The Experts below are selected from a list of 135147 Experts worldwide ranked by ideXlab platform
Fei Huang - One of the best experts on this subject based on the ideXlab platform.
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vortices circumfluence Symmetry Groups and darboux transformations of the 2 1 dimensional euler equation
Physical Review E, 2007Co-Authors: S Y Lou, Man Jia, Xiaoyan Tang, Fei HuangAbstract:The Euler equation (EE) is one of the basic equations in many physical fields such as fluids, plasmas, condensed matter, astrophysics, and oceanic and atmospheric dynamics. A Symmetry Group theorem of the (2+1) -dimensional EE is obtained via a simple direct method which is thus utilized to find exact analytical vortex and circumfluence solutions. A weak Darboux transformation theorem of the (2+1) -dimensional EE can be obtained for an arbitrary spectral parameter from the general Symmetry Group theorem. Possible applications of the vortex and circumfluence solutions to tropical cyclones, especially Hurricane Katrina 2005, are demonstrated.
Asher Yahalom - One of the best experts on this subject based on the ideXlab platform.
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lorentz Symmetry Group retardation intergalactic mass depletion and mechanisms leading to galactic rotation curves
arXiv: General Physics, 2020Co-Authors: Asher YahalomAbstract:The general theory of relativity (GR) is symmetric under smooth coordinate transformations, also known as diffeomorphisms. The general coordinate transformation Group has a linear subGroup denoted as the Lorentz Group of Symmetry, which is also maintained in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d'Alembert (wave) operator, which has a retarded potential solution. Galaxies are huge physical systems with dimensions of many tens of thousands of light years. Thus, any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects are neglected in the present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper, we will show that, by taking general relativity seriously without neglecting retardation effects, one can explain the radial velocities of galactic matter in the M33 galaxy without postulating dark matter.
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lorentz Symmetry Group retardation intergalactic mass depletion and mechanisms leading to galactic rotation curves
Symmetry, 2020Co-Authors: Asher YahalomAbstract:The general theory of relativity (GR) is symmetric under smooth coordinate transformations, also known as diffeomorphisms. The general coordinate transformation Group has a linear subGroup denoted as the Lorentz Group of Symmetry, which is also maintained in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d’Alembert (wave) operator, which has a retarded potential solution. Galaxies are huge physical systems with dimensions of many tens of thousands of light years. Thus, any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects are neglected in the present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper, we will show that, by taking general relativity seriously without neglecting retardation effects, one can explain the radial velocities of galactic matter in the M33 galaxy without postulating dark matter. It should be stressed that the current approach does not require that velocities v are high; in fact, the vast majority of galactic bodies (stars, gas) are substantially subluminal—in other words, the ratio of vc≪1. Typical velocities in galaxies are 100 km/s, which makes this ratio 0.001 or smaller. However, one should consider the fact that every gravitational system, even if it is made of subluminal bodies, has a retardation distance, beyond which the retardation effect cannot be neglected. Every natural system, such as stars and galaxies and even galactic clusters, exchanges mass with its environment, for example, the sun loses mass through solar wind and galaxies accrete gas from the intergalactic medium. This means that all natural gravitational systems have a finite retardation distance. The question is thus quantitative: how large is the retardation distance? For the M33 galaxy, the velocity curve indicates that the retardation effects cannot be neglected beyond a certain distance, which was calculated to be roughly 14,000 light years; similar analysis for other galaxies of different types has shown similar results. We demonstrate, using a detailed model, that this does not require a high velocity of gas or stars in or out of the galaxy and is perfectly consistent with the current observational knowledge of galactic and extra galactic material content and dynamics.
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a new diffeomorphism Symmetry Group of non barotropic magnetohydrodynamics
arXiv: Plasma Physics, 2018Co-Authors: Asher YahalomAbstract:The theorem of Noether dictates that for every continuous Symmetry Group of an Action the system must possess a conservation law. In this paper we discuss some subGroups of Arnold's labelling Symmetry diffeomorphism related to non-barotropic magnetohydrodynamics (MHD) and the conservations laws associated with them. Those include but are not limited to the metage translation Group and the associated topological conservations law of non-barotropic cross helicity.
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a new diffeomorphism Symmetry Group of magnetohydrodynamics
2013Co-Authors: Asher YahalomAbstract:Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. Yahalom (A four function variational principle for Barotropic magnetohydrodynamics, EPL 89, 34005 (2010) has shown that barotropic magnetohydrodynamics is mathematically equivalent to a four function field theory defined a by a Lagrangian for some topologies. The four functions include two surfaces whose intersections consist the magnetic field lines, the part of the velocity field not defined by the comoving magnetic field and the density. This Lagrangian admits a newly discovered Group of Diffeomorphism Symmetry. I discuss the Symmetry Group and derive the related Noether current.
Ashvin Vishwanath - One of the best experts on this subject based on the ideXlab platform.
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classification of interacting topological floquet phases in one dimension
arXiv: Strongly Correlated Electrons, 2016Co-Authors: Ashvin Vishwanath, Andrew C Potter, Takahiro MorimotoAbstract:Periodic driving of a quantum system can enable new topological phases with no analog in static systems. In this paper we systematically classify one-dimensional topological and Symmetry-protected topological (SPT) phases in interacting fermionic and bosonic quantum systems subject to periodic driving, which we dub Floquet SPTs (FSPTs). For physical realizations of interacting FSPTs, many-body localization by disorder is a crucial ingredient, required to obtain a stable phase that does not catastrophically heat to infinite temperature. We demonstrate that bosonic and fermionic FSPTs phases are classified by the same criteria as equilibrium phases, but with an enlarged Symmetry Group $\tilde G$, that now includes discrete time translation Symmetry associated with the Floquet evolution. In particular, 1D bosonic FSPTs are classified by projective representations of the enlarged Symmetry Group $H^2({\tilde G},U(1))$. We construct explicit lattice models for a variety of systems, and then formalize the classification to demonstrate the completeness of this construction. We also derive general constraints on localization and Symmetry based on the representation theory of the Symmetry Group, and show that Symmetry-preserving localized phases are possible only for Abelian Symmetry Groups. In particular, this rules out the possibility of many-body localized SPTs with continuous spin Symmetry.
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spin liquid states on the triangular and kagome lattices a projective Symmetry Group analysis of schwinger boson states
Physical Review B, 2006Co-Authors: Fa Wang, Ashvin VishwanathAbstract:A Symmetry-based analysis (projective Symmetry Group) is used to study spin-liquid phases on the triangular and Kagom\'e lattices in the Schwinger boson framework. A maximum of eight distinct ${Z}_{2}$ spin-liquid states are found for each lattice, which preserve all symmetries. Out of these only a few have nonvanishing nearest-neighbor amplitudes, which are studied in greater detail. On the triangular lattice, only two such states are present---the first (zero-flux state) is the well-known state introduced by Sachdev, which on condensation of spinons leads to the 120\ifmmode^\circ\else\textdegree\fi{} ordered state. The other solution, which we call the $\ensuremath{\pi}$-flux state has not previously been discussed. Spinon condensation leads to an ordering wave vector at the Brillouin zone edge centers, in contrast to the 120\ifmmode^\circ\else\textdegree\fi{} state. While the zero-flux state is more stable with just nearest-neighbor exchange, we find that the introduction of either next-neighbor antiferromagnetic exchange or four-spin ring exchange (of the sign obtained from a Hubbard model) tends to favor the $\ensuremath{\pi}$-flux state. On the Kagom\'e lattice four solutions are obtained---two have been previously discussed by Sachdev, which on spinon condensation give rise to the $q=0$ and $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ spin-ordered states. In addition we find two states with significantly larger values of the quantum parameter at which magnetic ordering occurs. For one of them this even exceeds unity ${\ensuremath{\kappa}}_{c}\ensuremath{\approx}2.0$ in a nearest-neighbor model, indicating that if stabilized, could remain spin disordered for physical values of the spin. This state is also stabilized by ring-exchange interactions with signs as derived from the Hubbard model.
Samuel Bieri - One of the best experts on this subject based on the ideXlab platform.
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projective Symmetry Group classification of chiral spin liquids
Physical Review B, 2016Co-Authors: Samuel Bieri, C Lhuillier, Laura MessioAbstract:We present a general review of the projective Symmetry Group classification of fermionic quantum spin liquids for lattice models of spin $S=1/2$. We then introduce a systematic generalization of the approach for symmetric ${\mathbb{Z}}_{2}$ quantum spin liquids to the one of chiral phases (i.e., singlet states that break time reversal and lattice reflection, but conserve their product). We apply this framework to classify and discuss possible chiral spin liquids on triangular and kagome lattices. We give a detailed prescription on how to construct quadratic spinon Hamiltonians and microscopic wave functions for each representation class on these lattices. Among the chiral ${\mathbb{Z}}_{2}$ states, we study the subset of U(1) phases variationally in the antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{d}$ Heisenberg model on the kagome lattice. We discuss static spin structure factors and Symmetry constraints on the bulk spectra of these phases.
Gregory W Moore - One of the best experts on this subject based on the ideXlab platform.
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moonshine superconformal Symmetry and quantum error correction
arXiv: High Energy Physics - Theory, 2020Co-Authors: Jeffrey A Harvey, Gregory W MooreAbstract:Special conformal field theories can have Symmetry Groups which are interesting sporadic finite simple Groups. Famous examples include the Monster Symmetry Group of a $c=24$ two-dimensional conformal field theory (CFT) constructed by Frenkel, Lepowsky and Meurman, and the Conway Symmetry Group of a $c=12$ CFT explored in detail by Duncan and Mack-Crane. The Mathieu moonshine connection between the K3 elliptic genus and the Mathieu Group $M_{24}$ has led to the study of K3 sigma models with large Symmetry Groups. A particular K3 CFT with a maximal Symmetry Group preserving $(4,4)$ superconformal Symmetry was studied in beautiful work by Gaberdiel, Taormina, Volpato, and Wendland. The present paper shows that in both the GTVW and $c=12$ theories the construction of superconformal generators can be understood via the theory of quantum error correcting codes. The automorphism Groups of these codes lift to Symmetry Groups in the CFT preserving the superconformal generators. In the case of the $N=1$ supercurrent of the GTVW model our result, combined with a result of T. Johnson-Freyd implies the Symmetry Group is the maximal subGroup of $M_{24}$ known as the sextet Group. (The sextet Group is also known as the holomorph of the hexacode.) Building on \cite{gtvw} the Ramond-Ramond sector of the GTVW model is related to the Miracle Octad Generator which in turn leads to a role for the Golay code as a Group of symmetries of RR states. Moreover, $(4,1)$ superconformal Symmetry suffices to define and decompose the elliptic genus of a K3 sigma model into characters of the $N=4$ superconformal algebra. The Symmetry Group preserving $(4,1)$ is larger than that preserving $(4,4)$.
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moonshine superconformal Symmetry and quantum error correction
Journal of High Energy Physics, 2020Co-Authors: Jeffrey A Harvey, Gregory W MooreAbstract:Special conformal field theories can have Symmetry Groups which are interesting sporadic finite simple Groups. Famous examples include the Monster Symmetry Group of a c = 24 two-dimensional conformal field theory (CFT) constructed by Frenkel, Lepowsky and Meurman, and the Conway Symmetry Group of a c = 12 CFT explored in detail by Duncan and Mack-Crane. The Mathieu moonshine connection between the K3 elliptic genus and the Mathieu Group M24 has led to the study of K3 sigma models with large Symmetry Groups. A particular K3 CFT with a maximal Symmetry Group preserving (4, 4) superconformal Symmetry was studied in beautiful work by Gaberdiel, Taormina, Volpato, and Wendland [41]. The present paper shows that in both the GTVW and c = 12 theories the construction of superconformal generators can be understood via the theory of quantum error correcting codes. The automorphism Groups of these codes lift to Symmetry Groups in the CFT preserving the superconformal generators. In the case of the N = 1 supercurrent of the GTVW model our result, combined with a result of T. Johnson-Freyd implies the Symmetry Group is the maximal subGroup of M24 known as the sextet Group. (The sextet Group is also known as the holomorph of the hexacode.) Building on [41] the Ramond-Ramond sector of the GTVW model is related to the Miracle Octad Generator which in turn leads to a role for the Golay code as a Group of symmetries of RR states. Moreover, (4, 1) superconformal Symmetry suffices to define and decompose the elliptic genus of a K3 sigma model into characters of the N = 4 superconformal algebra. The Symmetry Group preserving (4, 1) is larger than that preserving (4, 4).
