyer, P. Bouyer, G. Birkl, M. Lecrivain, F. Alves, C. Westbrook, and A. Aspect, Eur. Phys. J. D 1, 255 (1998)], it allows for easy compensation of remnant fields and very high stability, along with cost-effective realization and compactness. We describe and characterize our apparatus and demonstrate trapping and cooling of {sup 87}Rb atoms to quantum degeneracy. Pure Bose-Einstein condensates containing 10{sup 6} atoms are routinely realized on a half-minute cycle. In addition we test the stability of the magnetic trap by producing atom lasers.

  12. A singular one-dimensional bound state problem and its degeneracies

    NASA Astrophysics Data System (ADS)

    Erman, Fatih; Gadella, Manuel; Tunalı, Seçil; Uncu, Haydar

    2017-08-01

    We give a brief exposition of the formulation of the bound state problem for the one-dimensional system of N attractive Dirac delta potentials, as an N × N matrix eigenvalue problem (Φ A =ω A). The main aim of this paper is to illustrate that the non-degeneracy theorem in one dimension breaks down for the equidistantly distributed Dirac delta potential, where the matrix Φ becomes a special form of the circulant matrix. We then give elementary proof that the ground state is always non-degenerate and the associated wave function may be chosen to be positive by using the Perron-Frobenius theorem. We also prove that removing a single center from the system of N delta centers shifts all the bound state energy levels upward as a simple consequence of the Cauchy interlacing theorem.

  13. Influence of quantum degeneracy on the performance of a gas Stirling engine cycle

    NASA Astrophysics Data System (ADS)

    He, Ji-Zhou; Mao, Zhi-Yuan; Wang, Jian-Hui

    2006-09-01

    Based on the state equation of an ideal quantum gas, the regenerative loss of a Stirling engine cycle working with an ideal quantum gas is calculated. Thermal efficiency of the cycle is derived. Furthermore, under the condition of quantum degeneracy, several special thermal efficiencies are discussed. Ratios of thermal efficiencies versus the temperature ratio and volume ratio of the cycle are made. It is found that the thermal efficiency of the cycle not only depends on high and low temperatures but also on maximum and minimum volumes. In a classical gas state the thermal efficiency of the cycle is equal to that of the Carnot cycle. In an ideal quantum gas state the thermal efficiency of the cycle is smaller than that of the Carnot cycle. This will be significant for deeper understanding of the gas Stirling engine cycle.

  14. Orbital degeneracy removed by charge order in triangular antiferromagnet AgNiO2.

    PubMed

    Wawrzyńska, E; Coldea, R; Wheeler, E M; Mazin, I I; Johannes, M D; Sörgel, T; Jansen, M; Ibberson, R M; Radaelli, P G

    2007-10-12

    We report a high-resolution neutron diffraction study on the orbitally degenerate spin-1/2 hexagonal metallic antiferromagnet AgNiO2. A structural transition to a tripled unit cell with expanded and contracted NiO6 octahedra indicates sqrt[3]xsqrt[3] charge order on the Ni triangular lattice. This suggests charge order as a possible mechanism of lifting the orbital degeneracy in the presence of charge fluctuations, as an alternative to the more usual Jahn-Teller distortions. A novel magnetic ground state is observed at low temperatures with the electron-rich S=1 Ni sites arranged in alternating ferromagnetic rows on a triangular lattice, surrounded by a honeycomb network of nonmagnetic and metallic Ni ions. We also report first-principles band-structure calculations that explain microscopically the origin of these phenomena.

  15. Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems

    NASA Astrophysics Data System (ADS)

    Leykam, Daniel; Bliokh, Konstantin Y.; Huang, Chunli; Chong, Y. D.; Nori, Franco

    2017-01-01

    We analyze chiral topological edge modes in a non-Hermitian variant of the 2D Dirac equation. Such modes appear at interfaces between media with different "masses" and/or signs of the "non-Hermitian charge." The existence of these edge modes is intimately related to exceptional points of the bulk Hamiltonians, i.e., degeneracies in the bulk spectra of the media. We find that the topological edge modes can be divided into three families ("Hermitian-like," "non-Hermitian," and "mixed"); these are characterized by two winding numbers, describing two distinct kinds of half-integer charges carried by the exceptional points. We show that all the above types of topological edge modes can be realized in honeycomb lattices of ring resonators with asymmetric or gain-loss couplings.

  16. Very broad gain bandwidth parametric amplification in nonlinear crystals at critical wavelength degeneracy.

    PubMed

    Dabu, R

    2010-05-24

    Gain spectra were calculated at critical wavelength degeneracy (CWD) in a collinear phase-matching geometry optical parametric amplification (OPA) process. The frequency bandwidth available through CWD-OPA is broader compared to the gain bandwidth obtained by the non-collinear OPA geometry. A solution for very broad bandwidth chirped pulse amplification based on partially deuterated DKDP (P-DKDP) crystals, pumped by pulsed green lasers, is proposed. 1.38x10(14) Hz frequency bandwidth and peak intensity gain G approximately 62 were calculated in a 5-mm long 58% deuterated DKDP crystal, pumped by 527-nm wavelength at 64-GW/cm2 intensity. Parametric amplification at CWD in few-mm thin P-DKDP crystals, pumped by picosecond pulses of nearly 100-GW/cm2 intensity, possesses a true potential for generating high energy laser pulses compressible to one-cycle duration.

  17. Hyperspherical theory of the quantum Hall effect: The role of exceptional degeneracy

    NASA Astrophysics Data System (ADS)

    Daily, K. M.; Wooten, R. E.; Greene, Chris H.

    2015-09-01

    By separating the Schrödinger equation for N noninteracting spin-polarized fermions in two-dimensional hyperspherical coordinates, we demonstrate that fractional quantum Hall (FQH) states emerge naturally from degeneracy patterns of the antisymmetric free-particle eigenfunctions. In the presence of Coulomb interactions, the FQH states split off from a degenerate manifold and become observable as distinct quantized energy eigenstates with an energy gap. This alternative classification scheme is based on an approximate separability of the interacting N -fermion Schrödinger equation in the hyperradial coordinate, which sheds light on the emergence of Laughlin states as well as other FQH states. An approximate good collective quantum number, the grand angular momentum K from K -harmonic few-body theory, is shown to correlate with known FQH states at many filling factors observed experimentally.

  18. Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard

    NASA Astrophysics Data System (ADS)

    Gao, T.; Estrecho, E.; Bliokh, K. Y.; Liew, T. C. H.; Fraser, M. D.; Brodbeck, S.; Kamp, M.; Schneider, C.; Höfling, S.; Yamamoto, Y.; Nori, F.; Kivshar, Y. S.; Truscott, A. G.; Dall, R. G.; Ostrovskaya, E. A.

    2015-10-01

    Exciton-polaritons are hybrid light-matter quasiparticles formed by strongly interacting photons and excitons (electron-hole pairs) in semiconductor microcavities. They have emerged as a robust solid-state platform for next-generation optoelectronic applications as well as for fundamental studies of quantum many-body physics. Importantly, exciton-polaritons are a profoundly open (that is, non-Hermitian) quantum system, which requires constant pumping of energy and continuously decays, releasing coherent radiation. Thus, the exciton-polaritons always exist in a balanced potential landscape of gain and loss. However, the inherent non-Hermitian nature of this potential has so far been largely ignored in exciton-polariton physics. Here we demonstrate that non-Hermiticity dramatically modifies the structure of modes and spectral degeneracies in exciton-polariton systems, and, therefore, will affect their quantum transport, localization and dynamical properties. Using a spatially structured optical pump, we create a chaotic exciton-polariton billiard--a two-dimensional area enclosed by a curved potential barrier. Eigenmodes of this billiard exhibit multiple non-Hermitian spectral degeneracies, known as exceptional points. Such points can cause remarkable wave phenomena, such as unidirectional transport, anomalous lasing/absorption and chiral modes. By varying parameters of the billiard, we observe crossing and anti-crossing of energy levels and reveal the non-trivial topological modal structure exclusive to non-Hermitian systems. We also observe mode switching and a topological Berry phase for a parameter loop encircling the exceptional point. Our findings pave the way to studies of non-Hermitian quantum dynamics of exciton-polaritons, which may uncover novel operating principles for polariton-based devices.

  19. Dark matter distribution in the Coma cluster from galaxy kinematics: breaking the mass-anisotropy degeneracy

    NASA Astrophysics Data System (ADS)

    Łokas, Ewa L.; Mamon, Gary A.

    2003-08-01

    We study velocity moments of elliptical galaxies in the Coma cluster using Jeans equations. The dark matter distribution in the cluster is modelled by a generalized formula based upon the results of cosmological N-body simulations. Its inner slope (cuspy or flat), concentration and mass within the virial radius are kept as free parameters, as well as the velocity anisotropy, assumed independent of position. We show that the study of line-of-sight velocity dispersion alone does not allow us to constrain the parameters. By a joint analysis of the observed profiles of velocity dispersion and kurtosis, we are able to break the degeneracy between the mass distribution and velocity anisotropy. We determine the dark matter distribution at radial distances larger than 3 per cent of the virial radius and we find that the galaxy orbits are close to isotropic. Due to limited resolution, different inner slopes are found to be consistent with the data and we observe a strong degeneracy between the inner slope α and concentration c; the best-fitting profiles have the two parameters related with c= 19-9.6α. Our best-fitting Navarro-Frenk-White profile has concentration c= 9, which is 50 per cent higher than standard values found in cosmological simulations for objects of similar mass. The total mass within the virial radius of 2.9h-170 Mpc is 1.4 × 1015h-170 Msolar (with 30 per cent accuracy), 85 per cent of which is dark. At this distance from the cluster centre, the mass-to-light ratio in the blue band is 351h70 solar units. The total mass within the virial radius leads to estimates of the density parameter of the Universe, assuming that clusters trace the mass-to-light ratio and baryonic fraction of the Universe, with Ω0= 0.29 +/- 0.1.

  20. Local Rotational Symmetries.

    DTIC Science & Technology

    1985-08-01

    Symmetry representations can be computed robustly from input images and provide intuitive descriptions of elongated regions. For exam- pie , Figure 5...upper left), a squash (upper right), a pecan (lower left), and an eggplant (lower right). - 77 L 7 04 lI..’. Figure 4-15. Analysis of the images from...agree with my perceptions: some of the figures it analyzes as clearly one region seem to me to be on the borderline, e.g. the pecan in Figures 16 and

  1. Spontaneous Symmetry Breaking

    NASA Astrophysics Data System (ADS)

    Strocchi, Franco

    One of the most powerful ideas of modern theoretical physics is the mechanism of spontaneous symmetry breaking. It is at the basis of most of the recent achievements in the description of phase transitions in Statistical Mechanics as well as of collective phenomena in solid state physics. It has also made possible the unification of weak, electromagnetic and strong interactions in elementary particle physics. Philosophically, the idea is very deep and subtle (this is probably why its exploitation is a rather recent achievement) and the popular accounts do not fully do justice to it.

  2. Symmetry-Breaking Motility

    NASA Astrophysics Data System (ADS)

    Lee, Allen; Lee, Ha Youn; Kardar, Mehran

    2005-09-01

    Locomotion of bacteria by actin polymerization and in vitro motion of spherical beads coated with a protein catalyzing polymerization are examples of active motility. Starting from a simple model of forces locally normal to the surface of a bead, we construct a phenomenological equation for its motion. The singularities at a continuous transition between moving and stationary beads are shown to be related to the symmetries of its shape. Universal features of the phase behavior are calculated analytically and confirmed by simulations. Fluctuations in velocity are shown to be generically non-Maxwellian and correlated to the shape of the bead.

  3. Galactic oscillator symmetry

    NASA Technical Reports Server (NTRS)

    Rosensteel, George

    1995-01-01

    Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities.

  4. Applications of chiral symmetry

    SciTech Connect

    Pisarski, R.D.

    1995-03-01

    The author discusses several topics in the applications of chiral symmetry at nonzero temperature. First, where does the rho go? The answer: up. The restoration of chiral symmetry at a temperature T{sub {chi}} implies that the {rho} and a{sub 1} vector mesons are degenerate in mass. In a gauged linear sigma model the {rho} mass increases with temperature, m{sub {rho}}(T{sub {chi}}) > m{sub {rho}}(0). The author conjectures that at T{sub {chi}} the thermal {rho} - a{sub 1}, peak is relatively high, at about {approximately}1 GeV, with a width approximately that at zero temperature (up to standard kinematic factors). The {omega} meson also increases in mass, nearly degenerate with the {rho}, but its width grows dramatically with temperature, increasing to at least {approximately}100 MeV by T{sub {chi}}. The author also stresses how utterly remarkable the principle of vector meson dominance is, when viewed from the modern perspective of the renormalization group. Secondly, he discusses the possible appearance of disoriented chiral condensates from {open_quotes}quenched{close_quotes} heavy ion collisions. It appears difficult to obtain large domains of disoriented chiral condensates in the standard two flavor model. This leads to the last topic, which is the phase diagram for QCD with three flavors, and its proximity to the chiral critical point. QCD may be very near this chiral critical point, and one might thereby generated large domains of disoriented chiral condensates.

  5. Big-Bang nucleosynthesis: Constraints on nuclear reaction rates, neutrino degeneracy, inhomogeneous and Brans-Dicke models

    NASA Astrophysics Data System (ADS)

    Nakamura, Riou; Hashimoto, Masa-Aki; Ichimasa, Ryotaro; Arai, Kenzo

    We review the recent progress in the Big-Bang nucleosynthesis which includes the standard and nonstandard theory of cosmology, effects of neutrino degeneracy, and inhomogeneous nucleosynthesis within the framework of a Friedmann model. As for a nonstandard theory of gravitation, we adopt a Brans-Dicke theory which incorporates a cosmological constant. We constrain various parameters associated with each subject.

  6. Attenuation of Bragg backscattering of electromagnetic waves from density fluctuations near the region of polarization degeneracy in magnetoactive plasma

    SciTech Connect

    Gospodchikov, E. D. Khusainov, T. A.; Shalashov, A. G.

    2016-08-15

    Specific features of Bragg backscattering under conditions of strong polarization degeneracy near the cutoff surface in an anisotropic medium are studied analytically and numerically. It is shown that the linear interaction of normal waves can substantially affect wave scattering by suppressing the amplification of Bragg backscattering near the cutoff region in the case of weak coupling between normal waves.

  7. Communication: Effect of accidental mode degeneracy on Raman intensity in 2D materials: Hybrid functional study of bilayer phosphorene.

    PubMed

    Sun, Yi-Yang; Zhang, Shengbai

    2016-07-14

    Bulk black phosphorus has two optical phonon modes labeled as Ag (2) and B2u, respectively, that are nearly degenerate in frequency. However, density functional theory calculations using local or semi-local functionals cannot reproduce this degeneracy. Here, we propose a hybrid functional approach aided by van der Waals (vdW) force fields, which can accurately describe the lattice dynamic and electronic properties of both bulk and few-layer black phosphorus (phosphorene). Using this approach we show that in bilayer phosphorene, the two Raman modes derived from the B2u and Ag (2) modes could exhibit strong resonance as a result of the accidental degeneracy so that both modes could be observed in Raman experiment. Without the mode degeneracy, however, the Raman intensity of the B2u-derived mode would be too weak to be observed. We further show that the accidental degeneracy is correlated to the applied strain, which enables Raman spectroscopy to be a powerful tool for characterizing built-in strains in 2D materials, e.g., due to the interaction with substrates, which has emerged as an important issue in vdW epitaxy.

  8. Communication: Effect of accidental mode degeneracy on Raman intensity in 2D materials: Hybrid functional study of bilayer phosphorene

    NASA Astrophysics Data System (ADS)

    Sun, Yi-Yang; Zhang, Shengbai

    2016-07-01

    Bulk black phosphorus has two optical phonon modes labeled as Ag2 and B2u, respectively, that are nearly degenerate in frequency. However, density functional theory calculations using local or semi-local functionals cannot reproduce this degeneracy. Here, we propose a hybrid functional approach aided by van der Waals (vdW) force fields, which can accurately describe the lattice dynamic and electronic properties of both bulk and few-layer black phosphorus (phosphorene). Using this approach we show that in bilayer phosphorene, the two Raman modes derived from the B2u and Ag2 modes could exhibit strong resonance as a result of the accidental degeneracy so that both modes could be observed in Raman experiment. Without the mode degeneracy, however, the Raman intensity of the B2u-derived mode would be too weak to be observed. We further show that the accidental degeneracy is correlated to the applied strain, which enables Raman spectroscopy to be a powerful tool for characterizing built-in strains in 2D materials, e.g., due to the interaction with substrates, which has emerged as an important issue in vdW epitaxy.

  9. Unraveling the origins of conduction band valley degeneracies in Mg2Si(1-x)Sn(x) thermoelectrics.

    PubMed

    Kim, Chang-Eun; Soon, Aloysius; Stampfl, Catherine

    2016-01-14

    To better understand the thermoelectric efficiency of the Mg-based thermoelectrics, using hybrid density-functional theory, we study the microscopic origins of valley degeneracies in the conduction band of the solid solution Mg2Si(1-x)Sn(x) and its constituent components--namely, Mg2Si and Mg2Sn. In the solid solution of Mg2Si(1-x)Sn(x), the sublattices are expected to undergo either tensile or compressive strain in the light of Vegard's law. Interestingly, we find both tensile strain of Mg2Si and compressive strain of Mg2Sn enhance the conduction band valley degeneracy. We suggest that the optimal sublattice strain as one of the origins of the enhanced Seebeck coefficient in the Mg2Si(1-x)Sn(x) system. In order to visualize the enhanced band valley degeneracy at elevated temperatures, the ground state eigenvalues and weights are projected by convolution functions that account for high temperature effects. Our results provide theoretical evidences for the role of sublattice strain in the band valley degeneracy observed in Mg2Si(1-x)Sn(x).

  10. In search of symmetry lost.

    PubMed

    Wilczek, Frank

    2005-01-20

    Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world. The discrepancy is ascribed to a pervasive symmetry-breaking field, which fills all space uniformly, rendering the Universe a sort of exotic superconductor. So far, the evidence for these bold ideas is indirect. But soon the theory will undergo a critical test depending on whether the quanta of this symmetry-breaking field, the so-called Higgs particles, are produced at the Large Hadron Collider (due to begin operation in 2007).

  11. [Symmetries and homologies of Geomerida].

    PubMed

    Zarenkov, N A

    2005-01-01

    The symmetry of Earths life cover (Geomerida) was described generally by L.A. Zenkevich (1948). It coincides with the symmetry of geographic cover. Its symmetry elements are equatorial plane and three meridonal planes corresponded to oceans and continents. The hypsographic curve with point of inflection (symmetry element) on 3 km depth line should be added to these elements. The plankton and benthos communities as well as fauna of taxons are distributed symmetrically according these symmetry elements. Zenkevich model was successfully extrapolated to plankton by K.V. Beklemishev (1967, 1969) and to abyssal benthos by Sokolova M.N. (1986). The plankton communities inhabiting symmetrically located macrocirculations are considered as homologous. The character of circulation determines the trophic structure of plankton and benthos. In the case of high productivity of plankton, benthic grazing animals feed on sedimented particles have bilateral symmetric mouthpart. Otherwise they have to acquire food from water column and use cyclomeric mouthpart. Thus, the symmetry of macrocirculations determines the symmetry distribution of benthic animals with two major symmetries of mouthparts. The peculiarities of organisms' symmetry are discussed in the context of Pierre Curie principle and the ideas of K.V. Beklemishev concerning evolution of morphological axes.

  12. Symmetry breaking in confined fluids.

    PubMed

    Ruckenstein, Eli; Berim, Gersh O

    2010-02-26

    The recent progress in the theoretical investigation of the symmetry breaking (the existence of a stable state of a system, in which the symmetry is lower than the symmetry of the system itself) for classical and quantum fluids is reviewed. The emphasis is on the conditions which cause symmetry breaking in the density distribution for one component fluids and binary mixtures confined in a closed nanoslit between identical solid walls. The existing studies have revealed that two kinds of symmetry breaking can occur in such systems. First, a one-dimensional symmetry breaking occurs only in the direction normal to the walls as a fluid density profile asymmetric with respect of the middle of the slit and uniform in any direction parallel to the walls. Second, a two-dimensional symmetry breaking occurs in the fluid density distribution which is nonuniform in one of the directions parallel to the walls and asymmetrical in the direction normal to the walls. It manifests through liquid bumps and bridges in the fluid density distribution. For one component fluids, conditions of existence of symmetry breaking are provided in terms of the average fluid density, strength of fluid-solid interactions, distance at which the solid wall generates a hard core repulsion, and temperature. In the case of binary mixtures, the occurrence of symmetry breaking also depends on the composition of the confined mixtures. Copyright 2010 Elsevier B.V. All rights reserved.

  13. From Molecular Point Group Symmetry to Space Group Symmetry.

    ERIC Educational Resources Information Center

    Hathaway, Brian

    1979-01-01

    Describes undergraduate chemistry curricula in which the student is asked to either build a model of one asymmetric unit in the unit cell and to indicate the positions of the symmetry-related units by putting in key atoms, or to identify on a prebuild model the asymetric and symmetry-related units. (BB)

  14. Symmetry and surface symmetry energies in finite nuclei

    SciTech Connect

    Lee, S. J.; Mekjian, A. Z.

    2010-12-15

    A study of the properties of the symmetry energy of nuclei is presented based on density-functional theory. Calculations for finite nuclei are given so that the study includes isospin-dependent surface symmetry considerations as well as isospin-independent surface effects. Calculations are done at both zero and nonzero temperature. It is shown that the surface symmetry energy term is the most sensitive to the temperature while the bulk energy term is the least sensitive. It is also shown that the temperature-dependence terms are insensitive to the force used and even more insensitive to the existence of neutron skin. Results for a symmetry energy with both volume and surface terms are compared with a symmetry energy with only volume terms along the line of {beta} stability. Differences of several MeV are shown over a good fraction of the total mass range in A. Also given are calculations for the bulk, surface and Coulomb terms.

  15. Symmetry reduction related with nonlocal symmetry for Gardner equation

    NASA Astrophysics Data System (ADS)

    Ren, Bo

    2017-01-01

    Based on the truncated Painlevé method or the Möbious (conformal) invariant form, the nonlocal symmetry for the (1+1)-dimensional Gardner equation is derived. The nonlocal symmetry can be localized to the Lie point symmetry by introducing one new dependent variable. Thanks to the localization procedure, the finite symmetry transformations are obtained by solving the initial value problem of the prolonged systems. Furthermore, by using the symmetry reduction method to the enlarged systems, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, Painlevé II solutions are given. Especially, some special concrete soliton-cnoidal interaction solutions are analyzed both in analytical and graphical ways.

  16. NIF symmetry capsule modeling

    NASA Astrophysics Data System (ADS)

    Weber, S. V.; Casey, D. T.; Pino, J. E.; Rowley, D. P.; Smalyuk, V. A.; Spears, B. K.; Tipton, R. E.

    2013-10-01

    NIF CH ablator symmetry capsules are filled with hydrogen or helium gas. SymCaps have more moderate convergence ratios ~ 15 as opposed to ~ 35 for ignition capsules with DT ice layers, and better agreement has been achieved between simulations and experimental data. We will present modeling of capsules with CD layers and tritium fill, for which we are able to match the dependence of DT yield on recession distance of the CD layer from the gas. We can also match the performance of CH capsules with D3 He fill. The simulations include surface roughness, drive asymmetry, a mock-up of modulation introduced by the tent holding the capsule, and an empirical prescription for ablator-gas atomic mix. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

  17. Statistical mechanics of Floquet systems: The pervasive problem of near degeneracies

    NASA Astrophysics Data System (ADS)

    Hone, Daniel W.; Ketzmerick, Roland; Kohn, Walter

    2009-05-01

    Although the statistical mechanics of periodically driven (“Floquet”) systems in contact with a heat bath has some formal analogy with the traditional statistical mechanics of undriven systems, closer examination reveals radical differences. In Floquet systems all quasienergies ɛj can be placed in a finite frequency interval 0≤ɛj<ω (with ω the driving frequency and ℏ=1 ). Therefore, if we describe a Floquet system approximately by restricting its available state space to be spanned by a finite number N of basis states, then the number of near degeneracies ( |ɛj-ɛk|≤δ for arbitrarily small fixed δ ) in this interval grows without limit as N is increased. As we noted in a previous paper, this leads to pathologies, including drastic changes in Floquet states, as N tends to infinity. In earlier work on Floquet systems in contact with a heat bath these difficulties were often put aside by fixing N while taking the coupling to the bath to be smaller than any quasienergy difference. This led to a simple explicit theory for the reduced density matrix, with some major differences from the usual time-independent statistical mechanics. We show that, for weak but finite coupling between system and heat bath, the accuracy of a calculation within the truncated space spanned by the N lowest energy eigenstates of the undriven system is limited, as N increases indefinitely, only by the usual Born-Markov approximation, which neglects bath memory effects. As we seek higher accuracy by increasing N , we inevitably encounter quasienergy differences smaller than the system-bath coupling. We therefore derive here the equations for the steady-state reduced density matrix without restriction on the size of quasienergy splittings. In general, this matrix is no longer diagonal in the Floquet states. We analyze, in particular, the behavior near a weakly avoided crossing, where near degeneracies of quasienergies appear. In spite of the Floquet state pathologies, the explicit

  18. Symmetry in Sign Language Poetry

    ERIC Educational Resources Information Center

    Sutton-Spence, Rachel; Kaneko, Michiko

    2007-01-01

    This paper considers the range of ways that sign languages use geometric symmetry temporally and spatially to create poetic effect. Poets use this symmetry in sign language art to highlight duality and thematic contrast, and to create symbolic representations of beauty, order and harmony. (Contains 8 tables, 14 figures and 6 notes.)

  19. Symmetry in the Car Park

    ERIC Educational Resources Information Center

    Hancock, Karen

    2007-01-01

    In this article, the author presents a lesson on rotational symmetry which she developed for her students. The aim of the lesson was "to identify objects with rotational symmetry in the staff car park" and the success criteria were "pictures or sketches of at least six objects with different orders of rotation". After finding examples of…

  20. Symmetry in the basic sciences

    NASA Astrophysics Data System (ADS)

    Toole, Joseph E.; Jensen, David W.; Rogers, Mark E.; Chernek, Paul J.; Erstfeld, Thomas E.

    1989-04-01

    The basic mathematical theory behind plane symmetry groups is presented. This theory is then applied in classifying the symmetry of bounded figures, frieze patterns and wallpaper patterns. Recently developed algorithms are included to help analyze complex designs. Symmetry operations relevant to 3-D crystallography are discussed. In particular, the seven crystal systems that classify the 32 crystallographic point groups are described. These are then used to construct the Bravais lattices. The role is investigated of symmetry in biological forms. Specifically, work on growth and form of molluscan shells is reviewed with an attempt to explain the consequences of that growth and form to the natural history of the Chambered Nautilus and its ancestors. The central role symmetry has increasingly played in physics is looked at by examining the Principle of Least Action and the invariance of the Lagrangian under a transformation. Noether's Theorem guarantees that a conservation law is associated with each of these symmetries. Examples include the conservation of energy, linear momentum, and angular momentum, as well as the purely quantum mechanical symmetry of invariance under an exchange operation. A brief look at gauge theories is the final example of how symmetry has become a guiding principle in the formulation of new theories.

  1. Symmetry in the Car Park

    ERIC Educational Resources Information Center

    Hancock, Karen

    2007-01-01

    In this article, the author presents a lesson on rotational symmetry which she developed for her students. The aim of the lesson was "to identify objects with rotational symmetry in the staff car park" and the success criteria were "pictures or sketches of at least six objects with different orders of rotation". After finding examples of…

  2. Asymptotic symmetries on Killing horizons

    NASA Astrophysics Data System (ADS)

    Koga, Jun-Ichirou

    2001-12-01

    We investigate asymptotic symmetries regularly defined on spherically symmetric Killing horizons in Einstein theory with or without the cosmological constant. These asymptotic symmetries are described by asymptotic Killing vectors, along which the Lie derivatives of perturbed metrics vanish on a Killing horizon. We derive the general form of the asymptotic Killing vectors and find that the group of asymptotic symmetries consists of rigid O(3) rotations of a horizon two-sphere and supertranslations along the null direction on the horizon, which depend arbitrarily on the null coordinate as well as the angular coordinates. By introducing the notion of asymptotic Killing horizons, we also show that local properties of Killing horizons are preserved not only under diffeomorphisms but also under nontrivial transformations generated by the asymptotic symmetry group. Although the asymptotic symmetry group contains the Diff(S1) subgroup, which results from supertranslations dependent only on the null coordinate, it is shown that the Poisson brackets algebra of the conserved charges conjugate to asymptotic Killing vectors does not acquire nontrivial central charges. Finally, by considering extended symmetries, we discuss the fact that unnatural reduction of the symmetry group is necessary in order to obtain the Virasoro algebra with nontrivial central charges, which is not justified when we respect the spherical symmetry of Killing horizons.

  3. Symmetry in Sign Language Poetry

    ERIC Educational Resources Information Center

    Sutton-Spence, Rachel; Kaneko, Michiko

    2007-01-01

    This paper considers the range of ways that sign languages use geometric symmetry temporally and spatially to create poetic effect. Poets use this symmetry in sign language art to highlight duality and thematic contrast, and to create symbolic representations of beauty, order and harmony. (Contains 8 tables, 14 figures and 6 notes.)

  4. Symmetries in geology and geophysics.

    PubMed

    Turcotte, D L; Newman, W I

    1996-12-10

    Symmetries have played an important role in a variety of problems in geology and geophysics. A large fraction of studies in mineralogy are devoted to the symmetry properties of crystals. In this paper, however, the emphasis will be on scale-invariant (fractal) symmetries. The earth's topography is an example of both statistically self-similar and self-affine fractals. Landforms are also associated with drainage networks, which are statistical fractal trees. A universal feature of drainage networks and other growth networks is side branching. Deterministic space-filling networks with side-branching symmetries are illustrated. It is shown that naturally occurring drainage networks have symmetries similar to diffusion-limited aggregation clusters.

  5. Hyperbolic-symmetry vector fields.

    PubMed

    Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

    2015-12-14

    We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.

  6. Symmetry and repetition in perspective.

    PubMed

    van der Vloed, Gert; Csathó, Arpád; van der Helm, Peter A

    2005-09-01

    Although ecologically relevant, perspective views of symmetries and repetitions have hardly been investigated. Any symmetry or repetition that is not oriented orthogonally to the line of sight yields perspective distortions on the retina. In this study, these distortions are analyzed in terms of first-order structures (i.e., virtual lines between corresponding points) and second-order structures (i.e., correlation quadrangles formed by two virtual lines). In the literature, these structures have been proposed to guide the detection of fron to parallel symmetry and repetition. But what about perspective views? First, the analysis in this study shows that perspective distorts the retinal first-order and second-order structures of symmetry and repetition differently. Second, the results of two experiments on this distortion difference suggest that, in perspective views, symmetry and repetition detection is not preceded by normalization but occurs directly on the basis of the retinal first-order and second-order structures.

  7. Theory of nodal s ± -wave pairing symmetry in the Pu-based 115 superconductor family.

    PubMed

    Das, Tanmoy; Zhu, Jian-Xin; Graf, Matthias J

    2015-02-27

    The spin-fluctuation mechanism of superconductivity usually results in the presence of gapless or nodal quasiparticle states in the excitation spectrum. Nodal quasiparticle states are well established in copper-oxide, and heavy-fermion superconductors, but not in iron-based superconductors. Here, we study the pairing symmetry and mechanism of a new class of plutonium-based high-Tc superconductors and predict the presence of a nodal s(±) wave pairing symmetry in this family. Starting from a density-functional theory (DFT) based electronic structure calculation we predict several three-dimensional (3D) Fermi surfaces in this 115 superconductor family. We identify the dominant Fermi surface "hot-spots" in the inter-band scattering channel, which are aligned along the wavevector Q = (π, π, π), where degeneracy could induce sign-reversal of the pairing symmetry. Our calculation demonstrates that the s(±) wave pairing strength is stronger than the previously thought d-wave pairing; and more importantly, this pairing state allows for the existence of nodal quasiparticles. Finally, we predict the shape of the momentum- and energy-dependent magnetic resonance spectrum for the identification of this pairing symmetry.

  8. Node-surface and node-line fermions from nonsymmorphic lattice symmetries

    NASA Astrophysics Data System (ADS)

    Liang, Qi-Feng; Zhou, Jian; Yu, Rui; Wang, Zhi; Weng, Hongming

    2016-02-01

    We propose a kind of topological quantum state of semimetals in the quasi-one-dimensional (1D) crystal family BaMX 3 (M =V , Nb, or Ta; X =S or Se) by using symmetry analysis and first-principles calculation. We find that in BaVS3 the valence and conduction bands are degenerate in the kz=π /c plane (c is the lattice constant along the z ̂ axis) of the Brillouin zone (BZ). These nodal points form a node surface, and they are protected by a nonsymmorphic crystal symmetry consisting of a twofold rotation about the z ̂ axis and a half-translation along the same z ̂ axis. The band degeneracy in the node surface is lifted in BaTaS3 by including strong spin-orbit coupling (SOC) of Ta. The node surface is reduced into 1D node lines along the high-symmetry paths kx=0 and kx=±√{3 }ky on the kz=π /c plane. These node lines are robust against SOC and guaranteed by the symmetries of the P 63/m m c space group. These node-line states are entirely different from previous proposals which are based on the accidental band touchings. We also propose a useful material design for realizing topological node-surface and node-line semimetals.

  9. Cognitive Aging and Time Perception: Roles of Bayesian Optimization and Degeneracy

    PubMed Central

    Turgeon, Martine; Lustig, Cindy; Meck, Warren H.

    2016-01-01

    This review outlines the basic psychological and neurobiological processes associated with age-related distortions in timing and time perception in the hundredths of milliseconds-to-minutes range. The difficulty in separating indirect effects of impairments in attention and memory from direct effects on timing mechanisms is addressed. The main premise is that normal aging is commonly associated with increased noise and temporal uncertainty as a result of impairments in attention and memory as well as the possible reduction in the accuracy and precision of a central timing mechanism supported by dopamine-glutamate interactions in cortico-striatal circuits. Pertinent to these findings, potential interventions that may reduce the likelihood of observing age-related declines in timing are discussed. Bayesian optimization models are able to account for the adaptive changes observed in time perception by assuming that older adults are more likely to base their temporal judgments on statistical inferences derived from multiple trials than on a single trial’s clock reading, which is more susceptible to distortion. We propose that the timing functions assigned to the age-sensitive fronto-striatal network can be subserved by other neural networks typically associated with finely-tuned perceptuo-motor adjustments, through degeneracy principles (different structures serving a common function). PMID:27242513

  10. RESOLVING THE sin(I) DEGENERACY IN LOW-MASS MULTI-PLANET SYSTEMS

    SciTech Connect

    Batygin, Konstantin; Laughlin, Gregory

    2011-04-01

    Long-term orbital evolution of multi-planet systems under tidal dissipation often converges to a stationary state, known as the tidal fixed point. The fixed point is characterized by a lack of oscillations in the eccentricities and apsidal alignment among the orbits. Quantitatively, the nature of the fixed point is dictated by mutual interactions among the planets as well as non-Keplerian effects. We show that if a roughly coplanar system hosts a hot, sub-Saturn mass planet, and is tidally relaxed, separation of planet-planet interactions and non-Keplerian effects in the equations of motion leads to a direct determination of the true masses of the planets. Consequently, a 'snap-shot' observational determination of the orbital state resolves the sin(I) degeneracy and opens up a direct avenue toward identification of the true lowest-mass exoplanets detected. We present an approximate, as well as a general, mathematical framework for computation of the line-of-sight inclination of secular systems, and apply our models illustratively to the 61 Vir system. We conclude by discussing the observability of planetary systems to which our method is applicable and we set our analysis into a broader context by presenting a current summary of the various possibilities for determining the physical properties of planets from observations of their orbital states.

  11. Degeneracies and fluctuations of Néel skyrmions in confined geometries

    NASA Astrophysics Data System (ADS)

    Keesman, Rick; Leonov, A. O.; van Dieten, P.; Buhrandt, Stefan; Barkema, G. T.; Fritz, Lars; Duine, R. A.

    2015-10-01

    The recent discovery of tunable Dzyaloshinskii-Moriya interactions in layered magnetic materials with perpendicular magnetic anisotropy makes them promising candidates for stabilization and manipulation of skyrmions at elevated temperatures. In this article, we use Monte Carlo simulations to investigate the robustness of skyrmions in these materials against thermal fluctuations and finite-size effects. We find that in confined geometries and at finite temperatures skyrmions are present in a large part of the phase diagram. Moreover, we find that the confined geometry favors the skyrmion over the spiral phase when compared to infinitely large systems. Upon tuning the magnetic field through the skyrmion phase, the system undergoes a cascade of transitions in the magnetic structure through states of different number of skyrmions, elongated and half-skyrmions, and spiral states. We consider how quantum and thermal fluctuations lift the degeneracies that occur at these transitions, and find that states with more skyrmions are typically favored by fluctuations over states with less skyrmions. Finally, we comment on electrical detection of the various phases through the topological and anomalous Hall effects.

  12. Accidental degeneracy beats: A distinct type of beat phenomenon in nonlinear optical spectroscopy

    NASA Astrophysics Data System (ADS)

    Merchant, K. A.; Thompson, David E.; Fayer, M. D.

    2002-02-01

    A type of beat in nonlinear optical spectroscopy that is distinct from quantum beats (QB's) and polarization beats, is described. Like a quantum beat, this beat, which we refer to as an accidental degeneracy beat (ADB), can only be seen in multilevel systems. However, unlike quantum beats, which are the result of intramolecular interferences, ADB's are interferences between different subensembles of molecules in the sample. They require multilevel systems with spectral overlap. ADB's can appear as separate frequencies or as phase and amplitude contributions with the same frequency as that of quantum beats. A procedure for distinguishing between quantum beats and ADB's is outlined, and criteria under which ADB's are expected to be observed are delineated. Calculations of the spectrally resolved stimulated vibrational echo signal from an inhomogeneously broadened coupled anharmonic oscillator system are presented to illustrate the differences between the two types of beats. ADB's carry information about the anharmonicity of a system, while QB's carry information about intramolecular correspondence of transition frequencies in a multilevel system.

  13. Phase shifting interferometry based on a vibration sensor - feasibility study on elimination of the depth degeneracy

    NASA Astrophysics Data System (ADS)

    Lee, Seung Seok; Kim, Ju Ha; Choi, Eun Seo

    2017-04-01

    We proposed novel phase-shifting interferometry using a fiber-optic vibration sensor. The Doppler shift in the coiled fiber caused by vibrations can be used to detect the vibrations by using a fiber-optic interferometer. The principle can be applied to induce phase shifts. While applying vibrations to the coiled fiber at various vibration frequencies, we recorded the variations in the interference fringes. The interference fringe moved to longer wavelengths when a vibration frequency was increased from 38.00 to 38.40 kHz. Phase variations of 3.59 rad/kHz were obtained. The ability to accurately control the phase by using the vibrations in the coiled fiber was demonstrated by the elimination of the depth degeneracy using the complex signal generated by the phase-shifted interference fringes. Using vibrations to control phase shifting can be an acceptable alternative to conventional methods and can be applied to resolve the depth ambiguity in Fourier domain optical coherence tomography.

  14. Flat band degeneracy and near-zero refractive index materials in acoustic crystals

    NASA Astrophysics Data System (ADS)

    Wu, Shiqiao; Mei, Jun

    2016-01-01

    A Dirac-like cone is formed by utilizing the flat bands associated with localized modes in an acoustic crystal (AC) composed of a square array of core-shell-structure cylinders in a water host. Although the triply-degeneracy seems to arise from two almost-overlapping flat bands touching another curved band, the enlarged view of the band structure around the degenerate point reveals that there are actually two linear bands intersecting each other at the Brillouin zone center, with another flat band passing through the same crossing point. The linearity of dispersion relations is achieved by tuning the geometrical parameters of the cylindrical scatterers. A perturbation method is used to not only accurately predict the linear slopes of the dispersions, but also confirm the linearity of the bands from first principles. An effective medium theory based on coherent potential approximation is developed, and it shows that a slab made of the AC carries a near-zero refractive index around the Dirac-like point. Full-wave simulations are performed to unambiguously demonstrate the wave manipulating properties of the AC structures such as perfect transmission, unidirectional transmission and wave front shaping.

  15. Resolving the sin(I) Degeneracy in Low-mass Multi-planet Systems

    NASA Astrophysics Data System (ADS)

    Batygin, Konstantin; Laughlin, Gregory

    2011-04-01

    Long-term orbital evolution of multi-planet systems under tidal dissipation often converges to a stationary state, known as the tidal fixed point. The fixed point is characterized by a lack of oscillations in the eccentricities and apsidal alignment among the orbits. Quantitatively, the nature of the fixed point is dictated by mutual interactions among the planets as well as non-Keplerian effects. We show that if a roughly coplanar system hosts a hot, sub-Saturn mass planet, and is tidally relaxed, separation of planet-planet interactions and non-Keplerian effects in the equations of motion leads to a direct determination of the true masses of the planets. Consequently, a "snap-shot" observational determination of the orbital state resolves the sin(I) degeneracy and opens up a direct avenue toward identification of the true lowest-mass exoplanets detected. We present an approximate, as well as a general, mathematical framework for computation of the line-of-sight inclination of secular systems, and apply our models illustratively to the 61 Vir system. We conclude by discussing the observability of planetary systems to which our method is applicable and we set our analysis into a broader context by presenting a current summary of the various possibilities for determining the physical properties of planets from observations of their orbital states.

  16. CCDM model with spatial curvature and the breaking of ''dark degeneracy''

    SciTech Connect

    Jesus, J.F.; Andrade-Oliveira, F. E-mail: felipe.oliveira@port.ac.uk

    2016-01-01

    Creation of Cold Dark Matter (CCDM), in the context of Einstein Field Equations, leads to a negative creation pressure, which can be used to explain the accelerated expansion of the Universe. Recently, it has been shown that the dynamics of expansion of such models can not be distinguished from the concordance ΛCDM model, even at higher orders in the evolution of density perturbations, leading at the so called ''dark degeneracy''. However, depending on the form of the CDM creation rate, the inclusion of spatial curvature leads to a different behavior of CCDM when compared to ΛCDM, even at background level. With a simple form for the creation rate, namely, Γ∝1/H , we show that this model can be distinguished from ΛCDM, provided the Universe has some amount of spatial curvature. Observationally, however, the current limits on spatial flatness from CMB indicate that neither of the models are significantly favored against the other by current data, at least in the background level.

  17. Transient potassium channels augment degeneracy in hippocampal active dendritic spectral tuning

    PubMed Central

    Rathour, Rahul Kumar; Malik, Ruchi; Narayanan, Rishikesh

    2016-01-01

    Hippocampal pyramidal neurons express an intraneuronal map of spectral tuning mediated by hyperpolarization-activated cyclic-nucleotide-gated nonspecific-cation channels. Modeling studies have predicted a critical regulatory role for A-type potassium (KA) channels towards augmenting functional robustness of this map. To test this, we performed patch-clamp recordings from soma and dendrites of rat hippocampal pyramidal neurons, and measured spectral tuning before and after blocking KA channels using two structurally distinct pharmacological agents. Consistent with computational predictions, we found that blocking KA channels resulted in a significant reduction in resonance frequency and significant increases in input resistance, impedance amplitude and action-potential firing frequency across the somato-apical trunk. Furthermore, across all measured locations, blocking KA channels enhanced temporal summation of postsynaptic potentials and critically altered the impedance phase profile, resulting in a significant reduction in total inductive phase. Finally, pair-wise correlations between intraneuronal percentage changes (after blocking KA channels) in different measurements were mostly weak, suggesting differential regulation of different physiological properties by KA channels. Our results unveil a pivotal role for fast transient channels in regulating theta-frequency spectral tuning and intrinsic phase response, and suggest that degeneracy with reference to several coexisting functional maps is mediated by cross-channel interactions across the active dendritic arbor. PMID:27094086

  18. New families of superintegrable systems from k-step rational extensions, polynomial algebras and degeneracies

    NASA Astrophysics Data System (ADS)

    Marquette, Ian

    2015-04-01

    Four new families of two-dimensional quantum superintegrable systems are constructed from k-step extension of the harmonic oscillator and the radial oscillator. Their wavefunctions are related with Hermite and Laguerre exceptional orthogonal polynomials (EOP) of type III. We show that ladder operators obtained from alternative construction based on combinations of supercharges in the Krein-Adler and Darboux Crum (or state deleting and creating) approaches can be used to generate a set of integrals of motion and a corresponding polynomial algebra that provides an algebraic derivation of the full spectrum and total number of degeneracies. Such derivation is based on finite dimensional unitary representations (unirreps) and doesn't work for integrals build from standard ladder operators in supersymmetric quantum mechanics (SUSYQM) as they contain singlets isolated from excited states. In this paper, we also rely on a novel approach to obtain the finite dimensional unirreps based on the action of the integrals of motion on the wavefunctions given in terms of these EOP. We compare the results with those obtained from the Daskaloyannis approach and the realizations in terms of deformed oscillator algebras for one of the new families in the case of 1-step extension. This communication is a review of recent works.

  19. Degeneracy between θ23 octant and neutrino non-standard interactions at DUNE

    NASA Astrophysics Data System (ADS)

    Agarwalla, Sanjib Kumar; Chatterjee, Sabya Sachi; Palazzo, Antonio

    2016-11-01

    We expound in detail the degeneracy between the octant of θ23 and flavor-changing neutral-current non-standard interactions (NSI's) in neutrino propagation, considering the Deep Underground Neutrino Experiment (DUNE) as a case study. In the presence of such NSI parameters involving the e - μ (εeμ) and e - τ (εeτ) flavors, the νμ →νe and νbarμ →νbare appearance probabilities in long-baseline experiments acquire an additional interference term, which depends on one new dynamical CP-phase ϕeμ/eτ. This term sums up with the well-known interference term related to the standard CP-phase δ creating a source of confusion in the determination of the octant of θ23. We show that for values of the NSI coupling (taken one at-a-time) as small as few % (relative to the Fermi coupling constant GF), and for unfavorable combinations of the two CP-phases δ and ϕeμ/eτ, the discovery potential of the octant of θ23 gets completely lost.

  20. PT Symmetry and Spontaneous Symmetry Breaking in a Microwave Billiard

    NASA Astrophysics Data System (ADS)

    Bittner, S.; Dietz, B.; Günther, U.; Harney, H. L.; Miski-Oglu, M.; Richter, A.; Schäfer, F.

    2012-01-01

    We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the Hamiltonian, its eigenvalues are either real or complex conjugate on a curve, which passes through the EP. An appropriate basis choice reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP.

  1. Functional Symmetry of Endomembranes

    PubMed Central

    2007-01-01

    In higher eukaryotic cells pleiomorphic compartments composed of vacuoles, tubules and vesicles move from the endoplasmic reticulum (ER) and the plasma membrane to the cell center, operating in early biosynthetic trafficking and endocytosis, respectively. Besides transporting cargo to the Golgi apparatus and lysosomes, a major task of these compartments is to promote extensive membrane recycling. The endocytic membrane system is traditionally divided into early (sorting) endosomes, late endosomes and the endocytic recycling compartment (ERC). Recent studies on the intermediate compartment (IC) between the ER and the Golgi apparatus suggest that it also consists of peripheral (“early”) and centralized (“late”) structures, as well as a third component, designated here as the biosynthetic recycling compartment (BRC). We propose that the ERC and the BRC exist as long-lived “mirror compartments” at the cell center that also share the ability to expand and become mobilized during cell activation. These considerations emphasize the functional symmetry of endomembrane compartments, which provides a basis for the membrane rearrangements taking place during cell division, polarization, and differentiation. PMID:17267686

  2. Spin, mass, and symmetry

    SciTech Connect

    Peskin, M.E.

    1994-12-01

    When the strong interactions were a mystery, spin seemed to be just a complication on top of an already puzzling set of phenomena. But now that particle physicists have understood the strong, weak, and electromagnetic interactions, to be gauge theories, with matter built of quarks and leptons, it is recognized that the special properties of spin 1/2 and spin 1 particles have taken central role in the understanding of Nature. The lectures in this summer school will be devoted to the use of spin in unravelling detailed questions about the fundamental interactions. Thus, why not begin by posing a deeper question: Why is there spin? More precisely, why do the basic pointlike constituents of Nature carry intrinsic nonzero quanta of angular momentum? Though the authos has found no definite answer to this question, the pursuit of an answer has led through a wonderful tangle of speculations on the deep structure of Nature. Is spin constructed or is it fundamental? Is it the requirement of symmetry? In the furthest flights taken, it seems that space-time itself is too restrictive a notion, and that this must be generalized in order to gain a full appreciation of spin. In any case, there is no doubt that spin must play a central role in unlocking the mysteries of fundamental physics.

  3. Symmetry algebras of linear differential equations

    NASA Astrophysics Data System (ADS)

    Shapovalov, A. V.; Shirokov, I. V.

    1992-07-01

    The local symmetries of linear differential equations are investigated by means of proven theorems on the structure of the algebra of local symmetries of translationally and dilatationally invariant differential equations. For a nonparabolic second-order equation, the absence of nontrivial nonlinear local symmetries is proved. This means that the local symmetries reduce to the Lie algebra of linear differential symmetry operators. For the Laplace—Beltrami equation, all local symmetries reduce to the enveloping algebra of the algebra of the conformal group.

  4. Role of cavity degeneracy for high-order mode excitation in end-pumped solid-state lasers.

    PubMed

    Barré, Nicolas; Romanelli, Marco; Brunel, Marc

    2014-02-15

    The possibility of exciting laser modes such as Laguerre-Gaussian (LG) or Ince-Gaussian (IG) modes is discussed on the basis of a gain-matching integral. We reach the conclusion that, using tight pumping and away from degeneracy regions, only the IG(n,n)(e) modes can be excited. Furthermore, pure high-order modes with circular or elliptical nodal lines can never be excited. Only an approximation of such modes, which we call quasi-IG or quasi-LG modes, can be observed and only when the cavity is partially degenerate. We provide experimental results in perfect agreement with the theory and discuss the exact nature of the profiles observed at degeneracy in our experiments and elsewhere in the literature.

  5. Lattice-induced double-valley degeneracy lifting in graphene by a magnetic field.

    PubMed

    Luk'yanchuk, Igor A; Bratkovsky, Alexander M

    2008-05-02

    We show that the recently discovered double-valley splitting of the Landau levels in the quantum Hall effect in graphene can be explained as the perturbative orbital interaction of intravalley and intervalley microscopic orbital currents with a magnetic field. This effect is facilitated by the translationally noninvariant terms that correspond to graphene's crystallographic honeycomb symmetry but do not exist in the relativistic theory of massless Dirac fermions in quantum electrodynamics. We discuss recent data in view of these findings.

  6. Nonlinear electromagnetic fields and symmetries

    NASA Astrophysics Data System (ADS)

    Barjašić, Irena; Gulin, Luka; Smolić, Ivica

    2017-06-01

    We extend the classical results on the symmetry inheritance of the canonical electromagnetic fields, described by the Maxwell's Lagrangian, to a much wider class of models, which include those of the Born-Infeld, power Maxwell and the Euler-Heisenberg type. Symmetry inheriting fields allow the introduction of electromagnetic scalar potentials and these are proven to be constant on the Killing horizons. Finally, using the relations obtained along the analysis, we generalize and simplify the recent proof for the symmetry inheritance of the 3-dimensional case, as well as give the first constraint for the higher dimensional electromagnetic fields.

  7. Degeneracies when T=0 two body interaction matrix elements are set equal to zero: Talmi's method of calculating coefficients of fractional parentage to states forbidden by the Pauli principle

    NASA Astrophysics Data System (ADS)

    Robinson, Shadow J. Q.; Zamick, Larry

    2001-11-01

    In a previous work [S.J.Q. Robinson and Larry Zamick, Phys. Rev. C 63, 064416 (2001)] we studied the effects of setting all two body T=0 matrix elements to zero in shell model calculations for 43Ti (43Sc) and 44Ti. The results for 44Ti were surprisingly good despite the severity of this approximation. In single-j shell calculations (fn7/2) degeneracies arose between the T=12 I=(12)-1 and (132)-1 states in 43Sc as well as the T=12 I=(132)-2, (172)-1, and (192)-1 in 43Sc. For 44Ti the T=0 states 3+2, 7+2, 9+1, and 10+1 are degenerate as are the 10+2 and 12+1 states. The degeneracies can be explained by certain 6j symbols and 9j symbols either vanishing or being equal as indeed they are. Previously we used Regge symmetries of 6j symbols to explain the vanishing 6j and 9j symbols. In this work a simpler, more physical method is used. This is Talmi's method of calculating coefficients of fractional parentage (cfp) for identical particles to states which are forbidden by the Pauli principle. This is done for both the one particle cfp to handle 6j symbols and the two particle cfp for the 9j symbols. From this we learn that the common thread for the angular momenta I for which the above degeneracies occur is that these angular momenta cannot exist in the calcium isotopes in the f7/2 shell. There are no T=32 f37/2 states with angular momenta 12, 132, 172, and 192. In the same vein there are no T=2 f47/2 states with angular momenta 3, 7, 9, 10, or 12. For these angular momenta, all the states can be classified by the dual quantum numbers (Jπ,Jν).

  8. Network, degeneracy and bow tie. Integrating paradigms and architectures to grasp the complexity of the immune system

    PubMed Central

    2010-01-01

    Recently, the network paradigm, an application of graph theory to biology, has proven to be a powerful approach to gaining insights into biological complexity, and has catalyzed the advancement of systems biology. In this perspective and focusing on the immune system, we propose here a more comprehensive view to go beyond the concept of network. We start from the concept of degeneracy, one of the most prominent characteristic of biological complexity, defined as the ability of structurally different elements to perform the same function, and we show that degeneracy is highly intertwined with another recently-proposed organizational principle, i.e. 'bow tie architecture'. The simultaneous consideration of concepts such as degeneracy, bow tie architecture and network results in a powerful new interpretative tool that takes into account the constructive role of noise (stochastic fluctuations) and is able to grasp the major characteristics of biological complexity, i.e. the capacity to turn an apparently chaotic and highly dynamic set of signals into functional information. PMID:20701759

  9. Non-singular string cosmology in a 2d hybrid model

    NASA Astrophysics Data System (ADS)

    Florakis, I.; Kounnas, C.; Partouche, H.; Toumbas, N.

    2011-03-01

    The existence of non-singular string cosmologies is established in a class of two-dimensional supersymmetric Hybrid models at finite temperature. The left-moving sector of the Hybrid models gives rise to 16 real (N=4) spacetime supercharges as in the usual superstring models. The right-moving sector is non-supersymmetric at the massless level, but is characterized by MSDS symmetry, which ensures boson/fermion degeneracy of the right-moving massive levels. Finite temperature configurations, which are free of Hagedorn instabilities, are constructed in the presence of non-trivial “gravito-magnetic” fluxes. These fluxes inject non-trivial winding charge into the thermal vacuum and restore the thermal T-duality symmetry associated with the Euclidean time circle. Thanks to the unbroken right-moving MSDS symmetry, the one-loop string partition function is exactly calculable beyond any α‧-approximation. At the self-dual point new massless thermal states appear, sourcing localized spacelike branes, which can be used to connect a contracting thermal Universe to an expanding one. The resulting bouncing cosmology is free of any curvature singularities and the string coupling remains perturbative throughout the cosmological evolution.

  10. Partial Dynamical Symmetry in Molecules

    NASA Astrophysics Data System (ADS)

    Ping, Jia-Lun; Chen, Jin-Quan

    1997-03-01

    It is shown that any Hamiltonian involving only one- and two-bond interactions for a molecule withnbonds and having a point groupPas its symmetry group may have theSn⊃Ppartial dynamical symmetry, i.e., the Hamiltonian can be solved analytically for a part of the states, called the unique states. For example, theXY6molecule has theS6⊃Ohpartial dynamical symmetry. The model of Iachello and Oss forncoupled anharmonic oscillators is revisited in terms of the partial dynamical symmetry. The energies are obtained analytically for the nine unique levels of theXY6molecule and the structures of the eigenstates are disclosed for the first time, while for non-unique states they are obtained by diagonalizing the Hamiltonian in theS6⊃Ohsymmetry adapted basis with greatly reduced dimension.

  11. Classification of spacetimes with symmetry

    NASA Astrophysics Data System (ADS)

    Hicks, Jesse W.

    Spacetimes with symmetry play a critical role in Einstein's Theory of General Relativity. Missing from the literature is a correct, usable, and computer accessible classification of such spacetimes. This dissertation fills this gap; specifically, we. i) give a new and different approach to the classification of spacetimes with symmetry using modern methods and tools such as the Schmidt method and computer algebra systems, resulting in ninety-two spacetimes; ii) create digital databases of the classification for easy access and use for researchers; iii) create software to classify any spacetime metric with symmetry against the new database; iv) compare results of our classification with those of Petrov and find that Petrov missed six cases and incorrectly normalized a significant number of metrics; v) classify spacetimes with symmetry in the book Exact Solutions to Einstein's Field Equations Second Edition by Stephani, Kramer, Macallum, Hoenselaers, and Herlt and in Komrakov's paper Einstein-Maxwell equation on four-dimensional homogeneous spaces using the new software.

  12. Symmetries from the solution manifold

    NASA Astrophysics Data System (ADS)

    Aldaya, Víctor; Guerrero, Julio; Lopez-Ruiz, Francisco F.; Cossío, Francisco

    2015-07-01

    We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré-Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton-Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.

  13. Electroweak Symmetry Breaking: With Dynamics

    SciTech Connect

    Chivukula, R. Sekhar

    2005-03-22

    In this note I provide a brief description of models of dynamical electroweak symmetry breaking, including walking technicolor, top-color assisted technicolor, the top-quark seesaw model, and little higgs theories.

  14. Convergence behavior of multireference perturbation theory: Forced degeneracy and optimization partitioning applied to the beryllium atom

    NASA Astrophysics Data System (ADS)

    Finley, James P.; Chaudhuri, Rajat K.; Freed, Karl F.

    1996-07-01

    High-order multireference perturbation theory is applied to the 1S states of the beryllium atom using a reference (model) space composed of the \\|1s22s2> and the \\|1s22p2> configuration-state functions (CSF's), a system that is known to yield divergent expansions using Mo/ller-Plesset and Epstein-Nesbet partitioning methods. Computations of the eigenvalues are made through 40th order using forced degeneracy (FD) partitioning and the recently introduced optimization (OPT) partitioning. The former forces the 2s and 2p orbitals to be degenerate in zeroth order, while the latter chooses optimal zeroth-order energies of the (few) most important states. Our methodology employs simple models for understanding and suggesting remedies for unsuitable choices of reference spaces and partitioning methods. By examining a two-state model composed of only the \\|1s22p2> and \\|1s22s3s> states of the beryllium atom, it is demonstrated that the full computation with 1323 CSF's can converge only if the zeroth-order energy of the \\|1s22s3s> Rydberg state from the orthogonal space lies below the zeroth-order energy of the \\|1s22p2> CSF from the reference space. Thus convergence in this case requires a zeroth-order spectral overlap between the orthogonal and reference spaces. The FD partitioning is not capable of generating this type of spectral overlap and thus yields a divergent expansion. However, the expansion is actually asymptotically convergent, with divergent behavior not displayed until the 11th order because the \\|1s22s3s> Rydberg state is only weakly coupled with the \\|1s22p2> CSF and because these states are energetically well separated in zeroth order. The OPT partitioning chooses the correct zeroth-order energy ordering and thus yields a convergent expansion that is also very accurate in low orders compared to the exact solution within the basis.

  15. Broken Symmetries and Magnetic Dynamos

    NASA Technical Reports Server (NTRS)

    Shebalin, John V.

    2007-01-01

    Phase space symmetries inherent in the statistical theory of ideal magnetohydrodynamic (MHD) turbulence are known to be broken dynamically to produce large-scale coherent magnetic structure. Here, results of a numerical study of decaying MHD turbulence are presented that show large-scale coherent structure also arises and persists in the presence of dissipation. Dynamically broken symmetries in MHD turbulence may thus play a fundamental role in the dynamo process.

  16. Possible violations of spacetime symmetries

    NASA Astrophysics Data System (ADS)

    Urrutia, Luis

    2016-10-01

    The identification of symmetries has played a fundamental role in our understanding of physical phenomena. Nevertheless, in most cases such symmetries constitute only a zeroth-order approximation and they need to be broken so that the predictions of the theory are consistent with experimental observation. In particular, the almost sacred CPT and Lorentz symmetries, which are certainly part of the fundamental ideas of modern physics, need to be probed experimentally. Recently, such efforts have been intensified because different theoretical approaches aiming to understand the microstructure of space-time suggest the possibility that such symmetries could present minute violations. Up to now, and with increasing experimental sensitivities, no signs of violation have been found. Nevertheless, we observe that even the persistence of such negative results will have a profound impact. On one hand, they will provide those symmetries with a firm experimental basis. On the other, they will set stringent experimental bounds to be compared with the possible emergence of such violations in quantum gravity models based upon a discrete structure of space. We present a very general perspective of the research on Lorentz symmetry breaking, together with a review of a few specific topics.

  17. Widening the Scope of a Partial Dynamical Symmetry

    NASA Astrophysics Data System (ADS)

    Pereira, Wesley; Garcia, Ricardo; Zamick, Larry

    2015-10-01

    In a single j shell calculation in which only T = 1(even J) two-particle matrix elements were non-zero there was a partial dynamical symmetry e.g. for 2 protons and 2 neutrons in the f7/2 shell there is a degeneracy of states with angular momenta I = 3,7,9,10. These have non -zero components only for (Jp, Jn) = (4,6) or (6,4). These I's cannot occur for 4 identical partices (44 Ca).We then consider a ``123'' interaction which for J = 0 to 7 is (0,0,1,0,2,0,3,0). Then I = 6 and I = 8 also come into play. Fot these (Jp+Jn) is a good quantum number. One gets an equally spaced multidegerate levels (``vibrational spectra'') with separation of 1.5 MeV. Each of these levels has fixed (Jp+Jn. For(Jp+Jn) equal to 6 we have I = 3 an I = 6 as; for 8 we get 6,7 ,8; for 10,we get 3,7,9,10 and for 12 we get 10,12. In the g9/2 shell with a ``1234'' (Jp+Jn) ranges from 8 to 16 and in h11/2 with ``12345'' from 10 and 20. W.P. Garden State Stokes Alliance for Minorities Participation internship GSISAMP 2. R.G. REU fron NSF PHY-1263280.

  18. Spontaneous breaking of chiral symmetry for confining potentials

    NASA Astrophysics Data System (ADS)

    Le Yaouanc, A.; Oliver, L.; Pène, O.; Raynal, J.-C.

    1984-03-01

    Using the Bogoliubov-Valatin variational method, we show that the chiral-invariant vacuum is unstable for a color, fourth-component vector powerlike potential rα(0<α<3) independently of the strength of the coupling constant. The fermion self-energy is negative and dominates over the positive potential energy, destabilizing the vacuum by ψ¯ψ pair condensation. This self-energy is finite but infrared singular, reflecting the behavior of the potential at large distances. We give an analytical proof of the fact that the energy of the unbroken vacuum is not minimum. The proof extends to logarithmic potentials as α-->0, but breaks down for α>=3 (number of spatial dimensions) due to severe infrared singularities. If the confining potential possesses a spin-spin piece, there are critical values of its strength, depending on the power α, beyond which the stability of the chiral-invariant vacuum is restored. In the case of the harmonic oscillator α=2, the gap equation reduces to a non-linear second-order differential equation. We find (besides the usual chiral degeneracy) an infinite number of solutions breaking chiral symmetry, higher in energy as the number of their nodes increases. We compute the expectation value of ψ¯ψ and the mass gap for the new vacuum, the lowest solution in energy. The infrared singularity of the massless fermion self-energy is removed for the stable broken solution.

  19. Ultracold Fermi gases with emergent SU(N) symmetry

    NASA Astrophysics Data System (ADS)

    Cazalilla, Miguel A.; Rey, Ana Maria

    2014-12-01

    We review recent experimental and theoretical progress on ultracold alkaline-earth Fermi gases with emergent SU(N) symmetry. Emphasis is placed on describing the ground-breaking experimental achievements of recent years. The latter include (1) the cooling to below quantum degeneracy of various isotopes of ytterbium and strontium, (2) the demonstration of optical Feshbach resonances and the optical Stern-Gerlach effect, (3) the realization of a Mott insulator of 173Yb atoms, (4) the creation of various kinds of Fermi-Bose mixtures and (5) the observation of many-body physics in optical lattice clocks. On the theory side, we survey the zoo of phases that have been predicted for both gases in a trap and loaded into an optical lattice, focusing on two and three dimensional systems. We also discuss some of the challenges that lie ahead for the realization of such phases such as reaching the temperature scale required to observe magnetic and more exotic quantum orders. The challenge of dealing with collisional relaxation of excited electronic levels is also discussed.

  20. Control over the Emission Properties of [5]Helicenes Based on the Symmetry and Energy Levels of Their Molecular Orbitals.

    PubMed

    Kubo, Hiromu; Hirose, Takashi; Matsuda, Kenji

    2017-03-30

    The effect of different substituents on the fluorescence properties of [5]helicene derivatives was investigated in terms of molecular orbital symmetry. Unsubstituted [5]helicene is nonemissive due to the symmetry-forbidden S1 → S0 transition. However, the fluorescence emission rate constant (kf) of [5]helicenes is efficiently increased by removing the orbital degeneracy involved in the S1 → S0 transition. As a result, we achieved a [5]helicene derivative exhibiting a high fluorescence quantum yield (Φf = 0.23) and short emission lifetime (⟨τf⟩ = 1.5 ns), which is in marked contrast to unsubstituted [5]helicene (Φf = 0.04 and ⟨τf⟩ = 26 ns).

  1. Effects of time reversal symmetry on phonons in sapphire substrate for ZnO and GaN

    NASA Astrophysics Data System (ADS)

    Kunert, H. W.; Hoffmann, A.; Machatine, A. G. J.; Malherbe, J.; Barnas, J.; Kaczmarczyk, G.; Haboeck, U.; Seguin, R.

    2007-07-01

    Vibrational states in a crystal are classified according to the irreducible representations (irreps) of the corresponding factor group G0k/T. The wave vector k runs over the entire Brillouin zone (BZ). For trigonal BZs, the factor groups are determined by the symmetry points Γ, F, L, T, and the symmetry lines Λ, Σ, Y. When the irreps are complex, the time reversal symmetry has to be taken into account. Using the Frobenuis-Schur criterion adapted to space groups with real and complex irreps, we have investigated high symmetry points and lines of the phonons in trigonal crystals: Cr 2O 3,Fe 2O 3,Ti 2O 3,V 2O 3,FeCO 3,CaCO 3,CdCO 3,MgCO 3,MnCO 3,NaCO 3 and ZnCO 3, with the common space group D3d6( R3¯c). We have found several phonons which are influenced by the time reversal symmetry. Therefore, an extra degeneracy of phonons arises. The theoretical results are also compared with available experimental data.

  2. Polarization properties and disorder effects in H{sub 3} photonic crystal cavities incorporating site-controlled, high-symmetry quantum dot arrays

    SciTech Connect

    Surrente, Alessandro; Felici, Marco; Gallo, Pascal; Dwir, Benjamin; Rudra, Alok; Kapon, Eli; Biasiol, Giorgio

    2015-07-20

    We report on the effects of optical disorder on breaking the symmetry of the cavity modes of H{sub 3} photonic crystal cavities incorporating site-controlled pyramidal quantum dots (QDs) as the internal light source. The high in-plane symmetry of the polarization states of the pyramidal QDs simplifies the analysis of the polarization states of the H{sub 3} cavities. It is shown that the optical disorder induced by fabrication imperfections lifts the degeneracy of the two quadrupole cavity modes and tilts the elongation axes of the cavity mode patterns with respect to the ideal, hexagonal symmetry case. These results are useful for designing QD-cavity structures for polarization-entangled photon sources and few-QD lasers.

  3. Symmetry in polarimetric remote sensing

    NASA Technical Reports Server (NTRS)

    Nghiem, S. V.; Yueh, S. H.; Kwok, R.

    1993-01-01

    Relationships among polarimetric backscattering coefficients are derived from the viewpoint of symmetry groups. For both reciprocal and non-reciprocal media, symmetry encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered. The derived properties are general and valid to all scattering mechanisms, including volume and surface scatterings and their interactions, in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is also discussed. Orientations of spheroidal scatterers described by spherical, uniform, planophile, plagiothile, erectophile, and extremophile distributions are considered to derive their polarimetric backscattering characteristics. These distributions can be identified from the observed scattering coefficients by comparison with theoretical symmetry calculations. A new parameter is then defined to study scattering structures in geophysical media. Observations from polarimetric data acquired by the Jet Propulsion Laboratory airborne synthetic aperture radar over forests, sea ice, and sea surface are presented. Experimental evidences of the symmetry relationships are shown and their use in polarimetric remote sensing is illustrated. For forests, the coniferous forest in Mt. Shasta area (California) and mixed forest near Presque Isle (Maine) exhibit characteristics of the centrical symmetry at C-band. For sea ice in the Beaufort Sea, multi-year sea ice has a cross-polarized ratio e close to e(sub 0), calculated from symmetry, due to the randomness in the scattering structure. First-year sea ice has e much smaller than e(sub 0) due to the preferential alignment of the columnar structure of the ice. From polarimetric data of a sea surface in the Bering Sea, it is

  4. Symmetry in polarimetric remote sensing

    NASA Technical Reports Server (NTRS)

    Nghiem, S. V.; Yueh, S. H.; Kwok, R.

    1993-01-01

    Relationships among polarimetric backscattering coefficients are derived from the viewpoint of symmetry groups. For both reciprocal and non-reciprocal media, symmetry encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered. The derived properties are general and valid to all scattering mechanisms, including volume and surface scatterings and their interactions, in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is also discussed. Orientations of spheroidal scatterers described by spherical, uniform, planophile, plagiothile, erectophile, and extremophile distributions are considered to derive their polarimetric backscattering characteristics. These distributions can be identified from the observed scattering coefficients by comparison with theoretical symmetry calculations. A new parameter is then defined to study scattering structures in geophysical media. Observations from polarimetric data acquired by the Jet Propulsion Laboratory airborne synthetic aperture radar over forests, sea ice, and sea surface are presented. Experimental evidences of the symmetry relationships are shown and their use in polarimetric remote sensing is illustrated. For forests, the coniferous forest in Mt. Shasta area (California) and mixed forest near Presque Isle (Maine) exhibit characteristics of the centrical symmetry at C-band. For sea ice in the Beaufort Sea, multi-year sea ice has a cross-polarized ratio e close to e(sub 0), calculated from symmetry, due to the randomness in the scattering structure. First-year sea ice has e much smaller than e(sub 0) due to the preferential alignment of the columnar structure of the ice. From polarimetric data of a sea surface in the Bering Sea, it is

  5. Molecular partners of the X(3872) from heavy-quark spin symmetry: a fresh look

    NASA Astrophysics Data System (ADS)

    Baru, V.; Epelbaum, E.; Filin, A. A.; Hanhart, C.; Nefediev, A. V.

    2017-03-01

    The heavy-quark spin symmetry (HQSS) partners of the X(3872) molecule are investigated in a chiral effective field theory (EFT) approach which incorporates contact and one-pion exchange interactions. The integral equations of the Lippmann-Schwinger type are formulated and solved for the coupled-channel problem for the DD¯, DD¯*, and D*D¯* systems with the quantum numbers JPC = 1++, 1+-, 0++, and 2++. We confirm that, if the X(3872) is a 1++DD¯* molecular state then, in the strict heavy-quark limit, there exist three partner states, with the quantum numbers 1+-, 0++, and 2++, which are degenerate in mass. At first glance, this result looks natural only for the purely contact pionless theory since pions contribute differently to different transition potentials and, therefore, may lift the above degeneracy. Nevertheless, it is shown that, by an appropriate unitary transformation, the Lippmann-Schwinger equation in each channel still can be brought to a block-diagonal form, with the same blocks for all quantum numbers, so that the degeneracy of the bound states in different channels is preserved. We stress that neglecting some of the coupled-channel transitions in an inconsistent manner leads to a severe violation of HQSS and yields regulator-dependent results for the partner states. The effect of HQSS violation in combination with nonperturbative pion dynamics on the pole positions of the partner states is discussed.

  6. Topological phases on non-orientable surfaces: twisting by parity symmetry

    NASA Astrophysics Data System (ADS)

    Chan, AtMa P. O.; Teo, Jeffrey C. Y.; Ryu, Shinsei

    2016-03-01

    We discuss (2 + 1)D topological phases on non-orientable spatial surfaces, such as Möbius strip, real projective plane and Klein bottle, etc, which are obtained by twisting the parent topological phases by their underlying parity symmetries through introducing parity defects. We construct the ground states on arbitrary non-orientable closed manifolds and calculate the ground state degeneracy (GSD). Such degeneracy is shown to be robust against continuous deformation of the underlying manifold. We also study the action of the mapping class group on the multiplet of ground states on the Klein bottle. The physical properties of the topological states on non-orientable surfaces are deeply related to the parity symmetric anyons which do not have a notion of orientation in their statistics. For example, the number of ground states on the real projective plane equals the root of the number of distinguishable parity symmetric anyons, while the GSD on the Klein bottle equals the total number of parity symmetric anyons; in deforming the Klein bottle, the Dehn twist encodes the topological spins whereas the Y-homeomorphism tells the particle-hole relation of the parity symmetric anyons.

  7. Topological semimetal: a probable new state of quantum optical lattice gases protected by D4 symmetry

    NASA Astrophysics Data System (ADS)

    Sun, Kai; Liu, W. Vincent; Das Sarma, S.

    2011-03-01

    We demonstrate that a novel topological semimetal emerges as a parity-protected critical theory for fermionic atoms loaded in the p and d orbital bands of a two-dimensional optical lattice. The new quantum state is characterized by a parabolic band-degeneracy point with Berry flux 2 π , in sharp contrast to the π flux of Dirac points as in graphene. We prove that this topological liquid is a universal property for all lattices of D4 point group symmetry and the band degeneracy is protected by odd parity. Turning on interparticle repulsive interaction, the system undergoes a phase transition to a topological insulator, whose experimental signature includes chiral gapless domain-wall modes, reminiscent of quantum Hall edge states. KS and SDS acknowledge the support of JQI-NSF-PFC, AFOSR-MURI, ARO-DARPA-OLE and ARO-MURI. W.V.L. is supported by ARO and ARO-DARPA-OLE. We thank the KITP at UCSB for its hospitality where this research is supported in part by NSF Grant No. PHY05-51164.

  8. Comparing dualities and gauge symmetries

    NASA Astrophysics Data System (ADS)

    De Haro, Sebastian; Teh, Nicholas; Butterfield, Jeremy N.

    2017-08-01

    We discuss some aspects of the relation between dualities and gauge symmetries. Both of these ideas are of course multi-faceted, and we confine ourselves to making two points. Both points are about dualities in string theory, and both have the 'flavour' that two dual theories are 'closer in content' than you might think. For both points, we adopt a simple conception of a duality as an 'isomorphism' between theories: more precisely, as appropriate bijections between the two theories' sets of states and sets of quantities. The first point (Section 3) is that this conception of duality meshes with two dual theories being 'gauge related' in the general philosophical sense of being physically equivalent. For a string duality, such as T-duality and gauge/gravity duality, this means taking such features as the radius of a compact dimension, and the dimensionality of spacetime, to be 'gauge'. The second point (Sections 4-6) is much more specific. We give a result about gauge/gravity duality that shows its relation to gauge symmetries (in the physical sense of symmetry transformations that are spacetime-dependent) to be subtler than you might expect. For gauge theories, you might expect that the duality bijections relate only gauge-invariant quantities and states, in the sense that gauge symmetries in one theory will be unrelated to any symmetries in the other theory. This may be so in general; and indeed, it is suggested by discussions of Polchinski and Horowitz. But we show that in gauge/gravity duality, each of a certain class of gauge symmetries in the gravity/bulk theory, viz. diffeomorphisms, is related by the duality to a position-dependent symmetry of the gauge/boundary theory.

  9. Quantum graphs: PT -symmetry and reflection symmetry of the spectrum

    NASA Astrophysics Data System (ADS)

    Kurasov, P.; Majidzadeh Garjani, B.

    2017-02-01

    Not necessarily self-adjoint quantum graphs—differential operators on metric graphs—are considered. Assume in addition that the underlying metric graph possesses an automorphism (symmetry) P . If the differential operator is P T -symmetric, then its spectrum has reflection symmetry with respect to the real line. Our goal is to understand whether the opposite statement holds, namely, whether the reflection symmetry of the spectrum of a quantum graph implies that the underlying metric graph possesses a non-trivial automorphism and the differential operator is P T -symmetric. We give partial answer to this question by considering equilateral star-graphs. The corresponding Laplace operator with Robin vertex conditions possesses reflection-symmetric spectrum if and only if the operator is P T -symmetric with P being an automorphism of the metric graph.

  10. Revising the solution of the neutrino oscillation parameter degeneracies at neutrino factories

    SciTech Connect

    Gago, A. M.; Jones Perez, J.

    2007-02-01

    In the context of neutrino factories, we review the solution of the degeneracies in the neutrino oscillation parameters. In particular, we have set limits to sin{sup 2}2{theta}{sub 13} in order to accomplish the unambiguous determination of {theta}{sub 23} and {delta}. We have performed two different analysis. In the first, at a baseline of 3000 km, we simulate a measurement of the channels {nu}{sub e}{yields}{nu}{sub {mu}}, {nu}{sub e}{yields}{nu}{sub {tau}}, and {nu}{sub {mu}}{yields}{nu}{sub {mu}}, combined with their respective conjugate ones, with a muon energy of 50 GeV and a running time of five years. In the second, we merge the simulated data obtained at L=3000 km with the measurement of {nu}{sub e}{yields}{nu}{sub {mu}} channel at 7250 km, the so-called 'magic baseline.' In both cases, we have studied the impact of varying the {nu}{sub {tau}} detector efficiency-mass product ({epsilon}{sub {nu}{tau}xM{tau}}), at 3000 km, keeping unchanged the {nu}{sub {mu}} detector mass and its efficiency. At L=3000 km, we found the existence of degenerate zones, that correspond to values of {theta}{sub 13}, which are equal or almost equal to the true ones. These zones are extremely difficult to discard, even when we increase the number of events. However, in the second scenario, this difficulty is overcome, demonstrating the relevance of the 'magic baseline'. From this scenario, the best limits of sin{sup 2}2{theta}{sub 13}, reached at 3{sigma}, for sin{sup 2}2{theta}{sub 23}=0.95, 0.975, and 0.99 are: 0.008, 0.015, and 0.045, respectively, obtained at {delta}=0, and considering ({epsilon}{sub {nu}{tau}xM{tau}}){approx_equal}125, which is 5 times the initial efficiency-mass combination.

  11. Structure and Properties of High Symmetry Composites

    DTIC Science & Technology

    1990-07-27

    utilizing a 4-directional reinforcement. Reducing the close-to-cubic symmetry concept into practice in our laboratory by a three-dimensional braiding...modelled by utilizing the different elastic strain energy expressions produced by different combinations of symmetry elements. Symmetry in Materials The...rings is insignmicant. Utilizing the above assumptions, numerous textile structures possess holosymmetric cubic symmetry. This symmetry state is found in

  12. Particle-hole symmetry, many-body localization, and topological edge modes

    NASA Astrophysics Data System (ADS)

    Vasseur, Romain; Friedman, Aaron J.; Parameswaran, S. A.; Potter, Andrew C.

    We study the excited states of interacting fermions in one dimension with particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a combination of renormalization group methods and exact diagonalization. Absent interactions, the entire many-body spectrum exhibits infinite-randomness quantum critical behavior with highly degenerate excited states. We show that though interactions are an irrelevant perturbation in the ground state, they drastically affect the structure of excited states: even arbitrarily weak interactions split the degeneracies in favor of thermalization (weak disorder) or spontaneously broken particle-hole symmetry, driving the system into a many-body localized spin glass phase (strong disorder). In both cases, the quantum critical properties of the non-interacting model are destroyed, either by thermal decoherence or spontaneous symmetry breaking. This system then has the interesting and counterintuitive property that edges of the many-body spectrum are less localized than the center of the spectrum. We argue that our results rule out the existence of certain excited state symmetry-protected topological orders. Supported by the Gordon and Betty Moore Foundation's EPiQS Initiative (Grant GBMF4307 (ACP), the Quantum Materials Program at LBNL (RV), NSF Grant DMR-1455366 and UCOP Research Catalyst Award No. CA-15-327861 (SAP).

  13. Localization of Nonlocal Symmetries and Symmetry Reductions of Burgers Equation

    NASA Astrophysics Data System (ADS)

    Wu, Jian-Wen; Lou, Sen-Yue; Yu, Jun

    2017-05-01

    The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method. The auto-Bäcklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries. Furthermore, the interaction solutions of the solition-Kummer waves and the solition-Airy waves are obtained. Supported by the Global Change Research Program China under Grant No. 2015CB953904, the National Natural Science Foundations of China under Grant Nos. 11435005, 11175092, and 11205092, Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No. ZF1213, and K. C. Wong Magna Fund in Ningbo University

  14. Symmetry in finite phase plane

    NASA Astrophysics Data System (ADS)

    Zak, J.

    2010-03-01

    The known symmetries in one-dimensional systems are inversion and translations. These symmetries persist in finite phase plane, but a novel symmetry arises in view of the discrete nature of the coordinate xi and the momentum pi : xi and pi can undergo permutations. Thus, if xi assumes M discrete values, i = 0, 1,2,..., M - 1, a permutation will change the order of the set x0,x1,..., xM-1 into a new ordered set. Such a symmetry element does not exist for a continuous x-coordinate in an infinite phase plane. Thus, in a finite phase plane, translations can be replaced by permutations. This is also true for the inversion operator. The new permutation symmetry has been used for the construction of conjugate representations and for the splitting of the M-dimensional vector space into independent subspaces. This splitting is exhaustive in the sense that if M = iMi with Mi being prime numbers, the M-dimensional space splits into M1,M2,...Mn-dimensional independent subspaces. It is shown that following this splitting one can design new potentials with appropriate constants of motion. A related problem is the Weyl-Heisenberg group in the M-dimensional space which turns into a direct product of its subgroups in the Mi-dimensional subspaces. As an example we consider the case of M = 8.

  15. Symmetry Guide to Ferroaxial Transitions

    NASA Astrophysics Data System (ADS)

    Hlinka, J.; Privratska, J.; Ondrejkovic, P.; Janovec, V.

    2016-04-01

    The 212 species of the structural phase transitions with a macroscopic symmetry breaking are inspected with respect to the occurrence of the ferroaxial order parameter, the electric toroidal moment. In total, 124 ferroaxial species are found, some of them being also fully ferroelectric (62) or fully ferroelastic ones (61). This ensures a possibility of electrical or mechanical switching of ferroaxial domains. Moreover, there are 12 ferroaxial species that are neither ferroelectric nor ferroelastic. For each species, we have also explicitly worked out a canonical form for a set of representative equilibrium property tensors of polar and axial nature in both high-symmetry and low-symmetry phases. This information was gathered into the set of 212 mutually different symbolic matrices, expressing graphically the presence of nonzero independent tensorial components and the symmetry-imposed links between them, for both phases simultaneously. Symmetry analysis reveals the ferroaxiality in several currently debated materials, such as VO2 , LuFe2 O4 , and URu2 Si2 .

  16. Fearful symmetry in aposematic plants.

    PubMed

    Lev-Yadun, Simcha

    2011-11-01

    Symmetry has been proposed to increase the efficiency of visual aposematic displays in animals, and I suggest that it may also be true for many aposematic spiny or poisonous plants. For instance, in the very spiny plant taxa cacti, Aloe sp., Agave sp. and Euphorbia sp., which have been proposed to be aposematic because of their colorful spine system, the shoots, and in cacti, the spiny fruits as well, are usually radially symmetric. Moreover, in the radial symmetric shoots of Agave and Aloe their individual spiny leaves are also bilaterally symmetric. Spiny or poisonous fruits of various other taxa, the symmetric spiny leaf rosettes and flowering spiny heads of many Near Eastern species of the Asteraceae and other taxa, and poisonous colorful flowers in taxa that were proposed to be aposematic are also symmetric. Thus, in plants, like in animals, symmetry seems to be commonly associated with visual aposematism and probably contributes to its effectiveness. Symmetry may stem from developmental constraints, or like in flowers, have other signaling functions. However, because of the better perception of symmetry by animals it may exploit inherited modes of animal sensing that probably result in paying more attention to symmetric shapes. All these possible alternatives do not negate the probable deterring role of symmetry in plant aposematism.

  17. Structural Symmetry in Membrane Proteins.

    PubMed

    Forrest, Lucy R

    2015-01-01

    Symmetry is a common feature among natural systems, including protein structures. A strong propensity toward symmetric architectures has long been recognized for water-soluble proteins, and this propensity has been rationalized from an evolutionary standpoint. Proteins residing in cellular membranes, however, have traditionally been less amenable to structural studies, and thus the prevalence and significance of symmetry in this important class of molecules is not as well understood. In the past two decades, researchers have made great strides in this area, and these advances have provided exciting insights into the range of architectures adopted by membrane proteins. These structural studies have revealed a similarly strong bias toward symmetric arrangements, which were often unexpected and which occurred despite the restrictions imposed by the membrane environment on the possible symmetry groups. Moreover, membrane proteins disproportionately contain internal structural repeats resulting from duplication and fusion of smaller segments. This article discusses the types and origins of symmetry in membrane proteins and the implications of symmetry for protein function.

  18. Band Structures of Periodic Carbon Nanotube Junctions and Their Symmetries Analyzed by the Effective Mass Approximation

    NASA Astrophysics Data System (ADS)

    Tamura, Ryo; Tsukada, Masaru

    1999-03-01

    The band structures of the periodic nanotube junctions are investigated by the effective mass theory and the tight binding model. The periodic junctions are constructed by introducing pairs of a pentagonal defect and a heptagonal defect periodically in the carbon nanotube. We treat the periodic junctions composed by two kinds of metallic nanotubes with almost same radii, the ratio of which is between 0.7 and 1. The discussed energy region is near the undoped Fermi level. The energy bands are expressed with closed analytical forms by the effective mass theory. They are similar to the dispersion relation of Kronig-Penny model and coincide well with the numerical results by the tight binding model. The width of the gap and the band are in inverse proportion to the length of the unit cell. The degeneracy and repulsion between the two bands are determined only from symmetries.

  19. Shape phase transitions in odd-A nuclei

    SciTech Connect

    Alonso, C. E.; Arias, J. M.; Fortunato, L.; Vitturi, A.

    2008-11-11

    We investigate shape phase transitions in odd nuclei within the Interacting Boson Fermion Model. Special attention is given to the case of the transition from the vibrational behaviour to the stable axial deformation. The odd particle is assumed to be moving in the three single particle orbitals j = 1/2,3/2,5/2 with a boson-fermion Hamiltonian that leads to the occurrence of the SU{sup BF}(3) boson-fermion symmetry when the boson part approaches the SU(3) condition. Both energy spectra and electromagnetic transitions show characteristic patterns similar to those displayed by the even nuclei at the corresponding critical point. The role of the additional particle in characterizing the properties of the critical points in finite quantal systems is investigated by resorting to the formalism based on the intrinsic frame.

  20. U{sup BF}(5) to SU{sup BF}(3) shape phase transition in odd nuclei for j=1/2, 3/2, and 5/2 orbits: The role of the odd particle at the critical point

    SciTech Connect

    Alonso, C. E.; Arias, J. M.; Fortunato, L.; Vitturi, A.

    2009-01-15

    We investigate the phase transition in odd nuclei within the Interacting Boson Fermion Model in correspondence with the transition from spherical to stable axially deformed shape. The odd particle is assumed to be moving in the single-particle orbitals with angular momenta j=1/2,3/2,5/2 with a boson-fermion Hamiltonian that leads to the occurrence of the SU{sup BF}(3) boson-fermion symmetry when the boson part approaches the SU(3) condition. Both energy spectra and electromagnetic transitions show characteristic patterns similar to those displayed by the even nuclei at the corresponding critical point. The role of the additional particle in characterizing the properties of the critical points in finite quantal systems is investigated by resorting to the formalism based on the intrinsic frame.

  1. Resonantly amplified vibronic symmetry breaking

    NASA Astrophysics Data System (ADS)

    Poliakoff, E. D.; Rathbone, G. J.; Bozek, J. D.; Lucchese, R. R.

    2002-05-01

    In photoelectron spectroscopy, it is normally assumed that excitation of a single quantum of a non-totally symmetric vibrational mode is forbidden owing to symmetry constraints. Using vibrationally resolved photoelectron spectroscopy over a broad spectral range, we have shown that a previously overlooked mechanism can lead to these nominally forbidden transitions. Specifically, the photoelectron can mediate the oscillator strength for such a transition via resonantly amplified vibronic symmetry breaking, and this effect results from intrachannel rather than interchannel coupling. In our first experiments, we focused on bending excitation accompanying CO2 photoionization. Photoelectron spectroscopy on the CO_2^+(C^2Σ_g^+) state showed that the excitation of the (010) vibrational mode is mediated by a shape resonant continuum electron. The degree of vibrational excitation can be substantial, and extensions to other types of symmetry breaking are currently being investigated.

  2. Gravitation and spontaneous symmetry breaking

    SciTech Connect

    Bekenstein, J.D.

    1986-05-01

    It is pointed out that the Higgs field may be supplanted by an ordinary Klien-Gordon Field conformally coupled to the space-time curvature, and with very small, real, rest mass. Provided there is a bare cosmological constant of order of its square mass, this field can induce spontaneous symmetry breaking with a mass scale that can be as large as the Planck-Wheeler mass, but may be smaller. It can thus play a natural role in grand unified theroies. In the theory presented here the physical cosmological constant is small, being of order of the squared mass, and can meet observational constraints without having to be cancelled accurately. The physical gravitational constant differs somewhat from the coupling constant in Einstein's equation, and is temperature dependent in the broken symmetry regime. Symmetry restoration occurs at high temperature.

  3. Nonholonomic Mechanical Systems with Symmetry

    NASA Astrophysics Data System (ADS)

    Bloch, Anthony M.; Krishnaprasad, P. S.; Marsden, Jerrold E.; Murray, Richard M.

    1996-12-01

    This work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of Lagrangian mechanics and with a view to control-theoretical applications. The basic methodology is that of geometric mechanics applied to the Lagrange-d'Alembert formulation, generalizing the use of connections and momentum maps associated with a given symmetry group to this case. We begin by formulating the mechanics of nonholonomic systems using an Ehresmann connection to model the constraints, and show how the curvature of this connection enters into Lagrange's equations. Unlike the situation with standard configuration-space constraints, the presence of symmetries in the nonholonomic case may or may not lead to conservation laws. However, the momentum map determined by the symmetry group still satisfies a useful differential equation that decouples from the group variables. This momentum equation, which plays an important role in control problems, involves parallel transport operators and is computed explicitly in coordinates. An alternative description using a “body reference frame” relates part of the momentum equation to the components of the Euler-Poincaré equations along those symmetry directions consistent with the constraints. One of the purposes of this paper is to derive this evolution equation for the momentum and to distinguish geometrically and mechanically the cases where it is conserved and those where it is not. An example of the former is a ball or vertical disk rolling on a flat plane and an example of the latter is the snakeboard, a modified version of the skateboard which uses momentum coupling for locomotion generation. We construct a synthesis of the mechanical connection and the Ehresmann connection defining the constraints, obtaining an important new object we call the nonholonomic connection. When the nonholonomic connection is a principal connection for the given symmetry group, we show how to

  4. Bell Inequalities and Group Symmetry

    NASA Astrophysics Data System (ADS)

    Bolonek-Lasoń, Katarzyna

    2017-03-01

    Recently the method based on irreducible representations of finite groups has been proposed as a tool for investigating the more sophisticated versions of Bell inequalities (V. Ugǔr Gűney, M. Hillery, Phys. Rev. A90, 062121 ([2014]) and Phys. Rev. A91, 052110 ([2015])). In the present paper an example based on the symmetry group S 4 is considered. The Bell inequality violation due to the symmetry properties of regular tetrahedron is described. A nonlocal game based on the inequalities derived is described and it is shown that the violation of Bell inequality implies that the quantum strategies outperform their classical counterparts.

  5. Nonsupersymmetric Dualities from Mirror Symmetry

    NASA Astrophysics Data System (ADS)

    Kachru, Shamit; Mulligan, Michael; Torroba, Gonzalo; Wang, Huajia

    2017-01-01

    We study supersymmetry breaking perturbations of the simplest dual pair of (2 +1 )-dimensional N =2 supersymmetric field theories—the free chiral multiplet and N =2 super QED with a single flavor. We find dual descriptions of a phase diagram containing four distinct massive phases. The equivalence of the intervening critical theories gives rise to several nonsupersymmetric avatars of mirror symmetry: we find dualities relating scalar QED to a free fermion and Wilson-Fisher theories to both scalar and fermionic QED. Thus, mirror symmetry can be viewed as the multicritical parent duality from which these nonsupersymmetric dualities directly descend.

  6. Symmetries of coupled harmonic oscillators

    NASA Technical Reports Server (NTRS)

    Han, D.; Kim, Y. S.

    1993-01-01

    It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2).

  7. Iterates of maps with symmetry

    NASA Technical Reports Server (NTRS)

    Chossat, Pascal; Golubitsky, Martin

    1988-01-01

    Fixed-point bifurcation, period doubling, and Hopf bifurcation (HB) for iterates of equivariant mappings are investigated analytically, with a focus on HB in the presence of symmetry. An algebraic formulation for the hypotheses of the theorem of Ruelle (1973) is derived, and the case of standing waves in a system of ordinary differential equations with O(2) symmetry is considered in detail. In this case, it is shown that HB can lead directly to motion on an invariant 3-torus, with an unexpected third frequency due to drift of standing waves along the torus.

  8. Unparticles and electroweak symmetry breaking

    SciTech Connect

    Lee, Jong-Phil

    2008-11-23

    We investigate a scalar potential inspired by the unparticle sector for the electroweak symmetry breaking. The scalar potential contains the interaction between the standard model fields and unparticle sector. It is described by the non-integral power of fields that originates from the nontrivial scaling dimension of the unparticle operator. It is found that the electroweak symmetry is broken at tree level when the interaction is turned on. The scale invariance of unparticle sector is also broken simultaneously, resulting in a physical Higgs and a new lighter scalar particle.

  9. Symmetry analysis of cellular automata

    NASA Astrophysics Data System (ADS)

    García-Morales, V.

    2013-01-01

    By means of B-calculus [V. García-Morales, Phys. Lett. A 376 (2012) 2645] a universal map for deterministic cellular automata (CAs) has been derived. The latter is shown here to be invariant upon certain transformations (global complementation, reflection and shift). When constructing CA rules in terms of rules of lower range a new symmetry, “invariance under construction” is uncovered. Modular arithmetic is also reformulated within B-calculus and a new symmetry of certain totalistic CA rules, which calculate the Pascal simplices modulo an integer number p, is then also uncovered.

  10. Chiral symmetry in quarkyonic matter

    SciTech Connect

    Kojo, T.

    2012-05-15

    The 1/N{sub c} expansion classifies nuclear matter, deconfined quark matter, and Quarkyonic matter in low temperature region. We investigate the realization of chiral symmetry in Quarkyonic matter by taking into account condensations of chiral particle-hole pairs. It is argued that chiral symmetry and parity are locally violated by the formation of chiral spirals, <{psi}-bar exp (2i{mu}{sub q} z{gamma}{sup 0} {gamma}{sup z}){psi}> . An extension to multiple chiral spirals is also briefly discussed.

  11. Quantum Symmetries and Exceptional Collections

    NASA Astrophysics Data System (ADS)

    Karp, Robert L.

    2011-01-01

    We study the interplay between discrete quantum symmetries at certain points in the moduli space of Calabi-Yau compactifications, and the associated identities that the geometric realization of D-brane monodromies must satisfy. We show that in a wide class of examples, both local and compact, the monodromy identities in question always follow from a single mathematical statement. One of the simplest examples is the {{mathbb Z}_5} symmetry at the Gepner point of the quintic, and the associated D-brane monodromy identity.

  12. The Broken Symmetry of Time

    SciTech Connect

    Kastner, Ruth E.

    2011-11-29

    This paper seeks to clarify features of time asymmetry in terms of symmetry breaking. It is observed that, in general, a contingent situation or event requires the breaking of an underlying symmetry. The distinction between the universal anisotropy of temporal processes and the irreversibility of certain physical processes is clarified. It is also proposed that the Transactional Interpretation of quantum mechanics offers an effective way to explain general thermodynamic asymmetry in terms of the time asymmetry of radiation, where prior such efforts have fallen short.

  13. BRST symmetry and fictitious parameters

    NASA Astrophysics Data System (ADS)

    Nogueira, A. A.; Pimentel, B. M.

    2017-03-01

    Our goal in this work is to present the variational method of fictitious parameters and its connection with the Bechi-Rouet-Stora-Tyutin (BRST) symmetry. First, we implement the method in QED at zero temperature and then we extend the analysis to generalized QED at finite temperature. As we see the core of the study is the general statement in gauge theories at finite temperature, assigned by Tyutin work, that the physical degrees of freedom do not depend on the gauge choices, covariant or not, due to BRST symmetry.

  14. Chiral symmetry on the lattice

    SciTech Connect

    Creutz, M.

    1994-11-01

    The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model.

  15. Generation of <7 fs pulses at 800 nm from a blue-pumped optical parametric amplifier at degeneracy.

    PubMed

    Siddiqui, A M; Cirmi, G; Brida, D; Kärtner, F X; Cerullo, G

    2009-11-15

    We generate ultrabroadband pulses at 800 nm from an optical parametric amplifier (OPA) pumped by the second harmonic of a Ti:sapphire system and working at degeneracy. The OPA is seeded by a white-light continuum generated from a near-IR OPA pumped by the same laser. Nearly transform-limited <7 fs pulses, fully characterized in amplitude and phase, are obtained with a chirped mirror compressor. The system fills the gap around 800 nm for broadband continuum seeded OPAs pumped by Ti:sapphire-based sources.

  16. The relationship between noise correlation and the Green's function in the presence of degeneracy and the absence of equipartition

    USGS Publications Warehouse

    Tsai, V.C.

    2010-01-01

    Recent derivations have shown that when noise in a physical system has its energy equipartitioned into the modes of the system, there is a convenient relationship between the cross correlation of time-series recorded at two points and the Green's function of the system. Here, we show that even when energy is not fully equipartitioned and modes are allowed to be degenerate, a similar (though less general) property holds for equations with wave equation structure. This property can be used to understand why certain seismic noise correlation measurements are successful despite known degeneracy and lack of equipartition on the Earth. No claim to original US government works Journal compilation ?? 2010 RAS.

  17. Demonstration of CW mode locked Cr:forsterite laser using self-shortening and transverse mode degeneracy driven mode locking.

    PubMed

    George, J; Thakur, P; Bindra, K S; Oak, S M

    2014-11-10

    This paper reports a nearly Fourier transform limited CW mode locked Cr:forsterite laser at 1282 nm, with 131 fs pulse duration, based on self-shortening and transverse mode degeneracy (TMD) driven mode locking, operating near the point of fourth-order TMD. The cavity employs a combination of instantaneous intensity driven self-shortening, and operation on the right side of the fourth-order TMD, to generate the self-amplitude modulation necessary for self-mode locking.

  18. Feshbach resonances and weakly bound molecular states of boson-boson and boson-fermion NaK pairs

    NASA Astrophysics Data System (ADS)

    Viel, Alexandra; Simoni, Andrea

    2016-04-01

    We conduct a theoretical study of magnetically induced Feshbach resonances and near-threshold bound states in isotopic NaK pairs. Our calculations accurately reproduce Feshbach spectroscopy data on Na 40K and explain the origin of the observed multiplets in the p wave [Phys. Rev. A 85, 051602(R) (2012), 10.1103/PhysRevA.85.051602]. We apply the model to predict scattering and bound state threshold properties of the boson-boson Na 39K and Na 41K systems. We find that the Na 39K isotopic pair presents broad magnetic Feshbach resonances and favorable ground-state features for producing nonreactive polar molecules by two-photon association. Broad s -wave resonances are also predicted for Na 41K collisions.

  19. Super no-scale models in string theory

    NASA Astrophysics Data System (ADS)

    Kounnas, Costas; Partouche, Hervé

    2016-12-01

    We consider "super no-scale models" in the framework of the heterotic string, where the N = 4 , 2 , 1 → 0 spontaneous breaking of supersymmetry is induced by geometrical fluxes realizing a stringy Scherk-Schwarz perturbative mechanism. Classically, these backgrounds are characterized by a boson/fermion degeneracy at the massless level, even if supersymmetry is broken. At the 1-loop level, the vacuum energy is exponentially suppressed, provided the supersymmetry breaking scale is small, m3/2 ≪Mstring. We show that the "super no-scale string models" under consideration are free of Hagedorn-like tachyonic singularities, even when the supersymmetry breaking scale is large, m3/2 ≃Mstring. The vacuum energy decreases monotonically and converges exponentially to zero, when m3/2 varies from Mstring to 0. We also show that all Wilson lines associated to asymptotically free gauge symmetries are dynamically stabilized by the 1-loop effective potential, while those corresponding to non-asymptotically free gauge groups lead to instabilities and condense. The Wilson lines of the conformal gauge symmetries remain massless. When stable, the stringy super no-scale models admit low energy effective actions, where decoupling gravity yields theories in flat spacetime, with softly broken supersymmetry.

  20. Charge symmetry at the partonic level

    SciTech Connect

    Londergan, J. T.; Peng, J. C.; Thomas, A. W.

    2010-07-01

    This review article discusses the experimental and theoretical status of partonic charge symmetry. It is shown how the partonic content of various structure functions gets redefined when the assumption of charge symmetry is relaxed. We review various theoretical and phenomenological models for charge symmetry violation in parton distribution functions. We summarize the current experimental upper limits on charge symmetry violation in parton distributions. A series of experiments are presented, which might reveal partonic charge symmetry violation, or alternatively might lower the current upper limits on parton charge symmetry violation.

  1. Platonic Symmetry and Geometric Thinking

    ERIC Educational Resources Information Center

    Zsombor-Murray, Paul

    2007-01-01

    Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…

  2. Turning Students into Symmetry Detectives

    ERIC Educational Resources Information Center

    Wilders, Richard; VanOyen, Lawrence

    2011-01-01

    Exploring mathematical symmetry is one way of increasing students' understanding of art. By asking students to search designs and become pattern detectives, teachers can potentially increase their appreciation of art while reinforcing their perception of the use of math in their day-to-day lives. This article shows teachers how they can interest…

  3. The Symmetry of Natural Laws.

    ERIC Educational Resources Information Center

    Brown, Laurie M.

    This document is a monograph intended for advanced undergraduate students, or beginning graduate students, who have some knowledge of modern physics as well as classical physics, including the elementary quantum mechanical treatment of the hydrogen atom and angular momentum. The first chapter introduces symmetry and relates it to the mathematical…

  4. Symmetry of integrable cellular automaton

    NASA Astrophysics Data System (ADS)

    Hikami, Kazuhiro; Inoue, Rei

    2001-03-01

    We study an integrable cellular automaton which is called the box-ball system (BBS). The BBS can be derived directly from the integrable differential-difference equation by either ultradiscretization or crystallization. We clarify the integrable structure and the hidden symmetry of the BBS.

  5. Superdeformations and fermion dynamical symmetries

    SciTech Connect

    Wu, Cheng-Li . Dept. of Physics and Atmospheric Science Tennessee Univ., Knoxville, TN . Dept. of Physics and Astronomy Joint Inst. for Heavy Ion Research, Oak Ridge, TN )

    1990-01-01

    In this talk, I will present a link between nuclear collective motions and their underlying fermion dynamical symmetries. In particular, I will focus on the microscopic understanding of deformations. It is shown that the SU{sub 3} of the one major shell fermion dynamical symmetry model (FDSM) is responsible for the physics of low and high spins in normal deformation. For the recently observed phenomena of superdeformation, the physics of the problem dictates a generalization to a supershell structure (SFDSM), which also has an SU{sub 3} fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU{sub 3} symmetry. In both cases the dynamical Pauli effect plays a vital role. A particularly noteworthy discovery from this model is that the superdeformed ground band is not the usual unaligned band but the D-pair aligned (DPA) band, which sharply crosses the excited bands. The existence of such DPA band is a key point to understand many properties of superdeformation. Our studies also poses new experimental challenge. This is particularly interesting since there are now plans to build new and exciting {gamma}-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs.

  6. Baryon and chiral symmetry breaking

    SciTech Connect

    Gorsky, A.; Krikun, A.

    2014-07-23

    We briefly review the generalized Skyrmion model for the baryon recently suggested by us. It takes into account the tower of vector and axial mesons as well as the chiral symmetry breaking. The generalized Skyrmion model provides the qualitative explanation of the Ioffe’s formula for the baryon mass.

  7. Concomitant Ordering and Symmetry Lowering

    ERIC Educational Resources Information Center

    Boo, William O. J.; Mattern, Daniell L.

    2008-01-01

    Examples of concomitant ordering include magnetic ordering, Jahn-Teller cooperative ordering, electronic ordering, ionic ordering, and ordering of partially-filled sites. Concomitant ordering sets in when a crystal is cooled and always lowers the degree of symmetry of the crystal. Concomitant ordering concepts can also be productively applied to…

  8. Hidden local symmetry and beyond

    NASA Astrophysics Data System (ADS)

    Yamawaki, Koichi

    Gerry Brown was a godfather of our hidden local symmetry (HLS) for the vector meson from the birth of the theory throughout his life. The HLS is originated from very nature of the nonlinear realization of the symmetry G based on the manifold G/H, and thus is universal to any physics based on the nonlinear realization. Here, I focus on the Higgs Lagrangian of the Standard Model (SM), which is shown to be equivalent to the nonlinear sigma model based on G/H = SU(2)L ×SU(2)R/SU(2)V with additional symmetry, the nonlinearly-realized scale symmetry. Then, the SM does have a dynamical gauge boson of the SU(2)V HLS, “SM ρ meson”, in addition to the Higgs as a pseudo-dilaton as well as the NG bosons to be absorbed in to the W and Z. Based on the recent work done with Matsuzaki and Ohki, I discuss a novel possibility that the SM ρ meson acquires kinetic term by the SM dynamics itself, which then stabilizes the skyrmion dormant in the SM as a viable candidate for the dark matter, what we call “dark SM skyrmion (DSMS)”.

  9. Resonantly amplified vibronic symmetry breaking

    NASA Astrophysics Data System (ADS)

    Rathbone, G. J.; Poliakoff, E. D.; Bozek, John D.; Lucchese, R. R.

    2001-05-01

    The energy dependence of the vibrational branching ratio for exciting one quantum of bending is determined for CO2 4σg-1 photoionization. This nominally forbidden transition becomes allowed for a photoionization transition as a result of instantaneous symmetry breaking due to zero point motion, and is strongly enhanced by a continuum shape resonance.

  10. Quantitative Analysis of Face Symmetry.

    PubMed

    Tamir, Abraham

    2015-06-01

    The major objective of this article was to report quantitatively the degree of human face symmetry for reported images taken from the Internet. From the original image of a certain person that appears in the center of each triplet, 2 symmetric combinations were constructed that are based on the left part of the image and its mirror image (left-left) and on the right part of the image and its mirror image (right-right). By applying a computer software that enables to determine length, surface area, and perimeter of any geometric shape, the following measurements were obtained for each triplet: face perimeter and area; distance between the pupils; mouth length; its perimeter and area; nose length and face length, usually below the ears; as well as the area and perimeter of the pupils. Then, for each of the above measurements, the value C, which characterizes the degree of symmetry of the real image with respect to the combinations right-right and left-left, was calculated. C appears on the right-hand side below each image. A high value of C indicates a low symmetry, and as the value is decreasing, the symmetry is increasing. The magnitude on the left relates to the pupils and compares the difference between the area and perimeter of the 2 pupils. The major conclusion arrived at here is that the human face is asymmetric to some degree; the degree of asymmetry is reported quantitatively under each portrait.

  11. Symmetry-protected topological entanglement

    NASA Astrophysics Data System (ADS)

    Marvian, Iman

    2017-01-01

    We propose an order parameter for the symmetry-protected topological (SPT) phases which are protected by Abelian on-site symmetries. This order parameter, called the SPT entanglement, is defined as the entanglement between A and B , two distant regions of the system, given that the total charge (associated with the symmetry) in a third region C is measured and known, where C is a connected region surrounded by A , B , and the boundaries of the system. In the case of one-dimensional systems we prove that in the limit where A and B are large and far from each other compared to the correlation length, the SPT entanglement remains constant throughout a SPT phase, and furthermore, it is zero for the trivial phase while it is nonzero for all the nontrivial phases. Moreover, we show that the SPT entanglement is invariant under the low-depth quantum circuits which respect the symmetry, and hence it remains constant throughout a SPT phase in the higher dimensions as well. Also, we show that there is an intriguing connection between SPT entanglement and the Fourier transform of the string order parameters, which are the traditional tool for detecting SPT phases. This leads to an algorithm for extracting the relevant information about the SPT phase of the system from the string order parameters. Finally, we discuss implications of our results in the context of measurement-based quantum computation.

  12. Strong coupling electroweak symmetry breaking

    SciTech Connect

    Barklow, T.L.; Burdman, G.; Chivukula, R.S.

    1997-04-01

    The authors review models of electroweak symmetry breaking due to new strong interactions at the TeV energy scale and discuss the prospects for their experimental tests. They emphasize the direct observation of the new interactions through high-energy scattering of vector bosons. They also discuss indirect probes of the new interactions and exotic particles predicted by specific theoretical models.

  13. Circular codes, symmetries and transformations.

    PubMed

    Fimmel, Elena; Giannerini, Simone; Gonzalez, Diego Luis; Strüngmann, Lutz

    2015-06-01

    Circular codes, putative remnants of primeval comma-free codes, have gained considerable attention in the last years. In fact they represent a second kind of genetic code potentially involved in detecting and maintaining the normal reading frame in protein coding sequences. The discovering of an universal code across species suggested many theoretical and experimental questions. However, there is a key aspect that relates circular codes to symmetries and transformations that remains to a large extent unexplored. In this article we aim at addressing the issue by studying the symmetries and transformations that connect different circular codes. The main result is that the class of 216 C3 maximal self-complementary codes can be partitioned into 27 equivalence classes defined by a particular set of transformations. We show that such transformations can be put in a group theoretic framework with an intuitive geometric interpretation. More general mathematical results about symmetry transformations which are valid for any kind of circular codes are also presented. Our results pave the way to the study of the biological consequences of the mathematical structure behind circular codes and contribute to shed light on the evolutionary steps that led to the observed symmetries of present codes.

  14. Platonic Symmetry and Geometric Thinking

    ERIC Educational Resources Information Center

    Zsombor-Murray, Paul

    2007-01-01

    Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…

  15. Hidden local symmetry and beyond

    NASA Astrophysics Data System (ADS)

    Yamawaki, Koichi

    Gerry Brown was a godfather of our hidden local symmetry (HLS) for the vector meson from the birth of the theory throughout his life. The HLS is originated from very nature of the nonlinear realization of the symmetry G based on the manifold G/H, and thus is universal to any physics based on the nonlinear realization. Here, I focus on the Higgs Lagrangian of the Standard Model (SM), which is shown to be equivalent to the nonlinear sigma model based on G/H = SU(2)L × SU(2)R/SU(2)V with additional symmetry, the nonlinearly-realized scale symmetry. Then, the SM does have a dynamical gauge boson of the SU(2)V HLS, "SM ρ meson", in addition to the Higgs as a pseudo-dilaton as well as the NG bosons to be absorbed in to the W and Z. Based on the recent work done with Matsuzaki and Ohki, I discuss a novel possibility that the SM ρ meson acquires kinetic term by the SM dynamics itself, which then stabilizes the skyrmion dormant in the SM as a viable candidate for the dark matter, what we call "dark SM skyrmion (DSMS)".

  16. Turning Students into Symmetry Detectives

    ERIC Educational Resources Information Center

    Wilders, Richard; VanOyen, Lawrence

    2011-01-01

    Exploring mathematical symmetry is one way of increasing students' understanding of art. By asking students to search designs and become pattern detectives, teachers can potentially increase their appreciation of art while reinforcing their perception of the use of math in their day-to-day lives. This article shows teachers how they can interest…

  17. Concomitant Ordering and Symmetry Lowering

    ERIC Educational Resources Information Center

    Boo, William O. J.; Mattern, Daniell L.

    2008-01-01

    Examples of concomitant ordering include magnetic ordering, Jahn-Teller cooperative ordering, electronic ordering, ionic ordering, and ordering of partially-filled sites. Concomitant ordering sets in when a crystal is cooled and always lowers the degree of symmetry of the crystal. Concomitant ordering concepts can also be productively applied to…

  18. Monster symmetry and extremal CFTs

    NASA Astrophysics Data System (ADS)

    Gaiotto, Davide

    2012-11-01

    We test some recent conjectures about extremal selfdual CFTs, which are the candidate holographic duals of pure gravity in AdS 3. We prove that no c = 48 extremal selfdual CFT or SCFT may possess Monster symmetry. Furthermore, we disprove a recent argument against the existence of extremal selfdual CFTs of large central charge.

  19. From symmetries to number theory

    SciTech Connect

    Tempesta, P.

    2009-05-15

    It is shown that the finite-operator calculus provides a simple formalism useful for constructing symmetry-preserving discretizations of quantum-mechanical integrable models. A related algebraic approach can also be used to define a class of Appell polynomials and of L series.

  20. Symmetry Breaking During Drosophila Oogenesis

    PubMed Central

    Roth, Siegfried; Lynch, Jeremy A.

    2009-01-01

    The orthogonal axes of Drosophila are established during oogenesis through a hierarchical series of symmetry-breaking steps, most of which can be traced back to asymmetries inherent in the architecture of the ovary. Oogenesis begins with the formation of a germline cyst of 16 cells connected by ring canals. Two of these 16 cells have four ring canals, whereas the others have fewer. The first symmetry-breaking step is the selection of one of these two cells to become the oocyte. Subsequently, the germline cyst becomes surrounded by somatic follicle cells to generate individual egg chambers. The second symmetry-breaking step is the posterior positioning of the oocyte within the egg chamber, a process mediated by adhesive interactions with a special group of somatic cells. Posterior oocyte positioning is accompanied by a par gene-dependent repolarization of the microtubule network, which establishes the posterior cortex of the oocyte. The next two steps of symmetry breaking occur during midoogenesis after the volume of the oocyte has increased about 10-fold. First, a signal from the oocyte specifies posterior follicle cells, polarizing a symmetric prepattern present within the follicular epithelium. Second, the posterior follicle cells send a signal back to the oocyte, which leads to a second repolarization of the oocyte microtubule network and the asymmetric migration of the oocyte nucleus. This process again requires the par genes. The repolarization of the microtubule network results in the transport of bicoid and oskar mRNAs, the anterior and posterior determinants, respectively, of the embryonic axis, to opposite poles of the oocyte. The asymmetric positioning of the oocyte nucleus defines a cortical region of the oocyte where gurken mRNA is localized, thus breaking the dorsal–ventral symmetry of the egg and embryo. PMID:20066085

  1. Theory of nodal s±-wave pairing symmetry in the Pu-based 115 superconductor family

    DOE PAGES

    Das, Tanmoy; Zhu, Jian -Xin; Graf, Matthias J.

    2015-02-27

    The spin-fluctuation mechanism of superconductivity usually results in the presence of gapless or nodal quasiparticle states in the excitation spectrum. Nodal quasiparticle states are well established in copper-oxide, and heavy-fermion superconductors, but not in iron-based superconductors. Here, we study the pairing symmetry and mechanism of a new class of plutonium-based high-Tc superconductors and predict the presence of a nodal s⁺⁻ wave pairing symmetry in this family. Starting from a density-functional theory (DFT) based electronic structure calculation we predict several three-dimensional (3D) Fermi surfaces in this 115 superconductor family. We identify the dominant Fermi surface “hot-spots” in the inter-band scattering channel,more » which are aligned along the wavevector Q = (π, π, π), where degeneracy could induce sign-reversal of the pairing symmetry. Our calculation demonstrates that the s⁺⁻ wave pairing strength is stronger than the previously thought d-wave pairing; and more importantly, this pairing state allows for the existence of nodal quasiparticles. Finally, we predict the shape of the momentum- and energy-dependent magnetic resonance spectrum for the identification of this pairing symmetry.« less

  2. Field theory representation of mixed gauge-gravity symmetry-protected topological invariants, group cohomology and beyond

    NASA Astrophysics Data System (ADS)

    Wang, Juven; Gu, Zheng-Cheng; Wen, Xiao-Gang

    The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs, recently observed by Kapustin. We find new examples of mixed gauge-gravity actions for U(1) SPTs in 3+1D and 4+1D via the Stiefel-Whitney class and the gravitational Chern-Simons term. [Work based on Phys. Rev. Lett. 114, 031601 (2015) arXiv:1405.7689

  3. Theory of nodal s±-wave pairing symmetry in the Pu-based 115 superconductor family

    PubMed Central

    Das, Tanmoy; Zhu, Jian-Xin; Graf, Matthias J.

    2015-01-01

    The spin-fluctuation mechanism of superconductivity usually results in the presence of gapless or nodal quasiparticle states in the excitation spectrum. Nodal quasiparticle states are well established in copper-oxide, and heavy-fermion superconductors, but not in iron-based superconductors. Here, we study the pairing symmetry and mechanism of a new class of plutonium-based high-Tc superconductors and predict the presence of a nodal s+− wave pairing symmetry in this family. Starting from a density-functional theory (DFT) based electronic structure calculation we predict several three-dimensional (3D) Fermi surfaces in this 115 superconductor family. We identify the dominant Fermi surface “hot-spots” in the inter-band scattering channel, which are aligned along the wavevector Q = (π, π, π), where degeneracy could induce sign-reversal of the pairing symmetry. Our calculation demonstrates that the s+− wave pairing strength is stronger than the previously thought d-wave pairing; and more importantly, this pairing state allows for the existence of nodal quasiparticles. Finally, we predict the shape of the momentum- and energy-dependent magnetic resonance spectrum for the identification of this pairing symmetry. PMID:25721375

  4. Field-theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology, and beyond.

    PubMed

    Wang, Juven C; Gu, Zheng-Cheng; Wen, Xiao-Gang

    2015-01-23

    The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4+1)D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context.

  5. Theory of nodal s±-wave pairing symmetry in the Pu-based 115 superconductor family

    SciTech Connect

    Das, Tanmoy; Zhu, Jian -Xin; Graf, Matthias J.

    2015-02-27

    The spin-fluctuation mechanism of superconductivity usually results in the presence of gapless or nodal quasiparticle states in the excitation spectrum. Nodal quasiparticle states are well established in copper-oxide, and heavy-fermion superconductors, but not in iron-based superconductors. Here, we study the pairing symmetry and mechanism of a new class of plutonium-based high-Tc superconductors and predict the presence of a nodal s⁺⁻ wave pairing symmetry in this family. Starting from a density-functional theory (DFT) based electronic structure calculation we predict several three-dimensional (3D) Fermi surfaces in this 115 superconductor family. We identify the dominant Fermi surface “hot-spots” in the inter-band scattering channel, which are aligned along the wavevector Q = (π, π, π), where degeneracy could induce sign-reversal of the pairing symmetry. Our calculation demonstrates that the s⁺⁻ wave pairing strength is stronger than the previously thought d-wave pairing; and more importantly, this pairing state allows for the existence of nodal quasiparticles. Finally, we predict the shape of the momentum- and energy-dependent magnetic resonance spectrum for the identification of this pairing symmetry.

  6. New insight into the dispersion characteristics of electrostatic waves in ultradense plasmas: electron degeneracy and relativistic effects

    NASA Astrophysics Data System (ADS)

    Kourakis, I.; McKerr, M.; Elkamash, I. S.; Haas, F.

    2017-10-01

    The dispersion properties of electrostatic waves propagating in ultrahigh density plasma are investigated, from first principles, in a one-dimensional geometry. A self-consistent multispecies plasma fluid model is taken as starting point, incorporating electron degeneracy and relativistic effects. The inertia of all plasma components is retained, for rigor. Exact expressions are obtained for the oscillation frequency, and the phase and group velocity of electrostatic waves is computed. Two branches are obtained, viz. an acoustic low-frequency dispersion branch and an upper (optic-like) branch: these may be interpreted as ion-acoustic and electron plasma (Langmuir) waves, respectively, as in classical plasmas, yet bearing an explicit correction in account of relativistic and electron degeneracy effects. The electron plasma frequency is shown to reduce significantly at high values of the density, due to the relativistic effect. The result is compared with approximate models, wherein either electrons are considered inertialess (low-frequency ionic scale) or ions are considered to be stationary (Langmuir-wave limit).

  7. Charge 2 e /3 Superconductivity and Topological Degeneracies without Localized Zero Modes in Bilayer Fractional Quantum Hall States

    NASA Astrophysics Data System (ADS)

    Barkeshli, Maissam

    2016-08-01

    It has been recently shown that non-Abelian defects with localized parafermion zero modes can arise in conventional Abelian fractional quantum Hall (FQH) states. Here we propose an alternate route to creating, manipulating, and measuring topologically protected degeneracies in bilayer FQH states coupled to superconductors, without the creation of localized parafermion zero modes. We focus mainly on electron-hole bilayers, with a ±1 /3 Laughlin FQH state in each layer, with boundaries that are proximity coupled to a superconductor. We show that the superconductor induces charge 2 e /3 quasiparticle-pair condensation at each boundary of the FQH state, and that this leads to (i) topologically protected degeneracies that can be measured through charge sensing experiments and (ii) a fractional charge 2 e /3 ac Josephson effect. We demonstrate that an analog of non-Abelian braiding is possible, despite the absence of a localized zero mode. We discuss several practical advantages of this proposal over previous work, and also several generalizations.

  8. Accidental degeneracy in the spiropyran radical cation: charge transfer between two orthogonal rings inducing ultra-efficient reactivity.

    PubMed

    Mendive-Tapia, David; Kortekaas, Luuk; Steen, Jorn D; Perrier, Aurélie; Lasorne, Benjamin; Browne, Wesley R; Jacquemin, Denis

    2016-11-16

    Photochromism of the spiropyran radical cation to the corresponding merocyanine form is investigated by a combination of electrochemical oxidation, UV/vis absorption spectroscopy, spectroelectrochemistry and first-principles calculations (TD-DFT, CAS-SCF and CAS-PT2). First, we demonstrate that the ring-opening of mono-spiropyrans occurs upon one-electron oxidation and that it can be driven photochemically as well as thermally, with trapping of the merocyanine by protonation. Second, in order to explain this experimentally observed spectroelectrochemical behaviour we suggest a theoretical mechanism based on the reactivity of the two lowest electronic excited-states, which promotes effective electron transfer from the indoline (nitrogen-ring) to the pyran (oxygen-ring) moieties (and vice versa) through a conical intersection seam of degeneracy. Characterisation of the minimum energy conical intersection on this crossing revealed that it presents a rare diabatic trapping topology. The excited state molecule cannot escape from crossing the intersection seam due to the presence of only one degeneracy-lifting coordinate that efficiently channels into the formation of the merocyanine photoproduct, so giving rise to a "kitchen sink" funnel-like effect. Therefore, assuming rapid relaxation after vertical excitation to a higher electronic state, photoconversion cannot be avoided in the D1 electronic state, which rationalises the remarkably efficient visible light driven excited-state reactivity observed experimentally.

  9. Lifting the degeneracy between geometric and dynamic distortions using the sound horizon from the cosmic microwave background

    NASA Astrophysics Data System (ADS)

    Hawken, Adam J.; Abdalla, Fillipe B.; Hütsi, Gert; Lahav, Ofer

    2012-07-01

    The degeneracy between geometric (Alcock-Paczynski) and dynamic (redshift-space) distortions in the pattern of the galaxy distribution has been a long-standing problem in the study of the large-scale structure of the Universe. We examine the possibility of lifting this degeneracy and constraining cosmological parameters by using the baryon acoustic oscillation (BAO) scale as a feature of known physical size, the sound horizon rs≈ 150 Mpc. We calibrate this scale with the equivalent feature in the cosmic microwave background (CMB). First, we construct a toy model of a power spectrum which includes the BAO as well as geometric and dynamic distortions. By adding a prior on to the sound horizon of ˜1 per cent we show, using a Fisher matrix analysis, that error ellipses for line-of-sight and tangential distortion parameters shrink by a factor of 2 for a 20 (h-1 Gpc)3'DESpec/BigBOSS'-like galaxy survey including shot noise. This improvement is even more marked in smaller surveys. We also carry out a Monte Carlo nested sampling analysis on our parameter space. We find that Monte Carlo and Fisher methods can agree reasonably well for surveys with large volume but differ greatly for small volume surveys.

  10. PT Symmetry, Conformal Symmetry, and the Metrication of Electromagnetism

    NASA Astrophysics Data System (ADS)

    Mannheim, Philip D.

    2017-09-01

    We present some interesting connections between PT symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be PT symmetric, with it being iA_{μ } rather than A_{μ } itself that then appears in the connection. With this modification the standard minimal coupling of electromagnetism to fermions is obtained. Through the use of torsion we obtain a metricated theory of electromagnetism that treats its electric and magnetic sectors symmetrically, with a conformal invariant theory of gravity being found to emerge. An extension to the non-Abelian case is provided.

  11. Universal Formulation For Symmetries In Computed Flows

    NASA Technical Reports Server (NTRS)

    Pao, S. Paul; Abdol-Hamid, Khaled S.

    1995-01-01

    Universal formulation for high-order symmetries in boundary conditions on flows devised. Eliminates need for special procedures to incorporate symmetries and corresponding boundary conditions into computer codes solving Navier-Stokes and Euler equations of flow.

  12. An Elementary Course in Mathematical Symmetry.

    ERIC Educational Resources Information Center

    Rose, Bruce I.; Stafford, Robert D.

    1981-01-01

    A college course designed to teach students about the mathematics of symmetry using pieces of wallpaper and cloth designs is presented. Mathematical structures and the symmetry of graphic designs provide the starting point for instruction. (MP)

  13. An Elementary Course in Mathematical Symmetry.

    ERIC Educational Resources Information Center

    Rose, Bruce I.; Stafford, Robert D.

    1981-01-01

    A college course designed to teach students about the mathematics of symmetry using pieces of wallpaper and cloth designs is presented. Mathematical structures and the symmetry of graphic designs provide the starting point for instruction. (MP)

  14. Noether symmetries of Bianchi type II spacetimes

    NASA Astrophysics Data System (ADS)

    Hickman, Mark; Yazdan, Shair-a.

    2017-05-01

    This paper is devoted to investigate Noether symmetries of Bianchi type II spacetimes. We use the reduced involutive form of the determining equations to classify their possible algebras. We show that Noether symmetries contain both Killing vectors and homothetic motions.

  15. Symmetry perception in humans and macaques.

    PubMed

    Beck, Diane M; Pinsk, Mark A; Kastner, Sabine

    2005-09-01

    The human ability to detect symmetry has been a topic of interest to psychologists and philosophers since the 19th century, yet surprisingly little is known about the neural basis of symmetry perception. In a recent fMRI study, Sasaki and colleagues begin to remedy this situation. By identifying the neural structures that respond to symmetry in both humans and macaques, the authors lay the groundwork for understanding the neural mechanisms underlying symmetry perception.

  16. Flavored Peccei-Quinn symmetry

    NASA Astrophysics Data System (ADS)

    Ahn, Y. H.

    2015-03-01

    In an attempt to uncover any underlying physics in the standard model (SM), we suggest a μ - τ power law in the lepton sector, such that relatively large 13 mixing angle with bilarge ones can be derived. On the basis of this, we propose a neat and economical model for both the fermion mass hierarchy problem of the SM and a solution to the strong charge parity (C P ) problem, in a way that no domain wall problem occurs, based on A4×U (1 )X symmetry in a supersymmetric framework. Here we refer to the global U (1 )X symmetry that can explain the above problems as "flavored Peccei-Quinn symmetry." In the model, a direct coupling of the SM gauge singlet flavon fields responsible for spontaneous symmetry breaking to ordinary quarks and leptons, both of which are charged under U (1 )X, comes to pass through Yukawa interactions, and all vacuum expectation values breaking the symmetries are connected to each other. So the scale of Peccei-Quinn symmetry breaking is shown to be roughly located around the 1 012 GeV section through its connection to the fermion masses. The model predictions are shown to lie on the testable regions in the very near future through on-going experiments for neutrino oscillation, neutrinoless double beta decay, and the axion. We examine the model predictions, arisen from the μ - τ power law, on leptonic C P violation, neutrinoless double beta decay, and atmospheric mixing angle, and show that the fermion mass and mixing hierarchies are in good agreement with the present data. Interestingly, we show the model predictions on the axion mass ma≃2.53 ×1 0-5 eV and the axion coupling to photon ga γ γ≃1.33 ×1 0-15 GeV-1 . And subsequently the square of the ratio between them is shown to be one or two orders of magnitude lower than that of the conventional axion model.

  17. Superalgebra and fermion-boson symmetry

    PubMed Central

    Miyazawa, Hironari

    2010-01-01

    Fermions and bosons are quite different kinds of particles, but it is possible to unify them in a supermultiplet, by introducing a new mathematical scheme called superalgebra. In this article we discuss the development of the concept of symmetry, starting from the rotational symmetry and finally arriving at this fermion-boson (FB) symmetry. PMID:20228617

  18. Generalized partial dynamical symmetry in nuclei.

    PubMed

    Leviatan, A; Isacker, P Van

    2002-11-25

    We introduce the notion of a generalized partial dynamical-symmetry for which part of the eigenstates have part of the dynamical symmetry. This general concept is illustrated with the example of Hamiltonians with a partial dynamical O(6) symmetry in the framework of the interacting boson model. The resulting spectrum and electromagnetic transitions are compared with empirical data in 162Dy.

  19. Symmetry Breaking for Black-Scholes Equations

    NASA Astrophysics Data System (ADS)

    Yang, Xuan-Liu; Zhang, Shun-Li; Qu, Chang-Zheng

    2007-06-01

    Black-Scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for Black-Scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied. As a result, symmetry reductions and corresponding solutions for the resulting equations are obtained.

  20. Noether symmetries and duality transformations in cosmology

    NASA Astrophysics Data System (ADS)

    Paliathanasis, Andronikos; Capozziello, Salvatore

    2016-09-01

    We discuss the relation between Noether (point) symmetries and discrete symmetries for a class of minisuperspace cosmological models. We show that when a Noether symmetry exists for the gravitational Lagrangian, then there exists a coordinate system in which a reversal symmetry exists. Moreover, as far as concerns, the scale-factor duality symmetry of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations, and the reversal symmetry in the normal coordinates of the symmetry vector becomes scale-factor duality symmetry in the original coordinates. In particular, the same point symmetry as also the same reversal symmetry exists for the Brans-Dicke scalar field with linear potential while now the discrete symmetry in the original coordinates of the system depends on the Brans-Dicke parameter and it is a scale-factor duality when ωBD = 1. Furthermore, in the context of the O’Hanlon theory for f(R)-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.

  1. A valence bond analysis of electronic degeneracies in Jahn-Teller systems: low-lying states of the cyclopentadienyl radical and cation.

    PubMed

    Zilberg, Shmuel; Haas, Yehuda

    2002-09-11

    The lowest doublet electronic state of the cyclopentadienyl radical (CPDR) and the lowest singlet state of the cyclopentadienyl cation (CPDC) are distorted from the highly symmetric D(5h) structure due to the Jahn-Teller effect. A valence bond analysis based on the phase-change rule of Longuet-Higgins reveals that in both cases the distortion is due to the first-order Jahn-Teller effect. It is shown that, while for the radical an isolated Jahn-Teller degeneracy is expected, in the case of the cation the main Jahn-Teller degeneracy is accompanied by five satellite degeneracies. The method offers a chemically oriented way for identifying the distortive coordinates.

  2. Space-based Microlens Parallax Observation as a Way to Resolve the Severe Degeneracy between Microlens-parallax and Lens-orbital Effects

    NASA Astrophysics Data System (ADS)

    Han, C.; Udalski, A.; Lee, C.-U.; Gould, A.; Bozza, V.; Szymański, M. K.; Soszyński, I.; Skowron, J.; Mróz, P.; Poleski, R.; Pietrukowicz, P.; Kozłowski, S.; Ulaczyk, K.; Wyrzykowski, Ł.; Pawlak, M.; OGLE Collaboration; Albrow, M. D.; Chung, S.-J.; Kim, S.-L.; Cha, S.-M.; Jung, Y. K.; Kim, D.-J.; Lee, Y.; Park, B.-G.; Ryu, Y.-H.; Shin, I.-G.; Yee, J. C.; KMTNet Collaboration

    2016-08-01

    In this paper, we demonstrate the severity of the degeneracy between the microlens-parallax and lens-orbital effects by presenting the analysis of the gravitational binary-lens event OGLE-2015-BLG-0768. Despite the obvious deviation from the model based on the linear observer motion and the static binary, it is found that the residual can be almost equally well explained by either the parallactic motion of the Earth or the rotation of the binary-lens axis, resulting in the severe degeneracy between the two effects. We show that the degeneracy can be readily resolved with the additional data provided by space-based microlens parallax observations. By enabling us to distinguish between the two higher-order effects, space-based microlens parallax observations will not only make it possible to accurately determine the physical lens parameters but also to further constrain the orbital parameters of binary lenses.

  3. Structure and Degeneracy of Vortex Lattice Domains in Pure Superconducting Niobium: A Small-Angle Neutron Scattering Study

    SciTech Connect

    Laver, M.; Bowell, C.; Forgan, E. M.; Abrahamsen, A. B.; Fort, D.; Dewhurst, C. D.; Muhlbauer, S.; Christen, David K; Kohlbrecher, J.; Cubitt, R.; Ramos, S.

    2009-01-01

    High-purity niobium exhibits a surprisingly rich assortment of vortex lattice (VL) structures for fields applied parallel to a fourfold symmetry axis, with all observed VL phases made up of degenerate domains that spontaneously break some crystal symmetry. Yet a single regular hexagonal VL domain is observed at all temperatures and fields parallel to a threefold symmetry axis. We report a detailed investigation of the transition between these lush and barren VL landscapes, discovering new VL structures and phase transitions at high fields. We show that the number and relative population of VL domains is intrinsically tied to the underlying crystal symmetry. We discuss how subtle anisotropies of the crystal may generate the remarkable VLs observed.

  4. Soft terms from broken symmetries

    NASA Astrophysics Data System (ADS)

    Buican, Matthew; Komargodski, Zohar

    2010-02-01

    In theories of phyiscs beyond the Standard Model (SM), visible sector fields often carry quantum numbers under additional gauge symmetries. One could then imagine a scenario in which these extra gauge symmetries play a role in transmitting supersymmetry breaking from a hidden sector to the Supersymmetric Standard Model (SSM). In this paper we present a general formalism for studying the resulting hidden sectors and calculating the corresponding gauge mediated soft parameters. We find that a large class of generic models features a leading universal contribution to the soft scalar masses that only depends on the scale of Higgsing, even if the model is strongly coupled. As a by-product of our analysis, we elucidate some IR aspects of the correlation functions in General Gauge Mediation. We also discuss possible phenomenological applications.

  5. Symmetry of cardiac function assessment

    PubMed Central

    Bai, Xu-Fang; Ma, Amy X

    2016-01-01

    Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function. PMID:27582768

  6. Broken symmetries in multilayered perceptrons

    NASA Astrophysics Data System (ADS)

    Barkai, E.; Hansel, D.; Sompolinsky, H.

    1992-03-01

    The statistical mechanics of two-layered perceptrons with N input units, K hidden units, and a single output unit that makes a decision based on a majority rule (Committee Machine) are studied. Two architectures are considered. In the nonoverlapping case the hidden units do not share common inputs. In the fully connected case each hidden unit is connected to the entire input layer. In both cases the network realizes a random dichotomy of P inputs. The statistical properties of the space of solutions as a function of P is studied, using the replica method, and by numerical simulations, in the regime where N>>K. In the nonoverlapping architecture with continuously varying weights the capacity, defined as the maximal number of P per weight, (αc) is calculated under a replica-symmetric (RS) ansatz. At large K, αc diverges as K1/2 in contradiction with the rigorous upper bound, αcsymmetry-breaking effect. The instability of the RS solution is shown to occur at a value of α which remains finite in the large-K limit. A one-step replica-symmetry-breaking (RSB) ansatz is studied for K=3 and in the limit K goes to infinity. The results indicate that αc(K) diverges with K, probably logarithmically. The occurrence of RSB far below the capacity limit is confirmed by comparison of the theoretical results with numerical simulations for K=3. This symmetry breaking implies that unlike the single-layer perceptron case, the space of solutions of the two-layer perceptron breaks, beyond a critical value of α, into many disjoint subregions. The entropies of the connected subregions are almost degenerate, their relative difference being of order 1/N. In the case of a nonoverlapping Committee Machine with binary, i.e., +/-1 weights, αc<=1 is an upper bound for all K. The RS theory predicts αc=0.92 for K=3 and αc=0.95 for the large-K limit

  7. Facial symmetry in robust anthropometrics.

    PubMed

    Kalina, Jan

    2012-05-01

    Image analysis methods commonly used in forensic anthropology do not have desirable robustness properties, which can be ensured by robust statistical methods. In this paper, the face localization in images is carried out by detecting symmetric areas in the images. Symmetry is measured between two neighboring rectangular areas in the images using a new robust correlation coefficient, which down-weights regions in the face violating the symmetry. Raw images of faces without usual preliminary transformations are considered. The robust correlation coefficient based on the least weighted squares regression yields very promising results also in the localization of such faces, which are not entirely symmetric. Standard methods of statistical machine learning are applied for comparison. The robust correlation analysis can be applicable to other problems of forensic anthropology.

  8. CP symmetry in optical systems

    NASA Astrophysics Data System (ADS)

    Dana, Brenda; Bahabad, Alon; Malomed, Boris A.

    2015-04-01

    We introduce a model of a dual-core optical waveguide with opposite signs of the group-velocity dispersion in the two cores, and a phase-velocity mismatch between them. The coupler is embedded into an active host medium, which provides for the linear coupling of a gain-loss type between the two cores. The same system can be derived, without phenomenological assumptions, by considering the three-wave propagation in a medium with the quadratic nonlinearity, provided that the depletion of the second-harmonic pump is negligible. This linear system offers an optical realization of the charge-parity symmetry, while the addition of the intracore cubic nonlinearity breaks the symmetry. By means of direct simulations and analytical approximations, it is demonstrated that the linear system generates expanding Gaussian states, while the nonlinear one gives rise to broad oscillating solitons, as well as a general family of stable stationary gap solitons.

  9. Geometric symmetries in light nuclei

    NASA Astrophysics Data System (ADS)

    Bijker, R.

    2017-06-01

    The algebraic cluster model is is applied to study cluster states in the nuclei12C and16O. The observed level sequences can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the α-particles, i.e. an equilateral triangle for12C, and a regular tetrahedron for16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of α-particles.

  10. Explaining quantum spontaneous symmetry breaking

    NASA Astrophysics Data System (ADS)

    Liu, Chuang; Emch, Gérard G.

    Two accounts of quantum symmetry breaking (SSB) in the algebraic approach are compared: the representational and the decompositional account. The latter account is argued to be superior for understanding quantum SSB. Two exactly solvable models are given as applications of our account: the Weiss-Heisenberg model for ferromagnetism and the BCS model for superconductivity. Finally, the decompositional account is shown to be more conducive to the causal explanation of quantum SSB.

  11. Fermion mass without symmetry breaking

    NASA Astrophysics Data System (ADS)

    Catterall, Simon

    2016-01-01

    We examine a model of reduced staggered fermions in three dimensions interacting through an SO (4) invariant four fermion interaction. The model is similar to that considered in a recent paper by Ayyer and Chandrasekharan [1]. We present theoretical arguments and numerical evidence which support the idea that the system develops a mass gap for sufficiently strong four fermi coupling without producing a symmetry breaking fermion bilinear condensate. Massless and massive phases appear to be separated by a continuous phase transition.

  12. Symmetries in Lagrangian Field Theory

    NASA Astrophysics Data System (ADS)

    Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia

    2015-06-01

    By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.

  13. Fermion mass without symmetry breaking

    DOE PAGES

    Catterall, Simon

    2016-01-20

    We examine a model of reduced staggered fermions in three dimensions interacting through an SO (4) invariant four fermion interaction. The model is similar to that considered in a recent paper by Ayyer and Chandrasekharan. We present theoretical arguments and numerical evidence which support the idea that the system develops a mass gap for sufficiently strong four fermi coupling without producing a symmetry breaking fermion bilinear condensate. As a result, massless and massive phases appear to be separated by a continuous phase transition.

  14. Symmetry analysis of talus bone

    PubMed Central

    Islam, K.; Dobbe, A.; Komeili, A.; Duke, K.; El-Rich, M.; Dhillon, S.; Adeeb, S.; Jomha, N. M.

    2014-01-01

    Objective The main object of this study was to use a geometric morphometric approach to quantify the left-right symmetry of talus bones. Methods Analysis was carried out using CT scan images of 11 pairs of intact tali. Two important geometric parameters, volume and surface area, were quantified for left and right talus bones. The geometric shape variations between the right and left talus bones were also measured using deviation analysis. Furthermore, location of asymmetry in the geometric shapes were identified. Results Numerical results showed that talus bones are bilaterally symmetrical in nature, and the difference between the surface area of the left and right talus bones was less than 7.5%. Similarly, the difference in the volume of both bones was less than 7.5%. Results of the three-dimensional (3D) deviation analyses demonstrated the mean deviation between left and right talus bones were in the range of -0.74 mm to 0.62 mm. It was observed that in eight of 11 subjects, the deviation in symmetry occurred in regions that are clinically less important during talus surgery. Conclusions We conclude that left and right talus bones of intact human ankle joints show a strong degree of symmetry. The results of this study may have significance with respect to talus surgery, and in investigating traumatic talus injury where the geometric shape of the contralateral talus can be used as control. Cite this article: Bone Joint Res 2014;3:139–45. PMID:24802391

  15. Dark matter and global symmetries

    SciTech Connect

    Mambrini, Yann; Profumo, Stefano; Queiroz, Farinaldo S.

    2016-08-03

    General considerations in general relativity and quantum mechanics are known to potentially rule out continuous global symmetries in the context of any consistent theory of quantum gravity. Assuming the validity of such considerations, we derive stringent bounds from gamma-ray, X-ray, cosmic-ray, neutrino, and CMB data on models that invoke global symmetries to stabilize the dark matter particle. We compute up-to-date, robust model-independent limits on the dark matter lifetime for a variety of Planck-scale suppressed dimension-five effective operators. We then specialize our analysis and apply our bounds to specific models including the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. Here, assuming that (i) global symmetries are broken at the Planck scale, that (ii) the non-renormalizable operators mediating dark matter decay have O(1) couplings, that (iii) the dark matter is a singlet field, and that (iv) the dark matter density distribution is well described by a NFW profile, we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime

  16. Dark matter and global symmetries

    DOE PAGES

    Mambrini, Yann; Profumo, Stefano; Queiroz, Farinaldo S.

    2016-08-03

    General considerations in general relativity and quantum mechanics are known to potentially rule out continuous global symmetries in the context of any consistent theory of quantum gravity. Assuming the validity of such considerations, we derive stringent bounds from gamma-ray, X-ray, cosmic-ray, neutrino, and CMB data on models that invoke global symmetries to stabilize the dark matter particle. We compute up-to-date, robust model-independent limits on the dark matter lifetime for a variety of Planck-scale suppressed dimension-five effective operators. We then specialize our analysis and apply our bounds to specific models including the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Sawmore » models. Here, assuming that (i) global symmetries are broken at the Planck scale, that (ii) the non-renormalizable operators mediating dark matter decay have O(1) couplings, that (iii) the dark matter is a singlet field, and that (iv) the dark matter density distribution is well described by a NFW profile, we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime« less

  17. Dark matter and global symmetries

    NASA Astrophysics Data System (ADS)

    Mambrini, Yann; Profumo, Stefano; Queiroz, Farinaldo S.

    2016-09-01

    General considerations in general relativity and quantum mechanics are known to potentially rule out continuous global symmetries in the context of any consistent theory of quantum gravity. Assuming the validity of such considerations, we derive stringent bounds from gamma-ray, X-ray, cosmic-ray, neutrino, and CMB data on models that invoke global symmetries to stabilize the dark matter particle. We compute up-to-date, robust model-independent limits on the dark matter lifetime for a variety of Planck-scale suppressed dimension-five effective operators. We then specialize our analysis and apply our bounds to specific models including the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. Assuming that (i) global symmetries are broken at the Planck scale, that (ii) the non-renormalizable operators mediating dark matter decay have O (1) couplings, that (iii) the dark matter is a singlet field, and that (iv) the dark matter density distribution is well described by a NFW profile, we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime.

  18. Generalization of Friedberg-Lee symmetry

    NASA Astrophysics Data System (ADS)

    Huang, Chao-Shang; Li, Tianjun; Liao, Wei; Zhu, Shou-Hua

    2008-07-01

    We study the possible origin of Friedberg-Lee symmetry. First, we propose the generalized Friedberg-Lee symmetry in the potential by including the scalar fields in the field transformations, which can be broken down to the Friedberg-Lee symmetry spontaneously. We show that the generalized Friedberg-Lee symmetry allows a typical form of Yukawa couplings, and the realistic neutrino masses and mixings can be generated via the seesaw mechanism. If the right-handed neutrinos transform nontrivially under the generalized Friedberg-Lee symmetry, we can have the testable TeV scale seesaw mechanism. Second, we present two models with the SO(3)×U(1) global flavor symmetry in the lepton sector. After the flavor symmetry breaking, we can obtain the charged lepton masses, and explain the neutrino masses and mixings via the seesaw mechanism. Interestingly, the complete neutrino mass matrices are similar to those of the above models with generalized Friedberg-Lee symmetry. So the Friedberg-Lee symmetry is the residual symmetry in the neutrino mass matrix after the SO(3)×U(1) flavor symmetry breaking.

  19. Relativity symmetries and Lie algebra contractions

    NASA Astrophysics Data System (ADS)

    Cho, Dai-Ning; Kong, Otto C. W.

    2014-12-01

    We revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions under a new perspective on what constitutes a relativity symmetry. Contractions of an SO(m , n) symmetry as an isometry on an m + n dimensional geometric arena which generalizes the notion of spacetime are discussed systematically. One of the key results is five different contractions of a Galilean-type symmetry G(m , n) preserving a symmetry of the same type at dimension m + n - 1, e.g. a G(m , n - 1) , together with the coset space representations that correspond to the usual physical picture. Most of the results are explicitly illustrated through the example of symmetries obtained from the contraction of SO(2 , 4) , which is the particular case for our interest on the physics side as the proposed relativity symmetry for "quantum spacetime". The contractions from G(1 , 3) may be relevant to real physics.

  20. Symmetries in nuclei: New methods and applications

    NASA Astrophysics Data System (ADS)

    Caprio, Mark A.

    2011-04-01

    When a symmetry is a ``good'' symmetry of the nuclear system, as in the dynamical symmetries of the shell model and interacting boson model, this symmetry can directly give the spectroscopic properties of the nucleus, without the need for involved calculations. However, even if a symmetry is strongly broken, it nonetheless provides a calculational tool, classifying the basis states used in a full computational treatment of the many-body problem and greatly simplifying the underlying computational machinery. The symmetry then serves as the foundation for a physically meaningful truncation scheme for the calculation. This talk will provide an introduction to new applications of symmetry approaches to the nuclear problem, including the required mathematical developments. Supported by the US DOE under grant DE-FG02-95ER-40934 and by the Research Corporation for Science Advancement under a Cottrell Scholar Award.

  1. Symmetry constraints on many-body localization

    NASA Astrophysics Data System (ADS)

    Potter, Andrew C.; Vasseur, Romain

    2016-12-01

    We derive general constraints on the existence of many-body localized (MBL) phases in the presence of global symmetries, and show that MBL is not possible with symmetry groups that protect multiplets (e.g., all non-Abelian symmetry groups). Based on simple representation theoretic considerations, we derive general Mermin-Wagner-type principles governing the possible alternative fates of nonequilibrium dynamics in isolated, strongly disordered quantum systems. Our results rule out the existence of MBL symmetry-protected topological phases with non-Abelian symmetry groups, as well as time-reversal symmetry-protected electronic topological insulators, and in fact all fermion topological insulators and superconductors in the 10-fold way classification. Moreover, extending our arguments to systems with intrinsic topological order, we rule out MBL phases with non-Abelian anyons as well as certain classes of symmetry-enriched topological orders.

  2. Enhanced Facial Symmetry Assessment in Orthodontists

    PubMed Central

    Jackson, Tate H.; Clark, Kait; Mitroff, Stephen R.

    2013-01-01

    Assessing facial symmetry is an evolutionarily important process, which suggests that individual differences in this ability should exist. As existing data are inconclusive, the current study explored whether a group trained in facial symmetry assessment, orthodontists, possessed enhanced abilities. Symmetry assessment was measured using face and non-face stimuli among orthodontic residents and two control groups: university participants with no symmetry training and airport security luggage screeners, a group previously shown to possess expert visual search skills unrelated to facial symmetry. Orthodontic residents were more accurate at assessing symmetry in both upright and inverted faces compared to both control groups, but not for non-face stimuli. These differences are not likely due to motivational biases or a speed-accuracy tradeoff—orthodontic residents were slower than the university participants but not the security screeners. Understanding such individual differences in facial symmetry assessment may inform the perception of facial attractiveness. PMID:24319342

  3. Enhanced Facial Symmetry Assessment in Orthodontists.

    PubMed

    Jackson, Tate H; Clark, Kait; Mitroff, Stephen R

    2013-01-01

    Assessing facial symmetry is an evolutionarily important process, which suggests that individual differences in this ability should exist. As existing data are inconclusive, the current study explored whether a group trained in facial symmetry assessment, orthodontists, possessed enhanced abilities. Symmetry assessment was measured using face and non-face stimuli among orthodontic residents and two control groups: university participants with no symmetry training and airport security luggage screeners, a group previously shown to possess expert visual search skills unrelated to facial symmetry. Orthodontic residents were more accurate at assessing symmetry in both upright and inverted faces compared to both control groups, but not for non-face stimuli. These differences are not likely due to motivational biases or a speed-accuracy tradeoff-orthodontic residents were slower than the university participants but not the security screeners. Understanding such individual differences in facial symmetry assessment may inform the perception of facial attractiveness.

  4. Electronic Degeneracy and Intrinsic Magnetic Properties of EpitaxialNb: SrTiO3 Thin Films Controlled by Defects.

    PubMed

    Sarantopoulos, A; Ferreiro-Vila, E; Pardo, V; Magén, C; Aguirre, M H; Rivadulla, F

    2015-10-16

    We report thermoelectric power experiments in e-doped thin films of SrTiO3 (STO) which demonstrate that the electronic band degeneracy can be lifted through defect management during growth. We show that even small amounts of cationic vacancies, combined with epitaxial stress, produce a homogeneous tetragonal distortion of the films, resulting in a Kondo-like resistance upturn at low temperature, large anisotropic magnetoresistance, and nonlinear Hall effect. Ab initio calculations confirm a different occupation of each band depending on the degree of tetragonal distortion. The phenomenology reported in this Letter for tetragonally distorted e-doped STO thin films, is similar to that observed in LaAlO3/STO interfaces and magnetic STO quantum wells.

  5. The Valley-Degeneracy-Breaking Induced Arbitrary-Chern Number Insulator on Square Lattice and the Quantum Hall Effect

    NASA Astrophysics Data System (ADS)

    Wang, Yi-Xiang; Li, Fu-Xiang; Cao, Jie

    2015-02-01

    The arbitrary-Chern number (ACN) insulator describes the system with Chern number C that may be modulated beyond 0 and ±1. In this work, we take the two-orbit square lattice as an example to study the universal behavior of the Chern insulator under external magnetic field. The two-orbit square lattice may support the ACN phase when different types of hopping integrals are introduced to break the valley degeneracy. We will investigate the quantum Hall effect of the ACN phase, including the rule of the Hall steps and the Hall conductance around the charge neutral point. The results are further demonstrated by the ribbon dispersions and the corresponding edge states. We also try to detect the topological phase transition with the laser pulse by analyzing the excitation fraction and the corresponding valley polarization. Our studies may provide new routes to devise the novel valleytronics.

  6. Electronic Degeneracy and Intrinsic Magnetic Properties of EpitaxialNb : SrTiO3 Thin Films Controlled by Defects

    NASA Astrophysics Data System (ADS)

    Sarantopoulos, A.; Ferreiro-Vila, E.; Pardo, V.; Magén, C.; Aguirre, M. H.; Rivadulla, F.

    2015-10-01

    We report thermoelectric power experiments in e -doped thin films of SrTiO3 (STO) which demonstrate that the electronic band degeneracy can be lifted through defect management during growth. We show that even small amounts of cationic vacancies, combined with epitaxial stress, produce a homogeneous tetragonal distortion of the films, resulting in a Kondo-like resistance upturn at low temperature, large anisotropic magnetoresistance, and nonlinear Hall effect. Ab initio calculations confirm a different occupation of each band depending on the degree of tetragonal distortion. The phenomenology reported in this Letter for tetragonally distorted e -doped STO thin films, is similar to that observed in LaAlO3 /STO interfaces and magnetic STO quantum wells.

  7. A direct measurement of the mean occupation function of quasars: Breaking degeneracies between halo occupation distribution models

    SciTech Connect

    Chatterjee, Suchetana; Nguyen, My L.; Myers, Adam D.; Zheng, Zheng

    2013-12-20

    Recent work on quasar clustering suggests a degeneracy in the halo occupation distribution constrained from two-point correlation functions. To break this degeneracy, we make the first empirical measurement of the mean occupation function (MOF) of quasars at z ∼ 0.2 by matching quasar positions with groups and clusters identified in the MaxBCG sample. We fit two models to the MOF, a power law and a four-parameter model. The number distribution of quasars in host halos is close to Poisson, and the slopes of the MOF obtained from our best-fit models (for the power-law case) favor an MOF that monotonically increases with halo mass. The best-fit slopes are 0.53 ± 0.04 and 1.03 ± 1.12 for the power-law model and the four-parameter model, respectively. We measure the radial distribution of quasars within dark matter halos and find it to be adequately described by a power law with a slope –2.3 ± 0.4. We measure the conditional luminosity function (CLF) of quasars and show that there is no evidence that quasar luminosity depends on host halo mass, similar to the inferences drawn from clustering measurements. We also measure the conditional black hole mass function (CMF) of our quasars. Although the results are consistent with no dependence on halo mass, we observe a slight indication of downsizing of the black hole mass function. The lack of halo mass dependence in the CLF and CMF shows that quasars residing in galaxy clusters have characteristic luminosity and black hole mass scales.

  8. The mass-sheet degeneracy and time-delay cosmography: analysis of the strong lens RXJ1131-1231

    NASA Astrophysics Data System (ADS)

    Birrer, Simon; Amara, Adam; Refregier, Alexandre

    2016-08-01

    We present extended modelling of the strong lens system RXJ1131-1231 with archival data in two HST bands in combination with existing line-of-sight contribution and velocity dispersion estimates. Our focus is on source size and its influence on time-delay cosmography. We therefore examine the impact of mass-sheet degeneracy and especially the degeneracy pointed out by Schneider & Sluse (2013) [1] using the source reconstruction scale. We also extend on previous work by further exploring the effects of priors on the kinematics of the lens and the external convergence in the environment of the lensing system. Our results coming from RXJ1131-1231 are given in a simple analytic form so that they can be easily combined with constraints coming from other cosmological probes. We find that the choice of priors on lens model parameters and source size are subdominant for the statistical errors for H0 measurements of this systems. The choice of prior for the source is sub-dominant at present (2% uncertainty on H0) but may be relevant for future studies. More importantly, we find that the priors on the kinematic anisotropy of the lens galaxy have a significant impact on our cosmological inference. When incorporating all the above modeling uncertainties, we find H0 = 86.6+6.8-6.9 km s-1 Mpc-1, when using kinematic priors similar to other studies. When we use a different kinematic prior motivated by Barnabè et al. (2012) [2] but covering the same anisotropic range, we find H0 = 74.5+8.0-7.8 km s-1 Mpc-1. This means that the choice of kinematic modeling and priors have a significant impact on cosmographic inferences. The way forward is either to get better velocity dispersion measures which would down weight the impact of the priors or to construct physically motivated priors for the velocity dispersion model.

  9. Symmetry breaking and wake instabilities

    NASA Astrophysics Data System (ADS)

    Sengupta, Raja

    A numerical technique has been developed in the context of spatio-temporal stability analysis. The convective/absolute nature of instability determines the time-asymptotic response of a linearly unstable flow, either in the form an oscillator or in the form of a noise amplifier. This depends on the location of pinch point singularities of the dispersion relations obtained via linear stability analyses. A new and efficient approach to locate such singularities is presented. Local analyticity of the dispersion relations was exploited via the Cauchy-Riemann equations in a quasi-Newton's root- finding procedure employing numerical Jacobians. Initial guesses provided by temporal stability analyses have been shown to converge to the pinch points even in the presence of multiple saddle points for various Falkner- Skan wedge profiles. This effort was motivated by the phenomenon of spontaneous symmetry breaking in flow over a cone. At large enough incidence, a pair of vortices develop on the leeward side of the cone which eventually become asymmetric as the angle of attack is increased further. A conical, thin-layer Navier-Stokes solver was employed to investigate the effect of flowfield saddles in this process. The approximate factorization scheme incorporated in the solver was shown analytically to be symmetric to eliminate possible sources of asymmetry. Local grid resolution studies were performed to demonstrate the importance of correctly computing the leeside saddle point and the secondary separation and reattchment points. Topological studies of the flow field as it loses symmetry agreed well with previous qualitative experimental observations. However, the original goal of this study, to settle an ongoing controversy regarding the nature of the instability responsible for symmetry breaking, could not be realized due to computational inadequacy. It is conjectured that the process is governed by an absolute instability similar to that observed in a flow over a circular

  10. Duality symmetries and G+++ theories

    NASA Astrophysics Data System (ADS)

    Riccioni, Fabio; Steele, Duncan; West, Peter

    2008-02-01

    We show that the nonlinear realizations of all the very extended algebras G+++, except the B and C series which we do not consider, contain fields corresponding to all possible duality symmetries of the on-shell degrees of freedom of these theories. This result also holds for G+++2 and we argue that the nonlinear realization of this algebra accounts precisely for the form fields present in the corresponding supersymmetric theory. We also find a simple necessary condition for the roots to belong to a G+++ algebra.

  11. Geometric Baryogenesis from Shift Symmetry.

    PubMed

    De Simone, Andrea; Kobayashi, Takeshi; Liberati, Stefano

    2017-03-31

    We present a new scenario for generating the baryon asymmetry of the Universe that is induced by a Nambu-Goldstone (NG) boson. The shift symmetry naturally controls the operators in the theory while allowing the NG boson to couple to the spacetime geometry as well as to the baryons. The cosmological background thus sources a coherent motion of the NG boson, which leads to baryogenesis. Good candidates of the baryon-generating NG boson are the QCD axion and axionlike fields. In these cases, the axion induces baryogenesis in the early Universe and can also serve as dark matter in the late Universe.

  12. Killing symmetries as Hamiltonian constraints

    NASA Astrophysics Data System (ADS)

    Lusanna, Luca

    2016-02-01

    The existence of a Killing symmetry in a gauge theory is equivalent to the addition of extra Hamiltonian constraints in its phase space formulation, which imply restrictions both on the Dirac observables (the gauge invariant physical degrees of freedom) and on the gauge freedom. When there is a time-like Killing vector field only pure gauge electromagnetic fields survive in Maxwell theory in Minkowski space-time, while in ADM canonical gravity in asymptotically Minkowskian space-times only inertial effects without gravitational waves survive.

  13. History of electroweak symmetry breaking

    NASA Astrophysics Data System (ADS)

    Kibble, T. W. B.

    2015-07-01

    In this talk, I recall the history of the development of the unified electroweak theory, incorporating the symmetry-breaking Higgs mechanism, as I saw it from my standpoint as a member of Abdus Salam's group at Imperial College. I start by describing the state of physics in the years after the Second World War, explain how the goal of a unified gauge theory of weak and electromagnetic interactions emerged, the obstacles encountered, in particular the Goldstone theorem, and how they were overcome, followed by a brief account of more recent history, culminating in the historic discovery of the Higgs boson in 2012.

  14. Fermion mass without symmetry breaking

    SciTech Connect

    Catterall, Simon

    2016-01-20

    We examine a model of reduced staggered fermions in three dimensions interacting through an SO (4) invariant four fermion interaction. The model is similar to that considered in a recent paper by Ayyer and Chandrasekharan. We present theoretical arguments and numerical evidence which support the idea that the system develops a mass gap for sufficiently strong four fermi coupling without producing a symmetry breaking fermion bilinear condensate. As a result, massless and massive phases appear to be separated by a continuous phase transition.

  15. Contact symmetries and Hamiltonian thermodynamics

    SciTech Connect

    Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.

    2015-10-15

    It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production.

  16. Introduction to Electroweak Symmetry Breaking

    SciTech Connect

    Dawson,S.

    2008-10-02

    The Standard Model (SM) is the backbone of elementary particle physics-not only does it provide a consistent framework for studying the interactions of quark and leptons, but it also gives predictions which have been extensively tested experimentally. In these notes, I review the electroweak sector of the Standard Model, discuss the calculation of electroweak radiative corrections to observables, and summarize the status of SM Higgs boson searches. Despite the impressive experimental successes, however, the electroweak theory is not completely satisfactory and the mechanism of electroweak symmetry breaking is untested. I will discuss the logic behind the oft-repeated statement: 'There must be new physics at the TeV scale'. These lectures reflect my strongly held belief that upcoming results from the LHC will fundamentally change our understanding of electroweak symmetry breaking. In these lectures, I review the status of the electroweak sector of the Standard Model, with an emphasis on the importance of radiative corrections and searches for the Standard Model Higgs boson. A discussion of the special role of the TeV energy scale in electroweak physics is included.

  17. Extreme lattices: symmetries and decorrelation

    NASA Astrophysics Data System (ADS)

    Andreanov, A.; Scardicchio, A.; Torquato, S.

    2016-11-01

    We study statistical and structural properties of extreme lattices, which are the local minima in the density landscape of lattice sphere packings in d-dimensional Euclidean space {{{R}}d} . Specifically, we ascertain statistics of the densities and kissing numbers as well as the numbers of distinct symmetries of the packings for dimensions 8 through 13 using the stochastic Voronoi algorithm. The extreme lattices in a fixed dimension of space d (d≥slant 8 ) are dominated by typical lattices that have similar packing properties, such as packing densities and kissing numbers, while the best and the worst packers are in the long tails of the distribution of the extreme lattices. We also study the validity of the recently proposed decorrelation principle, which has important implications for sphere packings in general. The degree to which extreme-lattice packings decorrelate as well as how decorrelation is related to the packing density and symmetry of the lattices as the space dimension increases is also investigated. We find that the extreme lattices decorrelate with increasing dimension, while the least symmetric lattices decorrelate faster.

  18. Spinor Structure and Internal Symmetries

    NASA Astrophysics Data System (ADS)

    Varlamov, V. V.

    2015-10-01

    Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It is shown that tensor products of biquaternion algebras are associated with the each irreducible representation of the Lorentz group. Space-time discrete symmetries P, T and their combination PT are generated by the fundamental automorphisms of this algebraic background (Clifford algebras). Charge conjugation C is presented by a pseudoautomorphism of the complex Clifford algebra. This description of the operation C allows one to distinguish charged and neutral particles including particle-antiparticle interchange and truly neutral particles. Spin and charge multiplets, based on the interlocking representations of the Lorentz group, are introduced. A central point of the work is a correspondence between Wigner definition of elementary particle as an irreducible representation of the Poincaré group and SU(3)-description (quark scheme) of the particle as a vector of the supermultiplet (irreducible representation of SU(3)). This correspondence is realized on the ground of a spin-charge Hilbert space. Basic hadron supermultiplets of SU(3)-theory (baryon octet and two meson octets) are studied in this framework. It is shown that quark phenomenologies are naturally incorporated into presented scheme. The relationship between mass and spin is established. The introduced spin-mass formula and its combination with Gell-Mann-Okubo mass formula allows one to take a new look at the problem of mass spectrum of elementary particles.

  19. Duality symmetries in string theory

    SciTech Connect

    Nunez, Carmen A.

    1999-10-25

    The search for a unified theory of quantum gravity and gauge interactions leads naturally to string theory. This field of research has received a revival of interest after the discovery of duality symmetries in recent years. We present a self contained account of some non-perturbative aspects of string theory which have been recently understood. The spectrum and interactions of the five consistent superstring theories in ten dimensions are recollected and the fundamental principles underlying this initial stage in the construction of the theory are briefly reviewed. We next discuss some evidences that these apparently different superstrings are just different aspects of one unique theory. The key to this development is given by the non-perturbative duality symmetries which have modified and improved our understanding of string dynamics in many ways. In particular, by relating the fundamental objects of one theory to solitons of another theory, they have unraveled the presence of extended objects in the theory which stand on an equal footing with strings. We introduce these higher dimensional objects, named D-branes, and discuss applications of D-brane physics.

  20. Solving the degeneracy of the lepton-flavor mixing angle θATM by the T2KK two detector neutrino oscillation experiment

    NASA Astrophysics Data System (ADS)

    Hagiwara, Kaoru; Okamura, Naotoshi

    2008-01-01

    If the atmospheric neutrino oscillation amplitude, sin 22θATM is not maximal, there is a two fold ambiguity in the neutrino parameter space: sin 2θATM > 0.5 or sin 2θATM < 0.5. In this article, we study the impact of this degeneracy, the so-called octant degeneracy, on the T2KK experiment, which is a proposed extension of the T2K (Tokai-to-Kaimoka) neutrino oscillation experiment with an additional water Čerenkov detector placed in Korea. We find that the degeneracy between sin 2θATM = 0.40 and 0.60 can be resolved at the 3σ level for sin 22θRCT > 0.12 (0.08) for the optimal combination of a 3.0° off-axis beam (OAB) at SK (L = 295km) and a 0.5° OAB at L = 1000km with a far detector of 100kton volume, after 5 years of exposure with 1.0 (5.0) × 1021POT/year, if the hierarchy is normal. We also study the influence of the octant degeneracy on the capability of T2KK experiment to determine the mass hierarchy and the leptonic CP phase. The capability of rejecting the wrong mass hierarchy grows with increasing sin 2θATM when the hierarchy is normal, whereas it is rather insensitive to sin 2θATM for the inverted hierarchy. We also find that the 1σ allowed region of the CP phase is not affected significantly even when the octant degeneracy is not resolved. All our results are obtained for the 22.5 kton Super-Kamiokande as a near detector and without an anti-neutrino beam.