NASA Astrophysics Data System (ADS)
Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus
2013-07-01
the progress in experimental studies of artificial Abelian and non-Abelian gauge fields in recent years has been simply spectacular. Multiple leading groups are working on this subject and have already obtained a lot of seminal results. The papers in the special issue are ordered according to the date of acceptance. The issue opens with a review article by Zhou et al [1] on unconventional states of bosons with synthetic spin-orbit coupling. Next, the paper by Maldonado-Mundo et al [2] studies ultracold Fermi gases with artificial Rashba spin-orbit coupling in a 2D gas. Anderson and Charles [3], in contrast, discuss a three-dimensional spin-orbit coupling in a trap. Orth et al [4] investigate correlated topological phases and exotic magnetism with ultracold fermions, again in the presence of artificial gauge fields. The paper of Nascimbène [5] does not address the synthetic gauge fields directly, but describes an experimental proposal for realizing one-dimensional topological superfluids with ultracold atomic gases; obviously, this problem is well situated in the general and growing field of topological superfluids, in particular those realized in the presence of non-Abelian gauge fields/spin-orbit coupling. Graß et al [6] consider in their paper fractional quantum Hall states of a Bose gas with spin-orbit coupling induced by a laser. Particular attention is drawn here to the possibility of realizing states with non-Abelian anyonic excitations. Zheng et al [7] study properties of Bose gases with Raman-induced spin-orbit coupling. Kiffner et al [8] in their paper touch on another kind of system, namely ultracold Rydberg atoms. In particular they study the generation of Abelian and non-Abelian gauge fields in dipole-dipole interacting Rydberg atoms. The behaviour of fermions in synthetic non-Abelian gauge potentials is discussed by Shenoy and Vyasanakere [9]. The paper starts with the study of Rashbon condensates (i.e. Bose condensates in the presence of Rashba
NASA Astrophysics Data System (ADS)
Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus
2013-07-01
interesting and related effect, which arises from the interplay between strong magnetic field and lattice potentials, is the famous Hofstadter butterfly: the energy spectrum of a single particle moving on a lattice and subjected to a strong magnetic field displays a beautiful fractal structure as a function of the magnetic flux penetrating each elementary plaquette of the lattice. When the effects of interparticle interactions become dominant, two-dimensional gases of electrons exhibit even more exotic behaviour leading to the fractional quantum Hall effect. In certain conditions such a strongly interacting electron gas may form a highly correlated state of matter, the prototypical example being the celebrated Laughlin quantum liquid. Even more fascinating is the behaviour of bulk excitations (quasi-hole and quasi-particles): they are neither fermionic nor bosonic, but rather behave as anyons with fractional statistics intermediate between the two. Moreover, for some specific filling factors (ratio between the electronic density and the flux density), these anyons are proven to have an internal structure (several components) and non-Abelian braiding properties. Many of the above statements concern theoretical predictions—they have never been observed in condensed matter systems. For instance, the fractional values of the Hall conductance is seen as a direct consequence of the fractional statistics, but to date direct observation of anyons has not been possible in two-dimensional semiconductors. Realizing these predictions in experiments with atoms, ions, photons etc, which potentially allow the experimentalist to perform measurements complementary to those made in condensed matter systems, is thus highly desirable! Non-Abelian gauge fields couple the motional states of the particles to their internal degrees of freedom (such as hyperfine states for atoms or ions, electronic spins for electrons, etc). In this sense external non-Abelian fields extend the concept of spin
Non-Abelian gauge field theory in scale relativity
NASA Astrophysics Data System (ADS)
Nottale, Laurent; Célérier, Marie-Noëlle; Lehner, Thierry
2006-03-01
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the "scale-space." We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description.
Canonical non-Abelian dual transformations in supersymmetric field theories
Curtright, T.; Zachos, C.
1995-07-15
A generating functional {ital F} is found for a canonical non-Abelian dual transformation which maps the supersymmetric chiral O(4) {sigma} model to an equivalent supersymmetric extension of the dual {sigma} model. This {ital F} produces a mapping between the classical phase spaces of the two theories in which the bosonic (coordinate) fields transform nonlocally, the fermions undergo a local tangent space chiral rotation, and all currents (fermionic and bosonic) mix locally. Purely bosonic curvature-free currents of the chiral model become a {ital symphysis} of purely bosonic and fermion bilinear currents of the dual theory. The corresponding transformation functional {ital T} which relates wave functions in the two quantum theories is argued to be {ital exactly} given by {ital T}=exp({ital iF}).
Topological invariants measured for Abelian and non-Abelian monopole fields
NASA Astrophysics Data System (ADS)
Sugawa, Seiji; Salces Carcoba, Francisco; Perry, Abigail; Yue, Yuchen; Putra, Andika; Spielman, Ian
2016-05-01
Understanding the topological nature of physical systems is an important topic in contemporary physics, ranging from condensed matter to high energy. In this talk, I will present experiments measuring the 1st and 2nd Chern number in a four-level quantum system both with degenerate and non-degenerate energies. We engineered the system's Hamiltonian by coupling hyperfine ground states of rubidium-87 Bose-Einstein condensates with rf and microwave fields. We non-adiabatically drove the system and measured the linear response to obtain the local (non-Abelian) Berry curvatures. Then, the Chern numbers were evaluated on (hyper-)spherical manifolds in parameter space. We obtain Chern numbers close to unity for both the 1st and the 2nd Chern numbers. The non-zero Chern number can be interpreted as monopole residing inside the manifold. For our system, the monopoles correspond to a Dirac monopole for non-degenerate spectra and a Yang monopole for our degenerate case. We also show how the dynamical evolution under non-Abelian gauge field emerged in degenerate quantum system is different from non-degenerate case by showing path-dependent acquisition of non-Abelian geometric phase and Wilson loops.
Non-Abelian Aharonov-Bohm effect with the time-dependent gauge fields
NASA Astrophysics Data System (ADS)
Hosseini Mansoori, Seyed Ali; Mirza, Behrouz
2016-04-01
We investigate the non-Abelian Aharonov-Bohm (AB) effect for time-dependent gauge fields. We prove that the non-Abelian AB phase shift related to time-dependent gauge fields, in which the electric and magnetic fields are written in the adjoint representation of SU (N) generators, vanishes up to the first order expansion of the phase factor. Therefore, the flux quantization in a superconductor ring does not appear in the time-dependent Abelian or non-Abelian AB effect.
Field theory aspects of non-Abelian T-duality and {N} =2 linear quivers
NASA Astrophysics Data System (ADS)
Lozano, Yolanda; Núñez, Carlos
2016-05-01
In this paper we propose a linear quiver with gauge groups of increasing rank as field theory dual to the AdS 5 background constructed by Sfetsos and Thompson through non-Abelian T-duality. The formalism to study 4d {N} = 2 SUSY CFTs developed by Gaiotto and Maldacena is essential for our proposal. We point out an interesting relation between (Hopf) Abelian and non-Abelian T-dual backgrounds that allows to see both backgrounds as different limits of a solution constructed by Maldacena and Núñez. This suggests different completions of the long quiver describing the CFT dual to the nonAbelian T-dual background that match different observables.
Collective states of non-Abelian quasiparticles in a magnetic field
NASA Astrophysics Data System (ADS)
Levin, Michael; Halperin, Bertrand I.
2009-05-01
Motivated by the physics of the Moore-Read ν=1/2 state away from half filling, we investigate collective states of non-Abelian e/4 quasiparticles in a magnetic field. We consider two types of collective states: incompressible liquids and Wigner crystals. In the incompressible liquid case, we construct a natural series of states which can be thought of as a non-Abelian generalization of the Laughlin states. These states are associated with a series of hierarchical states derived from the Moore-Read state—the simplest of which occur at filling fraction 8/17 and 7/13. Interestingly, we find that the hierarchical states are Abelian even though their parent state is non-Abelian. In the Wigner crystal case, we construct two candidate states. We find that they, too, are Abelian—in agreement with previous analysis.
BCS-BEC crossover induced by a synthetic non-Abelian gauge field
Vyasanakere, Jayantha P.; Shenoy, Vijay B.; Zhang Shizhong
2011-07-01
We investigate the ground state of interacting spin-(1/2) fermions in three dimensions at a finite density ({rho}{approx}k{sub F}{sup 3}) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector {lambda}{identical_to}({lambda}{sub x},{lambda}{sub y},{lambda}{sub z}), whose magnitude {lambda} determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length (k{sub F}|a{sub s}| < or approx. 1), the ground state in the absence of the gauge field ({lambda}=0) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum ({lambda}=0). For large gauge couplings ({lambda}/k{sub F}>>1), the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)--we call these bosons ''rashbons.'' In the absence of interactions (a{sub s}=0{sup -}), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling {lambda}{sub T}. For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of {lambda} near {lambda}{sub T}. In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.
BCS-BEC crossover induced by a synthetic non-Abelian gauge field
NASA Astrophysics Data System (ADS)
Vyasanakere, Jayantha P.; Zhang, Shizhong; Shenoy, Vijay B.
2011-07-01
We investigate the ground state of interacting spin-(1)/(2) fermions in three dimensions at a finite density (ρ˜kF3) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector λ≡(λx,λy,λz), whose magnitude λ determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length (kF|as|≲1), the ground state in the absence of the gauge field (λ=0) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum (λ=0). For large gauge couplings (λ/kF≫1), the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)—we call these bosons “rashbons.” In the absence of interactions (as=0-), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling λT. For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of λ near λT. In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.
NASA Astrophysics Data System (ADS)
Markov, Yuri A.; Markova, Margaret A.; Shishmarev, Alexey A.
2010-10-01
Based on the most general principles of reality, gauge and reparametrization invariance, a problem of constructing the action describing dynamics of a classical color-charged particle interacting with background non-Abelian gauge and fermion fields is considered. The cases of the linear and quadratic dependence of a Lagrangian on background Grassmann fermion field are discussed. It is shown that in both cases in general there exists an infinite number of interaction terms, which should be included in the Lagrangian in question. Employing a simple iteration scheme, examples of the construction of the first few gauge-covariant currents and sources induced by a moving particle with non-Abelian charge are given. It is found that these quantities, by a suitable choice of parameters, exactly reproduce additional currents and sources previously obtained in Markov and Markova (2007 Nucl. Phys. A 784 443) on the basis of heuristic considerations.
Topological phase transitions on a triangular optical lattice with non-Abelian gauge fields
NASA Astrophysics Data System (ADS)
Iskin, M.
2016-03-01
We study the mean-field BCS-BEC evolution of a uniform Fermi gas on a single-band triangular lattice and construct its ground-state phase diagrams, showing a wealth of topological quantum phase transitions between gapped and gapless superfluids that are induced by the interplay of an out-of-plane Zeeman field and a generic non-Abelian gauge field.
Fendley, Paul; Fisher, Matthew P.A.; Nayak, Chetan
2009-07-15
We explain how (perturbed) boundary conformal field theory allows us to understand the tunneling of edge quasiparticles in non-Abelian topological states. The coupling between a bulk non-Abelian quasiparticle and the edge is due to resonant tunneling to a zero mode on the quasiparticle, which causes the zero mode to hybridize with the edge. This can be reformulated as the flow from one conformally invariant boundary condition to another in an associated critical statistical mechanical model. Tunneling from one edge to another at a point contact can split the system in two, either partially or completely. This can be reformulated in the critical statistical mechanical model as the flow from one type of defect line to another. We illustrate these two phenomena in detail in the context of the {nu}=5/2 quantum Hall state and the critical Ising model. We briefly discuss the case of Fibonacci anyons and conclude by explaining the general formulation and its physical interpretation.
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms.
Huo, Ming-Xia; Nie, Wei; Hutchinson, David A W; Kwek, Leong Chuan
2014-01-01
Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a "hairline" solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions. PMID:25103877
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms
NASA Astrophysics Data System (ADS)
Huo, Ming-Xia; Nie, Wei; Hutchinson, David A. W.; Kwek, Leong Chuan
2014-08-01
Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a ``hairline'' solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions.
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms
Huo, Ming-Xia; Nie, Wei; Hutchinson, David A. W.; Kwek, Leong Chuan
2014-01-01
Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a “hairline” solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions. PMID:25103877
Bound states of two spin-(1/2) fermions in a synthetic non-Abelian gauge field
Vyasanakere, Jayantha P.; Shenoy, Vijay B.
2011-03-01
We study the bound states of two spin-(1/2) fermions interacting via a contact attraction (characterized by a scattering length) in the singlet channel in three-dimensional space in presence of a uniform non-Abelian gauge field. The configuration of the gauge field that generates a Rashba-type spin-orbit interaction is described by three coupling parameters ({lambda}{sub x},{lambda}{sub y},{lambda}{sub z}). For a generic gauge field configuration, the critical scattering length required for the formation of a bound state is negative, i.e., shifts to the ''BCS side'' of the resonance. Interestingly, we find that there are special high-symmetry configurations (e.g., {lambda}{sub x}={lambda}{sub y}={lambda}{sub z}) for which there is a two-body bound state for anyscattering length however small and negative. Remarkably, the bound-state wave functions obtained for such configurations have nematic spin structure similar to those found in liquid {sup 3}He. Our results show that the BCS-BEC (Bose-Einstein condensation) crossover is drastically affected by the presence of a non-Abelian gauge field. We discuss possible experimental signatures of our findings both at high and low temperatures.
Condensing Non-Abelian Quasiparticles
Hermanns, M.
2010-02-05
A most interesting feature of certain fractional quantum Hall states is that their quasiparticles obey non-Abelian fractional statistics. So far, candidate non-Abelian wave functions have been constructed from conformal blocks in cleverly chosen conformal field theories. In this work we present a hierarchy scheme by which we can construct daughter states by condensing non-Abelian quasiparticles (as opposed to quasiholes) in a parent state, and show that the daughters have a non-Abelian statistics that differs from the parent. In particular, we discuss the daughter of the bosonic, spin-polarized Moore-Read state at nu=4/3 as an explicit example.
Simulation of non-Abelian lattice gauge fields with a single-component gas
NASA Astrophysics Data System (ADS)
Kosior, Arkadiusz; Sacha, Krzysztof
2014-07-01
We show that non-Abelian lattice gauge fields can be simulated with a single-component ultra-cold atomic gas in an optical-lattice potential. An optical lattice can be viewed as a Bravais lattice with a N-point basis. An atom located at different points of the basis can be considered as a particle in different internal states. The appropriate engineering of tunneling amplitudes of atoms in an optical lattice allows one to realize U(N) gauge potentials and control a mass of particles that experience such non-Abelian gauge fields. We provide and analyze a concrete example of an optical-lattice configuration that allows for simulation of a static U(2) gauge model with a constant Wilson loop and an adjustable mass of particles. In particular, we observe that the non-zero mass creates large conductive gaps in the energy spectrum, which could be important in the experimental detection of the transverse Hall conductivity.
Quantum phase transition of ultracold bosons in the presence of a non-Abelian synthetic gauge field
Grass, T.; Saha, K.; Sengupta, K.; Lewenstein, M.
2011-11-15
We study the Mott phases and the superfluid-insulator transition of two-component ultracold bosons on a square optical lattice in the presence of a non-Abelian synthetic gauge field, which renders a SU(2)-hopping matrix for the bosons. Using a resummed hopping expansion, we calculate the excitation spectra in the Mott insulating phases and demonstrate that the superfluid-insulator phase boundary displays a nonmonotonic dependence on the gauge-field strength. We also compute the momentum distribution of the bosons in the presence of the non-Abelian field and show that they develop peaks at nonzero momenta as the superfluid-insulator transition point is approached from the Mott side. Finally, we study the superfluid phases near the transition and discuss the induced spatial pattern of the superfluid density due to the presence of the non-Abelian gauge potential.
Fields in nonaffine bundles. IV. Harmonious non-Abelian currents in string defects
NASA Astrophysics Data System (ADS)
Carter, Brandon
2010-11-01
This article continues the study of the category of harmonious field models that was recently introduced as a kinetically nonlinear generalization of the well-known harmonic category of multiscalar fields over a supporting brane world sheet in a target space with a curved Riemannian metric. Like the perfectly harmonious case of which a familiar example is provided by ordinary barotropic perfect fluids, another important subcategory is the simply harmonious case, for which it is shown that as well as “wiggle” modes of the underlying brane world sheet, and sound type longitudinal modes, there will also be transverse shake modes that propagate at the speed of light. Models of this type are shown to arise from a non-Abelian generalization of the Witten mechanism for conducting string formation by ordinary scalar fields with a suitable quartic self-coupling term in the action.
NASA Astrophysics Data System (ADS)
Vyasanakere, Jayanth P.; Shenoy, Vijay B.
2013-03-01
A non-Abelian gauge field that induces a spin-orbit coupling on the motion of fermions engenders a BCS-BEC crossover even for weakly attracting fermions. The transition temperature at large spin-orbit coupling is known to be determined by the mass of the emergent boson - the rashbon. We obtain the transition temperature of the system as a function of the spin-orbit coupling by constructing and studying a Gaussian fluctuation (Nozieres-Schmitt-Rink) theory. These results will help guide the upcoming experiments on spin-orbit coupled fermions. In addition, this work suggests a route to enhance the transition temperature of a weakly attracting fermionic system by tuning the spin-orbit coupling. Work supported by CSIR, DST, DAE India
Dynamical symmetry breaking, gauge fields, and stability in four-Fermi, non-abelian interactions
Portney, M.N.
1983-01-01
The Nambu model of dynamical breaking of global symmetry is extended to the case of non-abelian SU(N) models. The possible patterns of symmetry breaking are investigated, and the masses of the composite spinless particles are found. Corresponding to each broken generator, this composite is the massless Goldstone boson. When the global symmetries are made local by the addition of gauge fields, the composite pseudoscalar Goldstone bosons disappear and the axial gauge fields become massive. This is analogous to the Higgs mechanism, but without the introduction of fundamental scalar fields. The composite scalar Goldstone bosons remain in the theory, and the vector gauge fields are still massless. This is in agreement with the charge conjugation argument. The stability of the possible solutions is discussed using several criteria. It is concluded that in theories with zero bare mass, if a nontrivial solution exists, the completely symmetric massive solution is realized. If the bare mass is symmetric and non-zero, asymmetric solutions may be found, with corresponding scalar Goldstone composites. These violate the persistent mass condition of Preskill and Weinberg.
Mass generation for non-Abelian antisymmetric tensor fields in a three-dimensional space-time
Medeiros, D. M.; Landim, R. R.; Almeida, C. A. S.
2001-06-15
Starting from a recently proposed Abelian topological model in 2+1 dimensions, which involve the Kalb-Ramond two form field, we study a non-Abelian generalization of the model. An obstruction for the generalization is detected. However, we show that the goal is achieved if we introduce a vectorial auxiliary field. Consequently, a model is proposed, exhibiting a non-Abelian topological mass generation mechanism in D=3, that provides mass for the Kalb-Ramond field. The covariant quantization of this model requires ghosts for ghosts. Therefore, in order to quantize the theory, we construct a complete set of Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST equations using the horizontality condition.
Gluon production from non-Abelian Weizsäcker-Williams fields in nucleus-nucleus collisions
NASA Astrophysics Data System (ADS)
Kovner, Alex; McLerran, Larry; Weigert, Heribert
1995-12-01
We consider the collisions of large nuclei using the theory of McLerran and Venugopalan. The two nuclei are ultrarelativistic and sources of non-Abelian Weizs¨acker-Williams fields. These sources are in the end averaged over all color orientations locally with a Gaussian weight. We show that there is a solution of the equations of motion for the two nucleus scattering problem where the fields are time and rapidity independent before the collision. After the collision the solution depends on proper time, but is independent of rapidity. We show how to extract the produced gluons from the classical evolution of the fields.
Magnetic-field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at ν = 5/2.
Willett, R L; Nayak, C; Shtengel, K; Pfeiffer, L N; West, K W
2013-11-01
We show that the resistance of the ν = 5/2 quantum Hall state, confined to an interferometer, oscillates with the magnetic field consistent with an Ising-type non-Abelian state. In three quantum Hall interferometers of different sizes, resistance oscillations at ν = 7/3 and integer filling factors have the magnetic field period expected if the number of quasiparticles contained within the interferometer changes so as to keep the area and the total charge within the interferometer constant. Under these conditions, an Abelian state such as the (3, 3, 1) state would show oscillations with the same period as at an integer quantum Hall state. However, in an Ising-type non-Abelian state there would be a rapid oscillation associated with the "even-odd effect" and a slower one associated with the accumulated Abelian phase due to both the Aharonov-Bohm effect and the Abelian part of the quasiparticle braiding statistics. Our measurements at ν = 5/2 are consistent with the latter. PMID:24237543
Abelian and non-Abelian bosonization: The operator solution of the WZW. sigma. model
do Amaral, R.L.P.G. ); Stephany Ruiz, J.E. )
1991-03-15
The complete equivalence between the Abelian and the non-Abelian bosonization formalisms for the treatment of SU({ital N}) fermions in two dimensions is analyzed and the operator solution of the Wess-Zumino-Witten nonlinear {sigma} model, written in terms of the scalar fields of the non-Abelian construction, is obtained. The importance of the order and disorder operators is stressed. In particular, they are used to show that an adequate reinterpretation of Mandelstam's formula gives the fermion representation in the non-Abelian bosonization formalism.
Confinement Driven by Scalar Field in 4d Non Abelian Gauge Theories
Chabab, Mohamed
2007-01-12
We review some of the most recent work on confinement in 4d gauge theories with a massive scalar field (dilaton). Emphasis is put on the derivation of confining analytical solutions to the Coulomb problem versus dilaton effective couplings to gauge terms. It is shown that these effective theories can be relevant to model quark confinement and may shed some light on confinement mechanism. Moreover, the study of interquark potential, derived from Dick Model, in the heavy meson sector proves that phenomenological investigation of tmechanism is more than justified and deserves more efforts.
Linear resistivity from non-abelian black holes
NASA Astrophysics Data System (ADS)
Herzog, Christopher P.; Huang, Kuo-Wei; Vaz, Ricardo
2014-11-01
Starting with the holographic p-wave superconductor, we show how to obtain a finite DC conductivity through a non-abelian gauge transformation. The translational symmetry is preserved. We obtain phenomenological similarities with high temperature cuprate superconductors. Our results suggest that a lattice or impurities are not essential to produce a finite DC resistivity with a linear temperature dependence. An analogous field theory calculation for free fermions, presented in the appendix, indicates our results may be a special feature of strong interactions.
Enhancing Gauge Symmetries of Non-Abelian Supersymmetric Chern-Simons Model
NASA Astrophysics Data System (ADS)
Gharavi, Kh. Bahalke; Monemzadeh, M.; Nejad, S. Abarghouei
2016-07-01
In this article, we study gauge symmetries of the Non-Abelian Supersymmetric Chern-Simons model (SCS) of SU(2) group at (2+1)-dimensions in the framework of the formalism of constrained systems. Since, broken gauge symmetries in this physical system lead to the presence of nonphysical degrees of freedom, the Non-Abelian SCS model is strictly constrained to second-class constraints. Hence, by introducing some auxiliary fields and using finite order BFT method, we obtain a gauge symmetric model by converting second-class constraint to first-class ones. Ultimately, the partition function of the model is obtained in the extended phase space.
Topological quantum liquids with quaternion non-Abelian statistics.
Xu, Cenke; Ludwig, Andreas W W
2012-01-27
Noncollinear magnetic order is typically characterized by a tetrad ground state manifold (GSM) of three perpendicular vectors or nematic directors. We study three types of tetrad orders in two spatial dimensions, whose GSMs are SO(3) = S(3)/Z(2), S(3)/Z(4), and S(3)/Q(8), respectively. Q(8) denotes the non-Abelian quaternion group with eight elements. We demonstrate that after quantum disordering these three types of tetrad orders, the systems enter fully gapped liquid phases described by Z(2), Z(4), and non-Abelian quaternion gauge field theories, respectively. The latter case realizes Kitaev's non-Abelian toric code in terms of a rather simple spin-1 SU(2) quantum magnet. This non-Abelian topological phase possesses a 22-fold ground state degeneracy on the torus arising from the 22 representations of the Drinfeld double of Q(8). PMID:22400884
Quantum structure of the non-Abelian Weizsäcker-Williams field for a very large nucleus
NASA Astrophysics Data System (ADS)
Kovchegov, Yuri V.
1997-05-01
We consider the McLerran-Venugopalan model for calculation of the small-x part of the gluon distribution function for a very large ultrarelativistic nucleus at weak coupling. We construct the Feynman diagrams which correspond to the classical Weizsäcker-Williams field found previously [Yu. V. Kovchegov, Phys. Rev. D 54, 5463 (1996)] as a solution of the classical equations of motion for the gluon field in the light-cone gauge. Analyzing these diagrams we obtain a limit for the McLerran-Venugopalan model. We show that as long as this limit is not violated a classical field can be used for the calculation of scattering amplitudes.
Quantum structure of the non-Abelian Weizs{umlt a}cker-Williams field for a very large nucleus
Kovchegov, Y.V.
1997-05-01
We consider the McLerran-Venugopalan model for calculation of the small-x part of the gluon distribution function for a very large ultrarelativistic nucleus at weak coupling. We construct the Feynman diagrams which correspond to the classical Weizs{umlt a}cker-Williams field found previously [Yu. V. Kovchegov, Phys. Rev. D {bold 54}, 5463 (1996)] as a solution of the classical equations of motion for the gluon field in the light-cone gauge. Analyzing these diagrams we obtain a limit for the McLerran-Venugopalan model. We show that as long as this limit is not violated a classical field can be used for the calculation of scattering amplitudes. {copyright} {ital 1997} {ital The American Physical Society}
Geometry and energy of non-Abelian vortices
Manton, Nicholas S.; Rink, Norman A.
2011-04-15
We study pure Yang-Mills theory on {Sigma}xS{sup 2}, where {Sigma} is a compact Riemann surface, and invariance is assumed under rotations of S{sup 2}. It is well known that the self-duality equations in this setup reduce to vortex equations on {Sigma}. If the Yang-Mills gauge group is SU(2), the Bogomolny vortex equations of the Abelian Higgs model are obtained. For larger gauge groups, one generally finds vortex equations involving several matrix-valued Higgs fields. Here we focus on Yang-Mills theory with gauge group SU(N)/Z{sub N} and a special reduction which yields only one non-Abelian Higgs field. One of the new features of this reduction is the fact that while the instanton number of the theory in four dimensions is generally fractional with denominator N, we still obtain an integral vortex number in the reduced theory. We clarify the relation between these two topological charges at a bundle geometric level. Another striking feature is the emergence of nontrivial lower and upper bounds for the energy of the reduced theory on {Sigma}. These bounds are proportional to the area of {Sigma}. We give special solutions of the theory on {Sigma} by embedding solutions of the Abelian Higgs model into the non-Abelian theory, and we relate our work to the language of quiver bundles, which has recently proved fruitful in the study of dimensional reduction of Yang-Mills theory.
Non-Abelian vortices and non-Abelian statistics
Lo, H.; Preskill, J. )
1993-11-15
We study the interactions of non-Abelian vortices in two spatial dimensions. These interactions have novel features, because the Aharonov-Bohm effect enables a pair of vortices to exchange quantum numbers. The cross section for vortex-vortex scattering is typically a multivalued function of the scattering angle. There can be an exchange contribution to the vortex-vortex scattering amplitude that adds coherently with the direct amplitude, even if the two vortices have distinct quantum numbers. Thus two vortices can be indistinguishable'' even though they are not the same.
Dynamical non-Abelian two-form: BRST quantization
Lahiri, A.
1997-04-01
When an antisymmetric tensor potential is coupled to the field strength of a gauge field via a BANDF coupling and a kinetic term for B is included, the gauge field develops an effective mass. The theory can be made invariant under a non-Abelian vector gauge symmetry by introducing an auxiliary vector field. The covariant quantization of this theory requires ghosts for ghosts. The resultant theory including gauge fixing and ghost terms is BRST invariant by construction, and therefore unitary. The construction of the BRST-invariant action is given for both Abelian and non-Abelian models of mass generation. {copyright} {ital 1997} {ital The American Physical Society}
Non-Abelian Anyons and Interferometry
NASA Astrophysics Data System (ADS)
Bonderson, Parsa Hassan
This thesis is primarily a study of the measurement theory of non-Abelian anyons through interference experiments. We give an introduction to the theory of anyon models, providing all the formalism necessary to apply standard quantum measurement theory to such systems. This formalism is then applied to give a detailed analysis of a Mach-Zehnder interferometer for arbitrary anyon models. In this treatment, we find that the collapse behavior exhibited by a target anyon in a superposition of states is determined by the monodromy of the probe anyons with the target. Such measurements may also be used to gain knowledge that would help to properly identify the anyon model describing an unknown system. The techniques used and results obtained from this model interferometer have general applicability, and we use them to also describe the interferometry measurements in a two point-contact interferometer proposed for non-Abelian fractional quantum Hall states. Additionally, we give the complete description of a number of important examples of anyon models, as well as their corresponding quantities that are relevant for interferometry. Finally, we give a partial classification of anyon models with small numbers of particle types.
Majorana meets Coxeter: Non-Abelian Majorana fermions and non-Abelian statistics
Yasui, Shigehiro; Itakura, Kazunori; Nitta, Muneto
2011-04-01
We discuss statistics of vortices having zero-energy non-Abelian Majorana fermions inside them. Considering the system of multiple non-Abelian vortices, we derive a non-Abelian statistics that differs from the previously derived non-Abelian statistics. The non-Abelian statistics presented here is given by a tensor product of two different groups, namely the non-Abelian statistics obeyed by the Abelian Majorana fermions and the Coxeter group. The Coxeter group is a symmetric group related to the symmetry of polytopes in a high-dimensional space. As the simplest example, we consider the case in which a vortex contains three Majorana fermions that are mixed with each other under the SO(3) transformations. We concretely present the representation of the Coxeter group in our case and its geometrical expressions in the high-dimensional Hilbert space constructed from non-Abelian Majorana fermions.
Non-Abelian dynamics in the resonant decay of the Higgs after inflation
Enqvist, Kari; Nurmi, Sami; Rusak, Stanislav E-mail: sami.nurmi@helsinki.fi
2014-10-01
We study the resonant decay of the Higgs condensate into weak gauge bosons after inflation and estimate the corrections arising from the non-Abelian self-interactions of the gauge fields. We find that non-Abelian interaction terms induce an effective mass which tends to shut down the resonance. For the broad resonance relevant for the Standard Model Higgs the produced gauge particles backreact on the dynamics of the Higgs condensate before the non-Abelian terms grow large. The non-Abelian terms can however significantly affect the final stages of the resonance after the backreaction. In the narrow resonance regime, which may be important for extensions of the Standard Model, the non-Abelian terms affect already the linear stage and terminate the resonance before the Higgs condensate is affected by the backreaction of decay products.
Non-Abelian black holes in D=5 maximal gauged supergravity
Cvetic, M.; Lue, H.; Pope, C. N.
2010-02-15
We investigate static non-Abelian black hole solutions of anti-de Sitter (AdS) Einstein-Yang-Mills-dilaton gravity, which is obtained as a consistent truncation of five-dimensional maximal gauged supergravity. If the dilaton is (consistently) set to zero, the remaining equations of motion, with a spherically-symmetric ansatz, may be derived from a superpotential. The associated first-order equations admit an explicit solution supported by a non-Abelian SU(2) gauge potential, which has a logarithmically growing mass term. In an extremal limit the horizon geometry becomes AdS{sub 2}xS{sup 3}. If the dilaton is also excited, the equations of motion cannot easily be solved explicitly, but we obtain the asymptotic form of the more general non-Abelian black holes in this case. An alternative consistent truncation, in which the Yang-Mills fields are set to zero, also admits a description in terms of a superpotential. This allows us to construct explicit wormhole solutions (neutral spherically-symmetric domain walls). These solutions may be generalized to dimensions other than five.
An Exact Chiral Spin Liquid with Non-Abelian Anyons
Yao, Hong
2010-04-06
We establish the existence of a chiral spin liquid (CSL) as the exact ground state of the Kitaev model on a decorated honeycomb lattice, which is obtained by replacing each site in the familiar honeycomb lattice with a triangle. The CSL state spontaneously breaks time reversal symmetry but preserves other symmetries. There are two topologically distinct CSLs separated by a quantum critical point. Interestingly, vortex excitations in the topologically nontrivial (Chern number {+-}1) CSL obey non-Abelian statistics.
Non-Abelian Braiding of Light.
Iadecola, Thomas; Schuster, Thomas; Chamon, Claudio
2016-08-12
Many topological phenomena first proposed and observed in the context of electrons in solids have recently found counterparts in photonic and acoustic systems. In this work, we demonstrate that non-Abelian Berry phases can arise when coherent states of light are injected into "topological guided modes" in specially fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order in which the guided beams are wound around one another. Notably, these effects survive the limit of large photon occupation, and can thus also be understood as wave phenomena arising directly from Maxwell's equations, without resorting to the quantization of light. We propose an optical interference experiment as a direct probe of this non-Abelian braiding of light. PMID:27563965
NASA Astrophysics Data System (ADS)
Iadecola, Thomas; Schuster, Thomas; Chamon, Claudio
2016-08-01
Many topological phenomena first proposed and observed in the context of electrons in solids have recently found counterparts in photonic and acoustic systems. In this work, we demonstrate that non-Abelian Berry phases can arise when coherent states of light are injected into "topological guided modes" in specially fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order in which the guided beams are wound around one another. Notably, these effects survive the limit of large photon occupation, and can thus also be understood as wave phenomena arising directly from Maxwell's equations, without resorting to the quantization of light. We propose an optical interference experiment as a direct probe of this non-Abelian braiding of light.
Non-Abelian quantum holonomy of hydrogenlike atoms
Mousolou, Vahid Azimi; Canali, Carlo M.; Sjoeqvist, Erik
2011-09-15
We study the Uhlmann holonomy [Rep. Math. Phys. 24, 229 (1986)] of quantum states for hydrogenlike atoms where the intrinsic spin and orbital angular momentum are coupled by the spin-orbit interaction and are subject to a slowly varying magnetic field. We show that the holonomy for the orbital angular momentum and spin subsystems is non-Abelian while the holonomy of the whole system is Abelian. Quantum entanglement in the states of the whole system is crucially related to the non-Abelian gauge structure of the subsystems. We analyze the phase of the Wilson loop variable associated with the Uhlmann holonomy and find a relation between the phase of the whole system and corresponding marginal phases. Based on the results for the model system, we provide evidence that the phase of the Wilson loop variable and the mixed-state geometric phase [E. Sjoeqvist et al., Phys. Rev. Lett. 85, 2845 (2000).] are generally inequivalent.
Designer non-Abelian anyon platforms: from Majorana to Fibonacci
NASA Astrophysics Data System (ADS)
Alicea, Jason; Stern, Ady
2015-12-01
The emergence of non-Abelian anyons from large collections of interacting elementary particles is a conceptually beautiful phenomenon with important ramifications for fault-tolerant quantum computing. Over the last few decades the field has evolved from a highly theoretical subject to an active experimental area, particularly following proposals for trapping non-Abelian anyons in ‘engineered’ structures built from well-understood components. In this short overview we briefly tour the impressive progress that has taken place in the quest for the simplest type of non-Abelian anyon—defects binding Majorana zero modes—and then turn to similar strategies for pursuing more exotic excitations. Specifically, we describe how interfacing simple quantum Hall systems with conventional superconductors yields ‘parafermionic’ generalizations of Majorana modes and even Fibonacci anyons—the latter enabling fully fault tolerant universal quantum computation. We structure our treatment in a manner that unifies these topics in a coherent way. The ideas synthesized here spotlight largely uncharted experimental territory in the field of quantum Hall physics that appears ripe for discovery.
Non-Abelian statistics of Luttinger holes in quantum wells
NASA Astrophysics Data System (ADS)
Simion, George; Lyanda-Geller, Yuli
2015-03-01
Non-Abelian quasiparticle excitations represent a key element of topologically protected quantum computing. Such exotic states appear in fractional quantum Hall (FQH) effect as eigenstates of N-body interaction potential. These potentials can be obtained by renormalization of electron-electron interactions in the presence of Landau level (LL) mixing. The properties of valence band holes makes them fundamentally different from electrons. In the presence of magnetic field, low-lying states do not exhibit fan-like diagram and several of the levels cross. Variation of magnetic field in the vicinity of level crossings serves as a knob that tunes LL mixing and enhances the 3-body interaction. 1 / 2 filling factor FQH is a state that was not observed in electron liquid, but has been observed for holes. The properties of the two dimensional charged quantum hole liquid in the presence of magnetic field are studied using the spherical geometry. The properties of the novel 1 / 2 state are discussed. Research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0010544.
A non-perturbative argument for the non-abelian Higgs mechanism
De Palma, G.; Strocchi, F.
2013-09-15
The evasion of massless Goldstone bosons by the non-abelian Higgs mechanism is proved by a non-perturbative argument in the local BRST gauge. -- Highlights: •The perturbative explanation of the Higgs mechanism (HM) is not under mathematical control. •We offer a non-perturbative proof of the absence of Goldstone bosons from the non-abelian HM. •Our non-perturbative proof in the BRST gauge avoids a mean field ansatz and expansion.
Viennot, David
2010-10-15
We show that the holonomy of a connection defined on a principal composite bundle is related by a non-Abelian Stokes theorem to the composition of the holonomies associated with the connections of the component bundles of the composite. We apply this formalism to describe the non-Abelian geometric phase (when the geometric phase generator does not commute with the dynamical phase generator). We find then an assumption to obtain a new kind of separation between the dynamical and the geometric phases. We also apply this formalism to the gauge theory of gravity in the presence of a Dirac spinor field in order to decompose the holonomy of the Lorentz connection into holonomies of the linear connection and of the Cartan connection.
Non-abelian dynamics in first-order cosmological phase transitions
Johnson, Mikkel B.; Kisslinger, Leonard S.; Henley, Ernest M.; Hwang, P. W-Y.; Stevens, T.
2004-01-01
Bubble collisions in cosmological phase transitions are explored, taking the non-abelian character of the gauge fields into account. Both the QCD and electroweak phase transitions are considered. Numerical solutions of the field equations in several limits are presented. The investigations reported in this talk have been motivated by an interest in studying cosmological phase transitions quantitatively, taking the non-abelian character of the gauge fields into account. Ultimately, we hope to identify observable consequences of cosmological phase transitions. First-order phase transitions proceed by nucleation of bubbles of the broken phase in the background of the symmetric phase. Bubble collisions are of special interest, as they may lead to observable effects such as correlations in the cosmic microwave background (CMB) or as seeds of galactic and extra-galactic magnetic fields. The quantum chromodynamic (QCD) and the electroweak (EW) phase transitions are both candidates of interest in these respects. The Lagrangian driving both the QCD and the EW phase transitions are essentially known and make it possible to approach the physics of the phase transitions from first principles. However, a difficulty to making reliable predictions is that the fundamental guage fields in both these instances are non-abelian: the gluon field in QCD and the W and Z fields in the EW case. The quantitative role of non-abelian fields in cosmological phase transitions is poorly known and difficult to calculate due to the nonlinearities arising from the non-abelian character of the gauge fields.
NASA Astrophysics Data System (ADS)
Ortín, Tomás; Ramírez, Pedro F.
2016-09-01
We construct a supersymmetric black ring solution of SU (2) N = 1, d = 5 Super-Einstein-Yang-Mills (SEYM) theory by adding a distorted BPST instanton to an Abelian black ring solution of the same theory. The change cannot be observed from spatial infinity: neither the mass, nor the angular momenta or the values of the scalars at infinity differ from those of the Abelian ring. The entropy is, however, sensitive to the presence of the non-Abelian instanton, and it is smaller than that of the Abelian ring, in analogy to what happens in the supersymmetric colored black holes recently constructed in the same theory and in N = 2, d = 4 SEYM. By taking the limit in which the two angular momenta become equal we derive a non-Abelian generalization of the BMPV rotating black-hole solution.
The non-Abelian gauge theory of matrix big bangs
NASA Astrophysics Data System (ADS)
O'Loughlin, Martin; Seri, Lorenzo
2010-07-01
We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantization to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will show that the quartic interaction is always subleading as one approaches the singularity and that close enough to t = 0 the evolution is driven by the diverging tachyonic mass term. The evolution towards asymptotically flat space-time also reveals some surprising features.
Non-Abelian discrete gauge symmetries in F-theory
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Pugh, Tom G.; Regalado, Diego
2016-02-01
The presence of non-Abelian discrete gauge symmetries in four-dimensional F-theory compactifications is investigated. Such symmetries are shown to arise from seven-brane configurations in genuine F-theory settings without a weak string coupling description. Gauge fields on mutually non-local seven-branes are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is completed into a generalisation of the Heisenberg group with either additional seven-brane gauge fields or R-R bulk gauge fields. The former case relies on having seven-brane fluxes, while the latter case requires torsion cohomology and is analysed in detail through the M-theory dual. Remarkably, the M-theory reduction yields an Abelian theory that becomes non-Abelian when translated into the correct duality frame to perform the F-theory limit. The reduction shows that the gauge coupling function depends on the gauged scalars and transforms non-trivially as required for the groups encountered. This field dependence agrees with the expectations for the kinetic mixing of seven-branes and is unchanged if the gaugings are absent.
Fermion structure of non-Abelian vortices in high density QCD
Yasui, Shigehiro; Itakura, Kazunori; Nitta, Muneto
2010-05-15
We study the internal structure of a non-Abelian vortex in color superconductivity with respect to quark degrees of freedom. Stable non-Abelian vortices appear in the color-flavor-locked phase whose symmetry SU(3){sub c+L+R} is further broken to SU(2){sub c+L+R} x U(1){sub c+L+R} at the vortex cores. Microscopic structure of vortices at scales shorter than the coherence length can be analyzed by the Bogoliubov-de Gennes equation (rather than the Ginzburg-Landau equation). We obtain quark spectra from the Bogoliubov-de Gennes equation by treating the diquark gap having the vortex configuration as a background field. We find that there are massless modes (zero modes) well-localized around a vortex, in the triplet and singlet states of the unbroken symmetry SU(2){sub c+L+R} x U(1){sub c+L+R}. The velocities v{sub i} of the massless modes (i=t, s for triplet and singlet) change at finite chemical potential {mu}{ne}0, and decrease as {mu} becomes large. Therefore, low energy excitations in the vicinity of the vortices are effectively described by 1+1 dimensional massless fermions whose velocities are reduced v{sub i}<1.
Non abelian hydrodynamics and heavy ion collisions
Calzetta, E.
2014-01-14
The goal of the relativistic heavy ion collisions (RHIC) program is to create a state of matter where color degrees of freedom are deconfined. The dynamics of matter in this state, in spite of the complexities of quantum chromodynamics, is largely determined by the conservation laws of energy momentum and color currents. Therefore it is possible to describe its main features in hydrodynamic terms, the very short color neutralization time notwithstanding. In this lecture we shall give a simple derivation of the hydrodynamics of a color charged fluid, by generalizing the usual derivation of hydrodynamics from kinetic theory to the non abelian case.
Non-Abelian geometric phase and long-range atomic forces
NASA Technical Reports Server (NTRS)
Zygelman, B.
1990-01-01
It is shown how gauge fields, or geometric phases, manifest as observable effects in both bound and free diatom systems. It is shown that, in addition to altering energy splittings in bound systems, geometric phases induce transitions in levels separated by a finite-energy gap. An example is given where the non-Abelian gauge field couples nondegenerate electronic levels in a diatom. This gauge-field coupling gives rise to an observable effect. It is shown that when the diatom is 'pulled apart', the non-Abelian geometric phase manifests as a long-range atomic force.
Matrix product states and the non-Abelian rotor model
NASA Astrophysics Data System (ADS)
Milsted, Ashley
2016-04-01
We use uniform matrix product states to study the (1 +1 )D O (2 ) and O (4 ) rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free non-Abelian lattice gauge theory on a "Hawaiian earring" graph for U (1 ) and S U (2 ), respectively. Applying tangent space methods to obtain ground states and determine the mass gap and the β function, we find excellent agreement with known results, locating the Berezinskii-Kosterlitz-Thouless transition for O (2 ) and successfully entering the asymptotic weak-coupling regime for O (4 ). To obtain a finite local Hilbert space, we truncate in the space of generalized Fourier modes of the gauge group, comparing the effects of different cutoff values. We find that higher modes become important in the crossover and weak-coupling regimes of the non-Abelian theory, where entanglement also suddenly increases. This could have important consequences for tensor network state studies of Yang-Mills on higher-dimensional graphs.
Sun, Fadi; Yu, Xiao-Lu; Ye, Jinwu; Fan, Heng; Liu, Wu-Ming
2013-01-01
The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non-Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and explore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase transition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops. PMID:23846153
Controlling and probing non-abelian emergent gauge potentials in spinor Bose-Fermi mixtures
Phuc, Nguyen Thanh; Tatara, Gen; Kawaguchi, Yuki; Ueda, Masahito
2015-01-01
Gauge fields, typified by the electromagnetic field, often appear as emergent phenomena due to geometrical properties of a curved Hilbert subspace, and provide a key mechanism for understanding such exotic phenomena as the anomalous and topological Hall effects. Non-abelian gauge potentials serve as a source of non-singular magnetic monopoles. Here we show that unlike conventional solid materials, the non-abelianness of emergent gauge potentials in spinor Bose-Fermi atomic mixtures can be continuously varied by changing the relative particle-number densities of bosons and fermions. The non-abelian feature is captured by an explicit dependence of the measurable spin current density of fermions in the mixture on the variable coupling constant. Spinor mixtures also provide us with a method to coherently and spontaneously generate a pure spin current without relying on the spin Hall effect. Such a spin current is expected to have potential applications in the new generation of atomtronic devices. PMID:26330292
Beyond parafermions: Defects and zero-modes in non-Abelian phases
NASA Astrophysics Data System (ADS)
Lindner, Netanel; Berg, Erez; Stern, Ady
Non-Abelian topological phases of matter can be utilized to encode and manipulate quantum information in a non-local manner, such that it is protected from imperfections in the implemented protocols and from interactions with the environment. The condition that the non-Abelian statistics of the anyons supports a computationally universal set of gates sets a very stringent requirement which is not met by many topological phases. We consider the possibility to enrich the possible topological operations supported by a non-Abelian topological phase by introducing defects into the system. We show that such defects bind zero modes which form a unique algebra that goes beyond the algebra of parafermions which describes defects in Abelian phases. For the case of a bi-layer containing Ising anyons, we show that by coupling zero modes one can obtain a set of topological operations that implements a universal set of gates.
Non-Abelian gerbes and enhanced Leibniz algebras
NASA Astrophysics Data System (ADS)
Strobl, Thomas
2016-07-01
We present the most general gauge-invariant action functional for coupled 1- and 2-form gauge fields with kinetic terms in generic dimensions, i.e., dropping eventual contributions that can be added in particular space-time dimensions only such as higher Chern-Simons terms. After appropriate field redefinitions it coincides with a truncation of the Samtleben-Szegin-Wimmer action. In the process one sees explicitly how the existence of a gauge-invariant functional enforces that the most general semistrict Lie 2-algebra describing the bundle of a non-Abelian gerbe gets reduced to a very particular structure, which, after the field redefinition, can be identified with the one of an enhanced Leibniz algebra. This is the first step towards a systematic construction of such functionals for higher gauge theories, with kinetic terms for a tower of gauge fields up to some highest form degree p , solved here for p =2 .
Cold Atoms in Non-Abelian Gauge Potentials: From the Hofstadter Moth to Lattice Gauge Theory
Osterloh, K.; Baig, M.; Santos, L.; Zoller, P.; Lewenstein, M.
2005-07-01
We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary kxk matrices. The single-particle dynamics in the case of intense U(2) vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.
Non-Abelian quantum error correction
NASA Astrophysics Data System (ADS)
Feng, Weibo
A quantum computer is a proposed device which would be capable of initializing, coherently manipulating, and measuring quantum states with sufficient accuracy to carry out new kinds of computations. In the standard scenario, a quantum computer is built out of quantum bits, or qubits, two-level quantum systems which replace the ordinary classical bits of a classical computer. Quantum computation is then carried out by applying quantum gates, the quantum equivalent of Boolean logic gates, to these qubits. The most fundamental barrier to building a quantum computer is the inevitable errors which occur when carrying out quantum gates and the loss of quantum coherence of the qubits due to their coupling to the environment (decoherence). Remarkably, it has been shown that in a quantum computer such errors and decoherence can be actively fought using what is known as quantum error correction. A closely related proposal for fighting errors and decoherence in a quantum computer is to build the computer out of so-called topologically ordered states of matter. These are states of matter which allow for the storage and manipulation of quantum states with a built in protection from error and decoherence. The excitations of these states are non-Abelian anyons, particle-like excitations which satisfy non-Abelian statistics, meaning that when two excitations are interchanged the result is not the usual +1 and -1 associated with identical Bosons or Fermions, but rather a unitary operation which acts on a multidimensional Hilbert space. It is therefore possible to envision computing with these anyons by braiding their world-lines in 2+1-dimensional spacetime. In this Dissertation we present explicit procedures for a scheme which lives at the intersection of these two approaches. In this scheme we envision a functioning ``conventional" quantum computer consisting of an array of qubits and the ability to carry out quantum gates on these qubits. We then give explicit quantum circuits
NASA Astrophysics Data System (ADS)
Kovchegov, Yuri V.
1996-11-01
We consider a very large ultrarelativistic nucleus. Assuming a simple model of the nucleus and weak coupling we find a classical solution for the gluon field of the nucleus and construct the two-dimensional color charge density for McLerran-Venugopalan model out of it. We prove that the density of states distribution, as a function of color charge density, is Gaussian, confirming the assumption made by McLerran and Venugopalan.
Kovchegov, Y.V.
1996-11-01
We consider a very large ultrarelativistic nucleus. Assuming a simple model of the nucleus and weak coupling we find a classical solution for the gluon field of the nucleus and construct the two-dimensional color charge density for McLerran-Venugopalan model out of it. We prove that the density of states distribution, as a function of color charge density, is Gaussian, confirming the assumption made by McLerran and Venugopalan. {copyright} {ital 1996 The American Physical Society.}
Quantum Hall effects in a non-Abelian honeycomb lattice
NASA Astrophysics Data System (ADS)
Li, Ling; Hao, Ningning; Liu, Guocai; Bai, Zhiming; Li, Zai-Dong; Chen, Shu; Liu, W. M.
2015-12-01
We study the tunable quantum Hall effects in a non-Abelian honeycomb optical lattice which is a multi-Dirac-point system. We find that the quantum Hall effects present different features with the change in relative strengths of several perturbations. Namely, the quantum spin Hall effect can be induced by gauge-field-dressed next-nearest-neighbor hopping, which, together with a Zeeman field, can induce the quantum anomalous Hall effect characterized by different Chern numbers. Furthermore, we find that the edge states of the multi-Dirac-point system represent very different features for different boundary geometries, in contrast with the generic two-Dirac-point system. Our study extends the borders of the field of quantum Hall effects in a honeycomb optical lattice with multivalley degrees of freedom.
The existence of self-dual vortices in a non-Abelian {Phi}{sup 2} Chern-Simons theory
Chen Shouxin; Wang Ying
2010-09-15
Applying the dynamic shooting method, we proved the existence of nontopological radially symmetric n-vortex solutions to the self-dual equation in non-Abelian Chern-Simons gauge theory with a {Phi}{sup 2}-type potential. Moreover, we obtained all possible radially symmetric nontopological bare (or 0-vortex) solutions in the non-Abelian Chern-Simons model. Meanwhile, we established the asymptotic behavior for the solutions as |x|{yields}{infinity}.
NASA Astrophysics Data System (ADS)
Iskin, M.
2016-01-01
We consider a two-component Fermi gas with attractive interactions on a square optical lattice, and study the interplay of Zeeman field, spin-orbit coupling, and next-nearest-neighbor hopping on the ground-state phase diagrams in the entire BCS-BEC evolution. In particular, we first classify and distinguish all possible superfluid phases by the momentum-space topology of their zero-energy quasiparticle-quasihole excitations, and then numerically establish a plethora of quantum phase transitions in between. These transitions are further signaled and evidenced by the changes in the corresponding topological invariant of the system, i.e., its Chern number. Lastly, we find that the superfluid phase exhibits a reentrant structure, separated by a fingering normal phase, the origin of which is traced back to the changes in the single-particle density of states.
Non-Abelian Effects on D-Branes
Russo, Jorge G.
2008-07-28
We review different non-Abelian configurations of D-branes. We then extend the Myers dielectric effect to configurations with angular momentum. The resulting time-dependent N D0-brane bound states can be interpreted as describing rotating fuzzy ellipsoids. A similar solution exists also in the presence of a RR magnetic field, that we study in detail. We show that, for any finite N, above a certain critical angular momentum it is energetically more favorable for the bound state system to dissociate into an Abelian configuration of N D0-branes moving independently. We further study D-string configurations representing fuzzy funnels deformed by the magnetic field and by the rotational motion.
On Geometrical Interpretation of Non-Abelian Flat Direction Constraints
NASA Astrophysics Data System (ADS)
Cleaver, G. B.; Nanopoulos, D. V.; Perkins, J. T.; Walker, J. W.
In order to produce a low-energy effective field theory from a string model, it is necessary to specify a vacuum state. In order that this vacuum be supersymmetric, it is well known that all field expectation values must be along so-called flat directions, leaving the F- and D-terms of the scalar potential to be zero. The situation becomes particularly interesting when one attempts to realize such directions while assigning vacuum expectation values to fields transforming under non-Abelian representations of the gauge group. Since the expectation value is now shared among multiple components of a field, satisfaction of flatness becomes an inherently geometrical problem in the group space. Furthermore, the possibility emerges that a single seemingly dangerous F-term might experience a self-cancellation among its components. The hope exists that the geometric language can provide an intuitive and immediate recognition of when the D and F conditions are simultaneously compatible, as well as a powerful tool for their comprehensive classification. This is the avenue explored in this paper, and applied to the cases of SU(2) and SO(2N), relevant respectively to previous attempts at reproducing the MSSM and the flipped SU(5) GUT. Geometrical interpretation of non-Abelian flat directions finds application to M-theory through the recent conjecture of equivalence between D-term strings and wrapped D-branes of Type II theory.1 Knowledge of the geometry of the flat direction "landscape" of a D-term string model could yield information about the dual brane model. It is hoped that the techniques encountered will be of benefit in extending the viability of the quasirealistic phenomenologies already developed.
Collective States of D(D3) Non-Abelian Anyons
NASA Astrophysics Data System (ADS)
Finch, P. E.; Frahm, H.
2013-11-01
We study an exactly solvable model of non-Abelian anyons symmetric under the quantum double of the dihedral group D3 on a one-dimensional lattice. Bethe ansatz methods are employed to compute the ground states of this model in different regions of the parameter space. The finite size spectrum is studied and the corresponding low energy field theories are identified.
Constraint Structure and Quantization of a Non-Abelian Gauge Theory by Means of Dirac Brackets
NASA Astrophysics Data System (ADS)
Bracken, Paul
An SO(3) non-Abelian gauge theory is introduced. The Hamiltonian density is determined and the constraint structure of the model is derived. The first-class constraints are obtained and gauge-fixing constraints are introduced into the model. Finally, using the constraints, the Dirac brackets can be determined and a canonical quantization is found using Dirac's procedure.
Experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers
NASA Astrophysics Data System (ADS)
Yin, Long-Jing; Qiao, Jia-Bin; Zuo, Wei-Jie; Li, Wen-Tian; He, Lin
2015-08-01
Non-Abelian gauge potentials are quite relevant in subatomic physics, but they are relatively rare in a condensed matter context. Here we report the experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers by scanning tunneling microscopy and spectroscopy. At a magic twisted angle, θ ≈(1.11±0.05 ) ∘ , a pronounced sharp peak, which arises from the nondispersive flat bands at the charge neutrality point, is observed in the tunneling density of states due to the action of the non-Abelian gauge fields. Moreover, we observe confined electronic states in the twisted bilayer, as manifested by regularly spaced tunneling peaks with energy spacing δ E ≈vF/D ≈70 meV (here vF is the Fermi velocity of graphene and D is the period of the moiré patterns). This indicates that the non-Abelian gauge potentials in twisted graphene bilayers confine low-energy electrons into a triangular array of quantum dots following the modulation of the moiré patterns. Our results also directly demonstrate that the Fermi velocity in twisted bilayers can be tuned from about 106m /s to zero by simply reducing the twisted angle of about 2∘.
The non-abelian tensor multiplet in loop space
NASA Astrophysics Data System (ADS)
Gustavsson, Andreas
2006-01-01
We introduce a non-abelian tensor multiplet directly in the loop space associated with flat six-dimensional Miskowski space-time, and derive the supersymmetry variations for on-shell Script N = (2,0) supersymmetry.
Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
NASA Astrophysics Data System (ADS)
Huang, Po-Hao; Chen, Jyong-Hao; Gomes, Pedro R. S.; Neupert, Titus; Chamon, Claudio; Mudry, Christopher
2016-05-01
We construct two-dimensional non-Abelian topologically ordered states by strongly coupling arrays of one-dimensional quantum wires via interactions. In our scheme, all charge degrees of freedom are gapped, so the construction can use either quantum wires or quantum spin chains as building blocks, with the same end result. The construction gaps the degrees of freedom in the bulk, while leaving decoupled states at the edges that are described by conformal field theories (CFT) in (1 +1 ) -dimensional space and time. We consider both the cases where time-reversal symmetry (TRS) is present or absent. When TRS is absent, the edge states are chiral and stable. We prescribe, in particular, how to arrive at all the edge states described by the unitary CFT minimal models with central charges c <1 . These non-Abelian spin liquid states have vanishing quantum Hall conductivities, but nonzero thermal ones. When TRS is present, we describe scenarios where the bulk state can be a non-Abelian, nonchiral, and gapped quantum spin liquid, or a gapless one. In the former case, we find that the edge states are also gapped. The paper provides a brief review of non-Abelian bosonization and affine current algebras, with the purpose of being self-contained. To illustrate the methods in a warm-up exercise, we recover the tenfold way classification of two-dimensional noninteracting topological insulators using the Majorana representation that naturally arises within non-Abelian bosonization. Within this scheme, the classification reduces to counting the number of null singular values of a mass matrix, with gapless edge modes present when left and right null eigenvectors exist.
NASA Astrophysics Data System (ADS)
Zhang, Yi; Vishwanath, Ashvin
2013-04-01
We use entanglement entropy signatures to establish non-Abelian topological order in projected Chern-insulator wave functions. The simplest instance is obtained by Gutzwiller projecting a filled band with Chern number C=2, whose wave function may also be viewed as the square of the Slater determinant of a band insulator. We demonstrate that this wave function is captured by the SU(2)2 Chern-Simons theory coupled to fermions. This is established most persuasively by calculating the modular S-matrix from the candidate ground-state wave functions, following a recent entanglement-entropy-based approach. This directly demonstrates the peculiar non-Abelian braiding statistics of Majorana fermion quasiparticles in this state. We also provide microscopic evidence for the field theoretic generalization, that the Nth power of a Chern number C Slater determinant realizes the topological order of the SU(N)C Chern-Simons theory coupled to fermions, by studying the SU(2)3 (Read-Rezayi-type state) and the SU(3)2 wave functions. An advantage of our projected Chern-insulator wave functions is the relative ease with which physical properties, such as entanglement entropy and modular S-matrix, can be numerically calculated using Monte Carlo techniques.
NASA Astrophysics Data System (ADS)
Zhang, Yi; Vishwanath, Ashvin
2013-03-01
We use entanglement entropy signatures to establish non-Abelian topological order in a new class of ground states, the projected Chern-insulator wave functions. The simplest instance is obtained by Gutzwiller projecting a filled band with Chern number C=2 which may also be viewed as the square of the band insulator Slater determinant. We demonstrate that this wave function is captured by the SU(2)2 Chern Simons theory coupled to fermions. In addition to the expected torus degeneracy and topological entanglement entropy, we also show that the modular S-matrix, extracted from entanglement entropy calculations, provides direct access to the peculiar non-Abelian braiding statistics of Majorana fermions in this state. We also provide microscopic evidence for the generalization (expected from the field theory), that the Nth power of a Chern number C Slater determinant realizes the topological order of the SU(N)C Chern Simons theory coupled to fermions, by studying the SU(2)3 and the SU(3)2 wave functions. An advantage of projected Chern insulator wave functions over lowest Landau level wave functions for the same phases is the relative ease with which physical properties, such as entanglement entropy, can be numerically calculated using Monte Carlo techniques.
Fast non-Abelian geometric gates via transitionless quantum driving
Zhang, J.; Kyaw, Thi Ha; Tong, D. M.; Sjöqvist, Erik; Kwek, Leong-Chuan
2015-01-01
A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer. PMID:26687580
Fast non-Abelian geometric gates via transitionless quantum driving
NASA Astrophysics Data System (ADS)
Zhang, J.; Kyaw, Thi Ha; Tong, D. M.; Sjöqvist, Erik; Kwek, Leong-Chuan
2015-12-01
A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.
Fast non-Abelian geometric gates via transitionless quantum driving.
Zhang, J; Kyaw, Thi Ha; Tong, D M; Sjöqvist, Erik; Kwek, Leong-Chuan
2015-01-01
A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer. PMID:26687580
Non-abelian symmetries in tensor networks: A quantum symmetry space approach
Weichselbaum, Andreas
2012-12-15
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){sub charge}, SU(2){sub spin}, SU(2){sub charge}, SU(3){sub 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: Black-Right-Pointing-Pointer We introduce a transparent framework for non-abelian symmetries in tensor networks. Black-Right-Pointing-Pointer The framework was successfully
Abelian and non-abelian D-brane effective actions
NASA Astrophysics Data System (ADS)
Koerber, P.
2004-09-01
In this Ph.D. thesis, accepted at the Vrije Universiteit Brussel, we review and elaborate on a method to find the D-brane effective action, based on BPS equations. Firstly, both for the Yang-Mills action and the Born-Infeld action it is shown that these configurations are indeed BPS, i.e. solutions to these equations saturate a Bogomolny bound and leave some supersymmetry unbroken. Next, we use the BPS equations as a tool to construct the D-brane effective action and require that (a deformation of) these equations should still imply the equations of motion in more general cases. In the abelian case we managed to calculate all order in four-derivative corrections to the effective action and the BPS equations while in the non-abelian case we obtained the effective action up to order 4. Furthermore, we discuss a check based on the spectrum of strings stretching between intersecting branes. Finally, this Ph.D. thesis also discusses the construction of a boundary superspace which would be the first step to use the method of Weyl invariance in N = 2 superspace in order to again construct the D-brane effective action. A more detailed summary of each section can be found in the introduction.
Topologically Massive Non-Abelian Theory:. Superfield Approach
NASA Astrophysics Data System (ADS)
Krishna, S.; Shukla, A.; Malik, R. P.
We apply the well-established techniques of geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism in the context of four (3+1)-dimensional (4D) dynamical non-Abelian 2-form gauge theory by exploiting its inherent "scalar" and "vector" gauge symmetry transformations and derive the corresponding off-shell nilpotent and absolutely anticommuting BRST and anti-BRST symmetry transformations. Our approach leads to the derivation of three (anti-)BRST invariant Curci-Ferrari (CF)-type restrictions that are found to be responsible for the absolute anticommutativity of the BRST and anti-BRST symmetry transformations. We derive the coupled Lagrangian densities that respect the (anti-)BRST symmetry transformations corresponding to the "vector" gauge transformations. We also capture the (anti-)BRST invariance of the CF-type restrictions and coupled Lagrangian densities within the framework of our superfield approach. We obtain, furthermore, the off-shell nilpotent (anti-)BRST symmetry transformations when the (anti-)BRST symmetry transformations corresponding to the "scalar" and "vector" gauge symmetries are merged together. These off-shell nilpotent "merged" (anti-)BRST symmetry transformations are, however, found to be non-anticommuting in nature.
Entanglement of Vortex Lattices for Ultracold Bose Gases in a Non-Abelian Gauge Potential
NASA Astrophysics Data System (ADS)
Cheng, Szu-Cheng; Jiang, T. F.; Jheng, Shih-Da; Atomic; Molecular Physics Team; Atomic; Molecular Physics Team
We develop a theory, referred to as the von Neumann lattice in a higher Landau level, for vortex lattices labelled by an integral number of flux quantums per unit cell in a higher Landau level. Using this lattice theory, we study the vortex lattice states of a pseudospin-1/2 ultracold Bose gas with contact interactions in a non-Abelian gauge potential. In addition to a uniform magnetic field, the Bose gas is also subjected to a non-Abelian gauge field, which creates an effect of the spin-orbit coupling to lift the spin degeneracy of the Landau levels. Because of interactions from the spin-orbit coupling, there are new degenerate points of the single particle spectrum due to the crossings of two Landau levels at certain coupling strengths. We show that interactions from the spin-orbit coupling force the nature and structure of the vortex lattice changing dramatically if the strength of the non-Abelian gauge field is increasing. We also find that the ground state of the vortex lattice at a degenerate point exhibits strong correlation and entanglement involving vortex lattices from different Landau levels. This entangled state builds the connection between two phases of vortex lattices during the first order phase transition of the adiabatic evolution.
Particle coupled to a heat bath in non-Abelian gauge potentials
NASA Astrophysics Data System (ADS)
Guingarey, Issoufou; Avossevou, Gabriel Y. H.
2015-12-01
We derive the quantum Langevin equation (QLE) for a harmonically single trapped cold atom subjected to artificial non-Abelian gauge potentials and linearly coupled to a heat bath. The independent-oscillator (IO) and the momentum-momenta coupling models are studied. In each case, the non-Abelian effect on the QLE is pointed out for a U(2 ) gauge transformation. For the IO model, only the generalized Lorentz force is modified by the appearance of an additive term. For the momentum-momenta coupling model, the generalized Lorentz force as well as the friction force are subjected to modifications. The dependence of the system on the magnetic field is explicit even if the gauge potential is uniform in space.
Non-Abelian vortices on a cylinder: Duality between vortices and walls
Eto, Minoru; Fujimori, Toshiaki; Isozumi, Youichi; Nitta, Muneto; Ohashi, Keisuke; Sakai, Norisuke; Ohta, Kazutoshi
2006-04-15
We investigate vortices on a cylinder in supersymmetric non-Abelian gauge theory with hypermultiplets in the fundamental representation. We identify moduli space of periodic vortices and find that a pair of wall-like objects appears as the vortex moduli is varied. Usual domain walls also can be obtained from the single vortex on the cylinder by introducing a twisted boundary condition. We can understand these phenomena as a T duality among D-brane configurations in type II superstring theories. Using this T-duality picture, we find a one-to-one correspondence between the moduli space of non-Abelian vortices and that of kinky D-brane configurations for domain walls.
Non-Abelian family symmetries as portals to dark matter
NASA Astrophysics Data System (ADS)
de Medeiros Varzielas, I.; Fischer, O.
2016-01-01
Non-Abelian family symmetries offer a very promising explanation for the flavour structure in the Standard Model and its extensions. We explore the possibility that dark matter consists in fermions that transform under a family symmetry, such that the visible and dark sector are linked by the familons - Standard Model gauge singlet scalars, responsible for spontaneously breaking the family symmetry. We study three representative models with non-Abelian family symmetries that have been shown capable to explain the masses and mixing of the Standard Model fermions.
Plasma analogy and non-Abelian statistics for Ising-type quantum Hall states
Bonderson, Parsa; Gurarie, Victor; Nayak, Chetan
2011-02-15
We study the non-Abelian statistics of quasiparticles in the Ising-type quantum Hall states which are likely candidates to explain the observed Hall conductivity plateaus in the second Landau level, most notably the one at filling fraction {nu}=5/2. We complete the program started in V. Gurarie and C. Nayak, [Nucl. Phys. B 506, 685 (1997)]. and show that the degenerate four-quasihole and six-quasihole wave functions of the Moore-Read Pfaffian state are orthogonal with equal constant norms in the basis given by conformal blocks in a c=1+(1/2) conformal field theory. As a consequence, this proves that the non-Abelian statistics of the excitations in this state are given by the explicit analytic continuation of these wave functions. Our proof is based on a plasma analogy derived from the Coulomb gas construction of Ising model correlation functions involving both order and (at most two) disorder operators. We show how this computation also determines the non-Abelian statistics of collections of more than six quasiholes and give an explicit expression for the corresponding conformal block-derived wave functions for an arbitrary number of quasiholes. Our method also applies to the anti-Pfaffian wave function and to Bonderson-Slingerland hierarchy states constructed over the Moore-Read and anti-Pfaffian states.
Non-Abelian strings in supersymmetric Yang-Mills
Shifman, M.
2012-09-26
I give a broad review of novel phenomena discovered in certain Yang-Mills theories: non-Abelian strings and confined monopoles. Then I explain how these phenomena allow one to study strong dynamics of gauge theories in four dimensions from two-dimensional models emerging on the string world sheet.
Probing Non-Abelian Statistics with Quasiparticle Interferometry
Bonderson, Parsa; Shtengel, Kirill; Slingerland, J.K.
2006-07-07
We examine interferometric experiments in systems that exhibit non-Abelian braiding statistics, expressing outcomes in terms of the modular S-matrix. In particular, this result applies to fractional quantum Hall interferometry, and we give a detailed treatment of the Read-Rezayi states, providing explicit predictions for the recently observed {nu}=12/5 plateau.
Strong-weak coupling duality in non-abelian gauge theories
NASA Astrophysics Data System (ADS)
Ferrari, Frank
1997-05-01
This is a general introduction to electric-magnetic duality in non-abelian gauge theories. In chapter I, I review the general ideas which led in the late 70s to the idea of electric/magnetic duality in quantum field theory. In chapters II and III, I focus mainly on N=2 supersymmetric theories. I present the lagrangians and explain in more or less detail the non-renormalization theorems, rigid special geometry, supersymmetric instanton calculus, charge fractionization, the semiclassical theory of monopoles, duality in Maxwell theory and the famous Seiberg-Witten solution. I discuss various physical applications, as electric charge confinement, chiral symmetry breaking or non-trivial superconformal theories in four dimensions. In Section II.3 new material is presented, related to the computation of the eta invariant of certain Dirac operators coupled minimally to non-trivial monopole field configurations. I explain how these invariants can be obtained exactly by a one-loop calculation in a suitable N=2 supersymmetric gauge theory. This is an unexpected application of the holomorphy properties of N=2 supersymmetry, and constitutes a tremendous simplification of the usual computation. An expanded version of these new results will be published soon.
NASA Astrophysics Data System (ADS)
Eto, Minoru; Murakami, Yoshihide
2015-03-01
Dyonic non-Abelian local/semi-global vortex strings are studied in detail in supersymmetric/non-supersymmetric Yang-Mills-Higgs theories. While the BPS tension formula is known to be the same as that for the BPS dyonic instanton, we find that the non-BPS tension formula is approximated very well by the well-known tension formula of the BPS dyon. We show that this mysterious tension formula for the dyonic non-BPS vortex stings can be understood from the perspective of a low energy effective field theory. Furthermore, we propose an efficient method to obtain an effective theory of a single vortex string, which includes not only lower derivative terms but also all order derivative corrections by making use of the tension formula. We also find a novel dyonic vortex string whose internal orientation vectors rotate in time and spiral along the string axis.
NASA Astrophysics Data System (ADS)
Kazakov, Alexander; Kolkovsky, V.; Adamus, Z.; Karczewski, G.; Wojtowicz, T.; Rokhinson, Leonid
2015-03-01
Several experiments detected signatures of Majorana fermions in nanowires, and the focus of current research is shifting toward systems where non-Abelian statistics of excitations can be demonstrated. To achieve this goal we are developing a new platform where non-Abelian excitations can be created and manipulated in a two-dimensional plane, with support for Majorana and higher order non-Abelian excitations. The system is based on CdTe quantum wells non-uniformly doped with paramagnetic impurities, which result in a complicate field-dependence of Zeeman splitting. A unique property of the system is that at high fields we can form a quantum Hall ferromagnet with gate-controllable spin polarization. Helical 1D edge channels formed along the edges of electrostatic gates may support generalized non-Abelian excitations in the fractional qunatum Hall regime, and Majorana and parafermion excitations in the presence of induced superconductivity. We will present results on the gate control of s-d exchange in specially designed heterostructures, demonstrate gate control of spin polarization at filling factor ν = 2 , and show spatial separation of quantum Hall states with different spin polarization using lithographically defined gates.
Non-Abelian bosonic currents in cosmic strings
Lilley, Marc; Di Marco, Fabrizio; Martin, Jerome; Peter, Patrick
2010-07-15
A non-Abelian generalization of the neutral Witten current-carrying string model is discussed in which the bosonic current carrier belongs to a two-dimensional representation of SU(2). We find that the current-carrying solutions can be of three different kinds: either the current spans a U(1) subgroup, and in which case one is left with an Abelian current-carrying string, or the three currents are all lightlike, traveling in the same direction (only left or right movers). The third, genuinely non-Abelian situation, cannot be handled within a cylindrically symmetric framework, but can be shown to depend on all possible string Lorentz invariant quantities that can be constructed out of the phase gradients.
Braiding non-Abelian quasiholes in fractional quantum Hall states.
Wu, Yang-Le; Estienne, B; Regnault, N; Bernevig, B Andrei
2014-09-12
Quasiholes in certain fractional quantum Hall states are promising candidates for the experimental realization of non-Abelian anyons. They are assumed to be localized excitations, and to display non-Abelian statistics when sufficiently separated, but these properties have not been explicitly demonstrated except for the Moore-Read state. In this work, we apply the newly developed matrix product state technique to examine these exotic excitations. For the Moore-Read and the Z_{3} Read-Rezayi states, we estimate the quasihole radii, and determine the correlation lengths associated with the exponential convergence of the braiding statistics. We provide the first microscopic verification for the Fibonacci nature of the Z_{3} Read-Rezayi quasiholes. We also present evidence for the failure of plasma screening in the nonunitary Gaffnian wave function. PMID:25259996
Identifying non-Abelian topological order through minimal entangled states.
Zhu, W; Gong, S S; Haldane, F D M; Sheng, D N
2014-03-01
The topological order is encoded in the pattern of long-range quantum entanglements, which cannot be measured by any local observable. Here we perform an exact diagonalization study to establish the non-Abelian topological order for topological band models through entanglement entropy measurement. We focus on the quasiparticle statistics of the non-Abelian Moore-Read and Read-Rezayi states on the lattice models with bosonic particles. We identify multiple independent minimal entangled states (MESs) in the ground state manifold on a torus. The extracted modular S matrix from MESs faithfully demonstrates the Ising anyon or Fibonacci quasiparticle statistics, including the quasiparticle quantum dimensions and the fusion rules for such systems. These findings unambiguously demonstrate the topological nature of the quantum states for these flatband models without using the knowledge of model wave functions. PMID:24655269
Electric-magnetic dualities in non-abelian and non-commutative gauge theories
NASA Astrophysics Data System (ADS)
Ho, Jun-Kai; Ma, Chen-Te
2016-08-01
Electric-magnetic dualities are equivalence between strong and weak coupling constants. A standard example is the exchange of electric and magnetic fields in an abelian gauge theory. We show three methods to perform electric-magnetic dualities in the case of the non-commutative U (1) gauge theory. The first method is to use covariant field strengths to be the electric and magnetic fields. We find an invariant form of an equation of motion after performing the electric-magnetic duality. The second method is to use the Seiberg-Witten map to rewrite the non-commutative U (1) gauge theory in terms of abelian field strength. The third method is to use the large Neveu Schwarz-Neveu Schwarz (NS-NS) background limit (non-commutativity parameter only has one degree of freedom) to consider the non-commutative U (1) gauge theory or D3-brane. In this limit, we introduce or dualize a new one-form gauge potential to get a D3-brane in a large Ramond-Ramond (R-R) background via field redefinition. We also use perturbation to study the equivalence between two D3-brane theories. Comparison of these methods in the non-commutative U (1) gauge theory gives different physical implications. The comparison reflects the differences between the non-abelian and non-commutative gauge theories in the electric-magnetic dualities. For a complete study, we also extend our studies to the simplest abelian and non-abelian p-form gauge theories, and a non-commutative theory with the non-abelian structure.
Universal Reconnection of Non-Abelian Cosmic Strings
Eto, Minoru; Hashimoto, Koji; Marmorini, Giacomo; Nitta, Muneto; Ohashi, Keisuke; Vinci, Walter
2007-03-02
We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision of two vortices, which is known to give the reconnection of the strings.
Non-Abelian anomalies on a curved space with torsion
Cognola, G.; Giacconi, P.
1989-05-15
Using path-integral methods and /zeta/-function regularization a nonperturbative derivation of non-Abelian-covariant and consistent anomalies on a curved space with torsion is given. All terms depending on torsion, that one has in the expression of the consistent anomaly, can be eliminated by adding suitable counterterms to the Lagrangian density. In this way, the well-known result of Bardeen is recovered. The so-called ''covariant anomaly'' will be discussed too.
Universal reconnection of non-Abelian cosmic strings.
Eto, Minoru; Hashimoto, Koji; Marmorini, Giacomo; Nitta, Muneto; Ohashi, Keisuke; Vinci, Walter
2007-03-01
We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision of two vortices, which is known to give the reconnection of the strings. PMID:17359147
Non-Abelian Berry-s phase effects and optical pumping of atoms
Segert, J.
1987-11-01
We predict experimentally verifiable manifestations of non-Abelian Berry's phase effects for atoms in external collinear electric and magnetic fields. The field strengths are arranged so as to cause accidental degeneracy between atomic states. The relevant theoretical results, which have been presented in detail elsewhere, are summarized and explained. We propose an experiment using optically pumped metastable multiplets of Pb/sup 208/ in an atomic beam apparatus to test these predictions. We estimate required experimental parameters, and conclude that the proposed experiment can realistically be performed. copyright 1987 Academic Press, Inc.
Probing Non-Abelian Statistics of Majorana Fermions in Ultracold Atomic Superfluid
Zhu Shiliang; Shao, L.-B.; Wang, Z. D.; Duan, L.-M.
2011-03-11
We propose an experiment to directly probe the non-Abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show that different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark-state subspace.
Detecting 3d Non-Abelian Anyons via Adiabatic Cooling
NASA Astrophysics Data System (ADS)
Yamamoto, Seiji; Freedman, Michael; Yang, Kun
2011-03-01
Majorana fermions lie at the heart of a number of recent developments in condensed matter physics. One important application is the realization of non-abelian statistics and consequently a foundation for topological quantum computation. Theoretical propositions for Majorana systems abound, but experimental detection has proven challenging. Most attempts involve interferometry, but the degeneracy of the anyon state can be leveraged to produce a cooling effect, as previously shown in 2d. We apply this method of anyon detection to the 3d anyon model of Teo and Kane. Like the Fu-Kane model, this involves a hybrid system of topological insulator (TI) and superconductor (SC). The Majorana modes are localized to anisotropic hedgehogs in the order parameter which appear at the TI-SC interface. The effective model bears some resemblance to the non-Abelian Higgs model with scalar coupling as studied, for example, by Jackiw and Rebbi. In order to make concrete estimates relevant to experiments, we use parameters appropriate to Ca doped Bi 2 Se 3 as the topological insulator and Cu doped Bi 2 Se 3 as the superconductor. We find a temperature window in the milli-Kelvin regime where the presence of 3d non-abelian anyons will lead to an observable cooling effect.
Universal attractor in a highly occupied non-Abelian plasma
NASA Astrophysics Data System (ADS)
Berges, J.; Boguslavski, K.; Schlichting, S.; Venugopalan, R.
2014-06-01
We study the thermalization process in highly occupied non-Abelian plasmas at weak coupling. The nonequilibrium dynamics of such systems is classical in nature and can be simulated with real-time lattice gauge theory techniques. We provide a detailed discussion of this framework and elaborate on the results reported in J. Berges, K. Boguslavski, S. Schlichting, and R. Venugopalan, Phys. Rev. D 89, 074011 (2014), 10.1103/PhysRevD.89.074011 along with novel findings. We demonstrate the emergence of universal attractor solutions, which govern the nonequilibrium evolution on large time scales both for nonexpanding and expanding non-Abelian plasmas. The turbulent attractor for a nonexpanding plasma drives the system close to thermal equilibrium on a time scale t ˜Q-1αs-7/4. The attractor solution for an expanding non-Abelian plasma leads to a strongly interacting albeit highly anisotropic system at the transition to the low-occupancy or quantum regime. This evolution in the classical regime is, within the uncertainties of our simulations, consistent with the "bottom up" thermalization scenario [R. Baier, A. H. Mueller, D. Schiff, and D. T. Son, Phys. Lett. B 502, 51 (2001), 10.1016/S0370-2693(01)00191-5]. While the focus of this paper is to understand the nonequilibrium dynamics in weak coupling asymptotics, we also discuss the relevance of our results for larger couplings in the early time dynamics of heavy ion collision experiments.
Understanding the physics of a possible non-Abelian fractional quantum hall effect state.
Pan, Wei; Crawford, Matthew; Tallakulam, Madhu; Ross, Anthony Joseph, III
2010-10-01
We wish to present in this report experimental results from a one-year Senior Council Tier-1 LDRD project that focused on understanding the physics of a possible non-Abelian fractional quantum Hall effect state. We first give a general introduction to the quantum Hall effect, and then present the experimental results on the edge-state transport in a special fractional quantum Hall effect state at Landau level filling {nu} = 5/2 - a possible non-Abelian quantum Hall state. This state has been at the center of current basic research due to its potential applications in fault-resistant topological quantum computation. We will also describe the semiconductor 'Hall-bar' devices we used in this project. Electron physics in low dimensional systems has been one of the most exciting fields in condensed matter physics for many years. This is especially true of quantum Hall effect (QHE) physics, which has seen its intellectual wealth applied in and has influenced many seemingly unrelated fields, such as the black hole physics, where a fractional QHE-like phase has been identified. Two Nobel prizes have been awarded for discoveries of quantum Hall effects: in 1985 to von Klitzing for the discovery of integer QHE, and in 1998 to Tsui, Stormer, and Laughlin for the discovery of fractional QHE. Today, QH physics remains one of the most vibrant research fields, and many unexpected novel quantum states continue to be discovered and to surprise us, such as utilizing an exotic, non-Abelian FQHE state at {nu} = 5/2 for fault resistant topological computation. Below we give a briefly introduction of the quantum Hall physics.
Infinite-randomness fixed points for chains of non-Abelian quasiparticles.
Bonesteel, N E; Yang, Kun
2007-10-01
One-dimensional chains of non-Abelian quasiparticles described by SU(2)k Chern-Simons-Witten theory can enter random singlet phases analogous to that of a random chain of ordinary spin-1/2 particles (corresponding to k-->infinity). For k=2 this phase provides a random singlet description of the infinite-randomness fixed point of the critical transverse field Ising model. The entanglement entropy of a region of size L in these phases scales as S(L) approximately lnd/3 log(2)L for large L, where d is the quantum dimension of the particles. PMID:17930652
Russian doll spectrum in a non-Abelian string-net ladder
NASA Astrophysics Data System (ADS)
Schulz, Marc Daniel; Dusuel, Sébastien; Vidal, Julien
2015-04-01
We study a string-net ladder in the presence of a string tension. Focusing on the simplest non-Abelian anyon theory with a quantum dimension larger than two, we determine the phase diagram and find a Russian doll spectrum featuring size-independent energy levels as well as highly degenerate zero-energy eigenstates. At the self-dual points, we compute the gap exactly by using a mapping onto the Temperley-Lieb chain. These results are in stark contrast with the ones obtained for Fibonacci or Ising theories.
Correlation-induced non-Abelian quantum holonomies
NASA Astrophysics Data System (ADS)
Johansson, Markus; Ericsson, Marie; Singh, Kuldip; Sjöqvist, Erik; Williamson, Mark S.
2011-04-01
In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the Lévay geometric phase (2004 J. Phys. A: Math. Gen. 37 1821) in the case of two-qubit systems undergoing local SU(2) evolutions.
Non-Abelian gauge invariance and the infrared approximation
Cho, H.h.; Fried, H.M.; Grandou, T.
1988-02-15
Two constructions are given of infrared approximations, defined by a nonlocal configuration-space restrictions, which preserve the local, non-Abelian gauge invariance of SU(N) two-dimensional QCD (QCD/sub 2/). These continuum infrared methods are used to estimate the quenched order parameter
NASA Astrophysics Data System (ADS)
Pogrebkov, A. K.
2016-06-01
We show that the non-Abelian Hirota difference equation is directly related to a commutator identity on an associative algebra. Evolutions generated by similarity transformations of elements of this algebra lead to a linear difference equation. We develop a special dressing procedure that results in an integrable non-Abelian Hirota difference equation and propose two regular reduction procedures that lead to a set of known equations, Abelian or non-Abelian, and also to some new integrable equations.
Non-Abelian gauge redundancy and entropic ambiguities
NASA Astrophysics Data System (ADS)
Balachandran, A. P.; de Queiroz, A. R.; Vaidya, S.
2015-04-01
The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. Therefore one reaches the remarkable possibility that there may be many entropies for a given state. We show that this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This ambiguity in entropy, which can occur at zero temperature, can often be traced to a gauge symmetry emergent from the non-trivial topological character of the configuration space of the underlying system. We also establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix. After demonstrating this entropy ambiguity for the simple example of the algebra of 2 × 2 matrices, we argue that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. We work out the simplest situation with such non-Abelian symmetry, that of an ethylene molecule.
NASA Astrophysics Data System (ADS)
Kondo, Kei-Ichi; Kato, Seikou; Shibata, Akihiro; Shinohara, Toru
2015-05-01
The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the Yang-Mills theory based on change of variables extending the decomposition of the SU(N) Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the SU(N) Wilson loop operator. Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole. We show especially that magnetic monopoles in the Yang-Mills theory can be constructed in a manifestly gauge-invariant way starting from the gauge-invariant Wilson loop operator and thereby the contribution from the magnetic monopoles can be extracted from the Wilson loop in a gauge-invariant way through the non-Abelian Stokes theorem for the Wilson loop operator, which is a prerequisite for exhibiting magnetic monopole dominance for quark
Non-abelian fractional quantum hall effect for fault-resistant topological quantum computation.
Pan, Wei; Thalakulam, Madhu; Shi, Xiaoyan; Crawford, Matthew; Nielsen, Erik; Cederberg, Jeffrey George
2013-10-01
Topological quantum computation (TQC) has emerged as one of the most promising approaches to quantum computation. Under this approach, the topological properties of a non-Abelian quantum system, which are insensitive to local perturbations, are utilized to process and transport quantum information. The encoded information can be protected and rendered immune from nearly all environmental decoherence processes without additional error-correction. It is believed that the low energy excitations of the so-called =5/2 fractional quantum Hall (FQH) state may obey non-Abelian statistics. Our goal is to explore this novel FQH state and to understand and create a scientific foundation of this quantum matter state for the emerging TQC technology. We present in this report the results from a coherent study that focused on obtaining a knowledge base of the physics that underpins TQC. We first present the results of bulk transport properties, including the nature of disorder on the 5/2 state and spin transitions in the second Landau level. We then describe the development and application of edge tunneling techniques to quantify and understand the quasiparticle physics of the 5/2 state.
Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons
NASA Astrophysics Data System (ADS)
Zhang, Yuhe; Sreejith, G. J.; Jain, J. K.
2015-08-01
The possibility of realizing bosonic fractional quantum Hall effect in ultracold atomic systems suggests a new route to producing and manipulating anyons, by introducing auxiliary bosons of a different species that capture quasiholes and thus inherit their nontrivial braiding properties. States with localized quasiholes at any desired locations can be obtained by annihilating the auxiliary bosons at those locations. We explore how this method can be used to generate non-Abelian quasiholes of the Moore-Read Pfaffian state for bosons at filling factor ν =1 . We show that a Hamiltonian with an appropriate three-body interaction can produce two-quasihole states in two distinct fusion channels of the topological "qubit." Characteristics of these states that are related to the non-Abelian nature can be probed and verified by a measurement of the effective relative angular momentum of the auxiliary bosons, which is directly related to their pair distribution function. Moore-Read states of more than two quasiholes can also be produced in a similar fashion. We investigate some issues related to the experimental feasibility of this approach, in particular, how large the systems should be for a realization of this physics and to what extent this physics carries over to systems with the more standard two-body contact interaction.
Experimental realization of non-abelian geometric gates with a superconducting three-level system
NASA Astrophysics Data System (ADS)
Abdumalikov, Abdufarrukh; Fink, J. M.; Juliusson, K.; Pechal, M.; Berger, S.; Wallraff, A.; Filipp, S.
2013-03-01
Geometric gates hold promise to provide the building blocks for robust quantum computation. In our experiments, we use a superconducting three-level system (transmon) to realize non-adiabatic non-abelian geometric gates. As computational basis we choose the ground and second excited states, while the first excited state acts as an ancilla state. The gates are realized by applying two resonant drives between the transmon levels. During the geometric gate ration of the amplitudes of the two drive tone is kept constant. Different gates are obtained for different ratio of the drive tones. We implement a Hadamard, a NOT and a phase gates with the fidelities of 95 % , 98 % , and 97 % as determined by full process tomography and maximum likelihood methods. We explicitly show the non-abelian nature of gates by applying two non-commuting gates in alternating order. The demonstrated holonomic gates are not exclusive to superconducting quantum devices, but can also be applied to other three level systems with similar energy level structure.
Critical string from non-Abelian vortex in four dimensions
NASA Astrophysics Data System (ADS)
Shifman, M.; Yung, A.
2015-11-01
In a class of non-Abelian solitonic vortex strings supported in certain N = 2 super-Yang-Mills theories we search for the vortex which can behave as a critical fundamental string. We use the Polchinski-Strominger criterion of the ultraviolet completeness. We identify an appropriate four-dimensional bulk theory: it has the U (2) gauge group, the Fayet-Iliopoulos term and four flavor hypermultiplets. It supports semilocal vortices with the world-sheet theory for orientational (size) moduli described by the weighted CP (2 , 2) model. The latter is superconformal. Its target space is six-dimensional. The overall Virasoro central charge is critical. We show that the world-sheet theory on the vortex supported in this bulk model is the bona fide critical string.
Asymptotically free scaling solutions in non-Abelian Higgs models
NASA Astrophysics Data System (ADS)
Gies, Holger; Zambelli, Luca
2015-07-01
We construct asymptotically free renormalization group trajectories for the generic non-Abelian Higgs model in four-dimensional spacetime. These ultraviolet-complete trajectories become visible by generalizing the renormalization/boundary conditions in the definition of the correlation functions of the theory. Though they are accessible in a controlled weak-coupling analysis, these trajectories originate from threshold phenomena which are missed in a conventional perturbative analysis relying on the deep Euclidean region. We identify a candidate three-parameter family of renormalization group trajectories interconnecting the asymptotically free ultraviolet regime with a Higgs phase in the low-energy limit. We provide estimates of their low-energy properties in the light of a possible application to the standard model Higgs sector. Finally, we find a two-parameter subclass of asymptotically free Coleman-Weinberg-type trajectories that do not suffer from a naturalness problem.
Simulation of non-Abelian gauge theories with optical lattices.
Tagliacozzo, L; Celi, A; Orland, P; Mitchell, M W; Lewenstein, M
2013-01-01
Many phenomena occurring in strongly correlated quantum systems still await conclusive explanations. The absence of isolated free quarks in nature is an example. It is attributed to quark confinement, whose origin is not yet understood. The phase diagram for nuclear matter at general temperatures and densities, studied in heavy-ion collisions, is not settled. Finally, we have no definitive theory of high-temperature superconductivity. Though we have theories that could underlie such physics, we lack the tools to determine the experimental consequences of these theories. Quantum simulators may provide such tools. Here we show how to engineer quantum simulators of non-Abelian lattice gauge theories. The systems we consider have several applications: they can be used to mimic quark confinement or to study dimer and valence-bond states (which may be relevant for high-temperature superconductors). PMID:24162080
Simulation of non-Abelian gauge theories with optical lattices
NASA Astrophysics Data System (ADS)
Tagliacozzo, L.; Celi, A.; Orland, P.; Mitchell, M. W.; Lewenstein, M.
2013-10-01
Many phenomena occurring in strongly correlated quantum systems still await conclusive explanations. The absence of isolated free quarks in nature is an example. It is attributed to quark confinement, whose origin is not yet understood. The phase diagram for nuclear matter at general temperatures and densities, studied in heavy-ion collisions, is not settled. Finally, we have no definitive theory of high-temperature superconductivity. Though we have theories that could underlie such physics, we lack the tools to determine the experimental consequences of these theories. Quantum simulators may provide such tools. Here we show how to engineer quantum simulators of non-Abelian lattice gauge theories. The systems we consider have several applications: they can be used to mimic quark confinement or to study dimer and valence-bond states (which may be relevant for high-temperature superconductors).
Matrix model for non-Abelian quantum Hall states
NASA Astrophysics Data System (ADS)
Dorey, Nick; Tong, David; Turner, Carl
2016-08-01
We propose a matrix quantum mechanics for a class of non-Abelian quantum Hall states. The model describes electrons which carry an internal SU(p ) spin. The ground states of the matrix model include spin-singlet generalizations of the Moore-Read and Read-Rezayi states and, in general, lie in a class previously introduced by Blok and Wen. The effective action for these states is a U(p ) Chern-Simons theory. We show how the matrix model can be derived from quantization of the vortices in this Chern-Simons theory and how the matrix model ground states can be reconstructed as correlation functions in the boundary WZW model.
Neutrino masses and non-abelian horizontal symmetries
NASA Astrophysics Data System (ADS)
Antonelli, V.; Caravaglios, F.; Ferrari, R.; Picariello, M.
2002-12-01
Recently neutrino experiments have made very significant progresses and our knowledge of neutrino masses and mixing has considerably improved. In a model-independent Monte Carlo approach, we have examined a very large class of textures, in the context of non-abelian horizontal symmetries; we have found that neutrino data select only those charged lepton matrices with left-right asymmetric texture. The large atmospheric mixing angle needs m23≃m33. This result, if combined with similar recent findings for the quark sector in the B oscillations, can be interpreted as a hint for SU(5) unification. In the neutrino sector strict neutrino anarchy is disfavored by data, and at least a factor 2 of suppression in the first row and column of the neutrino Majorana mass matrix is required.
Minimal non-Abelian model of atomic dark matter
NASA Astrophysics Data System (ADS)
Choquette, Jeremie; Cline, James M.
2015-12-01
A dark sector resembling the Standard Model, where the abundance of matter is explained by baryon and lepton asymmetries and stable constituents bind to form atoms, is a theoretically appealing possibility. We show that a minimal model with a hidden SU(2) gauge symmetry broken to U(1), with a Dirac fermion doublet, suffices to realize this scenario. Supplemented with a dark Higgs doublet that gets no vacuum expectation value, we readily achieve the dark matter asymmetry through leptogenesis. The model can simultaneously have three portals to the Standard Model, through the Higgs, non-Abelian kinetic mixing, and the heavy neutrino, with interesting phenomenology for direct and collider searches, as well as cosmologically relevant dark matter self-interactions. Exotic bound states consisting of two fermions and a doubly charged vector boson can exist in one phase of the theory.
Non-Abelian monopole in the parameter space of point-like interactions
NASA Astrophysics Data System (ADS)
Ohya, Satoshi
2014-12-01
We study non-Abelian geometric phase in N = 2 supersymmetric quantum mechanics for a free particle on a circle with two point-like interactions at antipodal points. We show that non-Abelian Berry's connection is that of SU(2) magnetic monopole discovered by Moody, Shapere and Wilczek in the context of adiabatic decoupling limit of diatomic molecule.
Non-Abelian chiral instabilities at high temperature on the lattice
NASA Astrophysics Data System (ADS)
Akamatsu, Yukinao; Rothkopf, Alexander; Yamamoto, Naoki
2016-03-01
We report on an exploratory lattice study on the phenomenon of chiral instabilities in non-Abelian gauge theories at high temperature. It is based on a recently constructed anomalous Langevin-type effective theory of classical soft gauge fields in the presence of a chiral number density n 5 = n R - n L. Evaluated in thermal equilibrium using classical lattice techniques it reveals that the fluctuating soft fields indeed exhibit a rapid energy increase at early times and we observe a clear dependence of the diffusion rate of topological charge (sphaleron rate) on the the initial n 5, relevant in both early universe baryogenesis and relativistic heavy-ion collisions. The topological charge furthermore shows a drift among distinct vacuum sectors, roughly proportional to the initial n 5 and in turn the chiral imbalance is monotonously reduced as required by helicity conservation.
Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory
Nielsen, H.B.; Rugh, H.H.; Rugh, S.E.
1996-12-31
We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a {open_quote}no go{close_quotes} for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a {open_quotes}continuum limit{close_quotes} in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left an important question to be further examined.
Transverse momentum diffusion and collisional jet energy loss in non-Abelian plasmas
Schenke, Bjoern; Strickland, Michael; Dumitru, Adrian; Nara, Yasushi; Greiner, Carsten
2009-03-15
We consider momentum broadening and energy loss of high-momentum partons in a hot non-Abelian plasma due to collisions. We solve the coupled system of Wong-Yang-Mills equations on a lattice in real time, including binary hard elastic collisions among the partons. The collision kernel is constructed such that the total collisional energy loss and momentum broadening are lattice-spacing independent. We find that the transport coefficient q corresponding to transverse momentum broadening receives sizable contributions from a power-law tail in the p{sub perpendicular} distribution of high-momentum partons. We establish the scaling of q and of dE/dx with density, temperature, and energy in the weak-coupling regime. We also estimate the nuclear modification factor R{sub AA} due to elastic energy loss of a jet in a classical Yang-Mills field.
Topological phase transitions with non-Abelian gauge potentials on square lattices
NASA Astrophysics Data System (ADS)
Chen, Yao-Hua; Li, Jian; Ting, C. S.
2013-11-01
We investigate the topological phase transition on interacting square lattices via the non-Abelian potential by employing the real-space cellular dynamical mean-field theory combining with the continuous-time Monte Carlo method. For a weak on-site Hubbard interaction, a topological band insulating state with a pair of gapless edge states is induced by a next-nearest-neighbor hopping. A phase transition from the metallic phase to the Mott insulating phase is observed when the interaction is increased. These two phases can be distinguished by detecting whether a bulk gap in the K-dependent spectral function exists. The whole phase diagrams as functions of the interaction, next-nearest-neighbor hopping energy, and temperature are presented. The experimental setup to observe these new interesting phase transitions is also discussed.
Robustness of non-Abelian holonomic quantum gates against parametric noise
Solinas, Paolo; Zanghi, Nino; Zanardi, Paolo
2004-10-01
We present a numerical study of the robustness of a specific class of non-Abelian holonomic quantum gates. We take into account the parametric noise due to stochastic fluctuations of the control fields which drive the time-dependent Hamiltonian along an adiabatic loop. The performance estimator used is the state fidelity between noiseless and noisy holonomic gates. We carry over our analysis with different correlation times and we find out that noisy holonomic gates seem to be close to the noiseless ones for 'short' and 'long' noise correlation times. This result can be interpreted as a consequence of the geometric nature of the holonomic operator. Our simulations have been performed by using parameters relevant to the excitonic proposal for the implementation of holonomic quantum computation [P. Solinas et al., Phys. Rev. B 67, 121307 (2003)].
Effective models of doped quantum ladders of non-Abelian anyons
NASA Astrophysics Data System (ADS)
Soni, Medha; Troyer, Matthias; Poilblanc, Didier
2016-01-01
Quantum spin models have been studied extensively in one and higher dimensions. Furthermore, these systems have been doped with holes to study t -J models of SU (2 ) spin-1/2. Their anyonic counterparts can be built from non-Abelian anyons, such as Fibonacci anyons described by SU (2) 3 theories, which are quantum deformations of the SU (2 ) algebra. Inspired by the physics of SU (2 ) spins, several works have explored ladders of Fibonacci anyons and also one-dimensional (1D) t -J models. Here, we aim to explore the combined effects of extended dimensionality and doping by studying ladders composed of coupled chains of interacting itinerant Fibonacci anyons. We show analytically that in the limit of strong rung couplings these models can be mapped onto effective 1D models. These effective models can either be gapped models of hole pairs, or gapless models described by t -J (or modified t -J -V ) chains of Fibonacci anyons, whose spectrum exhibits a fractionalization into charge and anyon degrees of freedom. The charge degrees of freedom are described by the hardcore boson spectra while the anyon sector is given by a chain of localized interacting anyons. By using exact diagonalizations for two-leg and three-leg ladders, we show that indeed the doped ladders show exactly the same behavior as that of t -J chains. In the strong ferromagnetic rung limit, we can obtain a new model that hosts two different kinds of Fibonacci particles, which we denote as the heavy τ 's and light τ 's. These two particle types carry the same (non-Abelian) topological charge but different (Abelian) electric charges. Once again, we map the two-dimensional ladder onto an effective chain carrying these heavy and light τ 's. We perform a finite size scaling analysis to show the appearance of gapless modes for certain anyon densities, whereas a topological gapped phase is suggested for another density regime.
Non-Abelian SU(2) Lattice Gauge Theories in Superconducting Circuits.
Mezzacapo, A; Rico, E; Sabín, C; Egusquiza, I L; Lamata, L; Solano, E
2015-12-11
We propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instance of a pure SU(2) gauge theory, using triangular plaquettes involving geometric frustration. This realization is the least demanding, in terms of quantum simulation resources, of a non-Abelian gauge dynamics. We present two superconducting architectures that can host the quantum simulation, estimating the requirements needed to run possible experiments. The proposal establishes a path to the experimental simulation of non-Abelian physics with solid-state quantum platforms. PMID:26705616
NASA Astrophysics Data System (ADS)
Willett, Robert; Manfra, Michael; Pfeiffer, Loren; Shtengel, Kirill; Nayak, Chetan
The excitations of charge e/4 at 5/2 filling factor are proposed to obey non-Abelian statistics. To test this, interferometry at fractional quantum Hall states can be performed that controllably braids edge currents around localized charges. We have conducted these measurements in a large number of interferometers of different sizes, also using multiple designs of high quality 2D electron heterostructures. We observe properties of the interference measurements at 5/2 that are specifically consistent with non-Abelian e/4. In particular, magnetic field sweeps around 5/2 show interference oscillations with frequency spectra that are consistent in detail with non-Abelian e/4 properties. Four frequency spectra peaks are observed corresponding to both e/4 and e/2 charges; importantly a rapid non-Abelian e/4 component is seen that is split due to beating between the two e/4 braiding processes. We review these results and their observation in a range of interferometer dimensions and in different heterostructure designs.
Heterotic non-Abelian string of a finite length
NASA Astrophysics Data System (ADS)
Monin, S.; Shifman, M.; Yung, A.
2016-06-01
We consider non-Abelian strings in N =2 supersymmetric quantum chromodynamics (QCD) with the U (N ) gauge group and Nf=N quark flavors deformed by a mass term for the adjoint matter. This deformation breaks N =2 supersymmetry down to N =1 . Dynamics of orientational zero modes on the string world sheet are described then by C P (N -1 ) model with N =(0 ,2 ) supersymmetry. We study the string of a finite length L assuming compactification on a cylinder (periodic boundary conditions). The world-sheet theory is solved in the large-N approximation. At N =∞ we find a rich phase structure in the (L ,u ) plane where u is a deformation parameter. At large L and intermediate u we find a phase with broken Z2 N symmetry, N vacua and a mass gap. At large values of L and u still larger we have the Z2 N-symmetric phase with a single vacuum and massless fermions. In both phases N =(0 ,2 ) supersymmetry is spontaneously broken. We also observe a phase with would-be broken SU (N ) symmetry at small L (it is broken only for N =∞ ). In the latter phase the mass gap vanishes and the vacuum energy is zero in the leading 1 /N approximation. We expect that at large but finite N corrections O (1 /N ) will break N =(0 ,2 ) supersymmetry. Simultaneously, the phase transitions will become rapid crossovers. Finally we discuss how the observed rich phase structure matches the N =(2 ,2 ) limit in which the world-sheet theory has a single phase with the mass gap independent of L .
A non-Abelian SO(8) monopole as generalization of Dirac-Yang monopoles for a 9-dimensional space
Le, Van-Hoang; Nguyen, Thanh-Son
2011-03-15
We establish an explicit form of a non-Abelian SO(8) monopole in a 9-dimensional space and show that it is indeed a direct generalization of Dirac and Yang monopoles. Using the generalized Hurwitz transformation, we have found a connection between a 16-dimensional harmonic oscillator and a 9-dimensional hydrogenlike atom in the field of the SO(8) monopole (MICZ-Kepler problem). Using the built connection the group of dynamical symmetry of the 9-dimensional MICZ-Kepler problem is found as SO(10, 2).
NASA Astrophysics Data System (ADS)
Das Sarma, S.; Nag, Amit; Sau, Jay D.
2016-07-01
We consider a simple conceptual question with respect to Majorana zero modes in semiconductor nanowires: can the measured nonideal values of the zero-bias-conductance-peak in the tunneling experiments be used as a characteristic to predict the underlying topological nature of the proximity induced nanowire superconductivity? In particular, we define and calculate the topological visibility, which is a variation of the topological invariant associated with the scattering matrix of the system as well as the zero-bias-conductance-peak heights in the tunneling measurements, in the presence of dissipative broadening, using precisely the same realistic nanowire parameters to connect the topological invariants with the zero-bias tunneling conductance values. This dissipative broadening is present in both (the existing) tunneling measurements and also (any future) braiding experiments as an inevitable consequence of a finite braiding time. The connection between the topological visibility and the conductance allows us to obtain the visibility of realistic braiding experiments in nanowires, and to conclude that the current experimentally accessible systems with nonideal zero-bias conductance peaks may indeed manifest (with rather low visibility) non-Abelian statistics for the Majorana zero modes. In general, we find that a large (small) superconducting gap (Majorana peak splitting) is essential for the manifestation of the non-Abelian braiding statistics, and in particular, a zero-bias conductance value of around half the ideal quantized Majorana value should be sufficient for the manifestation of non-Abelian statistics in experimental nanowires. Our work also establishes that as a matter of principle the topological transition associated with the emergence of Majorana zero modes in finite nanowires is always a crossover (akin to a quantum phase transition at finite temperature) requiring the presence of dissipative broadening (which must be larger than the Majorana energy
On Geometrical Interpretation of Non-Abelian D and F-Flat Direction Constraints
NASA Astrophysics Data System (ADS)
Walker, Joel; Cleaver, Gerald; Nanopoulos, Dimitri; Perkins, John
2004-10-01
In order to produce a low energy effective field theory from a string model, it is necessary to specify a vacuum state. In order that this vacuum be supersymmetric, it is well known that all field expectation values must be along so-called flat directions, leaving the F- and D-terms of the scalar potential to be zero. The situation becomes particularly interesting when one attempts to realize such directions while assigning VEVS to fields transforming under non-Abelian representations of the gauge group. Since the expectation value is now shared among multiple components of a field, satisfaction of flatness becomes an inherently geometrical problem in the group space. Furthermore, the possibility emerges that a single seemingly dangerous F-term might experience a self-cancellation among its components. The hope exists that the geometric language can provide an intuitive and immediate recognition of when the D and F conditions are simultaneously compatible, as well as a powerful tool for their comprehensive classification. This is the avenue explored in this study, and applied to the cases of SU(2) and SO(2N), relevant respectively to previous attempts at reproducing the MSSM and the flipped SU(5) GUT. It is hoped that the techniques encountered will be of benefit in extending the viability of the quasi-realistic phenomenologies already developed.
Phenomenological analysis of heterotic strings: Non-abelian constructions and landscape studies
NASA Astrophysics Data System (ADS)
Wasnik, Vaibhav Hemant
String theory offers the unique promise of unifying all the known forces in nature. However, the internal consistency of the theory requires that spacetime have more than four dimensions. As a result, the extra dimensions must be compactified in some manner and how this compactification takes place is critical for determining the low-energy physical predictions of the theory. In this thesis we examine two distinct consequences of this fact. First, almost all of the prior research in string model-building has examined the consequences of compactifying on so-called "abelian" orbifolds. However, the most general class of compactifications, namely those on non-abelian orbifolds, remains almost completely unexplored. This thesis focuses on the low-energy phenomenological consequences of compactifying strings on non-abelian orbifolds. One of the main interests in pursuing these theories is that they can, in principle, naturally give rise to low-energy models which simultaneously have N=1 supersymmetry along with scalar particles transforming in the adjoint of the gauge group. These features, which are exceedingly difficult to achieve through abelian orbifolds, are exciting because they are the key ingredients in understanding how grand unification can emerge from string theory. Second, the need to compactify gives rise to a huge "landscape" of possible resulting low-energy phenomenologies. One of the goals of the landscape program in string theory is then to extract information about the space of string vacua in the form of statistical correlations between phenomenological features that are otherwise uncorrelated in field theory. Such correlations would thus represent features of string theory that hold independently of a vacuum-selection principle. In this thesis, we study statistical correlations between two features which are likely to be central to any potential description of nature at high-energy scales: gauge symmetries and spacetime supersymmetry. We analyze
NASA Astrophysics Data System (ADS)
Zhu, W.; Gong, S. S.; Haldane, F. D. M.; Sheng, D. N.
2015-10-01
The non-Abelian topological order has attracted a lot of attention for its fundamental importance and exciting prospect of topological quantum computation. However, explicit demonstration or identification of the non-Abelian states and the associated statistics in a microscopic model is very challenging. Here, based on a density-matrix renormalization-group calculation, we provide a complete characterization of the universal properties of the bosonic Moore-Read state on a Haldane honeycomb lattice model at filling number ν =1 for larger systems, including both the edge spectrum and the bulk anyonic quasiparticle (QP) statistics. We first demonstrate that there are three degenerating ground states for each of which there is a definite anyonic flux threading through the cylinder. We identify the nontrivial countings for the entanglement spectrum in accordance with the corresponding conformal field theory. Through simulating a flux-inserting experiment, it is found that two of the Abelian ground states can be adiabatically connected, whereas the ground state in the Ising anyon sector evolves back to itself, which reveals the fusion rules between different QPs in real space. Furthermore, we calculate the modular matrices S and U , which contain all the information for the anyonic QPs, such as quantum dimensions, fusion rule, and topological spins.
Non-Abelian Gauge Groups for Real and Complex Amended Maxwell's Equations
NASA Astrophysics Data System (ADS)
Rauscher, E. A.
2002-04-01
We have developed an eight dimensional complex Minkowski space M4, compiled of four real dimensions and four imaginary dimensions, which is constant with Lorentz invariance and analytic continuation in the complex plane(1). Complexification, of Maxwell's equations requires a non-Abelian gauge group, which amends the usual theory which utilizes the usual unimodular Weyl U1 group. We have examined the modification of gauge conditions using higher symmetry groups such as SU2, SUn and other groups such as the SL(2,c) double cover group of the rotational group SO(3,1). The mappability of the twistor algebra and the spinor calculus is analyzed in the context of the electromagnetic theory. Thus we are led to new and interesting physics involving extended metrical space constraints, the usual transverse and also longitudinal, non Hertzian electric and magnetic field solutions to Maxwell's equations, possibly leading to new communications systems and antennae theory, non-zero solutions to Ñ·B, and a possible finite but small rest mass of the photon. Comparison of our theoretical approach is made to the work of T.W. Barrett and H.F. Hermuth?s work on amended Maxwell's theories. (1) C. Ramon and E. A. Rauscher, Found. of Phys. 10, 661 (1980)
Non-Abelian states in Fractional Quantum Hall effect in charge carrier hole systems
NASA Astrophysics Data System (ADS)
Simion, George; Lyanda-Geller, Yuli
Quasiparticle excitations obeying non-Abelian statistics represent the key element of topological quantum computing. Crossing of levels and strong coupling between angular momentum and orbital motion, described by Luttinger Hamiltonian, make properties of charge carrier holes different from those of electrons. Peculiarities of hole spectrum in magnetic field provide an opportunity for controlling Landau level mixing in charge carier hole systems. In order to describe Fractional Quantum Hall effect for holes, we propose a method to map hole spectrum and wavefunctions using a spherical shell. We investigate the experimentally observed ν = 1 / 2 state in spherical geometry. Haldane pseudopotentials are computed and the effect of Landau level mixing is evaluated. Exact diagonalization of Coulomb interaction in systems with eight to fourteen holes is performed. We determine that the ground state superposition with Abelian 331 state is very small and the overlap with Moore-Read state is significant. The quasihole and quasielectron excitations are discussed. Research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0010544.
Studying critical string emerging from non-Abelian vortex in four dimensions
NASA Astrophysics Data System (ADS)
Koroteev, P.; Shifman, M.; Yung, A.
2016-08-01
Recently a special vortex string was found [5] in a class of soliton vortices supported in four-dimensional Yang-Mills theories that under certain conditions can become infinitely thin and can be interpreted as a critical ten-dimensional string. The appropriate bulk Yang-Mills theory has the U (2) gauge group and the Fayet-Iliopoulos term. It supports semilocal non-Abelian vortices with the world-sheet theory for orientational and size moduli described by the weighted CP (2 , 2) model. The full target space is R4 ×Y6 where Y6 is a non-compact Calabi-Yau space. We study the above vortex string from the standpoint of string theory, focusing on the massless states in four dimensions. In the generic case all massless modes are non-normalizable, hence, no massless gravitons or vector fields are predicted in the physical spectrum. However, at the selfdual point (at strong coupling) weighted CP (2 , 2) admits deformation of the complex structure, resulting in a single massless hypermultiplet in the bulk. We interpret it as a composite "baryon."
Velocity-dependent models for non-Abelian/entangled string networks
Avgoustidis, A.; Shellard, E. P. S.
2008-11-15
We develop velocity-dependent models describing the evolution of string networks that involve several types of interacting strings, each with a different tension. These incorporate the formation of Y-type junctions with links stretching between colliding strings, while always ensuring energy conservation. These models can be used to describe network evolution for non-Abelian strings as well as cosmic superstrings. The application to Z{sub N} strings in which interactions are topologically constrained, demonstrates that a scaling regime is generally reached which involves a hierarchy of string densities with the lightest most abundant. We also study hybrid networks of cosmic superstrings, where energetic considerations are more important in determining interaction outcomes. We again find that networks tend towards scaling, with the three lightest network components being dominant and having comparable number densities, while the heavier string states are suppressed. A more quantitative analysis depends on the precise calculation of the string interaction matrix using the underlying string or field theory. Nevertheless, these results provide further evidence that the presence of junctions in a string network does not obstruct scaling.
Non-Abelian vortices at weak and strong coupling in mass deformed ABJM theory
NASA Astrophysics Data System (ADS)
Auzzi, Roberto; Kumar, S. Prem
2009-10-01
We find half-BPS vortex solitons, at both weak and strong coupling, in the Script N = 6 supersymmetric mass deformation of ABJM theory with U(N) × U(N) gauge symmetry and Chern-Simons level k. The strong coupling gravity dual is obtained by performing a Bbb Zk quotient of the Script N = 8 supersymmetric eleven dimensional supergravity background of Lin, Lunin and Maldacena corresponding to the mass deformed M2-brane theory. At weak coupling, the BPS vortices preserving six supersymmetries are found in the Higgs vacuum of the theory where the gauge symmetry is broken to U(1) × U(1). The classical vortex solitons break a colour-flavour locked global symmetry resulting in non-Abelian internal orientational moduli and a CP1 moduli space of solutions. At strong coupling and large k, upon reduction to type IIA strings, the vortex moduli space and its action are computed by a probe D0-brane in the dual geometry. The mass of the D0-brane matches the classical vortex mass. However, the gravity picture exhibits a six dimensional moduli space of solutions, a section of which can be identified as the CP1 we find classically, along with a Dirac monopole connection of strength k. It is likely that the extra four dimensions in the moduli space are an artifact of the strong coupling limit and of the supergravity approximation.
Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states
Barkeshli, Maissam; Wen Xiaogang
2011-09-15
We study continuous quantum phase transitions that can occur in bilayer fractional quantum Hall (FQH) systems as the interlayer tunneling and interlayer repulsion are tuned. We introduce a slave-particle gauge theory description of a series of continuous transitions from the (ppq) Abelian bilayer states to a set of non-Abelian FQH states, which we dub orbifold FQH states, of which the Z{sub 4} parafermion (Read-Rezayi) state is a special case. This provides an example in which Z{sub 2} electron fractionalization leads to non-Abelian topological phases. The naive ''ideal'' wave functions and ideal Hamiltonians associated with these orbifold states do not in general correspond to incompressible phases but, instead, lie at a nearby critical point. We discuss this unusual situation from the perspective of the pattern-of-zeros/vertex algebra frameworks and discuss implications for the conceptual foundations of these approaches. Due to the proximity in the phase diagram of these non-Abelian states to the (ppq) bilayer states, they may be experimentally relevant, both as candidates for describing the plateaus in single-layer systems at filling fractions 8/3 and 12/5 and as a way to tune to non-Abelian states in double-layer or wide quantum wells.
Dyonic String-Like Solution in a Non-Abelian Gauge Theory with Two Potentials
NASA Astrophysics Data System (ADS)
Tripathi, Buddhi Vallabh; Nandan, Hemwati; Purohit, K. D.
2016-04-01
Axially symmetric dyon solutions of a non-Abelian gauge theory model with two potentials are sought. While seeking axially symmetric (flux tube like solutions) for the model, we stumbled upon an exact solution which represents an infinite string-like dyonic configuration with cylindrical symmetry.
Abelian and non-Abelian states in ν = 2 / 3 bilayer fractional quantum Hall systems
NASA Astrophysics Data System (ADS)
Peterson, Michael; Wu, Yang-Le; Cheng, Meng; Barkeshli, Maissam; Wang, Zhenghan
There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that could potentially be realized in one- and two-component FQH systems at total filling fraction ν = n + 2 / 3 , for integer n. Some of these states even possess quasiparticles with non-Abelian statistics that are powerful enough for universal topological quantum computation, and are thus of particular interest. Here we initiate a systematic numerical study, using both exact diagonalization and variational Monte Carlo, to investigate the phase diagram of FQH systems at total filling fraction ν = n + 2 / 3 , including in particular the possibility of the non-Abelian Z4 parafermion state. In ν = 2 / 3 bilayers we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the Z4 state. On the other hand, in single-component systems at ν = 8 / 3 , we find that the Z4 parafermion state has significantly higher overlap with the exact ground state than the Laughlin state, together with a larger gap, suggesting that the experimentally observed ν = 8 / 3 state may be non-Abelian. Our results from the two complementary numerical techniques agree well with each other qualitatively. We acknowledge the Office of Research and Sponsored Programs at California State University Long Beach and Microsoft Station Q.
Escalante, Alberto Manuel-Cabrera, J.
2015-10-15
A detailed Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions is performed. We obtain for the theories under study the constraints, the gauge transformations, the generalized Faddeev–Jackiw brackets and we perform the counting of physical degrees of freedom. In addition, we compare our results with those found in the literature where the canonical analysis is developed, in particular, we show that both the generalized Faddeev–Jackiw brackets and Dirac’s brackets coincide to each other. Finally we discuss some remarks and prospects. - Highlights: • A detailed Faddeev–Jackiw analysis for exotic action of gravity is performed. • We show that Dirac’s brackets and Generalized [FJ] brackets are equivalent. • Without fixing the gauge exotic action is a non-commutative theory. • The fundamental gauge transformations of the theory are found. • Dirac and Faddeev–Jackiw approaches are compared.
Non-Abelian clouds around Reissner-Nordström black holes: The existence line
NASA Astrophysics Data System (ADS)
Radu, Eugen; Tchrakian, D. H.; Yang, Yisong
2016-06-01
A known feature of electrically charged Reissner-Nordström-anti-de Sitter planar black holes is that they can become unstable when considered as solutions of Einstein-Yang-Mills theory. The mechanism for this is that the linearized Yang-Mills equations in the background of the Reissner-Nordström (RN) black holes possess a normalizable zero mode, resulting in non-Abelian (nA) magnetic clouds near the horizon. In this work we show that the same pattern may occur also for asymptotically flat RN black holes. Different from the anti-de Sitter case, in the Minkowskian background the prerequisites for the existence of the nA clouds are (i) a large enough gauge group, and (ii) the presence of some extra interaction terms in the matter Lagrangian. To illustrate this mechanism we present two specific examples, one in four- and the other in five-dimensional asymptotically flat spacetime. In the first case, we augment the usual S U (3 ) Yang-Mills Lagrangian with a higher-order (quartic) curvature term, while for the second one we add the Chern-Simons density to the S O (6 ) Yang-Mills system. In both cases, an Abelian gauge symmetry is spontaneously broken near a RN black hole horizon with the appearance of a condensate of nA gauge fields. In addition to these two examples, we review the corresponding picture for anti-de Sitter black holes. All these solutions are studied both analytically and numerically, existence proofs being provided for nA clouds in the background of RN black holes. The proofs use shooting techniques which are suggested by and in turn offer insights for our numerical methods. They indicate that, for a black hole of given mass, appropriate electric charge values are required to ensure the existence of solutions interpolating desired boundary behavior at the horizons and spatial infinity.
Multiflavor QCD* on R_3 * S_1: Studying Transition From Abelian to Non-Abelian Confinement
Shifman, M.; Unsal, M.; /SLAC /Stanford U., Phys. Dept.
2009-03-31
The center-stabilized multiflavor QCD* theories formulated on R{sub 3} x S{sub 1} exhibit both Abelian and non-Abelian confinement as a function of the S{sub 1} radius, similar to the Seiberg-Witten theory as a function of the mass deformation parameter. For sufficiently small number of flavors and small r(S{sub 1}), we show occurrence of a mass gap in gauge fluctuations, and linear confinement. This is a regime of confinement without continuous chiral symmetry breaking ({chi}SB). Unlike one-flavor theories where there is no phase transition in r(S{sub 1}), the multiflavor theories possess a single phase transition associated with breaking of the continuous {chi}S. We conjecture that the scale of the {chi}SB is parametrically tied up with the scale of Abelian to non-Abelian confinement transition.
Non-Abelian magnetic black strings versus black holes
NASA Astrophysics Data System (ADS)
Mazharimousavi, S. Habib; Halilsoy, M.
2016-05-01
We present d+1 -dimensional pure magnetic Yang-Mills (YM) black strings (or 1-branes) induced by the d -dimensional Einstein-Yang-Mills-Dilaton black holes. The Born-Infeld version of the YM field makes our starting point which goes to the standard YM field through a limiting procedure. The lifting from black holes to black strings (with less number of fields) is done by adding an extra, compact coordinate. This amounts to the change of horizon topology from S^{d-2} to a product structure. Our black string in 5 dimensions is a rather special one, with uniform Hawking temperature and non-asymptotically flat structure. As the YM charge becomes large the string gets thinner to tend into a breaking point and transform into a 4-dimensional black hole.
NASA Astrophysics Data System (ADS)
Mross, David F.; Essin, Andrew; Alicea, Jason; Stern, Ady
2016-01-01
We show that boundaries of 3D weak topological insulators can become gapped by strong interactions while preserving all symmetries, leading to Abelian surface topological order. The anomalous nature of weak topological insulator surfaces manifests itself in a nontrivial action of symmetries on the quasiparticles; most strikingly, translations change the anyon types in a manner impossible in strictly 2D systems with the same symmetry. As a further consequence, screw dislocations form non-Abelian defects that trap Z4 parafermion zero modes.
Non-Abelian bremsstrahlung and azimuthal asymmetries in high energy p+A reactions
NASA Astrophysics Data System (ADS)
Gyulassy, M.; Levai, P.; Vitev, I.; Biró, T. S.
2014-09-01
We apply the GLV reaction operator solution to the Vitev-Gunion-Bertsch (VGB) boundary conditions to compute to all orders in nuclear opacity the non-Abelian gluon bremsstrahlung of event-by-event fluctuating beam jets in nuclear collisions. We evaluate analytically azimuthal Fourier moments of single gluon, vnM{1}, and even numbered 2ℓ gluon distribution, vnM{2ℓ}, inclusive distributions in high-energy p +A reactions as a function of harmonic n, target recoil cluster number, M, and gluon number, 2ℓ, at the RHIC and LHC. Multiple resolved clusters of recoiling target beam jets together with the projectile beam jet form color scintillation antenna (CSA) arrays that lead to characteristic boost-noninvariant trapezoidal rapidity distributions in asymmetric B+A nuclear collisions. The scaling of the intrinsically azimuthally anisotropic and long range in η nature of the non-Abelian bremsstrahlung leads to vn moments that are similar to results from hydrodynamic models, but due entirely to non-Abelian wave interference phenomena sourced by the fluctuating CSA. Our analytic nonflow solutions are similar to recent numerical saturation model predictions but differ by predicting a simple power-law hierarchy of both even and odd vn without invoking kT factorization. A test of the CSA mechanism is the predicted nearly linear η rapidity dependence of the vn(kT,η). Non-Abelian beam jet bremsstrahlung may, thus, provide a simple analytic solution to the beam energy scan puzzle of the near √s independence of vn(pT) moments observed down to 10 AGeV, where large-x valence-quark beam jets dominate inelastic dynamics. Recoil bremsstrahlung from multiple independent CSA clusters could also provide a partial explanation for the unexpected similarity of vn in p(D)+A and noncentral A+A at the same dN/dη multiplicity as observed at the RHIC and LHC.
Improved HDRG decoders for qudit and non-Abelian quantum error correction
NASA Astrophysics Data System (ADS)
Hutter, Adrian; Loss, Daniel; Wootton, James R.
2015-03-01
Hard-decision renormalization group (HDRG) decoders are an important class of decoding algorithms for topological quantum error correction. Due to their versatility, they have been used to decode systems with fractal logical operators, color codes, qudit topological codes, and non-Abelian systems. In this work, we develop a method of performing HDRG decoding which combines strengths of existing decoders and further improves upon them. In particular, we increase the minimal number of errors necessary for a logical error in a system of linear size L from \\Theta ({{L}2/3}) to Ω ({{L}1-ε }) for any ε \\gt 0. We apply our algorithm to decoding D({{{Z}}d}) quantum double models and a non-Abelian anyon model with Fibonacci-like fusion rules, and show that it indeed significantly outperforms previous HDRG decoders. Furthermore, we provide the first study of continuous error correction with imperfect syndrome measurements for the D({{{Z}}d}) quantum double models. The parallelized runtime of our algorithm is poly(log L) for the perfect measurement case. In the continuous case with imperfect syndrome measurements, the averaged runtime is O(1) for Abelian systems, while continuous error correction for non-Abelian anyons stays an open problem.
Pauli-Villars Regularization of Non-Abelian Gauge Theories
NASA Astrophysics Data System (ADS)
Hiller, J. R.
2016-04-01
As an extension of earlier work on QED, we construct a BRST-invariant Lagrangian for SU(N) Yang-Mills theory with fundamental matter, regulated by the inclusion of massive Pauli-Villars (PV) gluons and PV quarks. The underlying gauge symmetry for massless PV gluons is generalized to accommodate the PV-index-changing currents that are required by the regularization. Auxiliary adjoint scalars are used, in a mechanism due to Stueckelberg, to attribute mass to the PV gluons and the PV quarks. The addition of Faddeev-Popov ghosts then establishes a residual BRST symmetry. Although there are drawbacks to the approach, in particular the computational load of a large number of PV fields and a nonlocal interaction of the ghost fields, this formulation could provide a foundation for renormalizable nonperturbative solutions of light-front QCD in an arbitrary covariant gauge.
Pauli-Villars Regularization of Non-Abelian Gauge Theories
NASA Astrophysics Data System (ADS)
Hiller, J. R.
2016-07-01
As an extension of earlier work on QED, we construct a BRST-invariant Lagrangian for SU(N) Yang-Mills theory with fundamental matter, regulated by the inclusion of massive Pauli-Villars (PV) gluons and PV quarks. The underlying gauge symmetry for massless PV gluons is generalized to accommodate the PV-index-changing currents that are required by the regularization. Auxiliary adjoint scalars are used, in a mechanism due to Stueckelberg, to attribute mass to the PV gluons and the PV quarks. The addition of Faddeev-Popov ghosts then establishes a residual BRST symmetry. Although there are drawbacks to the approach, in particular the computational load of a large number of PV fields and a nonlocal interaction of the ghost fields, this formulation could provide a foundation for renormalizable nonperturbative solutions of light-front QCD in an arbitrary covariant gauge.
Jet broadening in unstable non-Abelian plasmas
Dumitru, Adrian; Schenke, Bjoern; Strickland, Michael; Nara, Yasushi
2008-08-15
We perform numerical simulations of the SU(2) Boltzmann-Vlasov equation including both hard elastic particle collisions and soft interactions mediated by classical Yang-Mills fields. Using this technique we calculate the momentum-space broadening of high-energy jets in real time for both locally isotropic and anisotropic plasmas. In both cases we introduce a separation scale that separates hard and soft interactions and demonstrate that our results for jet broadening are independent of the precise separation scale chosen. For an isotropic plasma this allows us to calculate the jet transport coefficient q-circumflex including hard and soft nonequilibrium dynamics. For an anisotropic plasma the jet transport coefficient becomes a tensor with q-circumflex{sub L}{ne}q-circumflex{sub perpendicular}. We find that for weakly coupled anisotropic plasmas the fields develop unstable modes, forming configurations where B{sub perpendicular}>E{sub perpendicular} and E{sub z}>B{sub z}, which lead to q-circumflex{sub L}>q-circumflex{sub perpendicular}. We study whether the effect is strong enough to explain the experimental observation that high-energy jets traversing the plasma perpendicular to the beam axis experience much stronger broadening in rapidity, {delta}{eta}, than in azimuth, {delta}{phi}.
Non-abelian binding energies from the lightcone bootstrap
NASA Astrophysics Data System (ADS)
Li, Daliang; Meltzer, David; Poland, David
2016-02-01
We analytically study the lightcone limit of the conformal bootstrap for 4-point functions containing scalars charged under global symmetries. We show the existence of large spin double-twist operators in various representations of the global symmetry group. We then compute their anomalous dimensions in terms of the central charge C T , current central charge C J , and the OPE coefficients of low dimension scalars. In AdS, these results correspond to the binding energy of two-particle states arising from the exchange of gravitons, gauge bosons, and light scalar fields. Using unitarity and crossing symmetry, we show that gravity is universal and attractive among different types of two-particle states, while the gauge binding energy can have either sign as determined by the representation of the two-particle state, with universal ratios fixed by the symmetry group. We apply our results to 4D {N}=1 SQCD and the 3D O( N) vector models. We also show that in a unitary CFT, if the current central charge C J stays finite when the global symmetry group becomes infinitely large, such as the N → ∞ limit of the O( N) vector model, then the theory must contain an infinite number of higher spin currents.
Role of nonlocal probes of thermalization for a strongly interacting non-Abelian plasma
NASA Astrophysics Data System (ADS)
Bellantuono, L.; Colangelo, P.; De Fazio, F.; Giannuzzi, F.; Nicotri, S.
2016-07-01
The thermalization process of an out-of-equilibrium boost-invariant strongly interacting non-Abelian plasma is investigated using a holographic method. Boundary sourcing, a distortion of the boundary metric, is employed to drive the system far from equilibrium. Thermalization is analyzed in the fully dynamical system through nonlocal probes: the equal-time two-point correlation function of large conformal dimension operators in the boundary theory, and Wilson loops of different shapes. A dependence of the thermalization time on the size of the probes is found, which can be compared to the result of local observables: the onset of thermalization is first observed at short distances.
A simple model for the evolution of a non-Abelian cosmic string network
NASA Astrophysics Data System (ADS)
Cella, G.; Pieroni, M.
2016-06-01
In this paper we present the results of numerical simulations intended to study the behavior of non-Abelian cosmic strings networks. In particular we are interested in discussing the variations in the asymptotic behavior of the system as we variate the number of generators for the topological defects. A simple model which allows for cosmic strings is presented and its lattice discretization is discussed. The evolution of the generated cosmic string networks is then studied for different values for the number of generators for the topological defects. Scaling solution appears to be approached in most cases and we present an argument to justify the lack of scaling for the residual cases.
Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
NASA Astrophysics Data System (ADS)
Lavau, Sylvain; Samtleben, Henning; Strobl, Thomas
2014-12-01
We disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six space-time dimensions. This is a coupled system of 1-form, 2-form, and 3-form gauge fields. We show that the algebraic consistency constraints governing this system permit to define a Lie 3-algebra, generalizing the structural Lie algebra of a standard Yang-Mills theory to the setting of a higher bundle. Reformulating the Lie 3-algebra in terms of a nilpotent degree 1 BRST-type operator Q, this higher bundle can be compactly described by means of a Q-bundle; its fiber is the shifted tangent of the Q-manifold corresponding to the Lie 3-algebra and its base the odd tangent bundle of space-time equipped with the de Rham differential. The generalized Bianchi identities can then be retrieved concisely from Q2 = 0, which encode all the essence of the structural identities. Gauge transformations are identified as vertical inner automorphisms of such a bundle, their algebra being determined from a Q-derived bracket.
NASA Astrophysics Data System (ADS)
Gadella, M.; Mateos-Guilarte, J.; Muñoz-Castañeda, J. M.; Nieto, L. M.
2016-01-01
In this contribution to the study of one-dimensional point potentials, we prove that if we take the limit q\\to 0 on a potential of the type {v}0δ (y)+2{v}1{δ }\\prime (y)+{w}0δ (y-q)+2{w}1{δ }\\prime (y-q), we obtain a new point potential of the type {u}0δ (y)+2{u}1{δ }\\prime (y), when u 0 and u 1 are related to v 0, v 1, w 0 and w 1 by a law with the structure of a group. This is the Borel subgroup of {{SL}}2({{R}}). We also obtain the non-abelian addition law from the scattering data. The spectra of the Hamiltonian in the decoupling cases emerging in the study are also described in full. It is shown that for the {v}1=+/- 1, {w}1=+/- 1 values of the {δ }\\prime couplings the singular Kurasov matrices become equivalent to Dirichlet at one side of the point interaction and Robin boundary conditions at the other side.
NASA Astrophysics Data System (ADS)
Goldman, N.; Gerbier, F.; Lewenstein, M.
2013-07-01
We describe a scheme to engineer non-Abelian gauge potentials on a square optical lattice using laser-induced transitions. We emphasize the case of two-electron atoms, where the electronic ground state g is laser-coupled to a metastable state e within a state-dependent optical lattice. In this scheme, the alternating pattern of lattice sites hosting g and e states depicts a chequerboard structure, allowing for laser-assisted tunnelling along both spatial directions. In this configuration, the nuclear spin of the atoms can be viewed as a ‘flavour’ quantum number undergoing non-Abelian tunnelling along nearest-neighbour links. We show that this technique can be useful to simulate the equivalent of the Haldane quantum Hall model using cold atoms trapped in square optical lattices, offering an interesting route to realize Chern insulators. The emblematic Haldane model is particularly suited to investigate the physics of topological insulators, but requires, in its original form, complex hopping terms beyond nearest-neighbouring sites. In general, this drawback inhibits a direct realization with cold atoms, using standard laser-induced tunnelling techniques. We demonstrate that a simple mapping allows us to express this model in terms of matrix hopping operators that are defined on a standard square lattice. This mapping is investigated for two models that lead to anomalous quantum Hall phases. We discuss the practical implementation of such models, exploiting laser-induced tunnelling methods applied to the chequerboard optical lattice.
NASA Astrophysics Data System (ADS)
Borgh, Magnus O.; Ruostekoski, Janne
2016-05-01
We demonstrate that multiple interaction-dependent defect core structures as well as dynamics of non-Abelian vortices can be realized in the biaxial nematic (BN) phase of a spin-2 atomic Bose-Einstein condensate (BEC). An experimentally simple protocol may be used to break degeneracy with the uniaxial nematic phase. We show that a discrete spin-space symmetry in the core may be reflected in a breaking of its spatial symmetry. The discrete symmetry of the BN order parameter leads to non-commuting vortex charges. We numerically simulate reconnection of non-Abelian vortices, demonstrating formation of the obligatory rung vortex. In addition to atomic BECs, non-Abelian vortices are theorized in, e.g., liquid crystals and cosmic strings. Our results suggest the BN spin-2 BEC as a prime candidate for their realization. We acknowledge financial support from the EPSRC.
NASA Astrophysics Data System (ADS)
Khan, Mayukh; Teo, Jeffrey; Hughes, Taylor
2015-03-01
Non-abelian anyons exhibit exotic braiding statistics which can be utilized to realize a universal topological quantum computer. In this work we focus on Fibonacci anyons which occur in Z3 Read Rezayi fractional quantum hall states. Traditionally they have been constructed using su(2)3 / u (1) coset theories. We introduce conformal field theories(CFTs) of exceptional and non-simply laced Lie Algebras at level 1, for example G2 ,F4 which host Fibonacci anyons. We realize these CFT's concretely on the 1d gapless edge of an anisotropic 2d system built out of coupled, interacting Luttinger wires. Interactions are introduced within a bundle of wires to fractionalize the original chiral bosons into different sectors. Next, we couple these sectors to get the desired topological phase in the bulk. The 2d bulk of the stack is gapped by backscattering terms between counterpropagating modes on different bundles. The emergence of this topological phase can be interpreted using techniques of anyon condensation . We also explicitly construct the Kac Moody algebra on the edge CFT using original bosonic degrees of freedom.We acknowledge support from NSF CAREER DMR-1351895(TH) and Simons Foundation (JT).
Collective Non-Abelian Instabilities in a Melting Color Glass Condensate
Romatschke, Paul; Venugopalan, Raju
2006-02-17
We present first results for (3+1)D simulations of SU(2) Yang-Mills equations for matter expanding into the vacuum after a heavy ion collision. Violations of boost invariance cause a non-Abelian Weibel instability leading soft modes to grow with proper time {tau} as exp({gamma}{radical}(g{sup 2}{mu}{tau})), where g{sup 2}{mu} is a scale arising from the saturation of gluons in the nuclear wave function. The scale for the growth rate {gamma} is set by a plasmon mass, defined as {omega}{sub pl}={kappa}{sub 0}{radical}(g{sup 2}{mu}/{tau}), generated dynamically in the collision. We compare the numerical ratio {gamma}/{kappa}{sub 0} to the corresponding value predicted by the hard thermal loop formalism for anisotropic plasmas.
Beta function in the non-Abelian Nambu-Jona-Lasinio model in four dimensions
Alves, Van Sergio; Pinheiro, S. V. L.; Nascimento, Leonardo; Pena, Francisco
2009-08-15
In this paper we present the structure of the renormalization group in non-Abelian Nambu-Jona-Lasinio model up to 1-loop order. The model is not perturbatively renormalizable in the usual power counting sense, but it is treated as an effective theory, valid in a scale of energy in which p<<{lambda}, where p is the external momenta of the loop and {lambda} is a massive parameter that characterizes the couplings of the nonrenormalizable vertex. We clarify the tensorial structure of the interaction vertices and calculate the functions of the renormalization group. The analysis of the fixed points of the theory is also presented using Zimmermann's procedure for reducing the coupling constants. We find that the origin is an infrared-stable fixed point at low energies and also there is a nontrivial ultraviolet stable fixed point, indicating that the theory could be perturbatively investigated in the low momentum regime.
Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium
Bliokh, K. Yu.; Frolov, D. Yu.; Kravtsov, Yu. A.
2007-05-15
A theory of electromagnetic wave propagation in a weakly anisotropic smoothly inhomogeneous medium is developed, based on the quantum-mechanical diagonalization procedure applied to Maxwell equations. The equations of motion for the translational (ray) and intrinsic (polarization) degrees of freedom are derived ab initio. The ray equations take into account the optical Magnus effect (spin Hall effect of photons) as well as trajectory variations owing to the medium anisotropy. Polarization evolution is described by the precession equation for the Stokes vector. In the generic case, the evolution of wave turns out to be non-Abelian: it is accompanied by mutual conversion of the normal modes and periodic oscillations of the ray trajectories analogous to electron zitterbewegung. The general theory is applied to examples of wave evolution in media with circular and linear birefringence.
Extended hubbard model with ring exchange: a route to a non-Abelian topological phase.
Freedman, Michael; Nayak, Chetan; Shtengel, Kirill
2005-02-18
We propose an extended Hubbard model on a 2D kagome lattice with an additional ring exchange term. The particles can be either bosons or spinless fermions. We analyze the model at the special filling fraction 1/6, where it is closely related to the quantum dimer model. We show how to arrive at an exactly soluble point whose ground state is the "d-isotopy" transition point into a stable phase with a certain type of non-Abelian topological order. Near the "special" values, d=2cos(pi/(k+2), this topological phase has anyonic excitations closely related to SU(2) Chern-Simons theory at level k. PMID:15783757
On the effective character of a non-abelian DBI action
NASA Astrophysics Data System (ADS)
Osorio, M. A. R.; Suárez, M.
2001-03-01
We study the way Lorentz covariance can be reconstructed from Matrix Theory as a IMF description of M-theory. The problem is actually related to the interplay between a non-abelian Dirac-Born-Infeld action and Super-Yang-Mills as its generalized non-relativistic approximation. All this physics shows up by means of an analysis of the asymptotic expansion of the Bessel functions Kν that profusely appear in the computations of amplitudes at finite temperature and solitonic calculations. We hope this might help to better understand the issue of getting a Lorentz covariant formulation in relation with the /N-->+∞ limit. There are also some computations that could be of some interest in Relativistic Statistical Mechanics.
Low energy dynamics of slender monopoles in non-Abelian superconductor
NASA Astrophysics Data System (ADS)
Arai, M.; Blaschke, F.; Eto, M.; Sakai, N.
2016-01-01
Low energy dynamics of magnetic monopoles and anti-monopoles in the U(2)c gauge theory is studied in the Higgs (non-Abelian superconducting) phase. The monopoles in this phase are slender ellipsoids, pierced by a vortex string. We investigate scattering of monopole with anti-monopole and find that they do not always decay into radiation, contrary to our naive intuition. They can repel, make bound states (magnetic mesons) or resonances. We point out that some part of solutions in 1 + 3 dimensions can be mapped exactly onto the sine-Gordon system in 1 + 1 dimensions in the first non-trivial order of rigid-body approximation and we provide analytic formulas for such solutions there.
Explicit non-Abelian monopoles and instantons in SU(N) pure Yang-Mills theory
Popov, Alexander D.
2008-06-15
It is well known that there are no static non-Abelian monopole solutions in pure Yang-Mills theory on Minkowski space R{sup 3,1}. I show that such solutions exist in SU(N) gauge theory on the spaces R{sup 2}xS{sup 2} and RxS{sup 1}xS{sup 2} with Minkowski signature (-+++). In the temporal gauge they are solutions of pure Yang-Mills theory on TxS{sup 2}, where T is R or S{sup 1}. Namely, imposing SO(3) invariance and some reality conditions, I consistently reduce the Yang-Mills model on the above spaces to a non-Abelian analog of the {phi}{sup 4} kink model whose static solutions give SU(N) monopole (-antimonopole) configurations on the space R{sup 1,1}xS{sup 2} via the above-mentioned correspondence. These solutions can also be considered as instanton configurations of Yang-Mills theory in 2+1 dimensions. The kink model on RxS{sup 1} admits also periodic sphaleron-type solutions describing chains of n kink-antikink pairs spaced around the circle S{sup 1} with arbitrary n>0. They correspond to chains of n static monopole-antimonopole pairs on the space RxS{sup 1}xS{sup 2} which can also be interpreted as instanton configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature (thermal time circle). I also describe similar solutions in Euclidean SU(N) gauge theory on S{sup 1}xS{sup 3} interpreted as chains of n instanton-anti-instanton pairs.
Lu Yuanming; Wang Ziqiang; Wen Xiaogang; Wang Zhenghan
2010-03-15
In the pattern-of-zeros approach to quantum Hall states, a set of data (n;m;S{sub a}|a=1,...,n;n,m,S{sub a} is n element of N) (called the pattern of zeros) is introduced to characterize a quantum Hall wave function. In this paper we find sufficient conditions on the pattern of zeros so that the data correspond to a valid wave function. Some times, a set of data (n;m;S{sub a}) corresponds to a unique quantum Hall state, while other times, a set of data corresponds to several different quantum Hall states. So in the latter cases, the pattern of zeros alone does not completely characterize the quantum Hall states. In this paper, we find that the following expanded set of data (n;m;S{sub a};c|a=1,...,n;n,m,S{sub a} is an element of N;c is an element of R) provides a more complete characterization of quantum Hall states. Each expanded set of data completely characterizes a unique quantum Hall state, at least for the examples discussed in this paper. The result is obtained by combining the pattern of zeros and Z{sub n} simple-current vertex algebra which describes a large class of Abelian and non-Abelian quantum Hall states PHI{sub Z{sub n}{sup sc}}. The more complete characterization in terms of (n;m;S{sub a};c) allows us to obtain more topological properties of those states, which include the central charge c of edge states, the scaling dimensions and the statistics of quasiparticle excitations.
Quiver gauge theory of non-Abelian vortices and noncommutative instantons in higher dimensions
Popov, Alexander D.; Szabo, Richard J.
2006-01-15
We construct explicit Bogomolnyi, Prasad, Sommerfeld (BPS) and non-BPS solutions of the Yang-Mills equations on the noncommutative space R{sub {theta}}{sup 2n}xS{sup 2} which have manifest spherical symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show that the solutions imply an equivalence between instantons on R{sub {theta}}{sup 2n}xS{sup 2} and non-Abelian vortices on R{sub {theta}}{sup 2n}, which can be interpreted as a blowing-up of a chain of D0-branes on R{sub {theta}}{sup 2n} into a chain of spherical D2-branes on R{sub {theta}}{sup 2n}xS{sup 2}. The low-energy dynamics of these configurations is described by a quiver gauge theory which can be formulated in terms of new geometrical objects generalizing superconnections. This formalism enables the explicit assignment of D0-brane charges in equivariant K-theory to the instanton solutions.
Numerical characterization of non-Abelian Moore-Read state in the microscopic lattice boson model
NASA Astrophysics Data System (ADS)
Zhu, Wei; Gong, Shoushu; Haldane, F. D. M.; Sheng, D. N.
2015-03-01
Identifying the interacting systems that host the non-Abelian (NA) topological phases have attracted intense attention in physics. Theoretically, it is possible to realize the NA Moore-Read (MR) state in bosonic system or double-layer system by coupling two Abelian fractional quantum Hall (FQH) states together. Here, based on the density matrix renormalization group and exact diagonalization calculations, we study two such examples in the microscopic lattice models and investigate their NA nature. In the first example, we provide a thorough characterization of the universal properties of MR state on Haldane honeycomb lattice model, including both the edge spectrum and the bulk anyonic quasiparticle statistics. By inspecting the entanglement spectral response to the U (1) flux, it is found that two of Abelian ground states can be adiabatically connected through a charge unit quasiparticle pumping from one edge to the other. In the second example, we study a double-layer bosonic FQH system built from the π-flux lattice model. Some evidences of NA nature has been identified, including the groundstate degeneracy and finite drag Hall conductance. The numerical methods we developed here provides a useful and practical way for detecting the full information of NA topological order. This research is supported by the U.S. Department of Energy, Office of Basic Energy Sciences under Grant No. DE-FG02-06ER46305.
Spin correlations and topological entanglement entropy in a non-Abelian spin-one spin liquid
NASA Astrophysics Data System (ADS)
Wildeboer, Julia; Bonesteel, N. E.
2016-07-01
We analyze the properties of a non-Abelian spin-one chiral spin liquid state proposed by Greiter and Thomale [Phys. Rev. Lett. 102, 207203 (2009), 10.1103/PhysRevLett.102.207203] using Monte Carlo. In this state the bosonic ν =1 Moore-Read Pfaffian wave function is used to describe a gas of bosonic spin flips on a square lattice with one flux quantum per plaquette. For toroidal geometries there is a three-dimensional space of these states corresponding to the topological degeneracy of the bosonic Moore-Read state on the torus. We show that spin correlations for different states in this space become indistinguishable for large system size. We also calculate the Renyi entanglement entropy for different system partitions to extract the topological entanglement entropy and provide evidence that the topological order of the lattice spin-liquid state is the same as that of the continuum Moore-Read state from which it is constructed.
Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
Fujiwara, Takanori; Fukui, Takahiro; Nitta, Muneto; Yasui, Shigehiro
2011-10-01
Color superconductivity in high-density QCD exhibits the color-flavor-locked phase. To explore zero modes in the color-flavor-locked phase in the presence of a non-Abelian vortex with an SU(2) symmetry in the vortex core, we apply the index theorem to the Bogoliubov-de Gennes (BdG) Hamiltonian. From the calculation of the topological index, we find that triplet, doublet and singlet sectors of SU(2) have certain number of chiral Majorana zero modes in the limit of vanishing chemical potential. We also solve the BdG equation by the use of the series expansion to show that the number of zero modes and their chirality match the result of the index theorem. From particle-hole symmetry of the BdG Hamiltonian, we conclude that if and only if the index of a given sector is odd, one zero mode survives generically for a finite chemical potential. We argue that this result should hold nonperturbatively even in the high-density limit.
Multiflavor QCD∗ on R3 ×S1: Studying transition from Abelian to non-Abelian confinement
NASA Astrophysics Data System (ADS)
Shifman, M.; Ünsal, M.
2009-11-01
The center-stabilized multiflavor QCD∗ theories formulated on R3 ×S1 exhibit both Abelian and non-Abelian confinement as a function of the S1 radius, similar to the Seiberg-Witten theory as a function of the mass deformation parameter. For sufficiently small number of flavors and small r (S1), we show occurrence of a mass gap in gauge fluctuations, and linear confinement. This is a regime of confinement without continuous chiral symmetry breaking (χSB). Unlike one-flavor theories where there is no phase transition in r (S1), the multiflavor theories possess a single phase transition associated with breaking of the continuous χS. We conjecture that the scale of the χSB is parametrically tied up with the scale of Abelian to non-Abelian confinement transition.
NASA Astrophysics Data System (ADS)
Matsudo, Ryutaro; Kondo, Kei-Ichi
2015-12-01
We give a gauge-independent definition of magnetic monopoles in the S U (N ) Yang-Mills theory through the Wilson loop operator. For this purpose, we give an explicit proof of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of the S U (N ) gauge group to derive a new form for the non-Abelian Stokes theorem. The new form is used to extract the magnetic-monopole contribution to the Wilson loop operator in a gauge-invariant way, which enables us to discuss confinement of quarks in any representation from the viewpoint of the dual superconductor vacuum.
NASA Astrophysics Data System (ADS)
Liu, Zhao; Vaezi, Abolhassan; Lee, Kyungmin; Kim, Eun-Ah
2015-08-01
Recent theoretical insights into the possibility of non-Abelian phases in ν =2 /3 fractional quantum Hall states revived the interest in the numerical phase diagram of the problem. We investigate the effect of various kinds of two-body interlayer couplings on the (330) bilayer state and exactly solve the Hamiltonian for up to 14 electrons on sphere and torus geometries. We consider interlayer tunneling, short-ranged repulsive/attractive pseudopotential interactions, and Coulomb repulsion. We find a 6-fold ground-state degeneracy on the torus when the interlayer hollow-core interaction is dominant. To identify the topological nature of this phase we measure the orbital-cut entanglement spectrum, quasihole counting, topological entanglement entropy, and wave-function overlap. Comparing the numerical results to the theoretical predictions, we interpret this 6-fold ground-state degeneracy phase to be the non-Abelian bilayer Fibonacci state.
A topological semimetal model with f-wave symmetry in a non-Abelian triangular optical lattice
NASA Astrophysics Data System (ADS)
Li, Ling; Bai, Zhiming; Hao, Ningning; Liu, Guocai
2016-08-01
We demonstrate that an chiral f-wave topological semimetal can be induced in a non-Abelian triangular optical lattice. We show that the f-wave symmetry topological semimetal is characterized by the topological invariant, i.e., the winding number W, with W=3 and is different from the semimetal with W=1 and 2 which have the p-wave and d-wave symmetry, respectively.
Competing Abelian and non-Abelian topological orders in ν =1 /3 +1 /3 quantum Hall bilayers
NASA Astrophysics Data System (ADS)
Geraedts, Scott; Zaletel, Michael P.; Papić, Zlatko; Mong, Roger S. K.
2015-05-01
Bilayer quantum Hall systems, realized either in two separated wells or in the lowest two subbands of a wide quantum well, provide an experimentally realizable way to tune between competing quantum orders at the same filling fraction. Using newly developed density matrix renormalization group techniques combined with exact diagonalization, we return to the problem of quantum Hall bilayers at filling ν =1 /3 +1 /3 . We first consider the Coulomb interaction at bilayer separation d , bilayer tunneling energy ΔSAS, and individual layer width w , where we find a phase diagram which includes three competing Abelian phases: a bilayer Laughlin phase (two nearly decoupled ν =1 /3 layers), a bilayer spin-singlet phase, and a bilayer symmetric phase. We also study the order of the transitions between these phases. A variety of non-Abelian phases has also been proposed for these systems. While absent in the simplest phase diagram, by slightly modifying the interlayer repulsion we find a robust non-Abelian phase which we identify as the "interlayer-Pfaffian" phase. In addition to non-Abelian statistics similar to the Moore-Read state, it exhibits a novel form of bilayer-spin charge separation. Our results suggest that ν =1 /3 +1 /3 systems merit further experimental study.
S-duality in SU(3) Yang-Mills theory with non-abelian unbroken gauge group
NASA Astrophysics Data System (ADS)
Schroers, B. J.; Bais, F. A.
1998-12-01
It is observed that the magnetic charges of classical monopole solutions in Yang-Mills-Higgs theory with non-abelian unbroken gauge group H are in one-to-one correspondence with coherent states of a dual or magnetic group H˜. In the spirit of the Goddard-Nuyts-Olive conjecture this observation is interpreted as evidence for a hidden magnetic symmetry of Yang-Mills theory. SU(3) Yang-Mills-Higgs theory with unbroken gauge group U(2) is studied in detail. The action of the magnetic group on semi-classical states is given explicitly. Investigations of dyonic excitations show that electric and magnetic symmetry are never manifest at the same time: Non-abelian magnetic charge obstructs the realisation of electric symmetry and vice-versa. On the basis of this fact the charge sectors in the theory are classified and their fusion rules are discussed. Non-abelian electric-magnetic duality is formulated as a map between charge sectors. Coherent states obey particularly simple fusion rules, and in the set of coherent states S-duality can be formulated as an SL(2, Z) mapping between sectors which leaves the fusion rules invariant.
From non-Abelian anyons to quantum computation to coin-flipping by telephone
NASA Astrophysics Data System (ADS)
Mochon, Carlos
Following their divorce, Alice and Bob would like to split some of their possessions by flipping a coin. Unwilling to meet in person, and without a trusted third party, they must figure out a scheme to flip the coin over a telephone that guarantees that neither party can cheat. The preceding scenario is the traditional definition of two-party coin-flipping. In a classical setting, without limits on the available computational power, one player can always guarantee a coin-flipping victory by cheating. However, by employing quantum communication it is possible to guarantee, with only information-theoretic assumptions, that neither party can win by cheating, with a probability greater than two thirds. Along with the description of such a protocol, this thesis derives a tight lower bound on the bias for a large family of quantum weak coin-flipping protocols, proving such a protocol optimal within the family. The protocol described herein is an improvement and generalization of one examined by Spekkens and Rudolph. The key steps of the analysis involve Kitaev's description of quantum coin-flipping as a semidefinite program whose dual problem provides a certificate that upper bounds the amount of cheating for each party. In order for such quantum protocols to be viable, though, a number of practical obstacles involving the communication and processing of quantum information must be resolved. In the second half of this thesis, a scheme for processing quantum information is presented, which uses non-abelian anyons that are the magnetic and electric excitations of a discrete-group quantum gauge theory. In particular, the connections between group structure and computational power are examined, generalizing previous work by Kitaev, Ogburn and Preskill. Anyon based computation has the advantage of being topological, which exponentially suppresses the rate of decoherence and the errors associated with the elementary quantum gates. Though no physical systems with such
Geometry and dynamics of a coupled 4 D-2 D quantum field theory
NASA Astrophysics Data System (ADS)
Bolognesi, Stefano; Chatterjee, Chandrasekhar; Evslin, Jarah; Konishi, Kenichi; Ohashi, Keisuke; Seveso, Luigi
2016-01-01
Geometric and dynamical aspects of a coupled 4 D-2 D interacting quantum field theory — the gauged nonAbelian vortex — are investigated. The fluctuations of the internal 2 D nonAbelian vortex zeromodes excite the massless 4 D Yang-Mills modes and in general give rise to divergent energies. This means that the well-known 2 D C{P}^{N-1} zeromodes associated with a nonAbelian vortex become nonnormalizable.
NASA Astrophysics Data System (ADS)
Khan, Mayukh; Teo, Jeffrey; Hughes, Taylor
2014-03-01
We consider bosonic abelian Fractional Quantum Hall (FQH) and Fractional Quantum Spin Hall (FQSH) states with edge theories drawn from the ADE Kac Moody algebras at level 1 . This set of systems have `anyonic' symmetries that leave braiding and fusion invariant Remarkably, the group of anyonic symmetries for this class of models is isomorphic to the symmetries of the Dynkin diagrams of the particular ADE Lie Algebra under consideration. The triality symmetry of the Dynkin diagram of so(8) leads to the largest anyonic symmetry group S3 (the permutation group on 3 elements). Each element of the anyonic symmetry group corresponds to a distinct way of gapping out the edge (i.e., each element corresponds to a Lagrangian subgroup). Junctions between two distinct gapped edges host non abelian twist defects with quantum dimensions (> 1). In the case of so(8) we have more exotic twist defects with non-abelian fusion. We acknowledge support from the U.S. Department of Energy, Division of Materials Sciences under Award No. DE-FG02- 07ER46453 (MK, TLH) and the Simons Foundation (JT).
Fractional Quantum Hall States at ν =13 /5 and 12 /5 and Their Non-Abelian Nature
NASA Astrophysics Data System (ADS)
Zhu, W.; Gong, S. S.; Haldane, F. D. M.; Sheng, D. N.
2015-09-01
Topological quantum states with non-Abelian Fibonacci anyonic excitations are widely sought after for the exotic fundamental physics they would exhibit, and for universal quantum computing applications. The fractional quantum Hall (FQH) state at a filling factor of ν =12 /5 is a promising candidate; however, its precise nature is still under debate and no consensus has been achieved so far. Here, we investigate the nature of the FQH ν =13 /5 state and its particle-hole conjugate state at 12 /5 with the Coulomb interaction, and we address the issue of possible competing states. Based on a large-scale density-matrix renormalization group calculation in spherical geometry, we present evidence that the essential physics of the Coulomb ground state (GS) at ν =13 /5 and 12 /5 is captured by the k =3 parafermion Read-Rezayi state (RR3), including a robust excitation gap and the topological fingerprint from the entanglement spectrum and topological entanglement entropy. Furthermore, by considering the infinite-cylinder geometry (topologically equivalent to torus geometry), we expose the non-Abelian GS sector corresponding to a Fibonacci anyonic quasiparticle, which serves as a signature of the RR3 state at 13 /5 and 12 /5 filling numbers.
The Fractional Quantum Hall States at ν = 13 / 5 and 12 / 5 and their Non-Abelian Nature
NASA Astrophysics Data System (ADS)
Zhu, W.; Gong, S. S.; Sheng, D. N.
Topological quantum states with non-Abelian Fibonacci anyonic excitations are widely sought after for their exotic fundamental physics and potential applications in universal quantum computing. The fractional quantum Hall (FQH) state at filling factor ν = 12 / 5 is such a promising candidate, however, its precise nature is still under debate and no consensus has been achieved so far. Here, we investigate the nature of the FQH ν = 13 / 5 state and its particle-hole conjugate state at 12 / 5 with the Coulomb interaction, and address the issue of possible competing states. Based on a large-scale density-matrix renormalization group (DMRG) calculation in spherical geometry, we present evidence that the essential physics of the Coulomb ground state (GS) at ν = 13 / 5 and 12 / 5 is captured by the k = 3 parafermion Read-Rezayi state (RR3), including a robust excitation gap and the topological fingerprint from entanglement spectrum and topological entanglement entropy. Furthermore, by considering the infinite-cylinder geometry (topologically equivalent to torus geometry), we expose the non-Abelian GS sector corresponding to a Fibonacci anyonic quasiparticle, which serves as a signature of the RR3 state at 13 / 5 and 12 / 5 filling numbers. This work is supported by the DOE Grants No. DE-FG02-06ER46305, DE-SC0002140, and the NSF Grant No. DMR-1408560.
Fractional Quantum Hall States at ν=13/5 and 12/5 and Their Non-Abelian Nature.
Zhu, W; Gong, S S; Haldane, F D M; Sheng, D N
2015-09-18
Topological quantum states with non-Abelian Fibonacci anyonic excitations are widely sought after for the exotic fundamental physics they would exhibit, and for universal quantum computing applications. The fractional quantum Hall (FQH) state at a filling factor of ν=12/5 is a promising candidate; however, its precise nature is still under debate and no consensus has been achieved so far. Here, we investigate the nature of the FQH ν=13/5 state and its particle-hole conjugate state at 12/5 with the Coulomb interaction, and we address the issue of possible competing states. Based on a large-scale density-matrix renormalization group calculation in spherical geometry, we present evidence that the essential physics of the Coulomb ground state (GS) at ν=13/5 and 12/5 is captured by the k=3 parafermion Read-Rezayi state (RR_{3}), including a robust excitation gap and the topological fingerprint from the entanglement spectrum and topological entanglement entropy. Furthermore, by considering the infinite-cylinder geometry (topologically equivalent to torus geometry), we expose the non-Abelian GS sector corresponding to a Fibonacci anyonic quasiparticle, which serves as a signature of the RR_{3} state at 13/5 and 12/5 filling numbers. PMID:26431006
NASA Astrophysics Data System (ADS)
Pesando, Igor
2016-09-01
We consider the simplest possible setting of non-abelian twist fields which corresponds to SU (2) monodromies. We first review the theory of hypergeometric function and of the solutions of the most general Fuchsian second order equation with three singularities. Then we solve the problem of writing the general solution with prescribed U (2) monodromies. We use this result to compute the classical string solution corresponding to three D2 branes in R4. Despite the fact that the configuration is supersymmetric the classical string solution is not holomorphic. Using the equation of motion and not the KLT approach we give a very simple expression for the classical action of the string. We find that the classical action is not proportional to the area of the triangle determined by the branes intersection points since the solution is not holomorphic. Phenomenologically this means that the Yukawa couplings for these supersymmetric configurations on non-factorized tori are suppressed with respect to the factorized case.
Hou, Chang-Yu; Chamon, Claudio
2006-10-01
We study a tunneling geometry defined by a single point-contact constriction that brings to close vicinity two points sitting at the same edge of a quantum Hall liquid, shortening the trip between the otherwise spatially separated points along the normal chiral edge path. This wormhole-like geometry allows for entrapping bulk quasiparticles between the edge path and the tunnel junction, possibly realizing a topologically protected qubit if the quasiparticles have non-Abelian statistics. We show how either noise or simpler voltage measurements along the edge can probe the non-Abelian nature of the trapped quasiparticles. PMID:17155280
NASA Astrophysics Data System (ADS)
Robertson, Christopher; Worth, Graham A.
2015-10-01
The vibronic coupling Hamiltonian is a standard model used to describe the potential energy surfaces of systems in which non-adiabatic coupling is a key feature. This includes Jahn-Teller and Renner-Teller systems. The model approximates diabatic potential energy functions as polynomials expanded about a point of high symmetry. One must ensure the model Hamiltonian belongs to the totally symmetric irreducible representation of this point group. Here, a simple approach is presented to generate functions that form a basis for totally symmetric irreducible representations of non-Abelian groups and apply it to D∞h (2D) and O (3D). For the O group, the use of a well known basis-generating operator is also required. The functions generated for D∞h are then used to construct a ten state, four coordinate model of acetylene. The calculated absorption spectrum is compared to the experimental spectrum to serve as a validation of the approach.
Sharma, Sandeep
2015-01-14
We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C{sub 2} dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10{sup 12} many-body states. While our calculated energy lies within the 0.3 mE{sub h} error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mE{sub h}, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (T{sub e}) of eight lowest lying excited states: a{sup 3}Π{sub u}, b{sup 3}Σ{sub g}{sup −}, A{sup 1}Π{sub u}, c{sup 3}Σ{sub u}{sup +}, B{sup 1}Δ{sub g}, B{sup ′1}Σ{sub g}{sup +}, d{sup 3}Π{sub g}, and C{sup 1}Π{sub g} are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations {sup 1}Σ{sub g}{sup +}, {sup 1}Σ{sub u}{sup +}, {sup 1}Σ{sub g}{sup −}, and {sup 1}Σ{sub u}{sup −}, to an estimated accuracy of 0.1 mE{sub h} of the exact result in this basis.
Non-Abelian {SU}{(3)}_{k} anyons: inversion identities for higher rank face models
NASA Astrophysics Data System (ADS)
Frahm, Holger; Karaiskos, Nikos
2015-12-01
The spectral problem for an integrable system of particles satisfying the fusion rules of {SU}{(3)}k is expressed in terms of exact inversion identities satisfied by the commuting transfer matrices of the integrable fused {A}2(1) interaction round a face model of Jimbo, Miwa and Okado. The identities are proven using local properties of the Boltzmann weights, in particular the Yang-Baxter equation and unitarity. They are closely related to the consistency conditions for the construction of eigenvalues obtained in the separation of variables approach to integrable vertex models.
Solitons and black holes in non-Abelian Einstein-Born-Infeld theory
NASA Astrophysics Data System (ADS)
Dyadichev, V. V.; Gal'tsov, D. V.
2000-08-01
Recently it was shown that the Born-Infeld modification of the quadratic Yang-Mills action gives rise to classical particle-like solutions in the flat space which have a striking similarity with the Bartnik-McKinnon solutions obtained within the gravity coupled Yang-Mills theory. We show that both families of solutions are continuously related within the framework of the Einstein-Born-Infeld theory via interpolating sequences of parameters. We also investigate an internal structure of the associated black holes and find that the Born-Infeld non-linearity changes drastically the black hole interior typical for the usual quadratic Yang-Mills theory. In the latter case a generic solution exhibits violent metric oscillations near the singularity. In the Born-Infeld case the generic interior solution is smooth, the metric tends to the standard Schwarzschild type singularity, and we did not observe internal horizons. Smoothing of the `violent' EYM singularity may be interpreted as a result of non-gravitational quantum effects.
Induced gravity I: real scalar field
NASA Astrophysics Data System (ADS)
Einhorn, Martin B.; Jones, D. R. Timothy
2016-01-01
We show that classically scale invariant gravity coupled to a single scalar field can undergo dimensional transmutation and generate an effective Einstein-Hilbert action for gravity, coupled to a massive dilaton. The same theory has an ultraviolet fixed point for coupling constant ratios such that all couplings are asymptotically free. However the catchment basin of this fixed point does not include regions of coupling constant parameter space compatible with locally stable dimensional transmutation. In a companion paper, we will explore whether this more desirable outcome does obtain in more complicated theories with non-Abelian gauge interactions.
Non-abelian dark matter solutions for Galactic gamma-ray excess and Perseus 3.5 keV X-ray line
Cheung, Kingman; Huang, Wei-Chih; Tsai, Yue-Lin Sming
2015-05-26
We attempt to explain simultaneously the Galactic center gamma-ray excess and the 3.5 keV X-ray line from the Perseus cluster based on a class of non-abelian SU(2) DM models, in which the dark matter and an excited state comprise a “dark” SU(2) doublet. The non-abelian group kinetically mixes with the standard model gauge group via dimensions-5 operators. The dark matter particles annihilate into standard model fermions, followed by fragmentation and bremsstrahlung, and thus producing a continuous spectrum of gamma-rays. On the other hand, the dark matter particles can annihilate into a pair of excited states, each of which decays back into the dark matter particle and an X-ray photon, which has an energy equal to the mass difference between the dark matter and the excited state, which is set to be 3.5 keV. The large hierarchy between the required X-ray and γ-ray annihilation cross-sections can be achieved by a very small kinetic mixing between the SM and dark sector, which effectively suppresses the annihilation into the standard model fermions but not into the excited state.
NASA Astrophysics Data System (ADS)
Aleshin, S. S.; Kazantsev, A. E.; Skoptsov, M. B.; Stepanyantz, K. V.
2016-05-01
We consider a general non-Abelian renormalizable {N} = 1 supersymmetric gauge theory, regularized by higher covariant derivatives without breaking the BRST invariance, and calculate one-loop divergences for a general form of higher derivative regulator and of the gauge fixing term. It is demonstrated that the momentum integrals giving the one-loop β-function are integrals of double total derivatives independently of a particular choice of the higher derivative term. Evaluating them we reproduce the well-known result for the one-loop β-function. Also we find that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in the considered approximation.
Comparison of NDVI fields obtained from different remote sensors
NASA Astrophysics Data System (ADS)
Escribano Rodriguez, Juan; Alonso, Carmelo; Tarquis, Ana Maria; Benito, Rosa Maria; Hernandez Díaz-Ambrona, Carlos
2013-04-01
Satellite image data have become an important source of information for monitoring vegetation and mapping land cover at several scales. Beside this, the distribution and phenology of vegetation is largely associated with climate, terrain characteristics and human activity. Various vegetation indices have been developed for qualitative and quantitative assessment of vegetation using remote spectral measurements. In particular, sensors with spectral bands in the red (RED) and near-infrared (NIR) lend themselves well to vegetation monitoring and based on them [(NIR - RED) / (NIR + RED)] Normalized Difference Vegetation Index (NDVI) has been widespread used. Given that the characteristics of spectral bands in RED and NIR vary distinctly from sensor to sensor, NDVI values based on data from different instruments will not be directly comparable. The spatial resolution also varies significantly between sensors, as well as within a given scene in the case of wide-angle and oblique sensors. As a result, NDVI values will vary according to combinations of the heterogeneity and scale of terrestrial surfaces and pixel footprint sizes. Therefore, the question arises as to the impact of differences in spectral and spatial resolutions on vegetation indices like the NDVI and their interpretation as a drought index. During 2012 three locations (at Salamanca, Granada and Córdoba) were selected and a periodic pasture monitoring and botanic composition were achieved. Daily precipitation, temperature and monthly soil water content were measurement as well as fresh and dry pasture weight. At the same time, remote sensing images were capture by DEIMOS-1 and MODIS of the chosen places. DEIMOS-1 is based on the concept Microsat-100 from Surrey. It is conceived for obtaining Earth images with a good enough resolution to study the terrestrial vegetation cover (20x20 m), although with a great range of visual field (600 km) in order to obtain those images with high temporal resolution and at a
Portable narcotics detector and the results obtained in field tests
NASA Astrophysics Data System (ADS)
Tumer, Tumay O.; Su, Chih-Wu; Kaplan, Christopher R.; Rigdon, Stephen W.
1997-02-01
A compact integrated narcotics detection instrument (CINDI) has been developed at NOVA R&D, Inc. with funding provided by the U.S. Coast Guard. CINDI is designed as a portable sensitive neutron backscatter detector which has excellent penetration for thick and high Z compartment barriers. It also has a highly sensitive detection system for backscattered neutrons and, therefore, uses a very weak californium-252 neutron source. Neutrons backscatter profusely from materials that have a large hydrogen content, such as narcotics. The rate of backscattered neutrons detected is analyzed by a microprocessor and displayed on the control panel. The operator guides the detector along a suspected area and displays in real time the backscattered neutron rate. CINDI is capable of detecting narcotics effectively behind panels made of steel, wood, fiberglass, or even lead-lined materials. This makes it useful for inspecting marine vessels, ship bulkheads, automobiles, structure walls or small sealed containers. The strong response of CINDI to hydrogen-rich materials such as narcotics makes it an effective tool for detecting concealed drugs. Its response has been field tested by NOVA, the U.S. Coast Guard and Brewt Power Systems. The results of the tests show excellent response and specificity to narcotic drugs. Several large shipments of concealed drugs have been discovered during these trials and the results are presented and discussed.
Inflating with large effective fields
Burgess, C.P.; Cicoli, M.; Quevedo, F.; Williams, M. E-mail: mcicoli@ictp.it E-mail: mwilliams@perimeterinsititute.ca
2014-11-01
We re-examine large scalar fields within effective field theory, in particular focussing on the issues raised by their use in inflationary models (as suggested by BICEP2 to obtain primordial tensor modes). We argue that when the large-field and low-energy regimes coincide the scalar dynamics is most effectively described in terms of an asymptotic large-field expansion whose form can be dictated by approximate symmetries, which also help control the size of quantum corrections. We discuss several possible symmetries that can achieve this, including pseudo-Goldstone inflatons characterized by a coset G/H (based on abelian and non-abelian, compact and non-compact symmetries), as well as symmetries that are intrinsically higher dimensional. Besides the usual trigonometric potentials of Natural Inflation we also find in this way simple large-field power laws (like V ∝ φ{sup 2}) and exponential potentials, V(φ) = ∑{sub k}V{sub x}e{sup −kφ/M}. Both of these can describe the data well and give slow-roll inflation for large fields without the need for a precise balancing of terms in the potential. The exponential potentials achieve large r through the limit |η| || ε and so predict r ≅ (8/3)(1-n{sub s}); consequently n{sub s} ≅ 0.96 gives r ≅ 0.11 but not much larger (and so could be ruled out as measurements on r and n{sub s} improve). We examine the naturalness issues for these models and give simple examples where symmetries protect these forms, using both pseudo-Goldstone inflatons (with non-abelian non-compact shift symmetries following familiar techniques from chiral perturbation theory) and extra-dimensional models.
Line of critical points in 2+1 dimensions: quantum critical loop gases and non-Abelian gauge theory.
Freedman, Michael; Nayak, Chetan; Shtengel, Kirill
2005-04-15
In this Letter, we (1) construct a one-parameter family of lattice models of interacting spins; (2) obtain their exact ground states; (3) derive a statistical-mechanical analogy which relates their ground states to O(n) loop gases; (4) show that the models are critical for d
NASA Astrophysics Data System (ADS)
Wang, Juven C.; Wen, Xiao-Gang
2015-01-01
String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group G and a 4-cocycle twist ω4 of G 's cohomology group H4(G ,R /Z ) in three-dimensional space and one-dimensional time (3 +1 D ) . We establish the topological spin and the spin-statistics relation for the closed strings and their multistring braiding statistics. The 3 +1 D twisted gauge theory can be characterized by a representation of a modular transformation group, SL (3 ,Z ) . We express the SL (3 ,Z ) generators Sx y z and Tx y in terms of the gauge group G and the 4-cocycle ω4. As we compactify one of the spatial directions z into a compact circle with a gauge flux b inserted, we can use the generators Sx y and Tx y of an SL (2 ,Z ) subgroup to study the dimensional reduction of the 3D topological order C3 D to a direct sum of degenerate states of 2D topological orders Cb2 D in different flux b sectors: C3 D=⊕bCb2 D . The 2D topological orders Cb2 D are described by 2D gauge theories of the group G twisted by the 3-cocycle ω3 (b ), dimensionally reduced from the 4-cocycle ω4. We show that the SL (2 ,Z ) generators, Sx y and Tx y, fully encode a particular type of three-string braiding statistics with a pattern that is the connected sum of two Hopf links. With certain 4-cocycle twists, we discover that, by threading a third string through two-string unlink into a three-string Hopf-link configuration, Abelian two-string braiding statistics is promoted to non-Abelian three-string braiding statistics.
Quantization of gauge fields, graph polynomials and graph homology
Kreimer, Dirk; Sars, Matthias; Suijlekom, Walter D. van
2013-09-15
We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian gauge theory quantized in a covariant gauge from scalar integrands for connected 3-regular graphs, obtained from the two Symanzik polynomials. The transition to the full gauge theory amplitude is obtained by the use of a third, new, graph polynomial, the corolla polynomial. This implies effectively a covariant quantization without ghosts, where all the relevant signs of the ghost sector are incorporated in a double complex furnished by the corolla polynomial–we call it cycle homology–and by graph homology. -- Highlights: •We derive gauge theory Feynman from scalar field theory with 3-valent vertices. •We clarify the role of graph homology and cycle homology. •We use parametric renormalization and the new corolla polynomial.
Anomaly cancelation in field theory and F-theory on a circle
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Kapfer, Andreas
2016-05-01
We study the manifestation of local gauge anomalies of four- and six-dimensional field theories in the lower-dimensional Kaluza-Klein theory obtained after circle compactification. We identify a convenient set of transformations acting on the whole tower of massless and massive states and investigate their action on the low-energy effective theories in the Coulomb branch. The maps employ higher-dimensional large gauge transformations and precisely yield the anomaly cancelation conditions when acting on the one-loop induced Chern-Simons terms in the three- and five-dimensional effective theory. The arising symmetries are argued to play a key role in the study of the M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact that all fully resolved F-theory geometries inducing multiple Abelian gauge groups or non-Abelian groups admit a certain set of symmetries, we are able to generally show the cancelation of pure Abelian or pure non-Abelian anomalies in these models.
NASA Astrophysics Data System (ADS)
Wei, Qun; Jia, Hongguang; Xuan, Ming
2008-12-01
In order to decrease the aerodynamic drag of supersonic image guide missile and design a non-spherical dome, the outflow field of the missile's dome is simulated using FLUENT. Based on the simulated results, the accurate density field of the outflow field at all kinds of flight conditions is obtained, and then the refractive index field of the outflow field is gotten according to the Gladstone-Dale law. The results show that the shock wave induces the heterogeneity of the refractive index field and the turbulent causes distortion. The outflow field is divided into several zones which are taken as equivalent lenses for aberration analysis.
Spin dynamics under local gauge fields in chiral spin-orbit coupling systems
NASA Astrophysics Data System (ADS)
Tan, S. G.; Jalil, M. B. A.; Fujita, T.; Liu, X. J.
2011-02-01
We present a theoretical description of local spin dynamics in magnetic systems with a chiral spin texture and finite spin-orbit coupling (SOC). Spin precession about the relativistic effective magnetic field in a SOC system gives rise to a non-Abelian SU(2) gauge field reminiscent of the Yang-Mills field. In addition, the adiabatic relaxation of electron spin along the local spin yields an U(1) ⊗ U(1) topological gauge (Berry) field. We derive the corresponding equation of motion i.e. modified Landau-Lifshitz-Gilbert (LLG) equation, for the local spin under the influence of these effects. Focusing on the SU(2) gauge, we obtain the spin torque magnitude, and the amplitude and frequency of spin oscillations in this system. Our theoretical estimates indicate significant spin torque and oscillations in systems with large spin-orbit coupling, which may be utilized in technological applications such as current-induced magnetization-switching and tunable microwave oscillators.
Quantum Fields Obtained from Convoluted Generalized White Noise Never Have Positive Metric
NASA Astrophysics Data System (ADS)
Albeverio, Sergio; Gottschalk, Hanno
2016-05-01
It is proven that the relativistic quantum fields obtained from analytic continuation of convoluted generalized (Lévy type) noise fields have positive metric, if and only if the noise is Gaussian. This follows as an easy observation from a criterion by Baumann, based on the Dell'Antonio-Robinson-Greenberg theorem, for a relativistic quantum field in positive metric to be a free field.
Gauge-covariant decomposition and magnetic monopole for G (2 ) Yang-Mills field
NASA Astrophysics Data System (ADS)
Matsudo, Ryutaro; Kondo, Kei-Ichi
2016-08-01
We provide a gauge-covariant decomposition of the Yang-Mills field with the exceptional gauge group G (2 ), which extends the field decomposition proposed by Cho, Duan-Ge, and Faddeev-Niemi for the S U (N ) Yang-Mills field. As an application of the decomposition, we derive a new expression of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of G (2 ). The resulting new form is used to define gauge-invariant magnetic monopoles in the G (2 ) Yang-Mills theory. Moreover, we obtain the quantization condition to be satisfied by the resulting magnetic charge. The method given in this paper is general enough to be applicable to any semisimple Lie group other than S U (N ) and G (2 ).
Sentandreu, E; Carbonell, L; Rodrigo, D; Carbonell, J V
2006-08-01
Pulsed electric field treatment has been claimed to produce more acceptable chilled citrus juices than those obtained by conventional thermal treatment. The pectin methylesterase activity and the acceptability of nine juices obtained from Clementine mandarins, Valencia oranges, and Ortanique fruits (hybrid of mandarin and orange), untreated, pasteurized (85 degrees C for 10 s), and treated by pulsed electric fields (25 kV/cm for 330 micros), were evaluated. The treatments, selected to reach a similar level of pectin methylesterase inactivation, produced juices that did not differ in acceptability from each other for the three varieties and in all cases were less acceptable than the untreated juice. PMID:16924935
Supersymmetric composite gauge fields with compensators
NASA Astrophysics Data System (ADS)
Nishino, Hitoshi; Rajpoot, Subhash
2016-06-01
We study supersymmetric composite gauge theory, supplemented with compensator mechanism. As our first example, we give the formulation of N = 1 supersymmetric non-Abelian composite gauge theory without the kinetic term of a non-Abelian gauge field. The important ingredient is the Proca-Stueckelberg-type compensator scalar field that makes the gauge-boson field equation non-singular, i.e., the field equation can be solved for the gauge field algebraically as a perturbative expansion. As our second example, we perform the gauging of chiral-symmetry for N = 1 supersymmetry in four dimensions by a composite gauge field. These results provide supporting evidence for the consistency of the mechanism that combines the composite gauge field formulations and compensator formulations, all unified under supersymmetry.
Non-Abellian field dynamics in the early stage of ultrarelativistic nuclear collisions
Rischke, D.H.
1997-09-22
It was argued that the gluon field of a large, ultrarelativistic nucleus can be considered as a classical field for small values of the longitudinal momentum fraction x and on transverse momentum scales {Lambda}{sup 2}{sub QCD} << k{sup 2}{perpendicular} << {mu}{sup 2}, where {mu}{sup 2} is the transverse area density of color charges. The authors estimated {mu} {approx} 0.4 GeV for collisions of Au-nuclei at RHIC energies. Based on this argument, the gluon field produced in a collision of two ultrarelativistic nuclei is computed perturbatively by solving the classical Yang-Mills equations order by order in the strong coupling constant g. It is shown that to first order in g, the spectrum of produced gluons is identical to that obtained in a perturbative quantum calculation of gluon Bremsstrahlung. It is also identical with that of a coherent quantum state generated by independent collisions between the (classical) color charges in the two nuclei. The perturbative solution is unstable under perturbations. The instabilities arise from the non-Abelian terms in the equations of motion for the gluon field, which enter only at higher order in the perturbative solution scheme. The decay rate of the perturbative solution is shown to be of order {mu}. Since the non-Abelian terms describe the self-interaction of the produced gluon field, and since such interactions lead to thermalization, the decay rate provides an estimate for the thermalization time scale of classical color fields in ultrarelativistic nuclear collisions. For Au-nuclei, this time scale is therefore of order 0.5 fm/c, in agreement with results for the kinetic thermalization time scale.
Jalilian-Marian, Jamal; Jeon, Sangyong; Venugopalan, Raju; Wirstam, Jens
2000-08-15
The one loop effective action in quantum field theory can be expressed as a quantum mechanical path integral over world lines, with internal symmetries represented by Grassmanian variables. In this paper, we develop a real time, many body, world line formalism for the one loop effective action. In particular, we study hot QCD and obtain the classical transport equations which, as Litim and Manuel have shown, reduce in the appropriate limit to the non-Abelian Boltzmann-Langevin equation first obtained by Boedeker. In the Vlasov limit, the classical kinetic equations are those that correspond to the hard thermal loop effective action. We also discuss the imaginary time world line formalism for a hot {phi}{sup 4} theory, and elucidate its relation to classical transport theory. (c) 2000 The American Physical Society.
Vázquez-Martínez, Guadalupe; Rodriguez, Mario H; Hernández-Hernández, Fidel; Ibarra, Jorge E
2004-04-01
An efficient strategy, based on a combination of procedures, was developed to obtain axenic cultures from field-collected samples of the cyanobacterium Phormidium animalis. Samples were initially cultured in solid ASN-10 medium, and a crude separation of major contaminants from P. animalis filaments was achieved by washing in a series of centrifugations and resuspensions in liquid medium. Then, manageable filament fragments were obtained by probe sonication. Fragmentation was followed by forceful washing, using vacuum-driven filtration through an 8-microm pore size membrane and an excess of water. Washed fragments were cultured and treated with a sequential exposure to four different antibiotics. Finally, axenic cultures were obtained from serial dilutions of treated fragments. Monitoring under microscope examination and by inoculation in Luria-Bertani (LB) agar plates indicated either axenicity or the degree of contamination throughout the strategy. PMID:15003694
Symmetries and vanishing couplings in string-derived low energy effective field theory
Kobayashi, Tatsuo
2012-07-27
We study 4D low-energy effective field theory, derived from heterotic string theory on the orbifolds. In particular, we study Abelian and non-Abelian discrete symmetries and their anomalies. Furthermore, stringy computations also provide with stringy coupling selection rules.
NASA Astrophysics Data System (ADS)
He, Han; Wang, Huaning; Yan, Yihua
2011-01-01
The Hinode satellite can obtain high-quality photospheric vector magnetograms of solar active regions and the simultaneous coronal loop images in soft X-ray and extreme ultraviolet (EUV) bands. In this paper, we continue the work of He and Wang (2008) and apply the newly developed upward boundary integration computational scheme for the nonlinear force-free field (NLFFF) extrapolation of the coronal magnetic field to the photospheric vector magnetograms acquired by the Spectro-Polarimeter of the Solar Optical Telescope aboard Hinode. Three time series vector magnetograms of the same solar active region, NOAA 10930, are selected for the NLFFF extrapolations, which were observed within the time interval of 26 h during 10-11 December 2006 when the active region crossed the central area of the Sun's disk. Parallel computation of the NLFFF extrapolation code was realized through OpenMP multithreaded, shared memory parallelism and Fortran 95 programming language for the extrapolation calculations. The comparison between the extrapolated field lines and the coronal loop images obtained by the X-Ray Telescope and the EUV Imaging Spectrometer of Hinode shows that, in the central area of the active region, the field line configurations generally agree with the coronal images, and the orientations of the field lines basically coincide with the coronal loop observations for all three successive magnetograms. This result supports the NLFFF model being used for tracing the time series evolution of the 3-D coronal magnetic structures as the responses of the quasi-equilibrium solar atmosphere to the vector magnetic field changes in the photosphere.
A system to obtain radiotracer uptake data simultaneously with NMR spectra in a high field magnet
Buchanan, M.; Marsden, P.K.; Garlick, P.B.; Mielke, C.H.
1996-06-01
Radiotracer techniques and nuclear magnetic resonance (NMR) spectroscopy are two complementary methods that are widely used to investigate cardiac metabolism. The authors have now developed a novel gamma photon detector system that will operate within a wide-bore, 9.4 T magnet. With this detector in position, it is possible to acquire radiotracer uptake data while simultaneously collecting NMR spectra. The advantages of this new system are firstly, that it enables correlations between radiotracer and NMR data to be made on individual rat hearts, and secondly that it allows the number of experiments required to obtain results of statistical significance to be greatly decreased. The extension of the system, to one in which positron emission tomography (PET) and magnetic resonance imaging (MRI) data are acquired simultaneously, clearly has enormous clinical potential. The detector consists of a NaI(Tl) scintillation crystal coupled to a magnetic field-insensitive photomultiplier tube by a 72.5 cm long, acrylic light pipe. This detector configuration satisfies the two, conflicting requirements of the crystal being near the sample, and thus in a high magnetic field, and the PMT being in a low magnetic field and thus far from the sample. In this paper the authors present the technical specifications of their new system together with what they believe are the first examples of simultaneously acquired NMR spectra and {sup 18}F-fluorodeoxyglucose ({sup 18}FDG) uptake data, obtained from isolated, perfused rat hearts.
Nonperturbative construction of massive Yang-Mills fields without the Higgs field
NASA Astrophysics Data System (ADS)
Kondo, Kei-Ichi
2013-01-01
In order to understand the so-called decoupling solution for gluon and ghost propagators in QCD, we give a nonperturbative construction of a massive vector field describing a non-Abelian massive spin-one particle, which has the correct physical degrees of freedom and is invariant under a modified Becchi-Rouet-Stora-Tyutin transformation, in a massive Yang-Mills model without the Higgs field, i.e., the Curci-Ferrari model. The resulting non-Abelian massive vector boson field is written by using a nonlinear but local transformation from the original fields in the Curci-Ferrari model. As an application, we write down a local mass term for the Yang-Mills field and a dimension-two condensate, which are exactly invariant under the modified Becchi-Rouet-Stora-Tyutin transformation, Lorentz transformation, and color rotation.
NASA Astrophysics Data System (ADS)
Markov, Yu. A.; Markova, M. A.
2015-06-01
The problem on mapping between two Lagrangian descriptions (using a commuting c-number spinor ψα or anticommuting pseudovector ξμ and pseudoscalar ξ5 variables) of the spin degrees of freedom of a color spinning massive particle interacting with background non-Abelian gauge field, is considered. A general analysis of the mapping between a pair of Majorana spinors (ψα, θα) (θα is some auxiliary anticommuting spinor) and a real anticommuting tensor aggregate (S, Vμ, T*μν, Aμ, P), is presented. A complete system of bilinear relations between the tensor quantities, is obtained. The analysis we have given is used for the above problem of the equivalence of two different ways of describing the spin degrees of freedom of the relativistic particle. The mapping of the kinetic term (iħ / 2) (θ bar θ) (ψ bar ˙ ψ - ψ bar ψ ˙), the term (1 / e) (θ bar θ)x˙μ (ψ bar γμ ψ) that provides a couple of the spinning variable ψ and the particle velocity x˙μ, and the interaction term ħ (θ bar θ)Qa Fμνa (ψ bar σμν ψ) with an external non-Abelian gauge field, are considered in detail. In the former case a corresponding system of bilinear identities including both the tensor variables and their derivatives (S ˙, V˙μ, ˙ μν *T, A˙μ, P ˙), is defined. A detailed analysis of the local bosonic symmetry of the Lagrangian with the commuting spinor ψα, is carried out. A connection of this symmetry with the local SUSY transformation of the Lagrangian containing anticommuting pseudovector and pseudoscalar variables, is considered. The approach of obtaining a supersymmetric Lagrangian in terms of the even ψα and odd θα spinors, is offered.
Jiménez-Muñoz, Juan C; Sobrino, José A
2006-09-20
Surface emissivities play an important role in thermal remote sensing, since knowledge of them is required to estimate land surface temperature with enough accuracy. They are also important in other environmental or geological studies. We show the results obtained for the emissivity spectra of different natural surfaces (water, green, and senescent vegetation) by applying the temperature and emissivity separation (TES) algorithm to ground-based measurements collected at the field with a multiband thermal radiometer. The results have been tested with data included in spectral libraries, and rms errors lower than 0.01 have been found, except for senescent vegetation. Two methods are also proposed to apply the TES algorithm to measurements achieved in the laboratory: (i) by heating the sample and (ii) using a box with reflective walls. PMID:16946789
Gauge anomalies in an effective field theory
Preskill, J. )
1991-09-01
A four-dimensional gauge theory with anomalous fermion content can be consistently quantized, provided that at least some gauge fields are permitted to have nonvanishing masses. Such a theory is nonrenormalizable; there is a maximal value of the ultraviolet cutoff {Lambda}, beyond which the locality of the theory breaks down. The maximal {Lambda} can be estimated in perturbation theory and has a qualitatively different character in Abelian and non-Abelian anomalous gauge theories.
The efficacy of field techniques for obtaining and storing blood samples from fishes.
Clark, T D; Donaldson, M R; Drenner, S M; Hinch, S G; Patterson, D A; Hills, J; Ives, V; Carter, J J; Cooke, S J; Farrell, A P
2011-11-01
Prompted by the dramatic increase in the use of blood analyses in fisheries research and monitoring, this study investigated the efficacy of common field techniques for sampling and storing blood from fishes. Three questions were addressed: (1) Do blood samples taken via rapid caudal puncture (the 'grab-and-stab' technique) yield similar results for live v. sacrificed groups of fishes? (2) Do rapidly obtained caudal blood samples accurately represent blood properties of fishes prior to capture? (3) Does storage of whole blood in an ice slurry for a working day (8·5 h) modify the properties of the plasma? It was shown that haematocrit, plasma ions, metabolites, stress hormones and sex hormones of caudal blood samples were statistically similar when taken from live v. recently sacrificed groups of adult coho salmon Oncorhynchus kisutch. Moreover, this study confirmed by using paired blood samples from cannulated O. kisutch that blood acquired through the caudal puncture technique (mean ±s.e. 142 ± 26 s after capture) was representative of fish prior to capture. Long-term (8·5 h) cold storage of sockeye salmon Oncorhynchus nerka whole blood caused significant decreases in plasma potassium and chloride, and a significant increase in plasma glucose. Previous research has suggested that these changes largely result from net movements of ions and molecules between the plasma and erythrocytes, movements that can occur within minutes of storage. Thus, blood samples from fishes should be centrifuged as quickly as practicable in the field for separation of plasma and erythrocytes to prevent potentially misleading data. PMID:22026608
Frisch, Priscilla C.; Andersson, B-G; Berdyugin, Andrei; Piirola, Vilppu; Funsten, Herbert O.; Magalhaes, Antonio M.; McComas, David J.; Schwadron, Nathan A.; Slavin, Jonathan D.; Wiktorowicz, Sloane J. E-mail: bgandersson@sofia.usra.ed E-mail: piirola@utu.f E-mail: mario@astro.iag.usp.b E-mail: nschwadron@guero.sr.unh.ed E-mail: sloane@berkeley.ed
2010-12-01
Variations in the spatial configuration of the interstellar magnetic field (ISMF) near the Sun can be constrained by comparing the ISMF direction at the heliosphere found from the Interstellar Boundary Explorer (IBEX) spacecraft observations of a 'Ribbon' of energetic neutral atoms (ENAs), with the ISMF direction derived from optical polarization data for stars within {approx}40 pc. Using interstellar polarization observations toward {approx}30 nearby stars within {approx}90{sup 0} of the heliosphere nose, we find that the best fits to the polarization position angles are obtained for a magnetic pole directed toward ecliptic coordinates of {lambda}, {beta} {approx} 263{sup 0}, 37{sup 0} (or galactic coordinates of l, b {approx} 38{sup 0}, 23{sup 0}), with uncertainties of {+-}35{sup 0} based on the broad minimum of the best fits and the range of data quality. This magnetic pole is 33{sup 0} from the magnetic pole that is defined by the center of the arc of the ENA Ribbon. The IBEX ENA ribbon is seen in sight lines that are perpendicular to the ISMF as it drapes over the heliosphere. The similarity of the polarization and Ribbon directions for the local ISMF suggests that the local field is coherent over scale sizes of tens of parsecs. The ISMF vector direction is nearly perpendicular to the flow of local interstellar material (ISM) through the local standard of rest, supporting a possible local ISM origin related to an evolved expanding magnetized shell. The local ISMF direction is found to have a curious geometry with respect to the cosmic microwave background dipole moment.
Fienen, M.; Hunt, R.; Krabbenhoft, D.; Clemo, T.
2009-01-01
Flow path delineation is a valuable tool for interpreting the subsurface hydrogeochemical environment. Different types of data, such as groundwater flow and transport, inform different aspects of hydrogeologie parameter values (hydraulic conductivity in this case) which, in turn, determine flow paths. This work combines flow and transport information to estimate a unified set of hydrogeologic parameters using the Bayesian geostatistical inverse approach. Parameter flexibility is allowed by using a highly parameterized approach with the level of complexity informed by the data. Despite the effort to adhere to the ideal of minimal a priori structure imposed on the problem, extreme contrasts in parameters can result in the need to censor correlation across hydrostratigraphic bounding surfaces. These partitions segregate parameters into faci??s associations. With an iterative approach in which partitions are based on inspection of initial estimates, flow path interpretation is progressively refined through the inclusion of more types of data. Head observations, stable oxygen isotopes (18O/16O) ratios), and tritium are all used to progressively refine flow path delineation on an isthmus between two lakes in the Trout Lake watershed, northern Wisconsin, United States. Despite allowing significant parameter freedom by estimating many distributed parameter values, a smooth field is obtained. Copyright 2009 by the American Geophysical Union.
NASA Astrophysics Data System (ADS)
Alonso, C.; Benito, R. M.; Tarquis, A. M.
2012-04-01
such complexities from remote sensing images and will applied in this study to see the scaling behavior for each sensor in generalized fractal dimensions. The studied area is located in the provinces of Caceres and Salamanca (east of Iberia Peninsula) with an extension of 32 x 32 km2. The altitude in the area varies from 1,560 to 320 m, comprising natural vegetation in the mountain area (forest and bushes) and agricultural crops in the valleys. Scaling analysis were applied to Landsat-5 and MODIS TERRA to the normalized derived vegetation index (NDVI) on the same region with one day of difference, 13 and 12 of July 2003 respectively. From these images the area of interest was selected obtaining 1024 x 1024 pixels for Landsat image and 128 x 128 pixels for MODIS image. This implies that the resolution for MODIS is 250x250 m. and for Landsat is 30x30 m. From the reflectance data obtained from NIR and RED bands, NDVI was calculated for each image focusing this study on 0.2 to 0.5 ranges of values. Once that both NDVI fields were obtained several fractal dimensions were estimated in each one segmenting the values in 0.20-0.25, 0.25-0.30 and so on to rich 0.45-0.50. In all the scaling analysis the scale size length was expressed in meters, and not in pixels, to make the comparison between both sensors possible. Results are discussed. Acknowledgements This work has been supported by the Spanish MEC under Projects No. AGL2010-21501/AGR, MTM2009-14621 and i-MATH No. CSD2006-00032
Clinical use of diodes and micro-chambers to obtain accurate small field output factor measurements.
Kairn, T; Charles, P H; Cranmer-Sargison, G; Crowe, S B; Langton, C M; Thwaites, D I; Trapp, J V
2015-06-01
There have been substantial advances in small field dosimetry techniques and technologies, over the last decade, which have dramatically improved the achievable accuracy of small field dose measurements. This educational note aims to help radiation oncology medical physicists to apply some of these advances in clinical practice. The evaluation of a set of small field output factors (total scatter factors) is used to exemplify a detailed measurement and simulation procedure and as a basis for discussing the possible effects of simplifying that procedure. Field output factors were measured with an unshielded diode and a micro-ionisation chamber, at the centre of a set of square fields defined by a micro-multileaf collimator. Nominal field sizes investigated ranged from 6 × 6 to 98 × 98 mm(2). Diode measurements in fields smaller than 30 mm across were corrected using response factors calculated using Monte Carlo simulations of the diode geometry and daisy-chained to match micro-chamber measurements at intermediate field sizes. Diode measurements in fields smaller than 15 mm across were repeated twelve times over three separate measurement sessions, to evaluate the reproducibility of the radiation field size and its correspondence with the nominal field size. The five readings that contributed to each measurement on each day varied by up to 0.26 %, for the "very small" fields smaller than 15 mm, and 0.18 % for the fields larger than 15 mm. The diode response factors calculated for the unshielded diode agreed with previously published results, within uncertainties. The measured dimensions of the very small fields differed by up to 0.3 mm, across the different measurement sessions, contributing an uncertainty of up to 1.2 % to the very small field output factors. The overall uncertainties in the field output factors were 1.8 % for the very small fields and 1.1 % for the fields larger than 15 mm across. Recommended steps for acquiring small field output
Realizations of magnetic-monopole gauge fields - Diatoms and spin precession
NASA Technical Reports Server (NTRS)
Moody, J.; Shapere, A.; Wilczek, F.
1986-01-01
It is found that the effective Hamiltonian for nuclear rotation in a diatom is equivalent to that of a charged particle in a background magnetic-monopole field. In certain cases, half-integer orbital angular momentum or non-Abelian fields occur. Furthermore, the effects of magnetic-monopole-like gauge fields can be experimentally observed in spin-resonance experiments with variable magnetic fields.
Lectures on Non-Abelian Bosonization
NASA Astrophysics Data System (ADS)
Tsvelik, A. M.
The following sections are included: * Introduction * Kac-Moody algebra * Conformal embedding. Sugawara Hamiltonian * SU(N)×SU(M) model * From the fermionic to WZNW model * The perturbed SUk(2) WZNW model * Correlation functions and Quasi Long Range order * Generalization from SU(2) to SU(N) * A model with Sp(2N) symmetry * Solution for the special case gcdw = gsc * Attraction in the orbital channel. Competing orders. Emergent integrability. ZN parafermions. * Parafermion zero modes * Conclusions and Acknowledgements * Appendix A. TBA equations for the Sp1(2N) model * Appendix B. Bosonization of of Z4 parafermions * References
The accuracy of far-field noise obtained by the mathematical extrapolation of near-field noise data
NASA Technical Reports Server (NTRS)
Ahtye, W. F.; Karel, S.
1975-01-01
Results are described of an analytical study of the accuracy and limitations of a technique that permits the mathematical extrapolation of near-field noise data to far-field conditions. The effects of the following variables on predictive accuracy of the far-field pressure were examined: (1) number of near-field microphones; (2) length of source distribution; (3) complexity of near-field and far-field distributions; (4) source-to-microphone distance; and (5) uncertainties in microphone data and imprecision in the location of the near-field microphones. It is shown that the most important parameters describing predictive accuracy are the number of microphones, the ratio of source length to acoustic wavelength, (L/wavelength), and the error in location of near-field microphones. If microphone measurement and location errors are not included, then far-field pressures can be accurately predicted up to L/wavelength values of 15 using approximately 50 microphones. For maximum microphone location errors of + or - 1 cm, only an accuracy of + or - 2-1/2 db can be attained with approximately 40 microphones for the highest L/wavelength of 10.
The accuracy of far-field noise obtained by the mathematical extrapolation of near-field noise data
NASA Technical Reports Server (NTRS)
Ahtye, W. F.; Karel, S.
1975-01-01
Results are presented for an analytical study of the accuracy and limitations of a technique that permits the mathematical extrapolation of near-field noise data to far-field conditions. The effects of the following variables on predictive accuracy of the far-field pressure were examined: (1) number of near-field microphones; (2) length of source distribution; (3) complexity of near-field and far-field distributions; (4) source-to-microphone distance; and (5) uncertainties in microphone data and imprecision in the location of the near-field microphones. It is shown that the most important parameters describing predictive accuracy are the number of microphones, the ratio of source length to acoustic wavelength (L/lambda), and the error in location of near-field microphones. For maximum microphone location errors of plus or minus 1 cm, only an accuracy of plus or minus 2.5 dB can be attained with approximately 40 microphones for the highest L/lambda of 10.
NASA Astrophysics Data System (ADS)
Wang, Tong-Tong; Fan, Hong-Yi
2016-12-01
Based on the one- and two-mode combinatorial squeezed state (H.Y. Fan, Phys. Rev. A. 41(3), 1526 (1990))which can enhance squeezing effect, we derive a new optical field by using partial tracing method, we not only obtain its density operator but also deduce its Wigner function by virtue of operators' Weyl ordering property. This new photon field possesses more photon numbers than the corresponding chaotic field, and can be applied to quantum controlling and quantum information processing.
Quality of field pennycress oil obtained by screw pressing and solvent extraction
Technology Transfer Automated Retrieval System (TEKTRAN)
Field pennycress (Thlasphi arvense L., Brassicaceae) is a winter annual that grows widely in temperate North America. Its seeds contain up to 36% oil (dry basis, db) with the major fatty acid being erucic acid (38 %). With an estimated seed production of 1,700 – 2,200 kg/ha, pennycress can be a majo...
Problems on the Analysis Results Obtained from the Geomagnetic Scalar Field
NASA Astrophysics Data System (ADS)
Isezaki, N.; Harada, M.; Sayanagi, K.; Matsuo, J.
2009-12-01
1.The scalar magnetic field TIA (Total Intensity Anomaly) has no physical formula describing the relation between M (Magnetization) and TIA. 2.Then MA could not be analyzed from TIA. 3.Anlyses of M from TIA have been done so far under assumption TIA=PTA (Projected Total Anomay on MF (Main Geomagnetic Field)), however, which caused the analysis error due to ɛT= TIA - PTA. 4.It is impossible to evaluate the error due to ɛT for the already published results so far because there were no PTA observations, but only TIA at present, then ɛT cannot be defined. 5.TA satisfies the Laplace’s equation, and TA can be adusted to the physically realizable data by solving this equation for TA. For the area where there is no bservation TA, we can interpolate them by solving the Dirichlet's problem as the boundary value problem. 6.TA varies its direction from place to place where MF is uniform in the small local area, then the magnetic poential for TA could not be defined in any place. 7.We strongly recommend to carry out the magnetic survey using a three component magnetometer to get TF and TA which have many advantages for magnetic analyses (magnetization, upward continuation etc.) which cannot be done using scalar TIA. 8.It is the case for time dependent TIA which varies with β=ωt (ω:time angular velocity) in Figure 1. Geometrical expression for ɛT. MF, TF and TA are the vectors of the main geomagnetic field, the total geomagnetic field, and the geomagnetic anomaly field respectively. MF, TF and TA are in this plane. MF= , TF= , TA= , PTA= , PTA= TIA= , and ɛT= . , ⊥ , and β=∠BAC, α=∠DBC. TA will rotate around the point B. for estimation of ɛT. If the magnitudes of MF and TA are assumed to be |MF|=50,000 nT and |TA|=1000 nT. Figure 2 shows the relative error (Isezaki etal 2009), defined by ɛT/TIA. For TIA from 1000 nT to -1000 nT. β changes from 0 at TIA=1,000 nT to the maximum ( TA/MF=0.02) where TA is almost perpendicular to MF and TIA 0nT. TF is produced by
GLOBAL TWIST OF SUNSPOT MAGNETIC FIELDS OBTAINED FROM HIGH-RESOLUTION VECTOR MAGNETOGRAMS
Tiwari, Sanjiv Kumar; Venkatakrishnan, P.; Sankarasubramanian, K. E-mail: pvk@prl.res.in
2009-09-10
The presence of fine structures in sunspot vector magnetic fields has been confirmed from Hinode as well as other earlier observations. We studied 43 sunspots based on the data sets taken from ASP/DLSP, Hinode (SOT/SP), and SVM (USO). In this Letter, (1) we introduce the concept of signed shear angle (SSA) for sunspots and establish its importance for non-force-free fields. (2) We find that the sign of global {alpha} (force-free parameter) is well correlated with that of the global SSA and the photospheric chirality of sunspots. (3) Local {alpha} patches of opposite signs are present in the umbra of each sunspot. The amplitude of the spatial variation of local {alpha} in the umbra is typically of the order of the global {alpha} of the sunspot. (4) We find that the local {alpha} is distributed as alternately positive and negative filaments in the penumbra. The amplitude of azimuthal variation of the local {alpha} in the penumbra is approximately an order of magnitude larger than that in the umbra. The contributions of the local positive and negative currents and {alpha} in the penumbra cancel each other giving almost no contribution for their global values for the whole sunspot. (5) Arc-like structures (partial rings) with a sign opposite to that of the dominant sign of {alpha} of the umbral region are seen at the umbral-penumbral boundaries of some sunspots. (6) Most of the sunspots studied belong to the minimum epoch of the 23rd solar cycle and do not follow the so-called hemispheric helicity rule.
Hernandez, P.
1995-02-01
This paper is an expansion of engineering notes prepared in 1961 to address the question of how to wind circular coils so as to obtain the maximum axial field with the minimum volume of conductor. At the time this was a germain question because of the advent of superconducting wires which were in very limited supply, and the rapid push for generation of very high fields, with little concern for uniformity.
Field-Obtained Soil Water Characteristic Curves and Hydraulic Conductivity Functions
NASA Astrophysics Data System (ADS)
Elvis, Ishimwe
A compacted clay liner (test pad) was constructed and instrumented with volumetric water content and soil matric potential sensors to determine soil water characteristic curves (SWCC) and hydraulic conductivity (k) functions. Specifically, the compacted clay liner was subjected to an infiltration cycle during a sealed double ring infiltrometer (SDRI) test followed by a drying cycle. After the drying cycle, Shelby tube samples were collected from the compacted clay liner and flexible wall permeability (FWP) tests were conducted on sub-samples to determine the saturated hydraulic conductivity. Moreover, two computer programs (RETC and UNSAT-H) were utilized to model the SWCCs and k-functions of the soil based on obtained measurements including the volumetric water content, the soil matric potential, and the saturated hudraulic conductivity (ks). Results obtained from the RETC program (s, r, α, n and ks) were ingested into UNSAT-H program to calculate the movement of water (rate and location) through the compacted clay liner. Although a linear wetting front (location of water infiltration as a function of time) is typically utilized for SDRI calculations, the use of a hyperbolic wetting front is recommended as a hyperbolic wetting front was modeled from the testing results. The suggested shape of the wetting front is associated with utilization of the desorption SWCC instead of the sorption SWCC and with relatively high values of ks (average value of 7.2E-7 cm/sec) were measured in the FWP tests while relatively low values of ks (average value of 1.2E-7 cm/sec) were measured in the SDRI test.
NASA Astrophysics Data System (ADS)
Miyazawa, D.; Kim, S. B.; Kitamura, H.; Ishizuka, D.; Hojo, K.
We have been studying the compact magnet for NMR device that consists of a stacked high temperature superconducting (HTS) GdBCO bulk annuli. We can generate the trapped magnetic field over 1.5 T at 77.4 K and 150 ppm/cm3 on inner diameter of 20 mm HTS bulks using field compensation methods. However, it is necessary to enlarge the inner diameter of the HTS bulk magnet because the diameter of commercial NMR probe is larger than 20 mm. In this paper, we studied an optimal shape of the stacked HTS bulk magnet to obtain the enlarged inner diameter using 3-D FEM based analysis. We was able to enlarge the inner diameter of the HTS bulk magnet from 20 mm to 34 mm remaining magnetic field strength of 1.5 T and magnetic field homogeneity of 666 ppm/cm3 by proposed passive field compensation method.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false How do I obtain approval to build pipelines and facilities connecting the well field to utilization facilities not located on Federal lands leased for geothermal resources? 3271.13 Section 3271.13 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF...
Manipulating Majorana zero modes on atomic rings with an external magnetic field
NASA Astrophysics Data System (ADS)
Li, Jian; Neupert, Titus; Bernevig, B. Andrei; Yazdani, Ali
2016-01-01
Non-Abelian quasiparticles have been predicted to exist in a variety of condensed matter systems. Their defining property is that an adiabatic braid between two of them results in a non-trivial change of the quantum state of the system. The simplest non-Abelian quasiparticles--the Majorana bound states--can occur in one-dimensional electronic nano-structures proximity-coupled to a bulk superconductor. Here we propose a set-up, based on chains of magnetic adatoms on the surface of a thin-film superconductor, in which the control over an externally applied magnetic field suffices to create and manipulate Majorana bound states. We consider specifically rings of adatoms and show that they allow for the creation, annihilation, adiabatic motion and braiding of pairs of Majorana bound states by varying the magnitude and orientation of the external magnetic field.
Manipulating Majorana zero modes on atomic rings with an external magnetic field.
Li, Jian; Neupert, Titus; Bernevig, B Andrei; Yazdani, Ali
2016-01-01
Non-Abelian quasiparticles have been predicted to exist in a variety of condensed matter systems. Their defining property is that an adiabatic braid between two of them results in a non-trivial change of the quantum state of the system. The simplest non-Abelian quasiparticles--the Majorana bound states--can occur in one-dimensional electronic nano-structures proximity-coupled to a bulk superconductor. Here we propose a set-up, based on chains of magnetic adatoms on the surface of a thin-film superconductor, in which the control over an externally applied magnetic field suffices to create and manipulate Majorana bound states. We consider specifically rings of adatoms and show that they allow for the creation, annihilation, adiabatic motion and braiding of pairs of Majorana bound states by varying the magnitude and orientation of the external magnetic field. PMID:26791080
Manipulating Majorana zero modes on atomic rings with an external magnetic field
Li, Jian; Neupert, Titus; Bernevig, B. Andrei; Yazdani, Ali
2016-01-01
Non-Abelian quasiparticles have been predicted to exist in a variety of condensed matter systems. Their defining property is that an adiabatic braid between two of them results in a non-trivial change of the quantum state of the system. The simplest non-Abelian quasiparticles—the Majorana bound states—can occur in one-dimensional electronic nano-structures proximity-coupled to a bulk superconductor. Here we propose a set-up, based on chains of magnetic adatoms on the surface of a thin-film superconductor, in which the control over an externally applied magnetic field suffices to create and manipulate Majorana bound states. We consider specifically rings of adatoms and show that they allow for the creation, annihilation, adiabatic motion and braiding of pairs of Majorana bound states by varying the magnitude and orientation of the external magnetic field. PMID:26791080
Azcona, J; Burguete, J
2014-06-01
Purpose: To obtain the pencil beam kernels that characterize a megavoltage photon beam generated in a FFF linac by experimental measurements, and to apply them for dose calculation in modulated fields. Methods: Several Kodak EDR2 radiographic films were irradiated with a 10 MV FFF photon beam from a Varian True Beam (Varian Medical Systems, Palo Alto, CA) linac, at the depths of 5, 10, 15, and 20cm in polystyrene (RW3 water equivalent phantom, PTW Freiburg, Germany). The irradiation field was a 50 mm diameter circular field, collimated with a lead block. Measured dose leads to the kernel characterization, assuming that the energy fluence exiting the linac head and further collimated is originated on a point source. The three-dimensional kernel was obtained by deconvolution at each depth using the Hankel transform. A correction on the low dose part of the kernel was performed to reproduce accurately the experimental output factors. The kernels were used to calculate modulated dose distributions in six modulated fields and compared through the gamma index to their absolute dose measured by film in the RW3 phantom. Results: The resulting kernels properly characterize the global beam penumbra. The output factor-based correction was carried out adding the amount of signal necessary to reproduce the experimental output factor in steps of 2mm, starting at a radius of 4mm. There the kernel signal was in all cases below 10% of its maximum value. With this correction, the number of points that pass the gamma index criteria (3%, 3mm) in the modulated fields for all cases are at least 99.6% of the total number of points. Conclusion: A system for independent dose calculations in modulated fields from FFF beams has been developed. Pencil beam kernels were obtained and their ability to accurately calculate dose in homogeneous media was demonstrated.
NASA Technical Reports Server (NTRS)
Tracy, M. B.; Plentovich, E. B.
1993-01-01
Static and fluctuating pressure distributions were obtained along the floor of a rectangular-box cavity in an experiment performed in the LaRC 0.3-Meter Transonic Cryogenic Tunnel. The cavity studied was 11.25 in. long and 2.50 in. wide with a variable height to obtain length-to-height ratios of 4.4, 6.7, 12.67, and 20.0. The data presented herein were obtained for yaw angles of 0 deg and 15 deg over a Mach number range from 0.2 to 0.9 at a Reynolds number of 30 x 10(exp 6) per ft with a boundary-layer thickness of approximately 0.5 in. The results indicated that open and transitional-open cavity flow supports tone generation at subsonic and transonic speeds at Mach numbers of 0.6 and above. Further, pressure fluctuations associated with acoustic tone generation can be sustained when static pressure distributions indicate that transitional-closed and closed flow fields exist in the cavity. Cavities that support tone generation at 0 deg yaw also supported tone generation at 15 deg yaw when the flow became transitional-closed. For the latter cases, a reduction in tone amplitude was observed. Both static and fluctuating pressure data must be considered when defining cavity flow fields, and the flow models need to be refined to accommodate steady and unsteady flows.
NASA Astrophysics Data System (ADS)
Kirsch, E.; McKenna-Lawlor, S.; Daly, P.; Korth, A.; Neubauer, F. M.; O'Sullivan, D.; Thompson, A.; Wenzel, K.-P.
1989-04-01
Measurements of low and high energy particles, as well as the magnetic field obtained by three different instruments during the Giotto-Halley encounter on March 13, 14, 1986 are used to study the field-line merging process. Spikes of 5-15 min duration in the high energy particle flux which are superimposed on the general intensity time profile are correlated with minima in the low energy particle flux and time periods of oppositely directed magnetic field lines. Strong changes in the pitch angle distribution of energetic ions are observed simultaneously. The observations are considered as evidence for sporadic field line merging processes in the front side of Halley's cometosheath which can accelerate ions and electrons up to E of about 300 keV.
Quantum fields in toroidal topology
Khanna, F.C.; Malbouisson, A.P.C.; Santana, A.E.
2011-10-15
The standard representation of c*-algebra is used to describe fields in compactified space-time dimensions characterized by topologies of the type {Gamma}{sub D}{sup d}=(S{sup 1}){sup d}xM{sup D-d}. The modular operator is generalized to introduce representations of isometry groups. The Poincare symmetry is analyzed and then we construct the modular representation by using linear transformations in the field modes, similar to the Bogoliubov transformation. This provides a mechanism for compactification of the Minkowski space-time, which follows as a generalization of the Fourier integral representation of the propagator at finite temperature. An important result is that the 2x2 representation of the real-time formalism is not needed. The end result on calculating observables is described as a condensate in the ground state. We initially analyze the free Klein-Gordon and Dirac fields, and then formulate non-abelian gauge theories in {Gamma}{sub D}{sup d}. Using the S-matrix, the decay of particles is calculated in order to show the effect of the compactification. - Highlights: > C*-algebra is used to describe fields in compactified space-time dimensions. > The space-time is characterized by toroidal topologies. > Representations of the Poincare group are studied by using the modular operator. > We derive non-abelian gauge theories in compactified regions of space-time. > We show the compactification effect in the decay of particles using the S-matrix.
Spin dynamics under local gauge fields in chiral spin-orbit coupling systems
Tan, S.G.; Jalil, M.B.A.; Fujita, T.; Liu, X.J.
2011-02-15
Research Highlights: > We derive a modified LLG equation in magnetic systems with spin-orbit coupling (SOC). > Our results are applied to magnetic multilayers, and DMS and magnetic Rashba systems. > SOC mediated magnetization switching is predicted in rare earth metals (large SOC). > The magnetization trajectory and frequency can be modulated by applied voltage. > This facilitates potential application as tunable microwave oscillators. - Abstract: We present a theoretical description of local spin dynamics in magnetic systems with a chiral spin texture and finite spin-orbit coupling (SOC). Spin precession about the relativistic effective magnetic field in a SOC system gives rise to a non-Abelian SU(2) gauge field reminiscent of the Yang-Mills field. In addition, the adiabatic relaxation of electron spin along the local spin yields an U(1) x U(1) topological gauge (Berry) field. We derive the corresponding equation of motion i.e. modified Landau-Lifshitz-Gilbert (LLG) equation, for the local spin under the influence of these effects. Focusing on the SU(2) gauge, we obtain the spin torque magnitude, and the amplitude and frequency of spin oscillations in this system. Our theoretical estimates indicate significant spin torque and oscillations in systems with large spin-orbit coupling, which may be utilized in technological applications such as current-induced magnetization-switching and tunable microwave oscillators.
NASA Astrophysics Data System (ADS)
Gunár, S.; Mackay, D. H.
2016-07-01
Aims: We analyze distributions of the magnetic field strength and prominence plasma (temperature, pressure, plasma β, and mass) using the 3D whole-prominence fine structure model. Methods: The model combines a 3D magnetic field configuration of an entire prominence, obtained from non-linear force-free field simulations, with a detailed semi-empirically derived description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along multiple fine structures within the 3D magnetic model. Results: We show that in the modeled prominence, the variations of the magnetic field strength and its orientation are insignificant on scales comparable to the smallest dimensions of the observed prominence fine structures. We also show the ability of the 3D whole-prominence fine structure model to reveal the distribution of the prominence plasma with respect to its temperature within the prominence volume. This provides new insights into the composition of the prominence-corona transition region. We further demonstrate that the values of the plasma β are small throughout the majority of the modeled prominences when realistic photospheric magnetic flux distributions and prominence plasma parameters are assumed. While this is generally true, we also find that in the region with the deepest magnetic dips, the plasma β may increase towards unity. Finally, we show that the mass of the modeled prominence plasma is in good agreement with the mass of observed non-eruptive prominences.
Lajoie, W.N. )
1988-09-01
Significant dose inhomogeneities may exist between the supraclavicular fossa (SCF) and the internal mammary chain (IMC) regions in the irregular L-shaped (hockey stick) field associated with breast cancer treatments. This dose inhomogeneity exists, in part, because of a positive air gap in the SCF and a negative air gap in the IMC locations. Independent of treatment technique, (i.e., whether anterior-posterior (AP) or oblique fields are used), accurate source-to-skin distance (SSD) values for the SCF, IMC, and axilla are necessary when doing an irregular field (Clarkson) dose calculation. However, when an oblique technique is used to treat the hockey stick field, obtaining non-central-axis SSDs is not as straightforward as when an AP technique is employed. The Mayo Off-axis Distance Indicator was constructed to slide into the blocking tray slot of the simulator or treatment machine. This mechanical measuring device provides quick and accurate SSD measurements for non-central-axis points under either AP or, more importantly, oblique treatment conditions.
NASA Astrophysics Data System (ADS)
Tolkova, Elena; Power, William
2011-06-01
To a tsunami wave, bays and harbors represent oscillatory systems, whose resonance (normal) modes determine the response to tsunami and consequently the potential hazard. The direct way to obtain the resonance modes of a water reservoir is by solving the boundary problem for the eigenfunctions of the linearized shallow-water wave equation. The principal difficulty of posing such a problem for a basin coupled to an ocean is specifying the boundary between the two. The technique developed in this work allows the normal modes of a semi-enclosed water body to be obtained without a-priori restricting the resonator area. The technique utilizes complex Empirical Orthogonal Function analysis of modeled tsunami wave fields. On the examples of Poverty Bay in New Zealand and Monterey Bay in California (United States), we demonstrate that the normal modes can be identified and isolated using the EOFs of a data set comprised of the concatenated time-series collected from different tsunami scenarios in a basin. The analysis of the modeled tsunami wave fields for the normal modes can also answer the question of how likely and under which conditions the different modes are exited, due to feasible natural events.
NASA Astrophysics Data System (ADS)
Lu, Cenney W.
Direct measurement of x-ray spectra produced by medical linear accelerators is not possible because of high intensity and energy of the radiation involved. Knowledge of energy spectra are very useful in determination of parameters that convert from ionization chamber measurements to absorbed dose. Many indirect methods for determination of x-ray spectra in therapy beams have been developed. In the present work photon beams generated by a 6-MV Varian 6000 linear accelerator were used to obtain small field (0.5 x 0.5 to 4.0 x 4.0 cm 2 at 0.5 cm increments per side) attenuation values in water for the depths from 5 to 30 cm, at 5 cm increments. Attenuation values lying between those depths were interpolated using the Newton-Coates method and attenuation data of zero-field was obtained by extrapolation. Based on the measured attenuation curves, the relative air kerma and photon energy x-ray spectra were derived for all investigating fields using a user input parameter program and an iterative procedure. The attenuation curves of the radiation fields were calculated using the reconstructed spectrum. They were compared with the measured attenuation data at each iteration step until a satisfactory fit between the measured and calculated attenuation curves was obtained. In order for derived spectra to be of practical use in radiotherapy treatment planning, they must accurate reproduce measured dose distribution data. From the knowledge of the incident beam attenuation and the incident x-ray energy spectrum for the zero-field, the percentage depth dose of the zero-field was calculated at different points along the Central Axis. The percentage depth doses of larger fields were calculated by applying of the Relative Scatter Factor to the percentage depth dose of the zero-field. The agreement was within 1.11% for all fields, ranging from 0.5 x 0.5 to 4.0 x 4.0 cm2 at 0.5 cm increments per side. Further, the reconstructed spectrum for 4 x 4 cm2 field size was used in Monte
Nicola, Wilten; Tripp, Bryan; Scott, Matthew
2016-01-01
A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks. PMID:26973503
NASA Astrophysics Data System (ADS)
Chau, J. L.; Woodman, R. F.; Flores, L. A.
2002-08-01
We present a summary of the statistical characteristics of echoes from ionospheric (E- and F-region) field-aligned irregularities obtained with the Piura VHF radar. This radar is located at ~ 7.0° dip latitude, just outside the equatorial electrojet (EEJ) region. Our results are based on (1) intermittent observations made between 1991 and 1999 just few days a year, and (2) continuous observations made between January 2000 and June 2001. During most of the intermittent observations, simultaneous measurements of EEJ and equatorial spread F (ESF) irregularities were performed with the Jicamarca VHF radar. From the continuous measurements, we have obtained the diurnal and seasonal characteristics of a variety of parameters (percentage of occurrence, signal-to-noise ratio and/or Doppler velocities) from the lower and upper E-region irregularities and also from F-region irregularities over Piura. For example, we have found that (1) the E-region echoes are stronger and occur more frequently during local summer (i.e. between December and March); (2) between May and June, the E-region echoes are weaker and occur less frequently; moreover, during these months, a semidiurnal wave with large amplitudes is observed in the meridional wind (> 100 ms- 1); (3) there is vertical wavelength of about 20 km in the Doppler velocity, particularly after midnight; (4) the lower (upper) E-region Doppler velocities are influenced mainly by meridional winds (equatorial F-region vertical drifts). In addition, we have observed that the seasonal and daily occurrences of Piura F-region irregularities are similar to the occurrence of topside ESF irregularities over Jicamarca. The likelihood of occurrence of F-region irregularities over Piura and, therefore, topside ESF over Jicamarca is greater when there are no E-region irregularities over Piura. On the other hand, there is more probability of observing bottomtype/bottomside ESF irregularities over Jicamarca when E-region irregularities are
Confinement effects from interacting chromo-magnetic and axion fields
NASA Astrophysics Data System (ADS)
Gaete, Patricio; Spallucci, Euro
2006-05-01
We study a non-Abelian gauge theory with a pseudo scalar coupling phiTr(F*μνFμν) in the case where a constant chromo-electric, or chromo-magnetic, strength expectation value is present. We compute the interaction potential within the framework of gauge-invariant, path-dependent, variables formalism. While in the case of a constant chromo-electric field strength expectation value the static potential remains Coulombic, in the case of a constant chromo-magnetic field strength the potential energy is the sum of a Coulombic and a linear potential, leading to the confinement of static charges.