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.
Alonso, C E; Arias, J M; Vitturi, A
2007-02-01
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. PMID:17358851
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
SU(8) Family Unification with Boson Fermion Balance
NASA Astrophysics Data System (ADS)
Adler, Stephen L.
2015-03-01
We formulate an SU(8) family unification model motivated by requiring that the theory should incorporate the graviton, gravitinos, and the fermions and gauge fields of the standard model, with boson.fermion balance. Gauge field SU(8) anomalies cancel between the gravitinos and spin 1/2 fermions. The 56 of scalars breaks SU(8) to SU(3)family×SU(5)×U(1)/Z5, with the fermion representation content needed for "flipped" SU(5) with three families, and with residual scalars in the 10 and overline {10} representations that break flipped SU(5) to the standard model. Dynamical symmetry breaking can account for the generation of 5 representation scalars needed to break the electroweak group. Yukawa couplings of the 56 scalars to the fermions are forbidden by chiral and gauge symmetries, so in the first stage of SU(8) breaking fermions remain massless. In the limit of vanishing gauge coupling, there are N = 1 and N = 8 supersymmetries relating the scalars to the fermions, which restrict the form of scalar self-couplings and should improve the convergence of perturbation theory, if not making the theory finite and "calculable." In an Appendix we give an analysis of symmetry breaking by a Higgs component, such as the (1, 1)(-15) of the SU(8) 56 under SU(8) ⊃ SU(3) × SU(5) × U(1), which has nonzero U(1) generator.
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…
Twisted vertex algebras, bicharacter construction and boson-fermion correspondences
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.
Feshbach resonance described by boson-fermion coupling
Domanski, T.
2003-07-01
We consider a possibility to describe the Feshbach resonance in terms of the boson-fermion (BF) model. Using such a model, we show that after a gradual disentangling of the boson from fermion subsystem, the resonant-type scattering between fermions is indeed generated. We decouple the subsystems via (a) the single step and (b) the continuous canonical transformation. With the second one, we investigate the feedback effects effectively leading to the finite amplitude of the scattering strength. We study them in detail in the normal T>T{sub c} and superconducting T{<=}T{sub c} states.
Study of {beta}-Decay in the Proton-Neutron Interacting Boson-Fermion Model
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.
Conformal symmetry breaking and degeneracy of high-lying unflavored mesons
NASA Astrophysics Data System (ADS)
Kirchbach, Mariana; Pallares-Rivera, Adrian; Compean, Cliffor; Raya, Alfredo
2012-08-01
We show that though conformal symmetry can be broken by the dilaton, such can happen without breaking the conformal degeneracy patterns in the spectra. Our argumentation goes as follows: We departure from the gauge-gravity duality which predicts on the boundaries of the AdS5 geometry a conformal theory, associated with QCD at high temperatures, and consider S1 × S3 slicing. The inverse radius, R, of S3 relates to the temperature of the deconfinement phase transition and has to satisfy, hslashc/R gg ΛQCD. On S3, whose isometry group is SO(4), we then focus on the eigenvalue problem of the conformal Laplacian there, given by , with standing for the Casimir invariant of the so(4) algebra. This eigenvalue problem describes the spectrum of a scalar particle, to be associated with a qbar q system. Such a spectrum is characterized by a (K + l)2-fold degeneracy of its levels, with K in [0, ∞). We then break the conformal S3 metric, ds2 = dχ2 + sin2 χ(dθ2 + sin2θdvarphi2) -in polar chi,θ, and azimuthal varphi coordinates- according to, ds~2 = e-bχ((1 + b2/4)dχ2 + sin2 chi(dθ2 + sin2θdvarphi2)), and attribute the symmetry breaking scale bhslash2c2/R2 to the dilaton. Next we show that the above metric deformation is equivalent to a breaking of the conformal curvature of S3 by a term proportional to b cot χ, and that the perturbed conformal Laplacian is equivalent to , with cκ a representation constant, and being again an so(4) Casimir invariant, but this time in a representation unitarily nonequivalent to the 4D rotational one. As long as the spectra before and after the symmetry breaking happen to be determined each by eigenvalues of a Casimir invariant of an so(4), no matter whether or not in a representation that generates the orthogonal group SO(4) as a subgroup of the conformal group SO(2,4), the degeneracy patterns remain unaltered though the conformal symmetry breaks at the level of the representation of the algebra. We fit the S3 radius and the hslash2c
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.
A Categorification of the Boson-Fermion Correspondence via Representation Theory of sl(∞)
NASA Astrophysics Data System (ADS)
Frenkel, Igor; Penkov, Ivan; Serganova, Vera
2016-02-01
In recent years different aspects of categorification of the boson-fermion correspondence have been studied. In this paper we propose a categorification of the boson-fermion correspondence based on the category of tensor modules of the Lie algebra sl(∞) of finitary infinite matrices. By T+} we denote the category of "polynomial" tensor sl(∞)-modules. There is a natural "creation" functor TN} : T+} to {T+}}, {M mapsto N ⊗ M, quad M,N in T+}. The key idea of the paper is to employ the entire category {T} of tensor sl(∞)-modules in order to define the "annihilation" functor {{DN} : {T+} to {T+}} corresponding to {{TN}}. We show that the relations allowing one to express fermions via bosons arise from relations in the cohomology of complexes of linear endofunctors on {{T+}}.
Superfluid transition temperature of the boson-fermion model on a lattice
Micnas, R.
2007-11-01
The properties of a mixture of mutually interacting bound electron pairs and itinerant fermions (the boson-fermion model) on a lattice are further studied. We determine the superconducting critical temperature from a pseudogap phase by applying a self-consistent T-matrix approach, which includes the pairing fluctuations and the boson self-energy effects. The analysis is made for a three dimensional cubic lattice with tight-binding dispersion for electrons and for both standard bosons and the case of hard-core bosons. The results describe the BCS-Bose-Einstein condensation crossover with varying position of the bosonic (local pair) level and give a further insight into the nature of resonance superfluidity in the boson-fermion model.
Klassen, Joel; Wen, Xiao-Gang
2015-10-14
We study a chain of ferromagnetic sites, ie nano-particles, molecules or atoms, on a substrate of fully gapped superconductors. We find that under quite realistic conditions, the fermion-number-parity symmetry Z₂(f) can spontaneously break. In other words, such a chain can realize a 1 + 1D fermionic topologically ordered state and the corresponding two-fold topological degeneracy on an open chain. Such a topological degeneracy becomes the so called Majorana zero mode in the non-interacting limit. PMID:26401725
Functional integrals and 1/h expansion in the boson-fermion model
NASA Astrophysics Data System (ADS)
Yan, Jun
2016-06-01
The effective action of boson-fermion model is derived by means of the functional integrals method and Popov-Faddeev canonical transformations. The energy gap equation and excitation spectrum equation are obtained from first order and second order perturbation expansions of functional determinant. In the long wave approximation, some analytical expressions of excitation spectrum are calculated by using the 1/h expansion technique, the results showed that analytical calculation is in good agreement with the numerical calculation. Moreover, the Nambu sum rules of Higgs bosons are analyzed and discussed.
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.
Phase transitions in the interacting boson fermion model: The {gamma}-unstable case
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.
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.
NASA Astrophysics Data System (ADS)
He, Xiao-Tao; Fattoyev, F. J.; Li, Bao-An; Newton, W. G.
2016-02-01
A thorough understanding of properties of neutron stars requires both a reliable knowledge of the equation of state (EOS) of super-dense nuclear matter and the strong-field gravity theories simultaneously. To provide information that may help break this EOS-gravity degeneracy, we investigate effects of nuclear symmetry energy on the gravitational binding energy of neutron stars within GR and the scalar-tensor subset of alternative gravity models. We focus on effects of the slope L of nuclear symmetry energy at saturation density and the high-density behavior of nuclear symmetry energy. We find that the variation of either the density slope L or the high-density behavior of nuclear symmetry energy leads to large changes in the binding energy of neutron stars. The difference in predictions using the GR and the scalar-tensor theory appears only for massive neutron stars, and even then is significantly smaller than the difference resulting from variations in the symmetry energy.
β -decay rates of Cs-131121 in the microscopic interacting boson-fermion model
NASA Astrophysics Data System (ADS)
Mardones, E.; Barea, J.; Alonso, C. E.; Arias, J. M.
2016-03-01
β -decay rates of Cs-131121 have been calculated in the framework of the neutron-proton interacting boson-fermion model (IBFM-2). For odd-A nuclei, the decay operator can be written in a relatively simple form in terms of the one-nucleon transfer operator. Previous studies of β decay in IBFM-2 were based on a transfer operator obtained by using the number operator approximation (NOA). In this work a new form of the one-nucleon transfer operator, derived microscopically without the NOA approximation, is used. The results from both approaches are compared and show that the deviation from experimental data is reduced without using the NOA approximation. Indications about the renormalization of the Fermi and Gamow-Teller matrix elements are discussed. This is a further step toward a more complete description of low-lying states in medium and heavy nuclei which is necessary to compute reliable matrix elements in studies of current active interest such as double-β decay or neutrino absorption experiments.
A quantum spin liquid with a large topological degeneracy
NASA Astrophysics Data System (ADS)
Tchernyshyov, Oleg; Wang, Haoyu; Wan, Yuan
We present a model of a quantum spin liquid in two dimensions with a large topological degeneracy. The model has spins of length S = 1 / 2 on sites of a triangular lattice interacting via a 6-spin term. As in models of Kitaev and Wen [1-3], elementary building blocks in our model are strings of several distinct types. Ends of these strings are elementary particles: 4 bosons and 3 fermions. Particles of different types are mutual semions. The degeneracy of the ground state on a torus is 2 7 - 1 = 64 . Elementary excitations of the model are boson-fermion pairs, which come in 3 × 4 = 12 distinct types Research funding comes from the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-FG02-08ER46544.
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.
NASA Astrophysics Data System (ADS)
Sowiński, Tomasz; Łaçki, Mateusz; Dutta, Omjyoti; Pietraszewicz, Joanna; Sierant, Piotr; Gajda, Mariusz; Zakrzewski, Jakub; Lewenstein, Maciej
2013-11-01
We study the ground-state properties of bosons loaded into the p band of a one-dimensional optical lattice. We show that the phase diagram of the system is substantially affected by the anharmonicity of the lattice potential. In particular, for a certain range of tunneling strength, the full many-body ground state of the system becomes degenerate. In this region, an additional symmetry of the system, namely, the parity of the occupation number of the chosen orbital, is spontaneously broken. The state with a nonvanishing staggered angular momentum, which breaks the time-reversal symmetry, becomes the true ground state of the system.
Sowiński, Tomasz; Łącki, Mateusz; Dutta, Omjyoti; Pietraszewicz, Joanna; Sierant, Piotr; Gajda, Mariusz; Zakrzewski, Jakub; Lewenstein, Maciej
2013-11-22
We study the ground-state properties of bosons loaded into the p band of a one-dimensional optical lattice. We show that the phase diagram of the system is substantially affected by the anharmonicity of the lattice potential. In particular, for a certain range of tunneling strength, the full many-body ground state of the system becomes degenerate. In this region, an additional symmetry of the system, namely, the parity of the occupation number of the chosen orbital, is spontaneously broken. The state with a nonvanishing staggered angular momentum, which breaks the time-reversal symmetry, becomes the true ground state of the system. PMID:24313497
{beta} decay of odd-A As to Ge isotopes in the interacting boson-fermion model
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.
Odd-even {sup 147-153}Pm isotopes within the neutron-proton interacting boson-fermion model
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.
On-chip generation of Einstein-Podolsky-Rosen states with arbitrary symmetry
NASA Astrophysics Data System (ADS)
Gräfe, Markus; Heilmann, René; Nolte, Stefan; Szameit, Alexander
2015-05-01
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.
On-chip generation of Einstein-Podolsky-Rosen states with arbitrary symmetry
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.
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.
Meyer, R.A. Nuclear Chemistry Division, Lawrence Livermore National Laboratory, Livermore, California 94550 ) Nagle, R.J. ) Brant, S. ) Frlez, E. ) Paar, V. ) ) Hopke, P.K. )
1990-02-01
We have studied the level properties of the {ital N}=39 nucleus {sup 71}Ge by gamma-ray spectroscopy following the beta decay of {sup 71}As, for which we measure a half-life of 65.30{plus minus}0.07 h. When we calculated the level structure of {sup 71}Ge within the framework of the interacting boson fermion model, we found good agreement with the experimentally determined level properties. Some evidence was found for the occurrence of levels built on the coexisting {sup 70}Ge-core intruder state.
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.
Meyer, R.A.; Jackson, S.V.; Brant, S.; Paar, V.
1996-12-01
Deexcitation properties of low-spin levels in {sup 105}Pd populated in the decay of {sup 105}Ag{sup {ital m}} and {sup 105}Ag{sup {ital g}} are investigated. The calculation for {sup 105}Pd is performed in the interacting boson-fermion model (IBFM), using a nearly spherical boson core corresponding to {sup 104}Pd. As a result, we obtain an approximate quasiweak-coupling pattern, which is in contrast to previously assumed symmetric rotor model calculations. Rather good agreement between theory and experiment was obtained. The extension of the IBFM calculations to lighter {ital N}=59 isotones is consistent with the recent discovery of coexisting structures and dual double-subshell closure in respective even-even core nuclei. {copyright} {ital 1996 The American Physical Society.}
On second quantization on noncommutative spaces with twisted symmetries
NASA Astrophysics Data System (ADS)
Fiore, Gaetano
2010-04-01
By the application of the general twist-induced sstarf-deformation procedure we translate second quantization of a system of bosons/fermions on a symmetric spacetime into a noncommutative language. The procedure deforms, in a coordinated way, the spacetime algebra and its symmetries, the wave-mechanical description of a system of n bosons/fermions, the algebra of creation and annihilation operators and also the commutation relations of the latter with functions of spacetime; our key requirement is the mode-decomposition independence of the quantum field. In a minimalistic view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind. In a non-conservative one, we obtain a closed, covariant framework for quantum field theory (QFT) on the corresponding noncommutative spacetime consistent with quantum mechanical axioms and Bose-Fermi statistics. One distinguishing feature is that the field commutation relations remain of the type 'field (anti)commutator=a distribution'. We illustrate the results by choosing as examples interacting non-relativistic and free relativistic QFT on Moyal space(time)s.
Reducing Degeneracy in Maximum Entropy Models of Networks
NASA Astrophysics Data System (ADS)
Horvát, Szabolcs; Czabarka, Éva; Toroczkai, Zoltán
2015-04-01
Based on Jaynes's maximum entropy principle, exponential random graphs provide a family of principled models that allow the prediction of network properties as constrained by empirical data (observables). However, their use is often hindered by the degeneracy problem characterized by spontaneous symmetry breaking, where predictions fail. Here we show that degeneracy appears when the corresponding density of states function is not log-concave, which is typically the consequence of nonlinear relationships between the constraining observables. Exploiting these nonlinear relationships here we propose a solution to the degeneracy problem for a large class of systems via transformations that render the density of states function log-concave. The effectiveness of the method is demonstrated on examples.
Accidental degeneracies in string compactification
NASA Astrophysics Data System (ADS)
Bais, F. A.; Taormina, A.
1986-11-01
The equivalence of the torus and group manifold compactification of strings is established. Accidental degeneracies are shown to occur for a large class of compactifications. This way many examples are obtained in which modular invariance does not uniquely fix the representation content of the spectrum.
Overcoming Degeneracies in Exoplanet Spectra
NASA Astrophysics Data System (ADS)
Benneke, Björn
2015-08-01
Spectroscopic observations of exoplanets can provide invaluable insights into the planets’ compositions, their formation and evolution histories, and even their habitability. Obtaining exoplanet spectra is observationally challenging; however, and we are generally limited to relatively low signal-to-noise, low spectral resolution, disk-integrated observations , often with relatively narrow wavelength coverage. This low data situation results in strong correlations and degeneracies between the different planet and atmospheric parameters of interest. In this talk, I will present a conceptual picture of how vital information about the planet is encoded in its observable spectrum. I will then give an overview about the wide range of correlations and degeneracies relevant to today’s exoplanet observations. Finally, I will demonstrate how some degeneracies can be overcome and improved constraints can be obtained by including prior knowledge of atmospheric chemistry and physics in the retrieval. I present a new atmospheric retrieval framework, SCARLET, that combines observational data and our prior (limited) knowledge of atmospheric processes in a statistical robust Bayesian framework. New results for hot Jupiters will be presented.
Coping with degeneracies in Delaunay triangulation
Beichl, I.; Sullivan, F.
1995-12-31
Degeneracy is a serious issue in geometry. In their original form, many geometric algorithms simply assume that there is no degeneracy. As a result, when these methods are used on data that is degenerate or nearly degenerate, they either fail to complete or else give nonsensical results. We will describe a new method that removes only those 3-d degeneracies that cause ambiguity in determining Delaunay tetrahedra and only those 3-d degeneracies that cause ambiguity in determining Delaunay triangles. The mathematical justification is based on classical results of real analysis. The proof identifies degeneracies with the polynomial derived from the determinants that express geometrical primitives. Our result is a probabilistic statement about the real numbers; with probability one, degeneracies are removed in real arithmetic. In floating-point arithmetic, detection of degeneracies is based on relative error criteria that we describe here.
The Simplicity of Perfect Atoms: Degeneracies in Supersymmetric Hydrogen
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.
On uniqueness and non-degeneracy of anisotropic polarons
NASA Astrophysics Data System (ADS)
Ricaud, Julien
2016-05-01
We study the anisotropic Choquard-Pekar equation which describes a polaron in an anisotropic medium. We prove the uniqueness and non-degeneracy of minimizers in a weakly anisotropic medium. In addition, for a wide range of anisotropic media, we derive the symmetry properties of minimizers and prove that the kernel of the associated linearized operator is reduced, apart from three functions coming from the translation invariance, to the kernel on the subspace of functions that are even in each of the three principal directions of the medium.
NASA Astrophysics Data System (ADS)
Erbe, B.; Schliemann, J.
2010-12-01
We report an unexpected systematic degeneracy between different multiplets in an inversion symmetric system of two coupled Gaudin models with homogeneous couplings, as occurring for example in the context of solid state quantum information processing. We construct the full degenerate subspace (being of macroscopic dimension), which turns out to lie in the kernel of the commutator between the two Gaudin models and the coupling term. Finally we investigate to what extent the degeneracy is related to the inversion symmetry of the system and find that indeed there is a large class of systems showing the same type of degeneracy.
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.
Nodal surfaces and interdimensional degeneracies
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.
Angular-overlap calculation of the Jahn-Teller stabilization energie for f-orbital degeneracies
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.
The effective degeneracy of protein normal modes
NASA Astrophysics Data System (ADS)
Na, Hyuntae; Song, Guang
2016-06-01
Normal modes are frequently computed and used to portray protein dynamics and interpret protein conformational changes. In this work, we investigate the nature of normal modes and find that the normal modes of proteins, especially those at the low frequency range (0–600 cm‑1), are highly susceptible to degeneracy. Two or more modes are degenerate if they have the same frequency and consequently any orthogonal transformation of them also is a valid representation of the mode subspace. Thus, degenerate modes can no longer characterize unique directions of motions as regular modes do. Though the normal modes of proteins are usually of different frequencies, the difference in frequency between neighboring modes is so small that, under even slight structural uncertainty that unavoidably exists in structure determination, it can easily vanish and as a result, a mode becomes effectively degenerate with its neighboring modes. This can be easily observed in that some modes seem to disappear and their matching modes cannot be found when the structure used to compute the modes is modified only slightly. We term this degeneracy the effective degeneracy of normal modes. This work is built upon our recent discovery that the vibrational spectrum of globular proteins is universal. The high density of modes observed in the vibrational frequency spectra of proteins renders their normal modes highly susceptible to degeneracy, under even the smallest structural uncertainty. Indeed, we find the degree of degeneracy of modes is proportional to the density of modes in the vibrational spectrum. This means that for modes at the same frequency, degeneracy is more severe for larger proteins. Degeneracy exists also in the modes of coarse-grained models, but to a much lesser extent than those of all-atom models. In closing, we discuss the implications of the effective degeneracy of normal modes: how it may significantly affect the ways in which normal modes are used in various normal modes
The effective degeneracy of protein normal modes.
Na, Hyuntae; Song, Guang
2016-01-01
Normal modes are frequently computed and used to portray protein dynamics and interpret protein conformational changes. In this work, we investigate the nature of normal modes and find that the normal modes of proteins, especially those at the low frequency range (0-600 cm(-1)), are highly susceptible to degeneracy. Two or more modes are degenerate if they have the same frequency and consequently any orthogonal transformation of them also is a valid representation of the mode subspace. Thus, degenerate modes can no longer characterize unique directions of motions as regular modes do. Though the normal modes of proteins are usually of different frequencies, the difference in frequency between neighboring modes is so small that, under even slight structural uncertainty that unavoidably exists in structure determination, it can easily vanish and as a result, a mode becomes effectively degenerate with its neighboring modes. This can be easily observed in that some modes seem to disappear and their matching modes cannot be found when the structure used to compute the modes is modified only slightly. We term this degeneracy the effective degeneracy of normal modes. This work is built upon our recent discovery that the vibrational spectrum of globular proteins is universal. The high density of modes observed in the vibrational frequency spectra of proteins renders their normal modes highly susceptible to degeneracy, under even the smallest structural uncertainty. Indeed, we find the degree of degeneracy of modes is proportional to the density of modes in the vibrational spectrum. This means that for modes at the same frequency, degeneracy is more severe for larger proteins. Degeneracy exists also in the modes of coarse-grained models, but to a much lesser extent than those of all-atom models. In closing, we discuss the implications of the effective degeneracy of normal modes: how it may significantly affect the ways in which normal modes are used in various normal modes
Mixed symmetry states and {beta} decays of odd-A Xe to I isotopes
Al-Khudair, Falih H.
2009-07-15
The energy spectra of the parent and daughter nuclei in the {beta} decays ({sup 121-127}Xe,{beta}{sup +121-127}I) are considered in the interacting boson fermion model (IBFM-2) with the g{sub 7/2},d{sub 5/2},d{sub 3/2},s{sub 1/2}, and h{sub 11/2} single-particle orbitals. Electromagnetic transition probabilities and branching ratios in odd {sup 121-127}I isotopes are investigated. Special attention is given to the occurrence of mixed symmetry states, and the F-spin structures of the wave functions are analyzed. The log{sub 10}ft values of the allowed {beta} decay transitions are calculated. It is found that the IBFM-2 results agree with the experimental data quite well.
Frustration and time-reversal symmetry breaking for Fermi and Bose-Fermi systems
NASA Astrophysics Data System (ADS)
Sacha, Krzysztof; Targońska, Katarzyna; Zakrzewski, Jakub
2012-05-01
The modulation of an optical lattice potential that breaks time-reversal symmetry enables the realization of complex tunneling amplitudes in the corresponding tight-binding model. For a superfluid Fermi gas in a triangular lattice potential with complex tunnelings, the pairing function acquires a complex phase, so the frustrated magnetism of fermions can be realized. Bose-Fermi mixtures of bosonic molecules and unbound fermions in the lattice also show interesting behavior. Due to boson-fermion coupling, the fermions become enslaved by the bosons and the corresponding pairing function takes the complex phase determined by the bosons. In the presence of bosons the Fermi system can reveal both gapped and gapless superfluidity.
Quantum adiabatic evolution with energy degeneracy levels
NASA Astrophysics Data System (ADS)
Zhang, Qi
2016-01-01
A classical-kind phase-space formalism is developed to address the tiny intrinsic dynamical deviation from what is predicted by Wilczek-Zee theorem during quantum adiabatic evolution on degeneracy levels. In this formalism, the Hilbert space and the aggregate of degenerate eigenstates become the classical-kind phase space and a high-dimensional subspace in the phase space, respectively. Compared with the previous analogous study by a different method, the current result is qualitatively different in that the first-order deviation derived here is always perpendicular to the degeneracy subspace. A tripod-scheme Hamiltonian with two degenerate dark states is employed to illustrate the adiabatic deviation with degeneracy levels.
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.
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).
NASA Astrophysics Data System (ADS)
Fang, Yi-Nan; Dong, Guo-Hui; Zhou, Duan-Lu; Sun, Chang-Pu
2016-04-01
Symmetry is conventionally described in a polarized manner that the system is either completely symmetric or completely asymmetric. Using group theoretical approach to overcome this dichotomous problem, we introduce the degree of symmetry (DoS) as a non-negative continuous number ranging from zero to unity. DoS is defined through an average of the fidelity deviations of Hamiltonian or quantum state over its transformation group G, and thus is computable by making use of the completeness relations of the irreducible representations of G. The monotonicity of DoS can effectively probe the extended group for accidental degeneracy while its multi-valued natures characterize some (spontaneous) symmetry breaking. Supported by the National Natural Science Foundation of China under Grant Nos. 11421063, 11534002, 11475254 and the National 973 Program under Grant Nos. 2014CB921403, 2012CB922104, and 2014CB921202
Extracting hidden symmetry from the energy spectrum
NASA Astrophysics Data System (ADS)
Yuzbashyan, Emil A.; Happer, William; Altshuler, Boris L.; Shastry, Sriram B.
2003-03-01
In this paper we revisit the problem of finding hidden symmetries in quantum mechanical systems. Our interest in this problem was renewed by nontrivial degeneracies of a simple spin Hamiltonian used to model spin relaxation in alkali-metal vapours. We consider this spin Hamiltonian in detail and use this example to outline a general approach to finding symmetries when eigenvalues and eigenstates of the Hamiltonian are known. We extract all nontrivial symmetries responsible for the degeneracy and show that the symmetry group of the Hamiltonian is SU(2). The symmetry operators have a simple meaning which becomes transparent in the limit of large spin. As an additional example we apply the method to the hydrogen atom.
Electronic orders in multiorbital Hubbard models with lifted orbital degeneracy
NASA Astrophysics Data System (ADS)
Hoshino, Shintaro; Werner, Philipp
2016-04-01
We study the symmetry-broken phases in two- and three-orbital Hubbard models with lifted orbital degeneracy using dynamical mean-field theory. On the technical level, we explain how symmetry relations can be exploited to measure the four-point correlation functions needed for the calculation of the lattice susceptibilities. In the half-filled two-orbital model with crystal-field splitting, we find an instability of the metallic phase to spin-orbital order with neither spin nor orbital moment. This ordered phase is shown to be related to the recently discovered fluctuating-moment induced spin-triplet superconducting state in the orbitally degenerate model with shifted chemical potential. In the three-orbital case, we consider the effect of a crystal-field splitting on the spin-triplet superconducting state in the model with positive Hund coupling, and the spin-singlet superconducting state in the case of negative Hund coupling. It is demonstrated that for certain crystal-field splittings the higher energy orbitals instead of the lower ones are relevant for superconductivity, and that Tc can be slightly enhanced by the crystal-field effect. We comment on the implications of our results for the superconductivity in strontium ruthenates, and for the recently reported light-enhanced superconducting state in alkali-metal-doped fullerides.
On dark degeneracy and interacting models
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.
Valley degeneracy in biaxially strained aluminum arsenide quantum wells
NASA Astrophysics Data System (ADS)
Prabhu-Gaunkar, S.; Birner, S.; Dasgupta, S.; Knaak, C.; Grayson, M.
2011-09-01
This paper describes a complete analytical formalism for calculating electron subband energy and degeneracy in strained multivalley quantum wells grown along any orientation with explicit results for AlAs quantum wells (QWs). In analogy to the spin index, the valley degree of freedom is justified as a pseudospin index due to the vanishing intervalley exchange integral. A standardized coordinate transformation matrix is defined to transform between the conventional-cubic-cell basis and the QW transport basis whereby effective mass tensors, valley vectors, strain matrices, anisotropic strain ratios, piezoelectric fields, and scattering vectors are all defined in their respective bases. The specific cases of (001)-, (110)-, and (111)-oriented aluminum arsenide (AlAs) QWs are examined, as is the unconventional (411) facet, which is of particular importance in AlAs literature. Calculations of electron confinement and strain for the (001), (110), and (411) facets determine the critical well width for crossover from double- to single-valley degeneracy in each system. The biaxial Poisson ratio is calculated for the high-symmetry lower Miller index (001)-, (110)-, and (111)-oriented QWs. An additional shear-strain component arises in the higher Miller index (411)-oriented QWs and we define and solve for a shear-to-biaxial strain ratio. The notation is generalized to address non-Miller-indexed planes so that miscut substrates can also be treated, and the treatment can be adapted to other multivalley biaxially strained systems. To help classify anisotropic intervalley scattering, a valley scattering primitive unit cell is defined in momentum space, which allows one to distinguish purely in-plane momentum scattering events from those that require an out-of-plane momentum component.
Scalar non-degeneracy and flavor unification
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.
The degeneracy of the free Dirac equation
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.
Dark degeneracy and interacting cosmic components
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.
Relativistic symmetries in nuclear single-particle spectra
NASA Astrophysics Data System (ADS)
Guo, Jian-You; Liang, Hao Zhao; Meng, Jie; Zhou, Shan-Gui
Symmetry is a fundamental concept in quantum 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. Since the pseudospin symmetry was recognized as a relativistic symmetry in 1990s, many special features, including the spin symmetry for anti-nucleons, and many new concepts have been introduced. In this Chapter, we will illustrate the schematic picture of spin and pseudospin symmetries, derive the basic formalism, highlight the recent progress from several different aspects, and discuss selected open issues in this topic.
Hidden in plain view: degeneracy in complex systems.
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. PMID:25543071
On the Degeneracies of the Mass-Squared Differences for Three-Neutrino Oscillations
NASA Astrophysics Data System (ADS)
Latimer, D. C.; Ernst, D. J.
Using an algebraic formulation, we explore two well-known degeneracies involving the mass-squared differences for three-neutrino oscillations assuming CP symmetry is conserved. For vacuum oscillation, we derive the expression for the mixing angles that permit invariance under the interchange of two mass-squared differences. This symmetry is most easily expressed in terms of an ascending mass order. This can be used to reduce the parameter space by one half in the absence of the MSW effect. For oscillations in matter, we derive within our formalism the known approximate degeneracy between the standard and inverted mass hierarchies in the limit of vanishing θ13. This is done with a mass ordering that permits the map Δ31↦-Δ31. Our techniques allow us to translate mixing angles in this mass order convention into their values for the ascending order convention. Using this dictionary, we demonstrate that the vacuum symmetry and the approximate symmetry invoked for oscillations in matter are distinctly different.
Hidden nonsymmorphic symmetry in optical lattices with one-dimensional spin-orbit coupling
NASA Astrophysics Data System (ADS)
Chen, Hua; Liu, Xiong-Jun; Xie, X. C.
2016-05-01
We uncover the nonsymmorphic symmetry and investigate its effects on the noncollinear band structures of a quasi-two-dimensional optical lattice with synthetic one-dimensional spin-orbit coupling and a tunable Zeeman field. The perpendicular Zeeman field breaks time-reversal symmetry and lifts the Kramers degeneracy which is protected by time-reversal and generalized inversion symmetries. Interestingly, we find that the degeneracy of Bloch bands on the border of the Brillouin zone is immune to the Zeeman field. This degeneracy, reminiscent of that in nonsymmorphic crystals, is protected by the hidden glide-plane symmetry that comprises a physical reflection involving both spatial and spin degrees of freedom followed by a nonprimitive lattice translation. Furthermore, we show that the band degeneracy can be lifted by the glide-plane-symmetry-breaking lattice potential. Finally, we propose to detect these effects by measuring a dynamical structure factor with optical Bragg spectroscopy.
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.
Macroscopic degeneracy and order in the 3D plaquette Ising model
NASA Astrophysics Data System (ADS)
Johnston, Desmond A.; Mueller, Marco; Janke, Wolfhard
2015-07-01
The purely plaquette 3D Ising Hamiltonian with the spins living at the vertices of a cubic lattice displays several interesting features. The symmetries of the model lead to a macroscopic degeneracy of the low-temperature phase and prevent the definition of a standard magnetic order parameter. Consideration of the strongly anisotropic limit of the model suggests that a layered, “fuki-nuke” order still exists and we confirm this with multi-canonical simulations. The macroscopic degeneracy of the low-temperature phase also changes the finite-size scaling corrections at the first-order transition in the model and we see this must be taken into account when analyzing our measurements.
Lifting of the Landau level degeneracy in graphene devices in a tilted magnetic field
NASA Astrophysics Data System (ADS)
Chiappini, F.; Wiedmann, S.; Novoselov, K.; Mishchenko, A.; Geim, A. K.; Maan, J. C.; Zeitler, U.
2015-11-01
We report on transport and capacitance measurements of graphene devices in magnetic fields up to 30 T. In both techniques, we observe the full splitting of Landau levels and we employ tilted field experiments to address the origin of the observed broken symmetry states. In the lowest energy level, the spin degeneracy is removed at filling factors ν =±1 and we observe an enhanced energy gap. In the higher levels, the valley degeneracy is removed at odd filling factors while spin polarized states are formed at even ν . Although the observation of odd filling factors in the higher levels points towards the spontaneous origin of the splitting, we find that the main contribution to the gap at ν =-4 ,-8 , and -12 is due to the Zeeman energy.
Ultracold polar molecules near quantum degeneracy.
Ospelkaus, S; Ni, K K; de Miranda, M H G; Neyenhuis, B; Wang, D; Kotochigova, S; Julienne, P S; Jin, D S; Ye, J
2009-01-01
We report the creation and characterization of a near quantum-degenerate gas of polar 40K-87Rb molecules in their absolute rovibrational ground state. Starting from weakly bound heteronuclear KRb Feshbach molecules, we implement precise control of the molecular electronic, vibrational, and rotational degrees of freedom with phase-coherent laser fields. In particular, we coherently transfer these weakly bound molecules across a 125 THz frequency gap in a single step into the absolute rovibrational ground state of the electronic ground potential. Phase coherence between lasers involved in the transfer process is ensured by referencing the lasers to two single components of a phase-stabilized optical frequency comb. Using these methods, we prepare a dense gas of 4 x 10(4) polar molecules at a temperature below 400 nK. This fermionic molecular ensemble is close to quantum degeneracy and can be characterized by a degeneracy parameter of T/T(F) = 3. We have measured the molecular polarizability in an optical dipole trap where the trap lifetime gives clues to interesting decay mechanisms. Given the large measured dipole moment of the KRb molecules of 0.5 Debye, the study of quantum degenerate molecular gases interacting via strong dipolar interactions is now within experimental reach. PACS numbers: 37.10.Mn, 37.10.Pq. PMID:20151553
Degeneracy and discreteness in cosmological model fitting
NASA Astrophysics Data System (ADS)
Teng, Huan-Yu; Huang, Yuan; Zhang, Tong-Jie
2016-03-01
We explore the problems of degeneracy and discreteness in the standard cosmological model (ΛCDM). We use the Observational Hubble Data (OHD) and the type Ia supernovae (SNe Ia) data to study this issue. In order to describe the discreteness in fitting of data, we define a factor G to test the influence from each single data point and analyze the goodness of G. Our results indicate that a higher absolute value of G shows a better capability of distinguishing models, which means the parameters are restricted into smaller confidence intervals with a larger figure of merit evaluation. Consequently, we claim that the factor G is an effective way of model differentiation when using different models to fit the observational data.
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.
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.
Parity-time-symmetry breaking in two-dimensional photonic crystals: Square lattice
NASA Astrophysics Data System (ADS)
Mock, Adam
2016-06-01
We consider theoretically materials whose electromagnetic properties possess parity-time (PT ) symmetry and are periodic in two dimensions. When designed for optical frequencies such structures are commonly known as two-dimensional (2D) photonic crystals. With the addition of PT symmetry the optical modes of 2D photonic crystals exhibit thresholdless spontaneous PT -symmetry breaking near the Brillouin zone boundary, which is analogous to what has previously been studied in PT -symmetric structures with one-dimensional periodicity. Consistent with previous work, we find that spontaneous PT -symmetry breaking occurs at band crossings in the photonic dispersion diagram. Due to the extra spatial degree of freedom in 2D periodic systems, their band structures contain more band crossings and higher-order degeneracies than their one-dimensional counterparts. This work provides a comprehensive theoretical analysis of spontaneous PT -symmetry breaking at these points in the band structure. We find that, as in the case of one-dimensional structures, photonic band gaps exist at k =0 . We also find that at points of degeneracy with order higher than 2, bands merge pairwise to form broken-PT -symmetry supermodes. If the degeneracy order is even, this means multiple pairs of bands can form distinct (nondegenerate) broken-symmetry supermodes. If the order of degeneracy is odd, at least one of the bands will have protected PT symmetry. At other points of degeneracy, we find that the PT symmetry of the modes may be protected and we provide a spatial mode symmetry argument to explain this behavior. Finally, we identify a point at which two broken-PT -symmetry supermodes become degenerate, creating a point of fourfold degeneracy in the broken-PT -symmetry regime.
Coexistence of orbital degeneracy lifting and superconductivity in iron-based superconductors
NASA Astrophysics Data System (ADS)
Miao, Hu; Richard, Pierre; Wu, Shangfei; Ma, Jun; Qian, Tian; Xing, Lingyi; Wang, Xiancheng; Jin, Changqing; Ding, Hong; Chou, Chungpin; Wang, Limin; Ku, Wei; Wang, Ziqiang
2014-03-01
In iron-based superconductors, local orbital fluctuations have been proposed to be directly responsible for the structural phase transition and closely related to the observed giant magnetic anisotropy and electronic nematicity. However, whether superconductivity can emerge from, or even coexist with orbital fluctuations, remains unclear. Here 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 SC state of Li(Fe1-xCox)As. Supported by theoretical simulations, we analyse the doping and temperature dependences of this band-splitting and demonstrate an intimate connection between ferro-orbital correlations and superconductivity. This work was supported by grants from CAS, MOST and NSFC. Theoretical study is supported by US DOE. This work is based in part on research conducted at the Synchrotron Radiation Center, which is primarily funded by the University of Wisconsin-Madison.
Breaking a dark degeneracy with gravitational waves
NASA Astrophysics Data System (ADS)
Lombriser, Lucas; Taylor, Andy
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 lesssim95 % of the speed of light with a damping of the wave amplitude that is gtrsim5 % 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.
Statistical description of the black hole degeneracy spectrum
Barbero G, J. Fernando; Villasenor, Eduardo J. S.
2011-05-15
We use mathematical methods based on generating functions to study the statistical properties of the black hole degeneracy spectrum in loop quantum gravity. In particular we will study the persistence of the observed effective quantization of the entropy as a function of the horizon area. We will show that this quantization disappears as the area increases despite the existence of black hole configurations with a large degeneracy. The methods that we describe here can be adapted to the study of the statistical properties of the black hole degeneracy spectrum for all the existing proposals to define black hole entropy in loop quantum gravity.
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
The degeneracy problem in non-canonical inflation
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.
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.
Degeneracies in long-baseline neutrino experiments from nonstandard interactions
NASA Astrophysics Data System (ADS)
Liao, Jiajun; Marfatia, Danny; Whisnant, Kerry
2016-05-01
We study parameter degeneracies that can occur in long-baseline neutrino appearance experiments due to nonstandard interactions (NSI) in neutrino propagation. For a single off-diagonal NSI parameter, and neutrino and antineutrino measurements at a single L /E , there exists a continuous four-fold degeneracy (related to the mass hierarchy and θ23 octant) that renders the mass hierarchy, octant, and C P phase unknowable. Even with a combination of NO ν A and T2K data, which in principle can resolve the degeneracy, both NSI and the C P phase remain unconstrained because of experimental uncertainties. A wide-band beam experiment like DUNE will resolve this degeneracy if the nonzero off-diagonal NSI parameter is ɛe μ. If ɛe τ is nonzero, or the diagonal NSI parameter ɛe e is O (1 ), a wrong determination of the mass hierarchy and of C P violation can occur at DUNE. The octant degeneracy can be further complicated by ɛe τ, but is not affected by ɛe e.
Large degeneracy of excited hadrons and quark models
Bicudo, P.
2007-11-01
The pattern of a large approximate degeneracy of the excited hadron spectra (larger than the chiral restoration degeneracy) is present in the recent experimental report of Bugg. Here we try to model this degeneracy with state of the art quark models. We review how the Coulomb Gauge chiral invariant and confining Bethe-Salpeter equation simplifies in the case of very excited quark-antiquark mesons, including angular or radial excitations, to a Salpeter equation with an ultrarelativistic kinetic energy with the spin-independent part of the potential. The resulting meson spectrum is solved, and the excited chiral restoration is recovered, for all mesons with J>0. Applying the ultrarelativistic simplification to a linear equal-time potential, linear Regge trajectories are obtained, for both angular and radial excitations. The spectrum is also compared with the semiclassical Bohr-Sommerfeld quantization relation. However, the excited angular and radial spectra do not coincide exactly. We then search, with the classical Bertrand theorem, for central potentials producing always classical closed orbits with the ultrarelativistic kinetic energy. We find that no such potential exists, and this implies that no exact larger degeneracy can be obtained in our equal-time framework, with a single principal quantum number comparable to the nonrelativistic Coulomb or harmonic oscillator potentials. Nevertheless we find it plausible that the large experimental approximate degeneracy will be modeled in the future by quark models beyond the present state of the art.
Degeneracy of Majorana bound states and fractional Josephson effect in a dirty SNS junction.
Ikegaya, S; Asano, Y
2016-09-21
We theoretically study the stability of more than one Majorana fermion appearing in a p-wave superconductor/dirty normal metal/p-wave superconductor junction in two-dimensions by using the chiral symmetry of a Hamiltonian. At the phase difference across the junction φ being π, we will show that all of the Majorana bound states in the normal metal belong to the same chirality. Due to this pure chiral feature, the Majorana bound states retain their high degree of degeneracy at zero energy even in the presence of a random potential. As a consequence, the resonant transmission of a Cooper pair via the degenerate Majorana bound states carries the Josephson current at [Formula: see text], which explains the fractional current-phase relationship discussed in a number of previous papers. PMID:27420174
Degeneracies and exotic phases in an isotropic frustrated spin-1/2 chain
NASA Astrophysics Data System (ADS)
Parvej, Aslam; Kumar, Manoranjan
2016-03-01
In the presence of an axial magnetic field, a frustrated isotropic J1 - J2 model system shows many exotic phases, such as vector chiral and multipolar phases. In this paper, the phase boundaries of these exotic phases are calculated based on the order parameters, energy level crossings and magnetization jumps in the system. The order parameter of the vector chiral phase is calculated using the broken symmetry states at a finite magnetic field. The exact diagonalization and the density matrix renormalization group results are used to show that the vector chiral phase exists only in a narrow range of J2/J1 parameter space. In the quadrupolar phase, the magnetization jumps can be associated with the binding energy of two magnons localized at two different legs of the zigzag chain. The energy level crossings and degeneracies in the presence of the axial magnetic field are studied in detail using the exact diagonalization method.
Degeneracy of Majorana bound states and fractional Josephson effect in a dirty SNS junction
NASA Astrophysics Data System (ADS)
Ikegaya, S.; Asano, Y.
2016-09-01
We theoretically study the stability of more than one Majorana fermion appearing in a p-wave superconductor/dirty normal metal/p-wave superconductor junction in two-dimensions by using the chiral symmetry of a Hamiltonian. At the phase difference across the junction φ being π, we will show that all of the Majorana bound states in the normal metal belong to the same chirality. Due to this pure chiral feature, the Majorana bound states retain their high degree of degeneracy at zero energy even in the presence of a random potential. As a consequence, the resonant transmission of a Cooper pair via the degenerate Majorana bound states carries the Josephson current at \\varphi =π -{{0}+} , which explains the fractional current-phase relationship discussed in a number of previous papers.
Accidental degeneracy of double Dirac cones in a phononic crystal
Chen, Ze-Guo; Ni, Xu; Wu, Ying; He, Cheng; Sun, Xiao-Chen; Zheng, Li-Yang; Lu, Ming-Hui; Chen, Yan-Feng
2014-01-01
Artificial honeycomb lattices with Dirac cone dispersion provide a macroscopic platform to study the massless Dirac quasiparticles and their novel geometric phases. In this paper, a quadruple-degenerate state is achieved at the center of the Brillouin zone in a two-dimensional honeycomb lattice phononic crystal, which is a result of accidental degeneracy of two double-degenerate states. In the vicinity of the quadruple-degenerate state, the dispersion relation is linear. Such quadruple degeneracy is analyzed by rigorous representation theory of groups. Using method, a reduced Hamiltonian is obtained to describe the linear Dirac dispersion relations of this quadruple-degenerate state, which is well consistent with the simulation results. Near such accidental degeneracy, we observe some unique properties in wave propagating, such as defect-insensitive propagating character and the Talbot effect. PMID:24714512
Pervasive flexibility in living technologies through degeneracy-based design.
Whitacre, James; Bender, Axel
2013-01-01
The capacity to adapt can greatly influence the success of systems that need to compensate for damaged parts, learn how to achieve robust performance in new environments, or exploit novel opportunities that originate from new technological interfaces or emerging markets. Many of the conditions in which technology is required to adapt cannot be anticipated during its design stage, thus creating a challenge for the designer. Inspired by the study of a range of biological systems, we propose that degeneracy-the realization of multiple, functionally versatile components with contextually overlapping functional redundancy-will support adaptation in technologies, because it effects pervasive flexibility, evolutionary innovation, and homeostatic robustness. We provide examples of degeneracy in a number of rudimentary living technologies, from military sociotechnical systems to swarm robotics, and we present design principles-including shared protocols, loose regulatory coupling, and functional versatility-that allow degeneracy to arise in both biological and man-made systems. PMID:23834594
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.
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. PMID:26086581
Degeneracy of energy levels of pseudo-Gaussian oscillators
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.
The simplicity of perfect atoms: Degeneracies in supersymmetric hydrogen
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.
The simplicity of perfect atoms: Degeneracies in supersymmetric hydrogen
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.
Quantification of degeneracy in Hodgkin-Huxley neurons on Newman-Watts small world network.
Man, Menghua; Zhang, Ya; Ma, Guilei; Friston, Karl; Liu, Shanghe
2016-08-01
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. PMID:27155043
Asfin, Ruslan E; Melikova, Sona M; Domanskaya, Alexandra V; Rodziewicz, Paweł; Rutkowski, Konstantin S
2016-05-26
The FTIR spectra of fluoroform trapped in argon and nitrogen matrixes are studied at T ∼ 10-30 K. The bands of E symmetry show the splitting effect in a nitrogen matrix, which is absent in an argon matrix. The effect is the most prominent in the case of the ν4 CH bending vibration. It decreases slightly with increasing temperature. Both static and Car-Parrinello molecular dynamic simulations suggest that the degeneracy lifting is due to C3v symmetry lowering caused by interactions between fluoroform and all neighbor N2 matrix molecules. PMID:27149085
Gap solitons in superfluid boson-fermion mixtures
Adhikari, Sadhan K.; Malomed, Boris A.
2007-10-15
Using coupled equations for the bosonic and fermionic order parameters, we construct families of gap solitons (GSs) in a nearly one-dimensional Bose-Fermi mixture trapped in a periodic optical-lattice (OL) potential, the boson and fermion components being in the states of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer superfluid, respectively. Fundamental GSs are compact states trapped, essentially, in a single cell of the lattice. Full families of such solutions are constructed in the first two band gaps of the OL-induced spectrum, by means of variational and numerical methods, which are found to be in good agreement. The families include both intragap and intergap solitons, with the chemical potentials of the boson and fermion components falling in the same or different band gaps, respectively. Nonfundamental states, extended over several lattice cells, are constructed too. The GSs are stable against strong perturbations.
NASA Astrophysics Data System (ADS)
Xu, Lin; Wang, Hai-Xiao; Xu, Ya-Dong; Chen, Huan-Yang; Jiang, Jian-Hua
2016-08-01
A simple core-shell two-dimensional photonic crystal is studied where the triangle lattice symmetry and $C_{6v}$ rotation symmetry leads to rich physics in the study of accidental degeneracy's in photonic bands. We systematically evaluate different types of accidental nodal points, depending on the dispersions around them and their topological properties, when the geometry and permittivity are continuously changed. These accidental nodal points can be the critical states lying between a topological phase and a normal phase and are thus important for the study of topological photonic states. In time-reversal systems, this leads to the photonic quantum spin Hall insulator where the spin is defined upon the orbital angular momentum for transverse-magnetic polarization. We study the topological phase transition as well as the properties of the edge and bulk states and their application potentials in optics.
Semiclassical degeneracies and ordering for highly frustrated magnets in a field
NASA Astrophysics Data System (ADS)
Hassan, S. R.; Moessner, R.
2006-03-01
We discuss ground-state selection by quantum fluctuations in frustrated magnets in a strong magnetic field. We show that there exist dynamical symmetries—one a generalization of Henley’s gauge like symmetry for collinear spins, the other the quantum relict of non collinear weathervane modes—which ensure a partial survival of the classical degeneracies. We illustrate these for the case of the kagome magnet, where we find zero-point energy differences to be rather small everywhere except near the collinear “up-up-down” configurations, where there is rotational but not translational symmetry breaking. In the effective Hamiltonian, we demonstrate the presence of a term sensitive to a topological “flux.” We discuss the connection of such problems to gauge theories by casting the frustrated lattices as medial lattices of appropriately chosen simplex lattices, and in particular we show how the magnetic field can be used to tune the physical sector of the resulting gauge theories.
Breaking the Symmetry in Molecular Nanorings
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
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.
Breaking the Symmetry in Molecular Nanorings.
Gong, Juliane Q; Favereau, Ludovic; Anderson, Harry L; Herz, Laura M
2016-01-21
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
Oscillation degeneracy in non-standard neutrino interactions
NASA Astrophysics Data System (ADS)
Wright, Warren
2016-06-01
The standard theory describing neutrino oscillations only uses the interactions predicted by the Standard Model of particle physics. However, there is plenty of room for non-standard interactions (NSI) to exist. This is because extra interactions are allowed by experimental error bars and even expected at some level from effective theory arguments. This research is focused on examining the phenomenological consequences of the new physics of NSI at large atmospheric neutrino detectors like IceCube DeepCore. Of particular focus are the degeneracies between and within the standard neutrino oscillation parameters and the NSI parameters. These degeneracies will be explored both analytically and numerically, and strategies to lift them will also be discussed. This research is largely based on [1].
Topological entanglement entropy, ground state degeneracy and holography
NASA Astrophysics Data System (ADS)
Parnachev, Andrei; Poovuttikul, Napat
2015-10-01
Topological entanglement entropy, a measure of the long-ranged entanglement, is related to the degeneracy of the ground state on a higher genus surface. The exact relation depends on the details of the topological theory. We consider a class of holographic models where such relation might be similar to the one exhibited by Chern-Simons theory in a certain large N limit. Both the non-vanishing topological entanglement entropy and the ground state degeneracy in these holographic models are consequences of the topological Gauss-Bonnet term in the dual gravitational description. A soft wall holographic model of confinement is used to generate finite correlation length but keep the disk topology of the entangling surface in the bulk, necessary for nonvanishing topological entanglement entropy.
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
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…
Chiral symmetry in rotating systems
NASA Astrophysics Data System (ADS)
Malik, Sham S.
2015-08-01
The triaxial rotating system at critical angular momentum I ≥Iband exhibits two enatiomeric (the left- and right-handed) forms. These enatiomers are related to each other through dynamical chiral symmetry. The chiral symmetry in rotating system is defined by an operator χ ˆ =Rˆy (π) T ˆ, which involves the product of two distinct symmetries, namely, continuous and discrete. Therefore, new guidelines are required for testing its commutation with the system Hamiltonian. One of the primary objectives of this study is to lay down these guidelines. Further, the possible impact of chiral symmetry on the geometrical arrangement of angular momentum vectors and investigation of observables unique to nuclear chiral-twins is carried out. In our model, the angular momentum components (J1, J2, J3) occupy three mutually perpendicular axes of triaxial shape and represent a non-planar configuration. At certain threshold energy, the equation of motion in angular momentum develops a second order phase transition and as a result two distinct frames (i.e., the left- and right-handed) are formed. These left- and right-handed states correspond to a double well system and are related to each other through chiral operator. At this critical angular momentum, the centrifugal and Coriolis interactions lower the barrier in the double well system. The tunneling through the double well starts, which subsequently lifts the degeneracy among the rotational states. A detailed analysis of the behavior of rotational energies, spin-staggering, and the electromagnetic transition probabilities of the resulting twin-rotational bands is presented. The ensuing model results exhibit similarities with many observed features of the chiral-twins. An advantage of our formalism is that it is quite simple and it allows us to pinpoint the understanding of physical phenomenon which lead to chiral-twins in rotating systems.
Ultra-broad bandwidth parametric amplification at degeneracy.
Limpert, J; Aguergaray, C; Montant, S; Manek-Hönninger, I; Petit, S; Descamps, D; Cormier, E; Salin, F
2005-09-19
We report on a novel approach of ultra-broad bandwidth parametric amplification around degeneracy. A bandwidth of up to 400 nm centered around 800 nm is amplified in a BBO crystal by using chirped pump pulses with a bandwitdth as broad as 10 nm. A supercontinuum signal is generated in a microstructured fiber, having to first order a quadratic chirp, which is necessary to ensure temporal overlap of the interacting waves over this broad bandwidth. Furthermore, we discuss the potential of this approach for an octave-spanning parametric amplification. PMID:19498762
Large and exact quantum degeneracy in a skyrmion magnet
NASA Astrophysics Data System (ADS)
Douçot, B.; Kovrizhin, D. L.; Moessner, R.
2016-03-01
We identify a large family of ground states of a topological C PN -1 skyrmion magnet whose classical degeneracy persists to all orders in a semiclassical expansion. This goes along with an exceptional robustness of the concomitant ground-state configurations, which are not at all dressed by quantum fluctuations. We trace these twin observations back to a common root: this class of topological ground states saturates a Bogomolny inequality. A similar phenomenology occurs in high-energy physics for some field theories exhibiting supersymmetry. We propose quantum Hall ferromagnets, where these skyrmions configurations arise naturally as ground states away from integer filling, as the best available laboratory realisations.
Degeneracy allows for both apparent homogeneity and diversification in populations
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
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.
Absence of Hole Confinement in Transition Metal Oxides with Orbital Degeneracy
NASA Astrophysics Data System (ADS)
Daghofer, Maria; Wohlfeld, Krzysztof; Oles, Andrzej M.; Arrigoni, Enrico; Horsch, Peter
2008-03-01
The compounds with orbital degrees of freedom exhibit many possible scenarios for hole propagation which in most cases lead to hole localization [1]. Here we investigate the spectral properties of a hole moving in a two-dimensional Hubbard model for strongly correlated t2g electrons. Although superexchange interactions are Ising-like, a quasi-one-dimensional coherent hole motion arises due to effective three-site terms. This mechanism is fundamentally different either from the hole motion via quantum fluctuations in the conventional spin model with SU(2) symmetry or from the eg orbital model [2]. The present orbital model describes also propagation of a hole in some eg compounds [3], and we argue that orbital degeneracy alone does not lead to hole self-localization. [1] J. Zaanen and A.M. Ole's, Phys. Rev. B 48, 7197 (1993). [2] J. van den Brink, P. Horsch, and A.M. Ole's, Phys. Rev. Lett. 85, 5174 (2000). [3] M. Daghofer, A.M. Ole's, and W. von der Linden, Phys. Rev. B 70, 184430 (2004).
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.
None
2011-10-06
- 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 ?massless? modes
Non-Hermitian Hamiltonians with unitary and antiunitary symmetries
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.
Epigenomics and the concept of degeneracy in biological systems
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
One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries. II. N Particles
NASA Astrophysics Data System (ADS)
Harshman, N. L.
2016-01-01
This is the second in a pair of articles that classify the configuration space and kinematic symmetry groups for N identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions. These symmetries explain degeneracies in the few-body spectrum and demonstrate how tuning the trap shape and the particle interactions can manipulate these degeneracies. The additional symmetries that emerge in the non-interacting limit and in the unitary limit of an infinitely strong contact interaction are sufficient to algebraically solve for the spectrum and degeneracy in terms of the one-particle observables. Symmetry also determines the degree to which the algebraic expressions for energy level shifts by weak interactions or nearly-unitary interactions are universal, i.e. independent of trap shape and details of the interaction. Identical fermions and bosons with and without spin are considered. This article analyzes the symmetries of N particles in asymmetric, symmetric, and harmonic traps; the prequel article treats the one, two and three particle cases.
NASA Astrophysics Data System (ADS)
Venderbos, J. W. F.
2016-03-01
In this work we introduce a symmetry classification for electronic density waves which break translational symmetry due to commensurate wave-vector modulations. The symmetry classification builds on the concept of extended point groups: symmetry groups which contain, in addition to the lattice point group, translations that do not map the enlarged unit cell of the density wave to itself, and become "nonsymmorphic"-like elements. Multidimensional representations of the extended point group are associated with degenerate wave vectors. Electronic properties such as (nodal) band degeneracies and topological character can be straightforwardly addressed, and often follow directly. To further flesh out the idea of symmetry, the classification is constructed so as to manifestly distinguish time-reversal invariant charge (i.e., site and bond) order, and time-reversal breaking flux order. For the purpose of this work, we particularize to spin-rotation invariant density waves. As a first example of the application of the classification we consider the density waves of a simple single- and two-orbital square lattice model. The main objective, however, is to apply the classification to two-dimensional (2D) hexagonal lattices, specifically the triangular and the honeycomb lattices. The multicomponent density waves corresponding to the commensurate M -point ordering vectors are worked out in detail. To show that our results generally apply to 2 D hexagonal lattices, we develop a general low-energy SU(3 ) theory of (spinless) saddle-point electrons.
Henley, E.M.
1981-09-01
Internal and space-time symmetries are discussed in this group of lectures. The first of the lectures deals with an internal symmetry, or rather two related symmetries called charge independence and charge symmetry. The next two discuss space-time symmetries which also hold approximately, but are broken only by the weak forces; that is, these symmetries hold for both the hadronic and electromagnetic forces. (GHT)
Symmetry for the nonadiabatic transition in Floquet states
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.
CMB power spectrum parameter degeneracies in the era of precision cosmology
Howlett, Cullan; Lewis, Antony; Hall, Alex; Challinor, Anthony E-mail: antony@cosmologist.info E-mail: adc1000@ast.cam.ac.uk
2012-04-01
Cosmological parameter constraints from the CMB power spectra alone suffer several well-known degeneracies. These degeneracies can be broken by numerical artefacts and also a variety of physical effects that become quantitatively important with high-accuracy data e.g. from the Planck satellite. We study degeneracies in models with flat and non-flat spatial sections, non-trivial dark energy and massive neutrinos, and investigate the importance of various physical degeneracy-breaking effects. We test the CAMB power spectrum code for numerical accuracy, and demonstrate that the numerical calculations are accurate enough for degeneracies to be broken mainly by true physical effects (the integrated Sachs-Wolfe effect, CMB lensing and geometrical and other effects through recombination) rather than numerical artefacts. We quantify the impact of CMB lensing on the power spectra, which inevitably provides degeneracy-breaking information even without using information in the non-Gaussianity. Finally we check the numerical accuracy of sample-based parameter constraints using CAMB and COSMOMC. In an appendix we document recent changes to CAMB's numerical treatment of massive neutrino perturbations, which are tested along with other recent improvements by our degeneracy exploration results.
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.
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.
Pseudospin symmetry in nuclear structure and its supersymmetric representation
NASA Astrophysics Data System (ADS)
Liang, H. Z.
2016-08-01
The quasi-degeneracy between the single-particle states (n,l,j=l+1/2) and (n-1,l+2,j=l+3/2) indicates a special and hidden symmetry in atomic nuclei—the so-called pseudospin symmetry (PSS)—which is an important concept in both spherical and deformed nuclei. A number of phenomena in nuclear structure have been successfully interpreted directly or implicitly by this symmetry, including nuclear superdeformed configurations, identical bands, quantized alignment, pseudospin partner bands, and so on. Since the PSS was recognized as a relativistic symmetry in 1990s, there have been comprehensive efforts to understand its properties in various systems and potentials. In this review, we mainly focus on the latest progress on the supersymmetric (SUSY) representation of PSS, and one of the key targets is to understand its symmetry-breaking mechanism in realistic nuclei in a quantitative and perturbative way. The SUSY quantum mechanics and its applications to the SU(2) and U(3) symmetries of the Dirac Hamiltonian are discussed in detail. It is shown that the origin of PSS and its symmetry-breaking mechanism, which are deeply hidden in the origin Hamiltonian, can be traced by its SUSY partner Hamiltonian. Essential open questions, such as the SUSY representation of PSS in the deformed system, are pointed out.
NASA Astrophysics Data System (ADS)
Tallents, G. J.
2016-09-01
Collisional-radiative models enable average ionization and ionization populations, plus the rates of absorption and emission of radiation to be calculated for plasmas not in thermal equilbrium. At high densities and low temperatures, electrons may have a high occupancy of the free electron quantum states and evaluations of rate coefficients need to take into account the free electron degeneracy. We demonstrate that electron degeneracy can reduce collisional rate coefficients by orders-of-magnitude from values calculated neglecting degeneracy. We show that assumptions regarding the collisional differential cross-section can alter collisional ionization and recombination rate coefficients by a further factor two under conditions relevant to inertial fusion.
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
Dynamic symmetries and quantum nonadiabatic transitions
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
Quantum degeneracy corrections to plasma line emission and to Saha equation
NASA Astrophysics Data System (ADS)
Molinari, V. G.; Mostacci, D.; Rocchi, F.; Sumini, M.
2003-09-01
The effect of quantum degeneracy on the electron collisional excitation is investigated, and its effects on line emission evaluated for applications to spectroscopy of dense, cold plasmas. A correction to Saha equation for weakly-degenerate plasmas is also presented.
Degeneracy between mass and spin in black-hole-binary waveforms
NASA Astrophysics Data System (ADS)
Baird, Emily; Fairhurst, Stephen; Hannam, Mark; Murphy, Patricia
2013-01-01
We explore the degeneracy between mass and spin in gravitational waveforms emitted by black-hole-binary coalescences. We focus on spin-aligned waveforms and obtain our results using phenomenological models that were tuned to numerical-relativity simulations. A degeneracy is known for low-mass binaries (particularly neutron-star binaries), where gravitational-wave detectors are sensitive to only the inspiral phase, and the waveform can be modeled by post-Newtonian theory. Here, we consider black-hole binaries, where detectors will also be sensitive to the merger and ringdown, and demonstrate that the degeneracy persists across a broad mass range. At low masses, the degeneracy is between mass ratio and the black-hole spins, with chirp mass accurately determined. At higher masses, the degeneracy persists but is not so clearly characterized by constant chirp mass as the merger and ringdown become more significant. We consider the importance of this degeneracy both for performing searches (including searches where only nonspinning templates are used) and in parameter extraction from observed systems. We compare observational capabilities between the early (˜2015) and final (2018 onwards) versions of the Advanced LIGO detector.
The effect of degeneracy parameter on Weibel instability in dense plasma
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.
Hypersensitive Transport in Photonic Crystals with Accidental Spatial Degeneracies
Makri, Eleana; Smith, Kyle; Chabanov, Andrey; Vitebskiy, Ilya; Kottos, Tsampikos
2016-01-01
A localized mode in a photonic layered structure can develop nodal points (nodal planes), where the oscillating electric field is negligible. Placing a thin metallic layer at such a nodal point results in the phenomenon of induced transmission. Here we demonstrate that if the nodal point is not a point of symmetry, then even a tiny alteration of the permittivity in the vicinity of the metallic layer drastically suppresses the localized mode along with the resonant transmission. This renders the layered structure highly reflective within a broad frequency range. Applications of this hypersensitive transport for optical and microwave limiting and switching are discussed. PMID:26903232
Hypersensitive Transport in Photonic Crystals with Accidental Spatial Degeneracies
NASA Astrophysics Data System (ADS)
Makri, Eleana; Smith, Kyle; Chabanov, Andrey; Vitebskiy, Ilya; Kottos, Tsampikos
2016-02-01
A localized mode in a photonic layered structure can develop nodal points (nodal planes), where the oscillating electric field is negligible. Placing a thin metallic layer at such a nodal point results in the phenomenon of induced transmission. Here we demonstrate that if the nodal point is not a point of symmetry, then even a tiny alteration of the permittivity in the vicinity of the metallic layer drastically suppresses the localized mode along with the resonant transmission. This renders the layered structure highly reflective within a broad frequency range. Applications of this hypersensitive transport for optical and microwave limiting and switching are discussed.
Hypersensitive Transport in Photonic Crystals with Accidental Spatial Degeneracies.
Makri, Eleana; Smith, Kyle; Chabanov, Andrey; Vitebskiy, Ilya; Kottos, Tsampikos
2016-01-01
A localized mode in a photonic layered structure can develop nodal points (nodal planes), where the oscillating electric field is negligible. Placing a thin metallic layer at such a nodal point results in the phenomenon of induced transmission. Here we demonstrate that if the nodal point is not a point of symmetry, then even a tiny alteration of the permittivity in the vicinity of the metallic layer drastically suppresses the localized mode along with the resonant transmission. This renders the layered structure highly reflective within a broad frequency range. Applications of this hypersensitive transport for optical and microwave limiting and switching are discussed. PMID:26903232
Chemical potential and reaction electronic flux in symmetry controlled reactions.
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. PMID:27237470
Schultz, Benjamin A; Damasceno, Pablo F; Engel, Michael; Glotzer, Sharon C
2015-03-24
The relationship between colloidal building blocks and their assemblies is an active field of research. As a strategy for targeting novel crystal structures, we examine the use of Voronoi particles, which are hard, space-filling particles in the shape of Voronoi cells of a target structure. Although Voronoi particles stabilize their target structure in the limit of high pressure by construction, the thermodynamic assembly of the same structure at moderate pressure, close to the onset of crystallization, is not guaranteed. Indeed, we find that a more symmetric crystal is often preferred due to additional entropic contributions arising from configurational or occupational degeneracy. We characterize the assembly behavior of the Voronoi particles in terms of the symmetries of the building blocks as well as the symmetries of crystal structures and demonstrate how controlling the degeneracies through a modification of particle shape and field-directed assembly can significantly improve the assembly propensity. PMID:25692863
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.
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.
One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: I. One, Two, and Three Particles
NASA Astrophysics Data System (ADS)
Harshman, N. L.
2016-01-01
This is the first in a pair of articles that classify the configuration space and kinematic symmetry groups for N identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions. These symmetries explain degeneracies in the few-body spectrum and demonstrate how tuning the trap shape and the particle interactions can manipulate these degeneracies. The additional symmetries that emerge in the non-interacting limit and in the unitary limit of an infinitely strong contact interaction are sufficient to algebraically solve for the spectrum and degeneracy in terms of the one-particle observables. Symmetry also determines the degree to which the algebraic expressions for energy level shifts by weak interactions or nearly-unitary interactions are universal, i.e. independent of trap shape and details of the interaction. Identical fermions and bosons with and without spin are considered. This article sequentially analyzes the symmetries of one, two and three particles in asymmetric, symmetric, and harmonic traps; the sequel article treats the N particle case.
A new method to break the mass sheet degeneracy using aperture moments
NASA Astrophysics Data System (ADS)
Rexroth, Markus; Natarajan, Priyamvada; Kneib, Jean-Paul
2016-04-01
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 the ambiguity that arises due to the fact that the addition of a constant surface mass density sheet does not alter the lensing observables. 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 n-th 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 SIS and NFW 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.
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.
Geometric intrinsic symmetries
Gozdz, A. Szulerecka, A.; Pedrak, A.
2013-08-15
The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.
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.
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.
Theory of a fermionic superfluid with SU(2) x SU(6) symmetry
Yip, S.-K.
2011-06-15
We study theoretically interspecies Cooper pairing in a fermionic system with SU(2) x SU(6) symmetry. We show that, with suitable unitary transformations, the order parameter for the ground state can be reduced to only two nonvanishing complex components. The ground state has a large degeneracy. We find that while some Goldstone modes have linear dispersion, others are quadratic at low frequencies. We compare our results with the case of SU(N).
Neutrinos and flavor symmetries
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.
Riazuddin
2010-05-01
The degenerate leptogenesis is studied when the degeneracy in two of the heavy right-handed neutrinos [the third one is irrelevant if {mu}-{tau} symmetry is assumed] is due to L{identical_to}(L{sub e}-L{sub {mu}-}L{sub {tau}}) discrete symmetry. It is shown that a sizable leptogenesis asymmetry ({epsilon}{>=}10{sup -6}) is possible. The level of degeneracy required also predicts the Majorana phase needed for the asymmetry and this prediction is testable since it is the same phase, which appears in the double {beta} decay. Implications of nonzero reactor angle {theta}{sub 13} are discussed. It is shown that the contribution from sin{sup 2{theta}}{sub 13} to the leptogenesis asymmetry parameter may even dominate. An accurate measurement of sin{sup 2{theta}}{sub 13} would have important implications for the mass degeneracy of heavy right-handed neutrinos.
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…
Chiral symmetry and chiral-symmetry breaking
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)
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.
Degeneracy in NLP and the development of results motivated by its presence
Fiacco, A.; Liu, J.
1994-12-31
We study notions of nondegeneracy and several levels of increasing degeneracy from the perspective of the local behavior of a local solution of a nonlinear program when problem parameters are slightly perturbed. This overview may be viewed as a structured survey of sensitivity and stability results: the focus is on progressive levels of degeneracy. We note connections of nondegeneracy with the convergence of algorithms and observe the striking parallel between the effects of nondegeneracy and degeneracy on optimality conditions, stability analysis and algorithmic convergence behavior. Although our orientation here is primarily interpretive and noncritical, we conclude that more effort is needed to unify optimality, stability and convergence theory and more results are needed in all three areas for radically degenerate problems.
Taraban, Marc B; Hyland, Laura L; Yu, Y Bruce
2013-09-01
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. PMID:23879188
CP violation effects on the neutrino degeneracy parameters in the Early Universe
NASA Astrophysics Data System (ADS)
Gava, Jérôme; Volpe, Cristina
2010-09-01
We explore possible CP violating effects, coming from the Dirac phase of the Maki-Nakagawa-Sakata-Pontecorvo matrix, on the neutrino degeneracy parameters, at the epoch of Big-Bang nucleosynthesis. We first demonstrate the conditions under which such effects can arise. In particular it requires that the initial muon and tau neutrino degeneracy parameters ξ differ. Then we solve numerically the kinetic equations for the three flavor neutrino density matrix with the goal of quantifying the impact of the Dirac phase on the electron neutrino degeneracy parameter ξν_e. The calculations include the vacuum term, the coupling to matter, the νν interaction and the collisions. Effects on ξν_e up to almost 1% and on Y of about 0.1% are found, depending on the initial conditions.
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.
Sekhar Chivukula
2010-01-08
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.
Gray, J E; Vogt, A
1997-01-01
Is symmetry informative? The answer is both yes and no. We examine what information and symmetry are and how they are related. Our approach is primarily mathematical, not because mathematics provides the final word, but because it provides an insightful and relatively precise starting point. Information theory treats transformations that messages undergo from source to destination. Symmetries are information that leave some property of interest unchanged. In this respect the studies of information and symmetry can both be regarded as a Quest for the identity transformation. PMID:9224554
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.
Tunable Splitting of the Ground-State Degeneracy in Quasi-One-Dimensional Parafermion Systems
NASA Astrophysics Data System (ADS)
Chen, Chun; Burnell, F. J.
2016-03-01
Systems with topologically protected ground-state degeneracies are currently of great interest due to their potential applications in quantum computing. In practice, this degeneracy is never exact, and the magnitude of the ground-state degeneracy splitting imposes constraints on the time scales over which information is topologically protected. In this Letter, we use an instanton approach to evaluate the splitting of topological ground-state degeneracy in quasi-1D systems with parafermion zero modes, in the specific case where parafermions are realized by inducing a superconducting gap in pairs of fractional quantum Hall edges. We show that, like 1D topological superconducting wires, this splitting has an oscillatory dependence on the chemical potential, which arises from an intrinsic Berry phase that produces interference between distinct instanton tunneling events. These Berry phases can be mapped to chiral phases in a (dual) quantum clock model using a Fradkin-Kadanoff transformation. Comparing our low-energy spectrum to that of phenomenological parafermion models allows us to evaluate the real and imaginary parts of the hopping integral between adjacent parafermionic zero modes as functions of the chemical potential.
Tunable Splitting of the Ground-State Degeneracy in Quasi-One-Dimensional Parafermion Systems.
Chen, Chun; Burnell, F J
2016-03-11
Systems with topologically protected ground-state degeneracies are currently of great interest due to their potential applications in quantum computing. In practice, this degeneracy is never exact, and the magnitude of the ground-state degeneracy splitting imposes constraints on the time scales over which information is topologically protected. In this Letter, we use an instanton approach to evaluate the splitting of topological ground-state degeneracy in quasi-1D systems with parafermion zero modes, in the specific case where parafermions are realized by inducing a superconducting gap in pairs of fractional quantum Hall edges. We show that, like 1D topological superconducting wires, this splitting has an oscillatory dependence on the chemical potential, which arises from an intrinsic Berry phase that produces interference between distinct instanton tunneling events. These Berry phases can be mapped to chiral phases in a (dual) quantum clock model using a Fradkin-Kadanoff transformation. Comparing our low-energy spectrum to that of phenomenological parafermion models allows us to evaluate the real and imaginary parts of the hopping integral between adjacent parafermionic zero modes as functions of the chemical potential. PMID:27015499
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…
Symmetries of Spectral Problems
NASA Astrophysics Data System (ADS)
Shabat, A.
Deriving abelian KdV and NLS hierarchies, we describe non-abelian symmetries and "pre-Lax" elementary approach to Lax pairs. Discrete symmetries of spectral problems are considered in Sect. 4.2. Here we prove Darboux classical theorem and discuss a modern theory of dressing chains.
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.
Symmetry-protected topological photonic crystal in three dimensions
NASA Astrophysics Data System (ADS)
Lu, Ling; Fang, Chen; Fu, Liang; Johnson, Steven G.; Joannopoulos, John D.; Soljačić, Marin
2016-04-01
Topology of electron wavefunctions was first introduced to characterize the quantum Hall states in two dimensions discovered in 1980 (ref. ). Over the past decade, it has been recognized that symmetry plays a crucial role in the classification of topological phases, leading to the broad notion of symmetry-protected topological phases. As a primary example, topological insulators are distinguished from normal insulators in the presence of time-reversal symmetry (). A three-dimensional (3D) topological insulator exhibits an odd number of protected surface Dirac cones, a unique property that cannot be realized in any 2D systems. Importantly, the existence of topological insulators requires Kramers’ degeneracy in spin-orbit coupled electronic materials; this forbids any direct analogue in boson systems. In this report, we discover a 3D topological photonic crystal phase hosting a single surface Dirac cone, which is protected by a crystal symmetry--the nonsymmorphic glide reflection rather than . Such a gapless surface state is fully robust against random disorder of any type. This bosonic topological band structure is achieved by applying alternating magnetization to gap out the 3D `generalized Dirac points’ discovered in the bulk of our crystal. The Z2 bulk invariant is characterized through the evolution of Wannier centres. Our proposal--readily realizable using ferrimagnetic materials at microwave frequencies--expands the scope of 3D topological materials from fermions to bosons.
Hidden conformal symmetry of the Kerr black hole
Castro, Alejandra; Maloney, Alexander; Strominger, Andrew
2010-07-15
Extreme and very-near-extreme spin J Kerr black holes have been conjectured to be holographically dual to two-dimensional (2D) conformal field theories (CFTs) with left and right central charges c{sub L}=c{sub R}=12J. In this paper it is observed that the 2D conformal symmetry of the scalar wave equation at low frequencies persists for generic nonextreme values of the mass M{ne}{radical}(J). Interestingly, this conformal symmetry is not derived from a conformal symmetry of the spacetime geometry except in the extreme limit. The 2{pi} periodic identification of the azimuthal angle {phi} is shown to correspond to a spontaneous breaking of the conformal symmetry by left and right temperatures T{sub L}=M{sup 2}/2{pi}J and T{sub R}={radical}(M{sup 4}-J{sup 2})/2{pi}J. The well-known low-frequency scalar-Kerr scattering amplitudes coincide with correlators of a 2D CFT at these temperatures. Moreover, the CFT microstate degeneracy inferred from the Cardy formula agrees exactly with the Bekenstein-Hawking area law for all M and J. These observations provide evidence for the conjecture that the Kerr black hole is dual to a c{sub L}=c{sub R}=12J 2D CFT at temperatures (T{sub L},T{sub R}) for every value of M and J.
Tensor network decompositions in the presence of a global symmetry
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.
Symmetry Effects in Computation
NASA Astrophysics Data System (ADS)
Yao, Andrew Chi-Chih
2008-12-01
The concept of symmetry has played a key role in the development of modern physics. For example, using symmetry, C.N. Yang and other physicists have greatly advanced our understanding of the fundamental laws of physics. Meanwhile, computer scientists have been pondering why some computational problems seem intractable, while others are easy. Just as in physics, the laws of computation sometimes can only be inferred indirectly by considerations of general principles such as symmetry. The symmetry properties of a function can indeed have a profound effect on how fast the function can be computed. In this talk, we present several elegant and surprising discoveries along this line, made by computer scientists using symmetry as their primary tool. Note from Publisher: This article contains the abstract only.
Aspects of emergent symmetries
NASA Astrophysics Data System (ADS)
Gomes, Pedro R. S.
2016-03-01
These are intended to be review notes on emergent symmetries, i.e. symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some background material and go through more recent problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. The aim is to discuss how these examples could help us to face other complex and fundamental problems.
Sequential flavor symmetry breaking
Feldmann, Thorsten; Jung, Martin; Mannel, Thomas
2009-08-01
The gauge sector of the standard model exhibits a flavor symmetry that allows for independent unitary transformations of the fermion multiplets. In the standard model the flavor symmetry is broken by the Yukawa couplings to the Higgs boson, and the resulting fermion masses and mixing angles show a pronounced hierarchy. In this work we connect the observed hierarchy to a sequence of intermediate effective theories, where the flavor symmetries are broken in a stepwise fashion by vacuum expectation values of suitably constructed spurion fields. We identify the possible scenarios in the quark sector and discuss some implications of this approach.
Exceptional point and degeneracy of the neutral Higgs boson system H-A
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.
Afferent hyperexcitability in neuropathic pain and the inconvenient truth about its degeneracy.
Ratté, Stéphanie; Prescott, Steven A
2016-02-01
Neuropathic pain, which arises from damage to the nervous system, is a major unmet clinical challenge. Reversing the neuronal hyperexcitability induced by nerve damage is a logical treatment strategy but has proven frustratingly difficult. Here, we propose a novel explanation for that difficulty. Changes in several different ion channels are individually sufficient to cause hyperexcitability in primary somatosensory neurons. Despite offering multiple drug targets, this scenario is problematic: if multiple sufficient changes are triggered by nerve injury, then no single change is necessary for hyperexcitability. This so-called degeneracy compromises therapeutic interventions because drug effects on any one ion channel can be circumvented by changes occurring in other ion channels. Overcoming degeneracy demands a more integrative approach to drug discovery. PMID:26363576
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.
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
SPIN-PRECESSION: BREAKING THE BLACK HOLE-NEUTRON STAR DEGENERACY
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.
Line Degeneracy and Strong Spin-Orbit Coupling of Light with Bulk Bianisotropic Metamaterials.
Guo, Qinghua; Gao, Wenlong; Chen, Jing; Liu, Yongmin; Zhang, Shuang
2015-08-01
Propagation of light in a medium is dictated by equifrequency surfaces (EFSs), which play a similar role as Fermi surfaces for electrons in crystals. Engineering the equifrequency surface of light through structuring a photonic medium enables superior control over light propagation that goes beyond natural materials. In this Letter, we show that a bulk metamaterial with a suitably designed bianisotropy can exhibit line degeneracy in its EFSs that consist of two ellipsoids of opposite helicity states intersecting with each other. Very interestingly, light propagating along the direction of the line degeneracy experiences strong spin-dependent photon deflection, or optical spin Hall effect, which may lead to applications in optical signal processing and spin-optical manipulations. We provide a realistic metamaterial design to show that the required bianisotropy can be readily obtained. PMID:26296131
Taraban, Marc B.; Hyland, Laura L.; Yu, Y. Bruce
2013-01-01
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 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. All these findings form a basis to design the approaches to novel biomaterials and provide additional insight on the opposite chirality of proteins and polysaccharides in biological world. PMID:23879188
Effect of valley degeneracy on spin susceptibility of a two-dimensional quantum electron liquid
Kumar, Krishan Singh, Gurvinder; Moudgil, R. K.
2014-04-24
We investigate theoretically the effect of valley degeneracy on the spin susceptibility of a two-dimensional quantum electron liquid by determining the spin-polarization dependence of the ground-state energy within the selfconsistent mean-field approximation of Singwi et al. Specifically, we have studied a two valley system as realized in the Si (100) inversion layer. In qualitative agreement with the recent quantum Monte Carlo study by Marchi et al., we find that the valley degeneracy results in suppression of spin susceptibility over the single valley case. However, the quality of agreement diminishes with increasing value of the coupling parameter r{sub s}. This indicates the limitation of mean-field theory to deal with the exchange-correlation effects in the strong coupling region. But, our results show considerable improvement over the random-phase approximation which ignores these correlations completely.
Dodging the dark matter degeneracy while determining the dynamics of dark energy
NASA Astrophysics Data System (ADS)
Busti, Vinicius C.; Clarkson, Chris
2016-05-01
One of the key issues in cosmology is to establish the nature of dark energy, and to determine whether the equation of state evolves with time. When estimating this from distance measurements there is a degeneracy with the matter density. We show that there exists a simple function of the dark energy equation of state and its first derivative which is independent of this degeneracy at all redshifts, and so is a much more robust determinant of the evolution of dark energy than just its derivative. We show that this function can be well determined at low redshift from supernovae using Gaussian Processes, and that this method is far superior to a variety of parameterisations which are also subject to priors on the matter density. This shows that parametrised models give very biased constraints on the evolution of dark energy.
NASA Astrophysics Data System (ADS)
Guo, Xiaofeng; Nandy, Ashesh
2003-02-01
Some 2-D and 3-D graphical representations of DNA sequences have been given by Gate, Nandy, Leong, Randic, and Guo et al. Based on 2-D graphical representation of DNA sequences, Raychaudhury and Nandy introduced the first-order moments of the x and y coordinates and the radius of the plot of a DNA sequence for indexing scheme and similarity measures of DNA sequences. In this Letter, based on Guo's novel 2-D graphical representation of DNA sequences of low degeneracy, we introduce the improved first-order moments of the x and y coordinates and the radius of DNA sequences, and the distance of two DNA sequences. The new descriptors of DNA sequences give a good numerical characterization of DNA sequences, which have lower degeneracy.
Molecular symmetry with quaternions.
Fritzer, H P
2001-09-01
A new and relatively simple version of the quaternion calculus is offered which is especially suitable for applications in molecular symmetry and structure. After introducing the real quaternion algebra and its classical matrix representation in the group SO(4) the relations with vectors in 3-space and the connection with the rotation group SO(3) through automorphism properties of the algebra are discussed. The correlation of the unit quaternions with both the Cayley-Klein and the Euler parameters through the group SU(2) is presented. Besides rotations the extension of quaternions to other important symmetry operations, reflections and the spatial inversion, is given. Finally, the power of the quaternion calculus for molecular symmetry problems is revealed by treating some examples applied to icosahedral symmetry. PMID:11666072
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.
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.
Dynamical symmetries for fermions
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.
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.
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.
Interaction of characteristic waves in a plasma in the case of triple degeneracy
NASA Astrophysics Data System (ADS)
Viatkin, V. M.; Novikov, V. V.
1989-06-01
The paper investigates waves transformation in an inhomogeneous magnetoplasma in regions where the three roots of the Booker quartic are equal. It is shown that an extraordinary wave incident on the interaction region splits into an ordinary wave and an extraordinary wave traveling in the same direction and a reflected ordinary wave. An ordinary wave incident on the triple-degeneracy point is completely transformed into an extraordinary wave.
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.
Red queen dynamics and the evolution of translational redundancy and degeneracy
NASA Astrophysics Data System (ADS)
Krakauer, David C.; Jansen, Vincent A. A.; Nowak, Martin
We explore adaptive theories for the diversity of protein translation based on the genetic code viewed as a primitive immune system. Immunity is acquired through a genetic mechanism of non-recognition of parasite genomes. Modifying the set of codons bound by tRNA anticodon molecules or changing the specificity of binding, reduces the replication rate of translational parasites such as viruses. Changing the binding specifity can be thought of in terms of varying degrees of redundancy an d degeneracy. Redundancy in the genetic code is commonly attributed to using a four base triplet mechanism to encode the 20 amino acids. This has been referred to as synonym redundancy. There are however at least a further two forms of redundancy associated with the code and one source of degeneracy. A first form of redundancy arises from decoding all 61 possible sense codons using fewer than 61 anticodons. Such a strategy involves reduced binding specificity. A second source of redundancy is present in the multiplicity of copies of each unique tRNA (tRNA copy redundancy). Degeneracy arises when different anticodons become associated with a single amino acid to increase specificity. Variation in these strategies across taxa ensures that the translational machinery is diverse whereas the code remains approximately constant. We construct a red queen theory for translational diversity: a theory in which host translational strategies - as defined by the degree of redundancy or degeneracy of anticodons - are const antly shifting through time to evade parasitism but where neither parasite nor host gains a systematic advantage.
Halogenated benzene radical cations and ground state degeneracy splitting by asymmetric substitution
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.
Single-centered black hole microstate degeneracies from instantons in supergravity
NASA Astrophysics Data System (ADS)
Murthy, Sameer; Reys, Valentin
2016-04-01
We obtain holographic constraints on the microscopic degeneracies of black holes by computing the exact macroscopic quantum entropy using localization, including the effects of string worldsheet instantons in the supergravity effective action. For 1/4 -BPS black holes in type II string theory on K3 × T 2, the constraints can be explicitly checked against expressions for the microscopic BPS counting functions that are known in terms of certain mock modular forms. We find that the effect of including the infinite sum over instantons in the holomorphic prepotential of the supergravity leads to a sum over Bessel functions with successively sub-leading arguments as in the Rademacher expansion of Jacobi forms — but begins to disagree with such a structure near an order where the mock modular nature becomes relevant. This leads to a systematic method to recover the polar terms of the microscopic degeneracies from the degeneracy of instantons (the Gromov-Witten invariants). We check explicitly that our formula agrees with the known microscopic answer for the first seven values of the magnetic charge invariant.
Irreversible dynamics, Onsager-Casimir symmetry, and an application to turbulence.
Ottinger, Hans Christian
2014-10-01
Irreversible contributions to the dynamics of nonequilibrium systems can be formulated in terms of dissipative, or irreversible, brackets. We discuss the structure of such irreversible brackets in view of a degeneracy implied by energy conservation, where we consider different types of symmetries of the bracket corresponding to the Onsager and Casimir symmetries of linear irreversible thermodynamics. Slip and turbulence provide important examples of antisymmetric irreversible brackets and offer guidance for the more general modeling of irreversible dynamics without entropy production. Conversely, turbulence modeling could benefit from elucidating thermodynamic structure. The examples suggest constructing antisymmetric irreversible brackets in terms of completely antisymmetric functions of three indices. Irreversible brackets without well-defined symmetry properties can arise for rare events, causing big configurational changes. PMID:25375452
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.
Chanowitz, M.S.
1990-09-01
The Higgs mechanism is reviewed in its most general form, requiring the existence of a new symmetry-breaking force and associated particles, which need not however be Higgs bosons. The first lecture reviews the essential elements of the Higgs mechanism, which suffice to establish low energy theorems for the scattering of longitudinally polarized W and Z gauge bosons. An upper bound on the scale of the symmetry-breaking physics then follows from the low energy theorems and partial wave unitarity. The second lecture reviews particular models, with and without Higgs bosons, paying special attention to how the general features discussed in lecture 1 are realized in each model. The third lecture focuses on the experimental signals of strong WW scattering that can be observed at the SSC above 1 TeV in the WW subenergy, which will allow direct measurement of the strength of the symmetry-breaking force. 52 refs., 10 figs.
Co-symmetry breakdown in problems of thermal convection in porous medium
NASA Astrophysics Data System (ADS)
Bratsun, Dmitry A.; Lyubimov, Dmitry V.; Roux, Bernard
We investigate two-dimensional thermal convection of saturating incompressible fluid in a horizontal cylinder filled with porous medium. The temperature distribution on the boundaries is time-independent and corresponds to the heating from below. At supercritical parameter values the problem has infinite number of stationary solutions for arbitrary shape of the region. This degeneracy is connected with the so-called co-symmetry property: the existence of the vector field which is orthogonal to the considered one. Non-coincidence of zeroes of these two fields leads generally speaking, to the degeneracy of the solutions. To destroy the degeneracy we add weak fluid seeping of the fluid through the boundaries either in vertical or in the horizontal direction. The breakdown of the family of the stationary solutions at high supercritical values of the Rayleigh number is studied in detail with the help of the corresponding normal form. Several limit cycles with the twisted leading manifolds appear as a result of the family destruction. To investigate the dynamical behavior the finite-dimensional models of the convection which maintain the breakdown of co-symmetry, are constructed on the base of the Galerkin approximation. The same scenario of the transition to chaos which seems to be connected with the co-symmetry breakdown, is recovered for both kinds of seeping. The quasi-periodic solution branches from the limit cycle. The further increase of the Peclet number leads to mode-locking, which is followed by the appearance of the homoclinic surface formed by the unstable manifold of the saddle periodic orbit; destruction of the latter surface leaves in the phase space the object with torus-like shape and non-integer fractal dimension.
NASA Astrophysics Data System (ADS)
Ismael, Jenann Tareq
1997-04-01
Structures of many different sorts arise in physics, e.g., the concrete structures of material bodies, the structure exemplified by the spatiotemporal configuration of a set of bodies, the structures of more abstract objects like states, state-spaces, laws, and so on. To each structure of any of these types there corresponds a set of transformations which map it onto itself. These are its symmetries. Increasingly ubiquitous in theoretical discussions in physics, the notion of symmetry is also at the root of some time-worn philosophical debates. This dissertation consists of a set of essays on topics drawn from places where the two fields overlap. The first essay is an informal introduction to the mathematical study of symmetry. The second essay defends a famous principle of Pierre Curie which states that the symmetries of a cause are always symmetries of its effect. The third essay takes up the case of reflection in space in the context of a controversy stemming from one of Kant's early arguments for the substantivality of space. The fourth essay is a discussion of the general conditions under which an asymmetry in a phenomenon suggests an asymmetry in the laws which govern it. The case of reflection in time-specifically, the theoretical strategy used in statistical mechanics to subsume the time-asymmetric phenomena of Thermodynamics under the time-symmetric classical dynamical laws-is used to illustrate the general points. The philosophical heart of the thesis lies in its fifth essay. Here a somewhat novel way of conceiving scientific theorizing is articulated, one suggested by the abstract mathematical perspective of symmetry.
NASA Astrophysics Data System (ADS)
de Vega, H. J.; Medrano, M. Ramon; Sanchez, N.
1992-07-01
We investigate the physical implications and particle content of superstring scattering in the supergravity shock-wave background recently found by us. The amplitudes for the different particle transmutation processes taking place in this geometry are explicitly computed for Gree-Schwarz superstring, including the new phenomena of fermion to boson and boson to fermion transmutations. Transition amplitudes among the ground states, first and second excited states are obtained. Particularly interesting are the amplitudes within the massless particle sector, which lead to physical massive particles upon supersymmetry breaking at low energies.
Beyond-mean-field boson-fermion model for odd-mass nuclei
NASA Astrophysics Data System (ADS)
Nomura, K.; Nikšić, T.; Vretenar, D.
2016-05-01
A novel method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is introduced, based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the even-even core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained in a self-consistent mean-field calculation determined by the choice of the energy density functional and pairing interaction. This method uniquely determines the parameters of the Hamiltonian of the boson core, and only the strength of the particle-core coupling is specifically adjusted to selected data for a particular nucleus. The approach is illustrated in a systematic study of low-energy excitation spectra and transition rates of axially deformed odd-mass Eu isotopes.
Boson-fermion representations of Lie superalgebras: The example of osp(1,2)
NASA Astrophysics Data System (ADS)
Blank, Jiří; Havlíček, Miloslav; Exner, Pavel; Lassner, Wolfgang
1982-03-01
A method for constructing infinite-dimensional representations of Lie superalgebras employing boson representations of their Lie subalgebras is outlined. As an example the osp(1,2) superalgebra is considered; explicit formulae for its generators in terms of one pair of boson operators, at most one pair of fermion ones, and at most one parameter are obtained, the Casimir operator being represented by a multiple of unity. The restriction of these representations to the real form of osp(1,2) is skew-symmetric in the even part and can be regarded as a natural generalization of skew-symmetric representations of real Lie algebras. Some other aspects of the presented construction are discussed.
NASA Astrophysics Data System (ADS)
West, Carl T.; Kottos, Tsampikos; Prosen, Tomaz
2010-03-01
We study a new class of chaotic systems with dynamical localization, where gain/loss processes break the hermiticity, while allowing for parity-time PT symmetry. For a value γPT of the gain/loss parameter the spectrum undergoes a spontaneous phase transition from real (exact phase) to complex values (broken phase). We develop a one parameter scaling theory for γPT, and show that chaos assists the exact PT-phase. Our results will have applications to the design of optical elements with PT-symmetry.
NASA Astrophysics Data System (ADS)
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Weakly broken galileon symmetry
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.
NASA Astrophysics Data System (ADS)
Moore, Gregory
The vanishing of the one-loop string cosmological constant in nontrivial non supersymmetric backgrounds can be understood by viewing the path integral as an inner product of orthogonal wave functions. For special backgrounds the string theory has an extra symmetry, expressed as a transformation on moduli space. When left- and right-moving wave functions transform in different representations of this symmetry the cosmological constant must vanish. Specific examples of the mechanism are given at one loop for theories in two and four dimensions. Various suggestions are made for the higher loop extension of this idea.
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
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.
Dilatation symmetry in higher dimensions and the vanishing of the cosmological constant.
Wetterich, C
2009-04-10
A wide class of dilatation symmetric effective actions in higher dimensions leads to a vanishing four-dimensional cosmological constant. This requires no tuning of parameters and results from the absence of an allowed potential for the scalar dilaton field. The field equations admit many solutions with flat four-dimensional space and nonvanishing gauge couplings. In a more general setting, these are candidates for asymptotic states of cosmological runaway solutions, where dilatation symmetry is realized dynamically if a fixed point is approached as time goes to infinity. Dilatation anomalies during the runaway can lift the degeneracy of solutions and lead to an observable dynamical dark energy. PMID:19392424
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.
Vakoc, B J; Yun, S H; Tearney, G J; Bouma, B E
2006-02-01
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
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.
A novel 2-D graphical representation of DNA sequences of low degeneracy
NASA Astrophysics Data System (ADS)
Guo, Xiaofeng; Randic, Milan; Basak, Subhash C.
2001-12-01
Some 2-D and 3-D graphical representations of DNA sequences have been given by Nandy, Leong and Mogenthaler, and Randic et al., which give visual characterizations of DNA sequences. In this Letter, we introduce a novel graphical representation of DNA sequences by taking four special vectors in 2-D space to represent the four nucleic acid bases in DNA sequences, so that a DNA sequence is denoted on a plane by a successive vector sequence, which is also a directed walk on the plane. It is showed that the novel graphical representation of DNA sequences has lower degeneracy and less overlapping.
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.
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)
Introduction to chiral symmetry
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.
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.
ERIC Educational Resources Information Center
McGehe, Carol
1991-01-01
Presents math activities, problems, and games for teaching elementary students to recognize the world's natural symmetry and understand the mathematical qualities it represents; suggests activities with construction paper, blocks, and calculators. Instructions for using the calculator to create palindromes are included. (SM)
Gauging without initial symmetry
NASA Astrophysics Data System (ADS)
Kotov, Alexei; Strobl, Thomas
2016-01-01
The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Σ, the original functional is extended appropriately by additional Lie(G) -valued 1-form gauge fields so as to lift the symmetry to Maps(Σ , G) . Physically relevant quantities are then to be obtained as the quotient of the solutions to the Euler-Lagrange equations by these gauge symmetries. In this article we show that one can construct a gauge theory for a standard sigma model in arbitrary space-time dimensions where the target metric is not invariant with respect to any rigid symmetry group, but satisfies a much weaker condition: It is sufficient to find a collection of vector fields va on the target M satisfying the extended Killing equationv a(i ; j) = 0 for some connection acting on the index a. For regular foliations this is equivalent to requiring the conormal bundle to the leaves with its induced metric to be invariant under leaf-preserving diffeomorphisms of M, which in turn generalizes Riemannian submersions to which the notion reduces for smooth leaf spaces M / ∼. The resulting gauge theory has the usual quotient effect with respect to the original ungauged theory: in this way, much more general orbits can be factored out than usually considered. In some cases these are orbits that do not correspond to an initial symmetry, but still can be generated by a finite-dimensional Lie group G. Then the presented gauging procedure leads to an ordinary gauge theory with Lie algebra valued 1-form gauge fields, but showing an unconventional transformation law. In general, however, one finds that the notion of an ordinary structural Lie group is too restrictive and should be replaced by the much more general notion of a structural Lie groupoid.
Gravity from Lorentz Symmetry Violation
Potting, Robertus
2006-06-19
In general relativity, the masslessness of gravitons can be traced to symmetry under diffeomorphisms. In this talk, we consider another possibility, whereby the masslessness arises from spontaneous violation of Lorentz symmetry.
Proton stopping using a full conserving dielectric function in plasmas at any degeneracy
Barriga-Carrasco, Manuel D.
2010-10-15
In this work, we present a dielectric function including the three conservation laws (density, momentum and energy) when we take into account electron-electron collisions in a plasma at any degeneracy. This full conserving dielectric function (FCDF) reproduces the random phase approximation (RPA) and Mermin ones, which confirms this outcome. The FCDF is applied to the determination of the proton stopping power. Differences among diverse dielectric functions in the proton stopping calculation are minimal if the plasma electron collision frequency is not high enough. These discrepancies can rise up to 2% between RPA values and the FCDF ones, and to 8% between the Mermin ones and FCDF ones. The similarity between RPA and FCDF results is not surprising, as all conservation laws are also considered in RPA dielectric function. Even for plasmas with low collision frequencies, those discrepancies follow the same behavior as for plasmas with higher frequencies. Then, discrepancies do not depend on the plasma degeneracy but essentially do on the value of the plasma collision frequency.
Degeneracy between warm and coupled cold dark matter: A clarifying note
NASA Astrophysics Data System (ADS)
Velten, Hermano; Borges, Humberto A.; Caramês, Thiago R. P.
2016-03-01
Wei et al. [Phys. Rev. D 88, 043510 (2013)] have proposed the existence of a cosmological degeneracy between warm dark matter (WDM), modified gravity and coupled cold dark matter (CDM) cosmologies at both the background expansion and the growth of density perturbation levels; i.e., corresponding cosmological data would not be able to differentiate such scenarios. Here, we will focus on the specific indistinguishability between warm dark matter plus cosmological constant (Λ ) and coupled scalar field CDM scenarios. Although the statement of Wei et al. is true for very specific conditions we present a more complete discussion on this issue and show in more detail that these models are indeed distinguishable. We show that the degeneracy breaks down since coupled models leave a specific signature in the redshift space distortion data which is absent in the uncoupled warm dark matter cosmologies. Furthermore, we complement our claim by providing the reasons which suggest that even at nonlinear level a breaking of such apparent equivalence is also expected.
Resolving the degeneracy in single Higgs production with Higgs pair production
NASA Astrophysics Data System (ADS)
Cao, Qing-Hong; Yan, Bin; Zhang, Dong-Ming; Zhang, Hao
2016-01-01
The Higgs boson production can be affected by several anomalous couplings, e.g. ct and cg anomalous couplings. Precise measurement of gg → h production yields two degenerate parameter spaces of ct and cg; one parameter space exhibits the SM limit while the other does not. Such a degeneracy could be resolved by Higgs boson pair production. In this work we adapt the strategy suggested by the ATLAS collaboration to explore the potential of distinguishing the degeneracy at the 14 TeV LHC. If the ct anomalous coupling is induced only by the operator H† HQbarL H ˜ tR, then the non-SM-like band could be excluded with an integrated luminosity of ˜ 210 fb-1. Making use of the fact that the Higgs boson pair is mainly produced through an s-wave scattering, we propose an analytical function to describe the fraction of signal events surviving a series of experimental cuts for a given invariant mass of Higgs boson pair. The function is model independent and can be applied to estimate the discovery potential of various NP models.
Quantum degeneracy effect on the work output from a Stirling cycle
NASA Astrophysics Data System (ADS)
Saygin, Hasan; Şişman, Altuǧ
2001-09-01
The effect of quantum degeneracy on the work output from a Stirling cycle working at quantum degeneracy conditions (QDCs) is analyzed. Expressions for net work outputs of Stirling power cycles working with monatomic ideal Bose and Fermi gases are derived by using the quantum ideal gas equation of state. Ratios of net work outputs of Stirling cycles working with Bose and Fermi gases to the net work output of a classical Stirling cycle (RWB and RWF, respectively) are obtained. Variations of RWB and RWF with TH are examined for a given temperature ratio (τ=TL/TH) and a specific volume ratio (rν=νH/νL). At QDC, it is seen that RWB has a maximum value, which is greater than unity. On the other hand, there is no maximum or minimum point for RWF and RWF⩽1 for any values of TH. Consequently, the use of Bose gas as a working fluid in a Stirling cycle provides an advantage since it causes the net work output per cycle to increase by consuming more heat energy. This fact is seen to be in the opposite direction for a Stirling cycle working with Fermi gas.
Gutzwiller approach to the Anderson lattice model with no orbital degeneracy
NASA Astrophysics Data System (ADS)
Vulović, Vladimir Z.; Abrahams, Elihu
1987-08-01
A new technique is used to obtain the Gutzwiller ground-state energy functional for the Anderson lattice model with no orbital degeneracy (ALM). For the Hubbard model, known expressions are derived with ease and simplicity. For the ALM, we derive the ground-state energy functional of Varma, Weber, and Randall. As a check on our Gutzwiller functional, we find an independent analytical upper bound for the ground-state energy of ALM with a dispersionless f band. For the case of a dispersionless f band and momentum-independent hybridization, in the Kondo regime, we derive analytical expressions for the ground-state energy, charge, and magnetic susceptibilities. For the special case of infinite Coulomb repulsion, we recover results of Rice and Ueda and of Fazekas and Brandow, notably the negative value of the magnetic susceptibility. The negative magnetic susceptibility persists in the entire Kondo region, i.e., finite-U effects do not stabilize the nonmagnetic Kondo state. This suggests that nonzero orbital degeneracy in the Anderson lattice model must be retained to describe heavy-fermion materials with a normal Fermi liquid ground state.
Unhappy vertices in artificial spin ice: new degeneracies from vertex frustration
NASA Astrophysics Data System (ADS)
Morrison, Muir J.; Nelson, Tammie R.; Nisoli, Cristiano
2013-04-01
In 1935, Pauling estimated the residual entropy of water ice with remarkable accuracy by considering the degeneracy of the ice rule solely at the vertex level. Indeed, his estimate works well for both the three-dimensional pyrochlore lattice and the two-dimensional six-vertex model, solved by Lieb in 1967. A similar estimate can be done for the honeycomb artificial spin. Indeed, its pseudo-ice rule, like the ice rule in Pauling and Lieb's systems, simply extends to the global ground state a degeneracy which is already present in the vertices. Unfortunately, the anisotropy of the magnetic interaction limits the design of inherently degenerate vertices in artificial spin ice, and the honeycomb is the only degenerate array produced so far. In this paper we show how to engineer artificial spin ice in a virtually infinite variety of degenerate geometries built out of non-degenerate vertices. In this new class of vertex models, the residual entropy follows not from a freedom of choice at the vertex level, but from the nontrivial relative arrangement of the vertices themselves. In such arrays not all of the vertices can be chosen in their lowest energy configuration. They are therefore vertex-frustrated and contain unhappy vertices. This can lead to residual entropy and to a variety of exotic states, such as sliding phases, smectic phases and emerging chirality. These new geometries will finally allow for the fabrication of many novel, extensively degenerate versions of artificial spin ice.
Chivukula, R. Sekhar; Simmons, Elizabeth H.; Di Chiara, Stefano; Foadi, Roshan
2009-11-01
We introduce a toy model implementing the proposal of using a custodial symmetry to protect the Zb{sub L}b{sub L} coupling from large corrections. This 'doublet-extended standard model' adds a weak doublet of fermions (including a heavy partner of the top quark) to the particle content of the standard model in order to implement an O(4)xU(1){sub X}{approx}SU(2){sub L}xSU(2){sub R}xP{sub LR}xU(1){sub X} symmetry in the top-quark mass generating sector. This symmetry is softly broken to the gauged SU(2){sub L}xU(1){sub Y} electroweak symmetry by a Dirac mass M for the new doublet; adjusting the value of M allows us to explore the range of possibilities between the O(4)-symmetric (M{yields}0) and standard-model-like (M{yields}{infinity}) limits. In this simple model, we find that the experimental limits on the Zb{sub L}b{sub L} coupling favor smaller M while the presence of a potentially sizable negative contribution to {alpha}T strongly favors large M. Comparison with precision electroweak data shows that the heavy partner of the top quark must be heavier than about 3.4 TeV, making it difficult to search for at LHC. This result demonstrates that electroweak data strongly limit the amount by which the custodial symmetry of the top-quark mass generating sector can be enhanced relative to the standard model. Using an effective field theory calculation, we illustrate how the leading contributions to {alpha}T, {alpha}S, and the Zb{sub L}b{sub L} coupling in this model arise from an effective operator coupling right-handed top quarks to the Z boson, and how the effects on these observables are correlated. We contrast this toy model with extradimensional models in which the extended custodial symmetry is invoked to control the size of additional contributions to {alpha}T and the Zb{sub L}b{sub L} coupling, while leaving the standard model contributions essentially unchanged.
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…
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…
PSEUDOSPIN SYMMETRY IN NUCLEI, SPIN SYMMETRY IN HADRONS
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.
A broken symmetry ontology: Quantum mechanics as a broken symmetry
Buschmann, J.E.
1988-01-01
The author proposes a new broken symmetry ontology to be used to analyze the quantum domain. This ontology is motivated and grounded in a critical epistemological analysis, and an analysis of the basic role of symmetry in physics. Concurrently, he is led to consider nonheterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows him to find a generalized principle of symmetry and a generalized symmetry-conservation formalisms. In particular, he clarifies the role of Noether's theorem in field theory. He shows how a broken symmetry ontology already operates in a description of the weak interactions. Finally, by showing how a broken symmetry ontology operates in the quantum domain, he accounts for the interpretational problem and the essential incompleteness of quantum mechanics. He proposes that the broken symmetry underlying this ontological domain is broken dilation invariance.
Chiral symmetry and pentaquarks
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.
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.
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.
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.
Broken vertex symmetry and finite zero-point entropy in the artificial square ice ground state
NASA Astrophysics Data System (ADS)
Gliga, Sebastian; Kákay, Attila; Heyderman, Laura J.; Hertel, Riccardo; Heinonen, Olle G.
2015-08-01
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. 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.
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.
NASA Astrophysics Data System (ADS)
Wang, Yuxuan; Cho, Gil Young; Hughes, Taylor L.; Fradkin, Eduardo
2016-04-01
We analyze the superconducting instabilities in the vicinity of the quantum-critical point of an inversion symmetry breaking order. We first show that the fluctuations of the inversion symmetry breaking order lead to two degenerate superconducting (SC) instabilities, one in the s -wave channel, and the other in a time-reversal invariant odd-parity pairing channel (the simplest case being the same as the of 3He-B phase). Remarkably, we find that unlike many well-known examples, the selection of the pairing symmetry of the condensate is independent of the momentum-space structure of the collective mode that mediates the pairing interaction. We found that this degeneracy is a result of the existence of a conserved fermionic helicity χ , and the two degenerate channels correspond to even and odd combinations of SC order parameters with χ =±1 . As a result, the system has an enlarged symmetry U (1 ) ×U (1 ) , with each U (1 ) corresponding to one value of the helicity χ . Because of the enlarged symmetry, this system admits exotic topological defects such as a fractional quantum vortex, which we show has a Majorana zero mode bound at its core. We discuss how the enlarged symmetry can be lifted by small perturbations, such as the Coulomb interaction or Fermi surface splitting in the presence of broken inversion symmetry, and we show that the resulting superconducting state can be topological or trivial depending on parameters. The U (1 ) ×U (1 ) symmetry is restored at the phase boundary between the topological and trivial SC states, and allows for a transition between topologically distinct SC phases without the vanishing of the order parameter. We present a global phase diagram of the superconducting states and discuss possible experimental implications.
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.
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.
Protein evolution. Pervasive degeneracy and epistasis in a protein-protein interface.
Podgornaia, Anna I; Laub, Michael T
2015-02-01
Mapping protein sequence space is a difficult problem that necessitates the analysis of 20(N) combinations for sequences of length N. We systematically mapped the sequence space of four key residues in the Escherichia coli protein kinase PhoQ that drive recognition of its substrate PhoP. We generated a library containing all 160,000 variants of PhoQ at these positions and used a two-step selection coupled to next-generation sequencing to identify 1659 functional variants. Our results reveal extensive degeneracy in the PhoQ-PhoP interface and epistasis, with the effect of individual substitutions often highly dependent on context. Together, epistasis and the genetic code create a pattern of connectivity of functional variants in sequence space that likely constrains PhoQ evolution. Consequently, the diversity of PhoQ orthologs is substantially lower than that of functional PhoQ variants. PMID:25657251
Giant and tunable valley degeneracy splitting in MoTe2
NASA Astrophysics Data System (ADS)
Li, Xiao; Qi, Jingshan; Niu, Qian; Feng, Ji
Valleys in monolayer transition-metal dichalcogenides seamlessly connect two basic carriers of quantum information, namely, the electron spin and photon helicity. Lifting the valley degeneracy is an attractive route to achieve further optoelectronic manipulations. However, the magnetic field only creates a very small valley splitting. We propose a strategy to create giant valley splitting by the proximity-induced Zeeman effect. Our first principles calculations of monolayer MoTe2 on a EuO substrate show that valley splitting over 300 meV can be generated. Interband transition energies become valley dependent, leading to selective spin-photon coupling by optical frequency tuning. The valley splitting is also continuously tunable by rotating the substrate magnetization. The giant and tunable valley splitting adds a different dimension to the exploration of unique optoelectronic devices based on magneto-optical coupling and magnetoelectric coupling.
Partially ferromagnetic electromagnet for trapping and cooling neutral atoms to quantum degeneracy
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.
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.
Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard.
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
2015-10-22
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. PMID:26458102
Thermal symmetry in isoscaling
Escudero, C. R.; Lopez, J. A.; Dorso, C. O.
2007-02-12
It is determined that isoscaling data, if produced by two isotopic reactions under similar thermodynamic conditions, should satisfy a simple numerical relationship. This, which helps to explore the symmetry of thermodynamic conditions of isotopic reactions, is studied using molecular dynamics simulations of 40Ca+40Ca, 48Ca+48Ca, and 52Ca+52Ca, at beam energies from 35 MeV / A to 85 MeV / A, and as a function of time. Strong deviations from the rule are detected in the beginning of the collision, with an excellent convergence at long times for some energies. A comparison with experimental data and other calculations is also included.
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.
Applications of chiral symmetry
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.
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.
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. PMID:27421389
Leptogenesis and residual CP symmetry
NASA Astrophysics Data System (ADS)
Chen, Peng; Ding, Gui-Jun; King, Stephen F.
2016-03-01
We discuss flavour dependent leptogenesis in the framework of lepton flavour models based on discrete flavour and CP symmetries applied to the type-I seesaw model. Working in the flavour basis, we analyse the case of two general residual CP symmetries in the neutrino sector, which corresponds to all possible semi-direct models based on a preserved Z 2 in the neutrino sector, together with a CP symmetry, which constrains the PMNS matrix up to a single free parameter which may be fixed by the reactor angle. We systematically study and classify this case for all possible residual CP symmetries, and show that the R-matrix is tightly constrained up to a single free parameter, with only certain forms being consistent with successful leptogenesis, leading to possible connections between leptogenesis and PMNS parameters. The formalism is completely general in the sense that the two residual CP symmetries could result from any high energy discrete flavour theory which respects any CP symmetry. As a simple example, we apply the formalism to a high energy S 4 flavour symmetry with a generalized CP symmetry, broken to two residual CP symmetries in the neutrino sector, recovering familiar results for PMNS predictions, together with new results for flavour dependent leptogenesis.
Symmetry fractionalization and twist defects
NASA Astrophysics Data System (ADS)
Tarantino, Nicolas; Lindner, Netanel H.; Fidkowski, Lukasz
2016-03-01
Topological order in two-dimensions can be described in terms of deconfined quasiparticle excitations—anyons—and their braiding statistics. However, it has recently been realized that this data does not completely describe the situation in the presence of an unbroken global symmetry. In this case, there can be multiple distinct quantum phases with the same anyons and statistics, but with different patterns of symmetry fractionalization—termed symmetry enriched topological order. When the global symmetry group G, which we take to be discrete, does not change topological superselection sectors—i.e. does not change one type of anyon into a different type of anyon—one can imagine a local version of the action of G around each anyon. This leads to projective representations and a group cohomology description of symmetry fractionalization, with the second cohomology group {H}2(G,{{ A }}{{abelian}}) being the relevant group. In this paper, we treat the general case of a symmetry group G possibly permuting anyon types. We show that despite the lack of a local action of G, one can still make sense of a so-called twisted group cohomology description of symmetry fractionalization, and show how this data is encoded in the associativity of fusion rules of the extrinsic ‘twist’ defects of the symmetry. Furthermore, building on work of Hermele (2014 Phys. Rev. B 90 184418), we construct a wide class of exactly-solvable models which exhibit this twisted symmetry fractionalization, and connect them to our formal framework.
Symmetry of Magnetically Ordered Quasicrystals
NASA Astrophysics Data System (ADS)
Lifshitz, Ron
1998-03-01
The notion of magnetic symmetry is reexamined in light of the recent observation of long-range magnetic order in icosahedral quasicrystals [Charrier et al., Phys. Rev. Lett. 78, 4637 (1997)]. The relation between the symmetry of a magnetically ordered (periodic or quasiperiodic) crystal, given in terms of a ``spin space group,'' and its neutron diffraction diagram is established. In doing so, an outline of a symmetry classification scheme for magnetically ordered quasiperiodic crystals, is provided. Predictions are given for the expected diffraction patterns of magnetically ordered icosahedral crystals, provided their symmetry is well described by icosahedral spin space groups.
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.
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…
Crystallographic and Spectroscopic Symmetry Notations.
ERIC Educational Resources Information Center
Sharma, B. D.
1982-01-01
Compares Schoenflies and Hermann-Mauguin notations of symmetry. Although the former (used by spectroscopists) and latter (used by crystallographers) both describe the same symmetry, there are distinct differences in the manner of description which may lead to confusion in correlating the two notations. (Author/JN)
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.)
Generalized Atkin-Lehner symmetry
NASA Astrophysics Data System (ADS)
Dienes, Keith R.
1990-09-01
Atkin-Lehner symmetry was proposed several years ago as a mechanism for obtaining a vanishing one-loop cosmological constant in nonsupersymmetric superstring models, but for models formulated in four-dimensional spacetime this symmetry cannot be realized. We therefore investigate various means of retaining the general Atkin-Lehner idea without having strict Atkin-Lehner symmetry. We first explicitly construct non-Atkin-Lehner-symmetric partition functions which not only lead to vanishing cosmological constants but which also avoid a recent proof that Atkin-Lehner-symmetric partition functions cannot arise from physically viable string models in greater than two dimensions. We then develop a systematic generalization of Atkin-Lehner symmetry, basing our considerations on the use of non-Hermitian operators as well as on a general class of possible congruence subgroups of the full modular group. We find that whereas in many instances our resulting symmetries reduce to either strict Atkin-Lehner symmetry or symmetries closely related to it, in other cases we obtain symmetries of a fundamentally new character. Our results therefore suggest possible new avenues for retaining the general Atkin-Lehner ``selection rule'' approach for obtaining a vanishing one-loop cosmological constant.
Generalized Atkin-Lehner symmetry
Dienes, K.R. )
1990-09-15
Atkin-Lehner symmetry was proposed several years ago as a mechanism for obtaining a vanishing one-loop cosmological constant in nonsupersymmetric superstring models, but for models formulated in four-dimensional spacetime this symmetry cannot be realized. We therefore investigate various means of retaining the general Atkin-Lehner idea without having strict Atkin-Lehner symmetry. We first explicitly construct non-Atkin-Lehner-symmetric partition functions which not only lead to vanishing cosmological constants but which also avoid a recent proof that Atkin-Lehner-symmetric partition functions cannot arise from physically viable string models in greater than two dimensions. We then develop a systematic generalization of Atkin-Lehner symmetry, basing our considerations on the use of non-Hermitian operators as well as on a general class of possible congruence subgroups of the full modular group. We find that whereas in many instances our resulting symmetries reduce to either strict Atkin-Lehner symmetry or symmetries closely related to it, in other cases we obtain symmetries of a fundamentally new character. Our results therefore suggest possible new avenues for retaining the general Atkin-Lehner selection rule'' approach for obtaining a vanishing one-loop cosmological constant.
Consequences of the complex character of the internal symmetry in supersymmetric theories
NASA Astrophysics Data System (ADS)
Gatto, R.; Sartori, G.
1987-06-01
The consequences of the invariance of the superpotential under the complexification G c of the internal symmetry group on the determination of the possible patterns of symmetry and supersymmetry breaking are established in a globally supersymmetric theory. In particular, in the case of global internal symmetry we show that a vacuum associaated to a point z, where G {z/c}≠ G {z/c} is always degenerate with a vacuum associated to a point z', where G {z'/c}= G {z'/c}; all the other degeneracies of the minimum of the potential on an orbit of G c are also determined and shown to be completely removed when the internal symmetry is gauged. The zeroes of the D-term of a supersymmetric gauge theory are characterized as the points of the closed orbits of G c which are at minimum distance from the origin; at these points G {z/c}= G {z/c}. It is rigorously proved that the minimum of the potential is zero if the gradient of the superpotential vanishes somewhere. It is also shown that the D-term necessarily vanishes at the minimum of the potential if the direction of spontaneous supersymmetry breaking is invariant by G.
SU(2) symmetry in a realistic spin-fermion model for cuprate superconductors
NASA Astrophysics Data System (ADS)
Kloss, T.; Montiel, X.; Pépin, C.
2015-05-01
We consider the pseudogap (PG) state of high-Tc superconductors in the form of a composite order parameter fluctuating between 2 pF -charge ordering and superconducting (SC) pairing. In the limit of linear dispersion and at the hot spots, both order parameters are related by a SU(2) symmetry, and the eight-hot-spot model of Efetov et al. [Nat. Phys. 9, 442 (2013), 10.1038/nphys2641] is recovered. In the general case, however, curvature terms of the dispersion will break this symmetry, and the degeneracy between both states is lifted. Taking the full momentum dependence of the order parameter into account, we measure the strength of this SU(2) symmetry breaking over the full Brillouin zone. For realistic dispersion relations including curvature we find generically that the SU(2) symmetry breaking is small and robust to the fermiology and that the symmetric situation is restored in the large paramagnon mass and coupling limit. Comparing the level splitting for different materials, we propose a scenario that could account for the competition between the PG and SC states in the phase diagram of high-Tc superconductors.
Theory of nodal s ± -wave pairing symmetry in the Pu-based 115 superconductor family.
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
Ultraviolet completion without symmetry restoration
NASA Astrophysics Data System (ADS)
Endlich, Solomon; Nicolis, Alberto; Penco, Riccardo
2014-03-01
We show that it is not possible to UV complete certain low-energy effective theories with spontaneously broken spacetime symmetries by embedding them into linear sigma models, that is, by adding "radial" modes and restoring the broken symmetries. When such a UV completion is not possible, one can still raise the cutoff up to arbitrarily higher energies by adding fields that transform nonlinearly under the broken symmetries, that is, new Goldstone bosons. However, this (partial) UV completion does not necessarily restore any of the broken symmetries. We illustrate this point by considering a concrete example in which a combination of spacetime and internal symmetries is broken down to a diagonal subgroup. Along the way, we clarify a recently proposed interpretation of inverse Higgs constraints as gauge-fixing conditions.
Asymptotic symmetries from finite boxes
NASA Astrophysics Data System (ADS)
Andrade, Tomás; Marolf, Donald
2016-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a 'box.' This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the anti-de Sitter and Poincaré asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2 + 1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS3 and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Symmetry inheritance of scalar fields
NASA Astrophysics Data System (ADS)
Smolić, Ivica
2015-07-01
Matter fields do not necessarily have to share the symmetries with the spacetime they live in. When this happens, we speak of the symmetry inheritance of fields. In this paper we classify the obstructions of symmetry inheritance by the scalar fields, both real and complex, and look more closely at the special cases of stationary and axially symmetric spacetimes. Since the symmetry noninheritance is present in the scalar fields of boson stars and may enable the existence of the black hole scalar hair, our results narrow the possible classes of such solutions. Finally, we define and analyse the symmetry noninheritance contributions to the Komar mass and angular momentum of the black hole scalar hair.
Transient potassium channels augment degeneracy in hippocampal active dendritic spectral tuning.
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
Transient potassium channels augment degeneracy in hippocampal active dendritic spectral tuning
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
Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy
NASA Astrophysics Data System (ADS)
Haas, Fernando; Mahmood, Shahzad
2015-11-01
Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.
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.
NASA Astrophysics Data System (ADS)
Delagrange, R.; Weil, R.; Kasumov, A.; Ferrier, M.; Bouchiat, H.; Deblock, R.
2016-05-01
In a π -Josephson junction, the supercurrent's sign is reversed due to the dephasing of superconducting pairs upon their traversal of the nonsuperconducting part. 0-π quantum transitions are extremely sensitive to electronic and magnetic correlations, providing powerful exploration tools of competing orders. In a quantum dot connected to superconducting reservoirs, the transition is governed by gate voltage. As shown recently, it can also be controlled by the superconducting phase in the case of strong competition between the superconducting proximity effect and Kondo correlations. We investigated here the current-phase relation in a clean carbon nanotube quantum dot, close to orbital degeneracy, in a regime of strong competition between local electronic correlations and superconducting proximity effect. We show that the nature of the transition depends crucially on the occupation and the width of the orbital levels, which determine their respective contribution to transport. When the transport of Cooper pairs takes place through only one of these levels, we find that the phase diagram of the phase-dependent 0-π transition is a universal characteristic of a discontinuous level-crossing quantum transition at zero temperature. In the case where the two levels are involved, the nanotube Josephson current exhibits a continuous 0-π transition, independent of the superconducting phase, revealing a different physical mechanism of the transition.
CCDM model with spatial curvature and the breaking of ``dark degeneracy''
NASA Astrophysics Data System (ADS)
Jesus, J. F.; Andrade-Oliveira, F.
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.
RESOLVING THE sin(I) DEGENERACY IN LOW-MASS MULTI-PLANET SYSTEMS
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.
Cognitive Aging and Time Perception: Roles of Bayesian Optimization and Degeneracy.
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
Cognitive Aging and Time Perception: Roles of Bayesian Optimization and Degeneracy
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
Huang, Z. )
1992-12-01
We examine an interesting scenario to solve the domain-wall problem recently suggested by Preskill, Trivedi, Wilczek, and Wise. The effective potential is calculated in the presence of the QCD axial anomaly. It is shown that some discrete symmetries such as {ital CP} and {ital Z}{sub 2} can be anomalous due to a so-called {ital K} term induced by instantons. We point out that the {ital Z}{sub 2} domain-wall problem in the two-doublet standard model can be resolved by two types of solutions: the {ital CP}-conserving one and the {ital CP}-breaking one. In the first case, there exist two {ital Z}{sub 2}-related local minima whose energy splitting is provided by the instanton effect. In the second case, there is only one unique vacuum so that the domain walls do not form at all. The consequences of this new source of {ital CP} violation are discussed and shown to be well within the experimental limits in weak interactions.
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. PMID:23066601
Geometrical spin symmetry and spin
Pestov, I. B.
2011-07-15
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
Spectral theorem and partial symmetries
Gozdz, A.; Gozdz, M.
2012-10-15
A novel method of the decompositon of a quantum system's Hamiltonian is presented. In this approach the criterion of the decomposition is determined by the symmetries possessed by the sub-Hamiltonians. This procedure is rather generic and independent of the actual global symmetry, or the lack of it, of the full Hamilton operator. A detailed investigation of the time evolution of the various sub-Hamiltonians, therefore the change in time of the symmetry of the physical object, is presented for the case of a vibrator-plus-rotor model. Analytical results are illustrated by direct numerical calculations.
Hidden symmetries and black holes
NASA Astrophysics Data System (ADS)
Frolov, Valeri P.
2009-10-01
The paper contains a brief review of recent results on hidden symmetries in higher dimensional black hole spacetimes. We show how the existence of a principal CKY tensor (that is a closed conformal Killing-Yano 2-form) allows one to generate a `tower' of Killing-Yano and Killing tensors responsible for hidden symmetries. These symmetries imply complete integrability of geodesic equations and the complete separation of variables in the Hamilton-Jacobi, Klein-Gordon, Dirac and gravitational perturbation equations in the general Kerr-NUT-(A)dS metrics. Equations of the parallel transport of frames along geodesics in these spacetimes are also integrable.
Tieri, Paolo; Grignolio, Andrea; Zaikin, Alexey; Mishto, Michele; Remondini, Daniel; Castellani, Gastone C; Franceschi, Claudio
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
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
Combining Flavour and CP Symmetries
NASA Astrophysics Data System (ADS)
Feruglio, Ferruccio
2013-07-01
I shortly review the impact of the most recent neutrino oscillation data on our attempts to construct a realistic model for neutrino masses and mixing angles. Models based on anarchy and its variants remain an open possibility, reinforced by the latest experimental findings. Many models based on discrete symmetries no longer work in their simplest realizations. I illustrate several proposals that can rescue discrete symmetries. In particular I discuss the possibility of combining discrete flavour symmetries and CP, and I describe a recently proposed symmetry breaking pattern that allows to predict all mixing parameters, angles and phases, in terms of a single real unknown. I analyze several explicit examples of this construction, providing new realistic mixing patterns.
Liu, Y.; Keller, J.
1996-09-01
It is proved that there exists an additional intrinsic symmetry in the left-handed and right-handed fermions (and other fields). The corresponding group of transformations is induced by the Poincar{acute e} translations in the space{endash}time manifold. This symmetry predicts an additional intrinsic energy-momentum for fermions. Considering this symmetry as local leads to introduction of a gauge field and of a nonintegrable phase angle, the corresponding Berry-type phase depends on the topology of the Riemannian space{endash}time manifold as determined by the vierbein. This additional symmetry provides us with the possibility of considering the fermions as gauge fields on the nonvector bundle. {copyright} {ital 1996 American Institute of Physics.}
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.
Trace formula for broken symmetry
Creagh, S.C.
1996-05-01
We derive a trace formula for systems that exhibit an approximate continuous symmetry. It interpolates between the sum over continuous families of periodic orbits that holds in the case of exact continuous symmetry, and the discrete sum over isolated orbits that holds when the symmetry is completely broken. It is based on a simple perturbation expansion of the classical dynamics, centered around the case of exact symmetry, and gives an approximation to the usual Gutzwiller formula when the perturbation is large. We illustrate the computation with some 2-dimensional examples: the deformation of the circular billiard into an ellipse, and anisotropic and anharmonic perturbations of a harmonic oscillator. Copyright {copyright} 1996 Academic Press, Inc.
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.
Ultracold Fermi gases with emergent SU(N) symmetry.
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 (173)Yb 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. PMID:25429615
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.
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.
Momentum dependence of symmetry energy
NASA Astrophysics Data System (ADS)
Coupland, Daniel D.; Youngs, Michael; Chajecki, Zbigniew; Lynch, William; Tsang, Betty; Zhang, Yingxun; Famiano, Michael; Ghosh, Tilak; Giacherio, B.; Kilburn, Micha; Lee, Jenny; Lu, Fei; Russotto, Paulo; Sanetullaev, Alisher; Showalter, Rachel; Verde, Giuseppe; Winkelbauer, Jack
2014-09-01
One of the main uncertainties in the Equation of State of neutron-rich nuclear matter concerns the density and momentum dependence of the nuclear symmetry energy. Some constraints on the density dependence of the symmetry energy at sub-saturation densities have been recently obtained. However questions remain, especially concerning the momentum dependence of the symmetry mean-field potential that can make the neutron and proton effective masses different. We probe the momentum dependence of this isovector mean-field potential by comparing the energy spectra of neutrons and protons emitted in 112Sn+112Sn and 124Sn +124Sn collisions at incident energies of E/A = 50 and 120 MeV. We achieve an experimental precision that can discriminate between transport model predictions for the n/p double ratio for different momentum dependencies of the symmetry mean-field potential. One of the main uncertainties in the Equation of State of neutron-rich nuclear matter concerns the density and momentum dependence of the nuclear symmetry energy. Some constraints on the density dependence of the symmetry energy at sub-saturation densities have been recently obtained. However questions remain, especially concerning the momentum dependence of the symmetry mean-field potential that can make the neutron and proton effective masses different. We probe the momentum dependence of this isovector mean-field potential by comparing the energy spectra of neutrons and protons emitted in 112Sn+112Sn and 124Sn+124Sn collisions at incident energies of E/A = 50 and 120 MeV. We achieve an experimental precision that can discriminate between transport model predictions for the n/p double ratio for different momentum dependencies of the symmetry mean-field potential. PHY-1102511.
Symmetry and quaternionic integrable systems
NASA Astrophysics Data System (ADS)
Gaeta, G.; Rodríguez, M. A.
2015-01-01
Given a hyperkahler manifold M, the hyperkahler structure defines a triple of symplectic structures on M; with these, a triple of Hamiltonians defines a so-called hyperHamiltonian dynamical system on M. These systems are integrable when can be mapped to a system of quaternionic oscillators. We discuss the symmetry of integrable hyperHamiltonian systems, i.e. quaternionic oscillators, and conversely how these symmetries characterize, at least in the Euclidean case, integrable hyperHamiltonian systems.
Dynamical symmetries in nuclear structure
Casten, R.F.
1986-01-01
In recent years the concept of dynamical symmetries in nuclei has witnessed a renaissance of interest and activity. Much of this work has been developed in the context of the Interacting Boson Approximation (or IBA) model. The appearance and properties of dynamical symmetries in nuclei will be reviewed, with emphasis on their characteristic signatures and on the role of the proton-neutron interaction in their formation, systematics and evolution. 36 refs., 20 figs.
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.
Anomalies and Discrete Chiral Symmetries
Creutz, M.
2009-09-07
The quantum anomaly that breaks the U(1) axial symmetry of massless multi-flavored QCD leaves behind a discrete flavor-singlet chiral invariance. With massive quarks, this residual symmetry has a close connection with the strong CP-violating parameter theta. One result is that if the lightest quarks are degenerate, then a first order transition will occur when theta passes through pi. The resulting framework helps clarify when the rooting prescription for extrapolating in the number of flavors is valid.
NASA Astrophysics Data System (ADS)
Lattanzi, F.; di Lauro, C.
2006-08-01
The effects of head-tail coupling in the mechanism of formation of combinations and overtones of perpendicular vibrational modes, in molecules like ethane and methanol, is investigated. For uncoupled head and tail the perpendicular modes have higher degeneracies, and the species of the components of their combinations or overtones span the irreducible representations occurring in the direct products Gs× Gs in the G36(EM) group (ethane) and E× E in the G6(EM) group (methanol). Head-tail coupling operators can transform these uncoupled fundamental vibrational modes into coupled modes of lower symmetries, and then the symmetry species of combinations and overtones must be contained in the direct product of these lower symmetry sets. It is shown that the operators which generate coupled sets of fundamental vibrational states of given symmetries, also work to generate combinations and overtones with the symmetry species predicted from those of the combining fundamentals. These mechanisms are ruled by the torsional Coriolis operators, which can tune more or less to resonance basis levels linked by specific head-tail coupling operators.
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.
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.
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.
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.
Hidden order in URu2Si2 originates from Fermi surface gapping induced by dynamic symmetry breaking.
Elgazzar, S; Rusz, J; Amft, M; Oppeneer, P M; Mydosh, J A
2009-04-01
Spontaneous, collective ordering of electronic degrees of freedom leads to second-order phase transitions that are characterized by an order parameter driving the transition. The notion of a 'hidden order' has recently been used for a variety of materials where a clear phase transition occurs without a known order parameter. The prototype example is the heavy-fermion compound URu(2)Si(2), where a mysterious hidden-order transition occurs at 17.5 K. For more than twenty years this system has been studied theoretically and experimentally without a firm grasp of the underlying physics. Here, we provide a microscopic explanation of the hidden order using density-functional theory calculations. We identify the Fermi surface 'hot spots' where degeneracy induces a Fermi surface instability and quantify how symmetry breaking lifts the degeneracy, causing a surprisingly large Fermi surface gapping. As the mechanism for the hidden order, we deduce spontaneous symmetry breaking through a dynamic mode of antiferromagnetic moment excitations. PMID:19234447
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
Parity-time symmetry broken by point-group symmetry
Fernández, Francisco M. Garcia, Javier
2014-04-15
We discuss a parity-time (PT) symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schrödinger equation for a particle in a square box with the PT-symmetric potential V(x, y) = iaxy. Perturbation theory clearly shows that some of the eigenvalues are complex for sufficiently small values of |a|. Point-group symmetry proves useful to guess if some of the eigenvalues may already be complex for all values of the coupling constant. We confirm those conclusions by means of an accurate numerical calculation based on the diagonalization method. On the other hand, the Schrödinger equation with the potential V(x, y) = iaxy{sup 2} exhibits real eigenvalues for sufficiently small values of |a|. Point group symmetry suggests that PT-symmetry may be broken in the former case and unbroken in the latter one.
Physical symmetry and lattice symmetry in the lattice Boltzmann method
Cao, N.; Chen, S.; Jin, S.; Martinez, D.
1997-01-01
The lattice Boltzmann method (LBM) is regarded as a specific finite difference discretization for the kinetic equation of the discrete velocity distribution function. We argue that for finite sets of discrete velocity models, such as LBM, the physical symmetry is necessary for obtaining the correct macroscopic Navier-Stokes equations. In contrast, the lattice symmetry and the Lagrangian nature of the scheme, which is often used in the lattice gas automaton method and the existing lattice Boltzmann methods and directly associated with the property of particle dynamics, is not necessary for recovering the correct macroscopic dynamics. By relaxing the lattice symmetry constraint and introducing other numerical discretization, one can also obtain correct hydrodynamics. In addition, numerical simulations for applications, such as nonuniform meshes and thermohydrodynamics can be easily carried out and numerical stability can be ensured by the Courant-Friedricks-Lewey condition and using the semi-implicit collision scheme. {copyright} {ital 1997} {ital The American Physical Society}
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).
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.
2016-04-01
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 noninteracting 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.
Four-port photonic structures with mirror-time reversal symmetries
NASA Astrophysics Data System (ADS)
Li, Huanan; Thomas, Roney; Ellis, F. M.; Kottos, Tsampikos
2016-07-01
We investigate the transport characteristics of a four-port gyrotropic photonic structure with mirror-time reversal symmetry. The structure consists of two coupled cavities with balanced amplification and attenuation. The cavities are placed on top of a gyrotropic substrate and are coupled to two bus waveguides. Using detail simulations in the microwave domain we demonstrate a strong non-reciprocal intra-guide port transport and an enhanced inter-guide port transmittance. The non-reciprocal features are dramatically amplified in the gain–loss parameter domain where an exceptional point degeneracy, for the associated isolated set-up, occurs. These results are explained theoretically in terms of an equivalent lumped circuit.
Broken SU(4) Symmetry and the Fractional Quantum Hall Effect in Graphene
NASA Astrophysics Data System (ADS)
Sodemann, I.; MacDonald, A. H.
2014-03-01
We describe a variational theory for incompressible ground states and charge gaps in the N =0 Landau level of graphene that accounts for the fourfold Landau level degeneracy and the short-range interactions that break SU(4) spin-valley invariance. Our approach explains the experimental finding that gaps at odd numerators are weak for 1<|ν|<2 and strong for 0<|ν|<1. We find that in the SU(4) invariant case the incompressible ground state at |ν|=1/3 is a three-component incompressible state, not the Laughlin state, and discuss the competition between these two states in the presence of SU(4) spin-valley symmetry-breaking terms.
Probing Radial age/metallicity degeneracy in early-type galaxies
NASA Astrophysics Data System (ADS)
Silva, David R.; Elston, Richard
1994-06-01
It has been generally concluded that the optical broad band color and line index gradients observed in early-type galaxies are driven by metallicity. Yet, this conclusion remains uncertain due to the age/metallicity degeneracy inherent in most optical data. Furthermore, optical broad-band colors are susceptible to reddening in the presence of dust. Near-infrared colors, on the other hand, are significantly less age sensitive than optical colors in old stellar populations and are much less affected by dust. In principle, the combination of optical and near-IR data should provide less ambivalent age and metallicity discrimination than using optical or near-IR data alone. To investigate this possibility, near-IR images of early-type galaxies with significant U-R gradients have been measured. Comparison of the optical and near-IR results leads to the primary conclusion that broad-band optical and near-IR gradients are not tracing metallicity in concert but are affected by different astrophysical parameters. Three general possibilites are discussed: reddening, radial age gradients, and differing metallicity sensitivities. Proving the absence or presence of significant reddening is difficult from broad-band colors alone. In the absence of reddening, the optical color gradients would suggest that age decreases wit radius, leading to somewhat contrived evolution scenarios. Alternatively, it is proposed that the optical color gradients may be tracing light element (e.g. CNO) abundances while the near-IR gradients are tracing Fe- peak element abundances. This scenario leads to the conclusion that many of these galaxies have enhanced nuclear (light/FE) ratios, consistent with the recently published studies of nuclear line indices in these galaxies. Given the quality of the current available data, these hypotheses remain somewhat unconstrained. Nevertheless, this study reinforces the necessity of obtaining data over a long spectral baseline to properly interpret the ensemble
Revising the solution of the neutrino oscillation parameter degeneracies at neutrino factories
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.
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.
On the symmetries of integrability
Bellon, M.; Maillard, J.M.; Viallet, C. )
1992-06-01
In this paper the authors show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group A{sub 2}{sup (1)}. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. The authors show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. The authors indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. The authors mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. The authors' results also yield the generalization of the condition q{sup n} = 1 so often mentioned in the theory of quantum groups, when no q parameter is available.
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 .
Symmetry breaking in molecular ferroelectrics.
Shi, Ping-Ping; Tang, Yuan-Yuan; Li, Peng-Fei; Liao, Wei-Qiang; Wang, Zhong-Xia; Ye, Qiong; Xiong, Ren-Gen
2016-07-11
Ferroelectrics are inseparable from symmetry breaking. Accompanying the paraelectric-to-ferroelectric phase transition, the paraelectric phase adopting one of the 32 crystallographic point groups is broken into subgroups belonging to one of the 10 ferroelectric point groups, i.e. C1, C2, C1h, C2v, C4, C4v, C3, C3v, C6 and C6v. The symmetry breaking is captured by the order parameter known as spontaneous polarization, whose switching under an external electric field results in a typical ferroelectric hysteresis loop. In addition, the responses of spontaneous polarization to other external excitations are related to a number of physical effects such as second-harmonic generation, piezoelectricity, pyroelectricity and dielectric properties. Based on these, this review summarizes recent developments in molecular ferroelectrics since 2011 and focuses on the relationship between symmetry breaking and ferroelectricity, offering ideas for exploring high-performance molecular ferroelectrics. PMID:27051889
CKM matrix and flavor symmetries
NASA Astrophysics Data System (ADS)
Araki, Takeshi; Ishida, Hiroyuki; Ishimori, Hajime; Kobayashi, Tatsuo; Ogasahara, Atsushi
2013-11-01
Following the way proposed recently by Hernandez and Smirnov, we seek possible residual symmetries in the quark sector with a focus on the von Dyck groups. We begin with two extreme cases in which both θ13 and θ23 or only θ13 are set to zero. Then, cases where all the Cabibbo-Kobayashi-Maskawa parameters are allowed to take nonzero values are explored. The Z7 symmetry is favorable to realize only the Cabibbo angle. On the other hand, larger groups are necessary in order to be consistent with all the mixing parameters. Possibilities of embedding the obtained residual symmetries into the Δ(6N2) series are also briefly discussed.
Symmetries in geometrical optics: theory
NASA Astrophysics Data System (ADS)
Szilagyi, M.; Mui, P. H.
1995-12-01
A study of light and charged-particle optical systems with inversion, reflection, rotation, translation, and/or glide symmetries is presented. The constraints imposed by the various symmetries on the first-order properties of a lens are investigated. In particular, the mathematical structures of the deflection vectors and the transfer matrices are described for various symmetrical systems. In the course of studying the translation and the glide symmetries, a simple technique for characterizing a general system of N identical components in series (or cascade) is also developed, based on the linear algebra theory of factoring matrices into Jordan canonical forms. Applications of these results are presented in a follow-up paper [J. Opt. Soc. Am. 12, XXXX (1995)]. Copyright (c) 1995 Optical Society of America
Heisenberg symmetry and hypermultiplet manifolds
NASA Astrophysics Data System (ADS)
Antoniadis, Ignatios; Derendinger, Jean-Pierre; Marios Petropoulos, P.; Siampos, Konstantinos
2016-04-01
We study the emergence of Heisenberg (Bianchi II) algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N = 2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U (1) × U (1) at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry - as opposed to Heisenberg ⋉ U (1). We finally discuss the realization of the latter by gauging appropriate Sp (2 , 4) generators in N = 2 conformal supergravity.
NASA Astrophysics Data System (ADS)
Wang, Juven C.; Santos, Luiz H.; Wen, Xiao-Gang
2015-05-01
The boundary of symmetry-protected topological states (SPTs) can harbor new quantum anomaly phenomena. In this work, we characterize the bosonic anomalies introduced by the 1+1D non-onsite-symmetric gapless edge modes of (2+1)D bulk bosonic SPTs with a generic finite Abelian group symmetry (isomorphic to G =∏iZNi=ZN1×ZN2×ZN3×⋯ ). We demonstrate that some classes of SPTs (termed "Type II") trap fractional quantum numbers (such as fractional ZN charges) at the 0D kink of the symmetry-breaking domain walls, while some classes of SPTs (termed "Type III") have degenerate zero energy modes (carrying the projective representation protected by the unbroken part of the symmetry), either near the 0D kink of a symmetry-breaking domain wall, or on a symmetry-preserving 1D system dimensionally reduced from a thin 2D tube with a monodromy defect 1D line embedded. More generally, the energy spectrum and conformal dimensions of gapless edge modes under an external gauge flux insertion (or twisted by a branch cut, i.e., a monodromy defect line) through the 1D ring can distinguish many SPT classes. We provide a manifest correspondence from the physical phenomena, the induced fractional quantum number, and the zero energy mode degeneracy to the mathematical concept of cocycles that appears in the group cohomology classification of SPTs, thus achieving a concrete physical materialization of the cocycles. The aforementioned edge properties are formulated in terms of a long wavelength continuum field theory involving scalar chiral bosons, as well as in terms of matrix product operators and discrete quantum lattice models. Our lattice approach yields a regularization with anomalous non-onsite symmetry for the field theory description. We also formulate some bosonic anomalies in terms of the Goldstone-Wilczek formula.
Unparticles and electroweak symmetry breaking
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.
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.
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.
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.
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).
NASA Astrophysics Data System (ADS)
Guo, Xiaoyang; Leng, Yuxin; Li, Yanyan; Li, Wenkai; Lu, Xiaoming; Xu, Yi; Li, Ruxin
2016-07-01
Broadband optical parametric amplification (OPA) in the near-infrared region (1.3-1.8 μm) is demonstrated in YCOB crystal pumped by 1 kHz Ti:sapphire based femtosecond laser at near critical wavelength degeneracy phase matching condition at first time. The gain bandwidth is closed to BIBO or BBO crystal OPA gain bandwidth. The energy obtained with 3.5 mm-thick YCOB reached 20 μJ with RMS 1.9%. After second harmonic generation, 17.6 fs pulse is obtained, and the pulse compressibility is demonstrated.
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.
NASA Astrophysics Data System (ADS)
Harder, H.; Macholl, S.; Maeder, H.; Fusina, L.; Ozier, I.
2010-06-01
For the principal isotopomer 14N32S19F3 of thiazyl trifluoride in the degenerate fundamental state (v5=1), the hyperfine structure has been investigated in the Q-branch spectrum between 8 and 26.5 GHz using microwave Fourier transform waveguide spectrometers with a resolution limit of ≈ 30 kHz. In addition to l% -type doubling spectra and l-type resonance transitions with (Δ k =% Δ l=± 2), perturbation-allowed spectra were measured with Δ % (k-l) =± 3, ± 6. The range in J was from 13 to 61; for the lower states, kl=-3, -2, -1, 0, +1. For all the transitions, the hyperfine patterns observed are predicted to be doublets when only the nitrogen quadrupole Hamiltonian HQN is taken into account. Doublets were indeed measured for transitions with Γ RV=% A1rightarrow A2, where Γ RV is the rovibrational symmetry. However, when Γ RV=Erightarrow E, triplets and quartets were observed in addition to doublets. These anomalous hyperfine patterns are shown to be due to the (Δ k=± 1) and (Δ k=% ± 2) matrix elements of the fluorine spin-rotation Hamiltonian H% NF characterized by the fluorine spin-rotation constants % c(1)=(cxz+czxast ) and c(2)=(cxx-cyy), respectively. These terms in HNF lift the parity degeneracy for Γ RV=E. The rovibrational Hamiltonian HRV was adopted from an earlier partner study. A good fit to the hyperfine data was obtained with a standard deviation of 3.1 kHz. In the fitting process, 12 rovibrational parameters were varied, while the remaining constants in HRV were left at the values of Ref. (1). In addition, 6 hyperfine parameters were determined: four in HQN, and two in HNF. It was found that \\vert c(1)\\vert =7.48(24) kHz and \\vert c(2)\\vert =2.423(22) kHz. This determination of \\vert c(1)\\vert is the first to be reported based on frequency measurements. The key to the observation of the parity doubling lies in the severe mixing into the eigenvectors of basis vectors with several different values of kl as a result of the clustering1
Spin symmetry in the antinucleon spectrum.
Zhou, Shan-Gui; Meng, Jie; Ring, P
2003-12-31
We discuss spin and pseudospin symmetry in the spectrum of single nucleons and single antinucleons in a nucleus. As an example we use relativistic mean field theory to investigate single antinucleon spectra. We find a very well developed spin symmetry in single antineutron and single antiproton spectra. The dominant components of the wave functions of the spin doublet are almost identical. This spin symmetry in antiparticle spectra and the pseudospin symmetry in particle spectra have the same origin. However, it turns out that the spin symmetry in antinucleon spectra is much better developed than the pseudospin symmetry in normal nuclear single particle spectra. PMID:14754045
Charge symmetry at the partonic level
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.
Superdeformations and fermion dynamical symmetries
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.
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…
Paper Models Illustrating Virus Symmetry.
ERIC Educational Resources Information Center
McCarthy, D. A.
1990-01-01
Instructions are given for constructing two models, one to illustrate the general principles of symmetry in T=1, T=3, and T=4 viruses, and the other to illustrate the disposition of protein subunits in the T=3 plant viruses and the picornaviruses. (Author/CW)
Entanglement renormalization and gauge symmetry
Tagliacozzo, L.; Vidal, G.
2011-03-15
A lattice gauge theory is described by a redundantly large vector space that is subject to local constraints and can be regarded as the low-energy limit of an extended lattice model with a local symmetry. We propose a numerical coarse-graining scheme to produce low-energy, effective descriptions of lattice models with a local symmetry such that the local symmetry is exactly preserved during coarse-graining. Our approach results in a variational ansatz for the ground state(s) and low-energy excitations of such models and, by extension, of lattice gauge theories. This ansatz incorporates the local symmetry in its structure and exploits it to obtain a significant reduction of computational costs. We test the approach in the context of a Z{sub 2} lattice gauge theory formulated as the low-energy theory of a specific regime of the toric code with a magnetic field, for lattices with up to 16x16 sites (16{sup 2}x2=512 spins) on a torus. We reproduce the well-known ground-state phase diagram of the model, consisting of a deconfined and spin-polarized phases separated by a continuous quantum phase transition, and obtain accurate estimates of energy gaps, ground-state fidelities, Wilson loops, and several other quantities.
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…
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…
From symmetries to number theory
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.
Circular codes, symmetries and transformations.
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. PMID:25008961
Strong coupling electroweak symmetry breaking
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.
Baryon and chiral symmetry breaking
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.
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…
Quantitative Analysis of Face Symmetry.
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. PMID:26080172
Theory of nodal s^{±}-wave pairing symmetry in the Pu-based 115 superconductor family
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-T_{c} 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.
Theory of nodal s±-wave pairing symmetry in the Pu-based 115 superconductor family
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
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
Theory of nodal s±-wave pairing symmetry in the Pu-based 115 superconductor family
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
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. PMID:25658993
NASA Astrophysics Data System (ADS)
Wang, Juven C.; Gu, Zheng-Cheng; Wen, Xiao-Gang
2015-01-01
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.
Barkeshli, Maissam
2016-08-26
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 2e/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 2e/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. PMID:27610873
PT Symmetry, Conformal Symmetry, and the Metrication of Electromagnetism
NASA Astrophysics Data System (ADS)
Mannheim, Philip D.
2016-05-01
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.
What symmetries can do for you
NASA Astrophysics Data System (ADS)
Nucci, M. C.
2015-04-01
Several applications of Lie symmetries and its generalisation are presented: from turning butterflies into tornados, to its applications in epidemics, population dynamics, and ultimately converting classical problems into the quantum realm. Applications of nonclassical symmetries are also illustrated.
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.
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.
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.
Shape phase transitions in odd-A nuclei
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.
Yet another symmetry breaking to be discovered
NASA Astrophysics Data System (ADS)
Yoshimura, M.
2016-07-01
The discovery of spontaneous symmetry breaking in particle physics was the greatest contribution in Nambu's achievements. There is another class of symmetries that exist in low-energy nature, yet is doomed to be broken at high energy, due to a lack of protection of the gauge symmetry. I shall review our approach to searching for this class of symmetry breaking, the lepton number violation linked to the generation of the matter-antimatter asymmetry in our universe.
Partial Dynamical Symmetry in Nuclear Systems
Escher, J E
2003-06-02
Partial dynamical symmetry (PDS) extends and complements the concepts of exact and dynamical symmetry. It allows one to remove undesired constraints from an algebraic theory, while preserving some of the useful aspects of a dynamical symmetry, and to study the effects of symmetry breaking in a controlled manner. An example of a PDS in an interacting fermion system is presented. The associated PDS Hamiltonians are closely related with a realistic quadrupole-quadrupole interaction and provide new insights into this important interaction.
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.; The 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.; The 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.
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.
Superalgebra and fermion-boson symmetry
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
Applications of Symmetry to Problem Solving.
ERIC Educational Resources Information Center
Leikin, Roza; Berman, Abraham; Zaslavsky, Orit
2000-01-01
Symmetry is an important mathematical concept that plays an extremely important role as a problem solving technique. Presents examples of problems from several branches of mathematics that can be solved using different types of symmetry. Discusses teachers' attitudes and beliefs regarding the use of symmetry in the solutions of these problems.…
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.
Symmetry of cardiac function assessment
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
Symmetry of cardiac function assessment.
Bai, Xu-Fang; Ma, Amy X
2016-09-01
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
Tensionless strings from worldsheet symmetries
NASA Astrophysics Data System (ADS)
Bagchi, Arjun; Chakrabortty, Shankhadeep; Parekh, Pulastya
2016-01-01
We revisit the construction of the tensionless limit of closed bosonic string theory in the covariant formulation in the light of Galilean conformal symmetry that rises as the residual gauge symmetry on the tensionless worldsheet. We relate the analysis of the fundamentally tensionless theory to the tensionless limit that is viewed as a contraction of worldsheet coordinates. Analysis of the quantum regime uncovers interesting physics. The degrees of freedom that appear in the tensionless string are fundamentally different from the usual string states. Through a Bogoliubov transformation on the worldsheet, we link the tensionless vacuum to the usual tensile vacuum. As an application, we show that our analysis can be used to understand physics of strings at very high temperatures and propose that these new degrees of freedom are naturally connected with the long-string picture of the Hagedorn phase of free string theory. We also show that tensionless closed strings behave like open strings.
NASA Astrophysics Data System (ADS)
Kesavan, Aruna; Ashtekar, Abhay
2016-03-01
Conservation laws of asymptotic symmetries are essential to quantify the amount of energy-momentum and angular momentum carried away by gravitational radiation from isolated systems. The asymptotic symmetry group of asymptotically flat spacetimes at null infinity is the Bondi-Metzner-Sachs (BMS) group. While the flux associated to an arbitrary BMS vector field was provided by Ashtekar and Streubel (1981) using symplectic methods, the tensorial expression of a corresponding two-dimensional charge integral linear in an arbitrary BMS vector field has not been available in the literature. We fill this gap by providing such a charge. I will discuss its properties and relation to Geroch's supermomentum and the charge of Dray and Streubel (1984).
Symmetry and Stochastic Gene Regulation
NASA Astrophysics Data System (ADS)
Ramos, Alexandre F.; Hornos, José E. M.
2007-09-01
Lorentz-like noncompact Lie symmetry SO(2,1) is found in a spin-boson stochastic model for gene expression. The invariant of the algebra characterizes the switch decay to equilibrium. The azimuthal eigenvalue describes the affinity between the regulatory protein and the gene operator site. Raising and lowering operators are constructed and their actions increase or decrease the affinity parameter. The classification of the noise regime of the gene arises from the group theoretical numbers.
NASA Astrophysics Data System (ADS)
Chen, Y. F.; Tung, J. C.; Chiang, P. Y.; Liang, H. C.; Huang, K. F.
2013-07-01
We employ the inhomogeneous Helmholtz equation to explore the influence of the fractional degeneracy and the pump distribution on the resonant lasing mode. Theoretical analyses clearly reveal the relationship between the fractional degeneracy and the emergence of the ray-wave duality. Furthermore, we perform thorough laser experiments to confirm the theoretical exploration that the resonant modes near the degenerate cavities are well localized on the ray trajectories under the condition of the off-axis pumping. We also exploit the derived wave functions to calculate the resonant strengths that can noticeably manifest the enhancements of the output powers in the degenerate cavities.
Symmetry analysis of talus bone
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
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.
Painlevé property, symmetries and symmetry reductions of the coupled Burgers system
NASA Astrophysics Data System (ADS)
Lian, Zeng-Ju; Chen, Li-Li; Lou, Sen-Yue
2005-08-01
The Painlevé property, inverse recursion operator, infinite number of symmetries and Lie symmetry reductions of the coupled Burgers equation are given explicitly. Three sets of infinitely many symmetries of the considered model are obtained by acting the recursion operator and the inverse recursion operator on the trivial symmetries such as the identity transformation, the space translation and the scaling transformation respectively. These symmetries constitute an infinite dimensional Lie algebra while its finite dimensional Lie point symmetry subalgebra is used to find possible symmetry reductions and then the group invariant solutions.
Lie group symmetries and Riemann function of Klein-Gordon-Fock equation with central symmetry
NASA Astrophysics Data System (ADS)
Kochetov, Bogdan A.
2014-06-01
In the present paper Lie symmetry group method is applied to find new exact invariant solutions for Klein-Gordon-Fock equation with central symmetry. The found invariant solutions are important for testing finite-difference computational schemes of various boundary value problems of Klein-Gordon-Fock equation with central symmetry. The classical admitted symmetries of the equation are found. The infinitesimal symmetries of the equation are used to find the Riemann function constructively.
Polyhedra with noncrystallographic symmetry as the orbits of crystallographic point symmetry groups
NASA Astrophysics Data System (ADS)
Ovsetsina, T. I.; Chuprunov, E. V.
2015-11-01
Polyhedra with noncrystallographic symmetry are analyzed as the orbits of crystallographic point symmetry groups on a set of smooth or structured ("hatched") planes. Polyhedra with symmetrically equivalent faces, obtained using crystallographic point groups but having noncrystallographic symmetry, and polyhedra, the symmetry group T of which is crystallographic but can be implemented only on the assumption of a noncrystallographic character of the internal structure of polyhedron, are studied. The results of the analysis for all 32 point symmetry groups are listed in table.
NASA Astrophysics Data System (ADS)
Cho, Gil Young; Shiozaki, Ken; Ludwig, Andreas; Ryu, Shinsei
We discuss the entanglement spectrum(ES) of (1+1)d gapped Lorentz invariant field theories in the vicinity of a conformal field theory (CFT). In particular, for a gapped theory obtained by perturbing a CFT in infinite space by relevant perturbations, we show that the low-lying ES for the half-line is equal to the physical spectrum of the gapless CFT defined on a finite interval of length L = log (ξ / a) , which is the spectrum of a boundary CFT. Here ξ is the correlation length, a a microscopic lattice scale, and our result applies in the ''scaling limit'' where ξ >> a . A similar property has been known to hold for Baxter's Corner Transfer Matrices of a class of very special, namely integrable lattice models, for the entire ES and independent of the scaling limit. In contrast, our result applies to completely general gapped Lorentz invariant theories in the scaling limit, without the requirement of integrability, for the low-lying ES. As a consequence, while on a finite interval of length 2 R the physical spectrum of the gapped theory is known to undergo a dramatic reorganization as 2 R crosses ξ, the bipartite ES remains unchanged up to an overall scale. We apply these to (1+1)d symmetry-protected topological phases and symmetry-protected degeneracy of ES.
Broken S flavor symmetry of leptons and quarks: Mass spectra and flavor mixing patterns
NASA Astrophysics Data System (ADS)
Xing, Zhi-zhong; Yang, Deshan; Zhou, Shun
2010-06-01
We apply the discrete S3 flavor symmetry to both lepton and quark sectors of the Standard Model extended by introducing one Higgs triplet and realizing the type-II seesaw mechanism for finite neutrino masses. The resultant mass matrices of charged leptons (Ml), neutrinos (Mν), up-type quarks (Mu) and down-type quarks (Md) have a universal form consisting of two terms: one is proportional to the identity matrix I and the other is proportional to the democracy matrix D. We argue that the textures of Ml, Mu and Md are dominated by the D term, while that of Mν is dominated by the I term. This hypothesis implies a near mass degeneracy of three neutrinos and can naturally explain why the mass matrices of charged fermions are strongly hierarchical, why the quark mixing matrix is close to I and why the lepton mixing matrix contains two large angles. We discuss a rather simple perturbation ansatz to break the S3 symmetry and obtain more realistic mass spectra of leptons and quarks as well as their flavor mixing patterns. We stress that the I term, which used to be ignored from Ml, Mu and Md, is actually important because it can significantly modify the smallest lepton flavor mixing angle θ13 or three quark flavor mixing angles.
SU(4) symmetry breaking revealed by magneto-optical spectroscopy in epitaxial graphene
NASA Astrophysics Data System (ADS)
Tan, Liang Z.; Orlita, Milan; Potemski, Marek; Sprinkle, Mike; Berger, Claire; de Heer, Walter; Louie, Steven; Martinez, Gerard
2015-03-01
Electron-electron and electron-phonon interactions break the spin and valley degeneracies of the lowest Landau level (LL) in graphene. Multiple theoretical models have been proposed for the broken symmetry ground state. Previous tilted magnetic field transport experiments have obtained partial information on the ground state by probing the spin degree of freedom. In this work, we show that, via the valley-dependent electron-phonon interaction, symmetry breaking of the valley degree of freedom can be detected in infra-red transmission signatures close to magneto-phonon resonances. We have performed infra-red magneto-transmission experiments on multi-layer epitaxial graphene samples in magnetic fields up to 35 T. Following the main optical transition involving the lowest LL, we observe a new absorption transition increasing in intensity with magnetic fields greater than 26 T. Our theoretical calculations quantitatively explain these features, and unambiguously identify the charge density wave as the ground state in our samples. This work was supported by National Science Foundation Grant No. DMR10-1006184, the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Computational resources have been provided by the NSF through XSEDE resources at NICS.
Spin-photon interaction in a cavity with time-reversal symmetry breaking
NASA Astrophysics Data System (ADS)
Goryachev, Maxim; Farr, Warrick G.; Creedon, Daniel L.; Tobar, Michael E.
2014-06-01
Employing a sapphire whispering gallery mode resonator, we demonstrate features of the spin-photon interaction in cavities with broken time-reflection symmetry. The broken symmetry leads to a lifting of the degeneracy between left-handed and right-handed polarized cavity photons, which results in an observable gyrotropic effect. In the high-Q cavity limit, such a situation requires a modification of the Tavis-Cummings Hamiltonian to take into account conservation of spin angular momentum and the corresponding selection rules. As a result, the system is represented by a system of two linearly coupled bosonic modes, with each one coupled to its own subensemble of two-level systems with different energy splittings. In the experimental example, these subensembles originate from Fe3+ impurity ions effectively seen as a two-level system at the interaction frequency. The temperature dependence of the population of each subensemble (in terms of effective susceptibility of the medium) is determined experimentally in accordance with the theoretical predictions revealing various paramagnetic impurity types in the solid. The regimes of backscatterer and spin ensemble domination are discussed and compared.
Enhanced Facial Symmetry Assessment in Orthodontists
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
Symmetry measures of the electron density.
Casanova, David; Alemany, Pere; Alvarez, Santiago
2010-10-01
In this communication we define electronic symmetry operation and symmetry group measures, eSOM and eSGM, respectively, develop the basic algorithms to obtain them, and give some examples of the possible applications of these new computational tools. These new symmetry measures based on the electron density have been tested in an analysis of (a) the inversion symmetry for heteronuclear diatomic molecules, for the eclipsed and staggered conformations of ethane and tetrafluoroethane, and for a series of octahedral sulfur halides; (b) the reflection symmetry of three different conformers of tetrafluoroethene; and (c) the loss of C(6) symmetry along the B(2u) distortion mode of benzene and an analysis of rotational symmetry for different six-member ring heterocycles. PMID:20652983
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.
Bhajun, Ricky; Guyon, Laurent; Gidrol, Xavier
2016-08-01
Modularity, feedback control, functional redundancy and bowtie architecture have been proposed as key factors that confer robustness to complex biological systems. MicroRNAs (miRNAs) are highly conserved but functionally dispensable. These antinomic properties suggest that miRNAs fine-tune gene expression rather than act as genetic switches. We synthesize published and unpublished data and hypothesize that miRNA pluripotentiality acts to buffer gene expression, while miRNA degeneracy tunes the expression of targets, thus providing robustness to gene expression networks. Furthermore, we propose a Lavallière-tie architecture by integrating signal transduction, miRNAs and protein expression data to model complex gene expression networks. PMID:27038488
González, José; Molina, Rafael A
2016-04-15
We investigate the development of novel surface states when 3D Dirac or Weyl semimetals are placed under circularly polarized electromagnetic radiation. We find that the hybridization between inverted Floquet bands opens, in general, a gap, which closes at so-called exceptional points found for complex values of the momentum. This corresponds to the appearance of midgap surface states in the form of evanescent waves decaying from the surface exposed to the radiation. We observe a phenomenon reminiscent of Landau quantization by which the midgap surface states get a large degeneracy proportional to the radiation flux traversing the surface of the semimetal. We show that all of these surface states carry angular current, leading to an angular modulation of their charge that rotates with the same frequency of the radiation, which should manifest in the observation of a macroscopic chiral current in the irradiated surface. PMID:27127980
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. PMID:26550891
NASA Astrophysics Data System (ADS)
González, José; Molina, Rafael A.
2016-04-01
We investigate the development of novel surface states when 3D Dirac or Weyl semimetals are placed under circularly polarized electromagnetic radiation. We find that the hybridization between inverted Floquet bands opens, in general, a gap, which closes at so-called exceptional points found for complex values of the momentum. This corresponds to the appearance of midgap surface states in the form of evanescent waves decaying from the surface exposed to the radiation. We observe a phenomenon reminiscent of Landau quantization by which the midgap surface states get a large degeneracy proportional to the radiation flux traversing the surface of the semimetal. We show that all of these surface states carry angular current, leading to an angular modulation of their charge that rotates with the same frequency of the radiation, which should manifest in the observation of a macroscopic chiral current in the irradiated surface.
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.
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.
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.
Hidden symmetries in jammed systems
NASA Astrophysics Data System (ADS)
Morse, Peter K.; Corwin, Eric I.
2016-07-01
There are deep, but hidden, geometric structures within jammed systems, associated with hidden symmetries. These can be revealed by repeated transformations under which these structures lead to fixed points. These geometric structures can be found in the Voronoi tesselation of space defined by the packing. In this paper we examine two iterative processes: maximum inscribed sphere (MIS) inversion and a real-space coarsening scheme. Under repeated iterations of the MIS inversion process we find invariant systems in which every particle is equal to the maximum inscribed sphere within its Voronoi cell. Using a real-space coarsening scheme we reveal behavior in geometric order parameters which is length-scale invariant.
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.
Unified framework of topological phases with symmetry
NASA Astrophysics Data System (ADS)
Gu, Yuxiang; Hung, Ling-Yan; Wan, Yidun
2014-12-01
In topological phases in 2 +1 dimensions, anyons fall into representations of quantum group symmetries. As proposed in our work [Hung and Wan, Int. J. Mod. Phys. B 28, 1450172 (2014), 10.1142/S0217979214501720], the physics of a symmetry enriched phase can be extracted by the mathematics of (hidden) quantum group symmetry breaking of a "parent phase." This offers a unified framework and classification of the symmetry enriched (topological) phases, including symmetry protected trivial phases as well. In this paper, we extend our investigation to the case where the "parent" phases are non-Abelian topological phases. We show explicitly how one can obtain the topological data and symmetry transformations of the symmetry enriched phases from that of the "parent" non-Abelian phase. Two examples are computed: (1) the Ising×Ising¯ phase breaks into the Z2 toric code with Z2 global symmetry; (2) the SU (2) 8 phase breaks into the chiral Fibonacci × Fibonacci phase with a Z2 symmetry, a first non-Abelian example of symmetry enriched topological phase beyond the gauge-theory construction.
NASA Astrophysics Data System (ADS)
Sameer, M. Ikhdair; Majid, Hamzavi
2013-04-01
Approximate analytical bound-state solutions of the Dirac particle in the fields of attractive and repulsive Rosen—Morse (RM) potentials including the Coulomb-like tensor (CLT) potential are obtained for arbitrary spin-orbit quantum number κ. The Pekeris approximation is used to deal with the spin-orbit coupling terms κ (κ± 1)r-2. In the presence of exact spin and pseudospin (p-spin) symmetries, the energy eigenvalues and the corresponding normalized two-component wave functions are found by using the parametric generalization of the Nikiforov—Uvarov (NU) method. The numerical results show that the CLT interaction removes degeneracies between the spin and p-spin state doublets.
Symmetry and Symmetry Breaking in Planetary Magnetic Fields
NASA Astrophysics Data System (ADS)
Cao, H.; Russell, C. T.; Aurnou, J. M.; Soderlund, K. M.; Dougherty, M. K.
2014-12-01
Six out of eight solar system planets currently possess global-scale intrinsic magnetic fields. Different symmetry and symmetry breaking with respect to the spin-axis and the equatorial plane of the host planet can be found for different planetary magnetic fields. With respect to the spin-axis, the magnetic fields of Mercury, Earth, Jupiter, and Saturn are dominated by the axisymmetric part while the magnetic fields of Uranus and Neptune show no such alignment. Moreover, non-axisymmetric components have not been determined unambiguously for the magnetic fields of Mercury and Saturn. With respect to the equatorial plane, the magnetic fields of Earth, Jupiter, and Saturn show small but non-negligible asymmetry while the magnetic field of Mercury shows a significant asymmetry. The magnetic fields of Uranus and Neptune likely possess similar strength in the two hemispheres divided by the equatorial plane, but this needs to be confirmed with future measurements. Here we present our interpretation of the magnetic fields of Mercury and Saturn, both of which are often referred to as anomalous dipolar dynamos. For Mercury, we will show that volumetrically distributed buoyancy sources in its liquid iron core can naturally lead to equatorial symmetry breaking in the dynamo generated magnetic field as observed by MESSENGER. We will also show that the size of the solid inner core inside Mercury is likely smaller than 1000 km and could be detected indirectly with high-spatial-resolution magnetic field measurements near Mercury's north pole. In addition, we will show that degree-2 longitudinal variations observed in the magnetic equator positions of Mercury could have an internal origin. For Saturn's magnetic field, although its extreme axisymmetry could in principle be explained by a stably-stratified electrically-conducting layer on top of the dynamo region, more features such as equator-to-pole field contrasts cannot be explained by this same mechanism simultaneously. Towards
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.
Contact symmetries and Hamiltonian thermodynamics
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.
Duality symmetries in string theory
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.
Introduction to Electroweak Symmetry Breaking
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.
Discrete symmetries and mixing of Dirac neutrinos
NASA Astrophysics Data System (ADS)
Esmaili, Arman; Smirnov, Alexei Yu.
2015-11-01
We study the mixing of the Dirac neutrinos in the residual symmetries approach. The key difference from the Majorana case is that the Dirac mass matrix may have larger symmetries: Gν=Zn with n ≥3 . The symmetry group relations have been generalized to the case of Dirac neutrinos. Using them, we have found all new relations between mixing parameters and corresponding symmetry assignments, which are in agreement with the present data. The viable relations exist only for the charged lepton residual symmetry Gℓ=Z2. The relations involve elements of the rows of the Pontecorvo-Maki-Nakagawa-Sakata matrix and lead to precise predictions of the 2-3 mixing angle and certain ranges of the C P violation phase. For larger symmetries Gℓ, an agreement with the data can be achieved if ˜10 % corrections related to breaking of Gℓ and Gν are included.
Symmetry properties in polarimetric remote sensing
NASA Technical Reports Server (NTRS)
Nghiem, S. V.; Yueh, S. H.; Kwok, R.; Li, F. K.
1992-01-01
This paper presents the relations among polarimetric backscattering coefficients from the viewpoint of symmetry groups. Symmetry of geophysical media encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered for both reciprocal and nonreciprocal cases. On the basis of the invariance under symmetry transformations in the linear polarization basis, the scattering coefficients are related by a set of equations which restrict the number of independent parameters in the polarimetric covariance matrix. The properties derived under these transformations are general and apply to all scattering mechanisms in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the derived symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is discussed. As a practical application, the results from this paper provide new methods for the external calibration of polarimetric radars without the deployment of man-made calibration targets.
Emergence of symmetry breaking in fucoid zygotes.
Homblé, Fabrice; Léonetti, Marc
2007-06-01
Fucoid zygotes are model cells for the study of symmetry breaking in plants. After fertilization, their initial spherical symmetry reduces to an axial symmetry, even in the absence of any external cue. This indicates that zygotes have an intrinsic ability to break symmetry in a way that is solely dependent on their internal biochemical and/or biophysical state. In our opinion, symmetry breaking is a self-organized process. It arises around the fucoid zygotes from the ion dynamics through channels (voltage-dependent calcium channels and a potassium leak) and outside the membrane (electrodiffusion owing to slower calcium diffusion compared with potassium). The robustness of this self-organized process and its lability ensure its relevance in plants where symmetry breaking is correlated with transcellular ion currents. PMID:17499009
Discrete flavor symmetries for degenerate solar neutrino pair and their predictions
NASA Astrophysics Data System (ADS)
Joshipura, Anjan S.; Patel, Ketan M.
2014-08-01
Flavor symmetries appropriate for describing a neutrino spectrum with degenerate solar pair and a third massive or massless neutrino are discussed. We demand that the required residual symmetries of the leptonic mass matrices be subgroups of some discrete symmetry group Gf. Gf can be a subgroup of SU(3) if the third neutrino is massive and we derive general results on the mixing angle predictions for various discrete subgroups of SU(3) divided into the two classes, called type C and D in Miller et al. [Theory and Applications of Finite Groups (John Wiley & Sons, New York, 1916)]. The main results are (a) All the SU(3) subgroups of type C fail in simultaneously giving correct θ13 and θ23. (b) All the groups of type D can predict a relation cos2θ13sin2θ23=1/3 among the mixing angles which appears to be a good zeroth order approximation. Among these, various Δ(6n2) groups with n ≥8 can simultaneously lead also to sin2θ13 in agreement with global fit at 3σ. (c) The group Σ(168)≅PSL(2,7) predicts near to the best fit value for θ13 and θ23 within the 1σ range. All discrete subgroups of U(3) with order <512 and having three-dimensional irreducible representation are considered as possible Gf when the third neutrino is massless. Only seven of them are shown to be viable and three of these can correctly predict θ13 and/or θ23. The solar angle remains undetermined at the leading order in all the cases due to degeneracy in the masses. A class of general perturbations which can correctly reproduce all the observables is discussed in the context of several groups which offer good leading order predictions.
The near-symmetry of proteins.
Bonjack-Shterengartz, Maayan; Avnir, David
2015-04-01
The majority of protein oligomers form clusters which are nearly symmetric. Understanding of that imperfection, its origins, and perhaps also its advantages requires the conversion of the currently used vague qualitative descriptive language of the near-symmetry into an accurate quantitative measure that will allow to answer questions such as: "What is the degree of symmetry deviation of the protein?," "how do these deviations compare within a family of proteins?," and so on. We developed quantitative methods to answer this type of questions, which are capable of analyzing the whole protein, its backbone or selected portions of it, down to comparison of symmetry-related specific amino-acids, and which are capable of visualizing the various levels of symmetry deviations in the form of symmetry maps. We have applied these methods on an extensive list of homomers and heteromers and found that apparently all proteins never reach perfect symmetry. Strikingly, even homomeric protein clusters are never ideally symmetric. We also found that the main burden of symmetry distortion is on the amino-acids near the symmetry axis; that it is mainly the more hydrophilic amino-acids that take place in symmetry-distortive interactions; and more. The remarkable ability of heteromers to preserve near-symmetry, despite the different sequences, was also shown and analyzed. The comprehensive literature on the suggested advantages symmetric oligomerizations raises a yet-unsolved key question: If symmetry is so advantageous, why do proteins stop shy of perfect symmetry? Some tentative answers to be tested in further studies are suggested in a concluding outlook. PMID:25354765
Scars of symmetries in quantum chaos
Delande, D.; Gay, J.C.
1987-10-19
The hydrogen atom in a magnetic field is a classically chaotic Hamiltonian system. The energy-level fluctuations have been shown recently to obey a random-matrix model. Here we go beyond the statistical analysis by studying the destruction of the low-field dynamical symmetries. We especially establish the existence of scars of symmetries in the chaotic regime. The symmetry properties are no longer associated with one given level, but fractalized onto clusters of levels, generating a long-range order.
Symmetry-protected single-photon subradiance
NASA Astrophysics Data System (ADS)
Cai, Han; Wang, Da-Wei; Svidzinsky, Anatoly A.; Zhu, Shi-Yao; Scully, Marlan O.
2016-05-01
We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shifts cannot be neglected. We find that antisymmetric states are subradiant states for distributions with reflection symmetry. Continuous symmetry can also be used to achieve subradiance. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.
Search for primordial symmetry breakings in CMB
NASA Astrophysics Data System (ADS)
Shiraishi, Maresuke
2016-06-01
There are possibilities to violate symmetries (e.g. parity and rotational invariance) in the primordial cosmological fluctuations. Such symmetry breakings can imprint very rich signatures in late-time phenomena, which may be possible to observe. Especially, Cosmic Microwave Background (CMB) will change its face drastically, corresponding to the symmetry-breaking types, since the harmonic-space representation is very sensitive to the statistical, spin and angular dependences of cosmological perturbations. Here, we discuss (1) general responses of CMB to the symmetry breakings, (2) some theoretical models creating interesting CMB signatures, and (3) aspects of the estimation from observational data.
Asymptotic symmetries of Yang-Mills theory
NASA Astrophysics Data System (ADS)
Strominger, Andrew
2014-07-01
Asymptotic symmetries at future null infinity ( +) of Minkowski space for electrodynamics with massless charged fields, as well as nonabelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through + suggests the symmetry group is infinite-dimensional. It is conjectured that the symmetries include a G Kac-Moody symmetry whose generators are "large" gauge transformations which approach locally holomorphic functions on the conformal two-sphere at + and are invariant under null translations. The Kac-Moody currents are constructed from the gauge field at the future boundary of +. The current Ward identities include Weinberg's soft photon theorem and its colored extension.
Evidence for tetrahedral symmetry in (16)O.
Bijker, R; Iachello, F
2014-04-18
We derive the rotation-vibration spectrum of a 4α configuration with tetrahedral symmetry Td and show evidence for the occurrence of this symmetry in the low-lying spectrum of (16)O. All vibrational states with A, E, and F symmetry appear to have been observed as well as the rotational bands with LP=0+, 3-, 4+, 6+ on the A states and part of the rotational bands built on the E, F states. We derive analytic expressions for the form factors and B(EL) values of the ground-state rotational band and show that the measured values support the tetrahedral symmetry of this band. PMID:24785032
A K3 sigma model with : symmetry
NASA Astrophysics Data System (ADS)
Gaberdiel, Matthias R.; Taormina, Anne; Volpato, Roberto; Wendland, Katrin
2014-02-01
The K3 sigma model based on the -orbifold of the D 4-torus theory is studied. It is shown that it has an equivalent description in terms of twelve free Majorana fermions, or as a rational conformal field theory based on the affine algebra . By combining these different viewpoints we show that the = (4 , 4) preserving symmetries of this theory are described by the discrete symmetry group : . This model therefore accounts for one of the largest maximal symmetry groups of K3 sigma models. The symmetry group involves also generators that, from the orbifold point of view, map untwisted and twisted sector states into one another.
Noether gauge symmetry approach in quintom cosmology
NASA Astrophysics Data System (ADS)
Aslam, Adnan; Jamil, Mubasher; Momeni, Davood; Myrzakulov, Ratbay; Rashid, Muneer Ahmad; Raza, Muhammad
2013-12-01
In literature usual point like symmetries of the Lagrangian have been introduced to study the symmetries and the structure of the fields. This kind of Noether symmetry is a subclass of a more general family of symmetries, called Noether gauge symmetries (NGS). Motivated by this mathematical tool, in this paper, we study the generalized Noether symmetry of quintom model of dark energy, which is a two component fluid model with quintessence and phantom scalar fields. Our model is a generalization of the Noether symmetries of a single and multiple components which have been investigated in detail before. We found the general form of the quintom potential in which the whole dynamical system has a point like symmetry. We investigated different possible solutions of the system for diverse family of gauge function. Specially, we discovered two family of potentials, one corresponds to a free quintessence (phantom) and the second is in the form of quadratic interaction between two components. These two families of potential functions are proposed from the symmetry point of view, but in the quintom models they are used as phenomenological models without clear mathematical justification. From integrability point of view, we found two forms of the scale factor: one is power law and second is de-Sitter. Some cosmological implications of the solutions have been investigated.
Issues in standard model symmetry breaking
Golden, M.
1988-04-01
This work discusses the symmetry breaking sector of the SU(2) x U(1) electroweak model. The first two chapters discuss Higgs masses in two simple Higgs models. The author proves low-enery theorems for the symmetry breaking sector: The threshold behavior of gauge-boson scattering is completely determined, whenever the symmetry breaking sector meets certain simple conditions. The author uses these theorems to derive event rates for the superconducting super collider (SSC). The author shows that the SSC may be able to determine whether the interactions of the symmetry breaking sector are strong or weak. 54 refs.
NASA Astrophysics Data System (ADS)
Harder, Hauke; Macholl, Sven; Mäder, Heinrich; Fusina, Luciano; Ozier, Irving
2010-03-01
For the principal isotopologue N14S32F193 of thiazyl trifluoride in the degenerate fundamental state (v5=1), the hyperfine structure has been investigated in the Q-branch spectrum between 8 and 26.5 GHz using microwave Fourier transform waveguide spectrometers with a resolution limit of ≈30 kHz. In addition to l-type doubling spectra and l-type resonance transitions with (Δk=Δl=±2), perturbation-allowed spectra were measured with Δ(k-l)=±3,±6. The range in J was from 13 to 61; for the lower states, kl=-3,-2,-1,0,+1. For all the transitions, the hyperfine patterns observed are predicted to be doublets when only the nitrogen quadrupole Hamiltonian HQN is taken into account. Doublets were indeed measured for transitions with ΓRV=A1↔A2, where ΓRV is the rovibrational symmetry. However, when ΓRV=E↔E, triplets and quartets were observed in addition to doublets. These anomalous hyperfine patterns are shown to be due to the (Δk=±1) and (Δk=±2) matrix elements of the fluorine spin-rotation Hamiltonian HSRF characterized by the fluorine spin-rotation constants c(1)=(1)/(2)(cxz+czx*) and c(2)=(1)/(2)(cxx-cyy), respectively. These terms in HSRF lift the parity degeneracy for ΓRV=E. The rovibrational Hamiltonian HRV was adopted from an earlier partner study [S. Macholl , J. Phys. Chem. A 113, 668 (2009)]. A good fit to the hyperfine data was obtained with a standard deviation of 3.1 kHz. In the fitting process, 12 rovibrational parameters were varied, while the remaining constants in HRV were left at the values of Macholl In addition, six hyperfine parameters were determined: four in HQN, and two in HSRF. It was found that |c(1)|=7.48(24) kHz and |c(2)|=2.423(22) kHz. This determination of c(1) is the first to be reported based on frequency measurements. In all the previous detections of parity doubling where the splittings were accounted for quantitatively, the levels involved had K=|k|=1 in studies of the ground vibrational state or G≡|k-l|=1 in
PREFACE: Symmetries in Science XV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2012-08-01
Logo Bregenz, the peaceful monastery of Mehrerau and the Opera on the Floating Stage again provided the setting for the international symposium 'Symmetries in Science'. The series which has been running for more than 30 years brings together leading theoreticians whose area of research is, in one way or another, related to symmetry. Since 1992 the meeting took place biannually in Brengez until 2003. In 2009, with the endorsement of the founder, Professor Bruno Gruber, we succeeded in re-establishing the series without external funding. The resounding success of that meeting encouraged us to continue in 2011 and, following on the enthusiasm and positive feedback of the participants, we expect to continue in 2013. Yet again, our meeting in 2011 was very international in flavour and brought together some 30 participants representing 12 nationalities, half of them from countries outside the European Union (from New Zealand to Mexico, Russia to Israel). The broad spectrum, a mixture of experienced experts and highly-motivated newcomers, the intensive exchange of ideas in a harmonious and relaxed atmosphere and the resulting joint projects are probably the secrets of why this meeting is considered to be so special to its participants. At the resumption in 2009 some leading experts and younger scientists from economically weak countries were unable to attend due to the lack of financial resources. This time, with the very worthy and unbureaucratic support of the 'Vereinigung von Freunden und Förderern der J W Goethe-Universität Frankfurt am Main' (in short: 'Friends and Supporters of the Frankfurt University'), it was possible for all candidates to participate. In particular some young, inspired scientists had the chance of presenting their work to a very competent, but also friendly, audience. We wish to thank the 'Freunde und Förderer' for supporting Symmetries in Science XV. Almost all participants contributed to the publication of this Conference Proceedings. There
NASA Astrophysics Data System (ADS)
Dutton, Aaron A.; Macciò, Andrea V.; Mendel, J. Trevor; Simard, Luc
2013-07-01
We use the relations between aperture stellar velocity dispersion (σap), stellar mass (MSPS) and galaxy size (Re) for a sample of ˜150 000 early-type galaxies from Sloan Digital Sky Survey/DR7 to place constraints on the stellar initial mass function (IMF) and dark halo response to galaxy formation. We build λ cold dark matter-based mass models that reproduce, by construction, the relations between galaxy size, light concentration and stellar mass, and use the spherical Jeans equations to predict σap. Given our model assumptions (including those in the stellar population synthesis models), we find that reproducing the median σap versus MSPS relation is not possible with both a universal IMF and a universal dark halo response. Significant departures from a universal IMF and/or dark halo response are required, but there is a degeneracy between these two solutions. We show that this degeneracy can be broken using the strength of the correlation between residuals of the velocity-mass (Δlog σap) and size-mass (Δlog Re) relations. The slope of this correlation, ∂VR ≡ Δlog σap/Δlog Re, varies systematically with galaxy mass from ∂VR ≃ -0.45 at MSPS ˜ 1010 M⊙ to ∂VR ≃ -0.15 at MSPS ˜ 1011.6 M⊙. The virial Fundamental Plane (FP) has ∂VR = -1/2, and thus we find that the tilt of the observed FP is mass dependent. Reproducing this tilt requires both a non-universal IMF and a non-universal halo response. Our best model has mass-follows-light at low masses (MSPS ≲ 1011.2 M⊙) and unmodified Navarro, Frenk and White haloes at MSPS ˜ 1011.5 M⊙. The stellar masses imply a mass-dependent IMF which is `lighter' than Salpeter at low masses and `heavier' than Salpeter at high masses.
Voit, E O
1992-04-01
An S-system is a set of first-order nonlinear differential equations that all have the same structure: The derivative of a variable is equal to the difference of two products of power-law functions. S-systems have been used as models for a variety of problems, primarily in biology. In addition, S-systems possess the interesting property that large classes of differential equations can be recast exactly as S-systems, a feature that has been proven useful in statistics and numerical analysis. Here, simple criteria are introduced that determine whether an S-system possesses certain types of symmetries and how the underlying transformation groups can be constructed. If a transformation group exists, families of solutions can be characterized, the number of S-system equations necessary for solution can be reduced, and some boundary value problems can be reduced to initial value problems. PMID:1591448
PREFACE: Symmetries in Science XVI
NASA Astrophysics Data System (ADS)
2014-10-01
This volume of the proceedings ''Symmetries in Science XVI'' is dedicated to the memory of Miguel Lorente and Allan Solomon who both participated several times in these Symposia. We lost not only two great scientists and colleagues, but also two wonderful persons of high esteem whom we will always remember. Dieter Schuch, Michael Ramek There is a German saying ''all good things come in threes'' and ''Symmetries in Science XVI'', convened July 20-26, 2013 at the Mehrerau Monastery, was our third in the sequel of these symposia since taking it over from founder Bruno Gruber who instigated it in 1988 (then in Lochau). Not only the time seemed to have been perfect (one week of beautiful sunshine), but also the medley of participants could hardly have been better. This time, 34 scientists from 16 countries (more than half outside the European Union) came together to report and discuss their latest results in various fields of science, all related to symmetries. The now customary grouping of renowned experts and talented newcomers was very rewarding and stimulating for all. The informal, yet intense, discussions at ''Gasthof Lamm'' occurred (progressively later) each evening till well after midnight and finally till almost daybreak! However, prior to the opening ceremony and during the conference, respectively, we were informed that Miguel Lorente and Allan Solomon had recently passed away. Both attended the SIS Symposia several times and had many friends among present and former participants. Professor Peter Kramer, himself a long-standing participant and whose 80th birthday commemoration prevented him from attending SIS XVI, kindly agreed to write the obituary for Miguel Lorente. Professors Richard Kerner and Carol Penson (both also former attendees) penned, at very short notice, the tribute to Allan Solomon. The obituaries are included in these Proceedings and further tributes have been posted to our conference website. In 28 lectures and an evening poster
Electroweak symmetry breaking via QCD.
Kubo, Jisuke; Lim, Kher Sham; Lindner, Manfred
2014-08-29
We propose a new mechanism to generate the electroweak scale within the framework of QCD, which is extended to include conformally invariant scalar degrees of freedom belonging to a larger irreducible representation of SU(3)c. The electroweak symmetry breaking is triggered dynamically via the Higgs portal by the condensation of the colored scalar field around 1 TeV. The mass of the colored boson is restricted to be 350 GeV≲mS≲3 TeV, with the upper bound obtained from perturbative renormalization group evolution. This implies that the colored boson can be produced at the LHC. If the colored boson is electrically charged, the branching fraction of the Higgs boson decaying into two photons can slightly increase, and moreover, it can be produced at future linear colliders. Our idea of nonperturbative electroweak scale generation can serve as a new starting point for more realistic model building in solving the hierarchy problem. PMID:25215976
Wormhole dynamics in spherical symmetry
Hayward, Sean A.
2009-06-15
A dynamical theory of traversable wormholes is detailed in spherical symmetry. Generically a wormhole consists of a tunnel of trapped surfaces between two mouths, defined as temporal outer trapping horizons with opposite senses, in mutual causal contact. In static cases, the mouths coincide as the throat of a Morris-Thorne wormhole, with surface gravity providing an invariant measure of the radial curvature or ''flaring-out''. The null energy condition must be violated at a wormhole mouth. Zeroth, first, and second laws are derived for the mouths, as for black holes. Dynamic processes involving wormholes are reviewed, including enlargement or reduction, and interconversion with black holes. A new area of wormhole thermodynamics is suggested.
Neutrino properties and fundamental symmetries
Bowles, T.J.
1996-07-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). There are two components to this work. The first is a development of a new detection scheme for neutrinos. The observed deficit of neutrinos from the Sun may be due to either a lack of understanding of physical processes in the Sun or may be due to neutrinos oscillating from one type to another during their transit from the Sun to the Earth. The Sudbury Neutrino Observatory (SNO) is designed to use a water Cerenkov detector employing one thousand tonnes of heavy water to resolve this question. The ability to distinguish muon and tau neutrinos from electron neutrinos is crucial in order to carry out a model-independent test of neutrino oscillations. We describe a developmental exploration of a novel technique to do this using {sup 3}He proportional counters. Such a method offers considerable advantages over the initially proposed method of using Cerenkov light from capture on NaCl in the SNO. The second component of this work is an exploration of optimal detector geometry for a time-reversal invariance experiment. The question of why time moves only in the forward direction is one of the most puzzling problems in modern physics. We know from particle physics measurements of the decay of kaons that there is a charge-parity symmetry that is violated in nature, implying time-reversal invariance violation. Yet, we do not understand the origin of the violation of this symmetry. To promote such an understanding, we are developing concepts and prototype apparatus for a new, highly sensitive technique to search for time-reversal-invariance violation in the beta decay of the free neutron. The optimized detector geometry is seven times more sensitive than that in previous experiments. 15 refs.
Flavor symmetries and fermion masses
Rasin, A.
1994-04-01
We introduce several ways in which approximate flavor symmetries act on fermions and which are consistent with observed fermion masses and mixings. Flavor changing interactions mediated by new scalars appear as a consequence of approximate flavor symmetries. We discuss the experimental limits on masses of the new scalars, and show that the masses can easily be of the order of weak scale. Some implications for neutrino physics are also discussed. Such flavor changing interactions would easily erase any primordial baryon asymmetry. We show that this situation can be saved by simply adding a new charged particle with its own asymmetry. The neutrality of the Universe, together with sphaleron processes, then ensures a survival of baryon asymmetry. Several topics on flavor structure of the supersymmetric grand unified theories are discussed. First, we show that the successful predictions for the Kobayashi-Maskawa mixing matrix elements, V{sub ub}/V{sub cb} = {radical}m{sub u}/m{sub c} and V{sub td}/V{sub ts} = {radical}m{sub d}/m{sub s}, are a consequence of a large class of models, rather than specific properties of a few models. Second, we discuss how the recent observation of the decay {beta} {yields} s{gamma} constrains the parameter space when the ratio of the vacuum expectation values of the two Higgs doublets, tan{Beta}, is large. Finally, we discuss the flavor structure of proton decay. We observe a surprising enhancement of the branching ratio for the muon mode in SO(10) models compared to the same mode in the SU(5) model.
Rare Isotopes and Fundamental Symmetries
NASA Astrophysics Data System (ADS)
Brown, B. Alex; Engel, Jonathan; Haxton, Wick; Ramsey-Musolf, Michael; Romalis, Michael; Savard, Guy
2009-01-01
Experiments searching for new interactions in nuclear beta decay / Klaus P. Jungmann -- The beta-neutrino correlation in sodium-21 and other nuclei / P. A. Vetter ... [et al.] -- Nuclear structure and fundamental symmetries/ B. Alex Brown -- Schiff moments and nuclear structure / J. Engel -- Superallowed nuclear beta decay: recent results and their impact on V[symbol] / J. C. Hardy and I. S. Towner -- New calculation of the isospin-symmetry breaking correlation to superallowed Fermi beta decay / I. S. Towner and J. C. Hardy -- Precise measurement of the [symbol]H to [symbol]He mass difference / D. E. Pinegar ... [et al.] -- Limits on scalar currents from the 0+ to 0+ decay of [symbol]Ar and isospin breaking in [symbol]Cl and [symbol]Cl / A. Garcia -- Nuclear constraints on the weak nucleon-nucleon interaction / W. C. Haxton -- Atomic PNC theory: current status and future prospects / M. S. Safronova -- Parity-violating nucleon-nucleon interactions: what can we learn from nuclear anapole moments? / B. Desplanques -- Proposed experiment for the measurement of the anapole moment in francium / A. Perez Galvan ... [et al.] -- The Radon-EDM experiment / Tim Chupp for the Radon-EDM collaboration -- The lead radius Eexperiment (PREX) and parity violating measurements of neutron densities / C. J. Horowitz -- Nuclear structure aspects of Schiff moment and search for collective enhancements / Naftali Auerbach and Vladimir Zelevinsky -- The interpretation of atomic electric dipole moments: Schiff theorem and its corrections / C. -P. Liu -- T-violation and the search for a permanent electric dipole moment of the mercury atom / M. D. Swallows ... [et al.] -- The new concept for FRIB and its potential for fundamental interactions studies / Guy Savard -- Collinear laser spectroscopy and polarized exotic nuclei at NSCL / K. Minamisono -- Environmental dependence of masses and coupling constants / M. Pospelov.
Nonlocalization of Nonlocal Symmetry and Symmetry Reductions of the Burgers Equation
NASA Astrophysics Data System (ADS)
Jin, Yan; Jia, Man; Lou, Sen-Yue
2012-12-01
Symmetry reduction method is one of the best ways to find exact solutions. In this paper, we study the possibility of symmetry reductions of the well known Burgers equation including the nonlocal symmetry. The related new group invariant solutions are obtained. Especially, the interactions among solitons, Airy waves, and Kummer waves are explicitly given.
Teaching symmetry in the introductory physics curriculum
Hill, C. T.; Lederman, L. M.
2000-01-01
Modern physics is largely defined by fundamental symmetry principles and Noether's Theorem. Yet these are not taught, or rarely mentioned, to beginning students, thus missing an opportunity to reveal that the subject of physics is as lively and contemporary as molecular biology, and as beautiful as the arts. We prescribe a symmetry module to insert into the curriculum, of a week's length.
Quantum Mechanical Observers and Time Reparametrization Symmetry
NASA Astrophysics Data System (ADS)
Konishi, Eiji
2012-07-01
We propose that the degree of freedom of measurement by quantum mechanical observers originates in the Goldstone mode of the spontaneously broken time reparametrization symmetry. Based on the classification of quantum states by their nonunitary temporal behavior as seen in the measurement processes, we describe the concepts of the quantum mechanical observers via the time reparametrization symmetry.
Symmetry Properties of Potentiometric Titration Curves.
ERIC Educational Resources Information Center
Macca, Carlo; Bombi, G. Giorgio
1983-01-01
Demonstrates how the symmetry properties of titration curves can be efficiently and rigorously treated by means of a simple method, assisted by the use of logarithmic diagrams. Discusses the symmetry properties of several typical titration curves, comparing the graphical approach and an explicit mathematical treatment. (Author/JM)
Hidden flavor symmetries of SO(10) GUT
NASA Astrophysics Data System (ADS)
Bajc, Borut; Smirnov, Alexei Yu.
2016-08-01
The Yukawa interactions of the SO(10) GUT with fermions in 16-plets (as well as with singlets) have certain intrinsic ("built-in") symmetries which do not depend on the model parameters. Thus, the symmetric Yukawa interactions of the 10 and 126 dimensional Higgses have intrinsic discrete Z2 ×Z2 symmetries, while the antisymmetric Yukawa interactions of the 120 dimensional Higgs have a continuous SU(2) symmetry. The couplings of SO(10) singlet fermions with fermionic 16-plets have U(1) 3 symmetry. We consider a possibility that some elements of these intrinsic symmetries are the residual symmetries, which originate from the (spontaneous) breaking of a larger symmetry group Gf. Such an embedding leads to the determination of certain elements of the relative mixing matrix U between the matrices of Yukawa couplings Y10, Y126, Y120, and consequently, to restrictions of masses and mixings of quarks and leptons. We explore the consequences of such embedding using the symmetry group conditions. We show how unitarity emerges from group properties and obtain the conditions it imposes on the parameters of embedding. We find that in some cases the predicted values of elements of U are compatible with the existing data fits. In the supersymmetric version of SO(10) such results are renormalization group invariant.
Topological phases protected by point group symmetry
NASA Astrophysics Data System (ADS)
Huang, Sheng-Jie; Song, Hao; Hermele, Michael
There has been remarkable progress in the theoretical understanding of symmetry protected topological (SPT) phases. However, most theories focus on internal, or on-site, symmetries, even though spatial symmetries are important in solids. In this talk, we classify bosonic SPT phases protected by crystalline point group symmetry, which we dub point group SPT (pgSPT) phases. Our approach is based on a procedure to reduce a d-dimensional pgSPT phase to lower-dimensional SPT phases protected by internal symmetry. For three-dimensional pgSPT phases, this approach allows us to gain insight into non-trivial properties at symmetry preserving surfaces. In particular, we obtain toy models for the surfaces of certain pgSPT phases at which there is a symmetry preserving Z2 topological order with anomalous symmetry fractionalization. We also discuss connections between bosonic pgSPT phases and electronic topological crystalline insulators. This research is supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award # DE-SC0014415.
Cubic Icosahedra? A Problem in Assigning Symmetry
ERIC Educational Resources Information Center
Lloyd, D. R.
2010-01-01
There is a standard convention that the icosahedral groups are classified separately from the cubic groups, but these two symmetry types have been conflated as "cubic" in some chemistry textbooks. In this note, the connection between cubic and icosahedral symmetries is examined, using a simple pictorial model. It is shown that octahedral and…
Copper Keplerates: High-Symmetry Magnetic Molecules.
Palacios, Maria A; Moreno Pineda, Eufemio; Sanz, Sergio; Inglis, Ross; Pitak, Mateusz B; Coles, Simon J; Evangelisti, Marco; Nojiri, Hiroyuki; Heesing, Christian; Brechin, Euan K; Schnack, Jürgen; Winpenny, Richard E P
2016-01-01
Keplerates are molecules that contain metal polyhedra that describe both Platonic and Archimedean solids; new copper keplerates are reported, with physical studies indicating that even where very high molecular symmetry is found, the low-temperature physics does not necessarily reflect this symmetry. PMID:26530901
Broken chiral symmetry on a null plane
Beane, Silas R.
2013-10-15
On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincaré generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstone’s theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann–Oakes–Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-plane description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model. -- Highlights: •A proof (the first) of Goldstone’s theorem on a null-plane is given. •The puzzle of chiral-symmetry breaking condensates on a null-plane is solved. •The emergence of spin-flavor symmetries in null-plane QCD is demonstrated.
Uvarov, Mikhail N; Kulik, Leonid V; Pichugina, Tatiana I; Dzuba, Sergei A
2011-05-01
X-band echo-detected electron paramagnetic resonance (ED EPR) spectra of triplet state of fullerene C(70) generated by continuous light illumination were found to correspond below 30K to a non-equilibrium electron spin polarization. Above 30K spectra are characteristic of Boltzmann equilibrium. Spectra were simulated fairly well with zero-field splitting parameters D=153 MHz and E and distributed within the range of 6-42 MHz. The origin of E distribution is attributed to the Jahn-Teller effect, which in glassy matrix is expected to depend on the local surrounding of a fullerene molecule (a so-called E-strain). In the center of ED EPR spectra a narrow hole was observed. With increase of the microwave pulse turning angle this hole transforms into a single narrow absorptive line. Numerical simulations by density matrix formalism confirm that central hole originates from a simultaneous excitation of both allowed electron spin transitions of the triplet (T(0)↔T(+) and T(0)↔T(-)), because of their degeneracy at this spectral position. Also explanations are given why this hole has not been observed in the previously reported experiments on continuous wave EPR and on ED EPR under laser pulse excitation. PMID:21339084
Degeneracy and Effective Mass in the Valence Band of Two-Dimensional (100)-GaAs Quantum Well Systems
NASA Astrophysics Data System (ADS)
Tarquini, Vinicio; Knighton, Talbot; Wu, Zhe; Huang, Jian; Pfeifer, Loren; West, Ken
2014-03-01
Quantum Hall measurement of two-dimensional high-mobility (μ ~ 2 × 106 cm2/(V .s)) hole systems confined in a 20 nm wide (100)-GaAs quantum well have been performed for charge densities between 4 - 5 × 1010 cm-2 in a temperature range of 10-160 mK. The Fourier analysis of the Shubnikov-de Haas (SdH) oscillations of the magnetoresistance vs. the inverse of the magnetic field 1 /B⊥ reveals a single peak, indicating a degenerate heavy hole (HH) band. The corresponding hole density p =(e / h) . f agrees with the Hall measurement result within 3 % . The HH degeneracy is understood through the diminishing Rashba spin-orbit interaction due to the low charge density and the nearly symmetric confinement. SdH oscillations fitted for 0.1 T <=B⊥ <= 0 . 25 T to the Dingle parameters yield an effective mass (m*) between 0.39 me and 0.51 me that increases moderately with increasing magnetic field and charge density, in very good agreement with previous cyclotron resonance measurements. NSF DMR-1105183
Degeneracy and effective mass in the valence band of two-dimensional (100)-GaAs quantum well systems
NASA Astrophysics Data System (ADS)
Tarquini, Vinicio; Knighton, Talbot; Wu, Zhe; Huang, Jian; Pfeiffer, Loren; West, Ken
2014-03-01
Quantum Hall measurement of two-dimensional high-mobility [μ ˜2×106 cm2/(V.s)] hole systems confined in a 20 nm wide (100)-GaAs quantum well have been performed for charge densities between 4 and 5 × 1010 cm-2 in a temperature range of 10-160 mK. The Fourier analysis of the Shubnikov-de Haas (SdH) oscillations of the magnetoresistance vs. the inverse of the magnetic field 1/B reveals a single peak, indicating a degenerate heavy hole (HH) band. The hole density p =(e/h).f agrees with the Hall measurement result within 3%. The HH band degeneracy is understood through the diminishing spin-orbit interaction due to the low charge density and the nearly symmetric confinement. SdH oscillations fitted for 0.08 T ≤ B ≤ 0.24 T to the Dingle parameters yield an effective mass between 0.30 and 0.50 me in good agreement with previous cyclotron resonance results.
Levy, Mel E-mail: mlevy@tulane.edu; Anderson, James S. M.; Zadeh, Farnaz Heidar; Ayers, Paul W. E-mail: mlevy@tulane.edu
2014-05-14
Properties of exact density functionals provide useful constraints for the development of new approximate functionals. This paper focuses on convex sums of ground-level densities. It is observed that the electronic kinetic energy of a convex sum of degenerate ground-level densities is equal to the convex sum of the kinetic energies of the individual degenerate densities. (The same type of relationship holds also for the electron-electron repulsion energy.) This extends a known property of the Levy-Valone Ensemble Constrained-Search and the Lieb Legendre-Transform refomulations of the Hohenberg-Kohn functional to the individual components of the functional. Moreover, we observe that the kinetic and electron-repulsion results also apply to densities with fractional electron number (even if there are no degeneracies), and we close with an analogous point-wise property involving the external potential. Examples where different degenerate states have different kinetic energy and electron-nuclear attraction energy are given; consequently, individual components of the ground state electronic energy can change abruptly when the molecular geometry changes. These discontinuities are predicted to be ubiquitous at conical intersections, complicating the development of universally applicable density-functional approximations.
NASA Astrophysics Data System (ADS)
Gerischer, Heinz; McIntyre, Robert
1985-08-01
We have calculated the differential surface capacitance for two different semiconductors MoSe2(0001) and WSe2(0001), as a function of applied potential, for the condition of degeneracy. The calculated curves are compared with the experimentally measured capacitance for the systems, MoSe2(0001) in propylene carbonate containing 0.1 M LiClO4, for a range of crystal conductivities, and WSe2(0001) in acetonitrile containing 0.2 M (C3H7)4N BF4. As expected the experimental values are significantly lower than the calculated values, since the measured capacitance is the total capacitance for the system which is described by the surface capacitance of the semiconductor in series with the Helmholtz capacitance. Calculations based on this model, using the data for the Helmholtz capacitance for a mercury electrode in the same electrolyte, are shown to be in good agreement with the measured values. The results are discussed with particular reference to the screening distance for the semiconductor surface charge in the degenerate region.
NASA Astrophysics Data System (ADS)
Bétrémieux, Yan
2016-03-01
Detection of the signature of Rayleigh scattering in the transmission spectrum of an exoplanet is increasingly becoming the target of observational campaigns because the spectral slope of the Rayleigh continuum enables one to determine the scaleheight of its atmosphere in the absence of hazes. However, this is only true when one ignores the refractive effects of the exoplanet's atmosphere. I illustrate with a suite of simple isothermal clear Jovian H2-He atmosphere models with various abundances of water that refraction can decrease significantly the spectral slope of the Rayleigh continuum and that it becomes flat in the infrared. This mimics a surface, or an optically thick cloud deck, at much smaller pressures than one can probe in the non-refractive case. The relative impact of refraction on an exoplanet's transmission spectrum decreases with atmospheric temperatures and increases with stellar temperature. Refraction is quite important from a retrieval's perspective for Jovian-like planets even at the highest atmospheric temperatures (1200 K) considered in this paper, and for all stellar spectral types. Indeed, refraction breaks in large part the retrieval degeneracy between abundances of chemical species and the planet's radius because the size of spectral features increases significantly with abundances, in stark contrast with the non-refractive case which simply shifts them to a larger or smaller effective radius. Abundances inferred assuming that the atmosphere is cloud-free are lower limits. These results show how important it is to include refraction in retrieval algorithms to interpret transmission spectra of gas giants accurately.
Degeneracy and effective mass in the valence band of two-dimensional (100)-GaAs quantum well systems
Tarquini, Vinicio Knighton, Talbot; Wu, Zhe; Huang, Jian; Pfeiffer, Loren; West, Ken
2014-03-03
Quantum Hall measurement of two-dimensional high-mobility [μ∼2×10{sup 6} cm{sup 2}/(V·s)] hole systems confined in a 20 nm wide (100)-GaAs quantum well have been performed for charge densities between 4 and 5 × 10{sup 10} cm{sup −2} in a temperature range of 10–160 mK. The Fourier analysis of the Shubnikov-de Haas (SdH) oscillations of the magnetoresistance vs. the inverse of the magnetic field 1/B reveals a single peak, indicating a degenerate heavy hole (HH) band. The hole density p=(e/h)·f agrees with the Hall measurement result within 3%. The HH band degeneracy is understood through the diminishing spin-orbit interaction due to the low charge density and the nearly symmetric confinement. SdH oscillations fitted for 0.08 T ≤ B ≤ 0.24 T to the Dingle parameters yield an effective mass between 0.30 and 0.50 m{sub e} in good agreement with previous cyclotron resonance results.
NASA Astrophysics Data System (ADS)
Markoff, Sera; Nowak, Michael A.; Gallo, Elena; Hynes, Robert; Wilms, Jörn; Plotkin, Richard M.; Maitra, Dipankar; Silva, Catia V.; Drappeau, Samia
2015-10-01
Over the past decade, evidence has mounted that several aspects of black hole (BH) accretion physics proceed in a mass-invariant way. One of the best examples of this scaling is the empirical “fundamental plane of BH accretion” relation linking mass, radio, and X-ray luminosity over eight orders of magnitude in BH mass. The currently favored theoretical interpretation of this relation is that the physics governing power output in weakly accreting BHs depends more on relative accretion rate than on mass. In order to test this theory, we explore whether a mass-invariant approach can simultaneously explain the broadband spectral energy distributions from two BHs at opposite ends of the mass scale but that are at similar Eddington accretion fractions. We find that the same model, with the same value of several fitted physical parameters expressed in mass-scaling units to enforce self-similarity, can provide a good description of two data sets from V404 Cyg and M81*, a stellar and supermassive BH, respectively. Furthermore, only one of several potential emission scenarios for the X-ray band is successful, suggesting it is the dominant process driving the fundamental plane relation at this accretion rate. This approach thus holds promise for breaking current degeneracies in the interpretation of BH high-energy spectra and for constructing better prescriptions of BH accretion for use in various local and cosmological feedback applications.
NASA Astrophysics Data System (ADS)
Deppe, M.; Hartmann, S.; Macovei, M. E.; Oeschler, N.; Nicklas, M.; Geibel, C.
2008-09-01
We grew single crystals of Yb2Pt6Al15 and investigated the magnetic properties of this compound by means of susceptibility χ(T), specific heat C(T), resistivity ρ (T) and thermoelectric power S(T) measurements. While all properties follow in general the behavior typical for Kondo-lattice systems, χ(T) and C(T)/T present broad maxima in the T range 17 35 K, which matches nicely the prediction of the Coqblin Schrieffer model for J= 7/2. A large degeneracy of the local moment is also supported by a reduced Kadowaki Woods ratio. Thus, the analysis of all investigated properties evidences Yb2Pt6Al15 to be a paramagnetic Kondo-lattice system with the whole J= 7/2 multiplet involved in the formation of the Kondo state, a Kondo temperature of the order of 60 K, and a heavy Fermi-liquid ground state with a Sommerfeld coefficient γ 0 = 0.33 J (mol-Yb)-1 K-2 corresponding to a mass enhancement of the order of 30.
Teaching Point-Group Symmetry with Three-Dimensional Models
ERIC Educational Resources Information Center
Flint, Edward B.
2011-01-01
Three tools for teaching symmetry in the context of an upper-level undergraduate or introductory graduate course on the chemical applications of group theory are presented. The first is a collection of objects that have the symmetries of all the low-symmetry and high-symmetry point groups and the point groups with rotational symmetries from 2-fold…
On Gauging Symmetry of Modular Categories
NASA Astrophysics Data System (ADS)
Cui, Shawn X.; Galindo, César; Plavnik, Julia Yael; Wang, Zhenghan
2016-05-01
Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase induces a group symmetry of its corresponding UMC. Gauging is a well-known theoretical tool to promote a global symmetry to a local gauge symmetry. We give a mathematical formulation of gauging in terms of higher category formalism. Roughly, given a UMC with a symmetry group G, gauging is a 2-step process: first extend the UMC to a G-crossed braided fusion category and then take the equivariantization of the resulting category. Gauging can tell whether or not two enriched topological phases of matter are different, and also provides a way to construct new UMCs out of old ones. We derive a formula for the {H^4} -obstruction, prove some properties of gauging, and carry out gauging for two concrete examples.
Tests of gravitational symmetries with radio pulsars
NASA Astrophysics Data System (ADS)
Shao, LiJing; Wex, Norbert
2016-09-01
Symmetries play important roles in modern theories of physical laws. In this paper, we review several experimental tests of important symmetries associated with the gravitational interaction, including the universality of free fall for self-gravitating bodies, time-shift symmetry in the gravitational constant, local position invariance and local Lorentz invariance of gravity, and spacetime translational symmetries. Recent experimental explorations for post-Newtonian gravity are discussed, of which, those from pulsar astronomy are highlighted. All of these tests, of very different aspects of gravity theories, at very different length scales, favor to very high precision the predictions of the strong equivalence principle (SEP) and, in particular, general relativity which embodies SEP completely. As the founding principles of gravity, these symmetries are motivated to be promoted to even stricter tests in future.
Symmetries in geology and geophysics
Turcotte, Donald L.; Newman, William I.
1996-01-01
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. PMID:11607719
Chiral symmetries associated with angular momentum
NASA Astrophysics Data System (ADS)
Bhattacharya, M.; Kleinert, M.
2014-03-01
In quantum mechanics courses, symmetries of a physical system are usually introduced as operators which commute with the Hamiltonian. In this paper we will consider chiral symmetries which anticommute with the Hamiltonian. Typically, introductory courses at the (under)graduate level do not discuss these simple, useful and beautiful symmetries at all. The first time a student encounters them is when the Dirac equation is discussed in a course on relativistic quantum mechanics, or when particle-hole symmetry is studied in the context of superconductivity. In this paper, we will show how chiral symmetries can be simply elucidated using the theory of angular momentum, which is taught in virtually all introductory quantum mechanics courses.
Anomalous Symmetry Fractionalization and Surface Topological Order
NASA Astrophysics Data System (ADS)
Chen, Xie; Burnell, F. J.; Vishwanath, Ashvin; Fidkowski, Lukasz
2015-10-01
In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways, leading to a variety of symmetry-enriched topological (SET) phases. While the symmetry fractionalization must be consistent with the fusion and braiding rules of the anyons, not all ostensibly consistent symmetry fractionalizations can be realized in 2D systems. Instead, certain "anomalous" SETs can only occur on the surface of a 3D symmetry-protected topological (SPT) phase. In this paper, we describe a procedure for determining whether a SET of a discrete, on-site, unitary symmetry group G is anomalous or not. The basic idea is to gauge the symmetry and expose the anomaly as an obstruction to a consistent topological theory combining both the original anyons and the gauge fluxes. Utilizing a result of Etingof, Nikshych, and Ostrik, we point out that a class of obstructions is captured by the fourth cohomology group H4(G ,U (1 )) , which also precisely labels the set of 3D SPT phases, with symmetry group G . An explicit procedure for calculating the cohomology data from a SET is given, with the corresponding physical intuition explained. We thus establish a general bulk-boundary correspondence between the anomalous SET and the 3D bulk SPT whose surface termination realizes it. We illustrate this idea using the chiral spin liquid [U (1 )2 ] topological order with a reduced symmetry Z2×Z2⊂SO (3 ) , which can act on the semion quasiparticle in an anomalous way. We construct exactly solved 3D SPT models realizing the anomalous surface terminations and demonstrate that they are nontrivial by computing three-loop braiding statistics. Possible extensions to antiunitary symmetries are also discussed.
NASA Astrophysics Data System (ADS)
Ghosh, Monojit; Ghoshal, Pomita; Goswami, Srubabati; Nath, Newton; Raut, Sushant K.
2016-01-01
The three major unknown neutrino oscillation parameters at the present juncture are the mass hierarchy, the octant of the mixing angle θ23 and the C P phase δC P . It is well known that the presence of hierarchy-δC P and octant degeneracies affects the unambiguous determination of these parameters. In this paper, we show that a comprehensive way to study the remaining parameter degeneracies is in the form of a generalized hierarchy-θ23-δC P degeneracy. This is best depicted as contours in the test (θ23-δC P ) plane for different representative true values of parameters. We show that the wrong-hierarchy and/or wrong-octant solutions can be further classified into eight different solutions depending on whether they occur with the wrong or right value of δC P. These eight solutions are different from the original eightfold degenerate solutions and can exist, in principle, even if θ13 is known. These multiple solutions, apart from affecting the determination of the true hierarchy and octant, also affect the accurate estimation of δC P. We identify which of these eight different degenerate solutions can occur in the test (θ23-δC P) parameter space, taking the long-baseline experiment NO ν A running in the neutrino mode as an example. The inclusion of the NO ν A antineutrino run removes the wrong-octant solutions appearing with both right and wrong hierarchy. Adding T2K data to this resolves the wrong hierarchy-right octant solutions to a large extent. The remaining wrong-hierarchy solutions can be removed by combining NO ν A +T 2 K with atmospheric neutrino data. We demonstrate this using ICAL@INO as the prototype atmospheric neutrino detector. We find that the degeneracies can be resolved at the 2 σ level by the combined data set, for the true parameter space considered in the study.
PREFACE: Symmetries in Science XIV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2010-04-01
Symmetries Logo This volume of the proceedings "Symmetries in Science XIV" is dedicated to the memory of our colleagues and dear friends Marcos Moshinsky and Yuriĭ Smirnov who regularly participated in these Symposia and were a great inspiration to many. We shall miss them. Dieter Schuch and Michael Ramek The international symposium "Symmetries in Science XIV" held at Collegium Mehrerau in Bregenz, Austria from July 19-24, 2009, attended by 32 scientists from 11 countries, was an experiment, performed by theoreticians. Aim of this experiment was to find out if the desire to revive or even continue this conference series was stronger than the very restricted pecuniary boundary conditions. It obviously was! After its establishment by Bruno Gruber in 1979, the biennial series settled in the very stimulating atmosphere of the monastery Mehrerau, which provided the ideal environment for a limited number of invited participants to exchange ideas, without parallel sessions, and pursue deeper discussions (at the latest in the evening at "Gasthof Lamm"). When the conference series terminated in 2003, former participants were quite disappointed. Meeting again at several (larger) conferences in subsequent years, there were repeated expressions of "the lack of a Bregenz-type meeting in our field nowadays" and the question of a possible "revitalization", even without external funding. After some hesitation, but also driven by our own desire to reinstate the series, we consulted Bruno who not only approved wholeheartedly but also offered his full support. It all finally led to the symposium in July 2009. The atmosphere was really like in the "good old days" and the interesting and thought-provoking presentations culminated in the publication of these Proceedings. We are grateful to Carl Bender for establishing contact with IOP making it possible for us to publish these Proceedings in the Journal of Physics Conference Series. A majority of the participants contributed to these
Natural quasicrystal with decagonal symmetry
Bindi, Luca; Yao, Nan; Lin, Chaney; Hollister, Lincoln S.; Andronicos, Christopher L.; Distler, Vadim V.; Eddy, Michael P.; Kostin, Alexander; Kryachko, Valery; MacPherson, Glenn J.; Steinhardt, William M.; Yudovskaya, Marina; Steinhardt, Paul J.
2015-01-01
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120 K to 1200 K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) ≤ 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula. PMID:25765857
Natural quasicrystal with decagonal symmetry.
Bindi, Luca; Yao, Nan; Lin, Chaney; Hollister, Lincoln S; Andronicos, Christopher L; Distler, Vadim V; Eddy, Michael P; Kostin, Alexander; Kryachko, Valery; MacPherson, Glenn J; Steinhardt, William M; Yudovskaya, Marina; Steinhardt, Paul J
2015-01-01
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120 K to 1200 K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) ≤ 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula. PMID:25765857
PREFACE: Symmetries in Science XVI
NASA Astrophysics Data System (ADS)
2014-10-01
This volume of the proceedings ''Symmetries in Science XVI'' is dedicated to the memory of Miguel Lorente and Allan Solomon who both participated several times in these Symposia. We lost not only two great scientists and colleagues, but also two wonderful persons of high esteem whom we will always remember. Dieter Schuch, Michael Ramek There is a German saying ''all good things come in threes'' and ''Symmetries in Science XVI'', convened July 20-26, 2013 at the Mehrerau Monastery, was our third in the sequel of these symposia since taking it over from founder Bruno Gruber who instigated it in 1988 (then in Lochau). Not only the time seemed to have been perfect (one week of beautiful sunshine), but also the medley of participants could hardly have been better. This time, 34 scientists from 16 countries (more than half outside the European Union) came together to report and discuss their latest results in various fields of science, all related to symmetries. The now customary grouping of renowned experts and talented newcomers was very rewarding and stimulating for all. The informal, yet intense, discussions at ''Gasthof Lamm'' occurred (progressively later) each evening till well after midnight and finally till almost daybreak! However, prior to the opening ceremony and during the conference, respectively, we were informed that Miguel Lorente and Allan Solomon had recently passed away. Both attended the SIS Symposia several times and had many friends among present and former participants. Professor Peter Kramer, himself a long-standing participant and whose 80th birthday commemoration prevented him from attending SIS XVI, kindly agreed to write the obituary for Miguel Lorente. Professors Richard Kerner and Carol Penson (both also former attendees) penned, at very short notice, the tribute to Allan Solomon. The obituaries are included in these Proceedings and further tributes have been posted to our conference website. In 28 lectures and an evening poster
Bilateral symmetry across Aphrodite Terra
NASA Technical Reports Server (NTRS)
Crumpler, L. S.; Head, J. W.; Campbell, D. B.
1987-01-01
There are three main highland areas on Venus: Beta Regio, Ishtar Terra and Aphrodite Terra. The latter is least known and the least mapped, yet existing analyses of Aphrodite Terra based on available Pioneer-Venus orbiter data suggest that it may be the site of extensive rifting. Some of the highest resolution (30 km) PV data (SAR) included most of the western half of Aphrodite Terra. Recent analysis of the SAR data together with Arecibo range-doppler topographic profiling (10 X 100 km horizontal and 10 m vertical resolution) across parts of Aphrodite, further characterized the nature of possible tectonic processes in the equatorial highlands. The existence of distinct topographic and radar morphologic linear discontinuities across the nearly east-west strike of Aphrodite Terra is indicated. Another prominent set of linear features is distinctly parallel to and orthogonal to the ground tracks of the PV spacecraft and are not included because of the possibility that they are artifacts. Study of the northwest trending cross-strike discontinuities (CSD's) and the nature of topographic and morphologic features along their strike suggest the presence of bilateral topographic and morphologic symmetry about the long axis of Aphrodite Terra.
Xu, Lin; Wang, Hai-Xiao; Xu, Ya-Dong; Chen, Huan-Yang; Jiang, Jian-Hua
2016-08-01
A simple core-shell two-dimensional photonic crystal is studied where the triangular lattice symmetry and the C_{6} point group symmetry give rich physics in accidental touching points of photonic bands. We systematically evaluate different types of accidental nodal points at the Brillouin zone center for transverse-magnetic harmonic modes when the geometry and permittivity of the core-shell material are continuously tuned. The accidental nodal points can have different dispersions and topological properties (i.e., Berry phases). These accidental nodal points can be the critical states lying between a topological phase and a normal phase of the photonic crystal. They are thus very important for the study of topological photonic states. We show that, without breaking time-reversal symmetry, by tuning the geometry of the core-shell material, a phase transition into the photonic quantum spin Hall insulator can be achieved. Here the "spin" is defined as the orbital angular momentum of a photon. We study the topological phase transition as well as the properties of the edge and bulk states and their application potentials in optics. PMID:27505772
Dynamical flavor origin of ZN symmetries
NASA Astrophysics Data System (ADS)
Sierra, D. Aristizabal; Dhen, Mikaël; Fong, Chee Sheng; Vicente, Avelino
2015-05-01
Discrete Abelian symmetries (ZN ) are a common "artifact" of beyond the standard model physics models. They provide different avenues for constructing consistent scenarios for lepton and quark mixing patterns, radiative neutrino mass generation as well as dark matter stabilization. We argue that these symmetries can arise from the spontaneous breaking of the Abelian U (1 ) factors contained in the global flavor symmetry transformations of the gauge-invariant kinetic Lagrangian. This will be the case provided the ultraviolet completion responsible for the Yukawa structure involves scalar fields carrying nontrivial U (1 ) charges. Guided by minimality criteria, we demonstrate the viability of this approach with two examples: first, we derive the "scotogenic" model Lagrangian, and second, we construct a setup where the spontaneous symmetry-breaking pattern leads to a Z3 symmetry which enables dark matter stability as well as neutrino mass generation at the two-loop order. This generic approach can be used to derive many other models, with residual ZN or ZN1×⋯×ZNk symmetries, establishing an intriguing link between flavor symmetries, neutrino masses and dark matter.
Relativity symmetries and Lie algebra contractions
Cho, Dai-Ning; Kong, Otto C.W.
2014-12-15
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.
Symmetries in fluctuations far from equilibrium.
Hurtado, Pablo I; Pérez-Espigares, Carlos; del Pozo, Jesús J; Garrido, Pedro L
2011-05-10
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. PMID:21493865
Symmetries in fluctuations far from equilibrium
Hurtado, Pablo I.; Pérez-Espigares, Carlos; del Pozo, Jesús J.; Garrido, Pedro L.
2011-01-01
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti–Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager’s reciprocity relations and Green–Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. PMID:21493865
Discrete symmetries and de Sitter spacetime
Cotăescu, Ion I. Pascu, Gabriel
2014-11-24
Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.
Electromagnetic Radiation under Explicit Symmetry Breaking
NASA Astrophysics Data System (ADS)
Sinha, Dhiraj; Amaratunga, Gehan A. J.
2015-04-01
We report our observation that radiation from a system of accelerating charges is possible only when there is explicit breaking of symmetry in the electric field in space within the spatial configuration of the radiating system. Under symmetry breaking, current within an enclosed area around the radiating structure is not conserved at a certain instant of time resulting in radiation in free space. Electromagnetic radiation from dielectric and piezoelectric material based resonators are discussed in this context. Finally, it is argued that symmetry of a resonator of any form can be explicitly broken to create a radiating antenna.
\\cal{PT} -symmetry in Rydberg atoms
NASA Astrophysics Data System (ADS)
Ziauddin; Chuang, You-Lin; Lee, Ray-Kuang
2016-07-01
We propose a scheme to realize parity-time ( {PT} )-symmetry in an ensemble of strongly interacting Rydberg atoms, which act as superatoms due to the dipole blockade mechanism. We show that Rydberg-dressed 87Rb atoms in a four-level inverted Y-type configuration is highly efficient to generate the refractive index for a probe field, with a symmetric (antisymmetric) profile spatially in the corresponding real (imaginary) part. Comparing with earlier investigations, the present scheme provides a versatile platform to control the system from {PT} -symmetry to non-PT -symmetry via different external parameters, i.e., coupling field detuning, probe field intensity and control field intensity.
Polytopes vibrations within Coxeter group symmetries
NASA Astrophysics Data System (ADS)
Chadzitaskos, Goce; Patera, Jiıř´; Szajewska, Marzena
2016-05-01
We are considering polytopes with exact reflection symmetry group G in the real 3-dimensional Euclidean space R3. By changing one simple element of the polytope (position of one vertex or length of an edge), one can retain the exact symmetry of the polytope by simultaneously changing other corresponding elements of the polytope. A simple method of using the symmetry of polytopes in order to determine several resonant frequencies is presented. Knowledge of these frequencies, or at least their ratios can be used for control of some principal changes of the polytopes.
Dark Matter from Binary Tetrahedral Flavor Symmetry
NASA Astrophysics Data System (ADS)
Eby, David; Frampton, Paul
2012-03-01
Binary Tetrahedral Flavor Symmetry, originally developed as a quark family symmetry and later adapted to leptons, has proved both resilient and versatile over the past decade. In 2008 a minimal T' model was developed to accommodate quark and lepton masses and mixings using a family symmetry of (T'xZ2). We examine an expansion of this earlier model using an additional Z2 group that facilitates predictions of WIMP dark matter, the Cabibbo angle, and deviations from Tribimaximal Mixing, while giving hints at the nature of leptogenesis.
Critical Symmetry and Supersymmetry in Nuclei
Iachello, Francesco
2006-04-26
The role of dynamic symmetries and supersymmetries in nuclei is reviewed. The concept of critical symmetry, appropriate to describe bosonic systems (even-even nuclei) at the critical point of a phase transition, is introduced, and the symmetry, E(5), at the critical point of spherical to {gamma}-unstable shape phase transition, is discussed. The recently introduced concept of critical supersymmetry, appropriate to describe mixed systems of bosons and fermions (odd-even nuclei) at the critical point of a phase transition is presented. The case of a j=3/2 particle at the critical point of spherical to {gamma}-unstable transition, called E(5/4), is discussed.
Mirror Symmetry for Quasi-Homogeneous Singularities
NASA Astrophysics Data System (ADS)
Rathnakumara, Himal; Jarvis, Tyler
2008-10-01
I will present an introduction to mirror symmetry in the context of string theory. Then I will describe an instance of mirror symmetry for singularties defined by quasi-homogeneous polynomials in weighted projective spaces. Milnor rings and the FJRW (Fan-Jarvis-Ruan-Witten) rings associated with these singularities and their relation to the Landua-Ginzburg A model and the Landua-Ginzburg B model will be explained. Results of the calculations for certain singularities for which the mirror symmetry conjecture has been verified will be presented.
Inversion symmetry protected topological insulators and superconductors
NASA Astrophysics Data System (ADS)
Lee, Dung-Hai; Lu, Yuan-Ming
2015-03-01
Three dimensional topological insulator represents a class of novel quantum phases hosting robust gapless boundary excitations, which is protected by global symmetries such as time reversal, charge conservation and spin rotational symmetry. In this work we systematically study another class of topological phases of weakly interacting electrons protected by spatial inversion symmetry, which generally don't support stable gapless boundary states. We classify these inversion-symmetric topological insulators and superconductors in the framework of K-theory, and construct their lattice models. We also discuss quantized response functions of these inversion-protected topological phases, which serve as their experimental signatures.
Bi, Huan -Yu; Wu, Xing -Gang; Ma, Yang; Ma, Hong -Hao; Brodsky, Stanley J.; Mojaza, Matin
2015-06-26
The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I); the other, more recent, method (PMC-II) uses the R_{δ}-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio R_{e+e–} and the Higgs partial width I'(H→bb¯). Both methods lead to the same resummed (‘conformal’) series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {β_{i}}-terms in the pQCD expansion are taken into account. In addition, we show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.
NASA Astrophysics Data System (ADS)
Bi, Huan-Yu; Wu, Xing-Gang; Ma, Yang; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin
2015-09-01
The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I); the other, more recent, method (PMC-II) uses the Rδ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio Re+e- and the Higgs partial width Γ (H → b b bar). Both methods lead to the same resummed ('conformal') series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {βi }-terms in the pQCD expansion are taken into account. We also show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.
PREFACE: Symmetries in Science XIV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2010-04-01
Symmetries Logo This volume of the proceedings "Symmetries in Science XIV" is dedicated to the memory of our colleagues and dear friends Marcos Moshinsky and Yuriĭ Smirnov who regularly participated in these Symposia and were a great inspiration to many. We shall miss them. Dieter Schuch and Michael Ramek The international symposium "Symmetries in Science XIV" held at Collegium Mehrerau in Bregenz, Austria from July 19-24, 2009, attended by 32 scientists from 11 countries, was an experiment, performed by theoreticians. Aim of this experiment was to find out if the desire to revive or even continue this conference series was stronger than the very restricted pecuniary boundary conditions. It obviously was! After its establishment by Bruno Gruber in 1979, the biennial series settled in the very stimulating atmosphere of the monastery Mehrerau, which provided the ideal environment for a limited number of invited participants to exchange ideas, without parallel sessions, and pursue deeper discussions (at the latest in the evening at "Gasthof Lamm"). When the conference series terminated in 2003, former participants were quite disappointed. Meeting again at several (larger) conferences in subsequent years, there were repeated expressions of "the lack of a Bregenz-type meeting in our field nowadays" and the question of a possible "revitalization", even without external funding. After some hesitation, but also driven by our own desire to reinstate the series, we consulted Bruno who not only approved wholeheartedly but also offered his full support. It all finally led to the symposium in July 2009. The atmosphere was really like in the "good old days" and the interesting and thought-provoking presentations culminated in the publication of these Proceedings. We are grateful to Carl Bender for establishing contact with IOP making it possible for us to publish these Proceedings in the Journal of Physics Conference Series. A majority of the participants contributed to these
Symmetry energy of warm nuclear systems
NASA Astrophysics Data System (ADS)
Agrawal, B. K.; De, J. N.; Samaddar, S. K.; Centelles, M.; Viñas, X.
2014-02-01
The temperature dependence of the symmetry energy and symmetry free energy coefficients of infinite nuclear matter and of finite nuclei is investigated. For infinite matter, both these coefficients are found to have a weaker dependence on temperature at densities close to saturation; at low but homogeneous densities, the temperature dependence becomes stronger. For finite systems, different definitions of symmetry energy coefficients are encountered in the literature yielding different values. A resolution to this problem is suggested from a global liquid-drop-inspired fit of the energies and free energies of a host of nuclei covering the entire periodic table. The hot nucleus is modeled in a subtracted finite-temperature Thomas-Fermi framework, with dynamical surface phonon coupling to nucleonic motion plugged in. Contrary to infinite nuclear matter, a substantial change in the symmetry energy coefficients is observed for finite nuclei with temperature.
RNA quaternary structure and global symmetry.
Jones, Christopher P; Ferré-D'Amaré, Adrian R
2015-04-01
Many proteins associate into symmetric multisubunit complexes. Structural analyses suggested that, by contrast, virtually all RNAs with complex 3D structures function as asymmetric monomers. Recent crystal structures revealed that several biological RNAs exhibit global symmetry at the level of their tertiary and quaternary structures. Here we survey known examples of global RNA symmetry, including the true quaternary symmetry of the bacteriophage ϕ29 prohead RNA (pRNA) and the internal pseudosymmetry of the single-chain flavin mononucleotide (FMN), glycine, and cyclic di-AMP (c-di-AMP) riboswitches. For these RNAs, global symmetry stabilizes the RNA fold, coordinates ligand-RNA interactions, and facilitates association with symmetric binding partners. PMID:25778613
Spatial Symmetries of the Local Densities
Rohozinski, S.; Dobaczewski, J.; Nazarewicz, Witold
2010-01-01
Spatial symmetries of the densities appearing in the nuclear Density Functional Theory are discussed. General forms of the local densities are derived by using methods of construction of isotropic tensor fields. The spherical and axial cases are considered.
Matrix Models, Emergent Spacetime and Symmetry Breaking
Grosse, Harald; Steinacker, Harold; Lizzi, Fedele
2009-12-15
We discuss how a matrix model recently shown to describe emergent gravity may contain extra degrees of freedom which reproduce some characteristics of the standard model, in particular the breaking of symmetries and the correct quantum numbers of fermions.
RNA quaternary structure and global symmetry
Jones, Christopher P.; Ferré-D'Amaré, Adrian R.
2015-01-01
Many proteins associate into symmetric multisubunit complexes. Structural analyses suggested that, in contrast, virtually all RNAs with complex three-dimensional structures function as asymmetric monomers. Recent crystal structures revealed that several biological RNAs exhibit global symmetry at the level of their tertiary and quaternary structures. Here, we survey known examples of global RNA symmetry, including the true quaternary symmetry of the bacteriophage ϕ29 prohead RNA (pRNA), and the internal pseudosymmetry of the single-chain flavin mononucleotide (FMN), glycine, and cyclic diadenosine monophosphate (c-di-AMP) riboswitches. For these RNAs, global symmetry stabilizes the RNA fold, coordinates ligand-RNA interactions, and facilitates association with symmetric binding partners. PMID:25778613
Spontaneous chiral symmetry breaking in metamaterials
NASA Astrophysics Data System (ADS)
Liu, Mingkai; Powell, David A.; Shadrivov, Ilya V.; Lapine, Mikhail; Kivshar, Yuri S.
2014-07-01
Spontaneous chiral symmetry breaking underpins a variety of areas such as subatomic physics and biochemistry, and leads to an impressive range of fundamental phenomena. Here we show that this prominent effect is now available in artificial electromagnetic systems, enabled by the advent of magnetoelastic metamaterials where a mechanical degree of freedom leads to a rich variety of strong nonlinear effects such as bistability and self-oscillations. We report spontaneous symmetry breaking in torsional chiral magnetoelastic structures where two or more meta-molecules with opposite handedness are electromagnetically coupled, modifying the system stability. Importantly, we show that chiral symmetry breaking can be found in the stationary response of the system, and the effect is successfully demonstrated in a microwave pump-probe experiment. Such symmetry breaking can lead to a giant nonlinear polarization change, energy localization and mode splitting, which provides a new possibility for creating an artificial phase transition in metamaterials, analogous to that in ferrimagnetic domains.
Modelling Symmetry Classes 233 and 432.
ERIC Educational Resources Information Center
Dutch, Steven I.
1986-01-01
Offers instructions and geometrical data for constructing solids of the enantiomorphous symmetry classes 233 and 432. Provides background information for each class and highlights symmetrical relationships and construction patterns. (ML)
Space and time from translation symmetry
Schwarz, A.
2010-01-15
We show that the notions of space and time in algebraic quantum field theory arise from translation symmetry if we assume asymptotic commutativity. We argue that this construction can be applied to string theory.
Matrix Models, Emergent Spacetime and Symmetry Breaking
NASA Astrophysics Data System (ADS)
Grosse, Harald; Lizzi, Fedele; Steinacker, Harold
2009-12-01
We discuss how a matrix model recently shown to describe emergent gravity may contain extra degrees of freedom which reproduce some characteristics of the standard model, in particular the breaking of symmetries and the correct quantum numbers of fermions.
Personal recollections on chiral symmetry breaking
NASA Astrophysics Data System (ADS)
Kobayashi, Makoto
2016-07-01
The author's work on the mass of pseudoscalar mesons is briefly reviewed. The emergence of the study of CP violation in the renormalizable gauge theory from consideration of chiral symmetry in the quark model is discussed.
Shift symmetry and inflation in supergravity
Brax, Philippe; Martin, Jerome
2005-07-15
We consider models of inflation in supergravity with a shift symmetry. We focus on models with one modulus and one inflaton field. The presence of this symmetry guarantees the existence of a flat direction for the inflaton field. Mildly breaking the shift symmetry using a superpotential which depends not only on the modulus, but also on the inflaton field allows one to lift the inflaton flat direction. Along the inflaton direction, the {eta} problem is alleviated. Combining the KKLT mechanism for modulus stabilization and a shift symmetry breaking superpotential of the chaotic inflation type, we find models reminiscent of 'mutated hybrid inflation' where the inflationary trajectory is curved in the modulus-inflaton plane. We analyze the phenomenology of these models and stress their differences with both chaotic and hybrid inflation.
Compact stars and the symmetry energy
NASA Astrophysics Data System (ADS)
Providência, Constana; Cavagnoli, Rafael; Menezes, Debora P.; Panda, Prafulla K.; Rabhi, Aziz
2013-02-01
The effect of the symmetry energy on some properties of compact stars which contain strange degrees of freedom is discussed. Both the onset of hyperons or kaon condensation will be considered. The hyperon-meson couplings are chosen according to experimental values of the hyperon nuclear matter potentials and possible uncertainties are considered. It is shown that a softer symmetry energy affects the onset of strangeness, namely neutral (negatively charged) strange particles set on at larger (smaller) densities, and gives rise to a smaller strangeness fraction as a function of density. A softer symmetry energy will possibily give rise to maximum mass configurations with larger masses. Hyperon-meson couplings have a strong effect on the mass of the star. It is shown that, for stars with masses above 1 Msolar, the radius of the star varies linearly with the symmetry energy slope L.
Symmetry and the Cosmic Microwave Background
NASA Technical Reports Server (NTRS)
Wollock, Edward J.
2012-01-01
A brief historical introduction to the development of observational astronomy and cosmology will be presented. The close relationship between the properties of light, symmetry, and our understanding the contents of our universe will be explored.
Composite fermions and broken symmetries in graphene.
Amet, F; Bestwick, A J; Williams, J R; Balicas, L; Watanabe, K; Taniguchi, T; Goldhaber-Gordon, D
2015-01-01
The electronic properties of graphene are described by a Dirac Hamiltonian with a four-fold symmetry of spin and valley. This symmetry may yield novel fractional quantum Hall (FQH) states at high magnetic field depending on the relative strength of symmetry-breaking interactions. However, observing such states in transport remains challenging in graphene, as they are easily destroyed by disorder. In this work, we observe in the first two Landau levels the two-flux composite-fermion sequences of FQH states between each integer filling factor. In particular, the odd-numerator fractions appear between filling factors 1 and 2, suggesting a broken-valley symmetry, consistent with our observation of a gap at charge neutrality and zero field. Contrary to our expectations, the evolution of gaps in a parallel magnetic field suggests that states in the first Landau level are not spin-polarized even up to very large out-of-plane fields. PMID:25562690
Composite fermions and broken symmetries in graphene
NASA Astrophysics Data System (ADS)
Amet, F.; Bestwick, A. J.; Williams, J. R.; Balicas, L.; Watanabe, K.; Taniguchi, T.; Goldhaber-Gordon, D.
2015-01-01
The electronic properties of graphene are described by a Dirac Hamiltonian with a four-fold symmetry of spin and valley. This symmetry may yield novel fractional quantum Hall (FQH) states at high magnetic field depending on the relative strength of symmetry-breaking interactions. However, observing such states in transport remains challenging in graphene, as they are easily destroyed by disorder. In this work, we observe in the first two Landau levels the two-flux composite-fermion sequences of FQH states between each integer filling factor. In particular, the odd-numerator fractions appear between filling factors 1 and 2, suggesting a broken-valley symmetry, consistent with our observation of a gap at charge neutrality and zero field. Contrary to our expectations, the evolution of gaps in a parallel magnetic field suggests that states in the first Landau level are not spin-polarized even up to very large out-of-plane fields.
Dynamical symmetry group and quantum splittings for a free particle on the group manifold AdS3
NASA Astrophysics Data System (ADS)
Chenaghlou, A.; Fakhri, H.
2005-08-01
It is shown that the set of all quantum states corresponding to the motion of a free particle on the group manifold AdS3 as the bases with two different labels, constitute a Hilbert space. The second label is bounded by the first one however, the first label is semibounded. The Casimir operator corresponding to the simultaneous and agreeable shifting generators of both labels along with the Cartan subalgebra generator describe the Hamiltonian of a free particle on AdS3 with dynamical symmetry group U(1,1) and infinite-fold degeneracy for the energy spectrum. The Hilbert space for the Lie algebra of the dynamical symmetry group is a reducible representation space. But the Hilbert subspaces constructed by all the bases which have a given constant value for the difference of two their labels, constitute an irreducible representation for it. It is also shown that the irreducible representation subspaces of the Lie algebras u(1,1) and u(2) are separately spanned by the bases which have the same value for the second and first labels, respectively. These two bunches of Hilbert subspaces present two different types of quantum splittings on the Hilbert space.
Convergence, Degeneracy, and Control
ERIC Educational Resources Information Center
Green, David W.; Crinion, Jenny; Price, Cathy J.
2006-01-01
Understanding the neural representation and control of language in normal bilingual speakers provides insights into the factors that constrain the acquisition of another language, insights into the nature of language expertise, and an understanding of the brain as an adaptive system. We illustrate both functional and structural brain changes…
Convergence, degeneracy and control.
Green, David W; Crinion, J; Price, Cathy J
2006-07-01
Understanding the neural representation and control of language in normal bilingual speakers provides insights into the factors that constrain the acquisition of another language, insights into the nature of language expertise and an understanding of the brain as an adaptive system. We illustrate both functional and structural brain changes associated with acquiring other languages and discuss the value of neuroimaging data in identifying individual differences and different phenotypes. Understanding normal variety is vital too if we are to understand the consequences of brain-damage in bilingual and polyglot speakers. PMID:18273402
Convergence, degeneracy and control
Green, David W.; Crinion, J.; Price, Cathy J.
2007-01-01
Understanding the neural representation and control of language in normal bilingual speakers provides insights into the factors that constrain the acquisition of another language, insights into the nature of language expertise and an understanding of the brain as an adaptive system. We illustrate both functional and structural brain changes associated with acquiring other languages and discuss the value of neuroimaging data in identifying individual differences and different phenotypes. Understanding normal variety is vital too if we are to understand the consequences of brain-damage in bilingual and polyglot speakers. PMID:18273402
Nanostructure symmetry: Relevance for physics and computing
Dupertuis, Marc-André; Oberli, D. Y.; Karlsson, K. F.; Dalessi, S.; Gallinet, B.; Svendsen, G.
2014-03-31
We review the research done in recent years in our group on the effects of nanostructure symmetry, and outline its relevance both for nanostructure physics and for computations of their electronic and optical properties. The exemples of C3v and C2v quantum dots are used. A number of surprises and non-trivial aspects are outlined, and a few symmetry-based tools for computing and analysis are shortly presented.
Noether's second theorem for BRST symmetries
Bashkirov, D.; Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.
2005-05-01
We present Noether's second theorem for graded Lagrangian systems of even and odd variables on an arbitrary body manifold X in a general case of BRST symmetries depending on derivatives of dynamic variables and ghosts of any finite order. As a preliminary step, Noether's second theorem for Lagrangian systems on fiber bundles Y{yields}X possessing gauge symmetries depending on derivatives of dynamic variables and parameters of arbitrary order is proved.
Symmetry breaking of quasihelical stellarator equilibria
Weening, R.H. )
1993-04-01
A mean-field Ohm's law is used to determine the effects of the bootstrap current on quasihelically symmetric stellarator equilibria. The Ohm's law leads to the conclusion that the effects of the bootstrap current break the quasihelical stellarator symmetry at second order in an inverse aspect ratio expansion of the magnetic field strength. The level of symmetry breaking suggests that good approximations to quasihelical stellarator fusion reactors may not be attainable.
Leptogenesis with Friedberg-Lee Symmetry
NASA Astrophysics Data System (ADS)
Araki, Takeshi; Geng, C. Q.
We consider the µ - τ symmetric Friedberg-Lee (FL) symmetry for the neutrino sector and show that a specific FL translation leads to the tribimaximal mixing pattern of the Maki-Nakagawa-Sakata (MNS) matrix. We also apply the symmetry to the type-I seesaw framework and address the baryon asymmetry of the universe through the leptogenesis mechanism. We try to establish a relation between the net baryon asymmetry and CP phases included in the MNS matrix.
Magnetohydrodynamic equilibria with incompressible flows: Symmetry approach
Cicogna, G.; Pegoraro, F.
2015-02-15
We identify and discuss a family of azimuthally symmetric, incompressible, magnetohydrodynamic plasma equilibria with poloidal and toroidal flows in terms of solutions of the Generalized Grad Shafranov (GGS) equation. These solutions are derived by exploiting the incompressibility assumption, in order to rewrite the GGS equation in terms of a different dependent variable, and the continuous Lie symmetry properties of the resulting equation and, in particular, a special type of “weak” symmetries.
Noether symmetries in the phase space
NASA Astrophysics Data System (ADS)
Díaz, Bogar; Galindo-Linares, Elizabeth; Ramírez-Romero, Cupatitzio; Silva-Ortigoza, Gilberto; Suárez-Xique, Román; Torres del Castillo, Gerardo F.; Velázquez, Mercedes
2014-09-01
The constants of motion of a mechanical system with a finite number of degrees of freedom are related to the variational symmetries of a Lagrangian constructed from the Hamiltonian of the original system. The configuration space for this Lagrangian is the phase space of the original system. The symmetries considered in this manner include transformations of the time and may not be canonical in the standard sense.
Symmetry energy in cold dense matter
NASA Astrophysics Data System (ADS)
Jeong, Kie Sang; Lee, Su Houng
2016-01-01
We calculate the symmetry energy in cold dense matter both in the normal quark phase and in the 2-color superconductor (2SC) phase. For the normal phase, the thermodynamic potential is calculated by using hard dense loop (HDL) resummation to leading order, where the dominant contribution comes from the longitudinal gluon rest mass. The effect of gluonic interaction on the symmetry energy, obtained from the thermodynamic potential, was found to be small. In the 2SC phase, the non-perturbative BCS paring gives enhanced symmetry energy as the gapped states are forced to be in the common Fermi sea reducing the number of available quarks that can contribute to the asymmetry. We used high density effective field theory to estimate the contribution of gluon interaction to the symmetry energy. Among the gluon rest masses in 2SC phase, only the Meissner mass has iso-spin dependence although the magnitude is much smaller than the Debye mass. As the iso-spin dependence of gluon rest masses is even smaller than the case in the normal phase, we expect that the contribution of gluonic interaction to the symmetry energy in the 2SC phase will be minimal. The different value of symmetry energy in each phase will lead to different prediction for the particle yields in heavy ion collision experiment.
Fluency Expresses Implicit Knowledge of Tonal Symmetry
Ling, Xiaoli; Li, Fengying; Qiao, Fuqiang; Guo, Xiuyan; Dienes, Zoltan
2016-01-01
The purposes of the present study were twofold. First, we sought to establish whether tonal symmetry produces processing fluency. Second, we sought to explore whether symmetry and chunk strength express themselves differently in fluency, as an indication of different mechanisms being involved for sub- and supra-finite state processing. Across two experiments, participants were asked to listen to and memorize artificial poetry showing a mirror symmetry (an inversion, i.e., a type of cross serial dependency); after this training phase, people completed a four-choice RT task in which they were presented with new artificial poetry. Participants were required to identify the stimulus displayed. We found that symmetry sped up responding to the second half of strings, indicating a fluency effect. Furthermore, there was a dissociation between fluency effects arising from symmetry vs. chunk strength, with stronger fluency effects for symmetry rather than chunks in the second half of strings. Taken together, we conjecture a divide between finite state and supra-finite state mechanisms in learning grammatical sequences. PMID:26869960
SUGRA new inflation with Heisenberg symmetry
Antusch, Stefan; Cefalà, Francesco E-mail: stefan.antusch@unibas.ch
2013-10-01
We propose a realisation of ''new inflation'' in supergravity (SUGRA), where the flatness of the inflaton potential is protected by a Heisenberg symmetry. Inflation can be associated with a particle physics phase transition, with the inflaton being a (D-flat) direction of Higgs fields which break some symmetry at high energies, e.g. of GUT Higgs fields or of Higgs fields for flavour symmetry breaking. This is possible since compared to a shift symmetry, which is usually used to protect a flat inflaton potential, the Heisenberg symmetry is compatible with a (gauge) non-singlet inflaton field. In contrast to conventional new inflation models in SUGRA, where the predictions depend on unknown parameters of the Kaehler potential, the model with Heisenberg symmetry makes discrete predictions for the primordial perturbation parameters which depend only on the order n at which the inflaton appears in the effective superpotential. The predictions for the spectral index n{sub s} can be close to the best-fit value of the latest Planck 2013 results.
Fluency Expresses Implicit Knowledge of Tonal Symmetry.
Ling, Xiaoli; Li, Fengying; Qiao, Fuqiang; Guo, Xiuyan; Dienes, Zoltan
2016-01-01
The purposes of the present study were twofold. First, we sought to establish whether tonal symmetry produces processing fluency. Second, we sought to explore whether symmetry and chunk strength express themselves differently in fluency, as an indication of different mechanisms being involved for sub- and supra-finite state processing. Across two experiments, participants were asked to listen to and memorize artificial poetry showing a mirror symmetry (an inversion, i.e., a type of cross serial dependency); after this training phase, people completed a four-choice RT task in which they were presented with new artificial poetry. Participants were required to identify the stimulus displayed. We found that symmetry sped up responding to the second half of strings, indicating a fluency effect. Furthermore, there was a dissociation between fluency effects arising from symmetry vs. chunk strength, with stronger fluency effects for symmetry rather than chunks in the second half of strings. Taken together, we conjecture a divide between finite state and supra-finite state mechanisms in learning grammatical sequences. PMID:26869960
Exploring symmetry in near-vacuum hohlraums
NASA Astrophysics Data System (ADS)
Berzak Hopkins, L.; Le Pape, S.; Divol, L.; Meezan, N.; MacKinnon, A.; Ho, D. D.; Jones, O.; Khan, S.; Ma, T.; Milovich, J.; Pak, A.; Ross, J. S.; Thomas, C.; Turnbull, D.; Amendt, P.; Wilks, S.; Zylstra, A.; Rinderknecht, H.; Sio, H.; Petrasso, R.
2015-11-01
Recent experiments with near-vacuum hohlraums, which utilize a minimal but non-zero helium fill, have demonstrated performance improvements relative to conventional gas-filled (0.96 - 1.6 mg/cc helium) hohlraums: minimal backscatter, reduced capsule drive degradation, and minimal suprathermal electron generation. Because this is a low laser-plasma interaction platform, implosion symmetry is controlled via pulse-shaping adjustments to laser power balance. Extending this platform to high-yield designs with high-density carbon capsules requires achieving adequate symmetry control throughout the pulse. In simulations, laser propagation is degraded suddenly by hohlraum wall expansion interacting with ablated capsule material. Nominal radiation-hydrodynamics simulations have not yet proven predictive on symmetry of the final hotspot, and experiments show more prolate symmetry than preshot calculations. Recent efforts have focused on understanding the discrepancy between simulated and measured symmetry and on alternate designs for symmetry control through varying cone fraction, trade-offs between laser power and energy, and modifications to case-to-capsule ratio. Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344.
NASA Astrophysics Data System (ADS)
He, Y. Z.; Liu, Y. M.; Bao, C. G.
2015-03-01
A generalized Gross-Pitaevskii equation adapted to the U(5 )⊃SO(5 )⊃SO(3 ) symmetry has been derived and solved for the spin-2 condensates. The spin-textile and the degeneracy of the ground state (g.s.) together with the factors affecting the stability of the g.s., such as the gap and the level density in the neighborhood of the g.s., have been studied. Based on a rigorous treatment of the spin-degrees of freedom, the spin-textiles can be understood in an N -body language. In addition to the ferro, polar, and cyclic phases, the g.s. might in a mixture of them when |M | is not equal to 0 and 2 N (M is the total magnetization). The great difference in the stability and degeneracy of the g.s. caused by varying φ (which marks the features of the interaction) and M is notable. Since the root-mean-square radius Rrms is an observable, efforts have been made to derive a set of formulas to relate Rrms and N ,ω (frequency of the trap), and φ . These formulas provide a way to check the theories with experimental data.
Spontaneous Symmetry Breaking in Nonrelativistic Systems
NASA Astrophysics Data System (ADS)
Watanabe, Haruki
The subject of condensed matter physics is very rich --- there are an infinite number of parameters producing a diversity of exciting phenomena. As a theorist, my goal is to distill general principles out of this complexity --- to construct theories that can coherently explain many known examples altogether. This thesis is composed of several attempts to develop such theories in topics related to spontaneously symmetry breaking. A remarkable feature of many-body interacting systems is that although they are described by equations respecting various symmetries, they may spontaneously organize into a state that explicitly breaks symmetries. Examples are numerous: various types of crystalline and magnetic orders, Bose-Einstein condensates of cold atoms, superfluids of liquid helium, chiral symmetry in QCD, neutron stars, and cosmic inflation. These systems with spontaneously broken continuous symmetries have gapless excitations, so called Nambu-Goldstone bosons (NGBs). Although the properties of NGBs are well understood in Lorentz-invariant systems, surprisingly, some basic properties of NGBs such as their number and dispersion in nonrelativistic systems have not been discussed from a general perspective. In the first part of this thesis, we solve this issue by developing and analyzing an effective Lagrangian that coherently captures the low-energy, long-distance physics of many different symmetry-breaking states all at once. Next, we examine whether these NGBs originating from spontaneous symmetry breaking remain to be well-defined excitations inside a metal, where low-energy electrons near Fermi surface can collide with them. Our result is a one equation criterion that specifies whether the interactions between electrons and NGBs can be ignored, or whether it completely changes their character. In the latter case, unusual phases of matter such as non-Fermi liquids may arise; in that case, NGBs are overdamped and cannot form particle-like excitations in spite of the
Perception of Mirror Symmetry in Autism Spectrum Disorders
ERIC Educational Resources Information Center
Falter, Christine M.; Bailey, Anthony J.
2012-01-01
Gestalt grouping in autism spectrum disorders (ASD) is selectively impaired for certain organization principles but for not others. Symmetry is a fundamental Gestalt principle characterizing many biological shapes. Sensitivity to symmetry was tested using the Picture Symmetry Test, which requires finding symmetry lines on pictures. Individuals…
Scalar Field Theories with Polynomial Shift Symmetries
NASA Astrophysics Data System (ADS)
Griffin, Tom; Grosvenor, Kevin T.; Hořava, Petr; Yan, Ziqi
2015-12-01
We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking. Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree P in spatial coordinates. These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrelativistic theories. Generic interactions in such theories break the polynomial shift symmetry explicitly to the constant shift. It is thus natural to ask: Given a Gaussian fixed point with polynomial shift symmetry of degree P, what are the lowest-dimension operators that preserve this symmetry, and deform the theory into a self-interacting scalar field theory with the shift symmetry of degree P? To answer this (essentially cohomological) question, we develop a new graph-theoretical technique, and use it to prove several classification theorems. First, in the special case of P = 1 (essentially equivalent to Galileons), we reproduce the known Galileon N-point invariants, and find their novel interpretation in terms of graph theory, as an equal-weight sum over all labeled trees with N vertices. Then we extend the classification to P > 1 and find a whole host of new invariants, including those that represent the most relevant (or least irrelevant) deformations of the corresponding Gaussian fixed points, and we study their uniqueness.
Residual symmetries of the gravitational field
NASA Astrophysics Data System (ADS)
Ayón-Beato, Eloy; Velázquez-Rodríguez, Gerardo
2016-02-01
We develop a geometric criterion that unambiguously characterizes the residual symmetries of a gravitational Ansatz. It also provides a systematic and effective computational procedure for finding all the residual symmetries of any gravitational Ansatz. We apply the criterion to several examples starting with the Collinson Ansatz for circular stationary axisymmetric spacetimes. We reproduce the residual symmetries already known for this Ansatz including their conformal symmetry, for which we identify the corresponding infinite generators spanning the two related copies of the Witt algebra. We also consider the noncircular generalization of this Ansatz and show how the noncircular contributions on the one hand break the conformal invariance and on the other hand enhance the standard translation symmetries of the circular Killing vectors to supertranslations depending on the direction along which the circularity is lost. As another application of the method, the well-known relation defining conjugate gravitational potentials introduced by Chandrasekhar, which makes possible the derivation of the Kerr black hole from a trivial solution of the Ernst equations, is deduced as a special point of the general residual symmetry of the Papapetrou Ansatz. In this derivation we emphasize how the election of Weyl coordinates, which determines the Papapetrou Ansatz, breaks also the conformal freedom of the stationary axisymmetric spacetimes. Additionally, we study AdS waves for any dimension generalizing the residual symmetries already known for lower dimensions and exhibiting a very complex infinite-dimensional Lie algebra containing three families: two of them span the semidirect sum of the Witt algebra and scalar supertranslations and the third generates vector supertranslations. Independently of this complexity we manage to comprehend the true meaning of the infinite connected group as the precise diffeomorphisms subgroup allowing to locally deform the AdS background into Ad
NASA Astrophysics Data System (ADS)
Lattanzi, F.; di Lauro, C.
It is shown that the torsional splitting patterns in methanol-like molecules, with the excitation of small amplitude vibrational modes in the methyl group, are determined by mechanisms that can be formulated in an almost identical fashion to that for ethane-like molecules. This is achieved by treating ethane-like molecules by the internal axis method (IAM) and methanol-like molecules by the principal axis method (PAM) or rho-axis method (RAM). Using the extended molecular groups G6(EM) or C6v(M) for methanol and G36(EM) for ethane, vibrations perpendicular to the internal rotation axis are conveniently described by modes of higher degeneracy (E for methanol and Gs for ethane) in the absence of coupling of top and frame. Head-tail coupling operators, except the cos-type barrier terms, lower the degeneracy, causing vibrational splittings. Coupled vibrational pairs with torsional splitting patterns that we call 'regular' (pure A1, A2 pairs for methanol and pure E1d, E2d pairs for ethane) or 'inverted' (pure B1, B2 pairs for methanol and pure E1s, E2s pairs for ethane) can be formed as limit cases. Actual splitting patterns occur between the above limits, and are basically determined by torsional Coriolis coupling, which can tune more or less to resonance pairs of uncoupled basis levels linked by specific head-tail coupling operators. The inversion of torsional splitting patterns, observed in perpendicular vibrational modes of the methyl group of methanol, can be predicted by these theoretical considerations. Similar considerations apply to molecules of G12 symmetry.
The small step toward asymmetry: Aesthetic judgment of broken symmetries.
Gartus, Andreas; Leder, Helmut
2013-01-01
Symmetry and complexity both affect the aesthetic judgment of abstract patterns. However, although beauty tends to be associated with symmetry, there are indications that small asymmetries can also be beautiful. We investigated the influence of small deviations from symmetry on people's aesthetic liking for abstract patterns. Breaking symmetry not only decreased patterns' symmetry but also increased their complexity. While an increase of complexity normally results in a higher liking, we found that even a small decrease of symmetry has a strong effect, such that patterns with slightly broken symmetries were significantly less liked than fully symmetric ones. PMID:24349695
Frigerio, Michele; Ma, Ernest
2007-11-01
The smallness of the 1-3 lepton mixing angle {theta}{sub 13} and of the neutrino mass-squared-difference ratio {delta}m{sub 12}{sup 2}/{delta}m{sub 23}{sup 2} can be understood as the departure from a common limit where they both vanish. We discuss in general the conditions for realizing the mass degeneracy of a pair of neutrinos and show that the vanishing of a CP violating phase is needed. We find that the discrete quaternion group Q of eight elements is the simplest family symmetry which correlates the smallness of {delta}m{sub 12}{sup 2} to the value of {theta}{sub 13}. In such a model we predict 0.12 < or approx. sin{theta}{sub 13} < or approx. 0.2 if the ordering of the neutrino mass spectrum is normal, and sin{theta}{sub 13} < or approx. 0.12 if it is inverted.
Yang, Shan; Al-Hashimi, Hashim M
2015-07-30
A growing number of studies employ time-averaged experimental data to determine dynamic ensembles of biomolecules. While it is well-known that different ensembles can satisfy experimental data to within error, the extent and nature of these degeneracies, and their impact on the accuracy of the ensemble determination remains poorly understood. Here, we use simulations and a recently introduced metric for assessing ensemble similarity to explore degeneracies in determining ensembles using NMR residual dipolar couplings (RDCs) with specific application to A-form helices in RNA. Various target ensembles were constructed representing different domain-domain orientational distributions that are confined to a topologically restricted (<10%) conformational space. Five independent sets of ensemble averaged RDCs were then computed for each target ensemble and a "sample and select" scheme used to identify degenerate ensembles that satisfy RDCs to within experimental uncertainty. We find that ensembles with different ensemble sizes and that can differ significantly from the target ensemble (by as much as ∑Ω ∼ 0.4 where ∑Ω varies between 0 and 1 for maximum and minimum ensemble similarity, respectively) can satisfy the ensemble averaged RDCs. These deviations increase with the number of unique conformers and breadth of the target distribution, and result in significant uncertainty in determining conformational entropy (as large as 5 kcal/mol at T = 298 K). Nevertheless, the RDC-degenerate ensembles are biased toward populated regions of the target ensemble, and capture other essential features of the distribution, including the shape. Our results identify ensemble size as a major source of uncertainty in determining ensembles and suggest that NMR interactions such as RDCs and spin relaxation, on their own, do not carry the necessary information needed to determine conformational entropy at a useful level of precision. The framework introduced here provides a general
Group Parametrized Tunneling and Local Symmetry Conditions
NASA Astrophysics Data System (ADS)
Harter, William; Mitchell, Justin
2010-06-01
Recently, Hougen showed an ad hoc symmetry-based parameterization scheme for analyzing tunneling dynamics and high resolution spectra of fluxional molecular structure similar to S-parameter analysis of superfine structure in SF_6 or NH_3 maser inversion dynamics by Feynman et.al. The problem is that ad hoc parametrization, like path integration in general, can lead to logjams of parameters or ``paths'' with no way to pick out the relevant ones. We show a way to identify and use relevant parameters for a tunneling Hamiltonian H having global G-symmetry-defined bases by first expressing H as a linear combination bar γ ^i {bar g}_i of operators in dual symmetry group bar G. The coefficients bar γ ^i are parameters that define a complete set of allowed paths for any H with G-symmetry and are related thru spectral decomposition of G to eigensolutions of H. Quantum G vs.bar G duality generalizes lab -vs. -body and state -vs. -particle. The number of relevant bar γ ^i-parameters is reduced if a system tends to stick in states of a local symmetry subgroup LsubsetG so the H spectrum forms level clusters labeled by induced representations d(ℓ)(L)\\uparrowG. A cluster-(ℓ) has one E(epsilon)-level labeled by G species (epsilon) for each L species (ℓ) in Depsilon(G)downarrowL by Frobenius reciprocity. Then we apply local symmetry conditions to each irrep Depsilon(bar γ ^i {bar g}_i) that has already been reduced with respect to local symmetry L. This amounts to setting each off-diagonal component Dj,kepsilon(H) to zero. Local symmetry conditions may tell which bar γ ^i-parameters are redundant or zero and directly determine d(ℓ)\\uparrowG tunneling matrix eigenvalues that give E(epsilon)-levels as well as eigenvectors. Otherwise one may need to choose a particular localizing subgroup chain LsubsetL_1subsetL_2...G and further reduce the number of path parameters to facilitate spectral fitting. J.T. Hougen, 2009 MSS RJ01, {J Mol Spect 123, 197 (1987) W.G. Harter and
Statistical palaeomagnetic field modelling and symmetry considerations
NASA Astrophysics Data System (ADS)
Hulot, G.; Bouligand, C.
2005-06-01
In the present paper, we address symmetry issues in the context of the so-called giant gaussian process (GGP) modelling approach, currently used to statistically analyse the present and past magnetic field of the Earth at times of stable polarity. We first recall the principle of GGP modelling, and for the first time derive the complete and exact constraints a GGP model should satisfy if it is to satisfy statistical spherical, axisymmetrical or equatorially symmetric properties. We note that as often correctly claimed by the authors, many simplifying assumptions used so far to ease the GGP modelling amount to make symmetry assumptions, but not always exactly so, because previous studies did not recognize that symmetry assumptions do not systematically require a lack of cross-correlations between Gauss coefficients. We further note that GGP models obtained so far for the field over the past 5Myr clearly reveal some spherical symmetry breaking properties in both the mean and the fluctuating field (as defined by the covariance matrix of the model) and some equatorial symmetry breaking properties in the mean field. Non-zonal terms found in the mean field of some models and mismatches between variances defining the fluctuating field (in models however not defined in a consistent way) would further suggest that axial symmetry also is broken. The meaning of this is discussed. Spherical symmetry breaking trivially testifies for the influence of the rotation of the Earth on the geodynamo (a long-recognized fact). Axial symmetry breaking, if confirmed, could hardly be attributed to anything else but some influence of the core-mantle boundary (CMB) conditions on the geodynamo (also a well-known fact). By contrast, equatorial symmetry breaking (in particular the persistence of an axial mean quadrupole) may not trivially be considered as evidence of some influence of CMB conditions. To establish this, one would need to better investigate whether or not this axial quadrupole has
The symmetries of the Carroll superparticle
NASA Astrophysics Data System (ADS)
Bergshoeff, Eric; Gomis, Joaquim; Parra, Lorena
2016-05-01
Motivated by recent applications of Carroll symmetries we investigate, using the method of nonlinear realizations, the geometry of flat and curved (AdS) Carroll space and the symmetries of a particle moving in such a space both in the bosonic as well as in the supersymmetric case. In the bosonic case we find that the Carroll particle possesses an infinite-dimensional symmetry which only in the flat case includes dilatations. The duality between the Bargmann and Carroll algebra, relevant for the flat case, does not extend to the curved case. In the supersymmetric case we study the dynamics of the { N }=1 AdS Carroll superparticle. Only in the flat limit we find that the action is invariant under an infinite-dimensional symmetry that includes a supersymmetric extension of the Lifshitz Carroll algebra with dynamical exponent z = 0. We also discuss in the flat case the extension to { N }=2 supersymmetry and show that the flat { N }=2 superparticle is equivalent to the (non-moving) { N }=1 superparticle and that therefore it is not BPS unlike its Galilei counterpart. This is due to the fact that in this case kappa-symmetry eliminates the linearized supersymmetry. In an appendix we discuss the { N }=2 curved case in three-dimensions only and show that there are two { N }=2 theories that are physically different.
Weyl-gauge symmetry of graphene
Iorio, Alfredo
2011-05-15
Research Highlights: > Graphene action's Weyl symmetry identifies shapes for which the DOS is invariant. > Electrons on graphene might experience a general-relativistic-like spacetime. > Rich mathematical structures, such as the Liouville's equation, naturally arise. - Abstract: The conformal invariance of the low energy limit theory governing the electronic properties of graphene is explored. In particular, it is noted that the massless Dirac theory in point enjoys local Weyl symmetry, a very large symmetry. Exploiting this symmetry in the two spatial dimensions and in the associated three dimensional spacetime, we find the geometric constraints that correspond to specific shapes of the graphene sheet for which the electronic density of states is the same as that for planar graphene, provided the measurements are made in accordance to the inner reference frame of the electronic system. These results rely on the (surprising) general relativistic-like behavior of the graphene system arising from the combination of its well known special relativistic-like behavior with the less explored Weyl symmetry. Mathematical structures, such as the Virasoro algebra and the Liouville equation, naturally arise in this three-dimensional context and can be related to specific profiles of the graphene sheet. Speculations on possible applications of three-dimensional gravity are also proposed.
Reflections on the concept of symmetry
NASA Astrophysics Data System (ADS)
Lorenz, Kuno
2005-10-01
The concept of symmetry is omnipresent, although originally, in Greek antiquity, distinctly different from the modern logical notion. In logic a binary relation R is called symmetric if xRy implies yRx. In Greek, "being symmetric" in general usage is synonymous with "being harmonious", and in technical usage, as in Euclid's Elements, it is synonymous with "commensurable". Due to the second meaning, which is close to the etymology of συ´μμɛτρoς, "with measure" has likewise to be read as "being [in] rational [ratios]" and displays the origin of the concept of rationality of establishing a proportion. Heraclitus can be read as a master of such connections. Exercising rationality is a case of simultaneously finding and inventing symmetries. On that basis a proposal is made of how to relate the modern logical notion of symmetry, a second-order concept, on the one hand with modern first-order usages of the term symmetric in geometry and other fields, and on the other hand with the notion of balance that derives from the ancient usage of symmetric. It is argued that symmetries as states of balance exist only in theory, in practice they function as norms vis-à-vis broken symmetries.
Symmetry in social exchange and health
NASA Astrophysics Data System (ADS)
Siegrist, Johannes
2005-10-01
Symmetry is a relevant concept in sociological theories of exchange. It is rooted in the evolutionary old norm of social reciprocity and is particularly important in social contracts. Symmetry breaking through violation of the norm of reciprocity generates strain in micro-social systems and, above all, in victims of non-symmetric exchange. In this contribution, adverse healthconsequences of symmetry breaking in contractual social exchange are analysed, with a main focus on the employment contract. Scientific evidence is derived from prospective epidemiological studies testing the model of effort-reward imbalance at work. Overall, a twofold elevated risk of incident disease is observed in employed men and women who are exposed to non-symmetric exchange. Health risks include coronary heart disease, depression and alcohol dependence, among others. Preliminary results suggest similar effects on health produced by symmetry breaking in other types of social relationships (e.g. partnership, parental roles). These findings underline the importance of symmetry in contractual social exchange for health and well-being.
Geometrical symmetries of nuclear systems: {{ D }}_{3h} and {{ T }}_{d} symmetries in light nuclei
NASA Astrophysics Data System (ADS)
Bijker, Roelof
2016-07-01
The role of discrete (or point-group) symmetries in α-cluster nuclei is discussed in the framework of the algebraic cluster model which describes the relative motion of the α-particles. Particular attention is paid to the discrete symmetry of the geometric arrangement of the α-particles, and the consequences for the structure of the corresponding rotational bands. The method is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in a simple way as a consequence of the underlying discrete symmetry that characterizes the geometrical configuration of the α-particles, i.e. an equilateral triangle with {{ D }}3h symmetry for 12C, and a tetrahedron with {{ T }}d symmetry for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of α-particles.
Symmetry-protected topological phases in noninteracting fermion systems
NASA Astrophysics Data System (ADS)
Wen, Xiao-Gang
2012-02-01
Symmetry-protected topological (SPT) phases are gapped quantum phases with a certain symmetry, which can all be smoothly connected to the same trivial product state if we break the symmetry. For noninteracting fermion systems with time reversal (T̂), charge conjugation (Ĉ), and/or U(1) (N̂) symmetries, the total symmetry group can depend on the relations between those symmetry operations, such as T̂N̂T̂-1=N̂ or T̂N̂T̂-1=-N̂. As a result, the SPT phases of those fermion systems with different symmetry groups have different classifications. In this paper, we use Kitaev's K-theory approach to classify the gapped free-fermion phases for those possible symmetry groups. In particular, we can view the U(1) as a spin rotation. We find that superconductors with the Sz spin-rotation symmetry are classified by Z in even dimensions, while superconductors with the time reversal plus the Sz spin-rotation symmetries are classified by Z in odd dimensions. We show that all 10 classes of gapped free-fermion phases can be realized by electron systems with certain symmetries. We also point out that, to properly describe the symmetry of a fermionic system, we need to specify its full symmetry group that includes the fermion number parity transformation (-)N̂. The full symmetry group is actually a projective symmetry group.
Discrete Abelian gauge symmetries and axions
NASA Astrophysics Data System (ADS)
Honecker, Gabriele; Staessens, Wieland
2015-07-01
We combine two popular extensions of beyond the Standard Model physics within the framework of intersecting D6-brane models: discrete ℤn symmetries and Peccei-Quinn axions. The underlying natural connection between both extensions is formed by the presence of massive U(1) gauge symmetries in D-brane model building. Global intersecting D6-brane models on toroidal orbifolds of the type T6/ℤ2N and T6/ℤ2 × ℤ2M with discrete torsion offer excellent playgrounds for realizing these extensions. A generation-dependent ℤ2 symmetry is identified in a global Pati-Salam model, while global left-right symmetric models give rise to supersymmetric realizations of the DFSZ axion model. In one class of the latter models, the axion as well as Standard Model particles carry a non-trivial ℤ3 charge.
Arbitrary lattice symmetries via block copolymer nanomeshes
Majewski, Pawel W.; Rahman, Atikur; Black, Charles T.; Yager, Kevin G.
2015-01-01
Self-assembly of block copolymers is a powerful motif for spontaneously forming well-defined nanostructures over macroscopic areas. Yet, the inherent energy minimization criteria of self-assembly give rise to a limited library of structures; diblock copolymers naturally form spheres on a cubic lattice, hexagonally packed cylinders and alternating lamellae. Here, we demonstrate multicomponent nanomeshes with any desired lattice symmetry. We exploit photothermal annealing to rapidly order and align block copolymer phases over macroscopic areas, combined with conversion of the self-assembled organic phase into inorganic replicas. Repeated photothermal processing independently aligns successive layers, providing full control of the size, symmetry and composition of the nanoscale unit cell. We construct a variety of symmetries, most of which are not natively formed by block copolymers, including squares, rhombuses, rectangles and triangles. In fact, we demonstrate all possible two-dimensional Bravais lattices. Finally, we elucidate the influence of nanostructure on the electrical and optical properties of nanomeshes. PMID:26100566
Facial symmetry assessment based on geometric features
NASA Astrophysics Data System (ADS)
Xu, Guoping; Cao, Hanqiang
2015-12-01
Face image symmetry is an important factor affecting the accuracy of automatic face recognition. Selecting high symmetrical face image could improve the performance of the recognition. In this paper, we proposed a novel facial symmetry evaluation scheme based on geometric features, including centroid, singular value, in-plane rotation angle of face and the structural similarity index (SSIM). First, we calculate the value of the four features according to the corresponding formula. Then, we use fuzzy logic algorithm to integrate the value of the four features into a single number which represents the facial symmetry. The proposed method is efficient and can adapt to different recognition methods. Experimental results demonstrate its effectiveness in improving the robustness of face detection and recognition.
Approximate gauge symmetry of composite vector bosons
NASA Astrophysics Data System (ADS)
Suzuki, Mahiko
2010-08-01
It can be shown in a solvable field theory model that the couplings of the composite vector bosons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair, we extend it to the case of bosons being constituents and find that the same phenomenon occurs in a more intriguing way. The functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry, in particular, how the strong binding and global current conservation conspire to generate such an approximate symmetry. Remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries.