Asymptotic symmetries, holography and topological hair
Mishra, Rashmish K.; Sundrum, Raman
2018-01-01
Asymptotic symmetries of AdS4 quantum gravity and gauge theory are derived by coupling the holographically dual CFT3 to Chern-Simons gauge theory and 3D gravity in a "probe" (large-level) limit. Despite the fact that the three-dimensional AdS4 boundary as a whole is consistent with only finite-dimensional asymptotic symmetries, given by AdS isometries, infinite-dimensional symmetries are shown to arise in circumstances where one is restricted to boundary subspaces with effectively two-dimensional geometry. A canonical example of such a restriction occurs within the 4D subregion described by a Wheeler-DeWitt wavefunctional of AdS4 quantum gravity. An AdS4 analog of Minkowski "super-rotation" asymptotic symmetry is probed by 3D Einstein gravity, yielding CFT2 structure (in a large central charge limit), via AdS3 foliation of AdS4 and the AdS3/CFT2 correspondence. The maximal asymptotic symmetry is however probed by 3D conformal gravity. Both 3D gravities have Chern-Simons formulation, manifesting their topological character. Chern-Simons structure is also shown to be emergent in the Poincare patch of AdS4, as soft/boundary limits of 4D gauge theory, rather than "put in by hand" as an external probe. This results in a finite effective Chern-Simons level. Several of the considerations of asymptotic symmetry structure are found to be simpler for AdS4 than for Mink4, such as non-zero 4D particle masses, 4D non-perturbative "hard" effects, and consistency with unitarity. The last of these in particular is greatly simplified because in some set-ups the time dimension is explicitly shared by each level of description: Lorentzian AdS4, CFT3 and CFT2. Relatedly, the CFT2 structure clarifies the sense in which the infinite asymptotic charges constitute a useful form of "hair" for black holes and other complex 4D states. An AdS4 analog of Minkowski "memory" effects is derived, but with late-time memory of earlier events being replaced by (holographic) "shadow" effects. Lessons
Soft pion theorem, asymptotic symmetry and new memory effect
Hamada, Yuta; Sugishita, Sotaro
2017-11-01
It is known that soft photon and graviton theorems can be regarded as the Ward-Takahashi identities of asymptotic symmetries. In this paper, we consider soft theorem for pions, i.e., Nambu-Goldstone bosons associated with a spontaneously broken axial symmetry. The soft pion theorem is written as the Ward-Takahashi identities of the S-matrix under asymptotic transformations. We investigate the asymptotic dynamics, and find that the conservation of charges generating the asymptotic transformations can be interpreted as a pion memory effect.
Centrally extended symmetry algebra of asymptotically Goedel spacetimes
International Nuclear Information System (INIS)
Compere, Geoffrey; Detournay, Stephane
2007-01-01
We define an asymptotic symmetry algebra for three-dimensional Goedel spacetimes supported by a gauge field which turns out to be the semi-direct sum of the diffeomorphisms on the circle with two loop algebras. A class of fields admitting this asymptotic symmetry algebra and leading to well-defined conserved charges is found. The covariant Poisson bracket of the conserved charges is then shown to be centrally extended to the semi-direct sum of a Virasoro algebra and two affine algebras. The subsequent analysis of three-dimensional Goedel black holes indicates that the Virasoro central charge is negative
Large gauge symmetries and asymptotic states in QED
Energy Technology Data Exchange (ETDEWEB)
Gabai, Barak; Sever, Amit [School of Physics and Astronomy, Tel Aviv University,Ramat Aviv 69978 (Israel)
2016-12-19
Large Gauge Transformations (LGT) are gauge transformations that do not vanish at infinity. Instead, they asymptotically approach arbitrary functions on the conformal sphere at infinity. Recently, it was argued that the LGT should be treated as an infinite set of global symmetries which are spontaneously broken by the vacuum. It was established that in QED, the Ward identities of their induced symmetries are equivalent to the Soft Photon Theorem. In this paper we study the implications of LGT on the S-matrix between physical asymptotic states in massive QED. In appose to the naively free scattering states, physical asymptotic states incorporate the long range electric field between asymptotic charged particles and were already constructed in 1970 by Kulish and Faddeev. We find that the LGT charge is independent of the particles’ momenta and may be associated to the vacuum. The soft theorem’s manifestation as a Ward identity turns out to be an outcome of not working with the physical asymptotic states.
Framework for an asymptotically safe standard model via dynamical breaking
DEFF Research Database (Denmark)
Abel, Steven; Sannino, Francesco
2017-01-01
We present a consistent embedding of the matter and gauge content of the Standard Model into an underlying asymptotically safe theory that has a well-determined interacting UV fixed point in the large color/flavor limit. The scales of symmetry breaking are determined by two mass-squared parameters...... with the breaking of electroweak symmetry being driven radiatively. There are no other free parameters in the theory apart from gauge couplings....
Asymptotically hyperbolic normalized Ricci flow and rotational symmetry
Bahuaud, Eric; Woolgar, Eric
2015-01-01
We consider the normalized Ricci flow evolving from an initial metric which is conformally compactifiable and asymptotically hyperbolic. We show that there is a unique evolving metric which remains in this class, and that the flow exists up to the time where the norm of the Riemann tensor diverges. Restricting to initial metrics which belong to this class and are rotationally symmetric, we prove that if the sectional curvature in planes tangent to the orbits of symmetry is initially nonpositi...
A note on asymptotic symmetries and soft-photon theorem
Energy Technology Data Exchange (ETDEWEB)
Mohd, Arif [SISSA - International School for Advanced Studies, via Bonomea, 265, 34136 Trieste (Italy); INFN, Sezione di Trieste,Trieste (Italy)
2015-02-10
We use the asymptotic data at conformal null-infinity ∋ to formulate Weinberg’s soft-photon theorem for Abelian gauge theories with massless charged particles. We show that the angle-dependent gauge transformations at ∋ are not merely a gauge redundancy, instead they are genuine symmetries of the radiative phase space. In the presence of these symmetries, Poisson bracket between gauge potentials is not well-defined. This does not pose an obstacle for the quantization of the radiative phase space, which proceeds by treating the conjugate electric field as the fundamental variable. Denoting by G{sub +} and G{sub −} as the group of gauge transformations at I{sup +} and I{sup −} respectively, Strominger has shown that a certain diagonal subgroup G{sub diag}⊂G{sub +}×G{sub −} is the symmetry of the S-matrix and Weinberg’s soft-photon theorem is the corresponding Ward identity. We give a systematic derivation of this result for Abelian gauge theories with massless charged particles. Our derivation is a slight generalization of the existing derivations since it is applicable even when the bulk spacetime is not exactly flat, but is only “almost” Minkowskian.
Asymptotically Safe Standard Model via Vectorlike Fermions
DEFF Research Database (Denmark)
Mann, R. B.; Meffe, J. R.; Sannino, F.
2017-01-01
We construct asymptotically safe extensions of the standard model by adding gauged vectorlike fermions. Using large number-of-flavor techniques we argue that all gauge couplings, including the hypercharge and, under certain conditions, the Higgs coupling, can achieve an interacting ultraviolet...
Asymptotic symmetries on the Kerr-Newman horizon without the anomaly of diffeomorphism invariance
International Nuclear Information System (INIS)
Koga, Jun-ichirou
2008-01-01
We analyze asymptotic symmetries on the Killing horizon of the four-dimensional Kerr-Newman black hole. We first derive the asymptotic Killing vectors on the Killing horizon, which describe the asymptotic symmetries, and find that the general form of these asymptotic Killing vectors is the universal one possessed by arbitrary Killing horizons. We then construct the phase space associated with the asymptotic symmetries. It is shown that the phase space of an extreme black hole either has the size comparable with a non-extreme black hole, or is small enough to exclude degeneracy, depending on whether or not the global structure of a Killing horizon particular to an extreme black hole is respected. We also show that the classical central charge in the Poisson brackets algebra of these asymptotic symmetries vanishes, which implies that there is not an anomaly of diffeomorphism invariance. By taking into account other results in the literature, we argue that the vanishing central charge on a black hole horizon, in an effective theory, looks consistent with the thermal feature of a black hole. We furthermore argue that the vanishing central charge implies that there are sufficiently many classical configurations that constitute a single macroscopic state, while these configurations are distinguished physically
arXiv Framework for an asymptotically safe Standard Model via dynamical breaking
Abel, Steven
2017-09-15
We present a consistent embedding of the matter and gauge content of the Standard Model into an underlying asymptotically safe theory that has a well-determined interacting UV fixed point in the large color/flavor limit. The scales of symmetry breaking are determined by two mass-squared parameters with the breaking of electroweak symmetry being driven radiatively. There are no other free parameters in the theory apart from gauge couplings.
Asymptotically Safe Standard Model Extensions arXiv
Pelaggi, Giulio Maria; Salvio, Alberto; Sannino, Francesco; Smirnov, Juri; Strumia, Alessandro
We consider theories with a large number NF of charged fermions and compute the renormalisation group equations for the gauge, Yukawa and quartic couplings resummed at leading order in NF. We construct extensions of the Standard Model where SU(2) and/or SU(3) are asymptotically safe. When the same procedure is applied to the Abelian U(1) factor, we find that the Higgs quartic can not be made asymptotically safe and stay perturbative at the same time.
International Nuclear Information System (INIS)
Hoenselaers, C.; Kinnersley, W.; Xanthopoulos, B.C.
1979-01-01
A new series of transformations is presented for generating stationary axially symmetric asymptotically flat vacuum solutions of Einstein's equations. The application requires only algebraic manipulations to be performed. Several examples are given of new stationary axisymmetric solutions obtained in this way. It is conjectured that the transformations, applied to the genral Weyl metric, can be used to generate systematically all stationary metrics with axial symmetry
Symmetry breaking: The standard model and superstrings
International Nuclear Information System (INIS)
Gaillard, M.K.
1988-01-01
The outstanding unresolved issue of the highly successful standard model is the origin of electroweak symmetry breaking and of the mechanism that determines its scale, namely the vacuum expectation value (vev)v that is fixed by experiment at the value v = 4m//sub w//sup 2///g 2 = (√2G/sub F/)/sup /minus/1/ ≅ 1/4 TeV. In this talk I will discuss aspects of two approaches to this problem. One approach is straightforward and down to earth: the search for experimental signatures, as discussed previously by Pierre Darriulat. This approach covers the energy scales accessible to future and present laboratory experiments: roughly (10/sup /minus/9/ /minus/ 10 3 )GeV. The second approach involves theoretical speculations, such as technicolor and supersymmetry, that attempt to explain the TeV scale. 23 refs., 5 figs
Symmetry breaking: The standard model and superstrings
Energy Technology Data Exchange (ETDEWEB)
Gaillard, M.K.
1988-08-31
The outstanding unresolved issue of the highly successful standard model is the origin of electroweak symmetry breaking and of the mechanism that determines its scale, namely the vacuum expectation value (vev)v that is fixed by experiment at the value v = 4m//sub w//sup 2///g/sup 2/ = (..sqrt..2G/sub F/)/sup /minus/1/ approx. = 1/4 TeV. In this talk I will discuss aspects of two approaches to this problem. One approach is straightforward and down to earth: the search for experimental signatures, as discussed previously by Pierre Darriulat. This approach covers the energy scales accessible to future and present laboratory experiments: roughly (10/sup /minus/9/ /minus/ 10/sup 3/)GeV. The second approach involves theoretical speculations, such as technicolor and supersymmetry, that attempt to explain the TeV scale. 23 refs., 5 figs.
Electroweak symmetry breaking beyond the Standard Model
Indian Academy of Sciences (India)
In this paper, two key issues related to electroweak symmetry breaking are addressed. First, how ﬁne-tuned different models are that trigger this phenomenon? Second, even if a light Higgs boson exists, does it have to be necessarily elementary? After a brief introduction, the ﬁne-tuning aspects of the MSSM, NMSSM, ...
PAAR, [No Value; VORKAPIC, D; DIEPERINK, AEL
1991-01-01
We investigate the energy-level statistics in dependence on the boson number and the underlying classical motion for a system or collective states of zero angular momentum in gamma-soft nuclei described in the framework of the O(6) dynamical symmetry of the interacting boson model. This presents a
Atmanspacher, Harald
2003-01-01
Many philosophical and scientific discussions of topics of mind-matter research make implicit assumptions, in various guises, about the distinction between mind and matter. Currently predominant positions are based on either reduction or emergence, providing either monistic or dualistic scenarios. A more-involved framework of thinking, which can be traced back to Spinoza and Leibniz, combines the two scenarios, dualistic (with mind and matter separated) and monistic (with mind and matter unseparated), in one single picture. Based on such a picture, the transition from a domain with mind and matter unseparated to separate mental and material domains can be viewed as a result of a general kind of symmetry breaking, which can be described formally in terms of inequivalent representations. The possibility of whether this symmetry breaking might be connected to the emergence of temporal directions from temporally non-directed or even non-temporal levels of reality will be discussed. Correlations between mental and material aspects of reality could then be imagined as remnants of such primordial levels. Different conceivable types of inequivalent representations would lead to correlations with different characteristics.
Null to time-like infinity Green’s functions for asymptotic symmetries in Minkowski spacetime
International Nuclear Information System (INIS)
Campiglia, Miguel
2015-01-01
We elaborate on the Green’s functions that appeared in http://dx.doi.org/10.1007/JHEP07(2015)115http://arxiv.org/abs/1509.01406 when generalizing, from massless to massive particles, various equivalences between soft theorems and Ward identities of large gauge symmetries. We analyze these Green’s functions in considerable detail and show that they form a hierarchy of functions which describe ‘boundary to bulk’ propagators for large U(1) gauge parameters, supertranslations and sphere vector fields respectively. As a consistency check we verify that the Green’s functions associated to the large diffeomorphisms map the Poincare group at null infinity to the Poincare group at time-like infinity.
Discrete symmetry breaking beyond the standard model
Dekens, Wouter Gerard
2015-01-01
The current knowledge of elementary particles and their interactions is summarized in the Standard Model of particle physics. Practically all the predictions of this model, that have been tested, were confirmed experimentally. Nonetheless, there are phenomena which the model cannot explain. For
Static black holes with axial symmetry in asymptotically AdS4 spacetime
Kichakova, Olga; Kunz, Jutta; Radu, Eugen; Shnir, Yasha
2016-02-01
The known static electrovacuum black holes in a globally AdS4 background have an event horizon which is geometrically a round sphere. In this work we argue that the situation is different in models with matter fields possessing an explicit dependence on the azimuthal angle φ , which, however, does not manifest at the level of the energy-momentum tensor. As a result, the full solutions are axially symmetric only, possessing a single (timelike) Killing vector field. Explicit examples of such static black holes are constructed in Einstein-(complex) scalar field and Einstein-Yang-Mills theories. The basic properties of these solutions are discussed, looking for generic features. For example, we notice that the horizon has an oblate spheroidal shape for solutions with a scalar field and a prolate one for black holes with Yang-Mills fields. The deviation from sphericity of the horizon geometry manifests itself in the holographic stress tensor. Finally, based on the results obtained in the probe limit, we conjecture the existence in Einstein-Maxwell theory of static black holes with axial symmetry only.
Directory of Open Access Journals (Sweden)
Stephen C. Anco
2017-02-01
Full Text Available A conservation law theorem stated by N. Ibragimov along with its subsequent extensions are shown to be a special case of a standard formula that uses a pair consisting of a symmetry and an adjoint-symmetry to produce a conservation law through a well-known Fréchet derivative identity. Furthermore, the connection of this formula (and of Ibragimov’s theorem to the standard action of symmetries on conservation laws is explained, which accounts for a number of major drawbacks that have appeared in recent work using the formula to generate conservation laws. In particular, the formula can generate trivial conservation laws and does not always yield all non-trivial conservation laws unless the symmetry action on the set of these conservation laws is transitive. It is emphasized that all local conservation laws for any given system of differential equations can be found instead by a general method using adjoint-symmetries. This general method is a kind of adjoint version of the standard Lie method to find all local symmetries and is completely algorithmic. The relationship between this method, Noether’s theorem and the symmetry/adjoint-symmetry formula is discussed.
Dobbs, David E.
2010-01-01
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…
Electro symmetry breaking and beyond the standard model
International Nuclear Information System (INIS)
Barklow, T.; Dawson, S.; Haber, H.E.
1995-05-01
The development of the Standard Model of particle physics is a remarkable success story. Its many facets have been tested at present day accelerators; no significant unambiguous deviations have yet been found. In some cases, the model has been verified at an accuracy of better than one part in a thousand. This state of affairs presents our field with a challenge. Where do we go from here? What is our vision for future developments in particle physics? Are particle physicists' recent successes a signal of the field's impending demise, or do real long-term prospects exist for further progress? We assert that the long-term health and intellectual vitality of particle physics depends crucially on the development of a new generation of particle colliders that push the energy frontier by an order of magnitude beyond present capabilities. In this report, we address the scientific issues underlying this assertion
Electro symmetry breaking and beyond the standard model
Energy Technology Data Exchange (ETDEWEB)
Barklow, T. [Stanford Linear Accelerator Center, Menlo Park, CA (United States); Dawson, S. [Brookhaven National Lab., Upton, NY (United States); Haber, H.E. [California Univ., Santa Cruz, CA (United States). Inst. for Particle Physics; Siegrist, J. [Lawrence Berkeley Lab., CA (United States)
1995-05-01
The development of the Standard Model of particle physics is a remarkable success story. Its many facets have been tested at present day accelerators; no significant unambiguous deviations have yet been found. In some cases, the model has been verified at an accuracy of better than one part in a thousand. This state of affairs presents our field with a challenge. Where do we go from here? What is our vision for future developments in particle physics? Are particle physicists` recent successes a signal of the field`s impending demise, or do real long-term prospects exist for further progress? We assert that the long-term health and intellectual vitality of particle physics depends crucially on the development of a new generation of particle colliders that push the energy frontier by an order of magnitude beyond present capabilities. In this report, we address the scientific issues underlying this assertion.
arXiv Radiative symmetry breaking from interacting UV fixed points
Abel, Steven
2017-09-28
It is shown that the addition of positive mass-squared terms to asymptotically safe gauge-Yukawa theories with perturbative UV fixed points leads to calculable radiative symmetry breaking in the IR. This phenomenon, and the multiplicative running of the operators that lies behind it, is akin to the radiative symmetry breaking that occurs in the supersymmetric standard model.
Directory of Open Access Journals (Sweden)
Ivan V. Protasov
2008-10-01
Full Text Available A ballean is a set endowed with some family of subsets which are called the balls. The properties of the family of balls are postulated in such a way that the balleans can be considered as a natural asymptotic counterparts of the uniform topological spaces. We introduce and study an asymptotic proximity as a counterpart of proximity relation for uniform topological space.
Horizontal, anomalous U(1) symmetry for the more minimal supersymmetric standard model
International Nuclear Information System (INIS)
Nelson, A.E.; Wright, D.
1997-01-01
We construct explicit examples with a horizontal, open-quotes anomalousclose quotes U(1) gauge group, which, in a supersymmetric extension of the standard model, reproduce qualitative features of the fermion spectrum and CKM matrix, and suppress FCNC and proton decay rates without the imposition of global symmetries. We review the motivation for such open-quotes moreclose quotes minimal supersymmetric standard models and their predictions for the sparticle spectrum. There is a mass hierarchy in the scalar sector which is the inverse of the fermion mass hierarchy. We show in detail why ΔS=2 FCNCs are greatly suppressed when compared with naive estimates for nondegenerate squarks. copyright 1997 The American Physical Society
Asymptotic structure of the Einstein-Maxwell theory on AdS3
Pérez, Alfredo; Riquelme, Miguel; Tempo, David; Troncoso, Ricardo
2016-02-01
The asymptotic structure of AdS spacetimes in the context of General Relativity coupled to the Maxwell field in three spacetime dimensions is analyzed. Although the fall-off of the fields is relaxed with respect to that of Brown and Henneaux, the variation of the canonical generators associated to the asymptotic Killing vectors can be shown to be finite once required to span the Lie derivative of the fields. The corresponding surface integrals then acquire explicit contributions from the electromagnetic field, and become well-defined provided they fulfill suitable integrability conditions, implying that the leading terms of the asymptotic form of the electromagnetic field are functionally related. Consequently, for a generic choice of boundary conditions, the asymptotic symmetries are broken down to {R}⊗ U(1)⊗ U(1) . Nonetheless, requiring compatibility of the boundary conditions with one of the asymptotic Virasoro symmetries, singles out the set to be characterized by an arbitrary function of a single variable, whose precise form depends on the choice of the chiral copy. Remarkably, requiring the asymptotic symmetries to contain the full conformal group selects a very special set of boundary conditions that is labeled by a unique constant parameter, so that the algebra of the canonical generators is given by the direct sum of two copies of the Virasoro algebra with the standard central extension and U (1). This special set of boundary conditions makes the energy spectrum of electrically charged rotating black holes to be well-behaved.
Nonminimal hints for asymptotic safety
Eichhorn, Astrid; Lippoldt, Stefan; Skrinjar, Vedran
2018-01-01
In the asymptotic-safety scenario for gravity, nonzero interactions are present in the ultraviolet. This property should also percolate into the matter sector. Symmetry-based arguments suggest that nonminimal derivative interactions of scalars with curvature tensors should therefore be present in the ultraviolet regime. We perform a nonminimal test of the viability of the asymptotic-safety scenario by working in a truncation of the renormalization group flow, where we discover the existence of an interacting fixed point for a corresponding nonminimal coupling. The back-coupling of such nonminimal interactions could in turn destroy the asymptotically safe fixed point in the gravity sector. As a key finding, we observe nontrivial indications of stability of the fixed-point properties under the impact of nonminimal derivative interactions, further strengthening the case for asymptotic safety in gravity-matter systems.
Twisted Spectral Triple for the Standard Model and Spontaneous Breaking of the Grand Symmetry
Energy Technology Data Exchange (ETDEWEB)
Devastato, Agostino, E-mail: agostino.devastato@na.infn.it; Martinetti, Pierre, E-mail: martinetti@dima.unige.it [Università di Napoli Federico II, Dipartimento di Fisica (Italy)
2017-03-15
Grand symmetry models in noncommutative geometry, characterized by a non-trivial action of functions on spinors, have been introduced to generate minimally (i.e. without adding new fermions) and in agreement with the first order condition an extra scalar field beyond the standard model, which both stabilizes the electroweak vacuum and makes the computation of the mass of the Higgs compatible with its experimental value. In this paper, we use a twist in the sense of Connes-Moscovici to cure a technical problem due to the non-trivial action on spinors, that is the appearance together with the extra scalar field of unbounded vectorial terms. The twist makes these terms bounded and - thanks to a twisted version of the first-order condition that we introduce here - also permits to understand the breaking to the standard model as a dynamical process induced by the spectral action, as conjectured in [24]. This is a spontaneous breaking from a pre-geometric Pati-Salam model to the almost-commutativegeometryofthestandardmodel,withtwoHiggs-likefields: scalar and vector.
Why are tensor field theories asymptotically free?
Rivasseau, V.
2015-09-01
In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a 1/p2 propagator and quartic interactions and on the comparison between the intermediate field representations of the vector, matrix and tensor cases. The transition from asymptotic freedom (tensor case) to asymptotic safety (matrix case) is related to the crossing symmetry of the matrix vertex, whereas in the vector case, the lack of asymptotic freedom (“Landau ghost”), as in the ordinary scalar φ^44 case, is simply due to the absence of any wave function renormalization at one loop.
Rhodes, G; Yoshikawa, S; Clark, A; Lee, K; McKay, R; Akamatsu, S
2001-01-01
Averageness and symmetry are attractive in Western faces and are good candidates for biologically based standards of beauty. A hallmark of such standards is that they are shared across cultures. We examined whether facial averageness and symmetry are attractive in non-Western cultures. Increasing the averageness of individual faces, by warping those faces towards an averaged composite of the same race and sex, increased the attractiveness of both Chinese (experiment 1) and Japanese (experiment 2) faces, for Chinese and Japanese participants, respectively. Decreasing averageness by moving the faces away from an average shape decreased attractiveness. We also manipulated the symmetry of Japanese faces by blending each original face with its mirror image to create perfectly symmetric versions. Japanese raters preferred the perfectly symmetric versions to the original faces (experiment 2). These findings show that preferences for facial averageness and symmetry are not restricted to Western cultures, consistent with the view that they are biologically based. Interestingly, it made little difference whether averageness was manipulated by using own-race or other-race averaged composites and there was no preference for own-race averaged composites over other-race or mixed-race composites (experiment 1). We discuss the implications of these results for understanding what makes average faces attractive. We also discuss some limitations of our studies, and consider other lines of converging evidence that may help determine whether preferences for average and symmetric faces are biologically based.
Asymptotics for incidence matrix classes
Cameron, Peter; Prellberg, Thomas; Stark, Dudley
2005-01-01
We define {\\em incidence matrices} to be zero-one matrices with no zero rows or columns. A classification of incidence matrices is considered for which conditions of symmetry by transposition, having no repeated rows/columns, or identification by permutation of rows/columns are imposed. We find asymptotics and relationships for the number of matrices with $n$ ones in these classes as $n\\to\\infty$.
Testing for bivariate spherical symmetry
Einmahl, J.H.J.; Gantner, M.
2012-01-01
An omnibus test for spherical symmetry in R2 is proposed, employing localized empirical likelihood. The thus obtained test statistic is distribution free under the null hypothesis. The asymptotic null distribution is established and critical values for typical sample sizes, as well as the asymptotic
Einmahl, John; Gan, Zhuojiong
Omnibus tests for central symmetry of a bivariate probability distribution are proposed. The test statistics compare empirical measures of opposite regions. Under rather weak conditions, we establish the asymptotic distribution of the test statistics under the null hypothesis; it follows that they
Steele, T G; Wang, Zhi-Wei; Contreras, D; Mann, R B
2014-05-02
We consider the generation of dark matter mass via radiative electroweak symmetry breaking in an extension of the conformal standard model containing a singlet scalar field with a Higgs portal interaction. Generating the mass from a sequential process of radiative electroweak symmetry breaking followed by a conventional Higgs mechanism can account for less than 35% of the cosmological dark matter abundance for dark matter mass M(s)>80 GeV. However, in a dynamical approach where both Higgs and scalar singlet masses are generated via radiative electroweak symmetry breaking, we obtain much higher levels of dark matter abundance. At one-loop level we find abundances of 10%-100% with 106 GeVdark matter mass. The dynamical approach also predicts a small scalar-singlet self-coupling, providing a natural explanation for the astrophysical observations that place upper bounds on dark matter self-interaction. The predictions in all three approaches are within the M(s)>80 GeV detection region of the next generation XENON experiment.
Asymptotic structure of gravity and supergravity in three dimensions
International Nuclear Information System (INIS)
Henneaux, M.
1984-01-01
It is shown that the asymptotic symmetry superalgebra of a generic solution to three-dimensional supergravity only contains space rotations and time translations. Accordingly, only energy and momentum can be meaningfully defined
Top mass from asymptotic safety
Eichhorn, Astrid; Held, Aaron
2018-02-01
We discover that asymptotically safe quantum gravity could predict the top-quark mass. For a broad range of microscopic gravitational couplings, quantum gravity could provide an ultraviolet completion for the Standard Model by triggering asymptotic freedom in the gauge couplings and bottom Yukawa and asymptotic safety in the top-Yukawa and Higgs-quartic coupling. We find that in a part of this range, a difference of the top and bottom mass of approximately 170GeV is generated and the Higgs mass is determined in terms of the top mass. Assuming no new physics below the Planck scale, we construct explicit Renormalization Group trajectories for Standard Model and gravitational couplings which link the transplanckian regime to the electroweak scale and yield a top pole mass of Mt,pole ≈ 171GeV.
International Nuclear Information System (INIS)
Nilles, Hans Peter
2012-04-01
Discrete (family) symmetries might play an important role in models of elementary particle physics. We discuss the origin of such symmetries in the framework of consistent ultraviolet completions of the standard model in field and string theory. The symmetries can arise due to special geometrical properties of extra compact dimensions and the localization of fields in this geometrical landscape. We also comment on anomaly constraints for discrete symmetries.
Energy Technology Data Exchange (ETDEWEB)
Nilles, Hans Peter [Bonn Univ. (Germany). Bethe Center for Theoretical Physics; Bonn Univ. (Germany). Physikalisches Inst.; Ratz, Michael [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-04-15
Discrete (family) symmetries might play an important role in models of elementary particle physics. We discuss the origin of such symmetries in the framework of consistent ultraviolet completions of the standard model in field and string theory. The symmetries can arise due to special geometrical properties of extra compact dimensions and the localization of fields in this geometrical landscape. We also comment on anomaly constraints for discrete symmetries.
Testing for bivariate spherical symmetry
Einmahl, J.H.J.; Gantner, M.
2012-01-01
An omnibus test for spherical symmetry in R2 is proposed, employing localized empirical likelihood. The thus obtained test statistic is distri- bution-free under the null hypothesis. The asymptotic null distribution is established and critical values for typical sample sizes, as well as the asymptotic ones, are presented. In a simulation study, the good perfor- mance of the test is demonstrated. Furthermore, a real data example is presented.
Asymptotically Safe Dark Matter
DEFF Research Database (Denmark)
Sannino, Francesco; Shoemaker, Ian M.
2015-01-01
We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....
Energy Technology Data Exchange (ETDEWEB)
Stumpf, Harald [Tuebingen Univ. (Germany). Inst. of Theoretical Physics
2011-03-15
By Lochak (theory) and Urutskoev (experiment) the hypothesis has been suggested that during electric discharges in water (fluids) light magnetic monopoles can be created which according to Lochak should be considered as a kind of excited neutrinos. Based on a quantum field theoretic development of de Broglie's and Heisenberg's fusion ideas and the results of preceding papers a transparent proof is given that such magnetic monopoles can occur during discharges. In the theoretical description these circumstances are formulated within the scope of an extended (effective) Standard Model and the monopoles with vanishing electric charge arise from neutrinos whose states are modified by the symmetry breaking caused by the discharge. In the introduction some technical implications are referred to. The article is divided into two parts. (orig.)
Asymptotic analysis and boundary layers
Cousteix, Jean
2007-01-01
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...
Asymptotics and Borel summability
Costin, Ovidiu
2008-01-01
Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers.To give a sense of how new methods are us
Witten, Edward
2016-03-01
In this talk, I will describe global and gauge symmetries and the interplay between them. The meaning of global symmetries is clear: they act on physical observables. Gauge symmetries are more elusive as they typically do not act on physical observables. Gauge symmetries are redundancies in the mathematical description of a physical system rather than properties of the system itself. The existence of nonperturbative dualities makes it clear that this distinction is unavoidable. Yet in our best understanding the gauge symmetries are deeper. The lepton number symmetries that are probed by the wonderful experimental results that will be reported in this session give an excellent illustration. They are regarded in the Standard Model as indirect consequences of gauge symmetries and they are expected to be only approximate. This expectation is supported by the observation of neutrino oscillations.
Testing for Bivariate Spherical Symmetry
Einmahl, J.H.J.; Gantner, M.
2010-01-01
An omnibus test for spherical symmetry in R2 is proposed, employing localized empirical likelihood. The thus obtained test statistic is distri- bution-free under the null hypothesis. The asymptotic null distribution is established and critical values for typical sample sizes, as well as the
Lattimore, Tor; Hutter, Marcus
2011-01-01
Artificial general intelligence aims to create agents capable of learning to solve arbitrary interesting problems. We define two versions of asymptotic optimality and prove that no agent can satisfy the strong version while in some cases, depending on discounting, there does exist a non-computable weak asymptotically optimal agent.
Asymptotic expansion of the Keesom integral
International Nuclear Information System (INIS)
Abbott, Paul C
2007-01-01
The asymptotic evaluation and expansion of the Keesom integral, K(a), is discussed at some length in Battezzati and Magnasco (2004 J. Phys. A: Math. Gen. 37 9677; 2005 J. Phys. A: Math. Gen. 38 6715). Here, using standard identities, it is shown that this triple integral can be reduced to a single integral from which the asymptotic behaviour is readily obtained using Laplace's method. (comment)
International Nuclear Information System (INIS)
Todorov, T.D.
1980-01-01
The set of asymptotic numbers A as a system of generalized numbers including the system of real numbers R, as well as infinitely small (infinitesimals) and infinitely large numbers, is introduced. The detailed algebraic properties of A, which are unusual as compared with the known algebraic structures, are studied. It is proved that the set of asymptotic numbers A cannot be isomorphically embedded as a subspace in any group, ring or field, but some particular subsets of asymptotic numbers are shown to be groups, rings, and fields. The algebraic operation, additive and multiplicative forms, and the algebraic properties are constructed in an appropriate way. It is shown that the asymptotic numbers give rise to a new type of generalized functions quite analogous to the distributions of Schwartz allowing, however, the operation multiplication. A possible application of these functions to quantum theory is discussed
Asymptotic Poincare lemma and its applications
International Nuclear Information System (INIS)
Ziolkowski, R.W.; Deschamps, G.A.
1984-01-01
An asymptotic version of Poincare's lemma is defined and solutions are obtained with the calculus of exterior differential forms. They are used to construct the asymptotic approximations of multidimensional oscillatory integrals whose forms are commonly encountered, for example, in electromagnetic problems. In particular, the boundary and stationary point evaluations of these integrals are considered. The former is applied to the Kirchhoff representation of a scalar field diffracted through an aperture and simply recovers the Maggi-Rubinowicz-Miyamoto-Wolf results. Asymptotic approximations in the presence of other (standard) critical points are also discussed. Techniques developed for the asymptotic Poincare lemma are used to generate a general representation of the Leray form. All of the (differential form) expressions presented are generalizations of known (vector calculus) results. 14 references, 4 figures
Quasi-extended asymptotic functions
International Nuclear Information System (INIS)
Todorov, T.D.
1979-01-01
The class F of ''quasi-extended asymptotic functions'' is introduced. It contains all extended asymptotic functions as well as some new asymptotic functions very similar to the Schwartz distributions. On the other hand, every two quasiextended asymptotic functions can be multiplied as opposed to the Schwartz distributions; in particular, the square delta 2 of an asymptotic function delta similar to Dirac's delta-function, is constructed as an example
Lectures on renormalization and asymptotic safety
International Nuclear Information System (INIS)
Nagy, Sandor
2014-01-01
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross–Neveu model, the nonlinear σ model, the sine–Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too. We also give a detailed analysis of infrared behavior of such scalar models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure is hidden by the singularity of the renormalization group equations. The theory spaces of these models show several similar properties, namely the models have the same phase and fixed point structure. The quantum Einstein gravity also exhibits similarities when considering the global aspects of its theory space since the appearing two phases there show analogies with the symmetric and the broken phases of the scalar models. These results be nicely uncovered by the functional renormalization group method
Degenerate asymptotic perturbation theory
International Nuclear Information System (INIS)
Hunziker, W.; Pillet, C.A.
1983-01-01
Asymptotic Rayleigh-Schroedinger perturbation theory for discrete eigenvalues is developed systematically in the general degenerate case. For this purpose we study the spectral properties of mxm - matrix functions A(kappa) of a complex variable kappa which have an asymptotic expansion ΣAsub(k)kappasup(k) as kappa->0. We show that asymptotic expansions for groups of eigenvalues and for the corresponding spectral projections of A(kappa) can be obtained from the set [Asub(k)] by analytic perturbation theory. Special attention is given to the case where A(kappa) is Borel-summable in some sector originating from kappa=0 with opening angle >π. Here we prove that the asymptotic series describe individual eigenvalues and eigenprojections of A(kappa) which are shown to be holomorphic in S near kappa=0 and Borel summable if Asub(k)sup(*)=Asub(k) for all k. We then fit these results into the scheme of Rayleigh-Schroedinger perturbation theory and we give some examples of asymptotic estimates for Schroedinger operators. (orig.)
International Nuclear Information System (INIS)
Dewar, R. L.
1995-01-01
A large part of physics consists of learning which asymptotic methods to apply where, yet physicists are not always taught asymptotics in a systematic way. Asymptotology is given using an example from aerodynamics, and a rent Phys. Rev. Letter Comment is used as a case study of one subtle way things can go wrong. It is shown that the application of local analysis leads to erroneous conclusions regarding the existence of a continuous spectrum in a simple test problem, showing that a global analysis must be used. The final section presents results on a more sophisticated example, namely the WKBJ solution of Mathieu equation. 13 refs., 2 figs
Jones, D S
1997-01-01
Many branches of science and engineering involve applications of mathematical analysis. An important part of applied analysis is asymptotic approximation which is, therefore, an active area of research with new methods and publications being found constantly. This book gives an introduction to the subject sufficient for scientists and engineers to grasp the fundamental techniques, both those which have been known for some time and those which have been discovered more recently. The asymptotic approximation of both integrals and differential equations is discussed and the discussion includes hy
Ramnath, Rudrapatna V
2012-01-01
This book addresses the task of computation from the standpoint of asymptotic analysis and multiple scales that may be inherent in the system dynamics being studied. This is in contrast to the usual methods of numerical analysis and computation. The technical literature is replete with numerical methods such as Runge-Kutta approach and its variations, finite element methods, and so on. However, not much attention has been given to asymptotic methods for computation, although such approaches have been widely applied with great success in the analysis of dynamic systems. The presence of differen
DEFF Research Database (Denmark)
Litim, Daniel F.; Sannino, Francesco
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet ...
Spacetime Exterior to a Star: Against Asymptotic Flatness
Directory of Open Access Journals (Sweden)
Roberts Mark D.
2016-01-01
Full Text Available In many circumstances the perfect fluid conservation equations can be directly integrated to give a geometric-thermodynamic equation: typically that the lapse N is the reciprocal of the enthalphy h, (N = 1/h. This result is aesthetically appealing as it depends only on the fluid conservation equations and does not depend on specific field equations such as Einstein's. Here the form of the geometric-thermodynamic equation is derived subject to spherical symmetry and also for the shift-free ADM formalism. There at least three applications of the geometric-thermodynamic equation, the most important being to the notion of asymptotic flatness and hence to spacetime exterior to a star. For asymptotic flatness one wants h → 0 and N → 1 simultaneously, but this is incompatible with the geometric-thermodynamic equation. Observational data and asymptotic flatness are discussed. It is argued that a version of Mach's principle does not allow asymptotic flatness.
Chiral fermions in asymptotically safe quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Meibohm, J. [Gothenburg University, Department of Physics, Goeteborg (Sweden); Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); Pawlowski, J.M. [Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung mbH, ExtreMe Matter Institute EMMI, Darmstadt (Germany)
2016-05-15
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions. (orig.)
A Bootstrap Test for Conditional Symmetry
Liangjun Su; Sainan Jin
2005-01-01
This paper proposes a simple consistent nonparametric test of conditional symmetry based on the principle of characteristic functions. The test statistic is shown to be asymptotically normal under the null hypothesis of conditional symmetry and consistent against any conditional asymmetric distributions. We also study the power against local alternatives, propose a bootstrap version of the test, and conduct a small Monte Carlo simulation to evaluate the finitesample performance of the test.
Asymptotics of relativistic spin networks
International Nuclear Information System (INIS)
Barrett, John W; Steele, Christopher M
2003-01-01
The stationary phase technique is used to calculate asymptotic formulae for SO(4) relativistic spin networks. For the tetrahedral spin network this gives the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j-symbol. For the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical calculations of the spin network evaluation. Finally, we discuss the asymptotics of the SO(3, 1) 10j-symbol
Hansen, Frederik F.; Langæble, Kasper; Mann, Robert B.; Sannino, Francesco; Steele, Tom G.; Wang, Zhi-Wei
2018-03-21
We determine the phase diagram of completely asymptotically free SU(Nc) gauge theories featuring Ns complex scalars and Nf Dirac quarks transforming according to the fundamental representation of the gauge group. The analysis is performed at the maximum known order in perturbation theory. We unveil a very rich dynamics and associated phase structure. Intriguingly, we discover that the completely asymptotically free conditions guarantee that the infrared dynamics displays long-distance conformality, and in a regime when perturbation theory is applicable. We conclude our analysis by determining the quantum corrected potential of the model and summarizing the possible patterns of radiative symmetry breaking. These models are of potential phenomenological interest as either elementary or composite ultraviolet finite extensions of the standard model.
Aniello, Paolo; Chruściński, Dariusz
2017-07-01
A symmetry witness is a suitable subset of the space of selfadjoint trace class operators that allows one to determine whether a linear map is a symmetry transformation, in the sense of Wigner. More precisely, such a set is invariant with respect to an injective densely defined linear operator in the Banach space of selfadjoint trace class operators (if and) only if this operator is a symmetry transformation. According to a linear version of Wigner’s theorem, the set of pure states—the rank-one projections—is a symmetry witness. We show that an analogous result holds for the set of projections with a fixed rank (with some mild constraint on this rank, in the finite-dimensional case). It turns out that this result provides a complete classification of the sets of projections with a fixed rank that are symmetry witnesses. These particular symmetry witnesses are projectable; i.e. reasoning in terms of quantum states, the sets of ‘uniform’ density operators of corresponding fixed rank are symmetry witnesses too.
Extended asymptotic functions - some examples
International Nuclear Information System (INIS)
Todorov, T.D.
1981-01-01
Several examples of extended asymptotic functions of two variables are given. This type of asymptotic functions has been introduced as an extension of continuous ordinary functions. The presented examples are realizations of some Schwartz distributions delta(x), THETA(x), P(1/xsup(n)) and can be multiplied in the class of the asymptotic functions as opposed to the theory of Schwartz distributions. The examples illustrate the method of construction of extended asymptotic functions similar to the distributions. The set formed by the extended asymptotic functions is also considered. It is shown, that this set is not closed with respect to addition and multiplication
Voisin, Claire
1999-01-01
This is the English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The first chapter is devoted to the geometry of Calabi-Yau manifolds, and the second describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry. The other chapters deal with more specialized aspects of the subject: the work of Candelas, de la Ossa, Greene, and Parkes, based on the fact that under the mirror symmetry hypothesis, the variation of Hodge structure of a Calabi-Yau threefold determines the Gromov-Witten invariants of its mirror; Batyrev's construction, which exhibits the mirror symmetry phenomenon between hypersurfaces of toric Fano varieties, after a combinatorial classification of the latter; the mathematical construction of the Gromov-Witten potential, and the proof of its crucial property (that it satisfies the WDVV equation), which makes it possible to construct a flat connection underlying a variation of Hodge structure in the ...
Asymptotic density and effective negligibility
Astor, Eric P.
In this thesis, we join the study of asymptotic computability, a project attempting to capture the idea that an algorithm might work correctly in all but a vanishing fraction of cases. In collaboration with Hirschfeldt and Jockusch, broadening the original investigation of Jockusch and Schupp, we introduce dense computation, the weakest notion of asymptotic computability (requiring only that the correct answer is produced on a set of density 1), and effective dense computation, where every computation halts with either the correct answer or (on a set of density 0) a symbol denoting uncertainty. A few results make more precise the relationship between these notions and work already done with Jockusch and Schupp's original definitions of coarse and generic computability. For all four types of asymptotic computation, including generic computation, we demonstrate that non-trivial upper cones have measure 0, building on recent work of Hirschfeldt, Jockusch, Kuyper, and Schupp in which they establish this for coarse computation. Their result transfers to yield a minimal pair for relative coarse computation; we generalize their method and extract a similar result for relative dense computation (and thus for its corresponding reducibility). However, all of these notions of near-computation treat a set as negligible iff it has asymptotic density 0. Noting that this definition is not computably invariant, this produces some failures of intuition and a break with standard expectations in computability theory. For instance, as shown by Hamkins and Miasnikov, the halting problem is (in some formulations) effectively densely computable, even in polynomial time---yet this result appears fragile, as indicated by Rybalov. In independent work, we respond to this by strengthening the approach of Jockusch and Schupp to avoid such phenomena; specifically, we introduce a new notion of intrinsic asymptotic density, invariant under computable permutation, with rich relations to both
Holography without translational symmetry
Vegh, David
2013-01-01
We propose massive gravity as a holographic framework for describing a class of strongly interacting quantum field theories with broken translational symmetry. Bulk gravitons are assumed to have a Lorentz-breaking mass term as a substitute for spatial inhomogeneities. This breaks momentum-conservation in the boundary field theory. At finite chemical potential, the gravity duals are charged black holes in asymptotically anti-de Sitter spacetime. The conductivity in these systems generally exhibits a Drude peak that approaches a delta function in the massless gravity limit. Furthermore, the optical conductivity shows an emergent scaling law: $|\\sigma(\\omega)| \\approx {A \\over \\omega^{\\alpha}} + B$. This result is consistent with that found earlier by Horowitz, Santos, and Tong who introduced an explicit inhomogeneous lattice into the system.
International Nuclear Information System (INIS)
Blum, Alexander Simon
2009-01-01
This thesis deals with the possibility of describing the flavor sector of the Standard Model of Particle Physics (with neutrino masses), that is the fermion masses and mixing matrices, with a discrete, non-abelian flavor symmetry. In particular, mass independent textures are considered, where one or several of the mixing angles are determined by group theory alone and are independent of the fermion masses. To this end a systematic analysis of a large class of discrete symmetries, the dihedral groups, is analyzed. Mass independent textures originating from such symmetries are described and it is shown that such structures arise naturally from the minimization of scalar potentials, where the scalars are gauge singlet flavons transforming non-trivially only under the flavor group. Two models are constructed from this input, one describing leptons, based on the group D 4 , the other describing quarks and employing the symmetry D 14 . In the latter model it is the quark mixing matrix element V ud - basically the Cabibbo angle - which is at leading order predicted from group theory. Finally, discrete flavor groups are discussed as subgroups of a continuous gauge symmetry and it is shown that this implies that the original gauge symmetry is broken by fairly large representations. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Blum, Alexander Simon
2009-06-10
This thesis deals with the possibility of describing the flavor sector of the Standard Model of Particle Physics (with neutrino masses), that is the fermion masses and mixing matrices, with a discrete, non-abelian flavor symmetry. In particular, mass independent textures are considered, where one or several of the mixing angles are determined by group theory alone and are independent of the fermion masses. To this end a systematic analysis of a large class of discrete symmetries, the dihedral groups, is analyzed. Mass independent textures originating from such symmetries are described and it is shown that such structures arise naturally from the minimization of scalar potentials, where the scalars are gauge singlet flavons transforming non-trivially only under the flavor group. Two models are constructed from this input, one describing leptons, based on the group D{sub 4}, the other describing quarks and employing the symmetry D{sub 14}. In the latter model it is the quark mixing matrix element V{sub ud} - basically the Cabibbo angle - which is at leading order predicted from group theory. Finally, discrete flavor groups are discussed as subgroups of a continuous gauge symmetry and it is shown that this implies that the original gauge symmetry is broken by fairly large representations. (orig.)
The symmetry of large N=4 holography
International Nuclear Information System (INIS)
Gaberdiel, Matthias R.; Peng, Cheng
2014-01-01
For the proposed duality relating a family of N=4 superconformal coset models to a certain supersymmetric higher spin theory on AdS 3 , the asymptotic symmetry algebra of the bulk description is determined. It is shown that, depending on the choice of the boundary charges, one may obtain either the linear or the non-linear superconformal algebra on the boundary. We compare the non-linear version of the asymptotic symmetry algebra with the non-linear coset algebra and find non-trivial agreement in the ’t Hooft limit, thus giving strong support for the proposed duality. As a by-product of our analysis we also show that the W ∞ symmetry of the coset theory is broken under the exactly marginal perturbation that preserves the N=4 superconformal algebra
Discrete symmetries in the MSSM
Energy Technology Data Exchange (ETDEWEB)
Schieren, Roland
2010-12-02
The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z{sup R}{sub 4} symmetry is discovered which solves the {mu}-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z{sup R}{sub 4} is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z{sup R}{sub 4} symmetry and other desirable features. (orig.)
Asymptotic behavior of observables in the asymmetric quantum Rabi model
Semple, J.; Kollar, M.
2018-01-01
The asymmetric quantum Rabi model with broken parity invariance shows spectral degeneracies in the integer case, that is when the asymmetry parameter equals an integer multiple of half the oscillator frequency, thus hinting at a hidden symmetry and accompanying integrability of the model. We study the expectation values of spin observables for each eigenstate and observe characteristic differences between the integer and noninteger cases for the asymptotics in the deep strong coupling regime, which can be understood from a perturbative expansion in the qubit splitting. We also construct a parent Hamiltonian whose exact eigenstates possess the same symmetries as the perturbative eigenstates of the asymmetric quantum Rabi model in the integer case.
More asymptotic safety guaranteed
Bond, Andrew D.; Litim, Daniel F.
2018-04-01
We study interacting fixed points and phase diagrams of simple and semisimple quantum field theories in four dimensions involving non-Abelian gauge fields, fermions and scalars in the Veneziano limit. Particular emphasis is put on new phenomena which arise due to the semisimple nature of the theory. Using matter field multiplicities as free parameters, we find a large variety of interacting conformal fixed points with stable vacua and crossovers inbetween. Highlights include semisimple gauge theories with exact asymptotic safety, theories with one or several interacting fixed points in the IR, theories where one of the gauge sectors is both UV free and IR free, and theories with weakly interacting fixed points in the UV and the IR limits. The phase diagrams for various simple and semisimple settings are also given. Further aspects such as perturbativity beyond the Veneziano limit, conformal windows, and implications for model building are discussed.
Asymptotically safe grand unification
Energy Technology Data Exchange (ETDEWEB)
Bajc, Borut [J. Stefan Institute,1000 Ljubljana (Slovenia); Sannino, Francesco [CP-Origins & the Danish IAS, University of Southern Denmark,Campusvej 55, DK-5230 Odense M (Denmark); Université de Lyon, France, Université Lyon 1, CNRS/IN2P3, UMR5822 IPNL,F-69622 Villeurbanne Cedex (France)
2016-12-28
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
Renormalization group and asymptotic freedom
International Nuclear Information System (INIS)
Morris, J.R.
1978-01-01
Several field theoretic models are presented which allow exact expressions of the renormalization constants and renormalized coupling constants. These models are analyzed as to their content of asymptotic free field behavior through the use of the Callan-Symanzik renormalization group equation. It is found that none of these models possesses asymptotic freedom in four dimensions
On asymptotics for difference equations
Rafei, M.
2012-01-01
In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the
Directory of Open Access Journals (Sweden)
Kirstin Peters
2010-11-01
Full Text Available A well-known result by Palamidessi tells us that πmix (the π-calculus with mixed choice is more expressive than πsep (its subset with only separate choice. The proof of this result argues with their different expressive power concerning leader election in symmetric networks. Later on, Gorla offered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of incestual processes (mixed choices that include both enabled senders and receivers for the same channel when running two copies in parallel. In both proofs, the role of breaking (initial symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result - based on a proper formalization of what it means to break symmetries without referring to another layer of the distinguishing problem domain of leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reasonable encoding from πmix into πsep. We indicate how the respective proofs can be adapted and exhibit the consequences of varying notions of uniformity and reasonableness. In each case, the ability to break initial symmetries turns out to be essential.
Energy Technology Data Exchange (ETDEWEB)
Walker-Loud, Andre [College of William and Mary, Williamsburg, VA (United States)
2016-10-14
The research supported by this grant is aimed at probing the limits of the Standard Model through precision low-energy nuclear physics. The work of the PI (AWL) and additional personnel is to provide theory input needed for a number of potentially high-impact experiments, notably, hadronic parity violation, Dark Matter direct detection and searches for permanent electric dipole moments (EDMs) in nucleons and nuclei. In all these examples, a quantitative understanding of low-energy nuclear physics from the fundamental theory of strong interactions, Quantum Chromo-Dynamics (QCD), is necessary to interpret the experimental results. The main theoretical tools used and developed in this work are the numerical solution to QCD known as lattice QCD (LQCD) and Effective Field Theory (EFT). This grant is supporting a new research program for the PI, and as such, needed to be developed from the ground up. Therefore, the first fiscal year of this grant, 08/01/2014-07/31/2015, has been spent predominantly establishing this new research effort. Very good progress has been made, although, at this time, there are not many publications to show for the effort. After one year, the PI accepted a job at Lawrence Berkeley National Laboratory, so this final report covers just a single year of five years of the grant.
Is radiative electroweak symmetry breaking consistent with a 125 GeV Higgs mass?
Steele, T G; Wang, Zhi-Wei
2013-04-12
The mechanism of radiative electroweak symmetry breaking occurs through loop corrections, and unlike conventional symmetry breaking where the Higgs mass is a parameter, the radiatively generated Higgs mass is dynamically predicted. Padé approximations and an averaging method are developed to extend the Higgs mass predictions in radiative electroweak symmetry breaking from five- to nine-loop order in the scalar sector of the standard model, resulting in an upper bound on the Higgs mass of 141 GeV. The mass predictions are well described by a geometric series behavior, converging to an asymptotic Higgs mass of 124 GeV consistent with the recent ATLAS and CMS Collaborations observations. Similarly, we find that the Higgs self-coupling converges to λ=0.23, which is significantly larger than its conventional symmetry breaking counterpart for a 124 GeV Higgs mass. In addition to this significant enhancement of the Higgs self-coupling and HH→HH scattering, we find that Higgs decays to gauge bosons are unaltered and the scattering processes WL(+)WL(+)→HH, ZLZL→HH are also enhanced, providing signals to distinguish conventional and radiative electroweak symmetry breaking mechanisms.
Blaha, Stephen
2011-01-01
This book is the second volume exploring the properties of faster than light particles (tachyons). The existence of tachyons has not been proved yet. But the instantaneous nature of Quantum Mechanics and the behavior of particles in Black Holes prove faster than light motion occurs in nature. In volume 1 the author showed that one can derive the form of The Standard Model of elementary particles if neutrinos and down-type quarks are tachyons. In this volume the author shows that these tachyons cause Parity, CP and CPT violation. Also the General Theory of Relativity is extended to Complex General Relativity and its vierbein version. The theory's complex coordinates are mapped to real-valued coordinates (that we observe) using a transformation composed of SU(3) and two SU(2)xU(1) groups - the very groups that appear in The Standard Model. Volume 1 showed that these same groups play a similar role in The Standard Model by mapping complex, faster than light coordinates to real-valued coordinates. Thus the same g...
Unitarity in gauge symmetry breaking on an orbifold
Abe, Y; Higashide, Y; Kobayashi, K; Matsunaga, M
2003-01-01
We study the unitarity bounds of scattering amplitudes in extra-dimensional gauge theory, in which the gauge symmetry is broken by the boundary conditions. The evaluation of the amplitude of the diagram including four massive gauge bosons in the external lines shows that the asymptotic power behavior of the amplitude is canceled. The calculation is carried out with the 5-dimensional standard model and the SU(5) grand unified theory, whose 5th dimensional coordinate is compactified on S sup 1 /Z sub 2. The gauge theories broken through the orbifolding preserve unitarity a high energies, similarly to the broken gauge theories in which the gauge bosons acquire masses through the Higgs mechanism. We show that the contributions of the Kaluza-Klein states play a crucial role in conserving the unitarity. (author)
Fibre bundles. Monopoles and internal symmetries
International Nuclear Information System (INIS)
Horvathy, P.A.; Rawnsley, J.H.
1985-01-01
Asymptotic monopole configurations are described in fibre-bundle terms. Bundle reduction -the geometric procedure for spontaneous symmetry breaking- is studied in detail: the monopole-bundle is reducible to a given subgroup K of the gauge group if and only if the Higgs charge satisfies a suitable constraint. The Yang-Mills connection reduces if and only if the non-Abelian charge vector belongs to the Lie algebra of K. The problem of ''global color'' can also be formulated in these terms. Our theory allows us to determine which subgroups K are internal symmetries of a given field configuration
Holographic Metals and Insulators with Helical Symmetry
Donos, Aristomenis; Kiritsis, Elias
2014-01-01
Homogeneous, zero temperature scaling solutions with Bianchi VII spatial geometry are constructed in Einstein-Maxwell-Dilaton theory. They correspond to quantum critical saddle points with helical symmetry at finite density. Assuming $AdS_{5}$ UV asymptotics, the small frequency/(temperature) dependence of the AC/(DC) electric conductivity along the director of the helix are computed. A large class of insulating and conducting anisotropic phases is found, as well as isotropic, metallic phases. Conduction can be dominated by dissipation due to weak breaking of translation symmetry or by a quantum critical current.
Holography in asymptotically flat spacetimes and the BMS group
International Nuclear Information System (INIS)
Arcioni, Giovanni; Dappiaggi, Claudio
2004-01-01
In a previous paper (Arcioni G and Dappiaggi C 2003 Preprint hep-th/0306142) we have started to explore the holographic principle in the case of asymptotically flat spacetimes and analysed, in particular, different aspects of the Bondi-Metzner-Sachs (BMS) group, namely the asymptotic symmetry group of any asymptotically flat spacetime. We continue this investigation in this paper. Having in mind an S-matrix approach with future and past null infinity playing the role of holographic screens on which the BMS group acts, we connect the IR sectors of the gravitational field with the representation theory of the BMS group. We analyse the (complicated) mapping between bulk and boundary symmetries pointing out differences with respect to the anti-de Sitter (AdS)/CFT set up. Finally, we construct a BMS phase space and a free Hamiltonian for fields transforming with respect to BMS representations. The last step is supposed to be an explorative investigation of the boundary data living on the degenerate null manifold at infinity
Standard Errors for Matrix Correlations.
Ogasawara, Haruhiko
1999-01-01
Derives the asymptotic standard errors and intercorrelations for several matrix correlations assuming multivariate normality for manifest variables and derives the asymptotic standard errors of the matrix correlations for two factor-loading matrices. (SLD)
Polynomial Asymptotes of the Second Kind
Dobbs, David E.
2011-01-01
This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…
Exact relativistic solution of disordered radiation with plane symmetry
International Nuclear Information System (INIS)
Fonseca Teixeira, A.F. da; Wolk, I.; Som, M.M.
1976-04-01
An exact solution of Einstein equations corresponding to an equilibrium distribution of disordered electromagnetic radiation with plane symmetry is obtained. This equilibrium is due solely to the gravitational and pressure effects inherent to the radiation. The distribution of radiation is found to be maximum and finite at the plane of symmetry, and to decrease monotonically in directions normal to this plane. The solution tends asymptotically to the static plane symmetric vacuum solution obtained by Levi-Civita. Timelike and null geodesics are discussed
Asymmetry, Symmetry and Beauty
Directory of Open Access Journals (Sweden)
Abbe R. Kopra
2010-07-01
Full Text Available Asymmetry and symmetry coexist in natural and human processes. The vital role of symmetry in art has been well demonstrated. This article highlights the complementary role of asymmetry. Further we show that the interaction of asymmetric action (recursion and symmetric opposition (sinusoidal waves are instrumental in generating creative features (relatively low entropy, temporal complexity, novelty (less recurrence in the data than in randomized copies and complex frequency composition. These features define Bios, a pattern found in musical compositions and in poetry, except for recurrence instead of novelty. Bios is a common pattern in many natural and human processes (quantum processes, the expansion of the universe, gravitational waves, cosmic microwave background radiation, DNA, physiological processes, animal and human populations, and economic time series. The reduction in entropy is significant, as it reveals creativity and contradicts the standard claim of unavoidable decay towards disorder. Artistic creations capture fundamental features of the world.
Asymptotic dynamics in perturbative quantum gravity and BMS supertranslations
Choi, Sangmin; Kol, Uri; Akhoury, Ratindranath
2018-01-01
Recently it has been shown that infrared divergences in the conventional S-matrix elements of gauge and gravitational theories arise from a violation of the conservation laws associated with large gauge symmetries. These infrared divergences can be cured by using the Faddeev-Kulish (FK) asymptotic states as the basis for S-matrix elements. Motivated by this connection, we study the action of BMS supertranslations on the FK asymptotic states of perturbative quantum gravity. We compute the BMS charge of the FK states and show that it characterizes the superselection sector to which the state belongs. Conservation of the BMS charge then implies that there is no transition between different superselection sectors, hence showing that the FK graviton clouds implement the necessary transition induced by the scattering process.
Toward convergence of the variational mass expansion in asymptotically free theories
Kneur, J L
2001-01-01
We re-examine a modification of perturbative expansions, valid for asymptotically free theories, producing "variationally improved" expansions of physical quantities relevant to dynamical (chiral) symmetry breaking. The large order behaviour of this expansion is shown to be drastically improved, for reasons analogous to the convergence properties of the delta-expansion of the anharmonic oscillator.
Setare, M. R.; Adami, H.
2018-01-01
We apply the new fall of conditions presented in the paper [1] on asymptotically flat spacetime solutions of Chern-Simons-like theories of gravity. We show that the considered fall of conditions asymptotically solve equations of motion of generalized minimal massive gravity. We demonstrate that there exist two type of solutions, one of those is trivial and the others are non-trivial. By looking at non-trivial solutions, for asymptotically flat spacetimes in the generalized minimal massive gravity, in contrast to Einstein gravity, cosmological parameter can be non-zero. We obtain the conserved charges of the asymptotically flat spacetimes in generalized minimal massive gravity, and by introducing Fourier modes we show that the asymptotic symmetry algebra is a semidirect product of a BMS3 algebra and two U (1) current algebras. Also we verify that the BMS3 algebra can be obtained by a contraction of the AdS3 asymptotic symmetry algebra when the AdS3 radius tends to infinity in the flat-space limit. Finally we find energy, angular momentum and entropy for a particular case and deduce that these quantities satisfy the first law of flat space cosmologies.
On extracting physical content from asymptotically flat spacetime metrics
International Nuclear Information System (INIS)
Kozameh, C; Newman, E T; Silva-Ortigoza, G
2008-01-01
A major issue in general relativity, from its earliest days to the present, is how to extract physical information from any solution or class of solutions to the Einstein equations. Though certain information can be obtained for arbitrary solutions, e.g., via geodesic deviation, in general, because of the coordinate freedom, it is often hard or impossible to do. Most of the time information is found from special conditions, e.g. degenerate principle null vectors, weak fields close to Minkowski space (using coordinates close to Minkowski coordinates), or from solutions that have symmetries or approximate symmetries. In the present work, we will be concerned with asymptotically flat spacetimes where the approximate symmetry is the Bondi-Metzner-Sachs group. For these spaces the Bondi 4-momentum vector and its evolution, found from the Weyl tensor at infinity, describes the total energy-momentum of the interior source and the energy-momentum radiated. By generalizing the structures (shear-free null geodesic congruences) associated with the algebraically special metrics to asymptotically shear-free null geodesic congruences, which are available in all asymptotically flat spacetimes, we give kinematic meaning to the Bondi 4-momentum. In other words, we describe the Bondi vector and its evolution in terms of a center of mass position vector, its velocity and a spin vector, all having clear geometric meaning. Among other items, from dynamic arguments, we define a unique (at our level of approximation) total angular momentum and extract its evolution equation in the form of a conservation law with an angular momentum flux
Asymptotic angular dependences of exclusive hadron large-angle scattering
International Nuclear Information System (INIS)
Goloskokov, S.V.; Kudinov, A.V.; Kuleshov, S.P.
1979-01-01
Asymptotic approach to the description of the large-angle scattering amplitudes of the meson-nucleon and nucleon-nucleon scattering is studied. The paper is based on the Mandelstam representation and quark counting rules. The crossing summetry, SU-3 symmetry and spin effects are taken into account. Formulae obtained are used for the description of the differential cross sections of πsup(+-)p, pp and pn scattering. The predictions about ksup(+-)p and p anti p scattering are made. It is shown that formulae provide quantitative description of experimental data for the considered reactions
Thermodynamics of asymptotically safe theories
DEFF Research Database (Denmark)
Rischke, Dirk H.; Sannino, Francesco
2015-01-01
We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze...
Root Asymptotics of Spectral Polynomials
Czech Academy of Sciences Publication Activity Database
Shapiro, B.; Tater, Miloš
2007-01-01
Roč. 47, č. 2 (2007), s. 33-36 ISSN 0355-2721 R&D Projects: GA MŠk LC06002 Institutional research plan: CEZ:AV0Z10480505 Keywords : asymptotic root -counting measure Subject RIV: BA - General Mathematics
Radiative symmetry breaking from interacting UV fixed points
DEFF Research Database (Denmark)
Abel, Steven; Sannino, Francesco
2017-01-01
It is shown that the addition of positive mass-squared terms to asymptotically safe gauge-Yukawa theories with perturbative UV fixed points leads to calculable radiative symmetry breaking in the IR. This phenomenon, and the multiplicative running of the operators that lies behind it, is akin...
Chiral symmetry and chiral-symmetry breaking
International Nuclear Information System (INIS)
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
Cosmological Reflection of Particle Symmetry
Directory of Open Access Journals (Sweden)
Maxim Khlopov
2016-08-01
Full Text Available The standard model involves particle symmetry and the mechanism of its breaking. Modern cosmology is based on inflationary models with baryosynthesis and dark matter/energy, which involves physics beyond the standard model. Studies of the physical basis of modern cosmology combine direct searches for new physics at accelerators with its indirect non-accelerator probes, in which cosmological consequences of particle models play an important role. The cosmological reflection of particle symmetry and the mechanisms of its breaking are the subject of the present review.
Asymptotic analysis of ultra-relativistic charge
International Nuclear Information System (INIS)
Burton, D.A.; Gratus, J.; Tucker, R.W.
2007-01-01
This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz-Dirac equation for a single point particle a simple model is proposed for a charged continuum interacting self-consistently with the Maxwell field in vacuo. The model is developed using intrinsic tensor field theory and exploits to the full the symmetry and light-cone structure of Minkowski spacetime. This permits the construction of a regular stress-energy tensor whose vanishing divergence determines a system of non-linear partial differential equations for the velocity and self-fields of accelerated charge. Within this covariant framework a particular perturbation scheme is motivated by an exact class of solutions to this system describing the evolution of a charged fluid under the combined effects of both self and external electromagnetic fields. The scheme yields an asymptotic approximation in terms of inhomogeneous linear equations for the self-consistent Maxwell field, charge current and time-like velocity field of the charged fluid and is defined as an ultra-relativistic configuration. To facilitate comparisons with existing accounts of beam dynamics an appendix translates the tensor formulation of the perturbation scheme into the language involving electric and magnetic fields observed in a laboratory (inertial) frame
Jaffé, Hans H
1977-01-01
This book, devoted exclusively to symmetry in chemistry and developed in an essentially nonmathematical way, is a must for students and researchers. Topics include symmetry elements and operations, multiple symmetry operations, multiplication tables and point groups, group theory applications, and crystal symmetry. Extensive appendices provide useful tables.
Effects of symmetry breaking in finite quantum systems
Energy Technology Data Exchange (ETDEWEB)
Birman, J.L. [Department of Physics, City College, City University of New York, New York, NY 10031 (United States); Nazmitdinov, R.G. [Departament de Fisica, Universitat de les Illes Balears, Palma de Mallorca 07122 (Spain); Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980 (Russian Federation); Yukalov, V.I., E-mail: yukalov@theor.jinr.ru [Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980 (Russian Federation)
2013-05-15
The review considers the peculiarities of symmetry breaking and symmetry transformations and the related physical effects in finite quantum systems. Some types of symmetry in finite systems can be broken only asymptotically. However, with a sufficiently large number of particles, crossover transitions become sharp, so that symmetry breaking happens similarly to that in macroscopic systems. This concerns, in particular, global gauge symmetry breaking, related to Bose–Einstein condensation and superconductivity, or isotropy breaking, related to the generation of quantum vortices, and the stratification in multicomponent mixtures. A special type of symmetry transformation, characteristic only for finite systems, is the change of shape symmetry. These phenomena are illustrated by the examples of several typical mesoscopic systems, such as trapped atoms, quantum dots, atomic nuclei, and metallic grains. The specific features of the review are: (i) the emphasis on the peculiarities of the symmetry breaking in finite mesoscopic systems; (ii) the analysis of common properties of physically different finite quantum systems; (iii) the manifestations of symmetry breaking in the spectra of collective excitations in finite quantum systems. The analysis of these features allows for the better understanding of the intimate relation between the type of symmetry and other physical properties of quantum systems. This also makes it possible to predict new effects by employing the analogies between finite quantum systems of different physical nature.
Kootstra, Gert; Nederveen, Arco; de Boer, Bart
2008-01-01
Humans are very sensitive to symmetry in visual patterns. Symmetry is detected and recognized very rapidly. While viewing symmetrical patterns eye fixations are concentrated along the axis of symmetry or the symmetrical center of the patterns. This suggests that symmetry is a highly salient feature. Existing computational models of saliency, however, have mainly focused on contrast as a measure of saliency. These models do not take symmetry into account. In this paper, we discuss local symmet...
Asymptotic functions and multiplication of distributions
International Nuclear Information System (INIS)
Todorov, T.D.
1979-01-01
Considered is a new type of generalized asymptotic functions, which are not functionals on some space of test functions as the Schwartz distributions. The definition of the generalized asymptotic functions is given. It is pointed out that in future the particular asymptotic functions will be used for solving some topics of quantum mechanics and quantum theory
Entangling power of the baker's map: Role of symmetries
International Nuclear Information System (INIS)
Abreu, Romulo F.; Vallejos, Raul O.
2006-01-01
The quantum baker map possesses two symmetries: a canonical 'spatial' symmetry, and a time-reversal symmetry. We show that, even when these features are taken into account, the asymptotic entangling power of the baker's map does not always agree with the predictions of random matrix theory. We have verified that the dimension of the Hilbert space is the crucial parameter that determines whether the entangling properties of the baker map are universal or not. For power-of-2 dimensions, i.e., qubit systems, an anomalous entangling power is observed; otherwise the behavior of the baker map is consistent with random matrix theories. We also derive a general formula that relates the asymptotic entangling power of an arbitrary unitary with properties of its reduced eigenvectors
Applications of chiral symmetry
International Nuclear Information System (INIS)
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 χ implies that the ρ and a 1 vector mesons are degenerate in mass. In a gauged linear sigma model the ρ mass increases with temperature, m ρ (T χ ) > m ρ (0). The author conjectures that at T χ the thermal ρ - a 1 , peak is relatively high, at about ∼1 GeV, with a width approximately that at zero temperature (up to standard kinematic factors). The ω meson also increases in mass, nearly degenerate with the ρ, but its width grows dramatically with temperature, increasing to at least ∼100 MeV by T χ . 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 quenchedclose 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
Spontaneous symmetry breakdown in gauge theories
International Nuclear Information System (INIS)
Scadron, M.D.
1982-01-01
The dynamical theory of spontaneous breakdown correctly predicts the bound states and relates the order parameters of electron-photon superconductivity and quark-gluon chiral symmetry. A similar statement cannot be made for the standard electro-weak gauge symmetry. (author)
Symmetry violation in weak decays
Vos, Kimberley Keri
2016-01-01
Our current knowledge of particle physics is described by the Standard Model (SM). This model, however, leaves important observations unexplained. To answer these outstanding questions, as of yet, unknown physics is required. In the search for new physics, symmetries and their breaking play a
Symmetry, empirical significance, and identity
Friederich, Simon
The article proposes a novel approach to the much discussed question of which symmetries have ‘direct empirical significance’ and which do not. The approach is based on a development of a recently proposed framework by Hilary Greaves and David Wallace, who claim that, contrary to the standard
The unusual asymptotics of three-sided prudent polygons
International Nuclear Information System (INIS)
Beaton, Nicholas R; Guttmann, Anthony J; Flajolet, Philippe
2010-01-01
We have studied the area-generating function of prudent polygons on the square lattice. Exact solutions are obtained for the generating function of two-sided and three-sided prudent polygons, and a functional equation is found for four-sided prudent polygons. This is used to generate series coefficients in polynomial time, and these are analysed to determine the asymptotics numerically. A careful asymptotic analysis of the three-sided polygons produces a most surprising result. A transcendental critical exponent is found, and the leading amplitude is not quite a constant, but is a constant plus a small oscillatory component with an amplitude approximately 10 -8 times that of the leading amplitude. This effect cannot be seen by any standard numerical analysis, but it may be present in other models. If so, it changes our whole view of the asymptotic behaviour of lattice models. (fast track communication)
Chiral symmetry on the lattice
Energy Technology Data Exchange (ETDEWEB)
Creutz, M.
1994-11-01
The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model.
Chiral symmetry on the lattice
International Nuclear Information System (INIS)
Creutz, M.
1994-11-01
The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model
Vladimir Sudakov and double-logarithmic asymptotics of amplitudes in QED, QCD and gravity
Directory of Open Access Journals (Sweden)
Lipatov L. N.
2017-01-01
Full Text Available We review the Sudakov results on the double logarithmic asymptotics of the electron form-factor which were based on his parametrization of the virtual particle momenta in the Feynman diagrams. The high energy amplitudes for various QED and QCD processes in the double-logarithmic approximation are obtained by using the Bethe-Salpeter approach and the evolution equations. The ultraviolet divergency of the graviton Regge trajectory allows to derive the infrared evolution equation for the graviton-graviton scattering amplitude with a double-logarithmic accuracy. The asymptotic behavior of this amplitude depends essentially on the rank N of the super-symmetry.
Discrete symmetries and their stringy origin
International Nuclear Information System (INIS)
Mayorga Pena, Damian Kaloni
2014-05-01
Discrete symmetries have proven to be very useful in controlling the phenomenology of theories beyond the standard model. In this work we explore how these symmetries emerge from string compactifications. Our approach is twofold: On the one hand, we consider the heterotic string on orbifold backgrounds. In this case the discrete symmetries can be derived from the orbifold conformal field theory, and it can be shown that they are in close relation with the orbifold geometry. We devote special attention to R-symmetries, which arise from discrete remnants of the Lorentz group in compact space. Further we discuss the physical implications of these symmetries both in the heterotic mini-landscape and in newly constructed models based on the Z 2 x Z 4 orbifold. In both cases we observe that the discrete symmetries favor particular locations in the orbifold where the particles of standard model should live. On the other hand we consider a class of F-theory models exhibiting an SU(5) gauge group, times additional U(1) symmetries. In this case, the smooth compactification background does not permit us to track the discrete symmetries as transparently as in orbifold models. Hence, we follow a different approach and search for discrete subgroups emerging after the U(1)s are broken. We observe that in this approach it is possible to obtain the standard Z 2 matter parity of the MSSM.
Witten, Edward
2018-02-01
In a modern understanding of particle physics, global symmetries are approximate and gauge symmetries may be emergent. This view, which has echoes in condensed-matter physics, is supported by a variety of arguments from experiment and theory.
Asymptotics of weighted random sums
DEFF Research Database (Denmark)
Corcuera, José Manuel; Nualart, David; Podolskij, Mark
2014-01-01
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We show that these sums converge in law to the integral...... of the weight process with respect to the Brownian motion when the distance between observations goes to zero. The result is obtained with the help of fractional calculus showing the power of this technique. This study, though interesting by itself, is motivated by an error found in the proof of Theorem 4...
Asymptotics for Associated Random Variables
Oliveira, Paulo Eduardo
2012-01-01
The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting
Naturalness of asymptotically safe Higgs
DEFF Research Database (Denmark)
Pelaggi, Giulio M.; Sannino, Francesco; Strumia, Alessandro
2017-01-01
We extend the list of theories featuring a rigorous interacting ultraviolet fixed point by constructing the first theory featuring a Higgs-like scalar with gauge, Yukawa and quartic interactions. We show that the theory enters a perturbative asymptotically safe regime at energies above a physical...... scale Λ. We determine the salient properties of the theory and use it as a concrete example to test whether scalars masses unavoidably receive quantum correction of order Λ. Having at our dispose a calculable model allowing us to precisely relate the IR and UV of the theory we demonstrate...
Wigner's Symmetry Representation Theorem
Indian Academy of Sciences (India)
IAS Admin
This article elucidates the important role the no- tion of symmetry has played in physics. It dis- cusses the proof of one of the important theorems of quantum mechanics, viz., Wigner's Symmetry. Representation Theorem. It also shows how the representations of various continuous and dis- crete symmetries follow from the ...
Rehren, K. -H.
1996-01-01
Weak C* Hopf algebras can act as global symmetries in low-dimensional quantum field theories, when braid group statistics prevents group symmetries. Possibilities to construct field algebras with weak C* Hopf symmetry from a given theory of local observables are discussed.
Symmetry, asymmetry and dissymmetry
International Nuclear Information System (INIS)
Wackenheim, A.; Zollner, G.
1987-01-01
The authors discuss the concept of symmetry and defect of symmetry in radiological imaging and recall the definition of asymmetry (congenital or constitutional) and dissymmetry (acquired). They then describe a rule designed for the cognitive method of automatic evaluation of shape recognition data and propose the use of reversal symmetry [fr
Polynomial Graphs and Symmetry
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
Energy Technology Data Exchange (ETDEWEB)
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)
Numerical relativity and asymptotic flatness
International Nuclear Information System (INIS)
Deadman, E; Stewart, J M
2009-01-01
It is highly plausible that the region of spacetime far from an isolated gravitating body is, in some sense, asymptotically Minkowskian. However theoretical studies of the full nonlinear theory, initiated by Bondi et al (1962 Proc. R. Soc. A 269 21-51), Sachs (1962 Proc. R. Soc. A 270 103-26) and Newman and Unti (1962 J. Math. Phys. 3 891-901), rely on careful, clever, a priori choices of a chart (and tetrad) and so are not readily accessible to the numerical relativist, who chooses her/his chart on the basis of quite different grounds. This paper seeks to close this gap. Starting from data available in a typical numerical evolution, we construct a chart and tetrad which are, asymptotically, sufficiently close to the theoretical ones, so that the key concepts of the Bondi news function, Bondi mass and its rate of decrease can be estimated. In particular, these estimates can be expressed in the numerical relativist's chart as numerical relativity recipes.
Parastatistics and gauge symmetries
International Nuclear Information System (INIS)
Govorkov, A.B.
1982-01-01
A possible formulation of gauge symmetries in the Green parafield theory is analysed and the SO(3) gauge symmetry is shown to be on a distinct status. The Greenberg paraquark hypothesis turns out to be not equivalent to the hypothesis of quark colour SU(3)sub(c) symmetry. Specific features of the gauge SO(3) symmetry are discussed, and a possible scheme where it is an exact subgroup of the broken SU(3)sub(c) symmetry is proposed. The direct formulation of the gauge principle for the parafield represented by quaternions is also discussed
Asymptotic safety, emergence and minimal length
International Nuclear Information System (INIS)
Percacci, Roberto; Vacca, Gian Paolo
2010-01-01
There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that (1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and (2) there is a sense in which asymptotic safety implies a minimal length. In doing so we also discuss possible signatures of asymptotic safety in scattering experiments.
Habibullin, I. T.; Poptsova, M. N.
2015-03-01
A method of the formal diagonalization of the discrete linear operator with a parameter is studied. In the case when the operator provides a Lax operator for a nonlinear quad system the formal diagonalization method allows one to describe effectively conservation laws and generalized symmetries for this system. Asymptotic representation of the Lax operators eigenfunctions are constructed and infinite series of conservation laws are described for the quad system connected with A3(1) affine Lie algebra, for the modified discrete Boussinesq system and for the discrete Tzitzeica equation. For a newly found multiquadratic discrete model conservation laws and several generalized symmetries are presented.
Symmetries of nonlinear ordinary differential equations: The ...
Indian Academy of Sciences (India)
2015-10-21
Oct 21, 2015 ... Lie point symmetries; -symmetries; Noether symmetries; contact symmetries; adjoint symmetries; nonlocal symmetries; hidden symmetries; ... 620 024, India; Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401, India ...
International Nuclear Information System (INIS)
Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan; Willett, Brian
2015-01-01
A q-form global symmetry is a global symmetry for which the charged operators are of space-time dimension q; e.g. Wilson lines, surface defects, etc., and the charged excitations have q spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries (q=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a subgroup). They can also have ’t Hooft anomalies, which prevent us from gauging them, but lead to ’t Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.
International Nuclear Information System (INIS)
Liu Hongzhun; Pan Zuliang; Li Peng
2006-01-01
In this article, we will derive an equality, where the Taylor series expansion around ε = 0 for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted. By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-Baecklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-Baecklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.
Non-Weyl asymptotics for quantum graphs with general coupling conditions
International Nuclear Information System (INIS)
Davies, E Brian; Exner, Pavel; Lipovsky, JirI
2010-01-01
Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in the case of Kirchhoff or anti-Kirchhoff conditions. While for graphs without permutation symmetry numerous examples of non-Weyl behaviour can be constructed. Furthermore, we present an insight into what makes the Kirchhoff/anti-Kirchhoff coupling particular from the resonance point of view. Finally, we demonstrate a generalization to quantum graphs with unequal edge weights.
On Consistent Nonparametric Statistical Tests of Symmetry Hypotheses
Directory of Open Access Journals (Sweden)
Jean-François Quessy
2016-05-01
Full Text Available Being able to formally test for symmetry hypotheses is an important topic in many fields, including environmental and physical sciences. In this paper, one concentrates on a large family of nonparametric tests of symmetry based on Cramér–von Mises statistics computed from empirical distribution and characteristic functions. These tests possess the highly desirable property of being universally consistent in the sense that they detect any kind of departure from symmetry as the sample size becomes large. The asymptotic behaviour of these test statistics under symmetry is deduced from the theory of first-order degenerate V-statistics. The issue of computing valid p-values is tackled using the multiplier bootstrap method suitably adapted to V-statistics, yielding elegant, easy-to-compute and quick procedures for testing symmetry. A special focus is put on tests of univariate symmetry, bivariate exchangeability and reflected symmetry; a simulation study indicates the good sampling properties of these tests. Finally, a framework for testing general symmetry hypotheses is introduced.
Symmetry and symmetry breaking in quantum mechanics
International Nuclear Information System (INIS)
Chomaz, Philippe
1998-01-01
In the world of infinitely small, the world of atoms, nuclei and particles, the quantum mechanics enforces its laws. The discovery of Quanta, this unbelievable castration of the Possible in grains of matter and radiation, in discrete energy levels compels us of thinking the Single to comprehend the Universal. Quantum Numbers, magic Numbers and Numbers sign the wave. The matter is vibration. To describe the music of the world one needs keys, measures, notes, rules and partition: one needs quantum mechanics. The particles reduce themselves not in material points as the scholars of the past centuries thought, but they must be conceived throughout the space, in the accomplishment of shapes of volumes. When Einstein asked himself whether God plays dice, there was no doubt among its contemporaries that if He exists He is a geometer. In a Nature reduced to Geometry, the symmetries assume their role in servicing the Harmony. The symmetries allow ordering the energy levels to make them understandable. They impose there geometrical rules to the matter waves, giving them properties which sometimes astonish us. Hidden symmetries, internal symmetries and newly conceived symmetries have to be adopted subsequently to the observation of some order in this world of Quanta. In turn, the symmetries provide new observables which open new spaces of observation
Particle shape reconstruction from the asymptotic small-angle scattering intensity
International Nuclear Information System (INIS)
Ciccariello, S.
2002-01-01
For two-phase samples, made up of equally shaped and oriented particles with a different size, the particle shape can be reconstructed from the relevant asymptotic iso-intensity surfaces if these are smooth revolution surfaces. This result, applied to a two-dimensional diffraction pattern with a C 2 -symmetry, determines the shape of the particle sections with the detector plane. The procedure is applied to an alloy sample and to a polymer solution under shear. (author)
Particle shape reconstruction from the asymptotic small-angle scattering intensity
Ciccariello, S
2002-01-01
For two-phase samples, made up of equally shaped and oriented particles with a different size, the particle shape can be reconstructed from the relevant asymptotic iso-intensity surfaces if these are smooth revolution surfaces. This result, applied to a two-dimensional diffraction pattern with a C sub 2 -symmetry, determines the shape of the particle sections with the detector plane. The procedure is applied to an alloy sample and to a polymer solution under shear. (author)
Asymptotic Helicity Conservation in SUSY
Gounaris, G J; Renard, F M
2010-01-01
We summarize the extensive work started in ref.1, according to which total helicity is conserved for any two-to-two process, at sqrt{s} larger than M_{SUSY} and fixed angles, in any SUSY extension of SM. Asymptotically the theorem is exact. But it may also have important implications at lower energies sqrt{s} close to M_{SUSY}. Up to now, these have been investigated to 1loop electroweak (EW) order for the processes ug to d W+, sd_L chi+; as well as the 17 gg to HH', and the 9 gg to VH processes, where H,H' denote Higgs or Goldstone bosons, and V=Z, W.
Asymptotic invariants of homotopy groups
Manin, Fedor
We study the homotopy groups of a finite CW complex X via constraints on the geometry of representatives of their elements. For example, one can measure the "size" of alpha ∈ pi n (X) by the optimal Lipschitz constant or volume of a representative. By comparing the geometrical structure thus obtained with the algebraic structure of the group, one can define functions such as growth and distortion in pin(X), analogously to the way that such functions are studied in asymptotic geometric group theory. We provide a number of examples and techniques for studying these invariants, with a special focus on spaces with few rational homotopy groups. Our main theorem characterizes those X in which all non-torsion homotopy classes are undistorted, that is, their volume distortion functions, and hence also their Lipschitz distortion functions, are linear.
Exponential asymptotics of homoclinic snaking
Dean, A. D.; Matthews, P. C.; Cox, S. M.; King, J. R.
2011-12-01
We study homoclinic snaking in the cubic-quintic Swift-Hohenberg equation (SHE) close to the onset of a subcritical pattern-forming instability. Application of the usual multiple-scales method produces a leading-order stationary front solution, connecting the trivial solution to the patterned state. A localized pattern may therefore be constructed by matching between two distant fronts placed back-to-back. However, the asymptotic expansion of the front is divergent, and hence should be truncated. By truncating optimally, such that the resultant remainder is exponentially small, an exponentially small parameter range is derived within which stationary fronts exist. This is shown to be a direct result of the 'locking' between the phase of the underlying pattern and its slowly varying envelope. The locking mechanism remains unobservable at any algebraic order, and can only be derived by explicitly considering beyond-all-orders effects in the tail of the asymptotic expansion, following the method of Kozyreff and Chapman as applied to the quadratic-cubic SHE (Chapman and Kozyreff 2009 Physica D 238 319-54, Kozyreff and Chapman 2006 Phys. Rev. Lett. 97 44502). Exponentially small, but exponentially growing, contributions appear in the tail of the expansion, which must be included when constructing localized patterns in order to reproduce the full snaking diagram. Implicit within the bifurcation equations is an analytical formula for the width of the snaking region. Due to the linear nature of the beyond-all-orders calculation, the bifurcation equations contain an analytically indeterminable constant, estimated in the previous work by Chapman and Kozyreff using a best fit approximation. A more accurate estimate of the equivalent constant in the cubic-quintic case is calculated from the iteration of a recurrence relation, and the subsequent analytical bifurcation diagram compared with numerical simulations, with good agreement.
Exponential asymptotics of homoclinic snaking
International Nuclear Information System (INIS)
Dean, A D; Matthews, P C; Cox, S M; King, J R
2011-01-01
We study homoclinic snaking in the cubic-quintic Swift–Hohenberg equation (SHE) close to the onset of a subcritical pattern-forming instability. Application of the usual multiple-scales method produces a leading-order stationary front solution, connecting the trivial solution to the patterned state. A localized pattern may therefore be constructed by matching between two distant fronts placed back-to-back. However, the asymptotic expansion of the front is divergent, and hence should be truncated. By truncating optimally, such that the resultant remainder is exponentially small, an exponentially small parameter range is derived within which stationary fronts exist. This is shown to be a direct result of the 'locking' between the phase of the underlying pattern and its slowly varying envelope. The locking mechanism remains unobservable at any algebraic order, and can only be derived by explicitly considering beyond-all-orders effects in the tail of the asymptotic expansion, following the method of Kozyreff and Chapman as applied to the quadratic-cubic SHE (Chapman and Kozyreff 2009 Physica D 238 319–54, Kozyreff and Chapman 2006 Phys. Rev. Lett. 97 44502). Exponentially small, but exponentially growing, contributions appear in the tail of the expansion, which must be included when constructing localized patterns in order to reproduce the full snaking diagram. Implicit within the bifurcation equations is an analytical formula for the width of the snaking region. Due to the linear nature of the beyond-all-orders calculation, the bifurcation equations contain an analytically indeterminable constant, estimated in the previous work by Chapman and Kozyreff using a best fit approximation. A more accurate estimate of the equivalent constant in the cubic-quintic case is calculated from the iteration of a recurrence relation, and the subsequent analytical bifurcation diagram compared with numerical simulations, with good agreement
Asymptotic Tracking Controller Design for Nonlinear Systems With Guaranteed Performance.
Fan, Bo; Yang, Qinmin; Jagannathan, Sarangapani; Sun, Youxian
2017-07-21
In this paper, a novel adaptive control strategy is presented for the tracking control of a class of multi-input-multioutput uncertain nonlinear systems with external disturbances to place user-defined time-varying constraints on the system state. Our contribution includes a step forward beyond the usual stabilization result to show that the states of the plant converge asymptotically, as well as remain within user-defined time-varying bounds. To achieve the new results, an error transformation technique is first established to generate an equivalent nonlinear system from the original one, whose asymptotic stability guarantees both the satisfaction of the time-varying restrictions and the asymptotic tracking performance of the original system. The uncertainties of the transformed system are overcome by an online neural network (NN) approximator, while the external disturbances and NN reconstruction error are compensated by the robust integral of the sign of the error signal. Via standard Lyapunov method, asymptotic tracking performance is theoretically guaranteed, and all the closed-loop signals are bounded. The requirement for a prior knowledge of bounds of uncertain terms is relaxed. Finally, simulation results demonstrate the merits of the proposed controller.
International Nuclear Information System (INIS)
Mainzer, K.
1988-01-01
Symmetry, disymmetry, chirality etc. are well-known topics in chemistry. But they cannot only be found on the molecular level of matter. Atoms and elementary particles in physics are also characterized by particular symmetry groups. Even living organisms and populations on the macroscopic level have functional properties of symmetry. The whole physical, chemical, and biological evolution seems to be regulated by the emergence of new symmetries and the breaking down of old ones. One is reminded of Heisenberg's famous statement: 'Die letzte Wurzel der Erscheinungen ist also nicht die Materie, sondern das mathematische Gesetz, die Symmetrie, die mathematische Form' (Wandlungen in den Grundlagen der Naturwissenschaften, 1959). Historically the belief in symmetry and simplicity of nature has a long philosophical tradition from the Pythagoreans, Plato and Greek astronomers to Kepler and modern scientists. Today, 'symmetries in nature' is a common topic of mathematics, physics, chemistry, and biology. A lot of Nobel prizes were given in honour of inquiries concerning symmetries in nature. The fascination of symmetries is not only motivated by science, but by art and religion too. Therefore 'symmetris in nature' is an interdisciplinary topic which may help to overcome C.P. Snow's 'Two Cultures' of natural sciences and humanities. (author) 17 refs., 21 figs
Testing spatial symmetry using contingency tables based on nearest neighbor relations.
Ceyhan, Elvan
2014-01-01
We consider two types of spatial symmetry, namely, symmetry in the mixed or shared nearest neighbor (NN) structures. We use Pielou's and Dixon's symmetry tests which are defined using contingency tables based on the NN relationships between the data points. We generalize these tests to multiple classes and demonstrate that both the asymptotic and exact versions of Pielou's first type of symmetry test are extremely conservative in rejecting symmetry in the mixed NN structure and hence should be avoided or only the Monte Carlo randomized version should be used. Under RL, we derive the asymptotic distribution for Dixon's symmetry test and also observe that the usual independence test seems to be appropriate for Pielou's second type of test. Moreover, we apply variants of Fisher's exact test on the shared NN contingency table for Pielou's second test and determine the most appropriate version for our setting. We also consider pairwise and one-versus-rest type tests in post hoc analysis after a significant overall symmetry test. We investigate the asymptotic properties of the tests, prove their consistency under appropriate null hypotheses, and investigate finite sample performance of them by extensive Monte Carlo simulations. The methods are illustrated on a real-life ecological data set.
Dual Symmetry in Gauge Theories
Koshkarov, A. L.
1997-01-01
Continuous dual symmetry in electrodynamics, Yang-Mills theory and gravitation is investigated. Dual invariant which leads to badly nonlinear motion equations is chosen as a Lagrangian of the pure classical dual nonlinear electrodynamics. In a natural manner some dual angle which is determined by the electromagnetic strengths at the point of the time-space appears in the model. Motion equations may well be interpreted as the equations of the standard Maxwell theory with source. Alternative in...
Inequalities and asymptotics for some moment integrals.
Abi-Khuzam, Faruk
2017-01-01
For [Formula: see text], we obtain two-sided inequalities for the moment integral [Formula: see text]. These are then used to give the exact asymptotic behavior of the integral as [Formula: see text]. The case [Formula: see text] corresponds to the asymptotics of Ball's inequality, and [Formula: see text] corresponds to a kind of novel "oscillatory" behavior.
Wijsman Orlicz Asymptotically Ideal -Statistical Equivalent Sequences
Directory of Open Access Journals (Sweden)
Bipan Hazarika
2013-01-01
in Wijsman sense and present some definitions which are the natural combination of the definition of asymptotic equivalence, statistical equivalent, -statistical equivalent sequences in Wijsman sense. Finally, we introduce the notion of Cesaro Orlicz asymptotically -equivalent sequences in Wijsman sense and establish their relationship with other classes.
Stark resonances: asymptotics and distributional Borel sum
International Nuclear Information System (INIS)
Caliceti, E.; Grecchi, V.; Maioli, M.
1993-01-01
We prove that the Stark effect perturbation theory of a class of bound states uniquely determines the position and the width of the resonances by Distributional Borel Sum. In particular the small field asymptotics of the width is uniquely related to the large order asymptotics of the perturbation coefficients. Similar results apply to all the ''resonances'' of the anharmonic and double well oscillators. (orig.)
The Poincare group as the symmetry group of canonical general relativity
International Nuclear Information System (INIS)
Beig, R.; Murchadha, N. o
1986-01-01
This work reconsiders the formulation, due to Regge and Teitelboim, of the phase space approach to General Relativity in the asymptotically flat context, phrasing it in the language of symplectic geometry. The necessary boundary conditions at spatial infinity are spelled out in detail. Precise meaning is given to the statement that, as a result of these boundary conditions, the Poincare group acts as a symmetry group on the phase space of G.R. This situation is compared with the spi-picture of Ashtekar and Hansen, where a larger asymptotic symmetry group is obtained. (Author)
International Nuclear Information System (INIS)
Alhassid, Y.; Leviatan, A.
1993-01-01
A novel symmetry structure, partial dynamical symmetry is introduced. The Hamiltonian is not invariant under the transformations of a group G and irreps of G are mixed in its eigenstates. it possesses, however, a partial set of eigenstates which do have good symmetry and can be labeled by irreps of G. A general algorithm to construct such Hamiltonians for a semi-simple group G is presented. (Author) 6 refs
On the algebraic realization of SU(4) symmetry
International Nuclear Information System (INIS)
Asatryan, G.M.; Zaslavsky, A.N.
1976-01-01
A possibility of nonlinear realization of the symmetry with linearization on the SU(4)xYxC group is discussed. Algebraic properties of SU(4) are restored from the Weinberg condition: amplitudes of goldstone scattering on particles should have a reasonable (as in the Regge theory) asymptotic behaviour. In this case the breaking appears to be minimal. Large values of psi meson masses lead to high-lying charmed trajectories in the SU(4) algebraic realization
Asymptotics of work distributions in a stochastically driven system
Manikandan, Sreekanth K.; Krishnamurthy, Supriya
2017-12-01
We determine the asymptotic forms of work distributions at arbitrary times T, in a class of driven stochastic systems using a theory developed by Nickelsen and Engel (EN theory) [D. Nickelsen and A. Engel, Eur. Phys. J. B 82, 207 (2011)], which is based on the contraction principle of large deviation theory. In this paper, we extend the theory, previously applied in the context of deterministically driven systems, to a model in which the driving is stochastic. The models we study are described by overdamped Langevin equations and the work distributions in path integral form, are characterised by having quadratic augmented actions. We first illustrate EN theory, for a deterministically driven system - the breathing parabola model, and show that within its framework, the Crooks fluctuation theorem manifests itself as a reflection symmetry property of a certain characteristic polynomial, which also determines the exact moment-generating-function at arbitrary times. We then extend our analysis to a stochastically driven system, studied in references [S. Sabhapandit, EPL 89, 60003 (2010); A. Pal, S. Sabhapandit, Phys. Rev. E 87, 022138 (2013); G. Verley, C. Van den Broeck, M. Esposito, New J. Phys. 16, 095001 (2014)], for both equilibrium and non-equilibrium steady state initial distributions. In both cases we obtain new analytic solutions for the asymptotic forms of (dissipated) work distributions at arbitrary T. For dissipated work in the steady state, we compare the large T asymptotic behaviour of our solution to the functional form obtained in reference [New J. Phys. 16, 095001 (2014)]. In all cases, special emphasis is placed on the computation of the pre-exponential factor and the results show excellent agreement with numerical simulations. Our solutions are exact in the low noise (β → ∞) limit.
Asymptotically simple spacetimes and mass loss due to gravitational waves
Saw, Vee-Liem
The cosmological constant Λ used to be a freedom in Einstein’s theory of general relativity (GR), where one had a proclivity to set it to zero purely for convenience. The signs of Λ or Λ being zero would describe universes with different properties. For instance, the conformal structure of spacetime directly depends on Λ: null infinity ℐ is a spacelike, null, or timelike hypersurface, if Λ > 0, Λ = 0, or Λ 0 in Einstein’s theory of GR. A quantity that depends on the conformal structure of spacetime, especially on the nature of ℐ, is the Bondi mass which in turn dictates the mass loss of an isolated gravitating system due to energy carried away by gravitational waves. This problem of extending the Bondi mass to a universe with Λ > 0 has spawned intense research activity over the past several years. Some aspects include a closer inspection on the conformal properties, working with linearization, attempts using a Hamiltonian formulation based on “linearized” asymptotic symmetries, as well as obtaining the general asymptotic solutions of de Sitter-like spacetimes. We consolidate on the progress thus far from the various approaches that have been undertaken, as well as discuss the current open problems and possible directions in this area.
The zonal satellite problem. III Symmetries
Directory of Open Access Journals (Sweden)
Mioc V.
2002-01-01
Full Text Available The two-body problem associated with a force field described by a potential of the form U =Sum(k=1,n ak/rk (r = distance between particles, ak = real parameters is resumed from the only standpoint of symmetries. Such symmetries, expressed in Hamiltonian coordinates, or in standard polar coordinates, are recovered for McGehee-type coordinates of both collision-blow-up and infinity-blow-up kind. They form diffeomorphic commutative groups endowed with a Boolean structure. Expressed in Levi-Civita’s coordinates, the problem exhibits a larger group of symmetries, also commutative and presenting a Boolean structure.
Discrete symmetries and solar neutrino mixing
Energy Technology Data Exchange (ETDEWEB)
Kapetanakis, D.; Mayr, P.; Nilles, H.P. (Physik Dept., Technische Univ. Muenchen, Garching (Germany) Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Muenchen (Germany))
1992-05-21
We study the question of resonant solar neutrino mixing in the framework of the supersymmetric extension of the standard model. Discrete symmetries that are consistent with solar neutrino mixing and proton stability are classified. In the minimal model they are shown to lead to two distinct patterns of allowed dimension-four operators. Imposing anomaly freedom, only three different discrete Z{sub N}-symmetries (with N=2, 3, 6) are found to be phenomenologically acceptable. (orig.).
Discrete symmetries and solar neutrino mixing
International Nuclear Information System (INIS)
Kapetanakis, D.; Mayr, P.; Nilles, H.P.
1992-01-01
We study the question of resonant solar neutrino mixing in the framework of the supersymmetric extension of the standard model. Discrete symmetries that are consistent with solar neutrino mixing and proton stability are classified. In the minimal model they are shown to lead to two distinct patterns of allowed dimension-four operators. Imposing anomaly freedom, only three different discrete Z N -symmetries (with N=2, 3, 6) are found to be phenomenologically acceptable. (orig.)
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.
Quantum symmetry for pedestrians
International Nuclear Information System (INIS)
Mack, G.; Schomerus, V.
1992-03-01
Symmetries more general than groups are possible in quantum therory. Quantum symmetries in the narrow sense are compatible with braid statistics. They are theoretically consistent much as supersymmetry is, and they could lead to degenerate multiplets of excitations with fractional spin in thin films. (orig.)
Schaft, A.J. van der
1987-01-01
It is argued that the existence of symmetries may simplify, as in classical mechanics, the solution of optimal control problems. A procedure for obtaining symmetries for the optimal Hamiltonian resulting from the Maximum Principle is given; this avoids the actual calculation of the optimal
2016-01-01
The Symmetry Festival is a science and art program series, the most important periodic event (see its history) to bring together scientists, artists, educators and practitioners interested in symmetry (its roots, what is behind, applications, etc.), or in the consequences of its absence.
Charged fluids with symmetries
Indian Academy of Sciences (India)
metric tensor field and generate constants of the motion along null geodesics for massless particles. Conformal symmetries arise in various physical applications. The existence of conformal symmetries in relativistic cosmological models, with restrictions on the matter content and fluid four-velocity, have been extensively ...
Symmetries in the world of elementary particles
International Nuclear Information System (INIS)
Horvath, D.; Hungarian Academy of Sciences, Debrecen
2003-01-01
Symmetries are leading to conservation laws and these are important features of interactions. Elementary particles are classified according to their spin into fermions and bosons with accordingly different symmetry features. Each particle has its corresponding antiparticle that is leading to the CPT symmetry. Particles can also be classified according to the type of interaction they take part in. Leptons are not taking part in the strong interaction, while the quark model can describe all particles. The model has been made complete with the introduction of a new quantum number, the colour. The next theoretical stage has been that of the GIM mechanism leading to the Standard Model, according to which all interactions are rooted in local symmetries. The carriers of the three basic interactions are: the photon for the electromagnetic one, the weak bosons for the weak interaction, and the gluons for the strong one. The Standard Model has been brought to its actual form by the Higgs mechanism, the spontaneous symmetry breaking. Further development of the model is envisaged. One direction might be that of super symmetry, which created the Minimal Supersymmetric Standard Model. (Gy.M.)
Asymptotic Conservation Laws in Classical Field Theory
International Nuclear Information System (INIS)
Anderson, I.M.; Torre, C.G.
1996-01-01
A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the Arnowitt-Deser-Misner energy in general relativity. copyright 1996 The American Physical Society
Upper bound on the Abelian gauge coupling from asymptotic safety
Eichhorn, Astrid; Versteegen, Fleur
2018-01-01
We explore the impact of asymptotically safe quantum gravity on the Abelian gauge coupling in a model including a charged scalar, confirming indications that asymptotically safe quantum fluctuations of gravity could trigger a power-law running towards a free fixed point for the gauge coupling above the Planck scale. Simultaneously, quantum gravity fluctuations balance against matter fluctuations to generate an interacting fixed point, which acts as a boundary of the basin of attraction of the free fixed point. This enforces an upper bound on the infrared value of the Abelian gauge coupling. In the regime of gravity couplings which in our approximation also allows for a prediction of the top quark and Higgs mass close to the experimental value [1], we obtain an upper bound approximately 35% above the infrared value of the hypercharge coupling in the Standard Model.
Testing fundamental symmetries using radioactive ion beams at ...
Indian Academy of Sciences (India)
paper we summarize some recent experimental developments at TRIUMF pertaining to fundamental symmetry tests. These tests use the atomic nucleus as a probe to search for physics beyond the Standard Model. Some recent results and future plans are discussed. Keywords. Standard Model; symmetries; radioactive ion ...
Fundamental symmetries and interactions-selected topics
Jungmann, Klaus P.
2015-01-01
In the field of fundamental interactions and symmetries numerous experiments are underway or planned in order to verify the standard model in particle physics, to search for possible extensions to it or to exploit the standard model for extracting most precise values for fundamental constants. We
Spectral asymptotic in the large coupling limit
Bruneau, V
2002-01-01
In this paper, we study a singular perturbation of an eigenvalues problem related to supra-conductor wave guides. Using boundary layer tools we perform a complete asymptotic expansion of the eigenvalues as the conductivity tends to $+\\infty$.
Asymptotic Likelihood Distribution for Correlated & Constrained Systems
Agarwal, Ujjwal
2016-01-01
It describes my work as summer student at CERN. The report discusses the asymptotic distribution of the likelihood ratio for total no. of parameters being h and 2 out of these being are constrained and correlated.
Large Deviations and Asymptotic Methods in Finance
Gatheral, Jim; Gulisashvili, Archil; Jacquier, Antoine; Teichmann, Josef
2015-01-01
Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find th...
One-sided asymptotically mean stationary channels
Simon, Francois
2014-01-01
This paper proposes an analysis of asymptotically mean stationary (AMS) communication channels. A hierarchy based on stability properties (stationarity, quasi-stationarity, recurrence and asymptotically mean stationarity) of channels is identified. Stationary channels are a subclass of quasi-stationary channels which are a subclass of recurrent AMS channels which are a subclass of AMS channels. These classes are proved to be stable under Markovian composition of channels (e.g., the cascade of...
Schwichtenberg, Jakob
2015-01-01
This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations.
DEFF Research Database (Denmark)
Avery, John Scales; Rettrup, Sten; Avery, James Emil
In theoretical physics, theoretical chemistry and engineering, one often wishes to solve partial differential equations subject to a set of boundary conditions. This gives rise to eigenvalue problems of which some solutions may be very difficult to find. For example, the problem of finding...... in such problems can be much reduced by making use of symmetry-adapted basis functions. The conventional method for generating symmetry-adapted basis sets is through the application of group theory, but this can be difficult. This book describes an easier method for generating symmetry-adapted basis sets...
Dynamical symmetries for fermions
International Nuclear Information System (INIS)
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 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
Gauge symmetry from decoupling
Directory of Open Access Journals (Sweden)
C. Wetterich
2017-02-01
Full Text Available Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang–Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.
Wigner's Symmetry Representation Theorem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 10. Wigner's Symmetry Representation Theorem: At the Heart of Quantum Field Theory! Aritra Kr Mukhopadhyay. General Article Volume 19 Issue 10 October 2014 pp 900-916 ...
Dynamical breakdown of chiral symmetry in vectorial theories: QED and QCD
International Nuclear Information System (INIS)
Garcia, J.C.M.
1987-01-01
Using a variational approach for the Effective Potential for composite operators we dicuss the dynamical breakdown of chiral symmetry in two vectorial theories: Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD). We study the energetic aspects of the problem calculating the Effective Potential with the asymptotic nonperturbative solutions of the Schwinger-Dyson equation for the fermion selfenergy. (author) [pt
Frameworks with crystallographic symmetry.
Borcea, Ciprian S; Streinu, Ileana
2014-02-13
Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in Euclidean spaces of arbitrary dimension. It is shown that natural parametrizations provide affine section descriptions for families of frameworks with a specified graph and symmetry. A simple geometrical setting for displacive phase transitions is obtained. Upper bounds are derived for the number of realizations of minimally rigid periodic graphs.
Interactions between constituent single symmetries in multiple symmetry
Treder, M.S.; Vloed, G. van der; Helm, P.A. van der
2011-01-01
As a rule, the discriminability of multiple symmetries from random patterns increases with the number of symmetry axes, but this number does not seem to be the only determinant. In particular, multiple symmetries with orthogonal axes seem better discriminable than multiple symmetries with
Symmetries applied to reactor calculations
International Nuclear Information System (INIS)
Makai, M.
1982-03-01
Three problems of a reactor-calculational model are discussed with the help of symmetry considerations. 1/ A coarse mesh method applicable to any geometry is derived. It is shown that the coarse mesh solution can be constructed from a few standard boundary value problems. 2/ A second stage homogenization method is given based on the Bloch theorem. This ensures the continuity of the current and the flux at the boundary. 3/ The validity of the micro-macro separation is shown for heterogeneous lattices. A formula for the neutron density is derived for cell homogenization. (author)
Directory of Open Access Journals (Sweden)
G. M. N’Guérékata
2018-01-01
Full Text Available The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.
Asymptotic I-Equivalence of Two Number Sequences and Asymptotic I-Regular Matrices
Directory of Open Access Journals (Sweden)
Hafize Gumus
2014-01-01
Full Text Available We study I-equivalence of the two nonnegative sequences x=xk and y=yk. Also we define asymptotic I-regular matrices and obtain conditions for a matrix A=ajk to be asymptotic I-regular.
Symmetries of Mücket-Treder's two-body problem
Mioc, V.
The two-body problem associated to the classical potential field proposed by Mücket and Treder (1977) is considered from the only standpoint of symmetries. The corresponding vector field in Hamiltonian or standard polar coordinates presents nice symmetries that form eight-element symmetric Abelian groups endowed with an idempotent structure. Expressed in Levi-Civita coordinates, the problem exhibits a sixteen-element group of symmetries, also Abelian and presenting an idempotent structure.
On asymptotics and resurgent structures of enumerative Gromov-Witten invariants
Energy Technology Data Exchange (ETDEWEB)
Couso-Santamaria, Ricardo [Lisboa Univ. (Portugal). Inst. Superior Tecnico (IST); Schiappa, Ricardo [Lisboa Univ. (Portugal). Inst. Superior Tecnico (IST); Geneve Univ. (Switzerland). Dept. de Physique Theoretique et Section de Mathematiques; Vaz, Ricardo [Lisboa Univ. (Portugal). Inst. Superior Tecnico (IST); DESY Hamburg (Germany). Theory Group
2016-05-15
Making use of large-order techniques in asymptotics and resurgent analysis, this work addresses the growth of enumerative Gromov-Witten invariants - in their dependence upon genus and degree of the embedded curve - for several different threefold Calabi-Yau toric-varieties. In particular, while the leading asymptotics of these invariants at large genus or at large degree is exponential, at combined large genus and degree it turns out to be factorial. This factorial growth has a resurgent nature, originating via mirror symmetry from the resurgent-transseries description of the B-model free energy. This implies the existence of nonperturbative sectors controlling the asymptotics of the Gromov-Witten invariants, which could themselves have an enumerative-geometry interpretation. The examples addressed include: the resolved conifold; the local surfaces local P{sup 2} and local P{sup 1} x P{sup 1}; the local curves and Hurwitz theory; and the compact quintic. All examples suggest very rich interplays between resurgent asymptotics and enumerative problems in algebraic geometry.
ASYMPTOTICS OF a PARTICLES TRANSPORT PROBLEM
Directory of Open Access Journals (Sweden)
Kuzmina Ludmila Ivanovna
2017-11-01
Full Text Available Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck in the pores. It is assumed that size distributions of the solid particles and the pores overlap. In this case, the main mechanism of particle retention is a size-exclusion: the particles pass freely through the large pores and get stuck at the inlet of the tiny pores that are smaller than the particle diameter. The concentrations of suspended and retained particles satisfy two quasi-linear differential equations of the first order. To solve the filtration problem, methods of nonlinear asymptotic analysis are used. Results: in a mathematical model of filtration of suspensions, which takes into account the dependence of the porosity and permeability of the porous medium on concentration of retained particles, the boundary between two phases is moving with variable velocity. The asymptotic solution to the problem is constructed for a small filtration coefficient. The theorem of existence of the asymptotics is proved. Analytical expressions for the principal asymptotic terms are presented for the case of linear coefficients and initial conditions. The asymptotics of the boundary of two phases is given in explicit form. Conclusions: the filtration problem under study can be solved analytically.
Gauged discrete symmetries and proton stability
International Nuclear Information System (INIS)
Mohapatra, Rabindra N.; Ratz, Michael
2007-01-01
We discuss the results of a search for anomaly-free Abelian Z N discrete symmetries that lead to automatic R-parity conservation and prevent dangerous higher-dimensional proton decay operators in simple extensions of minimal supersymmetric extension of the standard model based on the left-right symmetric group, the Pati-Salam group and SO(10). We require that the superpotential for the models have enough structures to be able to give correct symmetry breaking to minimal supersymmetric extension of the standard model and potentially realistic fermion masses. We find viable models in each of the extensions, and for all the cases, anomaly freedom of the discrete symmetry restricts the number of generations
International Nuclear Information System (INIS)
Kabulov, A.B.
2003-01-01
Atomic nuclei display different kinds of collective motion. The well known example - is the collective model arising from valent nucleons motion. The other a special kind of collective motion is cluster mode. If a collective model has quadrupole character, then cluster one has dipole character. In the boson formalism this model is describing by dynamic symmetry U(6) direct X U(4). The common Hamiltonian symmetrical to U(6) direct X U(4) group has a form H=H d +H p +V pd . In the paper the asymptotical wave function for dipole states connected with (N-1) bosons of s- and d-types is presented. In this case the problem for Hamiltonian eigenvalues is solving by analytical way. With use Elliot method and wave functions asymptotical form the operators for matrix elements of E2-, E1-, M1-transitions are cited
Aubrun, Guillaume
2017-01-01
The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twenty-first century, and quantum information theory (QIT) provides the mathematical framework for that quest. Over the last dozen or so years, it has become clear that quantum information theory is closely linked to geometric functional analysis (Banach space theory, operator spaces, high-dimensional probability), a field also known as asymptotic geometric analysis (AGA). In a nutshell, asymptotic geometric analysis investigates quantitative properties of convex sets, or other geometric structures, and their approximate symmetries as the dimension becomes large. This makes it especially relevant to quantum theory, where systems consisting of just a few particles naturally lead to models whose dimension is in the thousands, or even in the billions. Alice and Bob Meet Banach is aimed at multiple audiences connected through their interest in the interface of QIT and AGA: at quantum information resea...
Strings from massive higher spins: the asymptotic uniqueness of the Veneziano amplitude
Caron-Huot, Simon; Komargodski, Zohar; Sever, Amit; Zhiboedov, Alexander
2017-10-01
We consider weakly coupled theories of massive higher-spin particles. This class of models includes, for instance, tree-level String Theory and Large-N Yang-Mills theory. The S-matrix in such theories is a meromorphic function obeying unitarity and crossing symmetry. We discuss the (unphysical) regime s, t ≫ 1, in which we expect the amplitude to be universal and exponentially large. We develop methods to study this regime and show that the amplitude necessarily coincides with the Veneziano amplitude there. In particular, this implies that the leading Regge trajectory, j( t), is asymptotically linear in Yang-Mills theory. Further, our analysis shows that any such theory of higherspin particles has stringy excitations and infinitely many asymptotically parallel subleading trajectories. More generally, we argue that, under some assumptions, any theory with at least one higher-spin particle must have strings.
The optimal homotopy asymptotic method engineering applications
Marinca, Vasile
2015-01-01
This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011, and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five application...
Quantum Space-Time Deformed Symmetries Versus Broken Symmetries
Amelino-Camelia, G
2002-01-01
Several recent studies have concerned the faith of classical symmetries in quantum space-time. In particular, it appears likely that quantum (discretized, noncommutative,...) versions of Minkowski space-time would not enjoy the classical Lorentz symmetries. I compare two interesting cases: the case in which the classical symmetries are "broken", i.e. at the quantum level some classical symmetries are lost, and the case in which the classical symmetries are "deformed", i.e. the quantum space-time has as many symmetries as its classical counterpart but the nature of these symmetries is affected by the space-time quantization procedure. While some general features, such as the emergence of deformed dispersion relations, characterize both the symmetry-breaking case and the symmetry-deformation case, the two scenarios are also characterized by sharp differences, even concerning the nature of the new effects predicted. I illustrate this point within an illustrative calculation concerning the role of space-time symm...
On the asymptotics of dimers on tori
Kenyon, Richard W.; Sun, Nike; Wilson, David B.
2013-01-01
We study asymptotics of the dimer model on large toric graphs. Let $\\mathbb L$ be a weighted $\\mathbb{Z}^2$-periodic planar graph, and let $\\mathbb{Z}^2 E$ be a large-index sublattice of $\\mathbb{Z}^2$. For $\\mathbb L$ bipartite we show that the dimer partition function on the quotient $\\mathbb{L}/(\\mathbb{Z}^2 E)$ has the asymptotic expansion $\\exp[A f_0 + \\text{fsc} + o(1)]$, where $A$ is the area of $\\mathbb{L}/(\\mathbb{Z}^2 E)$, $f_0$ is the free energy density in the bulk, and $\\text{fsc...
Asymptotic stability of a catalyst particle
DEFF Research Database (Denmark)
Wedel, Stig; Michelsen, Michael L.; Villadsen, John
1977-01-01
The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0. These a......The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0...
Schwichtenberg, Jakob
2018-01-01
This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations. .
Energy Technology Data Exchange (ETDEWEB)
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.
Weiss, Asia; Whiteley, Walter
2014-01-01
This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures, and to explore the interaction of geometry, algebra, and combinatorics. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. The volume will also be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and gradu...
Symmetries for SM Alignment in multi-Higgs Doublet Models
Pilaftsis, Apostolos
2016-01-01
We derive the complete set of maximal symmetries for Standard Model (SM) alignment that may occur in the tree-level scalar potential of multi-Higgs Doublet Models, with $n > 2$ Higgs doublets. Our results generalize the symmetries of SM alignment, without decoupling of large mass scales or fine-tuning, previously obtained in the context of two-Higgs Doublet Models.
The Search for Symmetries in the Genetic Code:
Antoneli, Fernando; Forger, Michael; Hornos, José Eduardo M.
We give a full classification of the possible schemes for obtaining the distribution of multiplets observed in the standard genetic code by symmetry breaking in the context of finite groups, based on an extended notion of partial symmetry breaking that incorporates the intuitive idea of "freezing" first proposed by Francis Crick, which is given a precise mathematical meaning.
Electroweak symmetry breaking and Higgs physics: basic concepts
International Nuclear Information System (INIS)
Gomez-Bock, M; Mondragon, M; Muehlleitner, M; Noriega-Papaqui, R; Pedraza, I; Spira, M; Zerwas, P M
2005-01-01
We present an introduction to the basic concepts of electroweak symmetry breaking and Higgs physics within the Standard Model and its sypersymmetric extensions. A brief overview will also be given on alternative mechanisms of symmetry breaking. In addition to the theoretical basis, the present experimental status of Higgs physics and implications for future experiments at the LHC and e + e - linear colliders are discussed
Measures with symmetry properties
Schindler, Werner
2003-01-01
Symmetries and invariance principles play an important role in various branches of mathematics. This book deals with measures having weak symmetry properties. Even mild conditions ensure that all invariant Borel measures on a second countable locally compact space can be expressed as images of specific product measures under a fixed mapping. The results derived in this book are interesting for their own and, moreover, a number of carefully investigated examples underline and illustrate their usefulness and applicability for integration problems, stochastic simulations and statistical applications.
International Nuclear Information System (INIS)
Chimento, Luis P.
2002-01-01
We find the group of symmetry transformations under which the Einstein equations for the spatially flat Friedmann-Robertson-Walker universe are form invariant. They relate the energy density and the pressure of the fluid to the expansion rate. We show that inflation can be obtained from nonaccelerated scenarios by a symmetry transformation. We derive the transformation rule for the spectrum and spectral index of the curvature perturbations. Finally, the group is extended to investigate inflation in the anisotropic Bianchi type-I spacetime and the brane-world cosmology
Symmetry, structure, and spacetime
Rickles, Dean
2007-01-01
In this book Rickles considers several interpretative difficulties raised by gauge-type symmetries (those that correspond to no change in physical state). The ubiquity of such symmetries in modern physics renders them an urgent topic in philosophy of physics. Rickles focuses on spacetime physics, and in particular classical and quantum general relativity. Here the problems posed are at their most pathological, involving the apparent disappearance of spacetime! Rickles argues that both traditional ontological positions should be replaced by a structuralist account according to which relational
Maintaining symmetry of simulated likelihood functions
DEFF Research Database (Denmark)
Andersen, Laura Mørch
This paper suggests solutions to two different types of simulation errors related to Quasi-Monte Carlo integration. Likelihood functions which depend on standard deviations of mixed parameters are symmetric in nature. This paper shows that antithetic draws preserve this symmetry and thereby...
Electroweak symmetry breaking beyond the Standard Model
Indian Academy of Sciences (India)
. ... Figure 1. Cancellation of quadratic divergence to scalar mass-square between fermion and boson loops. (3) The SM is plagued by the hierarchy problem. ..... action should be un-suppressed, where gSM is a gauge or Yukawa coupling.
Electroweak symmetry breaking beyond the Standard Model
Indian Academy of Sciences (India)
potential: V = −. (gSM)4. 16π2 f 2 ln. ( 2 f 2. ) (H† H) + g2. SM(H† H)2 ,. (11). i.e., the bilinear term should have a one-loop suppression but, crucially, the quartic inter- action should be un-suppressed, where gSM is a gauge or Yukawa coupling. If both quadratic and quartic terms are suppressed, one cannot simultaneously ...
On iterative procedures of asymptotic inference
K.O. Dzhaparidze (Kacha)
1983-01-01
textabstractAbstract An informal discussion is given on performing an unconstrained maximization or solving non‐linear equations of statistics by iterative methods with the quadratic termination property. It is shown that if a miximized function, e.g. likelihood, is asymptotically quadratic, then
On asymptotic flatness and Lorentz charges
Compère, G.; Dehouck, F.; Virmani, A.
2011-01-01
In this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric divergence-free tensors that we construct from the equations
Nonsymmetric gravity has unacceptable global asymptotics
Damour, T.; Deser, S.; McCarthy, J.
1993-12-01
We analyze the radiative aspects of nonsymmetric gravity theory to show that, in contrast to General Relativity, its nonstationary solutions cannot simultaneously exhibit acceptable asymptotic behavior at both future and past null infinity: good behavior at future null infinity is only possible through the use of advanced potentials with concomitant unphysical behavior at past null infinity.
Large degree asymptotics of generalized Bessel polynomials
J.L. López; N.M. Temme (Nico)
2011-01-01
textabstractAsymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the
Asymptotic analysis of the Forward Search
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Bent
The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is made...
Asymptotic theory of integrated conditional moment tests
Bierens, H.J.; Ploberger, W.
1995-01-01
In this paper we derive the asymptotic distribution of the test statistic of a generalized version of the integrated conditional moment (ICM) test of Bierens (1982, 1984), under a class of Vn-local alternatives, where n is the sample size. The generalized version involved includes neural network
Dual Feynman rules - topological asymptotic freedom
International Nuclear Information System (INIS)
Chew, G.F.; Levinson, M.; California Univ., Berkeley
1983-01-01
Feynman-graph rules are formulated for the strong - interaction components of the topological expansion - defined as those graphs all of whose vertices are zero - entropy connected parts. These rules imply a ''topological asymptotic freedom'' and admit a corresponding perturbative evaluation where the zeroth order exhibits topological supersymmetry. (orig.)
Introduction to symmetry breaking and spin
International Nuclear Information System (INIS)
Ng, J.N.
1992-05-01
These lectures form an elementary introduction to the physics of symmetry breaking and the role polarization experiments play in the study of gauge symmetry breaking. Included here is an introduction to testing the electroweak sector of the standard model to one-loop and the use of oblique corrections as a probe of new physics. The second part of the lectures consists of an introduction to multiple Higgs models as sources of spontaneous CP violation. A brief discussion of using spin measurements in meson decays to study these sources of CP violation is also included. (author)
Interactions between constituent single symmetries in multiple symmetry.
Treder, Matthias Sebastian; van der Vloed, Gert; van der Helm, Peter A
2011-07-01
As a rule, the discriminability of multiple symmetries from random patterns increases with the number of symmetry axes, but this number does not seem to be the only determinant. In particular, multiple symmetries with orthogonal axes seem better discriminable than multiple symmetries with nonorthogonal axes. In six experiments on imperfect two-fold symmetry, we investigated whether this is due to extra structure in the form of so-called correlation rectangles, which arise only in the case of orthogonal axes, or to the relative orientation of the axes as such. The results suggest that correlation rectangles are not perceptually relevant and that the percept of a multiple symmetry results from an orientation-dependent interaction between the constituent single symmetries. The results can be accounted for by a model involving the analysis of symmetry at all orientations, smoothing (averaging over neighboring orientations), and extraction of peaks.
Molecular symmetry and spectroscopy
Bunker, Philip; Jensen, Per
2006-01-01
The first edition, by P.R. Bunker, published in 1979, remains the sole textbook that explains the use of the molecular symmetry group in understanding high resolution molecular spectra. Since 1979 there has been considerable progress in the field and a second edition is required; the original author has been joined in its writing by Per Jensen. The Material of the first edition has been reorganized and much has been added. The molecular symmetry group is now introduced early on, and the explanation of how to determine nuclear spin statistical weights has been consolidated in one chapter, after groups, symmetry groups, character tables and the Hamiltonian have been introduced. A description of the symmetry in the three-dimensional rotation group K(spatial), irreducible spherical tensor operators, and vector coupling coefficients is now included. The chapters on energy levels and selection rules contain a great deal of material that was not in the first edition (much of it was undiscovered in 1979), concerning ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 10. Groups and Symmetry: A Guide to Discovering Mathematics. Geetha Venkataraman. Book Review Volume 4 Issue 10 October 1999 pp 91-92. Fulltext. Click here to view fulltext PDF. Permanent link:
Symmetries in fundamental physics
Sundermeyer, Kurt
2014-01-01
Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P.Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also underst...
Introduction to Chiral Symmetry
Energy Technology Data Exchange (ETDEWEB)
Koch, Volker [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2017-05-09
These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. We will also discuss some effective chiral models such as the linear and nonlinear sigma model as well as the essential ideas of chiral perturbation theory. We will present some applications to the physics of ultrarelativistic heavy ion collisionsd.
Charged fluids with symmetries
Indian Academy of Sciences (India)
conformal Killing vector on the electromagnetic field tensor and the role of Maxwell's equations. 2. Conformal symmetries. Manifolds with structure may admit groups of transformations which preserve this struc- ture. A conformal motion preserves the metric up to a factor and maps null geodesics conformally. A conformal ...
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)
Symmetries in fundamental physics
Sundermeyer, Kurt
2014-01-01
Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P. Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also unders...
Jinzenji, Masao
2018-01-01
This book furnishes a brief introduction to classical mirror symmetry, a term that denotes the process of computing Gromov–Witten invariants of a Calabi–Yau threefold by using the Picard–Fuchs differential equation of period integrals of its mirror Calabi–Yau threefold. The book concentrates on the best-known example, the quintic hypersurface in 4-dimensional projective space, and its mirror manifold. First, there is a brief review of the process of discovery of mirror symmetry and the striking result proposed in the celebrated paper by Candelas and his collaborators. Next, some elementary results of complex manifolds and Chern classes needed for study of mirror symmetry are explained. Then the topological sigma models, the A-model and the B-model, are introduced. The classical mirror symmetry hypothesis is explained as the equivalence between the correlation function of the A-model of a quintic hyper-surface and that of the B-model of its mirror manifold. On the B-model side, the process of construct...
SYMMETRY OF COMPOSITE CRYSTALS
VANSMAALEN, S
1991-01-01
Composite crystals are crystals that consist of two or more subsystems, in first approximation each one having its own three-dimensional periodicity. The symmetry of these subsystems is then characterized by an ordinary space group. Due to their mutual interaction the true structure consists of a
Simulation of black hole collisions in asymptotically Anti-de Sitter spacetimes.
Bantilan, Hans; Romatschke, Paul
2015-02-27
We present results from the evolution of spacetimes that describe the merger of asymptotically global anti-de Sitter black holes in 5D with an SO(3) symmetry. Prompt scalar field collapse provides us with a mechanism for producing distinct trapped regions on the initial slice, associated with black holes initially at rest. We evolve these black holes towards a merger, and follow the subsequent ring down. The boundary stress tensor of the dual conformal field theory is conformally related to a stress tensor in Minkowski space that inherits an axial symmetry from the bulk SO(3). We compare this boundary stress tensor to its hydrodynamic counterpart with viscous corrections of up to second order, and compare the conformally related stress tensor to ideal hydrodynamic simulations in Minkowski space, initialized at various time slices of the boundary data. Our findings reveal far-from-hydrodynamic behavior at early times, with a transition to ideal hydrodynamics at late times.
Particle Physics and Symmetries in Noncommutative Geometry
Devastato, Agostino
2015-01-01
In the context of the spectral action and the noncommutative geometry approach to the physical fundamental interactions, we extend the standard model of particle physics introducing a model based on a larger symmetry in the attempt to obtain a new scalar field, bringing the Higgs mass in the vicinity of 126~GeV and to cure the instability problem of the electroweak vacuum. We also investigate whether inclusion of dimension six terms in the Standard Model Lagrangian or gravitational contributi...
Consequences of an Abelian family symmetry
International Nuclear Information System (INIS)
Ramond, P.
1996-01-01
The addition of an Abelian family symmetry to the Minimal Super-symmetric Standard Model reproduces the observed hierarchies of quark and lepton masses and quark mixing angles, only if it is anomalous. Green-Schwarz compensation of its anomalies requires the electroweak mixing angle to be sin 2 θ ω = 3/8 at the string scale, without any assumed GUT structure, suggesting a superstring origin for the standard model. The analysis is extended to neutrino masses and the lepton mixing matrix
Chiral Symmetry, Heavy Quark Symmetry and Bound States
Yoshida, Yuhsuke
1995-01-01
I investigate the bound state problems of lowest-lying mesons and heavy mesons. Chiral symmetry is essential when one consider lowest-lying mesons. Heavy quark symmetry plays an central role in considering the semi-leptonic form factors of heavy mesons. Various properties based on the symmetries are revealed using Bethe-Salpeter equations.
Precise study of asymptotic physics with subradiant ultracold molecules
McGuyer, B. H.; McDonald, M.; Iwata, G. Z.; Tarallo, M. G.; Skomorowski, W.; Moszynski, R.; Zelevinsky, T.
2015-01-01
Weakly bound molecules have physical properties without atomic analogues, even as the bond length approaches dissociation. For instance, the internal symmetries of homonuclear diatomic molecules result in the formation of two-body superradiant and subradiant excited states. Whereas superradiance has been demonstrated in a variety of systems, subradiance is more elusive owing to the inherently weak interaction with the environment. Here we characterize the properties of deeply subradiant molecular states with intrinsic quality factors exceeding 1013 via precise optical spectroscopy with the longest molecule-light coherent interaction times to date. We find that two competing effects limit the lifetimes of the subradiant molecules, with different asymptotic behaviours. The first is radiative decay via weak magnetic-dipole and electric-quadrupole interactions. We prove that its rate increases quadratically with the bond length, confirming quantum mechanical predictions. The second is non-radiative decay through weak gyroscopic predissociation, with a rate proportional to the vibrational mode spacing and sensitive to short-range physics. This work bridges the gap between atomic and molecular metrology based on lattice-clock techniques, enhancing our understanding of long-range interatomic interactions.
Avoidance of singularities in asymptotically safe Quantum Einstein Gravity
Energy Technology Data Exchange (ETDEWEB)
Kofinas, Georgios [Research Group of Geometry, Dynamical Systems and Cosmology,Department of Information and Communication Systems Engineering,University of the Aegean, Karlovassi 83200, Samos (Greece); Zarikas, Vasilios [Department of Electrical Engineering, Theory Division, ATEI of Central Greece,35100 Lamia (Greece); Department of Physics, Aristotle University of Thessaloniki,54124 Thessaloniki (Greece)
2015-10-30
New general spherically symmetric solutions have been derived with a cosmological “constant” Λ as a source. This Λ term is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed point. The importance of these solutions comes from the fact that they may describe the near to the centre region of black hole spacetimes as this is modified by the Renormalization Group scaling behaviour of the fields. The consistent set of field equations which respect the Bianchi identities is derived and solved. One of the solutions (with conventional sign of temporal-radial metric components) is timelike geodesically complete, and although there is still a curvature divergent origin, this is never approachable by an infalling massive particle which is reflected at a finite distance due to the repulsive origin. Another family of solutions (of both signatures) range from a finite radius outwards, they cannot be extended to the centre of spherical symmetry, and the curvature invariants are finite at the minimum radius.
Operational symmetries basic operations in physics
Saller, Heinrich
2017-01-01
This book describes the endeavour to relate the particle spectrum with representations of operational electroweak spacetime, in analogy to the atomic spectrum as characterizing representations of hyperbolic space. The spectrum of hyperbolic position space explains the properties of the nonrelativistic atoms; the spectrum of electroweak spacetime is hoped to explain those of the basic interactions and elementary particles. In this book, the theory of operational symmetries is developed from the numbers, from Plato’s and Kepler’s symmetries over the simple Lie groups to their applications in nonrelativistic, special relativistic and general relativistic quantum theories with the atomic spectrum for hyperbolic position and, in first attempts, the particle spectrum for electroweak spacetime. The standard model of elementary particles and interactions is characterized by a symmetry group. In general, as initiated by Weyl and stressed by Heisenberg, quantum theory can be built as a theory of operation groups an...
On Symmetries in Optimal Control
Schaft, A.J. van der
1986-01-01
We discuss the use of symmetries in solving optimal control problems. In particular a procedure for obtaining symmetries is given which can be performed before the actual calculation of the optimal control and optimal Hamiltonian.
Dual symmetry in gauge theories
International Nuclear Information System (INIS)
Koshkarov, A.L.
1997-01-01
Continuous dual symmetry in electrodynamics, Yang-Mills theory and gravitation is investigated. Dual invariant which leads to badly nonlinear motion equations is chosen as a Lagrangian of the pure classical dual nonlinear electrodynamics. In a natural manner some dual angle which is determined by the electromagnetic strengths at the point of the time-space appears in the model. Motion equations may well be interpreted as the equations of the standard Maxwell theory with source. Alternative interpretation is the quasi-Maxwell linear theory with magnetic charge. Analogous approach is possible in the Yang-Mills theory. In this case the dual-invariant non-Abelian theory motion equations possess the same instanton solutions as the conventional Yang-Mills equations have. An Abelian two-parameter dual group is found to exist in gravitation. Irreducible representations have been obtained: the curvature tensor was expanded into the sum of twice anti-self-dual and self-dual parts. Gravitational instantons are defined as (real )solutions to the usual duality equations. Central symmetry solutions to these equations are obtained. The twice anti-self-dual part of the curvature tensor may be used for introduction of new gravitational equations generalizing Einstein''s equations. However, the theory obtained reduces to the conformal-flat Nordstroem theory
Discrete symmetries with neutral mesons
Bernabéu, José
2018-01-01
Symmetries, and Symmetry Breakings, in the Laws of Physics play a crucial role in Fundamental Science. Parity and Charge Conjugation Violations prompted the consideration of Chiral Fields in the construction of the Standard Model, whereas CP-Violation needed at least three families of Quarks leading to Flavour Physics. In this Lecture I discuss the Conceptual Basis and the present experimental results for a Direct Evidence of Separate Reversal-in-Time T, CP and CPT Genuine Asymmetries in Decaying Particles like Neutral Meson Transitions, using Quantum Entanglement and the Decay as a Filtering Measurement. The eight transitions associated to the Flavour-CP eigenstate decay products of entangled neutral mesons have demonstrated with impressive significance a separate evidence of TRV and CPV in Bd-physics, whereas a CPTV asymmetry shows a 2σ effect interpreted as an upper limit. Novel CPTV observables are discussed for K physics at KLOE-2, including the difference between the semileptonic asymmetries from KL and KS, the ratios of double decay rate Intensities to Flavour-CP eigenstate decay products and the ω-effect. Their observation would lead to a change of paradigm beyond Quantum Field Theory, however there is nothing in Quantum Mechanics forbidding CPTV.
Symmetries, dimensional reduction, and topological quantum order
Nussinov, Zohar; Ortiz, Gerardo
2009-12-01
We prove sufficient conditions for Topological Quantum Order at zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries, thus providing a unifying framework based on a symmetry principle. All known examples of Topological Quantum Order display Gauge-Like Symmetries. Other systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges) and, most importantly, show the insufficiency of the energy spectrum, (recently defined) entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. Duality mappings illustrate that not withstanding the existence of spectral gaps, thermal fluctuations may impose restrictions on suggested topological quantum computing schemes. Our results allow us to go beyond standard topological field theories and engineer new systems with Topological Quantum Order.
Asymptotic formulas for sequence factorial of arithmetic progression
Aṣiru, Muniru A.
2014-08-01
This note provides asymptotic formulas for approximating the sequence factorial of members of a finite arithmetic progression by using Stirling, Burnside and other more accurate asymptotic formulas for large factorials that have appeared in the literature.
Asymptotic expansion of the wavelet transform with error term
Pathak, R S; Pathak, Ashish
2014-01-01
UsingWong's technique asymptotic expansion for the wavelet transform is derived and thereby asymptotic expansions for Morlet wavelet transform, Mexican Hat wavelet transform and Haar wavelet transform are obtained.
Symmetry and topology in evolution
International Nuclear Information System (INIS)
Lukacs, B.; Berczi, S.; Molnar, I.; Paal, G.
1991-10-01
This volume contains papers of an interdisciplinary symposium on evolution. The aim of this symposium, held in Budapest, Hungary, 28-29 May 1991, was to clear the role of symmetry and topology at different levels of the evolutionary processes. 21 papers were presented, their topics included evolution of the Universe, symmetry of elementary particles, asymmetry of the Earth, symmetry and asymmetry of biomolecules, symmetry and topology of lining objects, human asymmetry etc. (R.P.)
Applications of Classical Scaling Symmetry
Bludman, Sidney
2011-01-01
Any symmetry reduces a second-order differential equation to a first-order equation: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion (exemplified by scale-invariant hydrostatics), yield first-order {\\em non-conservation laws} between invariants. We obtain these conservation laws by extending Noether's Theorem to non-variational symmetries, and present a variational formulation of spherical a...
Quantum symmetries in particle interactions
International Nuclear Information System (INIS)
Shirkov, D.V.
1983-01-01
The concept of a quantum symmetry is introduced as a symmetry in the formulation of which quantum representations and specific quantum notions are used essentially. Three quantum symmetry principles are discussed: the principle of renormalizability (possibly super-renormalizability), the principle of local gauge symmetry, and the principle of supersymmetry. It is shown that these principles play a deterministic role in the development of quantum field theory. Historically their use has led to ever stronger restrictions on the interaction mechanism of quantum fields
Exploring central opacity and asymptotic scenarios in elastic hadron scattering
Fagundes, D. A.; Menon, M. J.; Silva, P. V. R. G.
2016-02-01
In the absence of a global description of the experimental data on elastic and soft diffractive scattering from the first principles of QCD, model-independent analyses may provide useful phenomenological insights for the development of the theory in the soft sector. With that in mind, we present an empirical study on the energy dependence of the ratio X between the elastic and total cross sections; a quantity related to the evolution of the hadronic central opacity. The dataset comprises all the experimental information available on proton-proton and antiproton-proton scattering in the c.m. energy interval 5 GeV-8 TeV. Generalizing previous works, we discuss four model-independent analytical parameterizations for X, consisting of sigmoid functions composed with elementary functions of the energy and three distinct asymptotic scenarios: either the standard black disk limit or scenarios above or below that limit. Our two main conclusions are the following: (1) although consistent with the experimental data, the black disk does not represent an unique solution; (2) the data reductions favor a semi-transparent scenario, with asymptotic average value for the ratio X bar = 0.30 ± 0.12. In this case, within the uncertainty, the asymptotic regime may already be reached around 1000 TeV. We present a comparative study of the two scenarios, including predictions for the inelastic channel (diffraction dissociation) and the ratio associated with the total cross-section and the elastic slope. Details on the selection of our empirical ansatz for X and physical aspects related to a change of curvature in this quantity at 80-100 GeV, indicating the beginning of a saturation effect, are also presented and discussed.
Emergence of Symmetries from Entanglement
CERN. Geneva
2016-01-01
Maximal Entanglement appears to be a key ingredient for the emergence of symmetries. We first illustrate this phenomenon using two examples: the emergence of conformal symmetry in condensed matter systems and the relation of tensor networks to holography. We further present a Principle of Maximal Entanglement that seems to dictate to a large extend the structure of gauge symmetry.
Group analysis and renormgroup symmetries
International Nuclear Information System (INIS)
Kovalev, V.F.; Pustovalov, V.V.; Shirkov, D.V.
1996-01-01
An original regular approach to constructing special type symmetries for boundary-value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries based on modern group analysis are described. An application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model. 35 refs
Broken symmetries in field theory
Kok, Mark Okker de
2008-01-01
The thesis discusses the role of symmetries in Quantum Field Theory. Quantum Field Theory is the mathematical framework to describe the physics of elementary particles. A symmetry here means a transformation under which the model at hand is invariant. Three types of symmetry are distinguished: 1.
Partial symmetries in nuclear spectroscopy
International Nuclear Information System (INIS)
Leviatan, A.
1996-01-01
The notions of exact, dynamical and partial symmetries are discussed in relation to nuclear spectroscopy. Explicit forms of Hamiltonians with partial SU(3) symmetry are presented in the framework of the interacting boson model of nuclei. An analysis of the resulting spectrum and electromagnetic transitions demonstrates the relevance of such partial symmetry to the spectroscopy of axially deformed nuclei. (Author)
Criteria for exponential asymptotic stability in the large of ...
African Journals Online (AJOL)
The purpose of this study is to provide necessary and sufficient conditions for exponential asymptotic stability in the large and uniform asymptotic stability of perturbations of linear systems with unbounded delays. A strong relationship is established between the two types of asymptotic stability. It is found that if the ...
A broken symmetry ontology: Quantum mechanics as a broken symmetry
International Nuclear Information System (INIS)
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
Dark discrete gauge symmetries
International Nuclear Information System (INIS)
Batell, Brian
2011-01-01
We investigate scenarios in which dark matter is stabilized by an Abelian Z N discrete gauge symmetry. Models are surveyed according to symmetries and matter content. Multicomponent dark matter arises when N is not prime and Z N contains one or more subgroups. The dark sector interacts with the visible sector through the renormalizable kinetic mixing and Higgs portal operators, and we highlight the basic phenomenology in these scenarios. In particular, multiple species of dark matter can lead to an unconventional nuclear recoil spectrum in direct detection experiments, while the presence of new light states in the dark sector can dramatically affect the decays of the Higgs at the Tevatron and LHC, thus providing a window into the gauge origin of the stability of dark matter.
Strong Electroweak Symmetry Breaking
Grinstein, Benjamin
2011-01-01
Models of spontaneous breaking of electroweak symmetry by a strong interaction do not have fine tuning/hierarchy problem. They are conceptually elegant and use the only mechanism of spontaneous breaking of a gauge symmetry that is known to occur in nature. The simplest model, minimal technicolor with extended technicolor interactions, is appealing because one can calculate by scaling up from QCD. But it is ruled out on many counts: inappropriately low quark and lepton masses (or excessive FCNC), bad electroweak data fits, light scalar and vector states, etc. However, nature may not choose the minimal model and then we are stuck: except possibly through lattice simulations, we are unable to compute and test the models. In the LHC era it therefore makes sense to abandon specific models (of strong EW breaking) and concentrate on generic features that may indicate discovery. The Technicolor Straw Man is not a model but a parametrized search strategy inspired by a remarkable generic feature of walking technicolor,...
Leadership, power and symmetry
DEFF Research Database (Denmark)
Spaten, Ole Michael
2016-01-01
Research publications concerning managers who coach their own employees are barely visible despite its wide- spread use in enterprises (McCarthy & Milner, 2013; Gregory & Levy, 2011; Crabb, 2011). This article focuses on leadership, power and moments of symmetry in the coaching relationship...... regarding managers coaching their employees and it is asked; what contributes to coaching of high quality when one reflects on the power aspect as being immanent? Fourteen middle managers coached five of their employees, and all members of each party wrote down cues and experiences immediately after each...... session. Thereafter we executed qualitative interviews with both managers and employees. Subsequently, a Thematic Analysis resulted in several themes, including power and moments of symmetry in the coaching relationship. One main conclusion is that the most fruitful coaching was obtained when the coachee...
de Boer, Jan; Freivogel, Ben; Kabir, Laurens; Lokhande, Sagar F.
2017-07-01
In the AdS/CFT correspondence, bulk information appears to be encoded in the CFT in a redundant way. A local bulk field corresponds to many different non-local CFT operators (precursors). We recast this ambiguity in the language of BRST symmetry, and propose that in the large N limit, the difference between two precursors is a BRST exact and ghost-free term. This definition of precursor ambiguities has the advantage that it generalizes to any gauge theory. Using the BRST formalism and working in a simple model with global symmetries, we re-derive a precursor ambiguity appearing in earlier work. Finally, we show within this model that the obtained ambiguity has the right number of parameters to explain the freedom to localize precursors within different spatial regions of the boundary order by order in the large N expansion.
International Nuclear Information System (INIS)
Bunakov, V.E.; Ivanov, I.B.
1999-01-01
Connections between the symmetries of Hamiltonian systems in classical and quantum mechanics, on one hand, and their regularity or chaoticity, on the other hand, are considered. The quantum-chaoticity criterion that was proposed previously and which was borrowed from the theory of compound-nucleus resonances is used to analyze the quantum diamagnetic Kepler problem - that is, the motion of a spinless charged particle in a Coulomb and a uniform magnetic field
International Nuclear Information System (INIS)
Herrero, O F
2010-01-01
Music and Physics are very close because of the symmetry that appears in music. A periodic wave is what music really is, and there is a field of Physics devoted to waves researching. The different musical scales are the base of all kind of music. This article tries to show how this musical scales are made, how the consonance is the base of many of them and how symmetric they are.
Symmetry and quantum mechanics
Corry, Scott
2016-01-01
This book offers an introduction to quantum mechanics for professionals, students, and others in the field of mathematics who have a minimal background in physics with an understanding of linear algebra and group theory. It covers such topics as Lie groups, algebras and their representations, and analysis (Hilbert space, distributions, the spectral Theorem, and the Stone-Von Neumann Theorem). The book emphasizes the role of symmetry and is useful to physicists as it provides a mathematical introduction to the topic.
Energy Technology Data Exchange (ETDEWEB)
Herrero, O F, E-mail: o.f.herrero@hotmail.co [Conservatorio Superior de Musica ' Eduardo Martinez Torner' Corrada del Obispo s/n 33003 - Oviedo - Asturias (Spain)
2010-06-01
Music and Physics are very close because of the symmetry that appears in music. A periodic wave is what music really is, and there is a field of Physics devoted to waves researching. The different musical scales are the base of all kind of music. This article tries to show how this musical scales are made, how the consonance is the base of many of them and how symmetric they are.
On asymptotic flatness and Lorentz charges
Energy Technology Data Exchange (ETDEWEB)
Compere, Geoffrey [KdV Institute for Mathematics, Universiteit van Amsterdam (Netherlands); Dehouck, Francois; Virmani, Amitabh, E-mail: gcompere@uva.nl, E-mail: fdehouck@ulb.ac.be, E-mail: avirmani@ulb.ac.be [Physique Theorique et Mathematique, Universite Libre de Bruxelles, Bruxelles (Belgium)
2011-07-21
In this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric divergence-free tensors that we construct from the equations of motion. Second, we show that the integrability of Einstein's equations in the asymptotic expansion is sufficient to establish the equivalence between counter-term charges defined from the variational principle and charges defined by Ashtekar and Hansen. These results clarify earlier constructions of conserved charges in the hyperboloid representation of spatial infinity. In showing this, the parity condition on the mass aspect is not needed. Along the way in establishing these results, we prove two lemmas on tensor fields on three-dimensional de Sitter spacetime stated by Ashtekar-Hansen and Beig-Schmidt and state and prove three additional lemmas.
Asymptotic mass degeneracies in conformal field theories
International Nuclear Information System (INIS)
Kani, I.; Vafa, C.
1990-01-01
By applying a method of Hardy and Ramanujan to characters of rational conformal field theories, we find an asymptotic expansion for degeneracy of states in the limit of large mass which is exact for strings propagating in more than two uncompactified space-time dimensions. Moreover we explore how the rationality of the conformal theory is reflected in the degeneracy of states. We also consider the one loop partition function for strings, restricted to physical states, for arbitrary (irrational) conformal theories, and obtain an asymptotic expansion for it in the limit that the torus degenerates. This expansion depends only on the spectrum of (physical and unphysical) relevant operators in the theory. We see how rationality is consistent with the smoothness of mass degeneracies as a function of moduli. (orig.)
Asymptotic Behavior of Certain Integrodifferential Equations
Directory of Open Access Journals (Sweden)
Said Grace
2016-01-01
Full Text Available This paper deals with asymptotic behavior of nonoscillatory solutions of certain forced integrodifferential equations of the form: atx′t′=e(t+∫ct(t-sα-1k(t,sf(s,x(sds, c>1, 0<α<1. From the obtained results, we derive a technique which can be applied to some related integrodifferential as well as integral equations.
Asymptotic Limits in Macroscopic Plasma Models
Jüngel, Ansgar
2000-01-01
A model hierarchy of macroscopic equations for plasmas consisting of electrons and ions is presented. The model equations are derived from the transient Euler-Poisson system in the zero-relaxation-time, zero-electron-mass and quasineutral limits. These asymptotic limits are performed using entropy estimates and compactness arguments. The resulting limits equations are Euler systems with a nonlinear Poisson equation and nonlinear drift-diffusion equations.
Cobimaximal lepton mixing from soft symmetry breaking
Grimus, W.; Lavoura, L.
2017-11-01
Cobimaximal lepton mixing, i.e.θ23 = 45 ° and δ = ± 90 ° in the lepton mixing matrix V, arises as a consequence of SV =V* P, where S is the permutation matrix that interchanges the second and third rows of V and P is a diagonal matrix of phase factors. We prove that any such V may be written in the form V = URP, where U is any predefined unitary matrix satisfying SU =U*, R is an orthogonal, i.e. real, matrix, and P is a diagonal matrix satisfying P2 = P. Using this theorem, we demonstrate the equivalence of two ways of constructing models for cobimaximal mixing-one way that uses a standard CP symmetry and a different way that uses a CP symmetry including μ-τ interchange. We also present two simple seesaw models to illustrate this equivalence; those models have, in addition to the CP symmetry, flavour symmetries broken softly by the Majorana mass terms of the right-handed neutrino singlets. Since each of the two models needs four scalar doublets, we investigate how to accommodate the Standard Model Higgs particle in them.
Asymptotic expansions for the Gaussian unitary ensemble
DEFF Research Database (Denmark)
Haagerup, Uffe; Thorbjørnsen, Steen
2012-01-01
Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian U...... and covariance considered above correspond to, respectively, the one- and two-dimensional Cauchy (or Stieltjes) transform of the ....... Unitary Ensemble (GUE). Using an analytical approach, we provide in the present paper an alternative proof of this asymptotic expansion in the GUE case. Specifically we derive for a random matrix Xn that where k is an arbitrary positive integer. Considered as mappings of g, we determine the coefficients...... aj(g), j ¿ N, as distributions (in the sense of L. Schwarts). We derive a similar asymptotic expansion for the covariance Cov{Trn[f(Xn)], Trn[g(Xn)]}, where f is a function of the same kind as g, and Trn = n trn. Special focus is drawn to the case where and for ¿, µ in C\\R. In this case the mean...
Rugari, Steven Louis
1992-01-01
We have carried out a search for broken reflection symmetry in the exotic nucleus ^{114 }Xe. Evidence for broken reflection symmetry has been previously observed in the actinide region, most notably Ra-Th nuclei, and more recently in the neutron rich nuclei ^{144}Ba, ^{146}Ce, and ^{146,148}Nd. This evidence has been discussed in terms of two conceptually different theoretical frameworks, namely alpha clustering and octupole deformation. The alpha clustering model makes global predictions of the relative strengths of enhanced electric dipole (E1) transitions characteristic of broken reflection symmetry, and predicts a dependence on isospin divided by nuclear mass (N-Z) ^2/A^2 of the reduced transition probability, B(E1), where A is the nuclear mass number and N and Z are, respectively, the neutron and proton number. The nuclei studied previously have approximately the same value of (N-Z)^2/A ^2 between 0.033 and 0.05. In ^ {114}Xe this parameter is much different, (N-Z)^2/A^2 =.0028, allowing for a test of the prediction. On the other hand, the octupole model description is less straightforward. Two terms contributing to the calculation of reduced transition strengths are based on the collective liquid drop model of nuclei and have a global dependence on A^2 Z^2. A third term, however, depends explicitly on the shell model description of the valence nucleons and can be large enough to remove this global dependence. The nucleus ^{114}Xe was produced in the heavy ion fusion evaporation reaction ^{60}Ni(^ {58}Ni,2p2n)^{114 }Xe in two separate measurements at Daresbury Laboratory and at Yale University. The nucleus was identified by means of a recoil mass spectrometer in the first reaction and by detection of evaporated neutrons in the second. Gamma ray spectra were collected in coincidence with these triggers using similar gamma detector setups. Information on the angular distributions of the gamma rays was collected for at least three separate angles in each
Asymptotical Mean Square Stability of Cohen-Grossberg Neural Networks with Random Delay
Directory of Open Access Journals (Sweden)
Enwen Zhu
2010-01-01
Full Text Available The asymptotical mean-square stability analysis problem is considered for a class of Cohen-Grossberg neural networks (CGNNs with random delay. The evolution of the delay is modeled by a continuous-time homogeneous Markov process with a finite number of states. The main purpose of this paper is to establish easily verifiable conditions under which the random delayed Cohen-Grossberg neural network is asymptotical mean-square stability. By employing Lyapunov-Krasovskii functionals and conducting stochastic analysis, a linear matrix inequality (LMI approach is developed to derive the criteria for the asymptotical mean-square stability, which can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.
Non-abelian symmetries in tensor networks: A quantum symmetry space approach
International Nuclear Information System (INIS)
Weichselbaum, Andreas
2012-01-01
A general framework for non-abelian symmetries is presented for matrix-product and tensor-network states in the presence of well-defined orthonormal local as well as effective basis sets. The two crucial ingredients, the Clebsch–Gordan algebra for multiplet spaces as well as the Wigner–Eckart theorem for operators, are accounted for in a natural, well-organized, and computationally straightforward way. The unifying tensor-representation for quantum symmetry spaces, dubbed QSpace, is particularly suitable to deal with standard renormalization group algorithms such as the numerical renormalization group (NRG), the density matrix renormalization group (DMRG), or also more general tensor networks such as the multi-scale entanglement renormalization ansatz (MERA). In this paper, the focus is on the application of the non-abelian framework within the NRG. A detailed analysis is presented for a fully screened spin- 3/2 three-channel Anderson impurity model in the presence of conservation of total spin, particle–hole symmetry, and SU(3) channel symmetry. The same system is analyzed using several alternative symmetry scenarios based on combinations of U(1) charge , SU(2) spin , SU(2) charge , SU(3) channel , as well as the enveloping symplectic Sp(6) symmetry. These are compared in detail, including their respective dramatic gain in numerical efficiency. In the Appendix, finally, an extensive introduction to non-abelian symmetries is given for practical applications, together with simple self-contained numerical procedures to obtain Clebsch–Gordan coefficients and irreducible operators sets. The resulting QSpace tensors can deal with any set of abelian symmetries together with arbitrary non-abelian symmetries with compact, i.e. finite-dimensional, semi-simple Lie algebras. - Highlights: ► We introduce a transparent framework for non-abelian symmetries in tensor networks. ► The framework was successfully applied within the numerical renormalization group.
Flavor symmetry and topology change in nuclear symmetry energy for compact stars
International Nuclear Information System (INIS)
Lee, Hyun Kyu; Rho, Mannque
2013-01-01
The nuclear symmetry energy figures crucially in the structure of asymmetric nuclei and, more importantly, in the equation of state (EoS) of compact stars. At present it is almost totally unknown, both experimentally and theoretically, in the density regime appropriate for the interior of neutron stars. Basing on a strong-coupled structure of dense baryonic matter encoded in the skyrmion crystal approach with a topology change and resorting to the notion of generalized hidden local symmetry in hadronic interactions, we address a variety of hitherto unexplored issues of nuclear interactions associated with the symmetry energy, i.e., kaon condensation and hyperons, possible topology change in dense matter, nuclear tensor forces, conformal symmetry, chiral symmetry, etc., in the EoS of dense compact-star matter. One of the surprising results coming from HLS structure that is distinct from what is given by standard phenomenological approaches is that at high density, baryonic matter is driven by renormalization group flow to the 'dilaton-limit fixed point' constrained by 'mended symmetries'. We further propose how to formulate kaon condensation and hyperons in compact-star matter in a framework anchored on a single effective Lagrangian by treating hyperons as the Callan–Klebanov kaon-skyrmion bound states simulated on crystal lattice. This formulation suggests that hyperons can figure in the stellar matter — if at all — when or after kaons condense, in contrast to the standard phenomenological approaches where the hyperons appear as the first strangeness degree of freedom in matter, thereby suppressing or delaying kaon condensation. In our simplified description of the stellar structure in terms of symmetry energies, which is compatible with that of the 1.97 solar mass star, kaon condensation plays a role of 'doorway state' to strange quark matter. (author)
asymptoticMK: A Web-Based Tool for the Asymptotic McDonald-Kreitman Test.
Haller, Benjamin C; Messer, Philipp W
2017-05-05
The McDonald-Kreitman (MK) test is a widely used method for quantifying the role of positive selection in molecular evolution. One key shortcoming of this test lies in its sensitivity to the presence of slightly deleterious mutations, which can severely bias its estimates. An asymptotic version of the MK test was recently introduced that addresses this problem by evaluating polymorphism levels for different mutation frequencies separately, and then extrapolating a function fitted to that data. Here, we present asymptoticMK, a web-based implementation of this asymptotic MK test. Our web service provides a simple R-based interface into which the user can upload the required data (polymorphism and divergence data for the genomic test region and a neutrally evolving reference region). The web service then analyzes the data and provides plots of the test results. This service is free to use, open-source, and available at http://benhaller.com/messerlab/asymptoticMK.html We provide results from simulations to illustrate the performance and robustness of the asymptoticMK test under a wide range of model parameters. Copyright © 2017 Haller and Messer.
Symmetries of nonlinear ordinary differential equations: The ...
Indian Academy of Sciences (India)
2015-10-21
Oct 21, 2015 ... Abstract. Lie symmetry analysis is one of the powerful tools to analyse nonlinear ordinary dif- ferential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries, contact symmetries, hidden symmetries, nonlocal symmetries ...
Symmetry and perturbation theory
Gaeta, Giuseppe
A co-chain map for the G invariant De Rham complex -- New examples of trihamiltonian structures linking different Lenard chains -- Wave propagation in an elastic medium: GDS equations -- Parametric excitation in nonlinear dynamics -- Collisionless action-minimizing trajectories for the equivariant 3-body problem in R2 -- The Lagrangian and Hamiltonian formulations for a special class of non-conservative systems -- Shadowing chains of collision orbits for the elliptic 3-body problem -- Similarity reductions of an optical model -- Fold, transcritical and pitchfork singularities for time-reversible systems -- Homographic three-body motions with positive and negative masses -- Remarks on conformal Killing tensors and separation of variables -- A regularity theory for optimal partition problems -- Lambda and mu-symmetries -- Potential symmetries and linearization of some evolution equations -- Periodic solutions for zero mass nonlinear wave equations -- Fundamental covariants in the invariant theory of Killing tensors -- Global geometry of 3-body trajectories with vanishing angular momentum -- The relation between the topological structure of the set of controllable affine systems and topological structures of the set of controllable homogenuous systems in low dimension -- On preservation of action variables for satellite librations in elliptic orbits with account of solar light pressure -- An explicit solution of the (quantum) elliptic Calogero-Sutherland model -- An application of the Melnikov integral to a restricted three body problem -- Reductions of integrable equations and automorphic Lie algebras -- Geometric reduction of Poisson operators -- Closed manifolds admitting metrics with the same geodesics -- A transcritical-flip bifurcation in a model for a robot-arm -- Alignment and the classification of Lorentz-signature tensors -- Renormalization group symmetry and gas dynamics -- Refined computation of hypernormal forms -- New order reductions for Euler
Yale, Paul B
2012-01-01
This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi
Symmetries leading to inflation
International Nuclear Information System (INIS)
Aguirregabiria, Juan M.; Lazkoz, Ruth; Chimento, Luis P.; Jakubi, Alejandro S.
2003-01-01
We present here the general transformation that leaves unchanged the form of the field equations for perfect fluid Friedmann-Robertson-Walker and Bianchi type V cosmologies. The symmetries found can be used as algorithms for generating new cosmological models from existing ones. A particular case of the general transformation is used to illustrate the crucial role played by the number of scalar fields in the occurrence of inflation. Related to this, we also study the existence and stability of Bianchi type V power law solutions
Farmer, David W
1995-01-01
In most mathematics textbooks, the most exciting part of mathematics-the process of invention and discovery-is completely hidden from the reader. The aim of Groups and Symmetry is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: Its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you. Suitable for a one-semester course at the beginning undergraduate level, there are no prerequ
Integrable systems and lie symmetries in classical mechanics
International Nuclear Information System (INIS)
Sen, T.
1986-01-01
The interrelationship between integrability and symmetries in classical mechanics is studied. Two-dimensional time- and velocity-independent potentials form the domain of the study. It is shown that, contrary to folklore, existence of a single finite symmetry does not ensure integrability. A method due to Darboux is used to construct potentials that admit a time-independent invariant. All potentials admitting invariants linear or quadratic in the momentum coordinates are constructed. These are the only integrable potentials which can be expressed as arbitrary functions of certain arguments. A complete construction of potentials admitting higher-order invariants does not seem possible. However, the necessary general forms for potentials that admit a particular invariant of arbitrary order are found. These invariants must be spherically symmetric in the leading terms. Two kinds of symmetries are studied: point Lie symmetries of the Newtonian equations of motion for conservative potentials, and point Noether symmetries of the action functionals obtained from the standard Lagrangians associated with these potentials. All conservative potentials which admit these symmetries are constructed. The class of potentials admitting Noether symmetries is shown to be a subclass of those admitting Lie symmetries
Directory of Open Access Journals (Sweden)
Nazife O. Koca
2016-12-01
Full Text Available We describe an extension of the pyritohedral symmetry in 3D to 4-dimensional Euclidean space and construct the group elements of the 4D pyritohedral group of order 576 in terms of quaternions. It turns out that it is a maximal subgroup of both the rank-4 Coxeter groups W (F4 and W (H4, implying that it is a group relevant to the crystallographic as well as quasicrystallographic structures in 4-dimensions. We derive the vertices of the 24 pseudoicosahedra, 24 tetrahedra and the 96 triangular pyramids forming the facets of the pseudo snub 24-cell. It turns out that the relevant lattice is the root lattice of W (D4. The vertices of the dual polytope of the pseudo snub 24-cell consists of the union of three sets: 24-cell, another 24-cell and a new pseudo snub 24-cell. We also derive a new representation for the symmetry group of the pseudo snub 24-cell and the corresponding vertices of the polytopes.
Bootstrap Dynamical Symmetry Breaking
Directory of Open Access Journals (Sweden)
Wei-Shu Hou
2013-01-01
Full Text Available Despite the emergence of a 125 GeV Higgs-like particle at the LHC, we explore the possibility of dynamical electroweak symmetry breaking by strong Yukawa coupling of very heavy new chiral quarks Q . Taking the 125 GeV object to be a dilaton with suppressed couplings, we note that the Goldstone bosons G exist as longitudinal modes V L of the weak bosons and would couple to Q with Yukawa coupling λ Q . With m Q ≳ 700 GeV from LHC, the strong λ Q ≳ 4 could lead to deeply bound Q Q ¯ states. We postulate that the leading “collapsed state,” the color-singlet (heavy isotriplet, pseudoscalar Q Q ¯ meson π 1 , is G itself, and a gap equation without Higgs is constructed. Dynamical symmetry breaking is affected via strong λ Q , generating m Q while self-consistently justifying treating G as massless in the loop, hence, “bootstrap,” Solving such a gap equation, we find that m Q should be several TeV, or λ Q ≳ 4 π , and would become much heavier if there is a light Higgs boson. For such heavy chiral quarks, we find analogy with the π − N system, by which we conjecture the possible annihilation phenomena of Q Q ¯ → n V L with high multiplicity, the search of which might be aided by Yukawa-bound Q Q ¯ resonances.
Wilczek, Frank
2004-01-01
Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world (8 pages) Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world. The discrepancy is ascribed to a pervasive symmetry-breaking field, which fills all space uniformly, rendering the Universe a sort of exotic superconductor. So far, the evidence for these bold ideas is indirect. But soon the theory will undergo a critical test depending on whether the quanta of this symmetry-breaking field, the so-called Higgs particles, are produced at the Large Hadron Collider (due to begin operation in 2007).
Realization of chiral symmetry in the ERG
International Nuclear Information System (INIS)
Echigo, Yoshio; Igarashi, Yuji
2011-01-01
We discuss within the framework of the ERG how chiral symmetry is realized in a linear σ model. A generalized Ginsparg-Wilson relation is obtained from the Ward-Takahashi identities for the Wilson action assumed to be bilinear in the Dirac fields. We construct a family of its non-perturbative solutions. The family generates the most general solutions to the Ward-Takahashi identities. Some special solutions are discussed. For each solution in this family, chiral symmetry is realized in such a way that a change in the Wilson action under non-linear symmetry transformation is canceled with a change in the functional measure. We discuss that the family of solutions reduces via a field redefinition to a family of the Wilson actions with some composite object of the scalar fields which has a simple transformation property. For this family, chiral symmetry is linearly realized with a continuum analog of the operator extension of γ 5 used on the lattice. We also show that there exist some appropriate Dirac fields which obey the standard chiral transformations with γ 5 in contrast to the lattice case. Their Yukawa interaction with scalars, however, becomes non-linear. (author)
Null hypersurface quantization, electromagnetic duality and asympotic symmetries of Maxwell theory
Bhattacharyya, Arpan; Hung, Ling-Yan; Jiang, Yikun
2018-03-01
In this paper we consider introducing careful regularization at the quantization of Maxwell theory in the asymptotic null infinity. This allows systematic discussions of the commutators in various boundary conditions, and application of Dirac brackets accordingly in a controlled manner. This method is most useful when we consider asymptotic charges that are not localized at the boundary u → ±∞ like large gauge transformations. We show that our method reproduces the operator algebra in known cases, and it can be applied to other space-time symmetry charges such as the BMS transformations. We also obtain the asymptotic form of the U(1) charge following from the electromagnetic duality in an explicitly EM symmetric Schwarz-Sen type action. Using our regularization method, we demonstrate that the charge generates the expected transformation of a helicity operator. Our method promises applications in more generic theories.
Asymptotically Honest Confidence Regions for High Dimensional
DEFF Research Database (Denmark)
Caner, Mehmet; Kock, Anders Bredahl
While variable selection and oracle inequalities for the estimation and prediction error have received considerable attention in the literature on high-dimensional models, very little work has been done in the area of testing and construction of confidence bands in high-dimensional models. However...... of the asymptotic covariance matrix of an increasing number of parameters which is robust against conditional heteroskedasticity. To our knowledge we are the first to do so. Next, we show that our confidence bands are honest over sparse high-dimensional sub vectors of the parameter space and that they contract...
Neutrino masses and family symmetry
International Nuclear Information System (INIS)
Grinstein, B.; Preskill, J.; Wise, M.B.
1985-01-01
Neutrino masses in the 100 eV-1 MeV range are permitted if there is a spontaneously broken global family symmetry that allows the heavy neutrinos to decay by Goldstone boson emission with a cosmologically acceptable lifetime. The family symmetry may be either abelian or nonabelian; we present models illustrating both possibilities. If the family symmetry is nonabelian, then the decay tau -> μ + Goldstone boson or tau -> e + Goldstone may have an observable rate. (orig.)
Exact dynamical and partial symmetries
Energy Technology Data Exchange (ETDEWEB)
Leviatan, A, E-mail: ami@phys.huji.ac.il [Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel)
2011-03-01
We discuss a hierarchy of broken symmetries with special emphasis on partial dynamical symmetries (PDS). The latter correspond to a situation in which a non-invariant Hamiltonian accommodates a subset of solvable eigenstates with good symmetry, while other eigenstates are mixed. We present an algorithm for constructing Hamiltonians with this property and demonstrate the relevance of the PDS notion to nuclear spectroscopy, to quantum phase transitions and to mixed systems with coexisting regularity and chaos.
Exact dynamical and partial symmetries
International Nuclear Information System (INIS)
Leviatan, A
2011-01-01
We discuss a hierarchy of broken symmetries with special emphasis on partial dynamical symmetries (PDS). The latter correspond to a situation in which a non-invariant Hamiltonian accommodates a subset of solvable eigenstates with good symmetry, while other eigenstates are mixed. We present an algorithm for constructing Hamiltonians with this property and demonstrate the relevance of the PDS notion to nuclear spectroscopy, to quantum phase transitions and to mixed systems with coexisting regularity and chaos.
The conservation of orbital symmetry
Woodward, R B
2013-01-01
The Conservation of Orbital Symmetry examines the principle of conservation of orbital symmetry and its use. The central content of the principle was that reactions occur readily when there is congruence between orbital symmetry characteristics of reactants and products, and only with difficulty when that congruence does not obtain-or to put it more succinctly, orbital symmetry is conserved in concerted reaction. This principle is expected to endure, whatever the language in which it may be couched, or whatever greater precision may be developed in its application and extension. The book ope
An introduction to Yangian symmetries
International Nuclear Information System (INIS)
Bernard, D.
1992-01-01
Some aspects of the quantum Yangians as symmetry algebras of two-dimensional quantum field theories are reviewed. They include two main issues: the first is the classical Heisenberg model, covering non-Abelian symmetries, generators of the symmetries and the semi-classical Yangians, an alternative presentation of the semi-classical Yangians, digression on Poisson-Lie groups. The second is the quantum Heisenberg chain, covering non-Abelian symmetries and the quantum Yangians, the transfer matrix and an alternative presentation of the Yangians, digression on the double Yangians. (K.A.) 15 refs
Leptogenesis and residual CP symmetry
International Nuclear Information System (INIS)
Chen, Peng; Ding, Gui-Jun; King, Stephen F.
2016-01-01
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.
Quarks, baryons and chiral symmetry
Hosaka, Atsushi
2001-01-01
This book describes baryon models constructed from quarks, mesons and chiral symmetry. The role of chiral symmetry and of quark model structure with SU(6) spin-flavor symmetry are discussed in detail, starting from a pedagogic introduction. Emphasis is placed on symmetry aspects of the theories. As an application, the chiral bag model is studied for nucleon structure, where important methods of theoretical physics, mostly related to the semiclassical approach for a system of strong interactions, are demonstrated. The text is more practical than formal; tools and ideas are explained in detail w
QCD diffraction: a critical phenomenon reflecting both confinement and chiral-symmetry breaking
International Nuclear Information System (INIS)
White, A.R.
1982-07-01
Arguments are presented for studying soft diffractive physics at anti p-p colliders in terms of Critical Pomeron Reggeon Field Theory. It is emphasized that both confinement and chiral-symmetry breaking play a vital role in the occurrence of the Critical Pomeron in QCD. SU(3) is the unique strong-interaction gauge group giving the Critical Pomeron and the maximum number of quarks allowed by asymptotic freedom is required for criticality
Frenod, Emmanuel
2013-01-01
In this note, a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical Methods; H-Measure-Based Numerical Methods; Two-Scale Numerical Methods and TSAPS: Two-Scale Asymptotic Preserving Schemes.
Tests of Lorentz Symmetry in the Gravitational Sector
Directory of Open Access Journals (Sweden)
Aurélien Hees
2016-12-01
Full Text Available Lorentz symmetry is one of the pillars of both General Relativity and the Standard Model of particle physics. Motivated by ideas about quantum gravity, unification theories and violations of CPT symmetry, a significant effort has been put the last decades into testing Lorentz symmetry. This review focuses on Lorentz symmetry tests performed in the gravitational sector. We briefly review the basics of the pure gravitational sector of the Standard-Model Extension (SME framework, a formalism developed in order to systematically parametrize hypothetical violations of the Lorentz invariance. Furthermore, we discuss the latest constraints obtained within this formalism including analyses of the following measurements: atomic gravimetry, Lunar Laser Ranging, Very Long Baseline Interferometry, planetary ephemerides, Gravity Probe B, binary pulsars, high energy cosmic rays, … In addition, we propose a combined analysis of all these results. We also discuss possible improvements on current analyses and present some sensitivity analyses for future observations.
Structural aspects of asymptotically safe black holes
Koch, Benjamin; Saueressig, Frank
2014-01-01
We study the quantum modifications of classical, spherically symmetric Schwarzschild (anti-) de Sitter black holes within quantum Einstein gravity. The quantum effects are incorporated through the running coupling constants Gk and Λk, computed within the exact renormalization group approach, and a common scale-setting procedure. We find that, in contrast to common intuition, it is actually the cosmological constant that determines the short-distance structure of the RG-improved black hole: in the asymptotic UV the structure of the quantum solutions is universal and given by the classical Schwarzschild-de Sitter solution, entailing a self-similarity between the classical and quantum regime. As a consequence asymptotically safe black holes evaporate completely and no Planck-size remnants are formed. Moreover, the thermodynamic entropy of the critical Nariai black hole is shown to agree with the microstate count based on the effective average action, suggesting that the entropy originates from quantum fluctuations around the mean-field geometry.
Integrable theories that are asymptotically CFT
Evans, J M; Jonathan M Evans; Timothy J Hollowood
1995-01-01
A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level k. In contrast to the more familiar situation of asymptotically free theories in which the fixed points are trivial, the sigma models considered here may be termed ``asymptotically CFT''. These theories have previously been conjectured to be quantum integrable; we confirm this by proposing a factorizable S-matrix to describe their infra-red behaviour and then carrying out a stringent test of this proposal. The test involves coupling the theory to a conserved charge and evaluating the response of the free-energy both in perturbation theory to one loop and directly from the S-matrix via the Thermodynamic Bethe Ansatz with a chemical potential at zero temperature. Comparison of these results provides convincing evidence in favour of the proposed S-matrix; it also yields the universal coefficients of the beta-func...
Almost normed spaces of functions with polynomial asymptotic behaviour
International Nuclear Information System (INIS)
Kudryavtsev, L D
2003-01-01
We consider a linear space of functions asymptotically approaching polynomials of degree not higher than a fixed one as the independent variable approaches infinity. Such a space cannot be normed if the functions in it possess a certain smoothness. For this reason the concept of almost normed space is introduced and the spaces in question, namely, spaces of functions asymptotically or strongly asymptotically approaching polynomials, are shown to be almost normed. The completeness of these spaces in the metric generated by their almost norm is also proved, the connection between the asymptotic approach and the strong asymptotic approach of functions to polynomials is studied, and a new (and shorter) proof of the criterion for the asymptotic approach of functions to polynomials is presented
Concepts of electroweak symmetry breaking and Higgs physics
Energy Technology Data Exchange (ETDEWEB)
Gomez-Bock, M. [Benemerita Univ., Puebla (Mexico). Inst. de Fisica; Mondragon, M. [Universidad Nacional Autonoma de Mexico, Mexico City (Mexico). Inst. de Fisica; Muehlleitner, M. [Laboratoire d' Annecy-Le-Vieux de Physique Theorique, 74 (France)]|[CERN - European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.; Spira, M. [Paul Scherrer Inst. (PSI), Villigen (Switzerland); Zerwas, P.M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)]|[RWTH Aachen (Germany). Inst. Theor. Physik E]|[Univ. Paris- Sud, Orsay (France). Laboratoire de Physique Theorique
2007-12-15
We present an introduction to the basic concepts of electroweak symmetry breaking and Higgs physics within the Standard Model and its supersymmetric extensions. A brief overview will also be given on alternative mechanisms of electroweak symmetry breaking. In addition to the theoretical basis, the present experimental status of Higgs physics and prospects at the Tevatron, the LHC and e{sup +}e{sup -} linear colliders are discussed. (orig.)
Concepts of electroweak symmetry breaking and Higgs physics
International Nuclear Information System (INIS)
Gomez-Bock, M.; Zerwas, P.M.; RWTH Aachen; Univ. Paris- Sud, Orsay
2007-12-01
We present an introduction to the basic concepts of electroweak symmetry breaking and Higgs physics within the Standard Model and its supersymmetric extensions. A brief overview will also be given on alternative mechanisms of electroweak symmetry breaking. In addition to the theoretical basis, the present experimental status of Higgs physics and prospects at the Tevatron, the LHC and e + e - linear colliders are discussed. (orig.)
Spectral distributions and symmetries
International Nuclear Information System (INIS)
Quesne, C.
1980-01-01
As it is now well known, the spectral distribution method has both statistical and group theoretical aspects which make for great simplifications in many-Fermion system calculations with respect to more conventional ones. Although both aspects intertwine and are equally essential to understand what is going on, we are only going to discuss some of the group theoretical aspects, namely those connected with the propagation of information, in view of their fundamental importance for the actual calculations of spectral distributions. To be more precise, let us recall that the spectral distribution method may be applied in principle to many-Fermion spaces which have a direct-product structure, i.e., are obtained by distributing a certain number n of Fermions over N single-particle states (O less than or equal to n less than or equal to N), as it is the case for instance for the nuclear shell model spaces. For such systems, the operation of a central limit theorem is known to provide us with a simplifying principle which, when used in conjunction with exact or broken symmetries, enables us to make definite predictions in those cases which are not amendable to exact shell model diagonalizations. The distribution (in energy) of the states corresponding to a fixed symmetry is then defined by a small number of low-order energy moments. Since the Hamiltonian is defined in few-particle subspaces embedded in the n-particlespace, the low-order moments, we are interested in, can be expressed in terms of simpler quantities defined in those few-particle subspaces: the information is said to propagate from the simple subspaces to the more complicated ones. The possibility of actually calculating spectral distributions depends upon the finding of simple ways to propagate the information
Systematic model building with flavor symmetries
Energy Technology Data Exchange (ETDEWEB)
Plentinger, Florian
2009-12-19
The observation of neutrino masses and lepton mixing has highlighted the incompleteness of the Standard Model of particle physics. In conjunction with this discovery, new questions arise: why are the neutrino masses so small, which form has their mass hierarchy, why is the mixing in the quark and lepton sectors so different or what is the structure of the Higgs sector. In order to address these issues and to predict future experimental results, different approaches are considered. One particularly interesting possibility, are Grand Unified Theories such as SU(5) or SO(10). GUTs are vertical symmetries since they unify the SM particles into multiplets and usually predict new particles which can naturally explain the smallness of the neutrino masses via the seesaw mechanism. On the other hand, also horizontal symmetries, i.e., flavor symmetries, acting on the generation space of the SM particles, are promising. They can serve as an explanation for the quark and lepton mass hierarchies as well as for the different mixings in the quark and lepton sectors. In addition, flavor symmetries are significantly involved in the Higgs sector and predict certain forms of mass matrices. This high predictivity makes GUTs and flavor symmetries interesting for both, theorists and experimentalists. These extensions of the SM can be also combined with theories such as supersymmetry or extra dimensions. In addition, they usually have implications on the observed matter-antimatter asymmetry of the universe or can provide a dark matter candidate. In general, they also predict the lepton flavor violating rare decays {mu} {yields} e{gamma}, {tau} {yields} {mu}{gamma}, and {tau} {yields} e{gamma} which are strongly bounded by experiments but might be observed in the future. In this thesis, we combine all of these approaches, i.e., GUTs, the seesaw mechanism and flavor symmetries. Moreover, our request is to develop and perform a systematic model building approach with flavor symmetries and
Asymptotic variance of grey-scale surface area estimators
DEFF Research Database (Denmark)
Svane, Anne Marie
Grey-scale local algorithms have been suggested as a fast way of estimating surface area from grey-scale digital images. Their asymptotic mean has already been described. In this paper, the asymptotic behaviour of the variance is studied in isotropic and sufficiently smooth settings, resulting...... in a general asymptotic bound. For compact convex sets with nowhere vanishing Gaussian curvature, the asymptotics can be described more explicitly. As in the case of volume estimators, the variance is decomposed into a lattice sum and an oscillating term of at most the same magnitude....
Symmetry chains and adaptation coefficients
International Nuclear Information System (INIS)
Fritzer, H.P.; Gruber, B.
1985-01-01
Given a symmetry chain of physical significance it becomes necessary to obtain states which transform properly with respect to the symmetries of the chain. In this article we describe a method which permits us to calculate symmetry-adapted quantum states with relative ease. The coefficients for the symmetry-adapted linear combinations are obtained, in numerical form, in terms of the original states of the system and can thus be represented in the form of numerical tables. In addition, one also obtains automatically the matrix elements for the operators of the symmetry groups which are involved, and thus for any physical operator which can be expressed either as an element of the algebra or of the enveloping algebra. The method is well suited for computers once the physically relevant symmetry chain, or chains, have been defined. While the method to be described is generally applicable to any physical system for which semisimple Lie algebras play a role we choose here a familiar example in order to illustrate the method and to illuminate its simplicity. We choose the nuclear shell model for the case of two nucleons with orbital angular momentum l = 1. While the states of the entire shell transform like the smallest spin representation of SO(25) we restrict our attention to its subgroup SU(6) x SU(2)/sub T/. We determine the symmetry chains which lead to total angular momentum SU(2)/sub J/ and obtain the symmetry-adapted states for these chains
Characterization of Partial Intrinsic Symmetries
Shehu, Aurela; Brunton, Alan; Wuhrer, Stefanie; Wand, Michael
2014-01-01
We present a mathematical framework and algorithm for characterizing and extracting partial intrinsic symmetries of surfaces, which is a fundamental building block for many modern geometry processing algorithms. Our goal is to compute all “significant” symmetry information of the shape, which we
Symmetry preservation during radiation damage
International Nuclear Information System (INIS)
Bhat, S.V.; Abdel-Gawad, M.M.H.
1991-01-01
An examination of radiation-damage processes consequent to high-energy irradiation in certain ammonium salts studied using ESR of free radicals together with the structural information available from neutron diffraction studies shows that, other factors being equal/nearly equal, symmetry-related bonds are preserved in preference to those unrelated to one another by any symmetry. (author). 23 refs., 3 tabs
Singlets of fermionic gauge symmetries
Bergshoeff, E.A.; Kallosh, R.E.; Rahmanov, M.A.
1989-01-01
We investigate under which conditions singlets of fermionic gauge symmetries which are "square roots of gravity" can exist. Their existence is non-trivial because there are no fields neutral in gravity. We tabulate several examples of singlets of global and local supersymmetry and Îº-symmetry and
Symmetry guide to ferroaxial transitions
Czech Academy of Sciences Publication Activity Database
Hlinka, Jiří; Přívratská, J.; Ondrejkovič, Petr; Janovec, Václav
2016-01-01
Roč. 116, č. 17 (2016), 1-6, č. článku 177602. ISSN 0031-9007 R&D Projects: GA ČR GA15-04121S Institutional support: RVO:68378271 Keywords : symmetry * symmetry breaking * ferroaxial Transitions * property tensors * Aizu species Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 8.462, year: 2016
Givental Graphs and Inversion Symmetry
Dunin-Barkovskiy, P.; Shadrin, S.; Spitz, L.
2013-01-01
Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to a Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in
Collective states and crossing symmetry
International Nuclear Information System (INIS)
Heiss, W.D.
1977-01-01
Collective states are usually described in simple terms but with the use of effective interactions which are supposed to contain more or less complicated contributions. The significance of crossing symmetry is discussed in this connection. Formal problems encountered in the attempts to implement crossing symmetry are pointed out
Symmetries in geology and geophysics.
Turcotte, D L; Newman, W I
1996-12-10
Symmetries have played an important role in a variety of problems in geology and geophysics. A large fraction of studies in mineralogy are devoted to the symmetry properties of crystals. In this paper, however, the emphasis will be on scale-invariant (fractal) symmetries. The earth's topography is an example of both statistically self-similar and self-affine fractals. Landforms are also associated with drainage networks, which are statistical fractal trees. A universal feature of drainage networks and other growth networks is side branching. Deterministic space-filling networks with side-branching symmetries are illustrated. It is shown that naturally occurring drainage networks have symmetries similar to diffusion-limited aggregation clusters.
Axions from chiral family symmetry
International Nuclear Information System (INIS)
Chang, D.; Pal, P.B.; Maryland Univ., College Park; Senjanovic, G.
1985-01-01
We investigate the possibility that family symmetry, Gsub(F), is spontaneously broken chiral global symmetry. We classify the interesting cases when family symmetry can result in an automatic Peccei-Quinn symmetry U(1)sub(PQ) and thus provide a solution to the strong CP problem. The result disfavors having two or four families. For more than four families, U(1)sub(PQ) is in general automatic. In the case of three families, a unique Higgs sector allows U(1)sub(PQ) in the simplest case of Gsub(F)=[SU(3)] 3 . Cosmological consideration also puts strong constraint on the number of families. For Gsub(F)=[SU(N)] 3 cosmology singles out the three-family (N=3) case as a unique solution if there are three light neutrinos. Possible implication of decoupling theorem as applied to family symmetry breaking is also discussed. (orig.)
Shape analysis with subspace symmetries
Berner, Alexander
2011-04-01
We address the problem of partial symmetry detection, i.e., the identification of building blocks a complex shape is composed of. Previous techniques identify parts that relate to each other by simple rigid mappings, similarity transforms, or, more recently, intrinsic isometries. Our approach generalizes the notion of partial symmetries to more general deformations. We introduce subspace symmetries whereby we characterize similarity by requiring the set of symmetric parts to form a low dimensional shape space. We present an algorithm to discover subspace symmetries based on detecting linearly correlated correspondences among graphs of invariant features. We evaluate our technique on various data sets. We show that for models with pronounced surface features, subspace symmetries can be found fully automatically. For complicated cases, a small amount of user input is used to resolve ambiguities. Our technique computes dense correspondences that can subsequently be used in various applications, such as model repair and denoising. © 2010 The Author(s).
Radiative violation of CP-symmetry
International Nuclear Information System (INIS)
Galvan Herrera, J.B.
1990-01-01
The left-right quiral symmetry is not conserved by the Standard model. A subgroup of the standard gauge group (SU(2) L ) breaks this symmetry in a explicit way. Moreover, the standard model, if there are theree or more matter generations, violates the CP discrete symmetry. This prediction has been experimentally demonstrated correct in the Kaon anti Kaon system. In this work some possible explanations to the CP violation parameter magnitude are researched. We have studied the variation of the Kobayashi-Maskawa matrix with the energy scale. To realize this work we have developed a general method to calculate the renormalization group equations of the Kobayashi-Maskawa matrix parameters. From these equations we could also calculate the renormalization group equation of the J parameter that characterizes the CP violation. This calculus has been applied in a concrete example: a typical supersymmetric model from superstring theories. This model can be seen like a natural extension of the supersymmetric standard model. This kind of models have a gauge group bigger that the standard one more particles and new terms of the Lagrangian. We have verified that such model provides us of a correct low energy fenomenology and, moreover other results, some particle spectrums have been developed. In the elaboration of this model some conditions, that the model has to respected to be compatible with the actual fenomenology, have been studied. The most interesting results of this thesis are the develop of a general method to calculate the renormalization group equations of the Kobayashi-Maskawa matrix parameters and the develop of a new mechanism of the radiative violation. This mechanism is related with the new terms of the Lagrangian. (Author)
Asymptotic Sharpness of Bounds on Hypertrees
Directory of Open Access Journals (Sweden)
Lin Yi
2017-08-01
Full Text Available The hypertree can be defined in many different ways. Katona and Szabó introduced a new, natural definition of hypertrees in uniform hypergraphs and investigated bounds on the number of edges of the hypertrees. They showed that a k-uniform hypertree on n vertices has at most (nk−1$\\left( {\\matrix{n \\cr {k - 1} } } \\right$ edges and they conjectured that the upper bound is asymptotically sharp. Recently, Szabó verified that the conjecture holds by recursively constructing an infinite sequence of k-uniform hypertrees and making complicated analyses for it. In this note we give a short proof of the conjecture by directly constructing a sequence of k-uniform k-hypertrees.
UV conformal window for asymptotic safety
Bond, Andrew D.; Litim, Daniel F.; Vazquez, Gustavo Medina; Steudtner, Tom
2018-02-01
Interacting fixed points in four-dimensional gauge theories coupled to matter are investigated using perturbation theory up to three loop order. It is shown how fixed points, scaling exponents, and anomalous dimensions are obtained as a systematic power series in a small parameter. The underlying ordering principle is explained and contrasted with conventional perturbation theory and Weyl consistency conditions. We then determine the conformal window with asymptotic safety from the complete next-to-next-to-leading order in perturbation theory. Limits for the conformal window arise due to fixed point mergers, the onset of strong coupling, or vacuum instability. A consistent picture is uncovered by comparing various levels of approximation. The theory remains perturbative in the entire conformal window, with vacuum stability dictating the tightest constraints. We also speculate about a secondary conformal window at strong coupling and estimate its lower limit. Implications for model building and cosmology are indicated.
Quantum defect theory and asymptotic methods
International Nuclear Information System (INIS)
Seaton, M.J.
1982-01-01
It is shown that quantum defect theory provides a basis for the development of various analytical methods for the examination of electron-ion collision phenomena, including di-electronic recombination. Its use in conjuction with ab initio calculations is shown to be restricted by problems which arise from the presence of long-range non-Coulomb potentials. Empirical fitting to some formulae can be efficient in the use of computer time but extravagant in the use of person time. Calculations at a large number of energy points which make no use of analytical formulae for resonance structures may be made less extravagant in computer time by the development of more efficient asymptotic methods. (U.K.)
Traversable asymptotically flat wormholes in Rastall gravity
Moradpour, H.; Sadeghnezhad, N.; Hendi, S. H.
2017-12-01
There are some gravitational theories in which the ordinary energy-momentum conservation law is not valid in the curved spacetime. Rastall gravity is one of the known theories in this regard which includes a non-minimal coupling between geometry and matter fields. Equipped with the basis of such theory, we study the properties of traversable wormholes with flat asymptotes. We investigate the possibility of exact solutions by a source with the baryonic matter state parameter. Our survey indicates that Rastall theory has considerable effects on the wormhole characteristics. In addition, we study various case studies and show that the weak energy condition may be met for some solutions. We also give a discussion regarding to traversability of such wormhole geometry with phantom sources.
Asymptotic freedom in the BV formalism
Elliott, Chris; Williams, Brian; Yoo, Philsang
2018-01-01
We define the β-function of a perturbative quantum field theory in the mathematical framework introduced by Costello - combining perturbative renormalization and the BV formalism - as the cohomology class of a certain functional measuring scale dependence of the effective interaction. We show that the one-loop β-function is a well-defined element of the obstruction-deformation complex for translation-invariant and classically scale-invariant theories, and furthermore that it is locally constant as a function on the space of classical interactions and computable as a rescaling anomaly, or as the logarithmic one-loop counterterm. We compute the one-loop β-function in first-order Yang-Mills theory, recovering the famous asymptotic freedom for Yang-Mills in a mathematical context.
Asymptotic stability of steady compressible fluids
Padula, Mariarosaria
2011-01-01
This volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids. It is intended for a wide audience of theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory. The focus is particularly on recent results concerning nonlinear asymptotic stability, which are independent of assumptions about the smallness of the initial data. Of particular interest is the loss of control that sometimes results when steady flows of compressible fluids are upset by large disturbances. The main ideas are illustrated in the context of three different physical problems: (i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous. (ii) An isothermal viscous gas in a domain with free boundaries. (iii) A h...
Asymptotic methods in mechanics of solids
Bauer, Svetlana M; Smirnov, Andrei L; Tovstik, Petr E; Vaillancourt, Rémi
2015-01-01
The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russi...
Asymptotic representation of relaxation oscillations in lasers
Grigorieva, Elena V
2017-01-01
In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.
Methods in half-linear asymptotic theory
Directory of Open Access Journals (Sweden)
Pavel Rehak
2016-10-01
Full Text Available We study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation $$ (r(t|y'|^{\\alpha-1}\\hbox{sgn} y''=p(t|y|^{\\alpha-1}\\hbox{sgn} y, $$ where r(t and p(t are positive continuous functions on $[a,\\infty$, $\\alpha\\in(1,\\infty$. The aim of this article is twofold. On the one hand, we show applications of a wide variety of tools, like the Karamata theory of regular variation, the de Haan theory, the Riccati technique, comparison theorems, the reciprocity principle, a certain transformation of dependent variable, and principal solutions. On the other hand, we solve open problems posed in the literature and generalize existing results. Most of our observations are new also in the linear case.
Asymptotic theory of weakly dependent random processes
Rio, Emmanuel
2017-01-01
Presenting tools to aid understanding of asymptotic theory and weakly dependent processes, this book is devoted to inequalities and limit theorems for sequences of random variables that are strongly mixing in the sense of Rosenblatt, or absolutely regular. The first chapter introduces covariance inequalities under strong mixing or absolute regularity. These covariance inequalities are applied in Chapters 2, 3 and 4 to moment inequalities, rates of convergence in the strong law, and central limit theorems. Chapter 5 concerns coupling. In Chapter 6 new deviation inequalities and new moment inequalities for partial sums via the coupling lemmas of Chapter 5 are derived and applied to the bounded law of the iterated logarithm. Chapters 7 and 8 deal with the theory of empirical processes under weak dependence. Lastly, Chapter 9 describes links between ergodicity, return times and rates of mixing in the case of irreducible Markov chains. Each chapter ends with a set of exercises. The book is an updated and extended ...
The asymptotic complexity of merging networks
DEFF Research Database (Denmark)
Miltersen, Peter Bro; Paterson, Mike; Tarui, Jun
1996-01-01
Let M(m,n) be the minimum number of comparatorsneeded in a comparator network that merges m elements x1≤x2≤&cdots;≤xm and n elements y1≤y2≤&cdots;≤yn , where n≥m . Batcher's odd-even merge yields the following upper bound: Mm,n≤1 2m+nlog 2m+on; in particular, Mn,n≤nlog 2n+On. We prove the following...... lower bound that matches the upper bound above asymptotically as n≥m→∞: Mm,n≥1 2m+nlog 2m-Om; in particular, Mn,n≥nlog 2n-On. Our proof technique extends to give similarily tight lower bounds for the size of monotone Boolean circuits for merging, and for the size of switching networks capable...... of realizing the set of permutations that arise from merging....
Group symmetries and information propagation
International Nuclear Information System (INIS)
Draayer, J.P.
1980-01-01
Spectroscopy concerns itself with the ways in which the Hamiltonian and other interesting operators defined in few-particle spaces are determined or determine properties of many-particle systems. But the action of the central limit theorem (CLT) filters the transmission of information between source and observed so whether propagating forward from a few-particle defining space, as is usual in theoretical studies, or projecting backward to it from measured things, each is only sensitive to averaged properties of the other. Our concern is with the propagation of spectroscopic information in the presence of good symmetries when filtering action of the CLT is effective. Specifically, we propose to address the question, What propagates and how. We begin with some examples, using both scalar and isospin geometries to illustrate simple propagation. Examples of matrix propagation are studied; contact with standard tensor algebra is established and an algorithm put forward for the expansion of any operator in terms of another set, complete or not; shell-model results for 20 Ne using a realistic interaction and two trace-equivalent forms are presented; and some further challenges are mentioned
Nuclear symmetries at low isospin
International Nuclear Information System (INIS)
Juillet, Olivier
1999-01-01
With the development of radioactive beams, an area of intense research in nuclear physics concerns the structure of exotic systems with roughly equal numbers of protons and neutrons. These nuclei might in fact develop a proton-neutron superfluidity whose importance compared to pairing correlations between like nucleons is currently investigated. The work presented in this thesis suggests to look at such a competition in an algebraic framework based on a Wigner SU(4) symmetry that combines the pseudo-spin and isospin degrees of freedom. After a detailed review of group theory in quantum mechanics, the validity of the pseudo-SU(4) classification is shown via a direct analysis of realistic shell model states. Its consequences on binding energies and β decay are also studied. Moreover, a simplified boson realisation with zero orbital angular momentum is used to find some physical features of N=Z nuclei such as the condensation of α-like structures or the destruction of isoscalar superfluid correlations by the spin-orbit potential. Finally, another bosonization scheme that includes quadrupole degrees of freedom (IBM-4 model) is tested for the first time by diagonalization of a full Hamiltonian deduced from a realistic shell model interaction. The quality of the results, especially for odd-odd nuclei, allows one to consider this boson approximation as an alternative to standard fermionic approaches for the collective structure of the exotic line N∼Z=28-50. (author) [fr
Symmetry-breaking instability in a prototypical driven granular gas.
Khain, Evgeniy; Meerson, Baruch
2002-08-01
Symmetry-breaking instability of a laterally uniform granular cluster (strip state) in a prototypical driven granular gas is investigated. The system consists of smooth hard disks in a two-dimensional box, colliding inelastically with each other and driven, at zero gravity, by a "thermal" wall. The limit of nearly elastic particle collisions is considered, and granular hydrodynamics with the Jenkins-Richman constitutive relations is employed. The hydrodynamic problem is completely described by two scaled parameters and the aspect ratio of the box. Marginal stability analysis predicts a spontaneous symmetry-breaking instability of the strip state, similar to that predicted recently for a different set of constitutive relations. If the system is big enough, the marginal stability curve becomes independent of the details of the boundary condition at the driving wall. In this regime, the density perturbation is exponentially localized at the elastic wall opposite the thermal wall. The short- and long-wavelength asymptotics of the marginal stability curves are obtained analytically in the dilute limit. The physics of the symmetry-breaking instability is discussed.
Symmetry facilitates shape constancy for smoothly curved 3D objects.
Lee, Young Lim; Saunders, Jeffrey A
2013-08-01
We tested whether the presence of symmetry improves shape discrimination across changes in viewpoint and lighting for smoothly curved 3D objects. We constructed symmetric and asymmetric versions of random 3D shapes by manipulating their spherical harmonic representations. Matched objects had the same power spectra and appear highly similar except for the presence of symmetry. Observers discriminated sequentially presented pairs of either symmetric or asymmetric objects. Objects were presented in conditions that provided different 3D cues: shading only, stereo only, and combined shading and stereo. To control for 2D cues, standard and test objects had matched boundary contours and were rendered with different light sources. Test objects were also rotated in depth by variable amounts (0° to 60°). Across all viewpoint and 3D cue conditions, we found that shape discrimination for symmetric objects was better than for asymmetric objects. The symmetry benefit was not limited to monocular viewing or to conditions with large rotations in depth. In a second experiment, we blocked trials by viewpoint rotation to eliminate uncertainty in object orientation. This improved performance for asymmetric objects relative to symmetric objects, suggesting that symmetry contributes by providing a cue to object orientation. However, a symmetry advantage was still observed in all shape cue conditions, so this was not the sole source of benefit. Our results demonstrate that symmetry improves shape constancy for smooth 3D objects and suggest that one role of symmetry is to provide a reference orientation for an object. 2013 APA, all rights reserved
Asymptotic Sampling for Reliability Analysis of Adhesive Bonded Stepped Lap Composite Joints
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Lund, Erik; Thomsen, Ole Thybo
2013-01-01
Reliability analysis coupled with finite element analysis (FEA) of composite structures is computationally very demanding and requires a large number of simulations to achieve an accurate prediction of the probability of failure with a small standard error. In this paper Asymptotic Sampling, which....... Three dimensional (3D) FEA is used for the structural analysis together with a design equation that is associated with a deterministic code-based design equation where reliability is secured by partial safety factors. The Tsai-Wu and the maximum principal stress failure criteria are used to predict...... failure in the composite and adhesive layers, respectively, and the results are compared with the target reliability level implicitly used in the wind turbine standard IEC 61400-1. The accuracy and efficiency of Asymptotic Sampling is investigated by comparing the results with predictions obtained using...
Energy Technology Data Exchange (ETDEWEB)
Peskin, M.E. [Stanford Univ., CA (United States)
1994-12-01
When the strong interactions were a mystery, spin seemed to be just a complication on top of an already puzzling set of phenomena. But now that particle physicists have understood the strong, weak, and electromagnetic interactions, to be gauge theories, with matter built of quarks and leptons, it is recognized that the special properties of spin 1/2 and spin 1 particles have taken central role in the understanding of Nature. The lectures in this summer school will be devoted to the use of spin in unravelling detailed questions about the fundamental interactions. Thus, why not begin by posing a deeper question: Why is there spin? More precisely, why do the basic pointlike constituents of Nature carry intrinsic nonzero quanta of angular momentum? Though the authos has found no definite answer to this question, the pursuit of an answer has led through a wonderful tangle of speculations on the deep structure of Nature. Is spin constructed or is it fundamental? Is it the requirement of symmetry? In the furthest flights taken, it seems that space-time itself is too restrictive a notion, and that this must be generalized in order to gain a full appreciation of spin. In any case, there is no doubt that spin must play a central role in unlocking the mysteries of fundamental physics.
Gravitation and Gauge Symmetries
Stewart, J
2002-01-01
The purpose of this book (I quote verbatim from the back cover) is to 'shed light upon the intrinsic structure of gravity and the principle of gauge invariance, which may lead to a consistent unified field theory', a very laudable aim. The content divides fairly clearly into four sections (and origins). After a brief introduction, chapters 2-6 review the 'Structure of gravity as a theory based on spacetime gauge symmetries'. This is fairly straightforward material, apparently based on a one-semester graduate course taught at the University of Belgrade for about two decades, and, by implication, this is a reasonably accurate description of its level and assumed knowledge. There follow two chapters of new material entitled 'Gravity in flat spacetime' and 'Nonlinear effects in gravity'. The final three chapters, entitled 'Supersymmetry and supergravity', 'Kaluza-Klein theory' and 'String theory' have been used for the basis of a one-semester graduate course on the unification of fundamental interactions. The boo...
Segmentation Using Symmetry Deviation
DEFF Research Database (Denmark)
Hollensen, Christian; Højgaard, L.; Specht, L.
2011-01-01
and evaluate the method. The method uses deformable registration on computed tomography(CT) to find anatomical symmetry deviations of Head & Neck squamous cell carcinoma and combining it with positron emission tomography (PET) images. The method allows the use anatomical and symmetrical information of CT scans...... segmentations on manual contours was evaluated using concordance index and sensitivity for the hypopharyngeal patients. The resulting concordance index and sensitivity was compared with the result of using a threshold of 3 SUV using a paired t-test. Results: The anatomical and symmetrical atlas was constructed...... and sensitivity of respectively 0.43±0.15 and 0.56±0.18 was acquired. It was compared to the concordance index of segmentation using absolute threshold of 3 SUV giving respectively 0.41±0.16 and 0.51±0.19 for concordance index and sensitivity yielding p-values of 0.33 and 0.01 for a paired t-test respectively....
International Nuclear Information System (INIS)
Peskin, M.E.
1994-01-01
When the strong interactions were a mystery, spin seemed to be just a complication on top of an already puzzling set of phenomena. But now that particle physicists have understood the strong, weak, and electromagnetic interactions, to be gauge theories, with matter built of quarks and leptons, it is recognized that the special properties of spin 1/2 and spin 1 particles have taken central role in the understanding of Nature. The lectures in this summer school will be devoted to the use of spin in unravelling detailed questions about the fundamental interactions. Thus, why not begin by posing a deeper question: Why is there spin? More precisely, why do the basic pointlike constituents of Nature carry intrinsic nonzero quanta of angular momentum? Though the authos has found no definite answer to this question, the pursuit of an answer has led through a wonderful tangle of speculations on the deep structure of Nature. Is spin constructed or is it fundamental? Is it the requirement of symmetry? In the furthest flights taken, it seems that space-time itself is too restrictive a notion, and that this must be generalized in order to gain a full appreciation of spin. In any case, there is no doubt that spin must play a central role in unlocking the mysteries of fundamental physics
Symmetries in nuclear structure
Allaart, K; Dieperink, A
1983-01-01
The 1982 summer school on nuclear physics, organized by the Nuclear Physics Division of the Netherlands' Physical Society, was the fifth in a series that started in 1963. The number of students attending has always been about one hundred, coming from about thirty countries. The theme of this year's school was symmetry in nuclear physics. This book covers the material presented by the enthusi astic speakers, who were invited to lecture on this subject. We think they have succeeded in presenting us with clear and thorough introductory talks at graduate or higher level. The time schedule of the school and the location allowed the participants to make many informal contacts during many social activities, ranging from billiards to surf board sailing. We hope and expect that the combination of a relaxed atmosphere during part of the time and hard work during most of the time, has furthered the interest in, and understanding of, nuclear physics. The organization of the summer school was made possible by substantia...
Quark diquark symmetry breaking
International Nuclear Information System (INIS)
Souza, M.M. de
1980-01-01
Assuming the baryons are made of quark-diquark pairs, the wave functions for the 126 allowed ground states are written. The quark creation and annihilations operators are generalized to describe the quark-diquark structure in terms of a parameter σ. Assuming that all quark-quark interactions are mediated by gluons transforming like an octet of vector mesons, the effective Hamiltonian and the baryon masses as constraint equations for the elements of the mass matrix is written. The symmetry is the SU(6) sub(quark)x SU(21) sub(diquark) broken by quark-quark interactions respectively invariant under U(6), U(2) sub(spin), U(3) and also interactions transforming like the eighth and the third components of SU(3). In the limit of no quark-diquark structure (σ = 0), the ground state masses is titted to within 1% of the experimental data, except for the Δ(1232), where the error is almost 2%. Expanding the decuplet mass equations in terms of σ and keeping terms only up to the second order, this error is reduced to 67%. (Author) [pt
Boonstra, Harm Jan Hugo
1996-01-01
The physics of elementary particles is currently described in terms of a very successful theory called the standard model. It describes all known elementary particles and their interactions except gravitational interactions. The standard model accommodates the quarks and the leptons which are the
Error estimates in horocycle averages asymptotics: challenges from string theory
Cardella, M.A.
2010-01-01
For modular functions of rapid decay, a classical result connects the error estimate in their long horocycle average asymptotic to the Riemann hypothesis. We study similar asymptotics, for modular functions with not that mild growing conditions, such as of polynomial growth and of exponential growth
An asymptotic solution of large-N QCD
Directory of Open Access Journals (Sweden)
Bochicchio Marco
2014-01-01
Full Text Available We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-N QCD, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic S-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic S-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the LS Z reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-N QCD, and in particular on any string solution.
Asymptotic Theory for Regressions with Smoothly Changing Parameters
DEFF Research Database (Denmark)
Hillebrand, Eric Tobias; Medeiros, Marcelo C.; Xu, Junyue
We derive asymptotic properties of the quasi maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual square-root-of-T ra...
Asymptotic theory for regressions with smoothly changing parameters
DEFF Research Database (Denmark)
Hillebrand, Eric; Medeiros, Marcelo; Xu, Junyue
2013-01-01
We derive asymptotic properties of the quasi maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual pT-rate and has an ...
Asymptotic functions and their application in quantum theory
International Nuclear Information System (INIS)
Khristov, Kh.Ya.; Damyanov, B.P.
1979-01-01
An asymptotic function introduced as a limit for a certain class of successions has been determined. The basic properties of the functions are given: continuity, differentiability, integrability. The fields of application of the asymptotic functions in the quantum field theory are presented. The shortcomings and potentialities of further development of the theory are enumerated
An efficient locally asymptotic parametric test in nonlinear ...
African Journals Online (AJOL)
Abstract. In this paper we deal with a locally asymptotic stringent test for a general class of nonlinear time series heteroscedastic models. Based on the local asymptotic normality (LAN) property of these models, we propose a scoretyp test statistic for testing hypotheses on the parameters appearing in the mean and variance ...
Some asymptotic properties of functions holomorphic in tubular domains
International Nuclear Information System (INIS)
Zavialov, B.I.
1988-10-01
For the function holomorphic in curved tubular domain the connection between asymptotic behaviour of real part of its boundary value at a given point of base manifold and asymptotic behaviour of the whole function from the inside of this domain is studied. (author). 3 refs
Asymptotic representation theorems for poverty indices | Lo | Afrika ...
African Journals Online (AJOL)
Abstract. We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotic of the bulk of poverty indices and issues in poverty ...
Asymptotic analysis, Working Note No. 1: Basic concepts and definitions
Energy Technology Data Exchange (ETDEWEB)
Garbey, M. [Universite Claude Bernard Lyon 1, 69 - Villeurbanne (France). Lab. d`Analyse Numerique; Kaper, H.G. [Argonne National Lab., IL (United States)
1993-07-01
In this note we introduce the basic concepts of asymptotic analysis. After some comments of historical interest we begin by defining the order relations O, o, and O{sup {number_sign}}, which enable us to compare the asymptotic behavior of functions of a small positive parameter {epsilon} as {epsilon} {down_arrow} 0. Next, we introduce order functions, asymptotic sequences of order functions and more general gauge sets of order functions and define the concepts of an asymptotic approximation and an asymptotic expansion with respect to a given gauge set. This string of definitions culminates in the introduction of the concept of a regular asymptotic expansion, also known as a Poincare expansion, of a function f : (0, {epsilon}{sub o}) {yields} X, where X is a normed vector space of functions defined on a domain D {epsilon} R{sup N}. We conclude the note with the asymptotic analysis of an initial value problem whose solution is obtained in the form of a regular asymptotic expansion.
Asymptotic expansions for high-contrast linear elasticity
Poveda, Leonardo A.
2015-03-01
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.
Asymptotic Con dence Bands for Density and Regression Functions ...
African Journals Online (AJOL)
Abstract. In this paper, we obtain asymptotic confidence bands for both the density and regression functions in the framework of nonparametric estimation. Beforehand, the asymptotic behaviors in probability of the kernel estimator of the density and the Nadaraya-Watson estimator of the regression function are described ...
Asymptotic time dependent neutron transport in multidimensional systems
International Nuclear Information System (INIS)
Nagy, M.E.; Sawan, M.E.; Wassef, W.A.; El-Gueraly, L.A.
1983-01-01
A model which predicts the asymptotic time behavior of the neutron distribution in multi-dimensional systems is presented. The model is based on the kernel factorization method used for stationary neutron transport in a rectangular parallelepiped. The accuracy of diffusion theory in predicting the asymptotic time dependence is assessed. The use of neutron pulse experiments for predicting the diffusion parameters is also investigated
Scale symmetry and virial theorem
International Nuclear Information System (INIS)
Westenholz, C. von
1978-01-01
Scale symmetry (or dilatation invariance) is discussed in terms of Noether's Theorem expressed in terms of a symmetry group action on phase space endowed with a symplectic structure. The conventional conceptual approach expressing invariance of some Hamiltonian under scale transformations is re-expressed in alternate form by infinitesimal automorphisms of the given symplectic structure. That is, the vector field representing scale transformations leaves the symplectic structure invariant. In this model, the conserved quantity or constant of motion related to scale symmetry is the virial. It is shown that the conventional virial theorem can be derived within this framework
Nonlinear electromagnetic fields and symmetries
Barjašić, Irena; Gulin, Luka; Smolić, Ivica
2017-06-01
We extend the classical results on the symmetry inheritance of the canonical electromagnetic fields, described by the Maxwell's Lagrangian, to a much wider class of models, which include those of the Born-Infeld, power Maxwell and the Euler-Heisenberg type. Symmetry inheriting fields allow the introduction of electromagnetic scalar potentials and these are proven to be constant on the Killing horizons. Finally, using the relations obtained along the analysis, we generalize and simplify the recent proof for the symmetry inheritance of the 3-dimensional case, as well as give the first constraint for the higher dimensional electromagnetic fields.
International Nuclear Information System (INIS)
Pan Qiyuan; Jing Jiliang
2008-01-01
The effect of the Hawking temperature on the entanglement and teleportation for the scalar field in a most general, static, and asymptotically flat black hole with spherical symmetry has been investigated. It has been shown that the same 'initial entanglement' for the state parameter α and its 'normalized partners'√(1-α 2 ) will be degraded by the Hawking effect with increasing Hawking temperature along two different trajectories except for the maximally entangled state. In the infinite Hawking temperature limit, corresponding to the case of the black hole evaporating completely, the state no longer has distillable entanglement for any α. It is interesting to note that the mutual information in this limit is equal to just half of the 'initially mutual information'. It has also been demonstrated that the fidelity of teleportation decreases as the Hawking temperature increases, which indicates the degradation of entanglement.
Supersymmetry and intermediate symmetry breaking in SO(10) superunification
International Nuclear Information System (INIS)
Asatryan, H.M.; Ioannisyan, A.N.
1985-01-01
A scheme of simultaneous breakdown of intermediate symmetry SO(10) → SU(3)sub(c) x U(1) x SU(2)sub(L) x SU(2)sub(R) and supersymmetry by means of a single scale parameter is suggested. This intermediate symmetry, which is preferable physically, owing to the broken supersymmetry has a minimum lying lower than SU(4) x SU(2)sub(L) x SU(2)sub(R). The intermediate symmetry is broken by the vacuum expectation value of the Higgs superfields. Owing to the quantum corrections the potential minimum turns out to correspond to breakdown of the intermediate symmetry up to the standard group SU(3)sub(c) x SU(2)sub(L) x U(1)sub(y). The value of the Weinberg angle is less than that in the supersymmetric SU(5) model and agrees with the experiment
Origin of constrained maximal CP violation in flavor symmetry
He, Hong-Jian; Rodejohann, Werner; Xu, Xun-Jie
2015-12-01
Current data from neutrino oscillation experiments are in good agreement with δ = -π/2 and θ23 =π/4 under the standard parametrization of the mixing matrix. We define the notion of ;constrained maximal CP violation; (CMCPV) for predicting these features and study their origin in flavor symmetry. We derive the parametrization-independent solution of CMCPV and give a set of equivalent definitions for it. We further present a theorem on how the CMCPV can be realized. This theorem takes the advantage of residual symmetries in neutrino and charged lepton mass matrices, and states that, up to a few minor exceptions, (| δ | ,θ23) = (π/2 ,π/4) is generated when those symmetries are real. The often considered μ- τ reflection symmetry, as well as specific discrete subgroups of O(3), is a special case of our theorem.
Preheating in an asymptotically safe quantum field theory
DEFF Research Database (Denmark)
Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-01-01
We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J...... fluctuations induced by the parametrically amplified entropy modes do not exceed the upper observational bounds puts a lower bound on the number of fields which the model followed in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F....... Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J. High Energy Phys. 01 (2016) 081] must contain. This bound also depends on the total number of e-foldings of the inflationary phase....
Exceeding the Asymptotic Limit of Polymer Drag Reduction
Choueiri, George H.; Lopez, Jose M.; Hof, Björn
2018-03-01
The drag of turbulent flows can be drastically decreased by adding small amounts of high molecular weight polymers. While drag reduction initially increases with polymer concentration, it eventually saturates to what is known as the maximum drag reduction (MDR) asymptote; this asymptote is generally attributed to the dynamics being reduced to a marginal yet persistent state of subdued turbulent motion. Contrary to this accepted view, we show that, for an appropriate choice of parameters, polymers can reduce the drag beyond the suggested asymptotic limit, eliminating turbulence and giving way to laminar flow. At higher polymer concentrations, however, the laminar state becomes unstable, resulting in a fluctuating flow with the characteristic drag of the MDR asymptote. Our findings indicate that the asymptotic state is hence dynamically disconnected from ordinary turbulence.
Strings, Branes and Symmetries
International Nuclear Information System (INIS)
Westerberg, A.
1997-01-01
Recent dramatic progress in the understanding of the non-perturbative structure of superstring theory shows that extended objects of various kinds, collectively referred to as p-branes, are an integral part of the theory. In this thesis, comprising an introductory text and seven appended research papers, we study various aspects of p-branes with relevance for superstring theory. The first part of the introductory text is a brief review of string theory focussing on the role of p-branes. In particular, we consider the so-called D-branes which currently are attracting a considerable amount of attention. The purpose of this part is mainly to put into context the results of paper 4, 5 and 6 concerning action functionals describing the low-energy dynamics of D-branes. The discussion of perturbative string theory given in this part of the introduction is also intended to provide some background to paper 2 which contains an application of the Reggeon-sewing approach to the construction of string vertices. The second part covers a rather different subject, namely higher-dimensional loop algebras and their cohomology, with the aim of facilitating the reading of papers 1, 3 and 7. The relation to p-branes is to be found in paper 1 where we introduce a certain higher-dimensional generalization of the loop algebra and discuss its potential applicability as a symmetry algebra for p-branes. Papers 3 and 7 are mathematically oriented out-growths of this paper addressing the issue of realizing algebras of this kind, known in physics as current algebras, in terms of pseudo differential operators (PSDOs). The main result of paper 3 is a proof of the equivalence between certain Lie-algebra cocycles on the space of second-quantizable PSDOs
The high energy asymptotic behavior of line shape cross sections and detailed balance
International Nuclear Information System (INIS)
Although line shape relaxation cross sections in the ''impact approximation'' do not obey detailed balance except in the very high temperature limit, they can be shown, in the Born approximation, to satisfy a somewhat similar asymptotic relation. In this empiric relation, first observed by Boissoles et al. [J. Chem. Phys. 90, 5392 (1989)], the complex conjugate of the cross section for the radiative transition if→i'f' is asymptotically equal to the cross section for the inverse transition i'f'→if. It is then shown that although cross sections calculated with the presumably more correct Fano collision operator also obey this relation, due to time reversal symmetry they also obey detailed balance. These two observations taken together imply that the imaginary part of line shape relaxation cross sections in the more exact theory decay much more rapidly with energy than the real parts and suggest a quick fix for relaxation cross sections calculated in the ''impact approximation,'' or as it is sometimes called, the Shafer--Gordon formalism. Numerical calculations of inelastic off-the-energy shell scattering of simple rigid spherelike models support these results and suggest that off-the-energy shell calculations with realistic models are not only desirable but also necessary for computing line shapes of partially overlapping lines
Symmetries in the Lagrangean formalism
International Nuclear Information System (INIS)
Grigore, D.R.
1987-09-01
We generalize the analysis of Levy-Leblond for lagrangean systems with symmetry. We prove that this analysis goes through practically unchanged and after that we analyse in detail some examples.(author)
Renormgroup symmetry for solution functionals
International Nuclear Information System (INIS)
Shirkov, D.V.; Kovalev, V.F.
2004-01-01
The paper contains generalization of the renormgroup algorithm for boundary value problems of mathematical physics and related concept of the renormgroup symmetry, formulated earlier by the authors with reference to models based on differential equations. These algorithm and symmetry are formulated now for models with nonlocal (integral) equations. We discuss in detail and illustrate by examples the applications of the generalized algorithm to models with nonlocal terms which appear as linear functionals of the solution. (author)
Asymptotic Behaviour of the QED Perturbation Series
Directory of Open Access Journals (Sweden)
Idrish Huet
2017-01-01
Full Text Available I will summarize the present state of a long-term effort to obtain information on the large-order asymptotic behaviour of the QED perturbation series through the effective action. Starting with the constant-field case, I will discuss the Euler-Heisenberg Lagrangian in various dimensions and up to the three-loop level. This Lagrangian holds the information on the N-photon amplitudes in the low-energy limit, and combining it with Spinor helicity methods explicit all-N results can be obtained at the one-loop and, for the “all +” amplitudes, also at the two-loop level. For the imaginary part of the Euler-Heisenberg Lagrangian, an all-loop formula has been conjectured independently by Affleck, Alvarez, and Manton for Scalar QED and by Lebedev and Ritus for Spinor QED. This formula can be related through a Borel dispersion relation to the leading large-N behaviour of the N-photon amplitudes. It is analytic in the fine structure constant, which is puzzling and suggests a diagrammatic investigation of the large-N limit in perturbation theory. Preliminary results of such a study for the 1+1 dimensional case throw doubt on the validity of the conjecture.
Asymptotically free theory with scale invariant thermodynamics
Ferrari, Gabriel N.; Kneur, Jean-Loïc; Pinto, Marcus Benghi; Ramos, Rudnei O.
2017-12-01
A recently developed variational resummation technique, incorporating renormalization group properties consistently, has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework of approximations such as in the hard-thermal-loop resummed perturbation theory. This method is used in the present work to evaluate thermodynamical quantities within the two-dimensional nonlinear sigma model, which, apart from providing a technically simpler testing ground, shares some common features with Yang-Mills theories, like asymptotic freedom, trace anomaly and the nonperturbative generation of a mass gap. The present application confirms that nonperturbative results can be readily generated solely by considering the lowest-order (quasiparticle) contribution to the thermodynamic effective potential, when this quantity is required to be renormalization group invariant. We also show that when the next-to-leading correction from the method is accounted for, the results indicate convergence, apart from optimally preserving, within the approximations here considered, the sought-after scale invariance.
Asymptotic Solutions of Serial Radial Fuel Shuffling
Directory of Open Access Journals (Sweden)
Xue-Nong Chen
2015-12-01
Full Text Available In this paper, the mechanism of traveling wave reactors (TWRs is investigated from the mathematical physics point of view, in which a stationary fission wave is formed by radial fuel drifting. A two dimensional cylindrically symmetric core is considered and the fuel is assumed to drift radially according to a continuous fuel shuffling scheme. A one-group diffusion equation with burn-up dependent macroscopic coefficients is set up. The burn-up dependent macroscopic coefficients were assumed to be known as functions of neutron fluence. By introducing the effective multiplication factor keff, a nonlinear eigenvalue problem is formulated. The 1-D stationary cylindrical coordinate problem can be solved successively by analytical and numerical integrations for associated eigenvalues keff. Two representative 1-D examples are shown for inward and outward fuel drifting motions, respectively. The inward fuel drifting has a higher keff than the outward one. The 2-D eigenvalue problem has to be solved by a more complicated method, namely a pseudo time stepping iteration scheme. Its 2-D asymptotic solutions are obtained together with certain eigenvalues keff for several fuel inward drifting speeds. Distributions of the neutron flux, the neutron fluence, the infinity multiplication factor kinf and the normalized power are presented for two different drifting speeds.
Qualitative and Asymptotic Theory of Detonations
Faria, Luiz
2014-11-09
Shock waves in reactive media possess very rich dynamics: from formation of cells in multiple dimensions to oscillating shock fronts in one-dimension. Because of the extreme complexity of the equations of combustion theory, most of the current understanding of unstable detonation waves relies on extensive numerical simulations of the reactive compressible Euler/Navier-Stokes equations. Attempts at a simplified theory have been made in the past, most of which are very successful in describing steady detonation waves. In this work we focus on obtaining simplified theories capable of capturing not only the steady, but also the unsteady behavior of detonation waves. The first part of this thesis is focused on qualitative theories of detonation, where ad hoc models are proposed and analyzed. We show that equations as simple as a forced Burgers equation can capture most of the complex phenomena observed in detonations. In the second part of this thesis we focus on rational theories, and derive a weakly nonlinear model of multi-dimensional detonations. We also show, by analysis and numerical simulations, that the asymptotic equations provide good quantitative predictions.
Electroweak Symmetry Breaking (1/3)
CERN. Geneva
2012-01-01
The focus of the lectures will be on the role of the Higgs boson in the mechanism of electroweak symmetry breaking, both in the Standard Model and in models of New Physics. In particular, I will discuss how a determination of its couplings to matter and gauge fields can give important information on the nature and origin of the Higgs boson. I will thus review the picture on Higgs couplings implied by the current experimental data and examine further interesting processes that can be measured in the future.
Electroweak Symmetry Breaking (2/3)
CERN. Geneva
2012-01-01
The focus of the lectures will be on the role of the Higgs boson in the mechanism of electroweak symmetry breaking, both in the Standard Model and in models of New Physics. In particular, I will discuss how a determination of its couplings to matter and gauge fields can give important information on the nature and origin of the Higgs boson. I will thus review the picture on Higgs couplings implied by the current experimental data and examine further interesting processes that can be measured in the future.
Electroweak Symmetry Breaking (3/3)
CERN. Geneva
2012-01-01
The focus of the lectures will be on the role of the Higgs boson in the mechanism of electroweak symmetry breaking, both in the Standard Model and in models of New Physics. In particular, I will discuss how a determination of its couplings to matter and gauge fields can give important information on the nature and origin of the Higgs boson. I will thus review the picture on Higgs couplings implied by the current experimental data and examine further interesting processes that can be measured in the future.
Gedanken Worlds without Higgs: QCD-Induced Electroweak Symmetry Breaking
Energy Technology Data Exchange (ETDEWEB)
Quigg, Chris; /Fermilab /Karlsruhe U., TTP; Shrock, Robert; /YITP, Stony Brook
2009-01-01
To illuminate how electroweak symmetry breaking shapes the physical world, we investigate toy models in which no Higgs fields or other constructs are introduced to induce spontaneous symmetry breaking. Two models incorporate the standard SU(3){sub c} {circle_times} SU(2){sub L} {circle_times} U(1){sub Y} gauge symmetry and fermion content similar to that of the standard model. The first class--like the standard electroweak theory--contains no bare mass terms, so the spontaneous breaking of chiral symmetry within quantum chromodynamics is the only source of electroweak symmetry breaking. The second class adds bare fermion masses sufficiently small that QCD remains the dominant source of electroweak symmetry breaking and the model can serve as a well-behaved low-energy effective field theory to energies somewhat above the hadronic scale. A third class of models is based on the left-right-symmetric SU(3){sub c} {circle_times} SU(2){sub L} {circle_times} SU(2){sub R} {circle_times} U(1)B?L gauge group. In a fourth class of models, built on SU(4){sub PS} {circle_times} SU(2){sub L} {circle_times} SU(2){sub R} gauge symmetry, lepton number is treated as a fourth color. Many interesting characteristics of the models stem from the fact that the effective strength of the weak interactions is much closer to that of the residual strong interactions than in the real world. The Higgs-free models not only provide informative contrasts to the real world, but also lead us to consider intriguing issues in the application of field theory to the real world.
A (critical) overview of electroweak symmetry breaking
International Nuclear Information System (INIS)
Csaki, Csaba
2010-01-01
This presentation discusses the following points: The standard Higgs, big vs. little hierarchy; Electroweak Symmetry Breaking in supersymmetry and little hierarchy of Minimal Supersymmetric Standard Model (MSSM): Buried Higgs, Bigger quartic (D-terms, Next-to-Minimal Supersymmetric Standard Model (NMSSM), fat Higgs,..); Strong dynamics and related models: Technicolor, Monopole condensate, Warped extra dimensions, Realistic RS, Higgs-less, Composite Higgs, Little Higgs. In summary, we do not understand how Higgs is light and still no trace of new physics. In Supersymmetry (SUSY) it calls for extension of MSSM. In strong dynamics models: electroweak penguin (EWP) usually issue (Warped extra dimension - composite Higgs, Higgs-less, Little Higgs, Technicolor, monopole condensation,..). None of them is fully convincing but LHC should settle these
Search for composite models with family gauge symmetries
International Nuclear Information System (INIS)
Zhou, B.R.; Huerta, R.
1985-01-01
We have analyzed a class of three-preon models based on a strategy expected to lead to family gauge symmetry SUsup(F)(n) and found that, in order to obey the assumption of asymptotic freedom and infrared confinement for the hypercolor group SUsub(H)(N), 't Hooft anomaly consistency conditions, especially the requirement of dynamical generation of quark-lepton masses by means of color condensates of exotic fermions, the only possible model is the three-fermion model with the hypercolor group SUsub(H)(4) and the family gauge group SUsup(F)(2). All the models considered which contain scalar-preons are excluded from being realistic models unless some new mechanism of quark-lepton mass generation is worked out. (orig.)
Symmetry analysis and conservation laws for a coupled (2 + 1)-dimensional hyperbolic system
Muatjetjeja, Ben; Khalique, Chaudry Masood
2015-05-01
This paper aims to perform Lie symmetry analysis and Noether symmetry classification of a coupled (2 + 1)-dimensional hyperbolic system. In the Lie analysis, the principal Lie algebra which is six dimensional extends in thirteen cases. It is further shown that four main cases arise in the Noether classification with respect to the standard Lagrangian. Moreover, conservation laws are established for the cases which admit Noether point symmetries.
Test of Pseudospin Symmetry in Deformed Nuclei
Ginocchio, J. N.; Leviatan, A.; Meng, J.; Zhou, Shan-Gui
2003-01-01
Pseudospin symmetry is a relativistic symmetry of the Dirac Hamiltonian with scalar and vector mean fields equal and opposite in sign. This symmetry imposes constraints on the Dirac eigenfunctions. We examine extensively the Dirac eigenfunctions of realistic relativistic mean field calculations of deformed nuclei to determine if these eigenfunctions satisfy these pseudospin symmetry constraints.
Symmetry and group theory in chemistry
Ladd, M
1998-01-01
A comprehensive discussion of group theory in the context of molecular and crystal symmetry, this book covers both point-group and space-group symmetries.Provides a comprehensive discussion of group theory in the context of molecular and crystal symmetryCovers both point-group and space-group symmetriesIncludes tutorial solutions
Test of pseudospin symmetry in deformed nuclei
International Nuclear Information System (INIS)
Ginocchio, J.N.; Leviatan, A.; Meng, J.; Zhou Shangui
2004-01-01
Pseudospin symmetry is a relativistic symmetry of the Dirac Hamiltonian with scalar and vector mean fields equal and opposite in sign. This symmetry imposes constraints on the Dirac eigenfunctions. We examine extensively the Dirac eigenfunctions of realistic relativistic mean field calculations of deformed nuclei to determine if these eigenfunctions satisfy these pseudospin symmetry constraints
Asymptotic Solution of the Theory of Shells Boundary Value Problem
Directory of Open Access Journals (Sweden)
I. V. Andrianov
2007-01-01
Full Text Available This paper provides a state-of-the-art review of asymptotic methods in the theory of plates and shells. Asymptotic methods of solving problems related to theory of plates and shells have been developed by many authors. The main features of our paper are: (i it is devoted to the fundamental principles of asymptotic approaches, and (ii it deals with both traditional approaches, and less widely used, new approaches. The authors have paid special attention to examples and discussion of results rather than to burying the ideas in formalism, notation, and technical details.
The asymptotic average-shadowing property and transitivity for flows
International Nuclear Information System (INIS)
Gu Rongbao
2009-01-01
The asymptotic average-shadowing property is introduced for flows and the relationships between this property and transitivity for flows are investigated. It is shown that a flow on a compact metric space is chain transitive if it has positively (or negatively) asymptotic average-shadowing property and a positively (resp. negatively) Lyapunov stable flow is positively (resp. negatively) topologically transitive provided it has positively (resp. negatively) asymptotic average-shadowing property. Furthermore, two conditions for which a flow is a minimal flow are obtained.
Asymptotic distribution of zeros of polynomials satisfying difference equations
Krasovsky, I. V.
2003-01-01
We propose a way to find the asymptotic distribution of zeros of orthogonal polynomials pn(x) satisfying a difference equation of the formB(x)pn(x+[delta])-C(x,n)pn(x)+D(x)pn(x-[delta])=0.We calculate the asymptotic distribution of zeros and asymptotics of extreme zeros of the Meixner and Meixner-Pollaczek polynomials. The distribution of zeros of Meixner polynomials shows some delicate features. We indicate the relation of our technique to the approach based on the Nevai-Dehesa-Ullman distribution.
Boundary asymptotics for a non-neutral electrochemistry model with small Debye length
Lee, Chiun-Chang; Ryham, Rolf J.
2018-04-01
This article addresses the boundary asymptotics of the electrostatic potential in non-neutral electrochemistry models with small Debye length in bounded domains. Under standard physical assumptions motivated by non-electroneutral phenomena in oxidation-reduction reactions, we show that the electrostatic potential asymptotically blows up at boundary points with respect to the bulk reference potential as the scaled Debye length tends to zero. The analysis gives a lower bound for the blow-up rate with respect to the model parameters. Moreover, the maximum potential difference over any compact subset of the physical domain vanishes exponentially in the zero-Debye-length limit. The results mathematically confirm the physical description that electrolyte solutions are electrically neutral in the bulk and are strongly electrically non-neutral near charged surfaces.
Asymptotically optimal data analysis for rejecting local realism
Energy Technology Data Exchange (ETDEWEB)
Zhang, Yanbao [Department of Physics, University of Colorado at Boulder, Boulder, Colorado 80309 (United States); Applied and Computational Mathematics Division, National Institute of Standards and Technology, Boulder, Colorado 80305 (United States); Glancy, Scott; Knill, Emanuel [Applied and Computational Mathematics Division, National Institute of Standards and Technology, Boulder, Colorado 80305 (United States)
2011-12-15
Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of quantum mechanics. One can quantify the violation witnessed by an experiment in terms of a statistical p value, which can be defined as the maximum probability according to local realism of a violation at least as high as that witnessed. Thus, high violation corresponds to small p value. We propose a prediction-based-ratio (PBR) analysis protocol whose p values are valid even if the prepared quantum state varies arbitrarily and local realistic models can depend on previous measurement settings and outcomes. It is therefore not subject to the memory loophole [J. Barrett et al., Phys. Rev. A 66, 042111 (2002)]. If the prepared state does not vary in time, the p values are asymptotically optimal. For comparison, we consider protocols derived from the number of standard deviations of violation of a Bell inequality and from martingale theory [R. Gill, e-print arXiv:quant-ph/0110137]. We find that the p values of the former can be too small and are therefore not statistically valid, while those derived from the latter are suboptimal. PBR p values do not require a predetermined Bell inequality and can be used to compare results from different tests of local realism independent of experimental details.
Asymptotic performance of regularized quadratic discriminant analysis based classifiers
Elkhalil, Khalil
2017-12-13
This paper carries out a large dimensional analysis of the standard regularized quadratic discriminant analysis (QDA) classifier designed on the assumption that data arise from a Gaussian mixture model. The analysis relies on fundamental results from random matrix theory (RMT) when both the number of features and the cardinality of the training data within each class grow large at the same pace. Under some mild assumptions, we show that the asymptotic classification error converges to a deterministic quantity that depends only on the covariances and means associated with each class as well as the problem dimensions. Such a result permits a better understanding of the performance of regularized QDA and can be used to determine the optimal regularization parameter that minimizes the misclassification error probability. Despite being valid only for Gaussian data, our theoretical findings are shown to yield a high accuracy in predicting the performances achieved with real data sets drawn from popular real data bases, thereby making an interesting connection between theory and practice.
Asymptotically optimal data analysis for rejecting local realism
International Nuclear Information System (INIS)
Zhang, Yanbao; Glancy, Scott; Knill, Emanuel
2011-01-01
Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of quantum mechanics. One can quantify the violation witnessed by an experiment in terms of a statistical p value, which can be defined as the maximum probability according to local realism of a violation at least as high as that witnessed. Thus, high violation corresponds to small p value. We propose a prediction-based-ratio (PBR) analysis protocol whose p values are valid even if the prepared quantum state varies arbitrarily and local realistic models can depend on previous measurement settings and outcomes. It is therefore not subject to the memory loophole [J. Barrett et al., Phys. Rev. A 66, 042111 (2002)]. If the prepared state does not vary in time, the p values are asymptotically optimal. For comparison, we consider protocols derived from the number of standard deviations of violation of a Bell inequality and from martingale theory [R. Gill, e-print arXiv:quant-ph/0110137]. We find that the p values of the former can be too small and are therefore not statistically valid, while those derived from the latter are suboptimal. PBR p values do not require a predetermined Bell inequality and can be used to compare results from different tests of local realism independent of experimental details.
Using MT2 to distinguish dark matter stabilization symmetries
International Nuclear Information System (INIS)
Agashe, Kaustubh; Kim, Doojin; Zhu Lijun; Walker, Devin G. E.
2011-01-01
We examine the potential of using colliders to distinguish models with parity (Z 2 ) stabilized dark matter (DM) from models in which the DM is stabilized by other symmetries, taking the latter to be a Z 3 symmetry for illustration. The key observation is that a heavier mother particle charged under a Z 3 stabilization symmetry can decay into one or two DM particles along with standard model particles. This can be contrasted with the decay of a mother particle charged under a parity symmetry; typically, only one DM particle appears in the decay chain. The arXiv:1003.0899 studied the distributions of visible invariant mass from the decay of a single such mother particle in order to highlight the resulting distinctive signatures of Z 3 symmetry versus parity symmetry stabilized dark matter candidates. We now describe a complementary study which focuses on decay chains of the two mother particles which are necessarily present in these events. We also include in our analysis the missing energy/momentum in the event. For the Z 3 symmetry stabilized mothers, the resulting inclusive final state can have two, three or four DM particles. In contrast, models with Z 2 symmetry can have only two. We show that the shapes and edges of the distribution of M T2 -type variables, along with ratio of the visible momentum/energy on the two sides of the event, are powerful in distinguishing these different scenarios. Finally we conclude by outlining future work which focuses on reducing combinatoric ambiguities from reconstructing multijet events. Increasing the reconstruction efficiency can allow better reconstruction of events with two or three dark matter candidates in the final state.
Prediction of Human Eye Fixations using Symmetry
Kootstra, Gert; Schomaker, Lambert R. B.
2009-01-01
Humans are very sensitive to symmetry in visual patterns. Reaction time experiments show that symmetry is detected and recognized very rapidly. This suggests that symmetry is a highly salient feature. Existing computational models of saliency, however, have mainly focused on contrast as a measure of saliency. In this paper, we discuss local symmetry as a measure of saliency. We propose a number of symmetry models and perform an eye-tracking study with human participants viewing photographic i...
Some Remarks on the Symmetry Kernel Test
Baszczyńska, Aleksandra
2013-01-01
The paper presents chosen statistical tests used to verify the hypothesis of the symmetry of random variable’s distribution. Detailed analysis of the symmetry kernel test is made. The properties of the regarded symmetry kernel test are compared with the other symmetry tests using Monte Carlo methods. The symmetry tests are used, as an example, in analysis of the distribution of the Human Development Index (HDI). W pracy przedstawiono wybrane statystyczne testy wykorzystywane w ...
Miller, G A
2003-01-01
Two new experiments have detected charge-symmetry breaking, the mechanism responsible for protons and neutrons having different masses. Symmetry is a crucial concept in the theories that describe the subatomic world because it has an intimate connection with the laws of conservation. The theory of the strong interaction between quarks - quantum chromodynamics - is approximately invariant under what is called charge symmetry. In other words, if we swap an up quark for a down quark, then the strong interaction will look almost the same. This symmetry is related to the concept of sup i sospin sup , and is not the same as charge conjugation (in which a particle is replaced by its antiparticle). Charge symmetry is broken by the competition between two different effects. The first is the small difference in mass between up and down quarks, which is about 200 times less than the mass of the proton. The second is their different electric charges. The up quark has a charge of +2/3 in units of the proton charge, while ...
Path integral and quasiclassical asymptotics of the Lie group
International Nuclear Information System (INIS)
Karasev, M.V.
1977-01-01
Solution of the Cauchy problem for the right-invariant differential operator on the Lie group is represented as a formal path integral. Finite-dimensional approximations of this integral and its quasiclassical asymptotics are written down
Robust methods and asymptotic theory in nonlinear econometrics
Bierens, Herman J
1981-01-01
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...
Asymptotic and transient analysis of stochastic core ecosystem models
Directory of Open Access Journals (Sweden)
Thomas C. Gard
2000-07-01
Full Text Available General results on ultimate boundedness and exit probability estimates for stochastic differential equations are applied to investigate asymptotic and transient properties of models of plankton-fish dynamics in uncertain environments
Pseudo-random number generator based on asymptotic deterministic randomness
International Nuclear Information System (INIS)
Wang Kai; Pei Wenjiang; Xia Haishan; Cheung Yiuming
2008-01-01
A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks
Pseudo-random number generator based on asymptotic deterministic randomness
Wang, Kai; Pei, Wenjiang; Xia, Haishan; Cheung, Yiu-ming
2008-06-01
A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks.
Asymptotic behavior of quark masses induced by instantons
International Nuclear Information System (INIS)
Carneiro, C.E.I.; Frenkel, J.
1984-02-01
A simple argument which shows that the dynamical mass induced by interactions of massless quarks with pseudo-particle configurations, behaves like p -6 for asymptotically large quark momenta is presented. (Author) [pt
Breaking of electroweak symmetry: origin and effects
International Nuclear Information System (INIS)
Delaunay, C.
2008-10-01
The Higgs boson appears as the corner stone of high energy physics, it might be the cause of the excess of matter that led to the formation of the structures of the universe and it seems that it drives the breaking of the electroweak symmetry. Moreover, when the stability at low energies of the Higgs boson is assured by an extra space dimension, it appears that this extra dimension can explain most issues in the flavor physics that are not understood by the standard model. The first chapter presents the main tools of effective field theories, the role of experimental data in the construction of theories valid beyond the standard model is discussed. The second chapter focuses on the electroweak baryogenesis that allows the testing of new physics via the electroweak phase transition. We detail the calculation of a Higgs potential at finite temperature. We follow the dynamics of the phase transition including nucleation an supercooling. Finally we investigate the prospects of gravity wave detection to see the effects of a strong electroweak phase transition. The 2 last chapters are dedicated to the physics of extra-dimension. The properties of the dynamics of scalar, vector fields with a 1/2 spin plunged in a 5 d. Anti de Sitter geometry are reviewed. We present a model of lepton masses and mixings based on the A 4 non-Abelian discrete symmetry. It is shown that this model does not contradict the tests of electroweak precision. (A.C.)
Symplectic structures and dynamical symmetry groups
International Nuclear Information System (INIS)
Torres del Castillo, G.F.; Velazquez Q, M.P.
2004-01-01
Apart from the total energy, the two-dimensional isotropic harmonic oscillator possesses three independent constants of motion which, with the standard symplectic structure, generates a dynamical symmetry group isomorphic to SU (2). We show that, by suitably redefining the symplectic structure, any of these three constants of motion can be used as a Hamiltonian, and that the remaining two, together with the total energy, generate a dynamical symmetry group isomorphic to SU (1,1). We also show that the standard energy levels of the quantum two-dimensional isotropic harmonic oscillator and their degeneracies are obtained making use of the appropriate representations of SU(1,1), provided that the canonical commutation relations are modified according to the new symplectic structure. Whereas in classical mechanics the different symplectic structures lead to equivalent formulations of the equations of motion, in quantum mechanics the modifications of the commutation relations should be accompanied by modifications in the interpretation of the formalism in order to obtain results equivalent to those found with the common relations. (Author) 12 refs
Asymptotic-induced numerical methods for conservation laws. Final report
International Nuclear Information System (INIS)
Garbey, M.; Scroggs, J.S.
1990-12-01
Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques
Asymptotic-induced numerical methods for conservation laws
Garbey, Marc; Scroggs, Jeffrey S.
1990-01-01
Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.
Asymptotical behaviour of pion electromagnetic form factor in QCD
International Nuclear Information System (INIS)
Efremov, A.V.; Radyushkin, A.V.
1978-01-01
In the framework of the renormalizable quantum field theory a new approach is developed to the investigation of asymptotical behaviour of two-particle bound state electromagnetic form factor. It is shown that the behaviour of the pion EM form factor in quantum chromodynamics at sufficiently large momentum transfers is controlled by the short-distance dynamics only. The formula is obtained which expresses the asymptotical behaviour of the pion form factor in terms of the fundamental constants of the theory
Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations
Directory of Open Access Journals (Sweden)
Zhinan Xia
2014-01-01
Full Text Available We define the concept of discrete weighted pseudo-S-asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo-S-asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem.
Soft theorems from anomalous symmetries
Huang, Yu-tin; Wen, Congkao
2015-12-01
We discuss constraints imposed by soft limits for effective field theories arising from symmetry breaking. In particular, we consider those associated with anomalous conformal symmetry as well as duality symmetries in supergravity. We verify these soft theorems for the dilaton effective action relevant for the a-theorem, as well as the one-loop effective action for N=4 supergravity. Using the universality of leading transcendental coefficients in the α' expansion of string theory amplitudes, we study the matrix elements of operator R 4 with half maximal supersymmetry. We construct the non-linear completion of R 4 that satisfies both single and double soft theorems up to seven points. This supports the existence of duality invariant completion of R 4.
Soft theorems from anomalous symmetries
Energy Technology Data Exchange (ETDEWEB)
Huang, Yu-tin [Department of Physics and Astronomy, National Taiwan University,Taipei 10617, Taiwan, ROC (China); Wen, Congkao [I.N.F.N. Sezione di Roma “Tor Vergata”,Via della Ricerca Scientifica, 00133 Roma (Italy)
2015-12-22
We discuss constraints imposed by soft limits for effective field theories arising from symmetry breaking. In particular, we consider those associated with anomalous conformal symmetry as well as duality symmetries in supergravity. We verify these soft theorems for the dilaton effective action relevant for the a-theorem, as well as the one-loop effective action for N=4 supergravity. Using the universality of leading transcendental coefficients in the α{sup ′} expansion of string theory amplitudes, we study the matrix elements of operator R{sup 4} with half maximal supersymmetry. We construct the non-linear completion of R{sup 4} that satisfies both single and double soft theorems up to seven points. This supports the existence of duality invariant completion of R{sup 4}.
Hidden Symmetries of Stochastic Models
Directory of Open Access Journals (Sweden)
Boyka Aneva
2007-05-01
Full Text Available In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The quadratic algebra defines a noncommutative space with a $SU_q(n$ quantum group action as its symmetry. Boundary processes amount to the appearance of parameter dependent linear terms in the algebraic relations and lead to a reduction of the $SU_q(n$ symmetry. We argue that the boundary operators of the asymmetric simple exclusion process generate a tridiagonal algebra whose irriducible representations are expressed in terms of the Askey-Wilson polynomials. The Askey-Wilson algebra arises as a symmetry of the boundary problem and allows to solve the model exactly.
Symmetry gauge theory for paraparticles
International Nuclear Information System (INIS)
Kursawe, U.
1986-01-01
In the present thesis it was shown that for identical particles the wave function of which has a more complicated symmetry than it is the case at the known kinds of particles, the bosons and fermions, a gauge theory can be formulated, the so-called 'symmetry gauge theory'. This theory has its origin alone in the symmetry of the particle wave functions and becomes first relevant when more than two particles are considered. It was shown that for particles with mixed-symmetrical wave functions, so-called 'paraparticles', the quantum mechanical state is no more described by one Hilbert-space element but by a many-dimensional subspace of this Hilbert space. The gauge freedom consists then just in the freedom of the choice of the basis in this subspace, the corresponding gauge group is the group of the unitary basis transformation in this subspace. (orig./HSI) [de
Kac-Moody algebra is not hidden symmetry of chiral models
International Nuclear Information System (INIS)
Devchand, C.; Schiff, J.
1997-01-01
A detailed examination of the infinite dimensional loop algebra of hidden symmetry transformations of the Principal Chiral Model reveals it to have a structure differing from a standard centreless Kac-Moody algebra. A new infinite dimensional Abelian symmetry algebra is shown to preserve a symplectic form on the space of solutions. (author). 15 refs
Symposium Symmetries in Science XIII
Gruber, Bruno J; Yoshinaga, Naotaka; Symmetries in Science XI
2005-01-01
This book is a collection of reviews and essays about the recent developments in the area of Symmetries and applications of Group Theory. Contributions have been written mostly at the graduate level but some are accessible to advanced undergraduates. The book is of interest to a wide audience and covers a broad range of topics with a strong degree of thematical unity. The book is part of a Series of books on Symmetries in Science and may be compared to the published Proceedings of the Colloquia on Group Theoretical Methods in Physics. Here, however, prevails a distinguished character for presenting extended reviews on present applications to Science, not restricted to Theoretical Physics.
Symmetry of intramolecular quantum dynamics
Burenin, Alexander V
2012-01-01
The main goal of this book is to give a systematic description of intramolecular quantum dynamics on the basis of only the symmetry principles. In this respect, the book has no analogs in the world literature. The obtained models lead to a simple, purely algebraic, scheme of calculation and are rigorous in the sense that their correctness is limited only to the correct choice of symmetry of the internal dynamics. The book is basically intended for scientists working in the field of molecular spectroscopy, quantum and structural chemistry.
Clifford algebraic symmetries in physics
International Nuclear Information System (INIS)
Salingaros, N.
1986-01-01
This paper reviews the following appearances of Clifford algebras in theoretical physics: statistical mechanics; general relativity; quantum electrodynamics; internal symmetries; the vee product; classical electrodynamics; charged-particle motion; and the Lorentz group. It is concluded that the power of the Clifford-algebraic description resides in its ability to perform representation-free calculations which are generalizations of the traditional vector algebra and that this considerable computational asset, in combination with the intrinsic symmetry, provides a practical framework for much of theoretical physics. 5 references
Renormalizable models with broken symmetries
International Nuclear Information System (INIS)
Becchi, C.; Rouet, A.; Stora, R.
1975-10-01
The results of the renormalized perturbation theory, in the absence of massless quanta, are summarized. The global symmetry breaking is studied and the associated currents are discussed in terms of the coupling with a classical Yang Mills field. Gauge theories are discussed; it is most likely that the natural set up should be the theory of fiber bundles and that making a choice of field coordinates makes the situation obscure. An attempt is made in view of clarifying the meaning of the Slavnov symmetry which characterizes gauge field theories [fr
Kastner, Ruth E.
2011-11-01
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.
International Nuclear Information System (INIS)
Kastner, Ruth E.
2011-01-01
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.
Scale symmetry of quantum solitons
International Nuclear Information System (INIS)
Chepilko, N.M.; Fujii, K.; Kobushkin, A.P.
1991-01-01
A collective-coordinate Lagrangian for a rotating and vibrating quantum soliton in the nonlinear σ-model is shown to possess a symmetry under scale transformation of the chiral field. Using this symmetry an integrodifferential equation for the chiral angle is obtained. A consistency condition between this equation and the Schroedinger equation for the quantum soliton is also discussed. At limiting cases (a vibrating, but not rotating soliton; or a rotating, but not vibrating soliton) the integrodifferential ones and the chiral angle becomes independent of the solution of the Schroedinger equation. 7 refs
Symmetry analysis of cellular automata
International Nuclear Information System (INIS)
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.
Microscopic basis of collective symmetries
International Nuclear Information System (INIS)
Arima, A.
1983-01-01
The seniority scheme of SU(2) symmetry in a single closed shell is an interaction to conserve seniority. It is suggested that an interaction simpler than delta interaction can be used to study the level structure of Pb isotopes. The concept of seniority number is introduced. Reduction formulae are then derived for one-body operators. Conservation of seniority in a single closed shell is treated. SU(6) symmetry of nuclear collective motion, or the SU(6) invariance of the boson system, is derived
Optical metamaterials with quasicrystalline symmetry: symmetry-induced optical isotropy
International Nuclear Information System (INIS)
Kruk, S.S.; Decker, M.; Helgert, Ch.; Neshev, D.N.; Kivshar, Y.S.; Staude, I.; Powell, D.A.; Pertsch, Th.; Menzel, Ch.; Helgert, Ch.; Etrich, Ch.; Rockstuhl, C.; Menzel, Ch.
2013-01-01
Taking advantage of symmetry considerations, we have analyzed the potential of various metamaterials to affect the polarization state of light upon oblique illumination. We have shown that depending on the angle of illumination, metamaterials are able to support specific polarization states. The presented methodology that using ellipticity and circular dichroism, provides an unambiguous language for discussing the impact of the inherent symmetry of the metamaterial lattices on their far-field response. Our findings allow the quantification analysis of the impact of inter-element coupling and lattice symmetry on the optical properties of metamaterials, and to separate this contribution from the response associated with a single meta-atom. In addition, we have studied the concept of optical quasicrystalline metamaterials, revealing that the absence of translational symmetry (periodicity) of quasicrystalline metamaterials causes an isotropic optical response, while the long-range positional order preserves the resonance properties. Our findings constitute an important step towards the design of optically isotropic metamaterials and metasurfaces. (authors)
Broken CP Symmetry and the Physics Nobel Prize–2008
Indian Academy of Sciences (India)
Admin
physics, CP violation and other topics which go beyond the standard model of elementary particle physics. akoto Kobayashi and Toshihide askawa (see ox 1) shared the physics Nobel Prize for 2008 with Yoichiro. Nambu “for the discovery of the origin of the broken symmetry which predicts the existence of at least three.
Symmetry Principles and Conservation Laws in Atomic and ...
Indian Academy of Sciences (India)
Symmetry Principles and Conservation Laws in. Atomic and Subatomic Physics – 2. P C Deshmukh .... dicated that parity conservation, though often assumed, had not been verified in weak interactions. Acting on ... The gauge bosons W§ have a charge of +1 and −1 unit, but the Z0 boson of the standard model is neutral.
International Nuclear Information System (INIS)
Kotel'nikov, G.A.
1994-01-01
An algorithm id proposed for research the symmetries of mathematical physics equation. The application of this algorithm to the Schroedinger equation permitted to establish, that in addition to the known symmetry the Schroedinger equation possesses also the relativistic symmetry
The master symmetry and time dependent symmetries of the differential–difference KP equation
International Nuclear Information System (INIS)
Khanizadeh, Farbod
2014-01-01
We first obtain the master symmetry of the differential–difference KP equation. Then we show how this master symmetry, through sl(2,C)-representation of the equation, can construct generators of time dependent symmetries. (paper)
Nussinov, Zohar; Batista, Cristian D.; Fradkin, Eduardo
2006-09-01
We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall systems, transition metal orbital systems, frustrated spin systems, (p+ip) superconducting arrays, and sliding Luttinger liquids. By considering space-time reflection symmetries, we illustrate that several of these systems are dual to each other. In some systems exhibiting these symmetries, low temperature local orders emerge by an "order out of disorder" effect while in other systems, the dimensional reduction precludes standard orders yet allows for multiparticle orders (including those of a topological nature).
PREFACE: Symmetries and Integrability of Difference Equations
Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane
2007-10-01
The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations (DE), like differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, and quantum field theory. It is thus crucial to develop tools to study and solve DEs. While the theory of symmetry and integrability for differential equations is now largely well-established, this is not yet the case for discrete equations. Although over recent years there has been significant progress in the development of a complete analytic theory of difference equations, further tools are still needed to fully understand, for instance, the symmetries, asymptotics and the singularity structure of difference equations. The series of SIDE meetings on Symmetries and Integrability of Difference Equations started in 1994. Its goal is to provide a platform for an international and interdisciplinary communication for researchers working in areas associated with integrable discrete systems, such as classical and quantum physics, computer science and numerical analysis, mathematical biology and economics, discrete geometry and combinatorics, theory of special functions, etc. The previous SIDE meetings took place in Estérel near Montréal, Canada (1994), at the University of
Symmetry groups of state vectors in canonical quantum gravity
International Nuclear Information System (INIS)
Witt, D.M.
1986-01-01
In canonical quantum gravity, the diffeomorphisms of an asymptotically flat hypersurface S, not connected to the identity, but trivial at infinity, can act nontrivially on the quantum state space. Because state vectors are invariant under diffeomorphisms that are connected to the identity, the group of inequivalent diffeomorphisms is a symmetry group of states associated with S. This group is the zeroth homotopy group of the group of diffeomorphisms fixing a frame of infinity on S. It is calculated for all hypersurfaces of the form S = S 3 /G-point, where the removed point is thought of as infinity on S and the symmetry group S is the zeroth homotopy group of the group of diffeomorphisms of S 3 /G fixing a point and frame, denoted π 0 Diff/sub F/(S 3 /G). Before calculating π 0 Diff/sub F/ (S 3 /G), it is necessary to find π 0 of the group of diffeomorphisms. Once π 0 Diff(S 3 /G) is known, π 0 Diff/sub x/ 0 (S 3 /G) is calculated using a fiber bundle involving Diff(S 3 /G), Diff/sub x/ 0 (S 3 /G), and S 3 /G. Finally, a fiber bundle involving Diff/sub F/(S 3 /G), Diff(S 3 /G), and the bundle of frames over S 3 /G is used along with π 0 Diff/sub x/ 0 (S 3 /G) to calculate π 0 Diff/sub F/(S 3 /G)
New symmetries for the gravitational S-matrix
International Nuclear Information System (INIS)
Campiglia, Miguel; Laddha, Alok
2015-01-01
In http://dx.doi.org/10.1103/PhysRevD.90.124028 we proposed a generalization of the BMS group G which is a semi-direct product of supertranslations and smooth diffeomorphisms of the conformal sphere. Although an extension of BMS, G is a symmetry group of asymptotically flat space times. By taking G as a candidate symmetry group of the quantum gravity S-matrix, we argued that the Ward identities associated to the generators of Diff(S 2 ) were equivalent to the Cachazo-Strominger subleading soft graviton theorem. Our argument however was based on a proposed definition of the Diff(S 2 ) charges which we could not derive from first principles as G does not have a well defined action on the radiative phase space of gravity. Here we fill this gap and provide a first principles derivation of the Diff(S 2 ) charges. The result of this paper, in conjunction with the results of http://arxiv.org/abs/1401.7026http://dx.doi.org/10.1103/PhysRevD.90.124028 prove that the leading and subleading soft theorems are equivalent to the Ward identities associated to G.
Phenomenology of induced electroweak symmetry breaking
International Nuclear Information System (INIS)
Chang, Spencer; Galloway, Jamison; Luty, Markus A.; Salvioni, Ennio; Tsai, Yuhsin
2015-01-01
We study the phenomenology of models of electroweak symmetry breaking where the Higgs potential is destabilized by a tadpole arising from the coupling to an “auxiliary” Higgs sector. The auxiliary Higgs sector can be either perturbative or strongly coupled, similar to technicolor models. Since electroweak symmetry breaking is driven by a tadpole, the cubic and quartic Higgs couplings can naturally be significantly smaller than their values in the standard model. The theoretical motivation for these models is that they can explain the 125 GeV Higgs mass in supersymmetry without fine-tuning. The auxiliary Higgs sector contains additional Higgs states that cannot decouple from standard model particles, so these models predict a rich phenomenology of Higgs physics beyond the standard model. In this paper we analyze a large number of direct and indirect constraints on these models. We present the current constraints after the 8 TeV run of the LHC, and give projections for the sensitivity of the upcoming 14 TeV run. We find that the strongest constraints come from the direct searches A 0 →Zh, A 0 →tt-bar, with weaker constraints from Higgs coupling fits. For strongly-coupled models, additional constraints come from ρ + →WZ where ρ + is a vector resonance. Our overall conclusion is that a significant parameter space for such models is currently open, allowing values of the Higgs cubic coupling down to 0.4 times the standard model value for weakly coupled models and vanishing cubic coupling for strongly coupled models. The upcoming 14 TeV run of the LHC will stringently test this scenario and we identify several new searches with discovery potential for this class of models.
An introduction to non-Abelian discrete symmetries for particle physicists
Ishimori, Hajime; Ohki, Hiroshi; Okada, Hiroshi; Shimizu, Yusuke; Tanimoto, Morimitsu
2012-01-01
These lecture notes provide a tutorial review of non-Abelian discrete groups and show some applications to issues in physics where discrete symmetries constitute an important principle for model building in particle physics. While Abelian discrete symmetries are often imposed in order to control couplings for particle physics - in particular model building beyond the standard model - non-Abelian discrete symmetries have been applied to understand the three-generation flavor structure in particular. Indeed, non-Abelian discrete symmetries are considered to be the most attractive choice for the flavor sector: model builders have tried to derive experimental values of quark and lepton masses, and mixing angles by assuming non-Abelian discrete flavor symmetries of quarks and leptons, yet, lepton mixing has already been intensively discussed in this context, as well. The possible origins of the non-Abelian discrete symmetry for flavors is another topic of interest, as they can arise from an underlying theory -...
A model of intrinsic symmetry breaking
International Nuclear Information System (INIS)
Ge, Li; Li, Sheng; George, Thomas F.; Sun, Xin
2013-01-01
Different from the symmetry breaking associated with a phase transition, which occurs when the controlling parameter is manipulated across a critical point, the symmetry breaking presented in this Letter does not need parameter manipulation. Instead, the system itself suddenly undergoes symmetry breaking at a certain time during its evolution, which is intrinsic symmetry breaking. Through a polymer model, it is revealed that the origin of the intrinsic symmetry breaking is nonlinearity, which produces instability at the instance when the evolution crosses an inflexion point, where this instability breaks the original symmetry
Charge symmetry at the partonic level
Energy Technology Data Exchange (ETDEWEB)
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.
The spin symmetry for deformed generalized Poeschl-Teller potential
International Nuclear Information System (INIS)
Wei Gaofeng; Dong Shihai
2009-01-01
In the case of spin symmetry we solve the Dirac equation with scalar and vector deformed generalized Poeschl-Teller (DGPT) potential and obtain exact energy equation and spinor wave functions for s-wave bound states. We find that there are only positive energy states for bound states in the case of spin symmetry based on the strong regularity restriction condition λ<-η for the wave functions. The energy eigenvalue approaches a constant when the potential parameter α goes to zero. Two special cases such as generalized PT potential and standard PT potential are also briefly discussed.
Directory of Open Access Journals (Sweden)
Naveen Reddy Admala
2013-01-01
Materials and methods: A sample of 120 patients (60 males and 60 females; mean age, 15 years; range, 16-22 years who had received orthodontic clinical examination at AME′s Dental College and Hospital were selected. Selection was made in such a way that following malocclusions with equal sexual distribution was possible from the patient database. Patients selected were classified into skeletal Class I (25 males and 25 females, Class II (25 males and 25 females and Class III (10 males and 10 females based on ANB angle. The number was predecided to be the same and also was based on the number of patients with following malocclusions reported to the department. Differences in length between distances from the points at which ear rods were inserted to the facial midline and the perpendicular distance from the softtissue menton to the facial midline were measured on a frontofacial photograph. Subjects with a discrepancy of more than three standard deviations of the measurement error were categorized as having left- or right-sided laterality. Results: Of subjects with facial asymmetry, 74.1% had a wider right hemiface, and 51.6% of those with chin deviation had left-sided laterality. These tendencies were independent of sex or skeletal jaw relationships. Conclusion: These results suggest that laterality in the normal asymmetry of the face, which is consistently found in humans, is likely to be a hereditary rather than an acquired trait.
From symmetries to number theory
International Nuclear Information System (INIS)
Tempesta, P.
2009-01-01
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.
Orthogonal symmetries and Clifford algebras
Indian Academy of Sciences (India)
a universal property of the even Clifford algebra in §3. ..... symmetry if σ2 = id. In the literature, such maps are sometimes also called “orthogonal involutions” (cf. Ch. III, §5 of [4]). We have, however, preferred to use the former ...... [7] Helmstetter J and Micali A, Quadratic mappings and Clifford algebras (Basel: Birkhäuser.
Exploiting symmetry in protocol testing
J.M.T. Romijn (Judi); J.G. Springintveld
1999-01-01
textabstractTest generation and execution are often hampered by the large state spaces of the systems involved. In automata (or transition system) based test algorithms, taking advantage of symmetry in the behavior of specification and implementation may substantially reduce the amount of tests. We
Second-quantized mirror symmetry
Ferrara, Sergio; Strominger, A; Vafa, C
1995-01-01
We propose and give strong evidence for a duality relating Type II theories on Calabi-Yau spaces and heterotic strings on K3 \\times T^2, both of which have N=2 spacetime supersymmetry. Entries in the dictionary relating the dual theories are derived from an analysis of the soliton string worldsheet in the context of N=2 orbifolds of dual N=4 compactifications of Type II and heterotic strings. In particular we construct a pairing between Type II string theory on a self-mirror Calabi-Yau space X with h^{11}= h^{21}= 11 and a (4, 0) background of heterotic string theory on K3\\times T^2. Under the duality transformation the usual first-quantized mirror symmetry of X becomes a second-quantized mirror symmetry which determines nonperturbative quantum effects. This enables us to compute the exact quantum moduli space. Mirror symmetry of X implies that the low-energy N=2 gauge theory is finite, even at enhanced symmetry points. This prediction is verified by direct computation on the heterotic side. Other branches of...
Lifshitz symmetries and nonrelativistic holography
Sybesma, Z.W.
2017-01-01
In this dissertation we cover topics within the main themes of Lifshitz symmetries and nonrelativistic holography. Nonrelativistic theories are typically less constrained than relativistic ones, which makes them often more cumbersome to work with. Via holography one can have acces to domains of a
Exploiting Symmetry on Parallel Architectures.
Stiller, Lewis Benjamin
1995-01-01
This thesis describes techniques for the design of parallel programs that solve well-structured problems with inherent symmetry. Part I demonstrates the reduction of such problems to generalized matrix multiplication by a group-equivariant matrix. Fast techniques for this multiplication are described, including factorization, orbit decomposition, and Fourier transforms over finite groups. Our algorithms entail interaction between two symmetry groups: one arising at the software level from the problem's symmetry and the other arising at the hardware level from the processors' communication network. Part II illustrates the applicability of our symmetry -exploitation techniques by presenting a series of case studies of the design and implementation of parallel programs. First, a parallel program that solves chess endgames by factorization of an associated dihedral group-equivariant matrix is described. This code runs faster than previous serial programs, and discovered it a number of results. Second, parallel algorithms for Fourier transforms for finite groups are developed, and preliminary parallel implementations for group transforms of dihedral and of symmetric groups are described. Applications in learning, vision, pattern recognition, and statistics are proposed. Third, parallel implementations solving several computational science problems are described, including the direct n-body problem, convolutions arising from molecular biology, and some communication primitives such as broadcast and reduce. Some of our implementations ran orders of magnitude faster than previous techniques, and were used in the investigation of various physical phenomena.
Symmetry structure and phase transitions
Indian Academy of Sciences (India)
We study chiral symmetry structure at finite density and temperature in the presence of external magnetic field and .... the case of neutron stars as a function of chemical potential µ associated with finite baryon number density we ..... work expended to create a bubble and are given by Rc = 2σ Ph(T) Pq(T) and Wc = 4πσR2.
Symmetry structure and phase transitions
Indian Academy of Sciences (India)
Spontaneous symmetry breaking is one of the most important concepts of all unified gauge theories. The idea that ... stable configurations of gauge and Higgs fields in the form of domain walls, cosmic strings and monopoles on the ..... pressure to balance the surface tension and the pressure of the hadron phase. The quark.
Experimental tests of fundamental symmetries
Jungmann, K. P.
2014-01-01
Ongoing experiments and projects to test our understanding of fundamental inter- actions and symmetries in nature have progressed significantly in the past few years. At high energies the long searched for Higgs boson has been found; tests of gravity for antimatter have come closer to reality;
Superdeformations and fermion dynamical symmetries
International Nuclear Information System (INIS)
Wu, Cheng-Li
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 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 3 fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU 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 γ-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs
Symmetry in labeled transition systems
I.A. van Langevelde
2003-01-01
textabstractSymmetry is defined for labeled transition systems, and it is shown how symmetrical systems can be symmetrically decomposed into components. The central question is under what conditions one such component may represent the whole system, in the sense that one symmetrical system is
Dark Energy and Spacetime Symmetry
Directory of Open Access Journals (Sweden)
Irina Dymnikova
2017-03-01
Full Text Available The Petrov classification of stress-energy tensors provides a model-independent definition of a vacuum by the algebraic structure of its stress-energy tensor and implies the existence of vacua whose symmetry is reduced as compared with the maximally symmetric de Sitter vacuum associated with the Einstein cosmological term. This allows to describe a vacuum in general setting by dynamical vacuum dark fluid, presented by a variable cosmological term with the reduced symmetry which makes vacuum fluid essentially anisotropic and allows it to be evolving and clustering. The relevant solutions to the Einstein equations describe regular cosmological models with time-evolving and spatially inhomogeneous vacuum dark energy, and compact vacuum objects generically related to a dark energy: regular black holes, their remnants and self-gravitating vacuum solitons with de Sitter vacuum interiors—which can be responsible for observational effects typically related to a dark matter. The mass of objects with de Sitter interior is generically related to vacuum dark energy and to breaking of space-time symmetry. In the cosmological context spacetime symmetry provides a mechanism for relaxing cosmological constant to a needed non-zero value.
On four dimensional mirror symmetry
International Nuclear Information System (INIS)
Losev, A.; Nekrasov, N.; Shatashvili, S.
2000-01-01
A conjecture relating instanton calculus in four dimensional supersymmetric theories and the deformation theory of Lagrangian submanifolds in C 2r invariant under a (subgroup of) Sp(2r,Z) is formulated. This is a four dimensional counterpart of the mirror symmetry of topological strings (relating Gromov-Witten invariants and generalized variations of Hodge structure). (orig.)
Kohn's theorem and Galilean symmetry
Zhang, P.-M.; Horvathy, P. A.
2011-08-01
The relation between the separability of a system of charged particles in a uniform magnetic field and Galilean symmetry is revisited using Duval's “Bargmann framework”. If the charge-to-mass ratios of the particles are identical, ea/ma=ɛ for all particles, then the Bargmann space of the magnetic system is isometric to that of an anisotropic harmonic oscillator. Assuming that the particles interact through a potential which only depends on their relative distances, the system splits into one representing the center of mass plus a decoupled internal part, and can be mapped further into an isolated system using Niederer's transformation. Conversely, the manifest Galilean boost symmetry of the isolated system can be “imported” to the oscillator and to the magnetic systems, respectively, to yield the symmetry used by Gibbons and Pope to prove the separability. For vanishing interaction potential the isolated system is free and our procedure endows all our systems with a hidden Schrödinger symmetry, augmented with independent internal rotations. All these properties follow from the cohomological structure of the Galilei group, as explained by Souriau's “décomposition barycentrique”.
International Nuclear Information System (INIS)
Damski, Bogdan; Zurek, Wojciech H
2008-01-01
We discuss the dynamics of a quantum phase transition in a spin-1 Bose-Einstein condensate when it is driven from the magnetized broken-symmetry phase to the unmagnetized 'symmetric' polar phase. We determine where the condensate goes out of equilibrium as it approaches the critical point, and compute the condensate magnetization at the critical point. This is done within a quantum Kibble-Zurek scheme traditionally employed in the context of symmetry-breaking quantum phase transitions. Then we study the influence of the non-equilibrium dynamics near a critical point on the condensate magnetization. In particular, when the quench stops at the critical point, nonlinear oscillations of magnetization occur. They are characterized by a period and an amplitude that are inversely proportional. If we keep driving the condensate far away from the critical point through the unmagnetized 'symmetric' polar phase, the amplitude of magnetization oscillations slowly decreases reaching a nonzero asymptotic value. That process is described by an equation that can be mapped onto the classical mechanical problem of a particle moving under the influence of harmonic and 'anti-friction' forces whose interplay leads to surprisingly simple fixed-amplitude oscillations. We obtain several scaling results relating the condensate magnetization to the quench rate, and verify numerically all analytical predictions
Asymptotic distribution of ∆AUC, NRIs, and IDI based on theory of U-statistics.
Demler, Olga V; Pencina, Michael J; Cook, Nancy R; D'Agostino, Ralph B
2017-09-20
The change in area under the curve (∆AUC), the integrated discrimination improvement (IDI), and net reclassification index (NRI) are commonly used measures of risk prediction model performance. Some authors have reported good validity of associated methods of estimating their standard errors (SE) and construction of confidence intervals, whereas others have questioned their performance. To address these issues, we unite the ∆AUC, IDI, and three versions of the NRI under the umbrella of the U-statistics family. We rigorously show that the asymptotic behavior of ∆AUC, NRIs, and IDI fits the asymptotic distribution theory developed for U-statistics. We prove that the ∆AUC, NRIs, and IDI are asymptotically normal, unless they compare nested models under the null hypothesis. In the latter case, asymptotic normality and existing SE estimates cannot be applied to ∆AUC, NRIs, or IDI. In the former case, SE formulas proposed in the literature are equivalent to SE formulas obtained from U-statistics theory if we ignore adjustment for estimated parameters. We use Sukhatme-Randles-deWet condition to determine when adjustment for estimated parameters is necessary. We show that adjustment is not necessary for SEs of the ∆AUC and two versions of the NRI when added predictor variables are significant and normally distributed. The SEs of the IDI and three-category NRI should always be adjusted for estimated parameters. These results allow us to define when existing formulas for SE estimates can be used and when resampling methods such as the bootstrap should be used instead when comparing nested models. We also use the U-statistic theory to develop a new SE estimate of ∆AUC. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.
Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size.
Directory of Open Access Journals (Sweden)
Richard B King
Full Text Available Body size, and, by extension, growth has impacts on physiology, survival, attainment of sexual maturity, fecundity, generation time, and population dynamics, especially in ectotherm animals that often exhibit extensive growth following attainment of sexual maturity. Frequently, growth is analyzed at the population level, providing useful population mean growth parameters but ignoring individual variation that is also of ecological and evolutionary significance. Our long-term study of Lake Erie Watersnakes, Nerodia sipedon insularum, provides data sufficient for a detailed analysis of population and individual growth. We describe population mean growth separately for males and females based on size of known age individuals (847 captures of 769 males, 748 captures of 684 females and annual growth increments of individuals of unknown age (1,152 males, 730 females. We characterize individual variation in asymptotic size based on repeated measurements of 69 males and 71 females that were each captured in five to nine different years. The most striking result of our analyses is that asymptotic size varies dramatically among individuals, ranging from 631-820 mm snout-vent length in males and from 835-1125 mm in females. Because female fecundity increases with increasing body size, we explore the impact of individual variation in asymptotic size on lifetime reproductive success using a range of realistic estimates of annual survival. When all females commence reproduction at the same age, lifetime reproductive success is greatest for females with greater asymptotic size regardless of annual survival. But when reproduction is delayed in females with greater asymptotic size, lifetime reproductive success is greatest for females with lower asymptotic size when annual survival is low. Possible causes of individual variation in asymptotic size, including individual- and cohort-specific variation in size at birth and early growth, warrant further
Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size
King, Richard B.
2016-01-01
Body size, and, by extension, growth has impacts on physiology, survival, attainment of sexual maturity, fecundity, generation time, and population dynamics, especially in ectotherm animals that often exhibit extensive growth following attainment of sexual maturity. Frequently, growth is analyzed at the population level, providing useful population mean growth parameters but ignoring individual variation that is also of ecological and evolutionary significance. Our long-term study of Lake Erie Watersnakes, Nerodia sipedon insularum, provides data sufficient for a detailed analysis of population and individual growth. We describe population mean growth separately for males and females based on size of known age individuals (847 captures of 769 males, 748 captures of 684 females) and annual growth increments of individuals of unknown age (1,152 males, 730 females). We characterize individual variation in asymptotic size based on repeated measurements of 69 males and 71 females that were each captured in five to nine different years. The most striking result of our analyses is that asymptotic size varies dramatically among individuals, ranging from 631–820 mm snout-vent length in males and from 835–1125 mm in females. Because female fecundity increases with increasing body size, we explore the impact of individual variation in asymptotic size on lifetime reproductive success using a range of realistic estimates of annual survival. When all females commence reproduction at the same age, lifetime reproductive success is greatest for females with greater asymptotic size regardless of annual survival. But when reproduction is delayed in females with greater asymptotic size, lifetime reproductive success is greatest for females with lower asymptotic size when annual survival is low. Possible causes of individual variation in asymptotic size, including individual- and cohort-specific variation in size at birth and early growth, warrant further investigation. PMID
Natural electroweak symmetry breaking from scale invariant Higgs mechanism
International Nuclear Information System (INIS)
Farzinnia, Arsham; He, Hong-Jian; Ren, Jing
2013-01-01
We construct a minimal viable extension of the standard model (SM) with classical scale symmetry. Its scalar sector contains a complex singlet in addition to the SM Higgs doublet. The scale-invariant and CP-symmetric Higgs potential generates radiative electroweak symmetry breaking à la Coleman–Weinberg, and gives a natural solution to the hierarchy problem, free from fine-tuning. Besides the 125 GeV SM-like Higgs particle, it predicts a new CP-even Higgs (serving as the pseudo-Nambu–Goldstone boson of scale symmetry breaking) and a CP-odd scalar singlet (providing the dark matter candidate) at weak scale. We systematically analyze experimental constraints from direct LHC Higgs searches and electroweak precision tests, as well as theoretical bounds from unitarity, triviality and vacuum stability. We demonstrate the viable parameter space, and discuss implications for new Higgs searches at the upcoming LHC runs and the on-going direct detections of dark matter
Test of Symmetries with Neutrons and Nuclei
International Nuclear Information System (INIS)
Paul, Stephan
2009-01-01
Precision experiments at low energies probing weak interaction are a very promising and complementary tool for investigating the structure of the electro-weak sector of the standard model, and for searching for new phenomena revealing signs for an underlaying new symmetry. With the advent of new technologies in particle trapping and production of beams for exotic nuclei as well as ultracold neutrons, we expect one or two orders of magnitude gain in precision. This corresponds to the progress expected by new high luminosity B-factories or the LHC. Domains studied are β-decays where decay correlations, partial or total decay rates may reveal the nature of the left-right structure of the interaction and the investigation of discrete symmetries. Here the search for a finite electric dipole moment which, due to its CP-violating nature were sensational by itself, could shed light on the structure of the vacuum at very small distances. Last but not least ideas of a mirror world can be extended to the sector of baryons which can be studied with neutrons.
Maiezza, Alessio; Nesti, Fabrizio; Senjanovic, Goran
2010-01-01
We revisit the issue of the limit on the scale of Left-Right symmetry breaking. We focus on the minimal SU(2)_L x SU(2)_R x U(1)_B-L gauge theory with the seesaw mechanism and discuss the two possibilities of defining Left-Right symmetry as parity or charge conjugation. In the commonly adopted case of parity, we perform a complete numerical study of the quark mass matrices and the associated left and right mixing matrices without any assumptions usually made in the literature about the ratio of vacuum expectation values. We find that the usual lower limit on the mass of the right-handed gauge boson from the K mass difference, M_WR>2.5TeV, is subject to a possible small reduction due to the difference between right and left Cabibbo angles. In the case of charge conjugation the limit on M_WR is somewhat more robust. However, the more severe bounds from CP-violating observables are absent in this case. In fact, the free phases can also resolve the present mild discrepancy between the Standard Model and CP-violat...
Quantizations of D = 3 Lorentz symmetry
Energy Technology Data Exchange (ETDEWEB)
Lukierski, J. [University of Wroclaw, Institute for Theoretical Physics, Wroclaw (Poland); Tolstoy, V.N. [University of Wroclaw, Institute for Theoretical Physics, Wroclaw (Poland); Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow (Russian Federation)
2017-04-15
Using the isomorphism o(3; C) ≅ sl(2; C) we develop a new simple algebraic technique for complete classification of quantum deformations (the classical r-matrices) for real forms o(3) and o(2,1) of the complex Lie algebra o(3; C) in terms of real forms of sl(2; C): su(2), su(1,1) and sl(2; R). We prove that the D = 3 Lorentz symmetry o(2,1) ≅ su(1,1) ≅ sl(2; R) has three different Hopf-algebraic quantum deformations, which are expressed in the simplest way by two standard su(1,1) and sl(2; R) q-analogs and by simple Jordanian sl(2; R) twist deformation. These quantizations are presented in terms of the quantum Cartan-Weyl generators for the quantized algebras su(1,1) and sl(2; R) as well as in terms of quantum Cartesian generators for the quantized algebra o(2,1). Finally, some applications of the deformed D = 3 Lorentz symmetry are mentioned. (orig.)
Generalized multiplicative error models: Asymptotic inference and empirical analysis
Li, Qian
This dissertation consists of two parts. The first part focuses on extended Multiplicative Error Models (MEM) that include two extreme cases for nonnegative series. These extreme cases are common phenomena in high-frequency financial time series. The Location MEM(p,q) model incorporates a location parameter so that the series are required to have positive lower bounds. The estimator for the location parameter turns out to be the minimum of all the observations and is shown to be consistent. The second case captures the nontrivial fraction of zero outcomes feature in a series and combines a so-called Zero-Augmented general F distribution with linear MEM(p,q). Under certain strict stationary and moment conditions, we establish a consistency and asymptotic normality of the semiparametric estimation for these two new models. The second part of this dissertation examines the differences and similarities between trades in the home market and trades in the foreign market of cross-listed stocks. We exploit the multiplicative framework to model trading duration, volume per trade and price volatility for Canadian shares that are cross-listed in the New York Stock Exchange (NYSE) and the Toronto Stock Exchange (TSX). We explore the clustering effect, interaction between trading variables, and the time needed for price equilibrium after a perturbation for each market. The clustering effect is studied through the use of univariate MEM(1,1) on each variable, while the interactions among duration, volume and price volatility are captured by a multivariate system of MEM(p,q). After estimating these models by a standard QMLE procedure, we exploit the Impulse Response function to compute the calendar time for a perturbation in these variables to be absorbed into price variance, and use common statistical tests to identify the difference between the two markets in each aspect. These differences are of considerable interest to traders, stock exchanges and policy makers.
A bridge between weak and strong coupling regions: BRS symmetries as a guiding principle
International Nuclear Information System (INIS)
Shintani, M.
1987-04-01
By imposing extended BRS symmetries on the Yang-Mills Lagrangian, we obtained two types of BRS invariant Lagrangians, i.e. Lagrangians of the non-gauge type and the gauge type. A Lagrangian of the non-gauge type, which was previously obtained by us, can yield the linearly rising potential between a quark and anti-quark pair at the one-loop level. By smoothly relating the running coupling constant in the confining region to that in the asymptotically free region, we deduce a relationship between the string tensions and Λ QCD , which shows good agreement with experiments. (author). 20 refs, 1 fig
Assessing symmetry of financial returns series
H. F. Coronel-Brizio; A. R. Hernandez-Montoya; Huerta-Quintanilla; M. Rodriguez-Achach; .
2007-01-01
Testing symmetry of a probability distribution is a common question arising from applications in several fields. Particularly, in the study of observables used in the analysis of stock market index variations, the question of symmetry has not been fully investigated by means of statistical procedures. In this work a distribution-free test statistic Tn for testing symmetry, derived by Einmahl and McKeague, based on the empirical likelihood approach, is used to address the study of symmetry of ...
Scaling Symmetry and Integrable Spherical Hydrostatics
Bludman, Sidney; Kennedy, Dallas C.
2011-01-01
Any symmetry reduces a second-order differential equation to a first integral: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion (exemplified by scale-invariant hydrostatics) yield first-order {\\em non-conservation laws} between invariants. We obtain these non-conservation laws by extending Noether's Theorem to non-variational symmetries and present an innovative variational formulation of sph...
Symmetry of the Pyritohedron and Lattices
Directory of Open Access Journals (Sweden)
Nazife O. Koca
2016-12-01
Full Text Available The pyritohedron consisting of twelve identical but non regular pentagonal faces and its dual pseudoicosahedron that possess the pyritohedral (Th symmetry play an essential role in understanding the crystallographic structures with the pyritohedral symmetry. The pyritohedral symmetry takes a simpler form in terms of quaternionic representation. We discuss the 3D crystals with the pyritohedral symmetry which can be derived from the Coxeter-Dynkin diagram of D3.
Baryon spectroscopy: symmetries, symmetry breaking and hadronic loops
International Nuclear Information System (INIS)
Zenczykowski, P.
1985-01-01
The problem of hadronic loop effects in baryon spectroscopy is thoroughly discussed. It is argued that such effects very likely constitute the dominant contribution to the observed splitting and mixing pattern of the (56,0 + ) and (70,1 - ) baryon multiplets. In particular, this dominance is demonstrated in the original Isgur-Karl-Koniuk model of baryons, in which hadronic loops are shown to provide an explanation for at least 2/3 of the observed size of splittings, both for the ground-state and excited baryons. The unitarity-induced mixing angles in the (70,1 - )-multiplet are also shown to be in good agreement with experiment. For the ground-state baryons the formula relating Σ-Λ and Δ-Ν mass differences - as originally derived by de Rujula, Georgi and Glashow from the single gluon exchange-is obtained from the hadronic loop effects as well. This (and other) results are derived after taking into account a complete set of symmetry-related hadronic loops. Consideration of such a complete set of symmetry-related processes is shown to be crucial in restoring proper symmetry properties of the calculated spectrum. 74 refs., 10 figs., 4 tabs. (author)
Prediction of human eye fixations using symmetry
Kootstra, Gert; Schomaker, Lambert
2009-01-01
Humans are very sensitive to symmetry in visual patterns. Reaction time experiments show that symmetry is detected and recognized very rapidly. This suggests that symmetry is a highly salient feature. Existing computational models of saliency, however, have mainly focused on contrast as a measure of
Symmetry and electromagnetism. Simetria y electromagnetismo
Energy Technology Data Exchange (ETDEWEB)
Fuentes Cobas, L.E.; Font Hernandez, R.
1993-01-01
An analytical treatment of electrostatic and magnetostatic field symmetry, as a function of charge and current distribution symmetry, is proposed. The Newmann Principle, related to the cause-effect symmetry relation, is presented and applied to the characterization of simple configurations. (Author) 5 refs.
Generalized partial dynamical symmetry in nuclei.
Leviatan, A; Isacker, P Van
2002-11-25
We introduce the notion of a generalized partial dynamical-symmetry for which part of the eigenstates have part of the dynamical symmetry. This general concept is illustrated with the example of Hamiltonians with a partial dynamical O(6) symmetry in the framework of the interacting boson model. The resulting spectrum and electromagnetic transitions are compared with empirical data in 162Dy.
Partial Dynamical Symmetry in Deformed Nuclei
International Nuclear Information System (INIS)
Leviatan, A.
1996-01-01
We discuss the notion of partial dynamical symmetry in relation to nuclear spectroscopy. Explicit forms of Hamiltonians with partial SU(3) symmetry are presented in the framework of the interacting boson model of nuclei. An analysis of the resulting spectrum and electromagnetic transitions demonstrates the relevance of such partial symmetry to the spectroscopy of axially deformed nuclei. copyright 1996 The American Physical Society
Simultaneous occurrence of distinct symmetries in nuclei
International Nuclear Information System (INIS)
Leviatan, A.
2016-01-01
We show that distinct emergent symmetries, such as partial dynamical symmetry and quasi dynamical symmetry, can occur simultaneously in the same or different eigenstates of the Hamiltonian. Implications for nuclear spectroscopy in the rare-earth region and for first-order quantum phase transitions between spherical and deformed shapes, are considered. (paper)
Generalized partial dynamical symmetry in nuclei
International Nuclear Information System (INIS)
Leviatan, A.; Isacker, P. van
2002-01-01
We introduce the notion of a generalized partial dynamical-symmetry for which part of the eigenstates have part of the dynamical symmetry. This general concept is illustrated with the example of Hamiltonians with a partial dynamical O(6) symmetry in the framework of the interacting boson model. The resulting spectrum and electromagnetic transitions are compared with empirical data in Dy 162
Partial Dynamical Symmetry in Deformed Nuclei
Energy Technology Data Exchange (ETDEWEB)
Leviatan, A. [Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel)
1996-07-01
We discuss the notion of partial dynamical symmetry in relation to nuclear spectroscopy. Explicit forms of Hamiltonians with partial SU(3) symmetry are presented in the framework of the interacting boson model of nuclei. An analysis of the resulting spectrum and electromagnetic transitions demonstrates the relevance of such partial symmetry to the spectroscopy of axially deformed nuclei. {copyright} {ital 1996 The American Physical Society.}
Involution symmetries and the PMNS matrix
Indian Academy of Sciences (India)
Palash B Pal
2017-10-09
Oct 9, 2017 ... approach, advocated first by Lam [1], one starts by look- ing at the symmetries of the low-energy Lagrangian, and tries to see which group can contain these symmetries. The bigger symmetry might then determine the PMNS matrix, or at least some information about its elements. In this paper, we are going ...
Heat Kernel Asymptotics of Zaremba Boundary Value Problem
Energy Technology Data Exchange (ETDEWEB)
Avramidi, Ivan G. [Department of Mathematics, New Mexico Institute of Mining and Technology (United States)], E-mail: iavramid@nmt.edu
2004-03-15
The Zaremba boundary-value problem is a boundary value problem for Laplace-type second-order partial differential operators acting on smooth sections of a vector bundle over a smooth compact Riemannian manifold with smooth boundary but with discontinuous boundary conditions, which include Dirichlet boundary conditions on one part of the boundary and Neumann boundary conditions on another part of the boundary. We study the heat kernel asymptotics of Zaremba boundary value problem. The construction of the asymptotic solution of the heat equation is described in detail and the heat kernel is computed explicitly in the leading approximation. Some of the first nontrivial coefficients of the heat kernel asymptotic expansion are computed explicitly.
Asymptotic chaos expansions in finance theory and practice
Nicolay, David
2014-01-01
Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (suc...
Asymptotic learning curve and renormalizable condition in statistical learning theory
International Nuclear Information System (INIS)
Watanabe, Sumio
2010-01-01
Bayes statistics and statistical physics have the common mathematical structure, where the log likelihood function corresponds to the random Hamiltonian. Recently, it was discovered that the asymptotic learning curves in Bayes estimation are subject to a universal law, even if the log likelihood function can not be approximated by any quadratic form. However, it is left unknown what mathematical property ensures such a universal law. In this paper, we define a renormalizable condition of the statistical estimation problem, and show that, under such a condition, the asymptotic learning curves are ensured to be subject to the universal law, even if the true distribution is unrealizable and singular for a statistical model. Also we study a nonrenormalizable case, in which the learning curves have the different asymptotic behaviors from the universal law.
Imaging lower mantle heterogeneities by asymptotic waveform inversion
Ko, J. Y. T.; Zhan, Z.
2017-12-01
Tomographic images from full waveform inversions (FWI) are starting to reveal fine details of Earth structures. However, the constructions of mesh and kernels for broadband waveforms based on full numerical methods are still computationally expensive, and choices of initial models are critical. Here we propose an asymptotic waveform inversion (AWI) technique based on an asymptotic forward method, which are much faster than full numerical methods. While the asymptotic approach does not work for full seismograms or arbitrarily complex medium, it demonstrates high accuracy for important seismic phases (e.g., P and S) for typical/enhanced velocity anomalies considered in Earth's middle and lower mantle. This allows us to use, instead of gradient-based optimization, direct/Monte Carlo search of the model space and provides more realistic uncertainty estimates. This new AWI method can be applied to image subducted slabs and large low shear wave velocity provinces (LLSVPs) in lower mantle with broadband waveforms.
Watermelon configurations with wall interaction: exact and asymptotic results
Energy Technology Data Exchange (ETDEWEB)
Krattenthaler, C [Institut Camille Jordan, Universite Claude Bernard Lyon-I, 21, avenue Claude Bernard, F-69622 Villeurbanne Cedex (France)
2006-06-15
We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.
Watermelon configurations with wall interaction: exact and asymptotic results
International Nuclear Information System (INIS)
Krattenthaler, C
2006-01-01
We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature
Watermelon configurations with wall interaction: exact and asymptotic results
Krattenthaler, C.
2006-06-01
We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.
Contact mechanics of articular cartilage layers asymptotic models
Argatov, Ivan
2015-01-01
This book presents a comprehensive and unifying approach to articular contact mechanics with an emphasis on frictionless contact interaction of thin cartilage layers. The first part of the book (Chapters 1–4) reviews the results of asymptotic analysis of the deformational behavior of thin elastic and viscoelastic layers. A comprehensive review of the literature is combined with the authors’ original contributions. The compressible and incompressible cases are treated separately with a focus on exact solutions for asymptotic models of frictionless contact for thin transversely isotropic layers bonded to rigid substrates shaped like elliptic paraboloids. The second part (Chapters 5, 6, and 7) deals with the non-axisymmetric contact of thin transversely isotropic biphasic layers and presents the asymptotic modelling methodology for tibio-femoral contact. The third part of the book consists of Chapter 8, which covers contact problems for thin bonded inhomogeneous transversely isotropic elastic layers, and Cha...
Symmetry realization of texture zeros
International Nuclear Information System (INIS)
Grimus, W.; Joshipura, A.S.; Lavoura, L.; Tanimoto, M.
2004-01-01
We show that it is possible to enforce texture zeros in arbitrary entries of the fermion mass matrices by means of Abelian symmetries; in this way, many popular mass-matrix textures find a symmetry justification. We propose two alternative methods which allow one to place zeros in any number of elements of the mass matrices that one wants. They are applicable simultaneously in the quark and lepton sectors. They are also applicable in grand unified theories. The number of scalar fields required by our methods may be large; still, in many interesting cases this number can be reduced considerably. The larger the desired number of texture zeros is, the simpler are the models which reproduce the texture. (orig.)
Wang, Zhijian; Xu, Bin; Zhejiang Collaboration
2011-03-01
In social science, laboratory experiment with human subjects' interaction is a standard test-bed for studying social processes in micro level. Usually, as in physics, the processes near equilibrium are suggested as stochastic processes with time-reversal symmetry (TRS). To the best of our knowledge, near equilibrium, the breaking time symmetry, as well as the existence of robust time anti-symmetry processes, has not been reported clearly in experimental economics till now. By employing Markov transition method to analysis the data from human subject 2x2 Games with wide parameters and mixed Nash equilibrium, we study the time symmetry of the social interaction process near Nash equilibrium. We find that, the time symmetry is broken, and there exists a robust time anti-symmetry processes. We also report the weight of the time anti-symmetry processes in the total processes of each the games. Evidences in laboratory marketing experiments, at the same time, are provided as one-dimension cases. In these cases, time anti-symmetry cycles can also be captured. The proposition of time anti-symmetry processes is small, but the cycles are distinguishable.
Symmetry and symmetry breaking in cancer: a foundational approach to the cancer problem.
Frost, J James; Pienta, Kenneth J; Coffey, Donald S
2018-02-20
Symmetry and symmetry breaking concepts from physics and biology are applied to the problem of cancer. Three categories of symmetry breaking in cancer are examined: combinatorial, geometric, and functional. Within these categories, symmetry breaking is examined for relevant cancer features, including epithelial-mesenchymal transition (EMT); tumor heterogeneity; tensegrity; fractal geometric and information structure; functional interaction networks; and network stabilizability and attack tolerance. The new cancer symmetry concepts are relevant to homeostasis loss in cancer and to its origin, spread, treatment and resistance. Symmetry and symmetry breaking could provide a new way of thinking and a pathway to a solution of the cancer problem.
Symmetries of the dual metrics
International Nuclear Information System (INIS)
Baleanu, D.
1998-01-01
The geometric duality between the metric g μν and a Killing tensor K μν is studied. The conditions were found when the symmetries of the metric g μν and the dual metric K μν are the same. Dual spinning space was constructed without introduction of torsion. The general results are applied to the case of Kerr-Newmann metric
Chiral symmetry and nucleon structure
Energy Technology Data Exchange (ETDEWEB)
Holstein, B.R. (Massachusetts Univ., Amherst, MA (United States). Dept. of Physics and Astromony Washington Univ., Seattle, WA (United States). Inst. for Nuclear Theory)
1992-01-01
Recently it has been realized that significant tests of the validity of QCD are available in low energy experiments (E < 500 MeV) by exploiting the property of (broken) chiral symmetry. This technique has been highly developed in The Goldstone boson sector by the work of Gasser and Leutwyler. Application to the nucleon system is much more difficult and is now being carefully developed.
Models of electroweak symmetry breaking
Pomarol, Alex
2015-01-01
This chapter present models of electroweak symmetry breaking arising from strongly interacting sectors, including both Higgsless models and mechanisms involving a composite Higgs. These scenarios have also been investigated in the framework of five-dimensional warped models that, according to the AdS/CFT correspondence, have a four-dimensional holographic interpretation in terms of strongly coupled field theories. We explore the implications of these models at the LHC.
International Nuclear Information System (INIS)
Becker, D.; Reuter, M.
2014-01-01
The most momentous requirement a quantum theory of gravity must satisfy is Background Independence, necessitating in particular an ab initio derivation of the arena all non-gravitational physics takes place in, namely spacetime. Using the background field technique, this requirement translates into the condition of an unbroken split-symmetry connecting the (quantized) metric fluctuations to the (classical) background metric. If the regularization scheme used violates split-symmetry during the quantization process it is mandatory to restore it in the end at the level of observable physics. In this paper we present a detailed investigation of split-symmetry breaking and restoration within the Effective Average Action (EAA) approach to Quantum Einstein Gravity (QEG) with a special emphasis on the Asymptotic Safety conjecture. In particular we demonstrate for the first time in a non-trivial setting that the two key requirements of Background Independence and Asymptotic Safety can be satisfied simultaneously. Carefully disentangling fluctuation and background fields, we employ a ‘bi-metric’ ansatz for the EAA and project the flow generated by its functional renormalization group equation on a truncated theory space spanned by two separate Einstein–Hilbert actions for the dynamical and the background metric, respectively. A new powerful method is used to derive the corresponding renormalization group (RG) equations for the Newton- and cosmological constant, both in the dynamical and the background sector. We classify and analyze their solutions in detail, determine their fixed point structure, and identify an attractor mechanism which turns out instrumental in the split-symmetry restoration. We show that there exists a subset of RG trajectories which are both asymptotically safe and split-symmetry restoring: In the ultraviolet they emanate from a non-Gaussian fixed point, and in the infrared they loose all symmetry violating contributions inflicted on them by the
Superconformal Symmetry, Supergravity and Cosmology
Kallosh, Renata E; Linde, Andrei D; Van Proeyen, A; Kallosh, Renata; Kofman, Lev; Linde, Andrei; Proeyen, Antoine Van
2000-01-01
We introduce the general N=1 gauge theory superconformally coupled to supergravity. The theory has local SU(2,2|1) symmetry and no dimensional parameters. The superconformal origin of the Fayet-Iliopoulos terms is clarified. The phase of this theory with spontaneously broken conformal symmetry gives various formulations of N=1 supergravity interacting with matter, depending on the choice of the R-symmetry fixing. We have found that the locally superconformal theory is useful for describing the physics of the early universe with a conformally flat FRW metric. Few applications of superconformal theory to cosmology include the study of i) particle production after inflation, particularly the non-conformal helicity 1/2 states of gravitino, ii) the super-Higgs effect in cosmology and the derivation of the equations for the gravitino interacting with any number of chiral and vector multiplets in the gravitational background with varying scalar fields, iii) the weak coupling limit of supergravity and gravitino-golds...
Dark matter and global symmetries
Directory of Open Access Journals (Sweden)
Yann Mambrini
2016-09-01
Full Text Available 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.
Vacuum energy in asymptotically flat 2 + 1 gravity
Energy Technology Data Exchange (ETDEWEB)
Miskovic, Olivera, E-mail: olivera.miskovic@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Olea, Rodrigo, E-mail: rodrigo.olea@unab.cl [Departamento de Ciencias Físicas, Universidad Andres Bello, Sazié 2212, Piso 7, Santiago (Chile); Roy, Debraj, E-mail: roy.debraj@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile)
2017-04-10
We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern–Simons formulation for the Poincaré group. The equivalent action is nothing but the Einstein–Hilbert term in the bulk plus half of the Gibbons–Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.
Asymptotic shape of solutions to nonlinear eigenvalue problems
Directory of Open Access Journals (Sweden)
Tetsutaro Shibata
2005-03-01
Full Text Available We consider the nonlinear eigenvalue problem $$ -u''(t = f(lambda, u(t, quad u mbox{greater than} 0, quad u(0 = u(1 = 0, $$ where $lambda > 0$ is a parameter. It is known that under some conditions on $f(lambda, u$, the shape of the solutions associated with $lambda$ is almost `box' when $lambda gg 1$. The purpose of this paper is to study precisely the asymptotic shape of the solutions as $lambda o infty$ from a standpoint of $L^1$-framework. To do this, we establish the asymptotic formulas for $L^1$-norm of the solutions as $lambda o infty$.
Bare coupling constants and asymptotic behaviour in reggeon field theory
International Nuclear Information System (INIS)
Baig, M.
1983-01-01
A relation between the values of bare coupling constants and the asymptotic behaviour of the reggeon field theory (RFT) is discussed. It is shown how the numerical values of bare coupling constants fix the starting point of renormalization group trajectories which, in turn, determine the asymptotic behaviour of the RFT. Applications to a pure pomeron theory and a pomeron plus f-pole model are discussed. Some nontrivial phenomenological information concerning the values of bare triple-Regge pomeron-f-pole coupling constants is obtained
Asymptotic analysis of spatial discretizations in implicit Monte Carlo
Energy Technology Data Exchange (ETDEWEB)
Densmore, Jeffery D [Los Alamos National Laboratory
2009-01-01
We perform an asymptotic analysis of spatial discretizations in Implicit Monte Carlo (IMC). We consider two asymptotic scalings: one that represents a time step that resolves the mean-free time, and one that corresponds to a fixed, optically large time step. We show that only the latter scaling results in a valid spatial discretization of the proper diffusion equation, and thus we conclude that IMC only yields accurate solutions when using optically large spatial cells if time steps are also optically large. We demonstrate the validity of our analysis with a set of numerical examples.
Asymptotic analysis of spatial discretizations in implicit Monte Carlo
Energy Technology Data Exchange (ETDEWEB)
Densmore, Jeffery D [Los Alamos National Laboratory
2008-01-01
We perform an asymptotic analysis of spatial discretizations in Implicit Monte Carlo (IMC). We consider two asymptotic scalings: one that represents a time step that resolves the mean-free time, and one that corresponds to a fixed, optically large time step. We show that only the latter scaling results in a valid spatial discretization of the proper diffusion equation, and thus we conclude that IMC only yields accurate solutions when using optically large spatial cells if time steps are also optically large, We demonstrate the validity of our analysis with a set of numerical examples.
Asymptotically Optimal Quantum Circuits for d-Level Systems
International Nuclear Information System (INIS)
Bullock, Stephen S.; O'Leary, Dianne P.; Brennen, Gavin K.
2005-01-01
Scalability of a quantum computation requires that the information be processed on multiple subsystems. However, it is unclear how the complexity of a quantum algorithm, quantified by the number of entangling gates, depends on the subsystem size. We examine the quantum circuit complexity for exactly universal computation on many d-level systems (qudits). Both a lower bound and a constructive upper bound on the number of two-qudit gates result, proving a sharp asymptotic of Θ(d 2n ) gates. This closes the complexity question for all d-level systems (d finite). The optimal asymptotic applies to systems with locality constraints, e.g., nearest neighbor interactions
Global Asymptotic Stability of Switched Neural Networks with Delays
Directory of Open Access Journals (Sweden)
Zhenyu Lu
2015-01-01
Full Text Available This paper investigates the global asymptotic stability of a class of switched neural networks with delays. Several new criteria ensuring global asymptotic stability in terms of linear matrix inequalities (LMIs are obtained via Lyapunov-Krasovskii functional. And here, we adopt the quadratic convex approach, which is different from the linear and reciprocal convex combinations that are extensively used in recent literature. In addition, the proposed results here are very easy to be verified and complemented. Finally, a numerical example is provided to illustrate the effectiveness of the results.
Asymptotic Confidence Regions for High-Dimensional Structured Sparsity
Stucky, Benjamin; van de Geer, Sara
2018-04-01
In the setting of high-dimensional linear regression models, we propose two frameworks for constructing pointwise and group confidence sets for penalized estimators which incorporate prior knowledge about the organization of the non-zero coefficients. This is done by desparsifying the estimator as in van de Geer et al. [18] and van de Geer and Stucky [17], then using an appropriate estimator for the precision matrix $\\Theta$. In order to estimate the precision matrix a corresponding structured matrix norm penalty has to be introduced. After normalization the result is an asymptotic pivot. The asymptotic behavior is studied and simulations are added to study the differences between the two schemes.
Dynamics of loops: asymptotic freedom and quark confinement
International Nuclear Information System (INIS)
Makeenko, Yu.M.; Migdal, A.A.
1980-01-01
New manifestly gauge invariant diagram technique in the loop space is developed. For that purpose a boot-strap ' equation, determining the self-consistent asymptotics, is solved in the framework of the perturbation theory. The boot-strap equation is equivalent to the system including the Bianchi identity and the planar equation accompanied by Euclidean boundary conditions. It is shown that the area law of quark confinement is a self-consistent solution of the boot-strap equation. The frame diagrams constructed by means of certain operator technique reproduce asymptotic freedom in the ultraviolet range
The asymptotic theory of resonance charge exchange between diatomics
International Nuclear Information System (INIS)
Yevsyev, A.V.; Radtsig, A.A.; Smirnov, B.M.
1982-01-01
The asymptotic theory of resonance charge exchange between a ground-state diatomic molecular ion and its neutral parent is presented. The parameters of the valence electron wavefunction and asymptotically precise exchange interaction potential are calculated. The role of rotational transitions is discussed. The vibrational excitation transfer is taken into account and the coupled equations, describing the charge exchange process between diatomics are solved both in limiting cases and numerically. The total charge transfer cross sections are calculated for many diatomic systems and the results are compared with experimental data. (author)
Selected asymptotic methods with applications to electromagnetics and antennas
Fikioris, George; Bakas, Odysseas N
2013-01-01
This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include som
Asymptotic solutions of diffusion models for risk reserves
Directory of Open Access Journals (Sweden)
S. Shao
2003-01-01
Full Text Available We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a special class of initial and boundary value problems defined by a linear diffusion equation. Armed with asymptotic analysis and perturbation theory, we obtain the asymptotic solutions of the diffusion models (possibly degenerate governing the conditional probability of ruin over a finite time in terms of interest rate.
Vacuum energy in asymptotically flat 2+1 gravity
Directory of Open Access Journals (Sweden)
Olivera Miskovic
2017-04-01
Full Text Available We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern–Simons formulation for the Poincaré group. The equivalent action is nothing but the Einstein–Hilbert term in the bulk plus half of the Gibbons–Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.
Convergence Theorem for Finite Family of Total Asymptotically Nonexpansive Mappings
Directory of Open Access Journals (Sweden)
E.U. Ofoedu
2015-11-01
Full Text Available In this paper we introduce an explicit iteration process and prove strong convergence of the scheme in a real Hilbert space $H$ to the common fixed point of finite family of total asymptotically nonexpansive mappings which is nearest to the point $u \\in H$. Our results improve previously known ones obtained for the class of asymptotically nonexpansive mappings. As application, iterative method for: approximation of solution of variational Inequality problem, finite family of continuous pseudocontractive mappings, approximation of solutions of classical equilibrium problems and approximation of solutions of convex minimization problems are proposed. Our theorems unify and complement many recently announced results.
ADM Mass for Asymptotically de Sitter Space-Time
International Nuclear Information System (INIS)
Huang Shiming; Yue Ruihong; Jia Dongyan
2010-01-01
In this paper, an ADM mass formula for asymptotically de Sitter(dS) space-time is derived from the energy-momentum tensor. We take the vacuum dS space as the background and investigate the ADM mass of the (d + 3)-dimensional sphere-symmetric space with a positive cosmological constant, and find that the ADM mass of asymptotically dS space is based on the ADM mass of Schwarzschild field and the cosmological background brings some small mass contribution as well. (general)
TAIL ASYMPTOTICS OF LIGHT-TAILED WEIBULL-LIKE SUMS
DEFF Research Database (Denmark)
Asmussen, Soren; Hashorva, Enkelejd; Laub, Patrick J.
2017-01-01
We consider sums of n i.i.d. random variables with tails close to exp{-x(beta)} for some beta > 1. Asymptotics developed by Rootzen (1987) and Balkema, Kluppelberg, and Resnick (1993) are discussed from the point of view of tails rather than of densities, using a somewhat different angle, and sup......We consider sums of n i.i.d. random variables with tails close to exp{-x(beta)} for some beta > 1. Asymptotics developed by Rootzen (1987) and Balkema, Kluppelberg, and Resnick (1993) are discussed from the point of view of tails rather than of densities, using a somewhat different angle...
Asymptotically safe and free chiral theories with and without scalars
DEFF Research Database (Denmark)
Mølgaard, E.; Sannino, Francesco
2017-01-01
We unveil the dynamics of four-dimensional chiral gauge-Yukawa theories featuring several scalar degrees of freedom transforming according to distinct representations of the underlying gauge group. We consider generalized Georgi-Glashow and Bars-Yankielowicz theories. We determine, to the maximum...... known order in perturbation theory, the phase diagram of these theories and further disentangle their ultraviolet asymptotic nature according to whether they are asymptotically free or safe. We therefore extend the number of theories that are known to be fundamental in the Wilsonian sense to the case...... of chiral gauge theories with scalars....
The Symmetry of Optical Field in Photonic Crystal Fibre with Trigonal Symmetry
Directory of Open Access Journals (Sweden)
Ivan Turek
2006-01-01
Full Text Available Some photographs of intensity of optical field of a photonic crystal fibre are presented in the contribution. Presented photographs document that the symmetry of photonic crystal creating the cladding of fibre is manifested in the symmetry of distribution of the optical field intensity. In case when more modes are excited in the fibre the symmetry of the generated field can be different as the symmetry of the eventual modes. How the symmetry may be changed is illustrated by amodel example.
Dynamical study of symmetries: breaking and restauration
International Nuclear Information System (INIS)
Schuck, P.
1986-09-01
First symmetry breaking (spontaneous) is explained and the physical implication discussed for infinite systems. The relation with phase transitions is indicated. Then the specific aspects of symmetry breaking in finite systems is treated and illustrated in detail for the case of translational invariance with the help of an oversimplified but exactly solvable model. The method of projection (restauration of symmetry) is explained for the static case and also applied to the model. Symmetry breaking in the dynamical case and for instance the notion of a soft mode responsible for the symmetry breaking is discussed in the case of superfluidity and another exactly solvable model is introduced. The Goldstone mode is treated in detail. Some remarks on analogies with the breaking of chiral symmetry are made. Some recent developments in the theory of symmetry restauration are briefly outlined [fr
International Nuclear Information System (INIS)
Misguich, J.H.
1978-09-01
The physical meaning of perturbed trajectories in turbulent fields is analysed. Special care is devoted to the asymptotic description of average trajectories for long time intervals, as occuring in many recent plasma turbulence theories. Equivalence is proved between asymptotic average trajectories described as well (i) by the propagators V(t,t-tau) for retrodiction and Wsub(J)(t,t+tau) for prediction, and (ii) by the long time secular behavior of the solution of the equations of motion. This confirms the equivalence between perturbed orbit theories and renormalized theories, including non-Markovian contributions
Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition
José, Jorge V.
2017-03-01
In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested
Asymptotics for Greeks under the constant elasticity of variance model
Kritski, Oleg L.; Zalmezh, Vladimir F.
2017-01-01
This paper is concerned with the asymptotics for Greeks of European-style options and the risk-neutral density function calculated under the constant elasticity of variance model. Formulae obtained help financial engineers to construct a perfect hedge with known behaviour and to price any options on financial assets.
Solute transport through porous media using asymptotic dispersivity
Indian Academy of Sciences (India)
In this paper, multiprocess non-equilibrium transport equation has been used, which accounts for both physical and chemical non-equilibrium for reactive transport through porous media. An asymptotic distance dependent dispersivity is used to embrace the concept of scale-dependent dispersion for solute transport in ...
Asymptotic absolute continuity for perturbed time-dependent ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Under various conditions on the second term, the perturbation, including (as a mini- mum) boundedness of second order derivatives (being locally uniform in t), we study the large-time behaviour of the dynamics U(t) generated by the family of H(t)'s. We are interested in a generalization of the notion of asymptotic velocity ...
Technicolor and the asymptotic behavior of dynamically generated masses
International Nuclear Information System (INIS)
Natale, A.A.
1984-01-01
Arguments are given in favor of a hard asymptotic behavior of dynamically generated masses, its consequences for technicolor models are analyzed and a model is proposed, where effects of flavor changing neutral currents are highly supressed and pseudo Goldstone bosons get masses of O(30-90) GeV. (Author) [pt
Penrose inequality for asymptotically AdS spaces
Energy Technology Data Exchange (ETDEWEB)
Itkin, Igor [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978 (Israel); Oz, Yaron, E-mail: yaronoz@post.tau.ac.il [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978 (Israel)
2012-02-28
In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background. If the inequality is violated by an initial Cauchy data, it suggests a creation of a naked singularity, thus providing means to consider the cosmic censorship hypothesis. We propose a general form of Penrose inequality for asymptotically locally AdS spaces.
Asymptotic behavior of stochastic two-dimensional Navier–Stokes ...
Indian Academy of Sciences (India)
ple, Caraballo et al in [4], have discussed the exponential behavior and stabilizability of stochastic 2D Navier–Stokes equations. The existence and uniqueness of solutions to the backward 2D stochastic Navier–Stokes equations was obtained in [10]. In [6], Caraballo and Real have considered the asymptotic behavior of ...
Asymptotics for Estimating Equations in Hidden Markov Models
DEFF Research Database (Denmark)
Hansen, Jørgen Vinsløv; Jensen, Jens Ledet
Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore a class of estimating equations is considered...
On asymptotic isotropy for a hydrodynamic model of liquid crystals
Czech Academy of Sciences Publication Activity Database
Dai, M.; Feireisl, Eduard; Rocca, E.; Schimperna, G.; Schonbek, M.E.
2016-01-01
Roč. 97, 3-4 (2016), s. 189-210 ISSN 0921-7134 Grant - others:European Research Council(XE) MATHEF(320078) Institutional support: RVO:67985840 Keywords : liquid crystal * Q-tensor description * long-time behavior Subject RIV: BA - General Mathematics Impact factor: 0.933, year: 2016 http://content.iospress.com/articles/asymptotic-analysis/asy1348
Asymptotic expansions of Mathieu functions in wave mechanics
International Nuclear Information System (INIS)
Hunter, G.; Kuriyan, M.
1976-01-01
Solutions of the radial Schroedinger equation containing a polarization potential r -4 are expanded in a form appropriate for large values of r. These expansions of the Mathieu functions are used in association with the numerical solution of the Schroedinger equation to impose the asymptotic boundary condition in the case of bound states, and to extract phase shifts in the case of scattering states
Summing of the asymptotic series in the quantum field theory
International Nuclear Information System (INIS)
Krasnikov, N.V.; Rubakov, V.A.; Tokarev, V.F.
1979-01-01
It is suggested to sum up the asymptotic series of the perturbation theory in the gphi 4 model by the method which stems naturally from the representation of the Green functions in terms of the continual integral. In this method the Green functions are analytical in the coupling constant in the region Re g >= 0. The method suggested is equivalent to the Borel one
Relaxing the parity conditions of asymptotically flat gravity
Compère, G.; Dehouck, F.
2011-01-01
Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counterterm