Multipoint correlators in the Abelian sandpile model
NASA Astrophysics Data System (ADS)
Poncelet, Adrien; Ruelle, Philippe
2017-12-01
We revisit the calculation of height correlations in the two-dimensional Abelian sandpile model by taking advantage of a technique developed recently by Kenyon and Wilson. The formalism requires to equip the usual graph Laplacian, ubiquitous in the context of cycle-rooted spanning forests, with a complex connection. In the case at hand, the connection is constant and localized along a semi-infinite defect line (zipper). In the appropriate limit of a trivial connection, it allows one to count spanning forests whose components contain prescribed sites, which are of direct relevance for height correlations in the sandpile model. Using this technique, we first rederive known 1- and 2-site lattice correlators on the plane and upper half-plane, more efficiently than what has been done so far. We also compute explicitly the (new) next-to-leading order in the distances (r-4 for 1-site on the upper half-plane, r-6 for 2-site on the plane). We extend these results by computing new correlators involving one arbitrary height and a few heights 1 on the plane and upper half-plane, for the open and closed boundary conditions. We examine our lattice results from the conformal point of view, and confirm the full consistency with the specific features currently conjectured to be present in the associated logarithmic conformal field theory.
Continuous Abelian Sandpile Model in Two Dimensional Lattice
NASA Astrophysics Data System (ADS)
Azimi-Tafreshi, N.; Lotfi, E.; Moghimi-Araghi, S.
We investigate a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so the general properties of the two models are identical. Yet the new model allows us to investigate some problems such as the effect of very small mass on the height probabilities, different boundary conditions, etc.
Height probabilities in the Abelian sandpile model on the generalized finite Bethe lattice
NASA Astrophysics Data System (ADS)
Chen, Haiyan; Zhang, Fuji
2013-08-01
In this paper, we study the sandpile model on the generalized finite Bethe lattice with a particular boundary condition. Using a combinatorial method, we give the exact expressions for all single-site probabilities and some two-site joint probabilities. As a by-product, we prove that the height probabilities of bulk vertices are all the same for the Bethe lattice with certain given boundary condition, which was found from numerical evidence by Grassberger and Manna ["Some more sandpiles," J. Phys. (France) 51, 1077-1098 (1990)], 10.1051/jphys:0199000510110107700 but without a proof.
A Probabilistic Approach to Zhang's Sandpile Model
NASA Astrophysics Data System (ADS)
Boer, Anne Fey-Den; Meester, Ronald; Quant, Corrie; Redig, Frank
2008-06-01
The current literature on sandpile models mainly deals with the abelian sandpile model (ASM) and its variants. We treat a less known - but equally interesting - model, namely Zhang’s sandpile. This model differs in two aspects from the ASM. First, additions are not discrete, but random amounts with a uniform distribution on an interval [ a, b]. Second, if a site topples - which happens if the amount at that site is larger than a threshold value E c (which is a model parameter), then it divides its entire content in equal amounts among its neighbors. Zhang conjectured that in the infinite volume limit, this model tends to behave like the ASM in the sense that the stationary measure for the system in large volumes tends to be peaked narrowly around a finite set. This belief is supported by simulations, but so far not by analytical investigations. We study the stationary distribution of this model in one dimension, for several values of a and b. When there is only one site, exact computations are possible. Our main result concerns the limit as the number of sites tends to infinity. We find that the stationary distribution, in the case a ≥ E c /2, indeed tends to that of the ASM (up to a scaling factor), in agreement with Zhang’s conjecture. For the case a = 0, b = 1 we provide strong evidence that the stationary expectation tends to sqrt{1/2}.
Absorbing phase transitions in deterministic fixed-energy sandpile models
NASA Astrophysics Data System (ADS)
Park, Su-Chan
2018-03-01
We investigate the origin of the difference, which was noticed by Fey et al. [Phys. Rev. Lett. 104, 145703 (2010), 10.1103/PhysRevLett.104.145703], between the steady state density of an Abelian sandpile model (ASM) and the transition point of its corresponding deterministic fixed-energy sandpile model (DFES). Being deterministic, the configuration space of a DFES can be divided into two disjoint classes such that every configuration in one class should evolve into one of absorbing states, whereas no configurations in the other class can reach an absorbing state. Since the two classes are separated in terms of toppling dynamics, the system can be made to exhibit an absorbing phase transition (APT) at various points that depend on the initial probability distribution of the configurations. Furthermore, we show that in general the transition point also depends on whether an infinite-size limit is taken before or after the infinite-time limit. To demonstrate, we numerically study the two-dimensional DFES with Bak-Tang-Wiesenfeld toppling rule (BTW-FES). We confirm that there are indeed many thresholds. Nonetheless, the critical phenomena at various transition points are found to be universal. We furthermore discuss a microscopic absorbing phase transition, or a so-called spreading dynamics, of the BTW-FES, to find that the phase transition in this setting is related to the dynamical isotropic percolation process rather than self-organized criticality. In particular, we argue that choosing recurrent configurations of the corresponding ASM as an initial configuration does not allow for a nontrivial APT in the DFES.
Absorbing phase transitions in deterministic fixed-energy sandpile models.
Park, Su-Chan
2018-03-01
We investigate the origin of the difference, which was noticed by Fey et al. [Phys. Rev. Lett. 104, 145703 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.145703], between the steady state density of an Abelian sandpile model (ASM) and the transition point of its corresponding deterministic fixed-energy sandpile model (DFES). Being deterministic, the configuration space of a DFES can be divided into two disjoint classes such that every configuration in one class should evolve into one of absorbing states, whereas no configurations in the other class can reach an absorbing state. Since the two classes are separated in terms of toppling dynamics, the system can be made to exhibit an absorbing phase transition (APT) at various points that depend on the initial probability distribution of the configurations. Furthermore, we show that in general the transition point also depends on whether an infinite-size limit is taken before or after the infinite-time limit. To demonstrate, we numerically study the two-dimensional DFES with Bak-Tang-Wiesenfeld toppling rule (BTW-FES). We confirm that there are indeed many thresholds. Nonetheless, the critical phenomena at various transition points are found to be universal. We furthermore discuss a microscopic absorbing phase transition, or a so-called spreading dynamics, of the BTW-FES, to find that the phase transition in this setting is related to the dynamical isotropic percolation process rather than self-organized criticality. In particular, we argue that choosing recurrent configurations of the corresponding ASM as an initial configuration does not allow for a nontrivial APT in the DFES.
NASA Astrophysics Data System (ADS)
Sánchez, R.; Newman, D. E.; Mier, J. A.
2018-05-01
Fractional transport equations are used to build an effective model for transport across the running sandpile cellular automaton [Hwa et al., Phys. Rev. A 45, 7002 (1992), 10.1103/PhysRevA.45.7002]. It is shown that both temporal and spatial fractional derivatives must be considered to properly reproduce the sandpile transport features, which are governed by self-organized criticality, at least over sufficiently long or large scales. In contrast to previous applications of fractional transport equations to other systems, the specifics of sand motion require in this case that the spatial fractional derivatives used for the running sandpile must be of the completely asymmetrical Riesz-Feller type. Appropriate values for the fractional exponents that define these derivatives in the case of the running sandpile are obtained numerically.
Statistical distributions of avalanche size and waiting times in an inter-sandpile cascade model
NASA Astrophysics Data System (ADS)
Batac, Rene; Longjas, Anthony; Monterola, Christopher
2012-02-01
Sandpile-based models have successfully shed light on key features of nonlinear relaxational processes in nature, particularly the occurrence of fat-tailed magnitude distributions and exponential return times, from simple local stress redistributions. In this work, we extend the existing sandpile paradigm into an inter-sandpile cascade, wherein the avalanches emanating from a uniformly-driven sandpile (first layer) is used to trigger the next (second layer), and so on, in a successive fashion. Statistical characterizations reveal that avalanche size distributions evolve from a power-law p(S)≈S-1.3 for the first layer to gamma distributions p(S)≈Sαexp(-S/S0) for layers far away from the uniformly driven sandpile. The resulting avalanche size statistics is found to be associated with the corresponding waiting time distribution, as explained in an accompanying analytic formulation. Interestingly, both the numerical and analytic models show good agreement with actual inventories of non-uniformly driven events in nature.
Multi-field plasma sandpile model in tokamaks and applications
NASA Astrophysics Data System (ADS)
Peng, X. D.; Xu, J. Q.
2016-08-01
A multi-field sandpile model of tokamak plasmas is formulated for the first time to simulate the dynamic process with interaction between avalanche events on the fast/micro time-scale and diffusive transports on the slow/macro time-scale. The main characteristics of the model are that both particle and energy avalanches of sand grains are taken into account simultaneously. New redistribution rules of a sand-relaxing process are defined according to the transport properties of special turbulence which allows the uphill particle transport. Applying the model, we first simulate the steady-state plasma profile self-sustained by drift wave turbulences in the Ohmic discharge of a tokamak. A scaling law as f = a q0 b + c for the relation of both center-density n ( 0 ) and electron (ion) temperatures T e ( 0 ) ( T i ( 0 ) ) with the center-safety-factor q 0 is found. Then interesting work about the nonlocal transport phenomenon observed in tokamak experiments proceeds. It is found that the core electron temperature increases rapidly in response to the edge cold pulse and inversely it decreases in response to the edge heat pulse. The results show that the nonlocal response of core electron temperature depending on the amplitudes of background plasma density and temperature is more remarkable in a range of gas injection rate. Analyses indicate that the avalanche transport caused by plasma drift instabilities with thresholds is a possible physical mechanism for the nonlocal transport in tokamaks. It is believed that the model is capable of being applied to more extensive questions occurring in the transport field.
Directed Abelian algebras and their application to stochastic models.
Alcaraz, F C; Rittenberg, V
2008-10-01
With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma_(tau)=32 ). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma_(tau)=1.780+/-0.005 .
NASA Technical Reports Server (NTRS)
Carlson, J. M.; Chayes, J. T.; Swindle, G. H.; Grannan, E. R.
1990-01-01
The scaling behavior of sandpile models is investigated analytically. First, it is shown that sandpile models contain a set of domain walls, referred to as troughs, which bound regions that can experience avalanches. It is further shown that the dynamics of the troughs is governed by a simple set of rules involving birth, death, and coalescence events. A simple trough model is then introduced, and it is proved that the model has a phase transition with the density of the troughs as an order parameter and that, in the thermodynamic limit, the trough density goes to zero at the transition point. Finally, it is shown that the observed scaling behavior is a consequence of finite-size effects.
NASA Astrophysics Data System (ADS)
Batac, Rene C.; Paguirigan, Antonino A., Jr.; Tarun, Anjali B.; Longjas, Anthony G.
2017-04-01
We propose a cellular automata model for earthquake occurrences patterned after the sandpile model of self-organized criticality (SOC). By incorporating a single parameter describing the probability to target the most susceptible site, the model successfully reproduces the statistical signatures of seismicity. The energy distributions closely follow power-law probability density functions (PDFs) with a scaling exponent of around -1. 6, consistent with the expectations of the Gutenberg-Richter (GR) law, for a wide range of the targeted triggering probability values. Additionally, for targeted triggering probabilities within the range 0.004-0.007, we observe spatiotemporal distributions that show bimodal behavior, which is not observed previously for the original sandpile. For this critical range of values for the probability, model statistics show remarkable comparison with long-period empirical data from earthquakes from different seismogenic regions. The proposed model has key advantages, the foremost of which is the fact that it simultaneously captures the energy, space, and time statistics of earthquakes by just introducing a single parameter, while introducing minimal parameters in the simple rules of the sandpile. We believe that the critical targeting probability parameterizes the memory that is inherently present in earthquake-generating regions.
On whole Abelian model dynamics
Chauca, J.; Doria, R.; Aprendanet, Petropolis, 25600
2012-09-24
Physics challenge is to determine the objects dynamics. However, there are two ways for deciphering the part. The first one is to search for the ultimate constituents; the second one is to understand its behaviour in whole terms. Therefore, the parts can be defined either from elementary constituents or as whole functions. Historically, science has been moving through the first aspect, however, quarks confinement and complexity are interrupting this usual approach. These relevant facts are supporting for a systemic vision be introduced. Our effort here is to study on the whole meaning through gauge theory. Consider a systemic dynamics orientedmore » through the U(1) - systemic gauge parameter which function is to collect a fields set {l_brace}A{sub {mu}I}{r_brace}. Derive the corresponding whole gauge invariant Lagrangian, equations of motion, Bianchi identities, Noether relationships, charges and Ward-Takahashi equations. Whole Lorentz force and BRST symmetry are also studied. These expressions bring new interpretations further than the usual abelian model. They are generating a systemic system governed by 2N+ 10 classical equations plus Ward-Takahashi identities. A whole dynamics based on the notions of directive and circumstance is producing a set determinism where the parts dynamics are inserted in the whole evolution. A dynamics based on state, collective and individual equations with a systemic interdependence.« less
Saeedi, Alireza; Jannesari, Mostafa; Gharibzadeh, Shahriar; Bakouie, Fatemeh
2018-04-01
Self-organized criticality (SOC) and stochastic oscillations (SOs) are two theoretically contradictory phenomena that are suggested to coexist in the brain. Recently it has been shown that an accumulation-release process like sandpile dynamics can generate SOC and SOs simultaneously. We considered the effect of the network structure on this coexistence and showed that the sandpile dynamics on a small-world network can produce two power law regimes along with two groups of SOs-two peaks in the power spectrum of the generated signal simultaneously. We also showed that external stimuli in the sandpile dynamics do not affect the coexistence of SOC and SOs but increase the frequency of SOs, which is consistent with our knowledge of the brain.
Qi, Junjian; Pfenninger, Stefan
In this paper, we propose a strategy to control the self-organizing dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model on complex networks by allowing some degree of failure tolerance for the nodes and introducing additional active dissipation while taking the risk of possible node damage. We show that the probability for large cascades significantly increases or decreases respectively when the risk for node damage outweighs the active dissipation and when the active dissipation outweighs the risk for node damage. By considering the potential additional risk from node damage, a non-trivial optimal active dissipation control strategy which minimizes the total cost inmore » the system can be obtained. Under some conditions the introduced control strategy can decrease the total cost in the system compared to the uncontrolled model. Moreover, when the probability of damaging a node experiencing failure tolerance is greater than the critical value, then no matter how successful the active dissipation control is, the total cost of the system will have to increase. This critical damage probability can be used as an indicator of the robustness of a network or system. Copyright (C) EPLA, 2015« less
Feynman rules for a whole Abelian model
Chauca, J.; Doria, R.; Soares, W.
2012-09-24
Feynman rules for an abelian extension of gauge theories are discussed and explicitly derived. Vertices with three and four abelian gauge bosons are obtained. A discussion on an eventual structure for the photon is presented.
A sandpile model of grain blocking and consequences for sediment dynamics in step-pool streams
NASA Astrophysics Data System (ADS)
Molnar, P.
2012-04-01
Coarse grains (cobbles to boulders) are set in motion in steep mountain streams by floods with sufficient energy to erode the particles locally and transport them downstream. During transport, grains are often blocked and form width-spannings structures called steps, separated by pools. The step-pool system is a transient, self-organizing and self-sustaining structure. The temporary storage of sediment in steps and the release of that sediment in avalanche-like pulses when steps collapse, leads to a complex nonlinear threshold-driven dynamics in sediment transport which has been observed in laboratory experiments (e.g., Zimmermann et al., 2010) and in the field (e.g., Turowski et al., 2011). The basic question in this paper is if the emergent statistical properties of sediment transport in step-pool systems may be linked to the transient state of the bed, i.e. sediment storage and morphology, and to the dynamics in sediment input. The hypothesis is that this state, in which sediment transporting events due to the collapse and rebuilding of steps of all sizes occur, is analogous to a critical state in self-organized open dissipative dynamical systems (Bak et al., 1988). To exlore the process of self-organization, a cellular automaton sandpile model is used to simulate the processes of grain blocking and hydraulically-driven step collapse in a 1-d channel. Particles are injected at the top of the channel and are allowed to travel downstream based on various local threshold rules, with the travel distance drawn from a chosen probability distribution. In sandpile modelling this is a simple 1-d limited non-local model, however it has been shown to have nontrivial dynamical behaviour (Kadanoff et al., 1989), and it captures the essence of stochastic sediment transport in step-pool systems. The numerical simulations are used to illustrate the differences between input and output sediment transport rates, mainly focussing on the magnification of intermittency and
On spectroscopy for a whole Abelian model
NASA Astrophysics Data System (ADS)
Chauca, J.; Doria, R.
2012-10-01
Postulated on the whole meaning a whole abelian gauge symmetry is being introduced. Various physical areas as complexity, statistical mechanics, quantum mechanics are partially supporting this approach where the whole is at origin. However, the reductionist crisis given by quark confinement definitely sustains this insight. It says that fundamental parts can not be seen isolatedely. Consequently, there is an experimental situation where the parts should be substituted by something more. This makes us to look for writing the wholeness principle under gauge theory. For this, one reinterprets the gauge parameter where instead of compensating fields it is organizing a systemic gauge symmetry. Now, it introduces a fields set {AμI} rotating under a common gauge symmetry. Thus, given a fields collection {AμI} as origin, the effort at this work is to investigate on its spectroscopy. Analyze for the abelian case the correspondent involved quanta. Understand that for a whole model diversity replaces elementarity. Derive the associated quantum numbers as spin, mass, charge, discrete symmetries in terms of such systemic symmetry. Observe how the particles diversity is manifested in terms of wholeness.
On spectroscopy for a whole Abelian model
Chauca, J.; Doria, R.; Aprendanet, Petropolis, 25600
Postulated on the whole meaning a whole abelian gauge symmetry is being introduced. Various physical areas as complexity, statistical mechanics, quantum mechanics are partially supporting this approach where the whole is at origin. However, the reductionist crisis given by quark confinement definitely sustains this insight. It says that fundamental parts can not be seen isolatedely. Consequently, there is an experimental situation where the parts should be substituted by something more. This makes us to look for writing the wholeness principle under gauge theory. For this, one reinterprets the gauge parameter where instead of compensating fields it is organizing a systemicmore » gauge symmetry. Now, it introduces a fields set {l_brace}A{sub {mu}I}{r_brace} rotating under a common gauge symmetry. Thus, given a fields collection {l_brace}A{sub {mu}I}{r_brace} as origin, the effort at this work is to investigate on its spectroscopy. Analyze for the abelian case the correspondent involved quanta. Understand that for a whole model diversity replaces elementarity. Derive the associated quantum numbers as spin, mass, charge, discrete symmetries in terms of such systemic symmetry. Observe how the particles diversity is manifested in terms of wholeness.« less
Lattice spin models for non-Abelian chiral spin liquids
Lecheminant, P.; Tsvelik, A. M.
2017-04-26
Here, we suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids—spin analogs of fractional non-Abelian quantum Hall states—with gapped bulk and gapless chiral edge excitations described by the SU(2) n Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of generalized spin-n/2 ladders with multi-spin-exchange interactions which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2) n gapless edge excitations.
Non Abelian T-duality in Gauged Linear Sigma Models
Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando
Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM’s as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they dependmore » in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.« less
Non Abelian T-duality in Gauged Linear Sigma Models
Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando; ...
2018-04-01
Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM’s as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they dependmore » in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.« less
Non Abelian T-duality in Gauged Linear Sigma Models
NASA Astrophysics Data System (ADS)
Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando; Santos-Silva, Roberto
2018-04-01
Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM's as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.
Model of chiral spin liquids with Abelian and non-Abelian topological phases
NASA Astrophysics Data System (ADS)
Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio; Tsvelik, A. M.
2017-12-01
We present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, the Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.
Stability of infinite derivative Abelian Higgs models
NASA Astrophysics Data System (ADS)
Ghoshal, Anish; Mazumdar, Anupam; Okada, Nobuchika; Villalba, Desmond
2018-04-01
Motivated by the stringy effects by modifying the local kinetic term of an Abelian Higgs field by the Gaussian kinetic term, we show that the Higgs field does not possess any instability; the Yukawa coupling between the scalar and the fermion, the gauge coupling, and the self interaction of the Higgs yields exponentially suppressed running at high energies, showing that such class of theory never suffers from vacuum instability. We briefly discuss its implications for the early Universe cosmology.
Model of chiral spin liquids with Abelian and non-Abelian topological phases
Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio
In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less
Model of chiral spin liquids with Abelian and non-Abelian topological phases
Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio; ...
2017-12-15
In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less
Gauge invariance for a whole Abelian model
Chauca, J.; Doria, R.; Soares, W.
Light invariance is a fundamental principle for physics be done. It generates Maxwell equations, relativity, Lorentz group. However there is still space for a fourth picture be developed which is to include fields with same Lorentz nature. It brings a new room for field theory. It says that light invariance does not work just to connect space and time but it also associates different fields with same nature. Thus for the ((1/2),(1/2)) representation there is a fields family {l_brace}A{sub {mu}I}{r_brace} to be studied. This means that given such fields association one should derive its corresponding gauge theory. This is themore » effort at this work. Show that there is a whole gauge theory to cover these fields relationships. Considering the abelian case, prove its gauge invariance. It yields the kinetic, massive, trilinear and quadrilinear gauge invariant terms.« less
Martin, Elliot; Shreim, Amer; Paczuski, Maya
2010-01-01
We define an activity-dependent branching ratio that allows comparison of different time series X(t). The branching ratio b(x) is defined as b(x)=E[xi(x)/x]. The random variable xi(x) is the value of the next signal given that the previous one is equal to x, so xi(x)=[X(t+1) | X(t)=x]. If b(x)>1, the process is on average supercritical when the signal is equal to x, while if b(x)<1, it is subcritical. For stock prices we find b(x)=1 within statistical uncertainty, for all x, consistent with an "efficient market hypothesis." For stock volumes, solar x-ray flux intensities, and the Bak-Tang-Wiesenfeld (BTW) sandpile model, b(x) is supercritical for small values of activity and subcritical for the largest ones, indicating a tendency to return to a typical value. For stock volumes this tendency has an approximate power-law behavior. For solar x-ray flux and the BTW model, there is a broad regime of activity where b(x) approximately equal 1, which we interpret as an indicator of critical behavior. This is true despite different underlying probability distributions for X(t) and for xi(x). For the BTW model the distribution of xi(x) is Gaussian, for x sufficiently larger than 1, and its variance grows linearly with x. Hence, the activity in the BTW model obeys a central limit theorem when sampling over past histories. The broad region of activity where b(x) is close to one disappears once bulk dissipation is introduced in the BTW model-supporting our hypothesis that it is an indicator of criticality.
NASA Astrophysics Data System (ADS)
Martin, Elliot; Shreim, Amer; Paczuski, Maya
2010-01-01
We define an activity-dependent branching ratio that allows comparison of different time series Xt . The branching ratio bx is defined as bx=E[ξx/x] . The random variable ξx is the value of the next signal given that the previous one is equal to x , so ξx={Xt+1∣Xt=x} . If bx>1 , the process is on average supercritical when the signal is equal to x , while if bx<1 , it is subcritical. For stock prices we find bx=1 within statistical uncertainty, for all x , consistent with an “efficient market hypothesis.” For stock volumes, solar x-ray flux intensities, and the Bak-Tang-Wiesenfeld (BTW) sandpile model, bx is supercritical for small values of activity and subcritical for the largest ones, indicating a tendency to return to a typical value. For stock volumes this tendency has an approximate power-law behavior. For solar x-ray flux and the BTW model, there is a broad regime of activity where bx≃1 , which we interpret as an indicator of critical behavior. This is true despite different underlying probability distributions for Xt and for ξx . For the BTW model the distribution of ξx is Gaussian, for x sufficiently larger than 1, and its variance grows linearly with x . Hence, the activity in the BTW model obeys a central limit theorem when sampling over past histories. The broad region of activity where bx is close to one disappears once bulk dissipation is introduced in the BTW model—supporting our hypothesis that it is an indicator of criticality.
The Abelian Higgs model on Optical Lattice?
NASA Astrophysics Data System (ADS)
Meurice, Yannick; Tsai, Shan-Wen; Bazavov, Alexei; Zhang, Jin
2015-03-01
We study the Lattice Gauge Theory of the U(1)-Higgs model in 1+1 dimensions in the strongly coupled regime. We discuss the plaquette corrections to the effective theory where link variables are integrated out. We discuss matching with the second-order perturbation theory effective Hamiltonian for various Bose-Hubbard models. This correspondence can be exploited for building a lattice gauge theory simulator on optical lattices. We propose to implement the quantum rotors which appear in the Hamiltonian formulation using Bose mixtures or p-orbitals. Recent progress on magnetic effects in 2+1 dimensions will be discussed. Supported by the Army Research Office of the Department of Defense under Award Number W911NF-13-1-0119.
On discrete symmetries for a whole Abelian model
Chauca, J.; Doria, R.; Aprendanet, Petropolis, 25600
Considering the whole concept applied to gauge theory a nonlinear abelian model is derived. A next step is to understand on the model properties. At this work, it will be devoted to discrete symmetries. For this, we will work based in two fields reference systems. This whole gauge symmetry allows to be analyzed through different sets which are the constructor basis {l_brace}D{sub {mu}},X{sup i}{sub {mu}}{r_brace} and the physical basis {l_brace}G{sub {mu}I}{r_brace}. Taking as fields reference system the diagonalized spin-1 sector, P, C, T and PCT symmetries are analyzed. They show that under this systemic model there are conservation laws drivenmore » for the parts and for the whole. It develops the meaning of whole-parity, field-parity and so on. However it is the whole symmetry that rules. This means that usually forbidden particles as pseudovector photons can be introduced through such whole abelian system. As result, one notices that the fields whole {l_brace}G{sub {mu}I}{r_brace} manifest a quanta diversity. It involves particles with different spins, masses and discrete quantum numbers under a same gauge symmetry. It says that without violating PCT symmetry different possibilities on discrete symmetries can be accommodated.« less
NASA Astrophysics Data System (ADS)
Kwon, Sungchul; Kim, Jin Min
2015-01-01
For a fixed-energy (FE) Manna sandpile model in one dimension, we investigate the effects of random initial conditions on the dynamical scaling behavior of an order parameter. In the FE Manna model, the density ρ of total particles is conserved, and an absorbing phase transition occurs at ρc as ρ varies. In this work, we show that, for a given ρ , random initial distributions of particles lead to the domain structure in which domains with particle densities higher and lower than ρc alternate with each other. In the domain structure, the dominant length scale is the average domain length, which increases via the coalescence of adjacent domains. At ρc, the domain structure slows down the decay of an order parameter and also causes anomalous finite-size effects, i.e., power-law decay followed by an exponential one before the quasisteady state. As a result, the interplay of particle conservation and random initial conditions causes the domain structure, which is the origin of the anomalous dynamical scaling behaviors for random initial conditions.
On non-abelian T-duality and deformations of supercoset string sigma-models
NASA Astrophysics Data System (ADS)
Borsato, Riccardo; Wulff, Linus
2017-10-01
We elaborate on the class of deformed T-dual (DTD) models obtained by first adding a topological term to the action of a supercoset sigma model and then performing (non-abelian) T-duality on a subalgebra \\tilde{g} of the superisometry algebra. These models inherit the classical integrability of the parent one, and they include as special cases the so-called homogeneous Yang-Baxter sigma models as well as their non-abelian T-duals. Many properties of DTD models have simple algebraic interpretations. For example we show that their (non-abelian) T-duals — including certain deformations — are again in the same class, where \\tilde{g} gets enlarged or shrinks by adding or removing generators corresponding to the dualised isometries. Moreover, we show that Weyl invariance of these models is equivalent to \\tilde{g} being unimodular; when this property is not satisfied one can always remove one generator to obtain a unimodular \\tilde{g} , which is equivalent to (formal) T-duality. We also work out the target space superfields and, as a by-product, we prove the conjectured transformation law for Ramond-Ramond (RR) fields under bosonic non-abelian T-duality of supercosets, generalising it to cases involving also fermionic T-dualities.
LETTER TO THE EDITOR: Bicomplexes and conservation laws in non-Abelian Toda models
NASA Astrophysics Data System (ADS)
Gueuvoghlanian, E. P.
2001-08-01
A bicomplex structure is associated with the Leznov-Saveliev equation of integrable models. The linear problem associated with the zero-curvature condition is derived in terms of the bicomplex linear equation. The explicit example of a non-Abelian conformal affine Toda model is discussed in detail and its conservation laws are derived from the zero-curvature representation of its equation of motion.
Haag duality for Kitaev’s quantum double model for abelian groups
NASA Astrophysics Data System (ADS)
Fiedler, Leander; Naaijkens, Pieter
2015-11-01
We prove Haag duality for cone-like regions in the ground state representation corresponding to the translational invariant ground state of Kitaev’s quantum double model for finite abelian groups. This property says that if an observable commutes with all observables localized outside the cone region, it actually is an element of the von Neumann algebra generated by the local observables inside the cone. This strengthens locality, which says that observables localized in disjoint regions commute. As an application, we consider the superselection structure of the quantum double model for abelian groups on an infinite lattice in the spirit of the Doplicher-Haag-Roberts program in algebraic quantum field theory. We find that, as is the case for the toric code model on an infinite lattice, the superselection structure is given by the category of irreducible representations of the quantum double.
Non-Abelian sigma models from Yang-Mills theory compactified on a circle
NASA Astrophysics Data System (ADS)
Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.
2018-06-01
We consider SU(N) Yang-Mills theory on R 2 , 1 ×S1, where S1 is a spatial circle. In the infrared limit of a small-circle radius the Yang-Mills action reduces to the action of a sigma model on R 2 , 1 whose target space is a 2 (N - 1)-dimensional torus modulo the Weyl-group action. We argue that there is freedom in the choice of the framing of the gauge bundles, which leads to more general options. In particular, we show that this low-energy limit can give rise to a target space SU (N) ×SU (N) /ZN. The latter is the direct product of SU(N) and its Langlands dual SU (N) /ZN, and it contains the above-mentioned torus as its maximal Abelian subgroup. An analogous result is obtained for any non-Abelian gauge group.
Non-Abelian cosmic string in the Starobinsky model of gravity
NASA Astrophysics Data System (ADS)
Morais Graça, J. P.; de Pádua Santos, A.; Bezerra de Mello, Eugênio R.; Bezerra, V. B.
In this paper, we analyze numerically the behavior of the solutions corresponding to a non-Abelian cosmic string in the framework of the Starobinsky model, i.e. where f(R) = R + ζR2. We perform the calculations for both an asymptotically flat and asymptotically (anti)-de Sitter spacetimes. We found that the angular deficit generated by the string decreases as the parameter ζ increases, in the case of a null cosmological constant. For a positive cosmological constant, we found that the cosmic horizon is affected in a nontrivial way by the parameter ζ.
Mohammed, Asadig; Murugan, Jeff; Nastase, Horatiu
2012-11-02
We present an embedding of the three-dimensional relativistic Landau-Ginzburg model for condensed matter systems in an N = 6, U(N) × U(N) Chern-Simons-matter theory [the Aharony-Bergman-Jafferis-Maldacena model] by consistently truncating the latter to an Abelian effective field theory encoding the collective dynamics of O(N) of the O(N(2)) modes. In fact, depending on the vacuum expectation value on one of the Aharony-Bergman-Jafferis-Maldacena scalars, a mass deformation parameter μ and the Chern-Simons level number k, our Abelianization prescription allows us to interpolate between the Abelian Higgs model with its usual multivortex solutions and a Ø(4) theory. We sketch a simple condensed matter model that reproduces all the salient features of the Abelianization. In this context, the Abelianization can be interpreted as giving a dimensional reduction from four dimensions.
Signatures of non-Abelian anyons in the thermodynamics of an interacting fermion model
NASA Astrophysics Data System (ADS)
Borcherding, Daniel; Frahm, Holger
2018-05-01
The contribution of anyonic degrees of freedom emerging in the non-Abelian spin sector of a one-dimensional system of interacting fermions carrying both spin and SU(N f ) orbital degrees of freedom to the thermodynamic properties of the latter is studied based on the exact solution of the model. For sufficiently small temperatures and magnetic fields the anyons appear as zero energy modes localized at the massive kink excitations (Tsvelik 2014 Phys. Rev. Lett. 113 066401). From their quantum dimension they are identified as spin- anyons. The density of kinks (and anyons) can be controlled by an external magnetic field leading to the formation of a collective state of these anyons described by a parafermion conformal field theory for large fields. Based on the numerical analysis of the thermodynamic Bethe ansatz equations we propose a phase diagram for the anyonic modes.
A simple model for the evolution of a non-Abelian cosmic string network
Cella, G.; Pieroni, M., E-mail: giancarlo.cella@pi.infn.it, E-mail: mauro.pieroni@apc.univ-paris7.fr
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 argumentmore » to justify the lack of scaling for the residual cases.« less
NASA Astrophysics Data System (ADS)
Adshead, Peter; Giblin, John T.; Weiner, Zachary J.
2017-12-01
We study preheating in models where a scalar inflaton is directly coupled to a non-Abelian S U (2 ) gauge field. In particular, we examine m2ϕ2 inflation with a conformal, dilatonlike coupling to the non-Abelian sector. We describe a numerical scheme that combines lattice gauge theory with standard finite difference methods applied to the scalar field. We show that a significant tachyonic instability allows for efficient preheating, which is parametrically suppressed by increasing the non-Abelian self-coupling. Additionally, we comment on the technical implementation of the evolution scheme and setting initial conditions.
NASA Astrophysics Data System (ADS)
Bevis, Neil; Hindmarsh, Mark; Kunz, Martin; Urrestilla, Jon
2007-03-01
We present the first field-theoretic calculations of the contribution made by cosmic strings to the temperature power spectrum of the cosmic microwave background (CMB). Unlike previous work, in which strings were modeled as idealized one-dimensional objects, we evolve the simplest example of an underlying field theory containing local U(1) strings, the Abelian Higgs model. Limitations imposed by finite computational volumes are overcome using the scaling property of string networks and a further extrapolation related to the lessening of the string width in comoving coordinates. The strings and their decay products, which are automatically included in the field theory approach, source metric perturbations via their energy-momentum tensor, the unequal-time correlation functions of which are used as input into the CMB calculation phase. These calculations involve the use of a modified version of CMBEASY, with results provided over the full range of relevant scales. We find that the string tension μ required to normalize to the WMAP 3-year data at multipole ℓ=10 is Gμ=[2.04±0.06(stat.)±0.12(sys.)]×10-6, where we have quoted statistical and systematic errors separately, and G is Newton’s constant. This is a factor 2 3 higher than values in current circulation.
Abelian F-theory models with charge-3 and charge-4 matter
NASA Astrophysics Data System (ADS)
Raghuram, Nikhil
2018-05-01
This paper analyzes U(1) F-theory models admitting matter with charges q = 3 and 4. First, we systematically derive a q = 3 construction that generalizes the previous q = 3 examples. We argue that U(1) symmetries can be tuned through a procedure reminiscent of the SU( N ) and Sp( N ) tuning process. For models with q = 3 matter, the components of the generating section vanish to orders higher than 1 at the charge-3 matter loci. As a result, the Weierstrass models can contain non-UFD structure and thereby deviate from the standard Morrison-Park form. Techniques used to tune SU( N ) models on singular divisors allow us to determine the non-UFD structures and derive the q = 3 tuning from scratch. We also obtain a class of a q=4 models by deforming a prior U(1) × U(1) construction. To the author's knowledge, this is the first published F-theory example with charge-4 matter. Finally, we discuss some conjectures regarding models with charges larger than 4.
Inert two-Higgs-doublet model strongly coupled to a non-Abelian vector resonance
NASA Astrophysics Data System (ADS)
Rojas-Abatte, Felipe; Mora, Maria Luisa; Urbina, Jose; Zerwekh, Alfonso R.
2017-11-01
We study the possibility of a dark matter candidate having its origin in an extended Higgs sector which, at least partially, is related to a new strongly interacting sector. More concretely, we consider an i2HDM (i.e., a Type-I two Higgs doublet model supplemented with a Z2 under which the nonstandard scalar doublet is odd) based on the gauge group S U (2 )1×S U (2 )2×U (1 )Y . We assume that one of the scalar doublets and the standard fermion transform nontrivially under S U (2 )1 while the second doublet transforms under S U (2 )2. Our main hypothesis is that standard sector is weakly coupled while the gauge interactions associated to the second group is characterized by a large coupling constant. We explore the consequences of this construction for the phenomenology of the dark matter candidate and we show that the presence of the new vector resonance reduces the relic density saturation region, compared to the usual i2DHM, in the high dark matter mass range. In the collider side, we argue that the mono-Z production is the channel which offers the best chances to manifest the presence of the new vector field. We study the departures from the usual i2HDM predictions and show that the discovery of the heavy vector at the LHC is challenging even in the mono-Z channel since the typical cross sections are of the order of 10-2 fb .
NASA Astrophysics Data System (ADS)
Gattringer, Christof; Göschl, Daniel; Marchis, Carlotta
2018-03-01
We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.
NASA Astrophysics Data System (ADS)
Tallarita, Gianni; Peterson, Adam
2018-04-01
We perform a numerical study of the phase diagram of the model proposed in [M. Shifman, Phys. Rev. D 87, 025025 (2013)., 10.1103/PhysRevD.87.025025], which is a simple model containing non-Abelian vortices. As per the case of Abrikosov vortices, we map out a region of parameter space in which the system prefers the formation of vortices in ordered lattice structures. These are generalizations of Abrikosov vortex lattices with extra orientational moduli in the vortex cores. At sufficiently large lattice spacing the low energy theory is described by a sum of C P (1 ) theories, each located on a vortex site. As the lattice spacing becomes smaller, when the self-interaction of the orientational field becomes relevant, only an overall rotation in internal space survives.
NASA Astrophysics Data System (ADS)
Cheraghalizadeh, J.; Najafi, M. N.; Dashti-Naserabadi, H.; Mohammadzadeh, H.
2017-11-01
The self-organized criticality on the random fractal networks has many motivations, like the movement pattern of fluid in the porous media. In addition to the randomness, introducing correlation between the neighboring portions of the porous media has some nontrivial effects. In this paper, we consider the Ising-like interactions between the active sites as the simplest method to bring correlations in the porous media, and we investigate the statistics of the BTW model in it. These correlations are controlled by the artificial "temperature" T and the sign of the Ising coupling. Based on our numerical results, we propose that at the Ising critical temperature Tc the model is compatible with the universality class of two-dimensional (2D) self-avoiding walk (SAW). Especially the fractal dimension of the loops, which are defined as the external frontier of the avalanches, is very close to DfSAW=4/3 . Also, the corresponding open curves has conformal invariance with the root-mean-square distance Rrms˜t3 /4 (t being the parametrization of the curve) in accordance with the 2D SAW. In the finite-size study, we observe that at T =Tc the model has some aspects compatible with the 2D BTW model (e.g., the 1 /log(L ) -dependence of the exponents of the distribution functions) and some in accordance with the Ising model (e.g., the 1 /L -dependence of the fractal dimensions). The finite-size scaling theory is tested and shown to be fulfilled for all statistical observables in T =Tc . In the off-critical temperatures in the close vicinity of Tc the exponents show some additional power-law behaviors in terms of T -Tc with some exponents that are reported in the text. The spanning cluster probability at the critical temperature also scales with L1/2, which is different from the regular 2D BTW model.
Cheraghalizadeh, J; Najafi, M N; Dashti-Naserabadi, H; Mohammadzadeh, H
2017-11-01
The self-organized criticality on the random fractal networks has many motivations, like the movement pattern of fluid in the porous media. In addition to the randomness, introducing correlation between the neighboring portions of the porous media has some nontrivial effects. In this paper, we consider the Ising-like interactions between the active sites as the simplest method to bring correlations in the porous media, and we investigate the statistics of the BTW model in it. These correlations are controlled by the artificial "temperature" T and the sign of the Ising coupling. Based on our numerical results, we propose that at the Ising critical temperature T_{c} the model is compatible with the universality class of two-dimensional (2D) self-avoiding walk (SAW). Especially the fractal dimension of the loops, which are defined as the external frontier of the avalanches, is very close to D_{f}^{SAW}=4/3. Also, the corresponding open curves has conformal invariance with the root-mean-square distance R_{rms}∼t^{3/4} (t being the parametrization of the curve) in accordance with the 2D SAW. In the finite-size study, we observe that at T=T_{c} the model has some aspects compatible with the 2D BTW model (e.g., the 1/log(L)-dependence of the exponents of the distribution functions) and some in accordance with the Ising model (e.g., the 1/L-dependence of the fractal dimensions). The finite-size scaling theory is tested and shown to be fulfilled for all statistical observables in T=T_{c}. In the off-critical temperatures in the close vicinity of T_{c} the exponents show some additional power-law behaviors in terms of T-T_{c} with some exponents that are reported in the text. The spanning cluster probability at the critical temperature also scales with L^{1/2}, which is different from the regular 2D BTW model.
NASA Astrophysics Data System (ADS)
Fernández-Melgarejo, José J.; Park, Minkyu; Shigemori, Masaki
2017-12-01
A supertube is a supersymmetric configuration in string theory which occurs when a pair of branes spontaneously polarizes and generates a new dipole charge extended along a closed curve. The dipole charge of a codimension-2 supertube is characterized by the U-duality monodromy as one goes around the supertube. For multiple codimension-2 supertubes, their monodromies do not commute in general. In this paper, we construct a supersymmetric solution of five-dimensional supergravity that describes two supertubes with such non-Abelian monodromies, in a certain perturbative expansion. In supergravity, the monodromies are realized as the multi-valuedness of the scalar fields, while in higher dimensions they correspond to non-geometric duality twists of the internal space. The supertubes in our solution carry NS5 and 5 2 2 dipole charges and exhibit the same monodromy structure as the SU(2) Seiberg-Witten geometry. The perturbative solution has AdS2 × S 2 asymptotics and vanishing four-dimensional angular momentum. We argue that this solution represents a microstate of four-dimensional black holes with a finite horizon and that it provides a clue for the gravity realization of a pure-Higgs branch state in the dual quiver quantum mechanics.
NASA Astrophysics Data System (ADS)
Finch, Peter E.; Flohr, Michael; Frahm, Holger
2018-02-01
We study two families of quantum models which have been used previously to investigate the effect of topological symmetries in one-dimensional correlated matter. Various striking similarities are observed between certain {Z}n quantum clock models, spin chains generalizing the Ising model, and chains of non-Abelian anyons constructed from the so(n)2 fusion category for odd n, both subject to periodic boundary conditions. In spite of the differences between these two types of quantum chains, e.g. their Hilbert spaces being spanned by tensor products of local spin states or fusion paths of anyons, the symmetries of the lattice models are shown to be closely related. Furthermore, under a suitable mapping between the parameters describing the interaction between spins and anyons the respective Hamiltonians share part of their energy spectrum (although their degeneracies may differ). This spin-anyon correspondence can be extended by fine-tuning of the coupling constants leading to exactly solvable models. We show that the algebraic structures underlying the integrability of the clock models and the anyon chain are the same. For n = 3,5,7 we perform an extensive finite size study—both numerical and based on the exact solution—of these models to map out their ground state phase diagram and to identify the effective field theories describing their low energy behaviour. We observe that the continuum limit at the integrable points can be described by rational conformal field theories with extended symmetry algebras which can be related to the discrete ones of the lattice models.
Generalised Sandpile Dynamics on Artificial and Real-World Directed Networks
Zachariou, Nicky; Expert, Paul; Takayasu, Misako; Christensen, Kim
2015-01-01
The main finding of this paper is a novel avalanche-size exponent τ ≈ 1.87 when the generalised sandpile dynamics evolves on the real-world Japanese inter-firm network. The topology of this network is non-layered and directed, displaying the typical bow tie structure found in real-world directed networks, with cycles and triangles. We show that one can move from a strictly layered regular lattice to a more fluid structure of the inter-firm network in a few simple steps. Relaxing the regular lattice structure by introducing an interlayer distribution for the interactions, forces the scaling exponent of the avalanche-size probability density function τ out of the two-dimensional directed sandpile universality class τ = 4/3, into the mean field universality class τ = 3/2. Numerical investigation shows that these two classes are the only that exist on the directed sandpile, regardless of the underlying topology, as long as it is strictly layered. Randomly adding a small proportion of links connecting non adjacent layers in an otherwise layered network takes the system out of the mean field regime to produce non-trivial avalanche-size probability density function. Although these do not display proper scaling, they closely reproduce the behaviour observed on the Japanese inter-firm network. PMID:26606143
Generalised Sandpile Dynamics on Artificial and Real-World Directed Networks.
Zachariou, Nicky; Expert, Paul; Takayasu, Misako; Christensen, Kim
2015-01-01
The main finding of this paper is a novel avalanche-size exponent τ ≈ 1.87 when the generalised sandpile dynamics evolves on the real-world Japanese inter-firm network. The topology of this network is non-layered and directed, displaying the typical bow tie structure found in real-world directed networks, with cycles and triangles. We show that one can move from a strictly layered regular lattice to a more fluid structure of the inter-firm network in a few simple steps. Relaxing the regular lattice structure by introducing an interlayer distribution for the interactions, forces the scaling exponent of the avalanche-size probability density function τ out of the two-dimensional directed sandpile universality class τ = 4/3, into the mean field universality class τ = 3/2. Numerical investigation shows that these two classes are the only that exist on the directed sandpile, regardless of the underlying topology, as long as it is strictly layered. Randomly adding a small proportion of links connecting non adjacent layers in an otherwise layered network takes the system out of the mean field regime to produce non-trivial avalanche-size probability density function. Although these do not display proper scaling, they closely reproduce the behaviour observed on the Japanese inter-firm network.
Introducing Abelian Groups Using Bullseyes and Jenga
ERIC Educational Resources Information Center
Smith, Michael D.
2016-01-01
The purpose of this article is to share a new approach for introducing students to the definition and standard examples of Abelian groups. The definition of an Abelian group is revised to include six axioms. A bullseye provides a way to visualize elementary examples and non-examples of Abelian groups. An activity based on the game of Jenga is used…
Consequences of an Abelian family symmetry
Ramond, P.
1996-01-01
The addition of an Abelian family symmetry to the Minimal Super-symmetric Standard Model reproduces the observed hierarchies of quark and lepton masses and quark mixing angles, only if it is anomalous. Green-Schwarz compensation of its anomalies requires the electroweak mixing angle to be sin{sup 2}{theta}{sub {omega}} = 3/8 at the string scale, without any assumed GUT structure, suggesting a superstring origin for the standard model. The analysis is extended to neutrino masses and the lepton mixing matrix.
Localization in abelian Chern-Simons theory
NASA Astrophysics Data System (ADS)
McLellan, B. D. K.
2013-02-01
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected, and abelian. The abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. The partition function is then formally computed using the technique of non-abelian localization. This study leads to a natural identification of the abelian Reidemeister-Ray-Singer torsion as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections for the class of Sasakian three-manifolds. The torsion part of the abelian Chern-Simons partition function is computed explicitly in terms of Seifert data for a given Sasakian three-manifold.
NASA Astrophysics Data System (ADS)
Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus
2013-07-01
Building a universal quantum computer is a central goal of emerging quantum technologies, which has the potential to revolutionize science and technology. Unfortunately, this future does not seem to be very close at hand. However, quantum computers built for a special purpose, i.e. quantum simulators , are currently developed in many leading laboratories. Many schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots, photonic networks, or superconducting circuits. The progress in experimental implementations is more than spectacular. Particularly interesting are those systems that simulate quantum matter evolving in the presence of gauge fields. In the quantum simulation framework, the generated (synthetic) gauge fields may be Abelian, in which case they are the direct analogues of the vector potentials commonly associated with magnetic fields. In condensed matter physics, strong magnetic fields lead to a plethora of fascinating phenomena, among which the most paradigmatic is perhaps the quantum Hall effect. The standard Hall effect consists in the appearance of a transverse current, when a longitudinal voltage difference is applied to a conducting sample. For quasi-two-dimensional semiconductors at low temperatures placed in very strong magnetic fields, the transverse conductivity, the ratio between the transverse current and the applied voltage, exhibits perfect and robust quantization, independent for instance of the material or of its geometry. Such an integer quantum Hall effect, is now understood as a deep consequence of underlying topological order. Although such a system is an insulator in the bulk, it supports topologically robust edge excitations which carry the Hall current. The robustness of these chiral excitations against backscattering explains the universality of the quantum Hall effect. Another
Conformal field theory construction for non-Abelian hierarchy wave functions
NASA Astrophysics Data System (ADS)
Tournois, Yoran; Hermanns, Maria
2017-12-01
The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular non-Abelian ones. Here we analyze a class of non-Abelian fractional quantum Hall model states which are generalizations of the Abelian Haldane-Halperin hierarchy. We derive their topological properties and show that the quasiparticles obey non-Abelian fusion rules of type su (q)k . For a subset of these states we are able to derive the conformal field theory description that makes the topological properties—in particular braiding—of the state manifest. The model states we study provide explicit wave functions for a large variety of interesting topological orders, which may be relevant for certain fractional quantum Hall states observed in the first excited Landau level.
Upper bound on the Abelian gauge coupling from asymptotic safety
NASA Astrophysics Data System (ADS)
Eichhorn, Astrid; Versteegen, Fleur
2018-01-01
We explore the impact of asymptotically safe quantum gravity on the Abelian gauge coupling in a model including a charged scalar, confirming indications that asymptotically safe quantum fluctuations of gravity could trigger a power-law running towards a free fixed point for the gauge coupling above the Planck scale. Simultaneously, quantum gravity fluctuations balance against matter fluctuations to generate an interacting fixed point, which acts as a boundary of the basin of attraction of the free fixed point. This enforces an upper bound on the infrared value of the Abelian gauge coupling. In the regime of gravity couplings which in our approximation also allows for a prediction of the top quark and Higgs mass close to the experimental value [1], we obtain an upper bound approximately 35% above the infrared value of the hypercharge coupling in the Standard Model.
Diffusion of massive particles around an Abelian-Higgs string
NASA Astrophysics Data System (ADS)
Saha, Abhisek; Sanyal, Soma
2018-03-01
We study the diffusion of massive particles in the space time of an Abelian Higgs string. The particles in the early universe plasma execute Brownian motion. This motion of the particles is modeled as a two dimensional random walk in the plane of the Abelian Higgs string. The particles move randomly in the space time of the string according to their geodesic equations. We observe that for certain values of their energy and angular momentum, an overdensity of particles is observed close to the string. We find that the string parameters determine the distribution of the particles. We make an estimate of the density fluctuation generated around the string as a function of the deficit angle. Though the thickness of the string is small, the length is large and the overdensity close to the string may have cosmological consequences in the early universe.
Mapping the Braiding Properties of Non-Abelian FQHE Liquids.
NASA Astrophysics Data System (ADS)
Prodan, Emil; Haldane, F. D. M.
2007-03-01
Non-Abelian FQHE (NAFQHE) states have elementary excitations that cannot be individually locally-created. When widely separated, they give rise to topological (quasi-)degeneracy of the quantum states; braiding of such non-Abelian quasiparticles (NAQP's) implements unitary transformations among the degenerate states that may be useful for ``topological quantum computing'' (TQC). We have developed a new technique for explicit computation of NAQP braiding in models exhibiting ideal NAFQHE behavior (where the topological degeneracy is exact), in particular the Moore-Read ν = 5/2 state. For systems of small numbers of NAQP's on a sphere, we have computed the non-Abelian Berry curvature and Hilbert space metric, as one NAQP is moved relative to a fixed configuration of the others, showing how the topological properties develop as the system size (NAQP separation) increases. We also studied the effect of perturbations (Coulomb interaction and substrate potentials) that lift the exact degeneracy, and become the dominant corrections when NAQP's are brought together so that quantum measurements can be made; these effects are likely to be crucial in determining whether TQC is viable in NAFQHE systems.
Gauge-independent Abelian mechanism of color confinement in gluodynamics
Suzuki, Tsuneo; Ishiguro, Katsuya; Sekido, Toru
Abelian mechanism of non-Abelian color confinement is observed in a gauge-independent way by high precision lattice Monte Carlo simulations in gluodynamics. An Abelian gauge field is extracted with no gauge fixing. Then we decompose the Abelian field into regular photon and singular monopole parts using the Hodge decomposition. We find that only the monopole part is responsible for the string tension. The investigation of the flux-tube profile then shows that an Abelian electric field defined in an arbitrary color direction is squeezed by the monopole supercurrent with the same color direction, and the quantitative features of flux squeezing are consistentmore » with those observed previously after Abelian projections with gauge fixing. Non-Abelian color confinement is explained in the framework of the gauge-independent Abelian dual Meissner effect.« less
Effect of the viscosity of the liquid on the angle of inclination of a wet sandpile*
NASA Astrophysics Data System (ADS)
Samadani, Azadeh; Kudrolli, Arshad
2002-03-01
We study the effect of liquids on the angle of inclination of a wet sandpile in a rotating drum system. In this system, the surface exhibits stick slip motion for slow rotation rates omega, and continuos avalanching above a critical omega. We will focus on the stick-slip regime, where the angle of inclination of the pile oscillates between the maximum angle of stability before an avalanche, and the angle of repose after the avalanche. Both angles are observed to increase and saturate as a function of the volume fraction of the fluid. Furthermore, by changing the viscosity of the fluid using water-glycerol mixtures, we observe that both the maximum angle of stability and the angle of repose increase with the viscosity of the fluid. There are two possible explanations for the increase of the angle of stability of the pile. First, there may be creep motion between the particles giving rise to viscous forces before an avalanche, that are too small to observe visually. The creep motion is also slower than the rate of increase of the surface due to rotation. Second, the average number of liquid bridges between particles may increase with viscosity. We will comment on both possibilities using experimental data and scaling arguments.
Gravitational waves from non-Abelian gauge fields at a tachyonic transition
NASA Astrophysics Data System (ADS)
Tranberg, Anders; Tähtinen, Sara; Weir, David J.
2018-04-01
We compute the gravitational wave spectrum from a tachyonic preheating transition of a Standard Model-like SU(2)-Higgs system. Tachyonic preheating involves exponentially growing IR modes, at scales as large as the horizon. Such a transition at the electroweak scale could be detectable by LISA, if these non-perturbatively large modes translate into non-linear dynamics sourcing gravitational waves. Through large-scale numerical simulations, we find that the spectrum of gravitational waves does not exhibit such IR features. Instead, we find two peaks corresponding to the Higgs and gauge field mass, respectively. We find that the gravitational wave production is reduced when adding non-Abelian gauge fields to a scalar-only theory, but increases when adding Abelian gauge fields. In particular, gauge fields suppress the gravitational wave spectrum in the IR. A tachyonic transition in the early Universe will therefore not be detectable by LISA, even if it involves non-Abelian gauge fields.
Flavored gauge mediation with discrete non-Abelian symmetries
NASA Astrophysics Data System (ADS)
Everett, Lisa L.; Garon, Todd S.
2018-05-01
We explore the model building and phenomenology of flavored gauge-mediation models of supersymmetry breaking in which the electroweak Higgs doublets and the S U (2 ) messenger doublets are connected by a discrete non-Abelian symmetry. The embedding of the Higgs and messenger fields into representations of this non-Abelian Higgs-messenger symmetry results in specific relations between the Standard Model Yukawa couplings and the messenger-matter Yukawa interactions. Taking the concrete example of an S3 Higgs-messenger symmetry, we demonstrate that, while the minimal implementation of this scenario suffers from a severe μ /Bμ problem that is well known from ordinary gauge mediation, expanding the Higgs-messenger field content allows for the possibility that μ and Bμ can be separately tuned, allowing for the possibility of phenomenologically viable models of the soft supersymmetry-breaking terms. We construct toy examples of this type that are consistent with the observed 125 GeV Higgs boson mass.
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.
Cosmological bounds on non-Abelian dark forces
NASA Astrophysics Data System (ADS)
Forestell, Lindsay; Morrissey, David E.; Sigurdson, Kris
2018-04-01
Non-Abelian dark gauge forces that do not couple directly to ordinary matter may be realized in nature. The minimal form of such a dark force is a pure Yang-Mills theory. If the dark sector is reheated in the early Universe, it will be realized as a set of dark gluons at high temperatures and as a collection of dark glueballs at lower temperatures, with a cosmological phase transition from one form to the other. Despite being dark, the gauge fields of the new force can connect indirectly to the standard model through nonrenormalizable operators. These operators will transfer energy between the dark and visible sectors, and they allow some or all of the dark glueballs to decay. In this work we investigate the cosmological evolution and decays of dark glueballs in the presence of connector operators to the standard model. Dark glueball decays can modify cosmological and astrophysical observables, and we use these considerations to put very strong limits on the existence of pure non-Abelian dark forces. On the other hand, if one or more of the dark glueballs are stable, we find that they can potentially make up the dark matter of the Universe.
Stern, Ady
2010-03-11
Quantum mechanics classifies all elementary particles as either fermions or bosons, and this classification is crucial to the understanding of a variety of physical systems, such as lasers, metals and superconductors. In certain two-dimensional systems, interactions between electrons or atoms lead to the formation of quasiparticles that break the fermion-boson dichotomy. A particularly interesting alternative is offered by 'non-Abelian' states of matter, in which the presence of quasiparticles makes the ground state degenerate, and interchanges of identical quasiparticles shift the system between different ground states. Present experimental studies attempt to identify non-Abelian states in systems that manifest the fractional quantum Hall effect. If such states can be identified, they may become useful for quantum computation.
Fresh look at the Abelian and non-Abelian Landau-Khalatnikov-Fradkin transformations
NASA Astrophysics Data System (ADS)
De Meerleer, T.; Dudal, D.; Sorella, S. P.; Dall'Olio, P.; Bashir, A.
2018-04-01
The Landau-Khalatnikov-Fradkin transformations (LKFTs) allow one to interpolate n -point functions between different gauges. We first offer an alternative derivation of these LKFTs for the gauge and fermions field in the Abelian (QED) case when working in the class of linear covariant gauges. Our derivation is based on the introduction of a gauge invariant transversal gauge field, which allows a natural generalization to the non-Abelian (QCD) case of the LKFTs. To our knowledge, within this rigorous formalism, this is the first construction of the LKFTs beyond QED. The renormalizability of our setup is guaranteed to all orders. We also offer a direct path integral derivation in the non-Abelian case, finding full consistency.
Global charges of stationary non-Abelian black holes.
Kleihaus, Burkhard; Kunz, Jutta; Navarro-Lérida, Francisco
2003-05-02
We consider stationary axially symmetric black holes in SU(2) Einstein-Yang-Mills-dilaton theory. We present a mass formula for these stationary non-Abelian black holes, which also holds for Abelian black holes. The presence of the dilaton field allows for rotating black holes, which possess nontrivial electric and magnetic gauge fields, but do not carry a non-Abelian charge. We further present a new uniqueness conjecture.
Non-Abelian Gauge Theory in the Lorentz Violating Background
NASA Astrophysics Data System (ADS)
Ganai, Prince A.; Shah, Mushtaq B.; Syed, Masood; Ahmad, Owais
2018-03-01
In this paper, we will discuss a simple non-Abelian gauge theory in the broken Lorentz spacetime background. We will study the partial breaking of Lorentz symmetry down to its sub-group. We will use the formalism of very special relativity for analysing this non-Abelian gauge theory. Moreover, we will discuss the quantisation of this theory using the BRST symmetry. Also, we will analyse this theory in the maximal Abelian gauge.
Collision dynamics of two-dimensional non-Abelian vortices
NASA Astrophysics Data System (ADS)
Mawson, Thomas; Petersen, Timothy C.; Simula, Tapio
2017-09-01
We study computationally the collision dynamics of vortices in a two-dimensional spin-2 Bose-Einstein condensate. In contrast to Abelian vortex pairs, which annihilate or pass through each other, we observe non-Abelian vortex pairs to undergo rungihilation—an event that converts the colliding vortices into a rung vortex. The resulting rung defect subsequently decays to another pair of non-Abelian vortices of different type, accompanied by a magnetization reversal.
Abelian Toda field theories on the noncommutative plane
NASA Astrophysics Data System (ADS)
Cabrera-Carnero, Iraida
2005-10-01
Generalizations of GL(n) abelian Toda and GL with tilde above(n) abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by algebra-valued gauge potentials dependent on the fields. This condition can be expressed as noncommutative Leznov-Saveliev equations which make possible to define the noncommutative generalizations as systems of second order differential equations, with an infinite chain of conserved currents. The actions corresponding to these field theories are also provided. The special cases of GL(2) Liouville and GL with tilde above(2) sinh/sine-Gordon are explicitly studied. It is also shown that from the noncommutative (anti-)self-dual Yang-Mills equations in four dimensions it is possible to obtain by dimensional reduction the equations of motion of the two-dimensional models constructed. This fact supports the validity of the noncommutative version of the Ward conjecture. The relation of our proposal to previous versions of some specific Toda field theories reported in the literature is presented as well.
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.
Semi-abelian Z-theory: NLSM+ ϕ 3 from the open string
NASA Astrophysics Data System (ADS)
Carrasco, John Joseph M.; Mafra, Carlos R.; Schlotterer, Oliver
2017-08-01
We continue our investigation of Z-theory, the second double-copy component of open-string tree-level interactions besides super-Yang-Mills (sYM). We show that the amplitudes of the extended non-linear sigma model (NLSM) recently considered by Cachazo, Cha, and Mizera are reproduced by the leading α '-order of Z-theory amplitudes in the semi-abelian case. The extension refers to a coupling of NLSM pions to bi-adjoint scalars, and the semi-abelian case involves to a partial symmetrization over one of the color orderings that characterize the Z-theory amplitudes. Alternatively, the partial symmetrization corresponds to a mixed interaction among abelian and non-abelian states in the underlying open-superstring amplitude. We simplify these permutation sums via monodromy relations which greatly increase the efficiency in extracting the α '-expansion of these amplitudes. Their α '-corrections encode higher-derivative interactions between NLSM pions and bi-colored scalars all of which obey the duality between color and kinematics. Through double-copy, these results can be used to generate the predictions of supersymmetric Dirac-Born-Infeld-Volkov-Akulov theory coupled with sYM as well as a complete tower of higher-order α '-corrections.
Non-Abelian statistics of vortices with non-Abelian Dirac fermions.
Yasui, Shigehiro; Hirono, Yuji; Itakura, Kazunori; Nitta, Muneto
2013-05-01
We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined nonlocally by Majorana fermions located at two spatially separated vortices.
Critical string from non-Abelian vortex in four dimensions
Shifman, M.; Yung, A.
2015-09-25
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. Lastly, we show that the world-sheet theory onmore » the vortex supported in this bulk model is the bona fide critical string.« less
Condensation of an ideal gas obeying non-Abelian statistics.
Mirza, Behrouz; Mohammadzadeh, Hosein
2011-09-01
We consider the thermodynamic geometry of an ideal non-Abelian gas. We show that, for a certain value of the fractional parameter and at the relevant maximum value of fugacity, the thermodynamic curvature has a singular point. This indicates a condensation such as Bose-Einstein condensation for non-Abelian statistics and we work out the phase transition temperature in various dimensions.
Existence of topological multi-string solutions in Abelian gauge field theories
NASA Astrophysics Data System (ADS)
Han, Jongmin; Sohn, Juhee
2017-11-01
In this paper, we consider a general form of self-dual equations arising from Abelian gauge field theories coupled with the Einstein equations. By applying the super/subsolution method, we prove that topological multi-string solutions exist for any coupling constant, which improves previously known results. We provide two examples for application: the self-dual Einstein-Maxwell-Higgs model and the gravitational Maxwell gauged O(3) sigma model.
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.
Self-Organized Criticality in an Asexual Model?
NASA Astrophysics Data System (ADS)
Chisholm, Colin; Jan, Naeem; Gibbs, Peter; Erzan, Ayşe.
Recent work has shown that the distribution of steady state mutations for an asexual ``bacteria'' model has features similar to that seen in Self-Organized Critical (SOC) sandpile model of Bak et al. We investigate this coincidence further and search for ``self-organized critical'' state for bacteria but instead find that the SOC sandpile critical behavior is very sensitive; critical behavior is destroyed with small perturbations effectively when the absorption of sand is introduced. It is only in the limit when the length of the genome of the bacteria tends to infinity that SOC properties are recovered for the asexual model.
Interaction of non-Abelian tensor gauge fields
NASA Astrophysics Data System (ADS)
Savvidy, George
2018-01-01
The non-Abelian tensor gauge fields take value in extended Poincaré algebra. In order to define the invariant Lagrangian we introduce a vector variable in two alternative ways: through the transversal representation of the extended Poincaré algebra and through the path integral over the auxiliary vector field with the U(1) Abelian action. We demonstrate that this allows to fix the unitary gauge and derive scattering amplitudes in spinor representation.
Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly
NASA Astrophysics Data System (ADS)
Wulff, Linus
2018-06-01
The equations that follow from kappa symmetry of the type II Green-Schwarz string are a certain deformation, by a Killing vector field K, of the type II supergravity equations. We analyze under what conditions solutions of these 'generalized' supergravity equations are trivial in the sense that they solve also the standard supergravity equations. We argue that for this to happen K must be null and satisfy dK =iK H with H = dB the NSNS three-form field strength. Non-trivial examples are provided by symmetric pp-wave solutions. We then analyze the consequences for non-abelian T-duality and the closely related homogenous Yang-Baxter sigma models. When one performs non-abelian T-duality of a string sigma model on a non-unimodular (sub)algebra one generates a non-vanishing K proportional to the trace of the structure constants. This is expected to lead to an anomaly but we show that when K satisfies the same conditions the anomaly in fact goes away leading to more possibilities for non-anomalous non-abelian T-duality.
Abelian Higgs cosmic strings: Small-scale structure and loops
Hindmarsh, Mark; Stuckey, Stephanie; Bevis, Neil
2009-06-15
Classical lattice simulations of the Abelian Higgs model are used to investigate small-scale structure and loop distributions in cosmic string networks. Use of the field theory ensures that the small-scale physics is captured correctly. The results confirm analytic predictions of Polchinski and Rocha 29 for the two-point correlation function of the string tangent vector, with a power law from length scales of order the string core width up to horizon scale. An analysis of the size distribution of string loops gives a very low number density, of order 1 per horizon volume, in contrast with Nambu-Goto simulations. Further, our loopmore » distribution function does not support the detailed analytic predictions for loop production derived by Dubath et al. 30. Better agreement to our data is found with a model based on loop fragmentation 32, coupled with a constant rate of energy loss into massive radiation. Our results show a strong energy-loss mechanism, which allows the string network to scale without gravitational radiation, but which is not due to the production of string width loops. From evidence of small-scale structure we argue a partial explanation for the scale separation problem of how energy in the very low frequency modes of the string network is transformed into the very high frequency modes of gauge and Higgs radiation. We propose a picture of string network evolution, which reconciles the apparent differences between Nambu-Goto and field theory simulations.« less
Abelian non-global logarithms from soft gluon clustering
NASA Astrophysics Data System (ADS)
Kelley, Randall; Walsh, Jonathan R.; Zuberi, Saba
2012-09-01
Most recombination-style jet algorithms cluster soft gluons in a complex way. This leads to previously identified correlations in the soft gluon phase space and introduces logarithmic corrections to jet cross sections, which are known as clustering logarithms. The leading Abelian clustering logarithms occur at least at next-to leading logarithm (NLL) in the exponent of the distribution. Using the framework of Soft Collinear Effective Theory (SCET), we show that new clustering effects contributing at NLL arise at each order. While numerical resummation of clustering logs is possible, it is unlikely that they can be analytically resummed to NLL. Clustering logarithms make the anti-kT algorithm theoretically preferred, for which they are power suppressed. They can arise in Abelian and non-Abelian terms, and we calculate the Abelian clustering logarithms at O ( {α_s^2} ) for the jet mass distribution using the Cambridge/Aachen and kT algorithms, including jet radius dependence, which extends previous results. We find that clustering logarithms can be naturally thought of as a class of non-global logarithms, which have traditionally been tied to non-Abelian correlations in soft gluon emission.
NASA Astrophysics Data System (ADS)
Lynn, Bryan W.; Starkman, Glenn D.
2017-09-01
The weak-scale U (1 )Y Abelian Higgs model (AHM) is the simplest spontaneous symmetry breaking (SSB) gauge theory: a scalar ϕ =1/√{2 }(H +i π )≡1/√{2 }H ˜ei π ˜/⟨H ⟩ and a vector Aμ. The extended AHM (E-AHM) adds certain heavy (MΦ2,Mψ2˜MHeavy2≫⟨H ⟩2˜mWeak2 ) spin S =0 scalars Φ and S =1/2 fermions ψ . In Lorenz gauge, ∂μAμ=0 , the SSB AHM (and E-AHM) has a global U (1 )Y conserved physical current, but no conserved charge. As shown by T. W. B. Kibble, the Goldstone theorem applies, so π ˜ is a massless derivatively coupled Nambu-Goldstone boson (NGB). Proof of all-loop-orders renormalizability and unitarity for the SSB case is tricky because the Becchi-Rouet-Stora-Tyutin (BRST)-invariant Lagrangian is not U (1 )Y symmetric. Nevertheless, Slavnov-Taylor identities guarantee that on-shell T-matrix elements of physical states Aμ,ϕ , Φ , ψ (but not ghosts ω , η ¯ ) are independent of anomaly-free local U (1 )Y gauge transformations. We observe here that they are therefore also independent of the usual anomaly-free U (1 )Y global/rigid transformations. It follows that the associated global current, which is classically conserved only up to gauge-fixing terms, is exactly conserved for amplitudes of physical states in the AHM and E-AHM. We identify corresponding "undeformed" [i.e. with full global U (1 )Y symmetry] Ward-Takahashi identities (WTI). The proof of renormalizability and unitarity, which relies on BRST invariance, is undisturbed. In Lorenz gauge, two towers of "1-soft-pion" SSB global WTI govern the ϕ -sector, and represent a new global U (1 )Y⊗BRST symmetry not of the Lagrangian but of the physics. The first gives relations among off-shell Green's functions, yielding powerful constraints on the all-loop-orders ϕ -sector SSB E-AHM low-energy effective Lagrangian and an additional global shift symmetry for the NGB: π ˜→π ˜+⟨H ⟩θ . A second tower, governing on-shell T-matrix elements, replaces the old Adler
A note on local BRST cohomology of Yang-Mills type theories with free Abelian factors
NASA Astrophysics Data System (ADS)
Barnich, Glenn; Boulanger, Nicolas
2018-05-01
We extend previous work on antifield dependent local Becchi-Rouet-Stora-Tyutin (BRST) cohomology for matter coupled gauge theories of Yang-Mills type to the case of gauge groups that involve free Abelian factors. More precisely, we first investigate in a model independent way how the dynamics enters the computation of the cohomology for a general class of Lagrangians in general spacetime dimensions. We then discuss explicit solutions in the case of specific models. Our analysis has implications for the structure of characteristic cohomology and for consistent deformations of the classical models, as well as for divergences/counterterms and for gauge anomalies that may appear during perturbative quantization.
Conserved quantities in non-Abelian monopole fields
NASA Astrophysics Data System (ADS)
Horváthy, P. A.; Ngome, J.-P.
2009-06-01
Van Holten’s covariant Hamiltonian framework is used to find conserved quantities for an isospin-carrying particle in a non-Abelian monopolelike field. For a Wu-Yang monopole we find the most general scalar potential such that the combined system admits a conserved Runge-Lenz vector. In the effective non-Abelian field for nuclear motion in a diatomic molecule due to Moody, Shapere, and Wilczek, a conserved angular momentum is constructed, despite the nonconservation of the electric charge. No Runge-Lenz vector has been found.
On Non-Abelian Extensions of 3-Lie Algebras
NASA Astrophysics Data System (ADS)
Song, Li-Na; Makhlouf, Abdenacer; Tang, Rong
2018-04-01
In this paper, we study non-abelian extensions of 3-Lie algebras through Maurer-Cartan elements. We show that there is a one-to-one correspondence between isomorphism classes of non-abelian extensions of 3-Lie algebras and equivalence classes of Maurer-Cartan elements in a DGLA. The structure of the Leibniz algebra on the space of fundamental objects is also analyzed. Supported by National Natural Science Foundation of China under Grant No. 11471139 and National Natural Science Foundation of Jilin Province under Grant No. 20170101050JC
Condition for confinement in non-Abelian gauge theories
NASA Astrophysics Data System (ADS)
Chaichian, Masud; Frasca, Marco
2018-06-01
We show that a criterion for confinement, based on the BRST invariance, holds in four dimensions, by solving a non-Abelian gauge theory with a set of exact solutions. The confinement condition we consider was obtained by Kugo and Ojima some decades ago. The current understanding of gauge theories permits us to apply the techniques straightforwardly for checking the validity of this criterion. In this way, we are able to show that the non-Abelian gauge theory is confining and that confinement is rooted in the BRST invariance and asymptotic freedom.
Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories
NASA Astrophysics Data System (ADS)
Ferreira, L. A.; Miramontes, J. Luis; Guillén, Joaquín Sánchez
1995-02-01
We consider the Hamiltonian reduction of the "two-loop" Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra G. The resulting reduced models, called Generalized Non-Abelian Conformal Affine Toda (G-CAT), are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-Abelian generalizations of the conformal affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the τ-functions, which are defined for any integrable highest weight representation of G, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed. We also introduce what we call the two-loop Virasoro algebra, describing extended symmetries of the two-loop WZNW models.
Quantization of higher abelian gauge theory in generalized differential cohomology
NASA Astrophysics Data System (ADS)
Szabo, R.
We review and elaborate on some aspects of the quantization of certain classes of higher abelian gauge theories using techniques of generalized differential cohomology. Particular emphasis is placed on the examples of generalized Maxwell theory and Cheeger-Simons cohomology, and of Ramond-Ramond fields in Type II superstring theory and differential K-theory.
Interacting Non-Abelian Anti-Symmetric Tensor Field Theories
NASA Astrophysics Data System (ADS)
Ekambaram, K.; Vytheeswaran, A. S.
2018-04-01
Non-Abelian Anti-symmetric Tensor fields interacting with vector fields have a complicated constraint structure. We enlarge the gauge invariance in this system. Relevant gauge invariant quantities including the Hamiltonian are obtained. We also make introductory remarks on a different but more complicated gauge theory.
A Finite Abelian Group of Two-Letter Inversions
ERIC Educational Resources Information Center
Balbuena, Sherwin E.
2015-01-01
In abstract algebra, the study of concrete groups is fundamentally important to beginners. Most commonly used groups as examples are integer addition modulo n, real number addition and multiplication, permutation groups, and groups of symmetry. The last two examples are finite non-abelian groups and can be investigated with the aid of concrete…
Abelian gauge symmetries in F-theory and dual theories
NASA Astrophysics Data System (ADS)
Song, Peng
In this dissertation, we focus on important physical and mathematical aspects, especially abelian gauge symmetries, of F-theory compactifications and its dual formulations within type IIB and heterotic string theory. F-theory is a non-perturbative formulation of type IIB string theory which enjoys important dualities with other string theories such as M-theory and E8 x E8 heterotic string theory. One of the main strengths of F-theory is its geometrization of many physical problems in the dual string theories. In particular, its study requires a lot of mathematical tools such as advanced techniques in algebraic geometry. Thus, it has also received a lot of interests among mathematicians, and is a vivid area of research within both the physics and the mathematics community. Although F-theory has been a long-standing theory, abelian gauge symmetry in Ftheory has been rarely studied, until recently. Within the mathematics community, in 2009, Grassi and Perduca first discovered the possibility of constructing elliptically fibered varieties with non-trivial toric Mordell-Weil group. In the physics community, in 2012, Morrison and Park first made a major advancement by constructing general F-theory compactifications with U(1) abelian gauge symmetry. They found that in such cases, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the blow-up of the weighted projective space P(1;1;2) at one point. Subsequent developments have been made by Cvetic, Klevers and Piragua extended the works of Morrison and Park and constructed general F-theory compactifications with U(1) x U(1) abelian gauge symmetry. They found that in the U(1) x U(1) abelian gauge symmetry case, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the del Pezzo surface dP2. In chapter 2 of this dissertation, I bring this a step further by
Dark gauge bosons: LHC signatures of non-abelian kinetic mixing
Argüelles, Carlos A.; He, Xiao-Gang; Ovanesyan, Grigory; ...
2017-04-20
We consider non-abelian kinetic mixing between the Standard Model and a dark sector gauge group associated with the presence of a scalar triplet. The magnitude of the resulting dark photon coupling ϵ is determined by the ratio of the triplet vacuum expectation value, constrained to by by electroweak precision tests, to the scale Λ of the effective theory. The corresponding effective operator Wilson coefficient can be while accommodating null results for dark photon searches, allowing for a distinctive LHC dark photon phenomenology. After outlining the possible LHC signatures, we illustrate by recasting current ATLAS dark photon results into the non-abelianmore » mixing context.« less
The static quark potential from the gauge independent Abelian decomposition
NASA Astrophysics Data System (ADS)
Cundy, Nigel; Cho, Y. M.; Lee, Weonjong; Leem, Jaehoon
2015-06-01
We investigate the relationship between colour confinement and the gauge independent Cho-Duan-Ge Abelian decomposition. The decomposition is defined in terms of a colour field n; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path-ordered integral of the non-Abelian gauge fields and an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. We circumvent path ordering without requiring an additional path integral. By using Stokes' theorem, we can compute the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by certain structures, which occur when one of the quantities parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these structures will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. Unlike most studies of confinement using the Abelian decomposition, we do not rely on a dual-Meissner effect to create the inter-quark potential. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and compare the electric and magnetic fields with the patterns expected theoretically. We find that the restricted field strength is dominated by objects which may be peaks of a single lattice spacing in size or extended string-like lines of electromagnetic flux. The objects are not isolated monopoles, as they generate electric fields in addition to magnetic fields, and the fields are not spherically symmetric, but may be either caused by a monopole/anti-monopole condensate, some other types of topological objects, or a combination of these. Removing these peaks removes the area law scaling of the string tension, suggesting that they are responsible for
NASA Astrophysics Data System (ADS)
Chatterjee, Chandrasekhar; Nitta, Muneto
2017-04-01
Color symmetry is spontaneously broken in quark matter at high density as a consequence of di-quark condensations with exhibiting color superconductivity. Non-Abelian vortices or color magnetic flux tubes stably exist in the color-flavor locked phase at asymptotically high density. The effective worldsheet theory of a single non-Abelian vortex was previously calculated in the singular gauge to obtain the C P2 model
Non-Abelian Bremsstrahlung and Azimuthal Asymmetries in High Energy p+A Reactions
Gyulassy, Miklos; Vitev, Ivan Mateev; Levai, Peter; ...
2014-09-25
Here we apply the GLV reaction operator solution to the Vitev-Gunion-Bertsch (VGB) boundary conditions to compute the all-order in nuclear opacity non-abelian gluon bremsstrahlung of event- by-event uctuating beam jets in nuclear collisions. We evaluate analytically azimuthal Fourier moments of single gluon, vmore » $$M\\atop{n}$$ {1}, and even number 2ℓ gluon, v$$M\\atop{n}$$ {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 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 character- istic boost non-invariant trapezoidal rapidity distributions in asymmetric B+A nuclear collisions. The scaling of intrinsically azimuthally anisotropic and long range in η nature of the non-Abelian bremsstrahlung leads to v n 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 non-flow solutions are similar to recent numerical saturation model predictions but differ by predicting a simple power-law hierarchy of both even and odd v n without invoking k T factorization. A test of CSA mechanism is the predicted nearly linear η rapidity dependence of the v n(k Tη). Non- Abelian beam jet bremsstrahlung may thus provide a simple analytic solution to Beam Energy Scan (BES) puzzle of the near $$\\sqrt{s}$$ independence of v n(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 v n in p(D) + A and non-central A + A at same dN=dη multiplicity as observed at RHIC and LHC.« less
Granule-by-granule reconstruction of a sandpile from x-ray microtomography data
Seidler, G. T.; Martinez, G.; Seeley, L. H.
2000-12-01
Mesoscale disordered materials are ubiquitous in industry and in the environment. Any fundamental understanding of the transport and mechanical properties of such materials must follow from a thorough understanding of their structure. However, in the overwhelming majority of cases, experimental characterization of such materials has been limited to first- and second-order structural correlation functions, i.e., the mean filling fraction and the structural autocorrelation function. We report here the successful combination of synchrotron x-ray microtomography and image processing to determine the full three-dimensional real-space structure of a model disordered material, a granular bed of relatively monodisperse glass spheres. Specifically, we determinemore » the center location and the local connectivity of each granule. This complete knowledge of structure can be used to calculate otherwise inaccessible high-order correlation functions. We analyze nematic order parameters for contact bonds to characterize the geometric anisotropy or fabric induced by the sample boundary conditions. Away from the boundaries we find short-range bond orientational order exhibiting characteristics of the underlying polytetrahedral structure.« less
Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator.
Li, Keren; Wan, Yidun; Hung, Ling-Yan; Lan, Tian; Long, Guilu; Lu, Dawei; Zeng, Bei; Laflamme, Raymond
2017-02-24
Topological orders can be used as media for topological quantum computing-a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular S and T matrices. In particular, we employ a nuclear magnetic resonance quantum simulator to study the properties of three topologically ordered matter phases described by the string-net model with two string types, including the Z_{2} toric code, doubled semion, and doubled Fibonacci. The third one, non-Abelian Fibonacci order is notably expected to be the simplest candidate for universal topological quantum computing. Our experiment serves as the basic module, built on which one can simulate braiding of non-Abelian anyons and ultimately, topological quantum computation via the braiding, and thus provides a new approach of investigating topological orders using quantum computers.
Anisotropic Bispectrum of Curvature Perturbations from Primordial Non-Abelian Vector Fields
NASA Astrophysics Data System (ADS)
Bartolo, Nicola; Dimastrogiovanni, Emanuela; Matarrese, Sabino; Riotto, Antonio
2009-10-01
We consider a primordial SU(2) vector multiplet during inflation in models where quantum fluctuations of vector fields are involved in producing the curvature perturbation. Recently, a lot of attention has been paid to models populated by vector fields, given the interesting possibility of generating some level of statistical anisotropy in the cosmological perturbations. The scenario we propose is strongly motivated by the fact that, for non-Abelian gauge fields, self-interactions are responsible for generating extra terms in the cosmological correlation functions, which are naturally absent in the Abelian case. We compute these extra contributions to the bispectrum of the curvature perturbation, using the δN formula and the Schwinger-Keldysh formalism. The primordial violation of rotational invariance (due to the introduction of the SU(2) gauge multiplet) leaves its imprint on the correlation functions introducing, as expected, some degree of statistical anisotropy in our results. We calculate the non-Gaussianity parameter fNL, proving that the new contributions derived from gauge bosons self-interactions can be important, and in some cases the dominat ones. We study the shape of the bispectrum and we find that it turns out to peak in the local configuration, with an amplitude that is modulated by the preferred directions that break statistical isotropy.
Time evolution of complexity in Abelian gauge theories
NASA Astrophysics Data System (ADS)
Hashimoto, Koji; Iizuka, Norihiro; Sugishita, Sotaro
2017-12-01
Quantum complexity is conjectured to probe inside of black hole horizons (or wormholes) via gauge gravity correspondence. In order to have a better understanding of this correspondence, we study time evolutions of complexities for Abelian pure gauge theories. For this purpose, we discretize the U (1 ) gauge group as ZN and also the continuum spacetime as lattice spacetime, and this enables us to define a universal gate set for these gauge theories and to evaluate time evolutions of the complexities explicitly. We find that to achieve a large complexity ˜exp (entropy), which is one of the conjectured criteria necessary to have a dual black hole, the Abelian gauge theory needs to be maximally nonlocal.
Construction of non-Abelian gauge theories on noncommutative spaces
NASA Astrophysics Data System (ADS)
Jurčo, B.; Möller, L.; Schraml, S.; Schupp, P.; Wess, J.
We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories.
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.
Quantum coherence generating power, maximally abelian subalgebras, and Grassmannian geometry
NASA Astrophysics Data System (ADS)
Zanardi, Paolo; Campos Venuti, Lorenzo
2018-01-01
We establish a direct connection between the power of a unitary map in d-dimensions (d < ∞) to generate quantum coherence and the geometry of the set Md of maximally abelian subalgebras (of the quantum system full operator algebra). This set can be seen as a topologically non-trivial subset of the Grassmannian over linear operators. The natural distance over the Grassmannian induces a metric structure on Md, which quantifies the lack of commutativity between the pairs of subalgebras. Given a maximally abelian subalgebra, one can define, on physical grounds, an associated measure of quantum coherence. We show that the average quantum coherence generated by a unitary map acting on a uniform ensemble of quantum states in the algebra (the so-called coherence generating power of the map) is proportional to the distance between a pair of maximally abelian subalgebras in Md connected by the unitary transformation itself. By embedding the Grassmannian into a projective space, one can pull-back the standard Fubini-Study metric on Md and define in this way novel geometrical measures of quantum coherence generating power. We also briefly discuss the associated differential metric structures.
Critical non-Abelian vortex in four dimensions and little string theory
NASA Astrophysics Data System (ADS)
Shifman, M.; Yung, A.
2017-08-01
As was shown recently, non-Abelian vortex strings supported in four-dimensional N =2 supersymmetric QCD with the U(2) gauge group and Nf=4 quark multiplets (flavors) become critical superstrings. In addition to the translational moduli, non-Abelian strings under consideration carry six orientational and size moduli. Together, they form a ten-dimensional target space required for a superstring to be critical. The target space of the string sigma model is a product of the flat four-dimensional space and a Calabi-Yau noncompact threefold, namely, the conifold. We study closed string states which emerge in four dimensions and identify them with hadrons of four-dimensional N =2 QCD. One massless state was found previously; it emerges as a massless hypermultiplet associated with the deformation of the complex structure of the conifold. In this paper, we find a number of massive states. To this end, we exploit the approach used in LST little string theory, namely, the equivalence between the critical string on the conifold and noncritical c =1 string with the Liouville field and a compact scalar at the self-dual radius. The states we find carry "baryonic" charge (its definition differs from standard). We interpret them as "monopole necklaces" formed (at strong coupling) by the closed string with confined monopoles attached.
Non-Abelian black string solutions of N = (2,0) , d = 6 supergravity
NASA Astrophysics Data System (ADS)
Cano, Pablo A.; Ortín, Tomás; Santoli, Camilla
2016-12-01
We show that, when compactified on a circle, N = (2, 0), d = 6 supergravity coupled to 1 tensor multiplet and n V vector multiplets is dual to N = (2 , 0) , d = 6 supergravity coupled to just n T = n V + 1 tensor multiplets and no vector multiplets. Both theories reduce to the same models of N = 2 , d = 5 supergravity coupled to n V 5 = n V + 2 vector fields. We derive Buscher rules that relate solutions of these theories (and of the theory that one obtains by dualizing the 3-form field strength) admitting an isometry. Since the relations between the fields of N = 2 , d = 5 supergravity and those of the 6-dimensional theories are the same with or without gaugings, we construct supersymmetric non-Abelian solutions of the 6-dimensional gauged theories by uplifting the recently found 5-dimensional supersymmetric non-Abelian black-hole solutions. The solutions describe the usual superpositions of strings and waves supplemented by a BPST instanton in the transverse directions, similar to the gauge dyonic string of Duff, Lü and Pope. One of the solutions obtained interpolates smoothly between two AdS3× S3 geometries with different radii.
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
Non-Abelian semilocal strings in N=2 supersymmetric QCD
Shifman, M.; Yung, A.; Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188300
2006-06-15
We consider a benchmark bulk theory in four dimensions: N=2 supersymmetric QCD with the gauge group U(N) and N{sub f} flavors of fundamental matter hypermultiplets (quarks). The nature of the Bogomol'nyi-Prasad-Sommerfield (BPS) strings in this benchmark theory crucially depends on N{sub f}. If N{sub f}{>=}N and all quark masses are equal, it supports non-Abelian BPS strings which have internal (orientational) moduli. If N{sub f}>N these strings become semilocal, developing additional moduli {rho} related to (unlimited) variations of their transverse size. Using the U(2) gauge group with N{sub f}=3, 4 as an example, we derive an effective low-energy theory on themore » (two-dimensional) string world sheet. Our derivation is field theoretic, direct and explicit: we first analyze the Bogomol'nyi equations for string-geometry solitons, suggest an ansatz, and solve it at large {rho}. Then we use this solution to obtain the world-sheet theory. In the semiclassical limit our result confirms the Hanany-Tong conjecture, which rests on brane-based arguments, that the world-sheet theory is an N=2 supersymmetric U(1) gauge theory with N positively and N{sub e}=N{sub f}-N negatively charged matter multiplets and the Fayet-Iliopoulos term determined by the four-dimensional coupling constant. We conclude that the Higgs branch of this model is not lifted by quantum effects. As a result, such strings cannot confine. Our analysis of infrared effects, not seen in the Hanany-Tong consideration, shows that, in fact, the derivative expansion can make sense only provided that the theory under consideration is regularized in the infrared, e.g. by the quark mass differences. The world-sheet action discussed in this paper becomes a bona fide low-energy effective action only if {delta}m{sub AB}{ne}0.« less
Penrose limits of Abelian and non-Abelian T-duals of AdS 5 × S 5 and their field theory duals
NASA Astrophysics Data System (ADS)
Itsios, Georgios; Nastase, Horatiu; Núñez, Carlos; Sfetsos, Konstantinos; Zacarías, Salomón
2018-01-01
We consider the backgrounds obtained by Abelian and non-Abelian T-duality applied on AdS 5 × S 5. We study geodesics, calculate Penrose limits and find the associated plane-wave geometries. We quantise the weakly coupled type-IIA string theory on these backgrounds. We study the BMN sector, finding operators that wrap the original quiver CFT. For the non-Abelian plane wave, we find a `flow' in the frequencies. We report some progress to understand this, in terms of deconstruction of a higher dimensional field theory. We explore a relation with the plane-wave limit of the Janus solution, which we also provide.
Minimal non-abelian supersymmetric Twin Higgs
Badziak, Marcin; Harigaya, Keisuke
2017-10-17
We propose a minimal supersymmetric Twin Higgs model that can accommodate tuning of the electroweak scale for heavy stops better than 10% with high mediation scales of supersymmetry breaking. A crucial ingredient of this model is a new SU(2) X gauge symmetry which provides a D-term potential that generates a large SU(4) invariant coupling for the Higgs sector and only small set of particles charged under SU(2) X , which allows the model to be perturbative around the Planck scale. The new gauge interaction drives the top yukawa coupling small at higher energy scales, which also reduces the tuning.
Non-Abelian holonomies, charge pumping, and quantum computation with Josephson junctions.
Faoro, Lara; Siewert, Jens; Fazio, Rosario
2003-01-17
Non-Abelian holonomies can be generated and detected in certain superconducting nanocircuits. Here we consider an example where the non-Abelian operations are related to the adiabatic charge dynamics of the Josephson network. We demonstrate that such a device can be applied both for adiabatic charge pumping and as an implementation of a quantum computer.
Dirichlet to Neumann operator for Abelian Yang-Mills gauge fields
NASA Astrophysics Data System (ADS)
Díaz-Marín, Homero G.
We consider the Dirichlet to Neumann operator for Abelian Yang-Mills boundary conditions. The aim is constructing a complex structure for the symplectic space of boundary conditions of Euler-Lagrange solutions modulo gauge for space-time manifolds with smooth boundary. Thus we prepare a suitable scenario for geometric quantization within the reduced symplectic space of boundary conditions of Abelian gauge fields.
Rotating black holes with non-Abelian hair
NASA Astrophysics Data System (ADS)
Kleihaus, Burkhard; Kunz, Jutta; Navarro-Lérida, Francisco
2016-12-01
We here review asymptotically flat rotating black holes in the presence of non-Abelian gauge fields. Like their static counterparts these black holes are no longer uniquely determined by their global charges. In the case of pure SU(2) Yang-Mills fields, the rotation generically induces an electric charge, while the black holes do not carry a magnetic charge. When a Higgs field is coupled, rotating black holes with monopole hair arise in the case of a Higgs triplet, while in the presence of a complex Higgs doublet the black holes carry sphaleron hair. The inclusion of a dilaton allows for Smarr type mass formulae.
Abelian tensor hierarchy in 4D N = 1 conformal supergravity
NASA Astrophysics Data System (ADS)
Aoki, Shuntaro; Higaki, Tetsutaro; Yamada, Yusuke; Yokokura, Ryo
2016-09-01
We consider Abelian tensor hierarchy in four-dimensional N = 1 supergravity in the conformal superspace formalism, where the so-called covariant approach is used to antisymmetric tensor fields. We introduce p-form gauge superfields as superforms in the conformal superspace. We solve the Bianchi identities under the constraints for the super-forms. As a result, each of form fields is expressed by a single gauge invariant superfield. We also show the relation between the superspace formalism and the superconformal tensor calculus.
Non-Abelian fractional topological insulators in three spatial dimensions from coupled wires
NASA Astrophysics Data System (ADS)
Iadecola, Thomas; Neupert, Titus; Chamon, Claudio; Mudry, Christopher
The study of topological order in three spatial dimensions constitutes a major frontier in theoretical condensed matter physics. Recently, substantial progress has been made in constructing (3+1)-dimensional Abelian topological states of matter from arrays of coupled quantum wires. In this talk, I will illustrate how wire constructions based on non-Abelian bosonization can be used to build and characterize non-Abelian symmetry-enriched topological phases in three dimensions. In particular, I will describe a family of states of matter, constructed in this way, that constitute a natural non-Abelian generalization of strongly correlated three dimensional fractional topological insulators. These states of matter support strongly interacting symmetry-protected gapless surface states, and host non-Abelian pointlike and linelike excitations in the bulk.
Metal-Insulator Transition Revisited for Cold Atoms in Non-Abelian Gauge Potentials
Satija, Indubala I.; National Institute of Standards and Technology, Gaithersburg, Maryland 20899; Dakin, Daniel C.
2006-11-24
We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. For Abelian gauges, such transitions occur when the magnetic flux penetrating the lattice plaquette is an irrational multiple of the magnetic flux quantum. Here we present the first study of these transitions for non-Abelian U(2) gauge fields. In contrast to the Abelian case, the spectrum and localization transition in the non-Abelian case is strongly influenced by atomic momenta. In addition to determining the localization boundary, the momentum fragments the spectrum. Other key characteristics of the non-Abelian case includemore » the absence of localization for certain states and satellite fringes around the Bragg peaks in the momentum distribution and an interesting possibility that the transition can be tuned by the atomic momenta.« less
On an example of a system of differential equations that are integrated in Abelian functions
NASA Astrophysics Data System (ADS)
Malykh, M. D.; Sevastianov, L. A.
2017-12-01
The short review of the theory of Abelian functions and its applications in mechanics and analytical theory of differential equations is given. We think that Abelian functions are the natural generalization of commonly used functions because if the general solution of the 2nd order differential equation depends algebraically on the constants of integration, then integrating this equation does not lead out of the realm of commonly used functions complemented by the Abelian functions (Painlevé theorem). We present a relatively simple example of a dynamical system that is integrated in Abelian integrals by “pairing” two copies of a hyperelliptic curve. Unfortunately, initially simple formulas unfold into very long ones. Apparently the theory of Abelian functions hasn’t been finished in the last century because without computer algebra systems it was impossible to complete the calculations to the end. All calculations presented in our report are performed in Sage.
Studying critical string emerging from non-Abelian vortex in four dimensions
Koroteev, P.; Shifman, M.; Yung, A.
2016-05-26
Recently a special vortex string was found 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. Here, the full target space ismore » $$\\mathbb R$$ 4 x Y 6 where is a non-compact Calabi–Yau space.« less
Anisotopic inflation with a non-abelian gauge field in Gauss-Bonnet gravity
Lahiri, Sayantani, E-mail: sayantani.lahiri@gmail.com
2017-01-01
In presence of Gauss-Bonnet corrections, we study anisotropic inflation aided by a massless SU(2) gauge field where both the gauge field and the Gauss-Bonnet term are non-minimally coupled to the inflaton. In this scenario, under slow-roll approximations, the anisotropic inflation is realized as an attractor solution with quadratic forms of inflaton potential and Gauss-Bonnet coupling function. We show that the degree of anisotropy is proportional to the additive combination of two slow-roll parameters of the theory. The anisotropy may become either positive or negative similar to the non-Gauss-Bonnet framework, a feature of the model for anisotropic inflation supported by amore » non-abelian gauge field but the effect of Gauss-Bonnet term further enhances or suppresses the generated anisotropy.« less
On spectral synthesis on element-wise compact Abelian groups
NASA Astrophysics Data System (ADS)
Platonov, S. S.
2015-08-01
Let G be an arbitrary locally compact Abelian group and let C(G) be the space of all continuous complex-valued functions on G. A closed linear subspace \\mathscr H\\subseteq C(G) is referred to as an invariant subspace if it is invariant with respect to the shifts τ_y\\colon f(x)\\mapsto f(xy), y\\in G. By definition, an invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis if \\mathscr H coincides with the closure in C(G) of the linear span of all characters of G belonging to \\mathscr H. We say that strict spectral synthesis holds in the space C(G) on G if every invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis. An element x of a topological group G is said to be compact if x is contained in some compact subgroup of G. A group G is said to be element-wise compact if all elements of G are compact. The main result of the paper is the proof of the fact that strict spectral synthesis holds in C(G) for a locally compact Abelian group G if and only if G is element-wise compact. Bibliography: 14 titles.
Non-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbations
NASA Astrophysics Data System (ADS)
Ariznabarreta, Gerardo; García-Ardila, Juan C.; Mañas, Manuel; Marcellán, Francisco
2018-05-01
In this paper, Geronimus–Uvarov perturbations for matrix orthogonal polynomials on the real line are studied and then applied to the analysis of non-Abelian integrable hierarchies. The orthogonality is understood in full generality, i.e. in terms of a nondegenerate continuous sesquilinear form, determined by a quasidefinite matrix of bivariate generalized functions with a well-defined support. We derive Christoffel-type formulas that give the perturbed matrix biorthogonal polynomials and their norms in terms of the original ones. The keystone for this finding is the Gauss–Borel factorization of the Gram matrix. Geronimus–Uvarov transformations are considered in the context of the 2D non-Abelian Toda lattice and noncommutative KP hierarchies. The interplay between transformations and integrable flows is discussed. Miwa shifts, τ-ratio matrix functions and Sato formulas are given. Bilinear identities, involving Geronimus–Uvarov transformations, first for the Baker functions, then secondly for the biorthogonal polynomials and its second kind functions, and finally for the τ-ratio matrix functions, are found.
Escalante, Alberto, E-mail: aescalan@ifuap.buap.mx; Manuel-Cabrera, J., E-mail: jmanuel@ifuap.buap.mx
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.more » • 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.« less
Origin of Abelian gauge symmetries in heterotic/F-theory duality
Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; ...
2016-04-07
Here, we study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, and also derive both the Calabi-Yau geometry and the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in theirmore » low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. And while the number of geometrically massless U(1)'s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)'s is found by taking into account a Stuckelberg mechanism in the lower-dimensional effective theory. Finally, in geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.« less
NASA Astrophysics Data System (ADS)
Saniga, Metod
1995-03-01
It is demonstrated that the kinematic 'peculiarity' of the early Sab galaxy NGC 4826 can easily be understood in terms of the Abelian Higgs (AH) model of spiral galaxies. A cylindrically symmetric AH vorto-source (-sink) with a disk-to-bulge ratio Omega greater than 1 is discussed and the distributions of the diagonal components of the corresponding stress-energy tensor Tmu,nu are presented. It is argued that the sign-changing component Tphiphi could account for the existence of two counter-rotating gas disks while negative values of Trr imply inward gas motions as observed in the outer and transition regions of the galaxy.
Unveiling a spinor field classification with non-Abelian gauge symmetries
NASA Astrophysics Data System (ADS)
Fabbri, Luca; da Rocha, Roldão
2018-05-01
A spinor fields classification with non-Abelian gauge symmetries is introduced, generalizing the U(1) gauge symmetries-based Lounesto's classification. Here, a more general classification, contrary to the Lounesto's one, encompasses spinor multiplets, corresponding to non-Abelian gauge fields. The particular case of SU(2) gauge symmetry, encompassing electroweak and electromagnetic conserved charges, is then implemented by a non-Abelian spinor classification, now involving 14 mixed classes of spinor doublets. A richer flagpole, dipole, and flag-dipole structure naturally descends from this general classification. The Lounesto's classification of spinors is shown to arise as a Pauli's singlet, into this more general classification.
Relativized problems with abelian phase group in topological dynamics.
McMahon, D
1976-04-01
Let (X, T) be the equicontinuous minimal transformation group with X = pi(infinity)Z(2), the Cantor group, and S = [unk](infinity)Z(2) endowed with the discrete topology acting on X by right multiplication. For any countable group T we construct a function F:X x S --> T such that if (Y, T) is a minimal transformation group, then (X x Y, S) is a minimal transformation group with the action defined by (x, y)s = [xs, yF(x, s)]. If (W, T) is a minimal transformation group and varphi:(Y, T) --> (W, T) is a homomorphism, then identity x varphi:(X x Y, S) --> (X x W, S) is a homomorphism and has many of the same properties that varphi has. For this reason, one may assume that the phase group is abelian (or S) without loss of generality for many relativized problems in topological dynamics.
Path-integral invariants in abelian Chern-Simons theory
NASA Astrophysics Data System (ADS)
Guadagnini, E.; Thuillier, F.
2014-05-01
We consider the U(1) Chern-Simons gauge theory defined in a general closed oriented 3-manifold M; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The non-perturbative path-integral is defined in the space of the gauge orbits of the connections which belong to the various inequivalent U(1) principal bundles over M; the different sectors of configuration space are labelled by the elements of the first homology group of M and are characterized by appropriate background connections. The gauge orbits of flat connections, whose classification is also based on the homology group, control the non-perturbative contributions to the mean values. The functional integration is carried out in any 3-manifold M, and the corresponding path-integral invariants turn out to be strictly related with the abelian Reshetikhin-Turaev surgery invariants.
Quantum corrections to non-Abelian SUSY theories on orbifolds
NASA Astrophysics Data System (ADS)
Groot Nibbelink, Stefan; Hillenbach, Mark
2006-07-01
We consider supersymmetric non-Abelian gauge theories coupled to hyper multiplets on five and six dimensional orbifolds, S/Z and T/Z, respectively. We compute the bulk and local fixed point renormalizations of the gauge couplings. To this end we extend supergraph techniques to these orbifolds by defining orbifold compatible delta functions. We develop their properties in detail. To cancel the bulk one-loop divergences the bulk gauge kinetic terms and dimension six higher derivative operators are required. The gauge couplings renormalize at the Z fixed points due to vector multiplet self interactions; the hyper multiplet renormalizes only non- Z fixed points. In 6D the Wess-Zumino-Witten term and a higher derivative analogue have to renormalize in the bulk as well to preserve 6D gauge invariance.
Topological degeneracy of non-Abelian states for dummies
NASA Astrophysics Data System (ADS)
Oshikawa, Masaki; Kim, Yong Baek; Shtengel, Kirill; Nayak, Chetan; Tewari, Sumanta
2007-06-01
We present a physical construction of degenerate groundstates of the Moore-Read Pfaffian states, which exhibits non-Abelian statistics, on general Riemann surface with genus g. The construction is given by a generalization of the recent argument [M.O., T. Senthil, Phys. Rev. Lett. 96 (2006) 060601] which relates fractionalization and topological order. The nontrivial groundstate degeneracy obtained by Read and Green [Phys. Rev. B 61 (2000) 10267] based on differential geometry is reproduced exactly. Some restrictions on the statistics, due to the fractional charge of the quasiparticle are also discussed. Furthermore, the groundstate degeneracy of the p + i p superconductor in two dimensions, which is closely related to the Pfaffian states, is discussed with a similar construction.
Abelianization and sequential confinement in 2 + 1 dimensions
NASA Astrophysics Data System (ADS)
Benvenuti, Sergio; Giacomelli, Simone
2017-10-01
We consider the lagrangian description of Argyres-Douglas theories of type A 2 N -1, which is a SU( N) gauge theory with an adjoint and one fundamental flavor. An appropriate reformulation allows us to map the moduli space of vacua across the duality, and to dimensionally reduce. Going down to three dimensions, we find that the adjoint SQCD "abelianizes": in the infrared it is equivalent to a N=4 linear quiver theory. Moreover, we study the mirror dual: using a monopole duality to "sequentially confine" quivers tails with balanced nodes, we show that the mirror RG flow lands on N=4 SQED with N flavors. These results make the supersymmetry enhancement explicit and provide a physical derivation of previous proposals for the three dimensional mirror of AD theories.
On spectral synthesis on zero-dimensional Abelian groups
NASA Astrophysics Data System (ADS)
Platonov, S. S.
2013-09-01
Let G be a zero-dimensional locally compact Abelian group all of whose elements are compact, and let C(G) be the space of all complex-valued continuous functions on G. A closed linear subspace \\mathscr H\\subseteq C(G) is said to be an invariant subspace if it is invariant with respect to the translations \\tau_y\\colon f(x)\\mapsto f(x+y), y\\in G. In the paper, it is proved that any invariant subspace \\mathscr H admits spectral synthesis, that is, \\mathscr H coincides with the closed linear span of the characters of G belonging to \\mathscr H. Bibliography: 25 titles.
Symplectic analysis of three-dimensional Abelian topological gravity
NASA Astrophysics Data System (ADS)
Cartas-Fuentevilla, R.; Escalante, Alberto; Herrera-Aguilar, Alfredo
2017-02-01
A detailed Faddeev-Jackiw quantization of an Abelian topological gravity is performed; we show that this formalism is equivalent and more economical than Dirac's method. In particular, we identify the complete set of constraints of the theory, from which the number of physical degrees of freedom is explicitly computed. We prove that the generalized Faddeev-Jackiw brackets and the Dirac ones coincide with each other. Moreover, we perform the Faddeev-Jackiw analysis of the theory at the chiral point, and the full set of constraints and the generalized Faddeev-Jackiw brackets are constructed. Finally we compare our results with those found in the literature and we discuss some remarks and prospects.
Scalar formalism for non-Abelian gauge theory
Hostler, L.C.
1986-09-01
The gauge field theory of an N-italic-dimensional multiplet of spin- 1/2 particles is investigated using the Klein--Gordon-type wave equation )Pi x (1+i-italicsigma) x Pi+m-italic/sup 2/)Phi = 0, Pi/sub ..mu../equivalentpartial/partiali-italicx-italic/sub ..mu../-e-italicA-italic/sub ..mu../, investigated before by a number of authors, to describe the fermions. Here Phi is a 2 x 1 Pauli spinor, and sigma repesents a Lorentz spin tensor whose components sigma/sub ..mu..//sub ..nu../ are ordinary 2 x 2 Pauli spin matrices. Feynman rules for the scalar formalism for non-Abelian gauge theory are derived starting from the conventional field theory of the multiplet and converting it to the new description. Themore » equivalence of the new and the old formalism for arbitrary radiative processes is thereby established. The conversion to the scalar formalism is accomplished in a novel way by working in terms of the path integral representation of the generating functional of the vacuum tau-functions, tau(2,1, xxx 3 xxx)equivalent<0-chemically bondT-italic(Psi/sub in/(2) Psi-bar/sub in/(1) xxx A-italic/sub ..mu../(3)/sub in/ xxx S-italic)chemically bond0->, where Psi/sub in/ is a Heisenberg operator belonging to a 4N-italic x 1 Dirac wave function of the multiplet. The Feynman rules obtained generalize earlier results for the Abelian case of quantum electrodynamics.« less
Non-Abelian S =1 chiral spin liquid on the kagome lattice
NASA Astrophysics Data System (ADS)
Liu, Zheng-Xin; Tu, Hong-Hao; Wu, Ying-Hai; He, Rong-Qiang; Liu, Xiong-Jun; Zhou, Yi; Ng, Tai-Kai
2018-05-01
We study S =1 spin liquid states on the kagome lattice constructed by Gutzwiller-projected px+i py superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices S and T , we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the S O (3) 1 (or, equivalently, S U (2) 2 ) field-theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study, we observe a topological phase transition from the NACSL to the Z2 Abelian spin liquid.
Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene.
Wu, Ying-Hai; Shi, Tao; Jain, Jainendra K
2017-08-09
The current proposals for producing non-Abelian anyons and Majorana particles, which are neither fermions nor bosons, are primarily based on the realization of topological superconductivity in two dimensions. We show theoretically that the unique Landau level structure of bilayer graphene provides a new possible avenue for achieving such exotic particles. Specifically, we demonstrate the feasibility of a "parton" fractional quantum Hall (FQH) state, which supports non-Abelian particles without the usual topological superconductivity. Furthermore, we advance this state as the fundamental explanation of the puzzling 1/2 FQH effect observed in bilayer graphene [ Kim et al. Nano Lett. 2015 , 15 , 7445 ] and predict that it will also occur in trilayer graphene. We indicate experimental signatures that differentiate the parton state from other candidate non-Abelian FQH states and predict that a transverse electric field can induce a topological quantum phase transition between two distinct non-Abelian FQH states.
A non-perturbative argument for the non-abelian Higgs mechanism
De Palma, G.; INFN, Sezione di Pisa, Pisa; Strocchi, F., E-mail: franco.strocchi@sns.it
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.
Non-Abelian Berry phase, instantons, and N=(0,4) supersymmetry
Laia, Joao N.
2010-12-15
In supersymmetric quantum mechanics, the non-Abelian Berry phase is known to obey certain differential equations. Here we study N=(0,4) systems and show that the non-Abelian Berry connection over R{sup 4n} satisfies a generalization of the self-dual Yang-Mills equations. Upon dimensional reduction, these become the tt* equations. We further study the Berry connection in N=(4,4) theories and show that the curvature is covariantly constant.
Mross, David F; Essin, Andrew; Alicea, Jason; Stern, Ady
2016-01-22
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 Z_{4} parafermion zero modes.
Radially separated classical lumps in non-Abelian gauge models
NASA Astrophysics Data System (ADS)
Burzlaff, Jürgen
1985-04-01
We search for smooth and time-independent finite-energy solutions to Yang-Mills-Higgs theory with an arbitrary compact gauge group. Excluding the monopole solutions which have been studied before, we concentrate on configurations with no long-range fields, which include the saddle points corresponding to noncontractible (hyper-) loops. It is shown that if the radial dependence of the fields is factorized, only one solution satisfies all these conditions. This solution is the one which has been studied before by Dashen, Hasslacher, and Neveu and by Boguta, and whose existence has recently been proved rigorously. Formulas for the asymptotic behavior of this solution are given.
Avalanches, breathers, and flow reversal in a continuous Lorenz-96 model
NASA Astrophysics Data System (ADS)
Blender, R.; Wouters, J.; Lucarini, V.
2013-07-01
For the discrete model suggested by Lorenz in 1996, a one-dimensional long-wave approximation with nonlinear excitation and diffusion is derived. The model is energy conserving but non-Hamiltonian. In a low-order truncation, weak external forcing of the zonal mean flow induces avalanchelike breather solutions which cause reversal of the mean flow by a wave-mean flow interaction. The mechanism is an outburst-recharge process similar to avalanches in a sandpile model.
Non-Abelian dark forces and the relic densities of dark glueballs
NASA Astrophysics Data System (ADS)
Forestell, Lindsay; Morrissey, David E.; Sigurdson, Kris
2017-01-01
Our understanding of the Universe is known to be incomplete, and new gauge forces beyond those of the Standard Model might be crucial to describing its observed properties. A minimal and well-motivated possibility is a pure Yang-Mills non-Abelian dark gauge force with no direct connection to the Standard Model. We determine here the relic abundances of the glueball bound states that arise in such theories and investigate their cosmological effects. Glueballs are first formed in a confining phase transition, and their relic densities are set by a network of annihilation and transfer reactions. The lightest glueball has no lighter states to annihilate into, and its yield is set mainly by 3 →2 number-changing processes which persistently release energy into the glueball gas during freeze-out. The abundances of the heavier glueballs are dominated by 2 →2 transfer reactions and tend to be much smaller than the lightest state. We also investigate potential connectors between the dark force and the Standard Model that allow some or all of the dark glueballs to decay. If the connection is weak, the lightest glueball can be very long-lived or stable and is a viable dark matter candidate. For stronger connections, the lightest glueball will decay quickly, but other heavier glueball states can remain stable and contribute to the dark matter density.
AGT relations for abelian quiver gauge theories on ALE spaces
NASA Astrophysics Data System (ADS)
Pedrini, Mattia; Sala, Francesco; Szabo, Richard J.
2016-05-01
We construct level one dominant representations of the affine Kac-Moody algebra gl̂k on the equivariant cohomology groups of moduli spaces of rank one framed sheaves on the orbifold compactification of the minimal resolution Xk of the Ak-1 toric singularity C2 /Zk. We show that the direct sum of the fundamental classes of these moduli spaces is a Whittaker vector for gl̂k, which proves the AGT correspondence for pure N = 2 U(1) gauge theory on Xk. We consider Carlsson-Okounkov type Ext-bundles over products of the moduli spaces and use their Euler classes to define vertex operators. Under the decomposition gl̂k ≃ h ⊕sl̂k, these vertex operators decompose as products of bosonic exponentials associated to the Heisenberg algebra h and primary fields of sl̂k. We use these operators to prove the AGT correspondence for N = 2 superconformal abelian quiver gauge theories on Xk.
Fast non-Abelian geometric gates via transitionless quantum driving.
Zhang, J; Kyaw, Thi Ha; Tong, D M; Sjöqvist, Erik; Kwek, Leong-Chuan
2015-12-21
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 fermionization and fractional quantum Hall transitions
NASA Astrophysics Data System (ADS)
Hui, Aaron; Mulligan, Michael; Kim, Eun-Ah
2018-02-01
There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall interplateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponent ν ≈2.3 and that ν is observed to be superuniversal, i.e., the same in the vicinity of distinct critical points [Sondhi et al., Rev. Mod. Phys. 69, 315 (1997), 10.1103/RevModPhys.69.315]. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with U (Nc) gauge group coupled to Nf=1 fermion. We study one class of theories in a controlled limit where Nf≫Nc and calculate ν to leading nontrivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent ν within the large Nf≫Nc expansion, they do offer a new parameter space of theories that is apparently different from prior works involving Abelian Chern-Simons gauge fields [Wen and Wu, Phys. Rev. Lett. 70, 1501 (1993), 10.1103/PhysRevLett.70.1501; Chen et al., Phys. Rev. B 48, 13749 (1993), 10.1103/PhysRevB.48.13749].
Non-Abelian strategies in quantum penny flip game
NASA Astrophysics Data System (ADS)
Mishima, Hiroaki
2018-01-01
In this paper, we formulate and analyze generalizations of the quantum penny flip game. In the penny flip game, one coin has two states, heads or tails, and two players apply alternating operations on the coin. In the original Meyer game, the first player is allowed to use quantum (i.e., non-commutative) operations, but the second player is still only allowed to use classical (i.e., commutative) operations. In our generalized games, both players are allowed to use non-commutative operations, with the second player being partially restricted in what operators they use. We show that even if the second player is allowed to use "phase-variable" operations, which are non-Abelian in general, the first player still has winning strategies. Furthermore, we show that even when the second player is allowed to choose one from two or more elements of the group U(2), the second player has winning strategies under certain conditions. These results suggest that there is often a method for restoring the quantum state disturbed by another agent.
Experimental realization of non-Abelian non-adiabatic geometric gates.
Abdumalikov, A A; Fink, J M; Juliusson, K; Pechal, M; Berger, S; Wallraff, A; Filipp, S
2013-04-25
The geometric aspects of quantum mechanics are emphasized most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a path in Hilbert space, that is, the space of quantum states of the system. The geometric phase is determined only by the shape of this path and is, in its simplest form, a real number. However, if the system has degenerate energy levels, then matrix-valued geometric state transformations, known as non-Abelian holonomies--the effect of which depends on the order of two consecutive paths--can be obtained. They are important, for example, for the creation of synthetic gauge fields in cold atomic gases or the description of non-Abelian anyon statistics. Moreover, there are proposals to exploit non-Abelian holonomic gates for the purposes of noise-resilient quantum computation. In contrast to Abelian geometric operations, non-Abelian ones have been observed only in nuclear quadrupole resonance experiments with a large number of spins, and without full characterization of the geometric process and its non-commutative nature. Here we realize non-Abelian non-adiabatic holonomic quantum operations on a single, superconducting, artificial three-level atom by applying a well-controlled, two-tone microwave drive. Using quantum process tomography, we determine fidelities of the resulting non-commuting gates that exceed 95 per cent. We show that two different quantum gates, originating from two distinct paths in Hilbert space, yield non-equivalent transformations when applied in different orders. This provides evidence for the non-Abelian character of the implemented holonomic quantum operations. In combination with a non-trivial two-quantum-bit gate, our method suggests a way to universal holonomic quantum computing.
Symmetric solitonic excitations of the (1 + 1)-dimensional Abelian-Higgs classical vacuum.
Diakonos, F K; Katsimiga, G C; Maintas, X N; Tsagkarakis, C E
2015-02-01
We study the classical dynamics of the Abelian-Higgs model in (1 + 1) space-time dimensions for the case of strongly broken gauge symmetry. In this limit the wells of the potential are almost harmonic and sufficiently deep, presenting a scenario far from the associated critical point. Using a multiscale perturbation expansion, the equations of motion for the fields are reduced to a system of coupled nonlinear Schrödinger equations. Exact solutions of the latter are used to obtain approximate analytical solutions for the full dynamics of both the gauge and Higgs field in the form of oscillons and oscillating kinks. Numerical simulations of the exact dynamics verify the validity of these solutions. We explore their persistence for a wide range of the model's single parameter, which is the ratio of the Higgs mass (m(H)) to the gauge-field mass (m(A)). We show that only oscillons oscillating symmetrically with respect to the "classical vacuum," for both the gauge and the Higgs field, are long lived. Furthermore, plane waves and oscillating kinks are shown to decay into oscillon-like patterns, due to the modulation instability mechanism.
New scheme for color confinement and violation of the non-Abelian Bianchi identities
NASA Astrophysics Data System (ADS)
Suzuki, Tsuneo; Ishiguro, Katsuya; Bornyakov, Vitaly
2018-02-01
A new scheme for color confinement in QCD due to violation of the non-Abelian Bianchi identities is proposed. The violation of the non-Abelian Bianchi identities (VNABI) Jμ is equal to Abelian-like monopole currents kμ defined by the violation of the Abelian-like Bianchi identities. Although VNABI is an adjoint operator satisfying the covariant conservation law DμJμ=0 , it satisfies, at the same time, the Abelian-like conservation law ∂μJμ=0 . The Abelian-like conservation law ∂μJμ=0 is also gauge-covariant. There are N2-1 conserved magnetic charges in the case of color S U (N ). The charge of each component of VNABI is quantized à la Dirac. The color-invariant eigenvalues λμ of VNABI also satisfy the Abelian conservation law ∂μλμ=0 and the magnetic charges of the eigenvalues are also quantized à la Dirac. If the color invariant eigenvalues condense in the QCD vacuum, each color component of the non-Abelian electric field Ea is squeezed by the corresponding color component of the solenoidal current Jμa. Then only the color singlets alone can survive as a physical state and non-Abelian color confinement is realized. This confinement picture is completely new in comparison with the previously studied monopole confinement scenario based on an Abelian projection after some partial gauge-fixing, where Abelian neutral states can survive as physical. To check if the scenario is realized in nature, numerical studies are done in the framework of lattice field theory by adopting pure S U (2 ) gauge theory for simplicity. Considering Jμ(x )=kμ(x ) in the continuum formulation, we adopt an Abelian-like definition of a monopole following DeGrand-Toussaint as a lattice version of VNABI, since the Dirac quantization condition of the magnetic charge is satisfied on lattice partially. To reduce severe lattice artifacts, we introduce various techniques of smoothing the thermalized vacuum. Smooth gauge fixings such as the maximal center gauge (MCG), block
Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure
NASA Astrophysics Data System (ADS)
Mong, Roger S. K.; Clarke, David J.; Alicea, Jason; Lindner, Netanel H.; Fendley, Paul; Nayak, Chetan; Oreg, Yuval; Stern, Ady; Berg, Erez; Shtengel, Kirill; Fisher, Matthew P. A.
2014-01-01
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here, we establish a similar correspondence between the Z3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that—unlike Ising anyons—allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a twofold ground-state degeneracy on a torus. In contrast to a p+ip superconductor, vortices do not yield additional particle types, yet depending on nonuniversal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.
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
Fault-tolerant Greenberger-Horne-Zeilinger paradox based on non-Abelian anyons.
Deng, Dong-Ling; Wu, Chunfeng; Chen, Jing-Ling; Oh, C H
2010-08-06
We propose a scheme to test the Greenberger-Horne-Zeilinger paradox based on braidings of non-Abelian anyons, which are exotic quasiparticle excitations of topological states of matter. Because topological ordered states are robust against local perturbations, this scheme is in some sense "fault-tolerant" and might close the detection inefficiency loophole problem in previous experimental tests of the Greenberger-Horne-Zeilinger paradox. In turn, the construction of the Greenberger-Horne-Zeilinger paradox reveals the nonlocal property of non-Abelian anyons. Our results indicate that the non-Abelian fractional statistics is a pure quantum effect and cannot be described by local realistic theories. Finally, we present a possible experimental implementation of the scheme based on the anyonic interferometry technologies.
Non-abelian anyons and topological quantum information processing in 1D wire networks
NASA Astrophysics Data System (ADS)
Alicea, Jason
2012-02-01
Topological quantum computation provides an elegant solution to decoherence, circumventing this infamous problem at the hardware level. The most basic requirement in this approach is the ability to stabilize and manipulate particles exhibiting non-Abelian exchange statistics -- Majorana fermions being the simplest example. Curiously, Majorana fermions have been predicted to arise both in 2D systems, where non-Abelian statistics is well established, and in 1D, where exchange statistics of any type is ill-defined. An important question then arises: do Majorana fermions in 1D hold the same technological promise as their 2D counterparts? In this talk I will answer this question in the affirmative, describing how one can indeed manipulate and harness the non-Abelian statistics of Majoranas in a remarkably simple fashion using networks formed by quantum wires or topological insulator edges.
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.
Non-Abelian monopole in the parameter space of point-like interactions
Ohya, Satoshi, E-mail: ohyasato@fjfi.cvut.cz
2014-12-15
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. - Highlights: • Supersymmetric quantum mechanics is an ideal playground for studying geometric phase. • We determine the parameter space of supersymmetric point-like interactions. • Berry’s connection is given by a Wu–Yang-like magnetic monopole in SU(2) Yang–Mills.
Condensation and critical exponents of an ideal non-Abelian gas
NASA Astrophysics Data System (ADS)
Talaei, Zahra; Mirza, Behrouz; Mohammadzadeh, Hosein
2017-11-01
We investigate an ideal gas obeying non-Abelian statistics and derive the expressions for some thermodynamic quantities. It is found that thermodynamic quantities are finite at the condensation point where their derivatives diverge and, near this point, they behave as \\vert T-Tc\\vert^{-ρ} in which Tc denotes the condensation temperature and ρ is a critical exponent. The critical exponents related to the heat capacity and compressibility are obtained by fitting numerical results and others are obtained using the scaling law hypothesis for a three-dimensional non-Abelian ideal gas. This set of critical exponents introduces a new universality class.
Moduli space potentials for heterotic non-Abelian flux tubes: Weak deformation
Shifman, M.; Yung, A.; Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188300
2010-09-15
We consider N=2 supersymmetric QCD with the U(N) gauge group (with no Fayet-Iliopoulos term) and N{sub f} flavors of massive quarks deformed by the mass term {mu} for the adjoint matter, W={mu}A{sup 2}, assuming that N{<=}N{sub f}<2N. This deformation breaks N=2 supersymmetry down to N=1. This theory supports non-Abelian flux tubes (strings) which are stabilized by W. They are referred to as F-term stabilized strings. We focus on the studies of such strings in the vacuum in which N squarks condense, at small {mu}, so that the Z{sub N} strings preserve, in a sense, their Bogomol'nyi-Prasad-Sommerfield nature. The (s)quark massesmore » are assumed to be nondegenerate. We calculate string tensions both in the classical and quantum regimes. Then we translate our results for the tensions in terms of the effective low-energy weighted CP(N{sub f}-1) model on the string world sheet. The bulk {mu} deformation makes this theory N=(0,2) supersymmetric heterotic weighted CP(N{sub f}-1) model in two dimensions. We find the deformation potential on the world sheet. This significantly expands the class of the heterotically deformed CP models emerging on the string world sheet compared to that suggested by Edalati and Tong. Among other things, we show that nonperturbative quantum effects in the bulk theory are exactly reproduced by the quantum effects in the world-sheet theory.« less
NASA Astrophysics Data System (ADS)
Hamhalter, Jan; Turilova, Ekaterina
2014-10-01
It is shown that any order isomorphism between the structures of unital associative JB subalgebras of JB algebras is given naturally by a partially linear Jordan isomorphism. The same holds for nonunital subalgebras and order isomorphisms preserving the unital subalgebra. Finally, we recover usual action of time evolution group on a von Neumann factor from group of automorphisms of the structure of Abelian subalgebras.
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∘.
Modified non-Abelian Toda field equations and twisted quasigraded Lie algebras
Skrypnyk, T.
We construct a new family of quasigraded Lie algebras that admit the Kostant-Adler scheme. They coincide with special quasigraded deformations of twisted subalgebras of the loop algebras. Using them we obtain new hierarchies of integrable equations in partial derivatives which we call 'modified' non-Abelian Toda field hierarchies.
Dual representation of lattice QCD with worldlines and worldsheets of Abelian color fluxes
NASA Astrophysics Data System (ADS)
Marchis, Carlotta; Gattringer, Christof
2018-02-01
We present a new dual representation for lattice QCD in terms of wordlines and worldsheets. The exact reformulation is carried out using the recently developed Abelian color flux method where the action is decomposed into commuting minimal terms that connect different colors on neighboring sites. Expanding the Boltzmann factors for these commuting terms allows one to reorganize the gauge field contributions according to links such that the gauge fields can be integrated out in closed form. The emerging constraints give the dual variables the structure of worldlines for the fermions and worldsheets for the gauge degrees of freedom. The partition sum has the form of a strong coupling expansion, and with the Abelian color flux approach discussed here all coefficients of the expansion are known in closed form. We present the dual form for three cases: pure SU(3) lattice gauge theory, strong coupling QCD and full QCD, and discuss in detail the constraints for the color fluxes and their physical interpretation.
Route to non-Abelian quantum turbulence in spinor Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Mawson, Thomas; Ruben, Gary; Simula, Tapio
2015-06-01
We have studied computationally the collision dynamics of spin-2 Bose-Einstein condensates initially confined in a triple-well trap. Depending on the phase structure of the initial-state spinor wave function, the collision of the three condensate fragments produces one of many possible vortex-antivortex lattices, after which the system transitions to quantum turbulence. We find that the emerging vortex lattice structures can be described in terms of multiwave interference. We show that the three-fragment collisions can be used to systematically produce staggered vortex-antivortex honeycomb lattices of fractional-charge vortices, whose collision dynamics are known to be non-Abelian. Such condensate collider experiments could potentially be used as a controllable pathway to generating non-Abelian superfluid turbulence with networks of vortex rungs.
Gauge equivalence of two different IAnsaaumlItze Rfor non-Abelian charged vortices
Paul, S.K.
1987-05-15
Recently the existence of non-Abelian charged vortices has been established by taking two different Ansa$uml: tze in SU(2) gauge theories. We point out that these two Ansa$uml: tze are in two topologically equivalent prescriptions. We show that they are gauge equivalent only at infinity. We also show that this gauge equivalence is not possible for Z/sub N/ vortices in SU(N) gauge theories for Ngreater than or equal to3.
Non-Abelian Yang-Mills analogue of classical electromagnetic duality
Chan, Hong-Mo; Faridani, J.; Tsun, T.S.
The classic question of non-Abelian Yang-Mills analogue to electromagnetic duality is examined here in a minimalist fashion at the strictly four-dimensional, classical field, and point charge level. A generalization of the Abelian Hodge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the Abelian theory. For example, there is a dual potential, but it is a two-indexed tensor {ital T}{sub {mu}{nu}} of the Freedman-Townsend-type. Though not itself functioning as such, {ital T}{sub {mu}{nu}} gives rise to a dual parallel transport {ital {tilde A}}{sub {mu}} for the phase of themore » wave function of the color magnetic charge, this last being a monopole of the Yang-Mills field but a source of the dual field. The standard color (electric) charge itself is found to be a monpole of {ital {tilde A}}{sub {mu}}. At the same time, the gauge symmetry is found doubled from say SU({ital N}) to SU({ital N}){times}SU({ital N}). A novel feature is that all equations of motion, including the standard Yang-Mills and Wong equations, are here derived from a ``universal`` principle, namely, the Wu-Yang criterion for monpoles, where interactions arise purely as a consequence of the topological definition of the monopole charge. The technique used is the loop space formulation of Polyakov.« less
NASA Astrophysics Data System (ADS)
Suzuki, Tsuneo
2018-02-01
Blockspin transformation of topological defects is applied to the violation of the non-Abelian Bianchi identity (VNABI) on lattice defined as Abelian monopoles. To get rid of lattice artifacts, we introduce (1) smooth gauge fixings such as the maximal center gauge (MCG), (2) blockspin transformations and (3) the tadpole-improved gauge action. The effective action can be determined by adopting the inverse Monte Carlo method. The coupling constants F (i ) of the effective action depend on the coupling of the lattice action β and the number of the blocking step n . But it is found that F (i ) satisfies a beautiful scaling; that is, they are a function of the product b =n a (β ) alone for lattice coupling constants 3.0 ≤β ≤3.9 and the steps of blocking 1 ≤n ≤12 . The effective action showing the scaling behavior can be regarded as an almost perfect action corresponding to the continuum limit, since a →0 as n →∞ for fixed b . The infrared effective monopole action keeps the global color invariance when smooth gauges such as MCG keeping the invariance are adopted. The almost perfect action showing the scaling is found to be independent of the smooth gauges adopted here as naturally expected from the gauge invariance of the continuum theory. Then we compare the results with those obtained by the analytic blocking method of topological defects from the continuum, assuming local two-point interactions are dominant as the infrared effective action. The action is formulated in the continuum limit while the couplings of these actions can be derived from simple observables calculated numerically on lattices with a finite lattice spacing. When use is made of Berezinskii-Kosterlitz-Thouless (BKT) transformation, the infrared monopole action can be transformed into that of the string model. Since large b =n a (β ) corresponds to the strong-coupling region in the string model, the physical string tension and the lowest glueball mass can be evaluated analytically
James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe; ...
2018-02-26
We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme-tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one andmore » two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro-modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.« less
James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe
We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme-tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one andmore » two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro-modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.« less
NASA Astrophysics Data System (ADS)
James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe; Robinson, Neil J.; Tsvelik, Alexei M.
2018-04-01
We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb–Liniger model, 1 + 1D quantum chromodynamics, as well as Landau–Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.
James, Andrew J A; Konik, Robert M; Lecheminant, Philippe; Robinson, Neil J; Tsvelik, Alexei M
2018-02-26
We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1 + 1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.
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.
Mimetic discretization of the Abelian Chern-Simons theory and link invariants
NASA Astrophysics Data System (ADS)
Di Bartolo, Cayetano; Grau, Javier; Leal, Lorenzo
2013-12-01
A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.
Various Forms of BRST Symmetry in Abelian 2-FORM Gauge Theory
NASA Astrophysics Data System (ADS)
Rai, Sumit Kumar; Mandal, Bhabani Prasad
We derive the various forms of BRST symmetry using Batalin-Fradkin-Vilkovisky approach in the case of Abelian 2-form gauge theory. We show that the so-called dual BRST symmetry is not an independent symmetry but the generalization of BRST symmetry obtained from the canonical transformation in the bosonic and ghost sector. We further obtain the new forms of both BRST and dual-BRST symmetry by making a general transformation in the Lagrange multipliers of the bosonic and ghost sector of the theory.
Mimetic discretization of the Abelian Chern-Simons theory and link invariants
Di Bartolo, Cayetano; Grau, Javier; Leal, Lorenzo
A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.
Abelian-Higgs phase of SU(2) QCD and glueball energy
NASA Astrophysics Data System (ADS)
Jia, Duojie
2008-07-01
It is shown that SU(2) QCD admits an dual Abelian-Higgs phase, with a Higgs vacuum of a type-II superconductor. This is done by using a connection decomposition for the gluon field and the random-direction approximation. Using a bag picture with soft wall, we presented a calculational procedure for the glueball energy based on the recent proof for wall-vortices [Nucl. Phys. B 741(2006)1]. Supported by National Natural Science Foundation of China (10547009) and Research Backbone Fostering Program of Knowledge and S&T Innovation Project of NWNU (KJCXGC 03-41)
Non-Abelian S-term dark energy and inflation
NASA Astrophysics Data System (ADS)
Rodríguez, Yeinzon; Navarro, Andrés A.
2018-03-01
We study the role that a cosmic triad in the generalized SU(2) Proca theory, specifically in one of the pieces of the Lagrangian that involves the symmetric version Sμν of the gauge field strength tensor Fμν, has on dark energy and primordial inflation. Regarding dark energy, the triad behaves asymptotically as a couple of radiation perfect fluids whose energy densities are negative for the S term but positive for the Yang-Mills term. This leads to an interesting dynamical fine-tuning mechanism that gives rise to a combined equation of state parameter ω ≃ - 1 and, therefore, to an eternal period of accelerated isotropic expansion for an ample spectrum of initial conditions. Regarding primordial inflation, one of the critical points of the associated dynamical system can describe a prolonged period of isotropic slow-roll inflation sustained by the S term. This period ends up when the Yang-Mills term dominates the energy density leading to the radiation dominated epoch. Unfortunately, in contrast to the dark energy case, the primordial inflation scenario is strongly sensitive to the coupling constants and initial conditions. The whole model, including the other pieces of the Lagrangian that involve Sμν, might evade the recent strong constraints coming from the gravitational wave signal GW170817 and its electromagnetic counterpart GRB 170817A.
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
2014-08-08
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
Some novel features in 2D non-Abelian theory: BRST approach
NASA Astrophysics Data System (ADS)
Srinivas, N.; Kumar, S.; Kureel, B. K.; Malik, R. P.
2017-08-01
Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss some novel features of a two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields). Besides the usual off-shell nilpotent and absolutely anticommutating (anti-)BRST symmetry transformations, we discuss the off-shell nilpotent and absolutely anticommutating (anti-)co-BRST symmetry transformations. Particularly, we lay emphasis on the existence of the coupled (but equivalent) Lagrangian densities of the 2D non-Abelian theory in view of the presence of (anti-)co-BRST symmetry transformations where we pin-point some novel features associated with the Curci-Ferrari (CF-)type restrictions. We demonstrate that these CF-type restrictions can be incorporated into the (anti-)co-BRST invariant Lagrangian densities through the fermionic Lagrange multipliers which carry specific ghost numbers. The modified versions of the Lagrangian densities (where we get rid of the new CF-type restrictions) respect some precise symmetries as well as a couple of symmetries with CF-type constraints. These observations are completely novel as far as the BRST formalism, with proper (anti-)co-BRST symmetries, is concerned.
Confining and repulsive potentials from effective non-Abelian gauge fields in graphene bilayers
NASA Astrophysics Data System (ADS)
González, J.
2016-10-01
We investigate the effect of shear and strain in graphene bilayers, under conditions where the distortion of the lattice gives rise to a smooth one-dimensional modulation in the stacking sequence of the bilayer. We show that strain and shear produce characteristic Moiré patterns which can have the same visual appearance on a large scale, but representing graphene bilayers with quite different electronic properties. The different features in the low-energy electronic bands can be ascribed to the effect of a fictitious non-Abelian gauge field mimicking the smooth modulation of the stacking order. Strained and sheared bilayers show a complementary behavior, which can be understood from the fact that the non-Abelian gauge field acts as a repulsive interaction in the former, expelling the electron density away from the stacking domain walls, while behaving as a confining interaction leading to localization of the electronic states in the sheared bilayers. In this latter case, the presence of the effective gauge field explains the development of almost flat low-energy bands, resembling the form of the zeroth Landau level characteristic of a Dirac fermion field. The estimate of the gauge field strength in those systems gives a magnitude of the order of several tens of tesla, implying a robust phenomenology that should be susceptible of being observed in suitably distorted bilayer samples.
Non-Abelian fractional quantum Hall states for hard-core bosons in one dimension
NASA Astrophysics Data System (ADS)
Paredes, Belén
2012-05-01
I present a family of one-dimensional bosonic liquids analogous to non-Abelian fractional quantum Hall states. A new quantum number is introduced to characterize these liquids, the chiral momentum, which differs from the usual angular or linear momentum in one dimension. As their two-dimensional counterparts, these liquids minimize a k-body hard-core interaction with the minimum total chiral momentum. They exhibit global order, with a hidden organization of the particles in k identical copies of a one-dimensional Laughlin state. For k=2 the state is a p-wave paired phase corresponding to the Pfaffian quantum Hall state. By imposing conservation of the total chiral momentum, an exact parent Hamiltonian is derived which involves long-range tunneling and interaction processes with an amplitude decaying with the chord distance. This family of non-Abelian liquids is shown to be in formal correspondence with a family of spin-(k)/(2) liquids which are total singlets made out of k indistinguishable resonating valence bond states. The corresponding spin Hamiltonians are obtained.
Lattice implementation of Abelian gauge theories with Chern-Simons number and an axion field
NASA Astrophysics Data System (ADS)
Figueroa, Daniel G.; Shaposhnikov, Mikhail
2018-01-01
Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark-gluon plasma. We present an explicit non-compact lattice formulation of the interaction between a shift-symmetric field and some U (1) gauge sector, a (x)FμνF˜μν, reproducing the continuum limit to order O (dxμ2) and obeying the following properties: (i) the system is gauge invariant and (ii) shift symmetry is exact on the lattice. For this end we construct a definition of the topological number density K =FμνF˜μν that admits a lattice total derivative representation K = Δμ+ Kμ, reproducing to order O (dxμ2) the continuum expression K =∂μKμ ∝ E → ṡ B → . If we consider a homogeneous field a (x) = a (t), the system can be mapped into an Abelian gauge theory with Hamiltonian containing a Chern-Simons term for the gauge fields. This allow us to study in an accompanying paper the real time dynamics of fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. When a (x) = a (x → , t) is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an O (dxμ2) accuracy). We discuss an iterative scheme allowing to overcome this difficulty.
A string realisation of Ω-deformed Abelian N =2* theory
NASA Astrophysics Data System (ADS)
Angelantonj, Carlo; Antoniadis, Ignatios; Samsonyan, Marine
2017-10-01
The N =2* supersymmetric gauge theory is a massive deformation of N = 4, in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-)Abelian N =2* theory, and compute suitable topological amplitudes, which are expressed as a double series expansion. The coefficients determine couplings of higher-dimensional operators in the effective supergravity action that involve powers of the anti-self-dual N = 2 chiral Weyl superfield and of self-dual gauge field strengths superpartners of the D5-brane coupling modulus. In the field theory limit, the result reproduces the Nekrasov partition function in the two-parameter Ω-background, in agreement with a recent proposal.
Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study
Zohar, Erez, E-mail: erez.zohar@mpq.mpg.de; Wahl, Thorsten B.; Burrello, Michele, E-mail: michele.burrello@mpq.mpg.de
Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of amore » simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.« less
Non-abelian factorisation for next-to-leading-power threshold logarithms
NASA Astrophysics Data System (ADS)
Bonocore, D.; Laenen, E.; Magnea, L.; Vernazza, L.; White, C. D.
2016-12-01
Soft and collinear radiation is responsible for large corrections to many hadronic cross sections, near thresholds for the production of heavy final states. There is much interest in extending our understanding of this radiation to next-to-leading power (NLP) in the threshold expansion. In this paper, we generalise a previously proposed all-order NLP factorisation formula to include non-abelian corrections. We define a nonabelian radiative jet function, organising collinear enhancements at NLP, and compute it for quark jets at one loop. We discuss in detail the issue of double counting between soft and collinear regions. Finally, we verify our prescription by reproducing all NLP logarithms in Drell-Yan production up to NNLO, including those associated with double real emission. Our results constitute an important step in the development of a fully general resummation formalism for NLP threshold effects.
Wire constructions of Abelian topological phases in three or more dimensions
NASA Astrophysics Data System (ADS)
Iadecola, Thomas; Neupert, Titus; Chamon, Claudio; Mudry, Christopher
2016-05-01
Coupled-wire constructions have proven to be useful tools to characterize Abelian and non-Abelian topological states of matter in two spatial dimensions. In many cases, their success has been complemented by the vast arsenal of other theoretical tools available to study such systems. In three dimensions, however, much less is known about topological phases. Since the theoretical arsenal in this case is smaller, it stands to reason that wire constructions, which are based on one-dimensional physics, could play a useful role in developing a greater microscopic understanding of three-dimensional topological phases. In this paper, we provide a comprehensive strategy, based on the geometric arrangement of commuting projectors in the toric code, to generate and characterize coupled-wire realizations of strongly interacting three-dimensional topological phases. We show how this method can be used to construct pointlike and linelike excitations, and to determine the topological degeneracy. We also point out how, with minor modifications, the machinery already developed in two dimensions can be naturally applied to study the surface states of these systems, a fact that has implications for the study of surface topological order. Finally, we show that the strategy developed for the construction of three-dimensional topological phases generalizes readily to arbitrary dimensions, vastly expanding the existing landscape of coupled-wire theories. Throughout the paper, we discuss Zm topological order in three and four dimensions as a concrete example of this approach, but the approach itself is not limited to this type of topological order.
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.
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.
Viennot, David
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 inmore » order to decompose the holonomy of the Lorentz connection into holonomies of the linear connection and of the Cartan connection.« less
Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries
Braun, Volker; Cvetič, Mirjam; Donagi, Ron
Here, we provide the first explicit example of Type IIB string theory compactication on a globally defined Calabi-Yau threefold with torsion which results in a fourdimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z 2 X Z 2. Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of secondmore » cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the four-dimensional theory.« less
Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries
Braun, Volker; Cvetič, Mirjam; Donagi, Ron; ...
2017-07-26
Here, we provide the first explicit example of Type IIB string theory compactication on a globally defined Calabi-Yau threefold with torsion which results in a fourdimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z 2 X Z 2. Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of secondmore » cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the four-dimensional theory.« less
NASA Astrophysics Data System (ADS)
Shifman, M.; Yung, A.
2018-03-01
Non-Abelian strings are considered in non-supersymmetric theories with fermions in various appropriate representations of the gauge group U(N). We derive the electric charge quantization conditions and the index theorems counting fermion zero modes in the string background both for the left-handed and right-handed fermions. In both cases we observe a non-trivial N dependence.
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
NASA Astrophysics Data System (ADS)
Srinivas, N.; Malik, R. P.
2017-11-01
We derive the off-shell nilpotent symmetries of the two (1 + 1)-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci-Ferrari (CF)-type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen (2, 2)-dimensional supermanifold. The latter is parametrized by the superspace coordinates ZM = (xμ,𝜃,𝜃¯) where xμ (with μ = 0, 1) are the bosonic coordinates and a pair of Grassmannian variables (𝜃,𝜃¯) obey the relationships: 𝜃2 = 𝜃¯2 = 0, 𝜃𝜃¯ + 𝜃¯𝜃 = 0. The topological nature of our 2D theory allows the existence of a tower of CF-type restrictions.
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.
Topological defects in the Georgi-Machacek model
NASA Astrophysics Data System (ADS)
Chatterjee, Chandrasekar; Kurachi, Masafumi; Nitta, Muneto
2018-06-01
We study topological defects in the Georgi-Machacek model in a hierarchical symmetry breaking in which extra triplets acquire vacuum expectation values before the doublet. We find a possibility of topologically stable non-Abelian domain walls and non-Abelian flux tubes (vortices or cosmic strings) in this model. In the limit of the vanishing U (1 )Y gauge coupling in which the custodial symmetry becomes exact, the presence of a vortex spontaneously breaks the custodial symmetry, giving rise to S2 Nambu-Goldstone (NG) modes localized around the vortex corresponding to non-Abelian fluxes. Vortices are continuously degenerated by these degrees of freedom, thereby called non-Abelian. By taking into account the U (1 )Y gauge coupling, the custodial symmetry is explicitly broken, the NG modes are lifted to become pseudo-NG modes, and all non-Abelian vortices fall into a topologically stable Z string. This is in contrast to the standard model in which Z strings are nontopological and are unstable in the realistic parameter region. Non-Abelian domain walls also break the custodial symmetry and are accompanied by localized S2 NG modes. Finally, we discuss the existence of domain wall solutions bounded by flux tubes, where their S2 NG modes match. The domain walls may quantum mechanically decay by creating a hole bounded by a flux tube loop, and would be cosmologically safe. Gravitational waves produced from unstable domain walls could be detected by future experiments.
Non-Abelian Geometric Phases Carried by the Quantum Noise Matrix
NASA Astrophysics Data System (ADS)
Bharath, H. M.; Boguslawski, Matthew; Barrios, Maryrose; Chapman, Michael
2017-04-01
Topological phases of matter are characterized by topological order parameters that are built using Berry's geometric phase. Berry's phase is the geometric information stored in the overall phase of a quantum state. We show that geometric information is also stored in the second and higher order spin moments of a quantum spin system, captured by a non-abelian geometric phase. The quantum state of a spin-S system is uniquely characterized by its spin moments up to order 2S. The first-order spin moment is the spin vector, and the second-order spin moment represents the spin fluctuation tensor, i.e., the quantum noise matrix. When the spin vector is transported along a loop in the Bloch ball, we show that the quantum noise matrix picks up a geometric phase. Considering spin-1 systems, we formulate this geometric phase as an SO(3) operator. Geometric phases are usually interpreted in terms of the solid angle subtended by the loop at the center. However, solid angles are not well defined for loops that pass through the center. Here, we introduce a generalized solid angle which is well defined for all loops inside the Bloch ball, in terms of which, we interpret the SO(3) geometric phase. This geometric phase can be used to characterize topological spin textures in cold atomic clouds.
Experimental state control by fast non-Abelian holonomic gates with a superconducting qutrit
NASA Astrophysics Data System (ADS)
Danilin, S.; Vepsäläinen, A.; Paraoanu, G. S.
2018-05-01
Quantum state manipulation with gates based on geometric phases acquired during cyclic operations promises inherent fault-tolerance and resilience to local fluctuations in the control parameters. Here we create a general non-Abelian and non-adiabatic holonomic gate acting in the (∣0〉, ∣2〉) subspace of a three-level (qutrit) transmon device fabricated in a fully coplanar design. Experimentally, this is realized by simultaneously coupling the first two transitions by microwave pulses with amplitudes and phases defined such that the condition of parallel transport is fulfilled. We demonstrate the creation of arbitrary superpositions in this subspace by changing the amplitudes of the pulses and the relative phase between them. We use two-photon pulses acting in the holonomic subspace to reveal the coherence of the state created by the geometric gate pulses and to prepare different superposition states. We also test the action of holonomic NOT and Hadamard gates on superpositions in the (| 0> ,| 2> ) subspace.
Scaling analysis of the non-Abelian quasiparticle tunneling in Z}}_k FQH states
NASA Astrophysics Data System (ADS)
Li, Qi; Jiang, Na; Wan, Xin; Hu, Zi-Xiang
2018-06-01
Quasiparticle tunneling between two counter propagating edges through point contacts could provide information on its statistics. Previous study of the short distance tunneling displays a scaling behavior, especially in the conformal limit with zero tunneling distance. The scaling exponents for the non-Abelian quasiparticle tunneling exhibit some non-trivial behaviors. In this work, we revisit the quasiparticle tunneling amplitudes and their scaling behavior in a full range of the tunneling distance by putting the electrons on the surface of a cylinder. The edge–edge distance can be smoothly tuned by varying the aspect ratio for a finite size cylinder. We analyze the scaling behavior of the quasiparticles for the Read–Rezayi states for and 4 both in the short and long tunneling distance region. The finite size scaling analysis automatically gives us a critical length scale where the anomalous correction appears. We demonstrate this length scale is related to the size of the quasiparticle at which the backscattering between two counter propagating edges starts to be significant.
Scaling analysis of the non-Abelian quasiparticle tunneling in [Formula: see text] FQH states.
Li, Qi; Jiang, Na; Wan, Xin; Hu, Zi-Xiang
2018-06-27
Quasiparticle tunneling between two counter propagating edges through point contacts could provide information on its statistics. Previous study of the short distance tunneling displays a scaling behavior, especially in the conformal limit with zero tunneling distance. The scaling exponents for the non-Abelian quasiparticle tunneling exhibit some non-trivial behaviors. In this work, we revisit the quasiparticle tunneling amplitudes and their scaling behavior in a full range of the tunneling distance by putting the electrons on the surface of a cylinder. The edge-edge distance can be smoothly tuned by varying the aspect ratio for a finite size cylinder. We analyze the scaling behavior of the quasiparticles for the Read-Rezayi [Formula: see text] states for [Formula: see text] and 4 both in the short and long tunneling distance region. The finite size scaling analysis automatically gives us a critical length scale where the anomalous correction appears. We demonstrate this length scale is related to the size of the quasiparticle at which the backscattering between two counter propagating edges starts to be significant.
Non-Abelian fermion parity interferometry of Majorana bound states in a Fermi sea
NASA Astrophysics Data System (ADS)
Dahan, Daniel; Tanhayi Ahari, Mostafa; Ortiz, Gerardo; Seradjeh, Babak; Grosfeld, Eytan
We study the quantum dynamics of Majorana and regular fermion bound states coupled to a one-dimensional lead. The dynamics following the quench in the coupling to the lead exhibits a series of dynamical revivals as the bound state propagates in the lead and reflects from the boundaries. We show that the nature of revivals for a single Majorana bound state depends uniquely on the presence of a resonant level in the lead. When two spatially separated Majorana modes are coupled to the lead, the revivals depend only on the phase difference between their host superconductors. Remarkably, the quench in this case effectively performs a fermion-parity interferometry between Majorana bound states, revealing their unique non-Abelian braiding. Using both analytical and numerical techniques, we find the pattern of fermion parity transfers following the quench, study its evolution in the presence of disorder and interactions, and thus, ascertain the fate of Majorana in a rough Fermi sea. Work supported in part by BSF Grant No. 2014345, ISF Grant Nos. 401/12 and 1626/16, EU Seventh Framework Programme (FP7/2007-2013) Grant No. 303742, NSF CAREER Grant DMR-1350663 and the College of Arts and Sciences at Indiana University.
Discontinuous decompaction of a falling sandpile
NASA Astrophysics Data System (ADS)
Duran, J.; Mazozi, T.; Luding, S.; Clément, E.; Rajchenbach, J.
1996-02-01
We investigate experimentally and via computer simulations the fall of a two dimensional granular material in a rectangular container with friction only at lateral walls. We study the decompaction modes of the granular assembly, which is a basic question relevant to the general dynamics of a noncohesive powder. We observe during the fall the possible occurrence of successive cracks splitting the initial pile into smaller blocks as time passes. These cracks preferentially occur in the lower part of the array, resulting in an ascending decompaction wave in the bulk. We show experimentally how this effect is related to the surface roughness of the boundaries. A heuristic continuum theory is proposed that rationalizes the experimental results. Furthermore, event driven simulations, including particle rotations and friction, parallel nicely the experimental observations. In the simulations, we find strong pressure fluctuations at the boundaries correlated to the occurrence of arches.
Temme, F P
2004-03-01
The physics of dual group scalar invariants (SIs) as (Lie algebraic) group measures (L-GMs) and its significance to non-Abelian NMR spin systems motivates this overview of uniform general-2n [AX](2n) spin evolution, which represents an extensive addendum to Corio's earlier (essentially restricted) view of Abelian spin system SU(2)-based SI-cardinalities. The [Formula: see text] values in [J. Magn. Reson., 134 (1998) 131] arise from strictly linear recoupled time-reversal invariance (TRI) models. In contrast, here we discuss the physical significance of an alternative polyhedral combinatorics approach to democratic recoupling (DR), a property inherent in both the TRI and statistical sampling. Recognition of spin ensemble SIs as being L-GMs over isomorphic algebras is invaluable in many DR-based NMR problems. Various [AX]n model spin systems, including the [AX]3 bis odd-odd parity spin system, are examined as direct applications of these L-GM- and combinatorial-based SI ideas. Hence in place of /SI/=15 (implied by Corio's [Formula: see text] approach), the bis 3-fold spin system cardinality is seen now as constrained to a single invariant on an isomorphic product algebra under L-GMs, in accord with the subspectral analysis of Jones et al. [Canad. J. Chem., 43 (1965) 683]. The group projective ideas cited here for DR (as cf. to graph theoretic views) apply to highly degenerate non-Abelian problems. Over dual tensorial bases, they define models of spin dynamical evolution whose (SR) quasiparticle superboson carrier (sub)spaces are characterised by SIs acting as explicit auxiliary labels [Physica, A198 (1993) 245; J. Math. Chem., 31 (2002) 281]. A deeper [Formula: see text] network-based view of spin-alone space developed in Balasubramanian's work [J. Chem. Phys., 78 (1983) 6358] is especially important, (e.g.) in the study of spin waves [J. Math. Chem., 31 (2002) 363]. Beyond the specific NMR SIs derived here, there are DR applications where a sporadic, still higher, 2
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)
Greschner, S.; Piraud, M.; Heidrich-Meisner, F.; McCulloch, I. P.; Schollwöck, U.; Vekua, T.
2016-12-01
We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex fluids, vortex lattices, charge density waves, and the biased-ladder phase. Our work focuses on the subset of these states that breaks a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.
NASA Astrophysics Data System (ADS)
Canfora, Fabrizio; Giacomini, Alex; Oliva, Julio
2010-08-01
It is shown that on curved backgrounds, the Coulomb gauge Faddeev-Popov operator can have zero modes even in the Abelian case. These zero modes cannot be eliminated by restricting the path integral over a certain region in the space of gauge potentials. The conditions for the existence of these zero modes are studied for static spherically symmetric spacetimes in arbitrary dimensions. For this class of metrics, the general analytic expression of the metric components in terms of the zero modes is constructed. Such expression allows one to find the asymptotic behavior of background metrics, which induce zero modes in the Coulomb gauge, an interesting example being the three-dimensional anti-de Sitter spacetime. Some of the implications for quantum field theory on curved spacetimes are discussed.
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 C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10(12) many-body states. While our calculated energy lies within the 0.3 mEh 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 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a(3)Πu, b(3)Σg (-), A(1)Πu, c(3)Σu (+), B(1)Δg, B(') (1)Σg (+), d(3)Πg, and C(1)Πg 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 (1)Σg (+), (1)Σu (+), (1)Σg (-), and (1)Σu (-), to an estimated accuracy of 0.1 mEh of the exact result in this basis.
NASA Astrophysics Data System (ADS)
Sharma, Sandeep
2015-01-01
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 C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 1012 many-body states. While our calculated energy lies within the 0.3 mEh 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 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a3Πu, b 3 Σg - , A1Πu, c 3 Σu + , B1Δg, B ' 1 Σg + , d3Πg, and C1Πg 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 1 Σg + , 1 Σu + , 1 Σg - , and 1 Σu - , to an estimated accuracy of 0.1 mEh of the exact result in this basis.
An approach to collective behavior in cell cultures: modeling and analysis of ECIS data
NASA Astrophysics Data System (ADS)
Rabson, David; Lafalce, Evan; Lovelady, Douglas; Lo, Chun-Min
2011-03-01
We review recent results in which statistical measures of noise in ECIS data distinguished healthy cell cultures from cancerous or poisoned ones: after subtracting the ``signal,'' the 1 /fα noise in the healthy cultures shows longer short-time and long-time correlations. We discuss application of an artificial neural network to detect the cancer signal, and we demonstrate a computational model of cell-cell communication that produces signals similar to those of the experimental data. The simulation is based on the q -state Potts model with inspiration from the Bak-Tang-Wiesenfeld sand-pile model. We view the level of organization larger than cells but smaller than organs or tissues as a kind of ``mesoscopic'' biological physics, in which few-body interactions dominate, and the experiments and computational model as ways of exploring this regime.
Sharma, Sandeep, E-mail: sanshar@gmail.com
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 ofmore » 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.« less
More on ghosts in the Dvali-Gabadaze-Porrati model
Gorbunov, Dmitry; Sibiryakov, Sergei; Koyama, Kazuya
2006-02-15
It is shown by an explicit calculation that the excitations about the self-accelerating cosmological solution of the Dvali-Gabadaze-Porrati model contain a ghost mode. This raises serious doubts about viability of this solution. Our analysis reveals the similarity between the quadratic theory for the perturbations around the self-accelerating universe and an Abelian gauge model with two Stueckelberg fields.
The Kitaev honeycomb model on surfaces of genus g ≥ 2
NASA Astrophysics Data System (ADS)
Brennan, John; Vala, Jiří
2018-05-01
We present a construction of the Kitaev honeycomb lattice model on an arbitrary higher genus surface. We first generalize the exact solution of the model based on the Jordan–Wigner fermionization to a surface with genus g = 2, and then use this as a basic module to extend the solution to lattices of arbitrary genus. We demonstrate our method by calculating the ground states of the model in both the Abelian doubled {Z}}}2 phase and the non-Abelian Ising topological phase on lattices with the genus up to g = 6. We verify the expected ground state degeneracy of the system in both topological phases and further illuminate the role of fermionic parity in the Abelian phase.
NASA Astrophysics Data System (ADS)
Sachs, M. K.; Yoder, M. R.; Turcotte, D. L.; Rundle, J. B.; Malamud, B. D.
2012-05-01
Extreme events that change global society have been characterized as black swans. The frequency-size distributions of many natural phenomena are often well approximated by power-law (fractal) distributions. An important question is whether the probability of extreme events can be estimated by extrapolating the power-law distributions. Events that exceed these extrapolations have been characterized as dragon-kings. In this paper we consider extreme events for earthquakes, volcanic eruptions, wildfires, landslides and floods. We also consider the extreme event behavior of three models that exhibit self-organized criticality (SOC): the slider-block, forest-fire, and sand-pile models. Since extrapolations using power-laws are widely used in probabilistic hazard assessment, the occurrence of dragon-king events have important practical implications.
NASA Astrophysics Data System (ADS)
Pareek, Tribhuvan Prasad
2015-09-01
In this article, we develop an exact (nonadiabatic, nonperturbative) density matrix scattering theory for a two component quantum liquid which interacts or scatters off from a generic spin-dependent quantum potential. The generic spin dependent quantum potential [Eq. (1)] is a matrix potential, hence, adiabaticity criterion is ill-defined. Therefore the full matrix potential should be treated nonadiabatically. We succeed in doing so using the notion of vectorial matrices which allows us to obtain an exact analytical expression for the scattered density matrix (SDM), ϱsc [Eq. (30)]. We find that the number or charge density in scattered fluid, Tr(ϱsc), expressions in Eqs. (32) depends on nontrivial quantum interference coefficients, Qα β 0ijk, which arises due to quantum interference between spin-independent and spin-dependent scattering amplitudes and among spin-dependent scattering amplitudes. Further it is shown that Tr(ϱsc) can be expressed in a compact form [Eq. (39)] where the effect of quantum interference coefficients can be included using a vector Qαβ, which allows us to define a vector order parameterQ. Since the number density is obtained using an exact scattered density matrix, therefore, we do not need to prove that Q is non-zero. However, for sake of completeness, we make detailed mathematical analysis for the conditions under which the vector order parameterQ would be zero or nonzero. We find that in presence of spin-dependent interaction the vector order parameterQ is necessarily nonzero and is related to the commutator and anti-commutator of scattering matrix S with its dagger S† [Eq. (78)]. It is further shown that Q≠0, implies four physically equivalent conditions,i.e., spin-orbital entanglement is nonzero, non-Abelian scattering phase, i.e., matrices, scattering matrix is nonunitary and the broken time reversal symmetry for SDM. This also implies that quasi particle excitation are anyonic in nature, hence, charge fractionalization is a
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.
NASA Astrophysics Data System (ADS)
Temme, F. P.
2004-03-01
The physics of dual group scalar invariants (SIs) as (Lie algebraic) group measures (L-GMs) and its significance to non-Abelian NMR spin systems motivates this overview of uniform general-2 n [ AX] 2 n spin evolution, which represents an extensive addendum to Corio's earlier (essentially restricted) view of Abelian spin system SU(2)-based SI-cardinalities. The |D 0( U)|((⊗SU(2)) (2n))|SI| values in [J. Magn. Reson., 134 (1998) 131] arise from strictly linear recoupled time-reversal invariance (TRI) models. In contrast, here we discuss the physical significance of an alternative polyhedral combinatorics approach to democratic recoupling (DR), a property inherent in both the TRI and statistical sampling. Recognition of spin ensemble SIs as being L-GMs over isomorphic algebras is invaluable in many DR-based NMR problems. Various [ AX] n model spin systems, including the [ AX] 3bis odd-odd parity spin system, are examined as direct applications of these L-GM- and combinatorial-based SI ideas. Hence in place of | SI|=15 (implied by Corio's | D0|((⊗ SU(2)) 2 n) approach), the bis 3-fold spin system cardinality is seen now as constrained to a single invariant on an isomorphic product algebra under L-GMs, in accord with the subspectral analysis of Jones et al. [Canad. J. Chem., 43 (1965) 683]. The group projective ideas cited here for DR (as cf. to graph theoretic views) apply to highly degenerate non-Abelian problems. Over dual tensorial bases, they define models of spin dynamical evolution whose (SR) quasiparticle superboson carrier (sub)spaces are characterised by SIs acting as explicit auxiliary labels [Physica, A198 (1993) 245; J. Math. Chem., 31 (2002) 281]. A deeper S2n network-based view of spin-alone space developed in Balasubramanian's work [J. Chem. Phys., 78 (1983) 6358] is especially important, (e.g.) in the study of spin waves [J. Math. Chem., 31 (2002) 363]. Beyond the specific NMR SIs derived here, there are DR applications where a sporadic, still
Inhomogeneous generalizations of Bianchi type VIh models with perfect fluid
NASA Astrophysics Data System (ADS)
Roy, S. R.; Prasad, A.
1991-07-01
Inhomogeneous universes admitting an Abelian G2 of isometry and filled with perfect fluid have been derived. These contain as special cases exact homogeneous universes of Bianchi type VIh. Many of these universes asymptotically tend to homogeneous Bianchi VIh universes. The models have been discussed for their physical and kinematical behaviors.
Non-abelian vector boson dark matter, its unified route and signatures at the LHC
NASA Astrophysics Data System (ADS)
Barman, Basabendu; Bhattacharya, Subhaditya; Patra, Sunando Kumar; Chakrabortty, Joydeep
2017-12-01
Vector boson dark matter (DM) appears in SU(2)N extension (N stands for neutral) of Standard Model (SM) where an additional global U(1)P symmetry is assumed and results in a generalized lepton number defined as: L=P+T3N. Breaking of U(1)P leads to the breaking of L to (‑1)L, thus stabilizing DM through modified R=(‑1)3B+L+2J. This model, already discussed in literature, offers several novel features to elaborate upon. For example, t-channel annihilation and dominant s-channel direct search, along with co-annihilation, helps the DM to evade stringent direct search bounds from LUX and XENON1T after satisfying relic density constraints. On the other hand, the exotic particles of the model can be produced at the Large Hadron Collider (LHC) yielding multilepton final states. Hadronically quiet four lepton signal with large missing energy, in specific, is shown to provide a smoking gun signature of such a framework. We study the details of E(6) → SM SU(2)N breaking patterns (through D-parity odd/even cases) which yield important phenomenological consequences.
Lorentz-violating SO(3) model: Discussing unitarity, causality, and 't Hooft-Polyakov monopoles
Scarpelli, A.P. Baeta; Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ; Helayeel-Neto, J.A.
2006-05-15
In this paper, we extend the analysis of the Lorentz-violating Quantum Electrodynamics to the non-Abelian case: an SO(3) Yang-Mills Lagrangian with the addition of the non-Abelian Chern-Simons-type term. We consider the spontaneous symmetry breaking of the model and inspect its spectrum in order to check if unitarity and causality are respected. An analysis of the topological structure is also carried out and we show that a 't Hooft-Polyakov solution for monopoles is still present.
Holographic entropy and real-time dynamics of quarkonium dissociation in non-Abelian plasma
Iatrakis, Ioannis; Kharzeev, Dmitri E.
2016-04-26
The peak of the heavy quark pair entropy at the deconfinement transition, observed in lattice QCD, suggests that the transition is effectively driven by the increase of the entropy of bound states. The growth of the entropy with the interquark distance leads to the emergent entropic force that induces dissociation of quarkonium states. Since the quark-gluon plasma around the transition point is a strongly coupled system, we use the gauge-gravity duality to study the entropy of heavy quarkonium and the real-time dynamics of its dissociation. In particular, we employ the improved holographic QCD model as a dual description of largemore » N c Yang-Mills theory. Studying the dynamics of the fundamental string between the quarks placed on the boundary, we find that the entropy peaks at the transition point. We also study the real-time dynamics of the system by considering the holographic string falling in the black hole horizon where it equilibrates. As a result, in the vicinity of the deconfinement transition, the dissociation time is found to be less than a fermi, suggesting that the entropic destruction is the dominant dissociation mechanism in this temperature region.« less
Dark matter and neutrino mass from the smallest non-Abelian chiral dark sector
NASA Astrophysics Data System (ADS)
Berryman, Jeffrey M.; de Gouvêa, André; Kelly, Kevin J.; Zhang, Yue
2017-10-01
All pieces of concrete evidence for phenomena outside the standard model (SM)—neutrino masses and dark matter—are consistent with the existence of new degrees of freedom that interact very weakly, if at all, with those in the SM. We propose that these new degrees of freedom organize themselves into a simple dark sector, a chiral S U (3 )×S U (2 ) gauge theory with the smallest nontrivial fermion content. Similar to the SM, the dark S U (2 ) is spontaneously broken while the dark S U (3 ) confines at low energies. At the renormalizable level, the dark sector contains massless fermions—dark leptons—and stable massive particles—dark protons. We find that dark protons with masses between 10 and 100 TeV satisfy all current cosmological and astrophysical observations concerning dark matter even if dark protons are a symmetric thermal relic. The dark leptons play the role of right-handed neutrinos and allow simple realizations of the seesaw mechanism or the possibility that neutrinos are Dirac fermions. In the latter case, neutrino masses are also parametrically different from charged-fermion masses and the lightest neutrino is predicted to be massless. Since the new "neutrino" and "dark-matter" degrees of freedom interact with one another, these two new-physics phenomena are intertwined. Dark leptons play a nontrivial role in early Universe cosmology while indirect searches for dark matter involve, decisively, dark-matter annihilations into dark leptons. These, in turn, may lead to observable signatures at high-energy neutrino and gamma-ray observatories, especially once one accounts for the potential Sommerfeld enhancement of the annihilation cross section, derived from the low-energy dark-sector effective theory, a possibility we explore quantitatively in some detail.
Asymptotically safe standard model extensions?
NASA Astrophysics Data System (ADS)
Pelaggi, Giulio Maria; Plascencia, Alexis D.; Salvio, Alberto; Sannino, Francesco; Smirnov, Juri; Strumia, Alessandro
2018-05-01
We consider theories with a large number NF of charged fermions and compute the renormalization group equations for the gauge, Yukawa and quartic couplings resummed at leading order in 1 /NF. We construct extensions of the standard model where SU(2) and/or SU(3) are asymptotically safe. When the same procedure is applied to the Abelian U(1) factor, we find that the Higgs quartic can not be made asymptotically safe and stay perturbative at the same time.
NASA Astrophysics Data System (ADS)
Adler, Stephen L.
2018-02-01
We give a detailed analysis of an Abelianized gauge field model in which a Rarita-Schwinger spin-3/2 field is directly coupled to a spin-1/2 field. The model permits a perturbative expansion in powers of the gauge field coupling, and from the Feynman rules for the model we calculate the chiral anomaly.
ERIC Educational Resources Information Center
Kohl, Timothy
2012-01-01
A pair of elementary exercises, one from topology, the other from group theory are such that if one replaces three words in the topology problem, you get the group theory problem and vice-versa. This suggests connections between the two that are explored here.
NASA Astrophysics Data System (ADS)
Wu, Tailung; Wan, Zhong; Kazakov, Aleksandr; Wang, Ying; Simion, George; Liang, Jingcheng; West, Kenneth W.; Baldwin, Kirk; Pfeiffer, Loren N.; Lyanda-Geller, Yuli; Rokhinson, Leonid P.
2018-06-01
We propose an experimentally feasible platform to realize parafermions (high-order non-Abelian excitations) based on spin transitions in the fractional quantum Hall effect regime. As a proof of concept we demonstrate a local control of the spin transition at a filling factor 2/3 and formation of a conducting fractional helical domain wall (fhDW) along a gate boundary. Coupled to an s -wave superconductor these fhDWs are expected to support parafermionic excitations. We present exact diagonalization numerical studies of fhDWs and show that they indeed possess electronic and magnetic structures needed for the formation of parafermions. A reconfigurable network of fhDWs will allow manipulation and braiding of parafermionic excitations in multigate devices.
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.
Wolf, C.
1993-02-01
We study the screening of a central Abelian dyon by a surrounding dyon cloud in a two potential theory of electromagnetism. A generalized formula for the Debye screening length is obtained and a Thomas - Fermi Model for a charged cloud surrounding a central Dyonic Core is studied. 20 refs.
Light Z' in heterotic string standardlike models
NASA Astrophysics Data System (ADS)
Athanasopoulos, P.; Faraggi, A. E.; Mehta, V. M.
2014-05-01
The discovery of the Higgs boson at the LHC supports the hypothesis that the Standard Model provides an effective parametrization of all subatomic experimental data up to the Planck scale. String theory, which provides a viable perturbative approach to quantum gravity, requires for its consistency the existence of additional gauge symmetries beyond the Standard Model. The construction of heterotic string models with a viable light Z' is, however, highly constrained. We outline the construction of standardlike heterotic string models that allow for an additional Abelian gauge symmetry that may remain unbroken down to low scales. We present a string inspired model, consistent with the string constraints.
NASA Astrophysics Data System (ADS)
Lin, Chien-Hung
2017-05-01
We generalize the string-net construction to multiple flavors of strings, each of which is labeled by the elements of an Abelian group Gi. The same flavor of strings can branch, while different flavors of strings can cross one another and thus they form intersecting string nets. We systematically construct the exactly soluble lattice Hamiltonians and the ground-state wave functions for the intersecting string-net condensed phases. We analyze the braiding statistics of the low-energy quasiparticle excitations and find that our model can realize all the topological phases as the string-net model with group G =∏iGi . In this respect, our construction provides various ways of building lattice models which realize topological order G , corresponding to different partitions of G and thus different flavors of string nets. In fact, our construction concretely demonstrates the Künneth formula by constructing various lattice models with the same topological order. As an example, we construct the G =Z2×Z2×Z2 string-net model which realizes a non-Abelian topological phase by properly intersecting three copies of toric codes.
A model for two-dimensional bursty turbulence in magnetized plasmas
Servidio, Sergio; Primavera, Leonardo; Carbone, Vincenzo
2008-01-15
The nonlinear dynamics of two-dimensional electrostatic interchange modes in a magnetized plasma is investigated through a simple model that replaces the instability mechanism due to magnetic field curvature by an external source of vorticity and mass. Simulations in a cylindrical domain, with a spatially localized and randomized source at the center of the domain, reveal the eruption of mushroom-shaped bursts that propagate radially and are absorbed by the boundaries. Burst sizes and the interburst waiting times exhibit power-law statistics, which indicates long-range interburst correlations, similar to what has been found in sandpile models for avalanching systems. It is shown frommore » the simulations that the dynamics can be characterized by a Yaglom relation for the third-order mixed moment involving the particle number density as a passive scalar and the ExB drift velocity, and hence that the burst phenomenology can be described within the framework of turbulence theory. Statistical features are qualitatively in agreement with experiments of intermittent transport at the edge of plasma devices, and suggest that essential features such as transport can be described by this simple model of bursty turbulence.« less
NASA Astrophysics Data System (ADS)
Chandran, A.; Schulz, Marc D.; Burnell, F. J.
2016-12-01
Many phases of matter, including superconductors, fractional quantum Hall fluids, and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical mechanics has primarily been studied in unconstrained Hilbert spaces. In this paper, we investigate whether constrained Hilbert spaces permit local thermalization. Specifically, we explore whether the eigenstate thermalization hypothesis (ETH) holds in a pinned Fibonacci anyon chain, which serves as a representative case study. We first establish that the constrained Hilbert space admits a notion of locality by showing that the influence of a measurement decays exponentially in space. This suggests that the constraints are no impediment to thermalization. We then provide numerical evidence that ETH holds for the diagonal and off-diagonal matrix elements of various local observables in a generic disorder-free nonintegrable model. We also find that certain nonlocal observables obey ETH.
NASA Astrophysics Data System (ADS)
Nishino, Hitoshi; Rajpoot, Subhash
2018-03-01
We formulate an N = (2 , 0) system in D = 3 + 3 dimensions consisting of a Yang-Mills (YM)-multiplet (ˆ μ ˆ IA, λˆI), a self-dual non-Abelian tensor multiplet (ˆ μ ˆ ν ˆ IB, χˆI ,φˆI), and an extra vector multiplet (C ˆ μ ˆ IC, ρˆI). We next perform the dimensional reductions of this system into D = 2 + 2, and obtain N = (1 , 1) systems with a self-dual YM-multiplet (AIμ ,λI), a self-dual tensor multiplet (BIμν , χI , φI), and an extra vector multiplet (CIμ , ρI). In D = 2 + 2, we reach two distinct theories: 'Theory-I' and 'Theory-II'. The former has the self-dual field-strength Hμν(+)I of CIμ already presented in our recent paper, while the latter has anti-self-dual field strength Hμν(-)I. As an application, we show that Theory-II actually generates supersymmetric-KdV equations in D = 1 + 1. Our result leads to a new conclusion that the D = 3 + 3 theory with non-Abelian tensor multiplet can be a 'Grand Master Theory' for self-dual multiplet and self-dual YM-multiplet in D = 2 + 2, that in turn has been conjectured to be the 'Master Theory' for all supersymmetric integrable theories in D ≤ 3.
Dashti-Naserabadi, H; Najafi, M N
2017-10-01
We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension D_{u}=4. After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions. We found that the exponent of the distribution function of avalanche mass is the same for the d-dimensional cross sections and the d-dimensional BTW model for d=2 and 3. The geometrical quantities, however, have completely different behaviors with respect to the same-dimensional BTW model. By analyzing the FSS theory for the geometrical exponents of the two-dimensional cross sections, we propose that the 2D induced models have degrees of similarity with the Gaussian free field (GFF). Although some local exponents are slightly different, this similarity is excellent for the fractal dimensions. The most important one showing this feature is the fractal dimension of loops d_{f}, which is found to be 1.50±0.02≈3/2=d_{f}^{GFF}.
NASA Astrophysics Data System (ADS)
Dashti-Naserabadi, H.; Najafi, M. N.
2017-10-01
We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension Du=4 . After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions. We found that the exponent of the distribution function of avalanche mass is the same for the d -dimensional cross sections and the d -dimensional BTW model for d =2 and 3. The geometrical quantities, however, have completely different behaviors with respect to the same-dimensional BTW model. By analyzing the FSS theory for the geometrical exponents of the two-dimensional cross sections, we propose that the 2D induced models have degrees of similarity with the Gaussian free field (GFF). Although some local exponents are slightly different, this similarity is excellent for the fractal dimensions. The most important one showing this feature is the fractal dimension of loops df, which is found to be 1.50 ±0.02 ≈3/2 =dfGFF .
A minimal model of neutrino flavor
NASA Astrophysics Data System (ADS)
Luhn, Christoph; Parattu, Krishna Mohan; Wingerter, Akın
2012-12-01
Models of neutrino mass which attempt to describe the observed lepton mixing pattern are typically based on discrete family symmetries with a non-Abelian and one or more Abelian factors. The latter so-called shaping symmetries are imposed in order to yield a realistic phenomenology by forbidding unwanted operators. Here we propose a supersymmetric model of neutrino flavor which is based on the group T 7 and does not require extra {Z} N or U(1) factors in the Yukawa sector, which makes it the smallest realistic family symmetry that has been considered so far. At leading order, the model predicts tribimaximal mixing which arises completely accidentally from a combination of the T 7 Clebsch-Gordan coefficients and suitable flavon alignments. Next-to-leading order (NLO) operators break the simple tribimaximal structure and render the model compatible with the recent results of the Daya Bay and Reno collaborations which have measured a reactor angle of around 9°. Problematic NLO deviations of the other two mixing angles can be controlled in an ultraviolet completion of the model. The vacuum alignment mechanism that we use necessitates the introduction of a hidden flavon sector that transforms under a {Z} 6 symmetry, thereby spoiling the minimality of our model whose flavor symmetry is then T 7 × {Z} 6.
Modeling the Self-Organized Critical Behavior of Earth's Plasma Sheet Reconnection Dynamics
NASA Astrophysics Data System (ADS)
Klimas, A.; Uritsky, V.; Baker, D.
2006-05-01
Analyses of Polar UVI auroral image data (Uritsky et al. JGR, 2002; GRL, 2003, 2006) show that bright night- side high-latitude UV emissions exhibit so many of the key properties of systems in self-organized criticality that an alternate interpretation has become virtually impossible. It is now necessary to find and model the source of this behavior. We note that the most common models of self-organized criticality are numerical sandpiles. These are, at root, models that govern the transport of some quantity from a region where it is loaded to another where it is unloaded. Transport is enabled by the excitation of a local threshold instability; it is intermittent and bursty, and it exhibits a number of scale-free statistical properties. Searching for a system in the magnetosphere that is analogous and that, in addition, is known to produce auroral signatures, we focus on the reconnection dynamics of the plasma sheet. In our previous work, a driven reconnection model has been constructed and has been under study (Klimas et al. JGR, 2004; GRL 2005). The transport of electromagnetic (primarily magnetic) energy carried by the Poynting flux into the reconnection region of the model has been examined. All of the analysis techniques, and more, that have been applied to the auroral image data have also been applied to this Poynting flux. Here, we report new results showing that this model also exhibits so many of the key properties of systems in self-organized criticality that an alternate interpretation is implausible. Further, we find a strong correlation between these key properties of the model and those of the auroral UV emissions. We suggest that, in general, the driven reconnection model is an important step toward a realistic plasma physical model of self-organized criticality and we conclude, more specifically, that it is also a step in the right direction toward modeling the multiscale reconnection dynamics of the magnetotail.
Modeling the Self-organized Critical Behavior of the Plasma Sheet Reconnection Dynamics
NASA Technical Reports Server (NTRS)
Klimas, Alex; Uritsky, Vadim; Baker, Daniel
2006-01-01
Analyses of Polar UVI auroral image data reviewed in our other presentation at this meeting (V. Uritsky, A. Klimas) show that bright night-side high-latitude UV emissions exhibit so many of the key properties of systems in self-organized criticality (SOC) that an alternate interpretation has become virtually impossible. It is now necessary to find and model the source of this behavior. We note that the most common models of self-organized criticality are numerical sandpiles. These are, at root, models that govern the transport of some quantity from a region where it is loaded to another where it is unloaded. Transport is enabled by the excitation of a local threshold instability; it is intermittent and bursty, and it exhibits a number of scale-free statistical properties. Searching for a system in the magnetosphere that is analogous and that, in addition, is known to produce auroral signatures, we focus on the reconnection dynamics of the plasma sheet. In our previous work, a driven reconnection model has been constructed and has been under study. The transport of electromagnetic (primarily magnetic) energy carried by the Poynting flux into the reconnection region of the model has been examined. All of the analysis techniques, and more, that have been applied to the auroral image data have also been applied to this Poynting flux. Here, we report new results showing that this model also exhibits so many of the key properties of systems in self-organized criticality that an alternate interpretation is implausible. Further, we find a strong correlation between these key properties of the model and those of the auroral UV emissions. We suggest that, in general, the driven reconnection model is an important step toward a realistic plasma physical model of self-organized criticality and we conclude, more specifically, that it is also a step in the right direction toward modeling the multiscale reconnection dynamics of the magnetotail.
Modeling the Self-organized Critical Behavior of Earth's Plasma Sheet Reconnection Dynamics
NASA Technical Reports Server (NTRS)
Klimas, Alexander J.
2006-01-01
Analyses of Polar UVI auroral image data show that bright night-side high-latitude W emissions exhibit so many of the key properties of systems in self-organized criticality that an alternate interpretation has become virtually impossible. These analyses will be reviewed. It is now necessary to find and model the source of this behavior. We note that the most common models of self-organized criticality are numerical sandpiles. These are, at root, models that govern the transport of some quantity from a region where it is loaded to another where it is unloaded. Transport is enabled by the excitation of a local threshold instability; it is intermittent and bursty, and it exhibits a number of scale-free statistical properties. Searching for a system in the magnetosphere that is analogous and that, in addition, is known to produce auroral signatures, we focus on the reconnection dynamics of the magnetotail plasma sheet. In our previous work, a driven reconnection model has been constructed and has been under study. The transport of electromagnetic (primarily magnetic) energy carried by the Poynting flux into the reconnection region of the model has been examined. All of the analysis techniques (and more) that have been applied to the auroral image data have also been applied to this Poynting flux. New results will be presented showing that this model also exhibits so many of the key properties of systems in self-organized criticality that an alternate interpretation is implausible. A strong correlation between these key properties of the model and those of the auroral UV emissions will be demonstrated. We suggest that, in general, the driven reconnection model is an important step toward a realistic plasma physical model of self-organized criticality and we conclude, more specifically, that it is also a step in the right direction toward modeling the multiscale reconnection dynamics of the magnetotail.
Spin waves, vortices, fermions, and duality in the Ising and Baxter models
Ogilvie, M.C.
1981-10-15
Field-theoretic methods are applied to a number of two-dimensional lattice models with Abelian symmetry groups. It is shown, using a vortex+spin-wave decomposition, that the Z/sub p/-Villain models are related to a class of continuum field theories with analogous duality properties. Fermion operators for these field theories are discussed. In the case of the Ising model, the vortices and spin-waves conspire to produce a free, massive Majorana field theory in the continuum limit. The continuum limit of the Baxter model is also studied, and the recent results of Kadanoff and Brown are rederived and extended.
Beta functions in Chirally deformed supersymmetric sigma models in two dimensions
NASA Astrophysics Data System (ADS)
Vainshtein, Arkady
2016-10-01
We study two-dimensional sigma models where the chiral deformation diminished the original 𝒩 = (2, 2) supersymmetry to the chiral one, 𝒩 = (0, 2). Such heterotic models were discovered previously on the world sheet of non-Abelian stringy solitons supported by certain four-dimensional 𝒩 = 1 theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the β functions in terms of the anomalous dimensions analogous to the NSVZ β function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation.
Beta Functions in Chirally Deformed Supersymmetric Sigma Models in Two Dimensions
NASA Astrophysics Data System (ADS)
Vainshtein, Arkady
We study two-dimensional sigma models where the chiral deformation diminished the original 𝒩 =(2, 2) supersymmetry to the chiral one, 𝒩 =(0, 2). Such heterotic models were discovered previously on the world sheet of non-Abelian stringy solitons supported by certain four-dimensional 𝒩 = 1 theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the β functions in terms of the anomalous dimensions analogous to the NSVZ β function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation.
Modeling electron fractionalization with unconventional Fock spaces.
Cobanera, Emilio
2017-08-02
It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion carries charge e/m and spin 1/2. Just like taking a root of a complex number, taking a root of a fermion yields a mildly non-unique result. As a consequence, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality [Formula: see text] of the lattice by basic physical considerations. One particular family of fermion-root quasiparticles is directly connected to the parafermion zero-energy modes expected to emerge in certain mesoscopic devices involving fractional quantum Hall states. Hence, as an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling.
Left passage probability of Schramm-Loewner Evolution
NASA Astrophysics Data System (ADS)
Najafi, M. N.
2013-06-01
SLE(κ,ρ⃗) is a variant of Schramm-Loewner Evolution (SLE) which describes the curves which are not conformal invariant, but are self-similar due to the presence of some other preferred points on the boundary. In this paper we study the left passage probability (LPP) of SLE(κ,ρ⃗) through field theoretical framework and find the differential equation governing this probability. This equation is numerically solved for the special case κ=2 and hρ=0 in which hρ is the conformal weight of the boundary changing (bcc) operator. It may be referred to loop erased random walk (LERW) and Abelian sandpile model (ASM) with a sink on its boundary. For the curve which starts from ξ0 and conditioned by a change of boundary conditions at x0, we find that this probability depends significantly on the factor x0-ξ0. We also present the perturbative general solution for large x0. As a prototype, we apply this formalism to SLE(κ,κ-6) which governs the curves that start from and end on the real axis.
Left passage probability of Schramm-Loewner Evolution.
Najafi, M N
2013-06-01
SLE(κ,ρ[over arrow]) is a variant of Schramm-Loewner Evolution (SLE) which describes the curves which are not conformal invariant, but are self-similar due to the presence of some other preferred points on the boundary. In this paper we study the left passage probability (LPP) of SLE(κ,ρ[over arrow]) through field theoretical framework and find the differential equation governing this probability. This equation is numerically solved for the special case κ=2 and h(ρ)=0 in which h(ρ) is the conformal weight of the boundary changing (bcc) operator. It may be referred to loop erased random walk (LERW) and Abelian sandpile model (ASM) with a sink on its boundary. For the curve which starts from ξ(0) and conditioned by a change of boundary conditions at x(0), we find that this probability depends significantly on the factor x(0)-ξ(0). We also present the perturbative general solution for large x(0). As a prototype, we apply this formalism to SLE(κ,κ-6) which governs the curves that start from and end on the real axis.
NASA Astrophysics Data System (ADS)
Jiménez, A.; Posadas, A. M.
2006-09-01
Cellular automata are simple mathematical idealizations of natural systems and they supply useful models for many investigations in natural science. Examples include sandpile models, forest fire models, and slider block models used in seismology. In the present paper, they have been used for establishing temporal relations between the energy releases of the seismic events that occurred in neighboring parts of the crust. The catalogue is divided into time intervals, and the region is divided into cells which are declared active or inactive by means of a threshold energy release criterion. Thus, a pattern of active and inactive cells which evolves over time is determined. A stochastic cellular automaton is constructed starting with these patterns, in order to simulate their spatio-temporal evolution, by supposing a Moore's neighborhood interaction between the cells. The best model is chosen by maximizing the mutual information between the past and the future states. Finally, a Probabilistic Seismic Hazard Map is given for the different energy releases considered. The method has been applied to the Greece catalogue from 1900 to 1999. The Probabilistic Seismic Hazard Maps for energies corresponding to m = 4 and m = 5 are close to the real seismicity after the data in that area, and they correspond to a background seismicity in the whole area. This background seismicity seems to cover the whole area in periods of around 25-50 years. The optimum cell size is in agreement with other studies; for m > 6 the optimum area increases according to the threshold of clear spatial resolution, and the active cells are not so clustered. The results are coherent with other hazard studies in the zone and with the seismicity recorded after the data set, as well as provide an interaction model which points out the large scale nature of the earthquake occurrence.
Geometry in transition in four dimensions: A model of emergent geometry in the early universe
NASA Astrophysics Data System (ADS)
Ydri, Badis; Khaled, Ramda; Ahlam, Rouag
2016-10-01
We study a six matrix model with global S O (3 )×S O (3 ) symmetry containing at most quartic powers of the matrices. This theory exhibits a phase transition from a geometrical phase at low temperature to a Yang-Mills matrix phase with no background geometrical structure at high temperature. This is an exotic phase transition in the same universality class as the three matrix model but with important differences. The geometrical phase is determined dynamically, as the system cools, and is given by a fuzzy sphere background SN2×SN2, with an Abelian gauge field which is very weakly coupled to two normal scalar fields.
Gauge turbulence, topological defect dynamics, and condensation in Higgs models
Gasenzer, Thomas; McLerran, Larry; Pawlowski, Jan M.; ...
2014-07-28
The real-time dynamics of topological defects and turbulent configurations of gauge fields for electric and magnetic confinement are studied numerically within a 2+1D Abelian Higgs model. It is shown that confinement is appearing in such systems equilibrating after a strong initial quench such as the overpopulation of the infrared modes. While the final equilibrium state does not support confinement, metastable vortex defect configurations appearing in the gauge field are found to be closely related to the appearance of physically observable confined electric and magnetic charges. These phenomena are seen to be intimately related to the approach of a non-thermal fixedmore » point of the far-from-equilibrium dynamical evolution, signaled by universal scaling in the gauge-invariant correlation function of the Higgs field. Even when the parameters of the Higgs action do not support condensate formation in the vacuum, during this approach, transient Higgs condensation is observed. We discuss implications of these results for the far-from-equilibrium dynamics of Yang–Mills fields and potential mechanisms of how confinement and condensation in non-Abelian gauge fields can be understood in terms of the dynamics of Higgs models. These suggest that there is an interesting new class of dynamics of strong coherent turbulent gauge fields with condensates.« less
A four-dimensional model with the fermionic determinant exactly evaluated
NASA Astrophysics Data System (ADS)
Mignaco, J. A.; Rego Monteiro, M. A.
1986-07-01
A method is presented to compute the fermion determinant of some class of field theories. By this method the following results of the fermion determinant in two dimensions are easily recovered: (i) Schwinger model without reference to a particular gauge. (ii) QCD in the light-cone gauge. (iii) Gauge invariant result of QCD. The method is finally applied to give an analytical solution of the fermion determinant of a four-dimensional, non-abelian, Dirac-like theory with massless fermions interacting with an external vector field through a pseudo-vectorial coupling. Fellow of the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), Brazil.
Constructive tensorial group field theory II: the {U(1)-T^4_4} model
NASA Astrophysics Data System (ADS)
Lahoche, Vincent
2018-05-01
In this paper, we continue our program of non-pertubative constructions of tensorial group field theories (TGFT). We prove analyticity and Borel summability in a suitable domain of the coupling constant of the simplest super-renormalizable TGFT which contains some ultraviolet divergencies, namely the color-symmetric quartic melonic rank-four model with Abelian gauge invariance, nicknamed . We use a multiscale loop vertex expansion. It is an extension of the loop vertex expansion (the basic constructive technique for non-local theories) which is required for theories that involve non-trivial renormalization.
Li, Hui; Haldane, F D M
2008-07-04
We study the "entanglement spectrum" (a presentation of the Schmidt decomposition analogous to a set of "energy levels") of a many-body state, and compare the Moore-Read model wave function for the nu=5/2 fractional quantum Hall state with a generic 5/2 state obtained by finite-size diagonalization of the second-Landau-level-projected Coulomb interactions. Their spectra share a common "gapless" structure, related to conformal field theory. In the model state, these are the only levels, while in the "generic" case, they are separated from the rest of the spectrum by a clear "entanglement gap", which appears to remain finite in the thermodynamic limit. We propose that the low-lying entanglement spectrum can be used as a "fingerprint" to identify topological order.
Cogenerating and pre-annihilating dark matter by a new gauge interaction in a unified model
Barr, S. M.; Scherrer, Robert J.
2016-05-31
Here, grand unified theories based on large groups (with rank ≥ 6) are a natural context for dark matter models. They contain Standard-Model-singlet fermions that could be dark matter candidates, and can contain new non-abelian interactions whose sphalerons convert baryons, leptons, and dark matter into each other, ''cogenerating" a dark matter asymmetry comparable to the baryon asymmetry. In this paper it is shown that the same non-abelian interactions can ''pre-annihilate" the symmetric component of heavy dark matter particles χ, which then decay late into light stable dark matter particles ζ that inherit their asymmetry. We derive cosmological constraints on themore » parameters of such models. The mass of χ must be < 3000 TeV and their decays must happen when 2 × 10 –7 < T dec/mχ < 10 –4. It is shown that such decays can come from d=5 operators with coefficients of order 1/MGUT or 1/M Pℓ. We present a simple realization of our model based on the group SU(7).« less
Poisson-Lie duals of the η deformed symmetric space sigma model
NASA Astrophysics Data System (ADS)
Hoare, Ben; Seibold, Fiona K.
2017-11-01
Poisson-Lie dualising the η deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated λ deformed model. In this paper we investigate when the η deformed model can be dualised with respect to a subgroup G0 of G. Starting from the first-order action on the complexified group and integrating out the degrees of freedom associated to different subalgebras, we find it is possible to dualise when G0 is associated to a sub-Dynkin diagram. Additional U1 factors built from the remaining Cartan generators can also be included. The resulting construction unifies both the Poisson-Lie dual with respect to G and the complete abelian dual of the η deformation in a single framework, with the integrated algebras unimodular in both cases. We speculate that extending these results to the path integral formalism may provide an explanation for why the η deformed AdS5 × S5 superstring is not one-loop Weyl invariant, that is the couplings do not solve the equations of type IIB supergravity, yet its complete abelian dual and the λ deformed model are.
A noncompact Weyl-Einstein-Yang-Mills model: A semiclassical quantum gravity
NASA Astrophysics Data System (ADS)
Dengiz, Suat
2017-08-01
We construct and study perturbative unitarity (i.e., ghost and tachyon analysis) of a 3 + 1-dimensional noncompact Weyl-Einstein-Yang-Mills model. The model describes a local noncompact Weyl's scale plus SU(N) phase invariant Higgs-like field,conformally coupled to a generic Weyl-invariant dynamical background. Here, the Higgs-like sector generates the Weyl's conformal invariance of system. The action does not admit any dimensionful parameter and genuine presence of de Sitter vacuum spontaneously breaks the noncompact gauge symmetry in an analogous manner to the Standard Model Higgs mechanism. As to flat spacetime, the dimensionful parameter is generated within the dimensional transmutation in quantum field theories, and thus the symmetry is radiatively broken through the one-loop Effective Coleman-Weinberg potential. We show that the mere expectation of reducing to Einstein's gravity in the broken phases forbids anti-de Sitter space to be its stable vacua. The model is unitary in de Sitter and flat vacua around which a massless graviton, N2 - 1 massless scalar bosons, N massless Dirac fermions, N2 - 1 Proca-type massive Abelian and non-Abelian vector bosons are generically propagated.
Tool for physics beyond the standard model
NASA Astrophysics Data System (ADS)
Newby, Christopher A.
The standard model (SM) of particle physics is a well studied theory, but there are hints that the SM is not the final story. What the full picture is, no one knows, but this thesis looks into three methods useful for exploring a few of the possibilities. To begin I present a paper by Spencer Chang, Nirmal Raj, Chaowaroj Wanotayaroj, and me, that studies the Higgs boson. The scalar particle first seen in 2012 may be the vanilla SM version, but there is some evidence that its couplings are different than predicted. By means of increasing the Higgs' coupling to vector bosons and fermions, we can be more consistent with the data. Next, in a paper by Spencer Chang, Gabriel Barello, and me, we elaborate on a tool created to study dark matter (DM) direct detection. The original work by Anand. et al. focused on elastic dark matter, whereas we extended this work to include the in elastic case, where different DM mass states enter and leave the collision. We also examine several direct detection experiments with our new framework to see if DAMA's modulation can be explained while avoiding the strong constraints imposed by the other experiments. We find that there are several operators that can do this. Finally, in a paper by Spencer Chang, Gabriel Barello, and me, we study an interesting phenomenon know as kinetic mixing, where two gauge bosons can share interactions with particles even though these particles aren't charged under both gauge groups. This, in and of itself, is not new, but we discuss a different method of obtaining this mixing where instead of mixing between two Abelian groups one of the groups is Nonabelian. Using this we then see that there is an inherent mass scale in the mixing strength; something that is absent in the Abelian-Abelian case. Furthermore, if the Nonabelian symmetry is the SU(2)L of the SM then the mass scale of the physics responsible for the mixing is about 1 TeV, right around the sweet spot for detection at the LHC. This dissertation
New excitations in the Thirring model
NASA Astrophysics Data System (ADS)
Cortés, J. L.; Gamboa, J.; Schmidt, I.; Zanelli, J.
1998-12-01
The quantization of the massless Thirring model in the light-cone using functional methods is considered. The need to compactify the coordinate x- in the light-cone spacetime implies that the quantum effective action for left-handed fermions contains excitations similar to abelian instantons produced by composite of left-handed fermions. Right-handed fermions don't have a similar effective action. Thus, quantum mechanically, chiral symmetry must be broken as a result of the topological excitations. The conserved charge associated to the topological states is quantized. Different cases with only fermionic excitations or bosonic excitations or both can occur depending on the boundary conditions and the value of the coupling.
Subsampling effects in neuronal avalanche distributions recorded in vivo
Priesemann, Viola; Munk, Matthias HJ; Wibral, Michael
2009-01-01
Background Many systems in nature are characterized by complex behaviour where large cascades of events, or avalanches, unpredictably alternate with periods of little activity. Snow avalanches are an example. Often the size distribution f(s) of a system's avalanches follows a power law, and the branching parameter sigma, the average number of events triggered by a single preceding event, is unity. A power law for f(s), and sigma = 1, are hallmark features of self-organized critical (SOC) systems, and both have been found for neuronal activity in vitro. Therefore, and since SOC systems and neuronal activity both show large variability, long-term stability and memory capabilities, SOC has been proposed to govern neuronal dynamics in vivo. Testing this hypothesis is difficult because neuronal activity is spatially or temporally subsampled, while theories of SOC systems assume full sampling. To close this gap, we investigated how subsampling affects f(s) and sigma by imposing subsampling on three different SOC models. We then compared f(s) and sigma of the subsampled models with those of multielectrode local field potential (LFP) activity recorded in three macaque monkeys performing a short term memory task. Results Neither the LFP nor the subsampled SOC models showed a power law for f(s). Both, f(s) and sigma, depended sensitively on the subsampling geometry and the dynamics of the model. Only one of the SOC models, the Abelian Sandpile Model, exhibited f(s) and sigma similar to those calculated from LFP activity. Conclusion Since subsampling can prevent the observation of the characteristic power law and sigma in SOC systems, misclassifications of critical systems as sub- or supercritical are possible. Nevertheless, the system specific scaling of f(s) and sigma under subsampling conditions may prove useful to select physiologically motivated models of brain function. Models that better reproduce f(s) and sigma calculated from the physiological recordings may be
3d Abelian dualities with boundaries
NASA Astrophysics Data System (ADS)
Aitken, Kyle; Baumgartner, Andrew; Karch, Andreas; Robinson, Brandon
2018-03-01
We establish the action of three-dimensional bosonization and particle-vortex duality in the presence of a boundary, which supports a non-anomalous two-dimensional theory. We confirm our prescription using a microscopic realization of the duality in terms of a Euclidean lattice.
Constructing topological models by symmetrization: A projected entangled pair states study
NASA Astrophysics Data System (ADS)
Fernández-González, Carlos; Mong, Roger S. K.; Landon-Cardinal, Olivier; Pérez-García, David; Schuch, Norbert
2016-10-01
Symmetrization of topologically ordered wave functions is a powerful method for constructing new topological models. Here we study wave functions obtained by symmetrizing quantum double models of a group G in the projected entangled pair states (PEPS) formalism. We show that symmetrization naturally gives rise to a larger symmetry group G ˜ which is always non-Abelian. We prove that by symmetrizing on sufficiently large blocks, one can always construct wave functions in the same phase as the double model of G ˜. In order to understand the effect of symmetrization on smaller patches, we carry out numerical studies for the toric code model, where we find strong evidence that symmetrizing on individual spins gives rise to a critical model which is at the phase transitions of two inequivalent toric codes, obtained by anyon condensation from the double model of G ˜.
Entanglement entropy and entanglement spectrum of the Kitaev model.
Yao, Hong; Qi, Xiao-Liang
2010-08-20
In this letter, we obtain an exact formula for the entanglement entropy of the ground state and all excited states of the Kitaev model. Remarkably, the entanglement entropy can be expressed in a simple separable form S = SG+SF, with SF the entanglement entropy of a free Majorana fermion system and SG that of a Z2 gauge field. The Z2 gauge field part contributes to the universal "topological entanglement entropy" of the ground state while the fermion part is responsible for the nonlocal entanglement carried by the Z2 vortices (visons) in the non-Abelian phase. Our result also enables the calculation of the entire entanglement spectrum and the more general Renyi entropy of the Kitaev model. Based on our results we propose a new quantity to characterize topologically ordered states--the capacity of entanglement, which can distinguish the st ates with and without topologically protected gapless entanglement spectrum.
Section sigma models coupled to symplectic duality bundles on Lorentzian four-manifolds
NASA Astrophysics Data System (ADS)
Lazaroiu, C. I.; Shahbazi, C. S.
2018-06-01
We give the global mathematical formulation of a class of generalized four-dimensional theories of gravity coupled to scalar matter and to Abelian gauge fields. In such theories, the scalar fields are described by a section of a surjective pseudo-Riemannian submersion π over space-time, whose total space carries a Lorentzian metric making the fibers into totally-geodesic connected Riemannian submanifolds. In particular, π is a fiber bundle endowed with a complete Ehresmann connection whose transport acts through isometries between the fibers. In turn, the Abelian gauge fields are "twisted" by a flat symplectic vector bundle defined over the total space of π. This vector bundle is endowed with a vertical taming which locally encodes the gauge couplings and theta angles of the theory and gives rise to the notion of twisted self-duality, of crucial importance to construct the theory. When the Ehresmann connection of π is integrable, we show that our theories are locally equivalent to ordinary Einstein-Scalar-Maxwell theories and hence provide a global non-trivial extension of the universal bosonic sector of four-dimensional supergravity. In this case, we show using a special trivializing atlas of π that global solutions of such models can be interpreted as classical "locally-geometric" U-folds. In the non-integrable case, our theories differ locally from ordinary Einstein-Scalar-Maxwell theories and may provide a geometric description of classical U-folds which are "locally non-geometric".
NASA Astrophysics Data System (ADS)
Banerjee, D.; Jiang, F.-J.; Olesen, T. Z.; Orland, P.; Wiese, U.-J.
2018-05-01
We consider the (2 +1 ) -dimensional S U (2 ) quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges [which transform nontrivially under the Z (2 ) center of the S U (2 ) gauge group] are confined to each other by fractionalized strings with a delocalized Z (2 ) flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the three-dimensional Ising universality class separates two confining phases: one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.
Investigating Complexity Using Excel and Visual Basic.
ERIC Educational Resources Information Center
Zetie, K. P.
2001-01-01
Shows how some of the simple ideas in complexity can be investigated using a spreadsheet and a macro written in Visual Basic. Shows how the sandpile model of Bak, Chao, and Wiesenfeld can be simulated and animated. The model produces results that cannot easily be predicted from its properties. (Author/MM)
Yang Baxter and anisotropic sigma and lambda models, cyclic RG and exact S-matrices
NASA Astrophysics Data System (ADS)
Appadu, Calan; Hollowood, Timothy J.; Price, Dafydd; Thompson, Daniel C.
2017-09-01
Integrable deformation of SU(2) sigma and lambda models are considered at the classical and quantum levels. These are the Yang-Baxter and XXZ-type anisotropic deformations. The XXZ type deformations are UV safe in one regime, while in another regime, like the Yang-Baxter deformations, they exhibit cyclic RG behaviour. The associ-ated affine quantum group symmetry, realized classically at the Poisson bracket level, has q a complex phase in the UV safe regime and q real in the cyclic RG regime, where q is an RG invariant. Based on the symmetries and RG flow we propose exact factorizable S-matrices to describe the scattering of states in the lambda models, from which the sigma models follow by taking a limit and non-abelian T-duality. In the cyclic RG regimes, the S-matrices are periodic functions of rapidity, at large rapidity, and in the Yang-Baxter case violate parity.
Decorated tensor network renormalization for lattice gauge theories and spin foam models
NASA Astrophysics Data System (ADS)
Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian
2016-05-01
Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.
NASA Astrophysics Data System (ADS)
Majorana-Fermi-Segre, E.-L.; Antonoff-Overhauser-Salam, Marvin-Albert-Abdus; Siegel, Edward Carl-Ludwig
2013-03-01
Majorana-fermions, being their own antiparticles, following non-Abelian anyon/semion quantum-statistics: in Zhang et.al.-...-Detwiler et.al.-...``Worlds-in-Collision'': solid-state/condensed-matter - physics spin-orbit - coupled topological-excitations in superconductors and/or superfluids -to- particle-physics neutrinos: ``When `Worlds' Collide'', analysis via Siegel[Schrodinger Centenary Symp., Imperial College, London (1987); in The Copenhagen-Interpretation Fifty-Years After the Como-Lecture, Symp. Fdns. Mod.-Phys., Joensu(1987); Symp. on Fractals, MRS Fall-Mtg., Boston(1989)-5-papers!!!] ``complex quantum-statistics in fractal-dimensions'', which explains hidden-dark-matter(HDM) IN Siegel ``Sephirot'' scenario for The Creation, uses Takagi[Prog.Theo.Phys. Suppl.88,1(86)]-Ooguri[PR D33,357(85)] - Picard-Lefschetz-Arnol'd-Vassil'ev[``Principia Read After 300 Years'', Not.AMS(1989); quantum-theory caveats comment-letters(1990); Applied Picard-Lefschetz Theory, AMS(2006)] - theorem quantum-statistics, which via Euler- formula becomes which via de Moivre- -formula further becomes which on unit-circle is only real for only, i.e, for, versus complex with imaginary-damping denominator for, i.e, for, such that Fermi-Dirac quantum-statistics for
Yang-Baxter deformations of W2,4 × T1,1 and the associated T-dual models
NASA Astrophysics Data System (ADS)
Sakamoto, Jun-ichi; Yoshida, Kentaroh
2017-08-01
Recently, for principal chiral models and symmetric coset sigma models, Hoare and Tseytlin proposed an interesting conjecture that the Yang-Baxter deformations with the homogeneous classical Yang-Baxter equation are equivalent to non-abelian T-dualities with topological terms. It is significant to examine this conjecture for non-symmetric (i.e., non-integrable) cases. Such an example is the W2,4 ×T 1 , 1 background. In this note, we study Yang-Baxter deformations of type IIB string theory defined on W2,4 ×T 1 , 1 and the associated T-dual models, and show that this conjecture is valid even for this case. Our result indicates that the conjecture would be valid beyond integrability.
Wilsonian dark matter in string derived Z' model
NASA Astrophysics Data System (ADS)
Delle Rose, L.; Faraggi, A. E.; Marzo, C.; Rizos, J.
2017-09-01
The dark matter issue is among the most perplexing in contemporary physics. The problem is more enigmatic due to the wide range of possible solutions, ranging from the ultralight to the supermassive. String theory gives rise to plausible dark matter candidates due to the breaking of the non-Abelian grand unified theory (GUT) symmetries by Wilson lines. The physical spectrum then contains states that do not satisfy the quantization conditions of the unbroken GUT symmetry. Given that the Standard Model states are identified with broken GUT representations, and provided that any ensuing symmetry breakings are induced by components of GUT states, a remnant discrete symmetry remains that forbids the decay of the Wilsonian states. A class of such states are obtained in a heterotic-string-derived Z' model. The model exploits the spinor-vector duality symmetry, observed in the fermionic Z2×Z2 heterotic-string orbifolds, to generate a Z'∈E6 symmetry that may remain unbroken down to low energies. The E6 symmetry is broken at the string level with discrete Wilson lines. The Wilsonian dark matter candidates in the string-derived model are S O (10 ), and hence Standard Model, singlets and possess non-E6 U(1)Z' charges. Depending on the U(1)Z' breaking scale and the reheating temperature they give rise to different scenarios for the relic abundance, and are in accordance with the cosmological constraints.
Landslides, forest fires, and earthquakes: examples of self-organized critical behavior
NASA Astrophysics Data System (ADS)
Turcotte, Donald L.; Malamud, Bruce D.
2004-09-01
Per Bak conceived self-organized criticality as an explanation for the behavior of the sandpile model. Subsequently, many cellular automata models were found to exhibit similar behavior. Two examples are the forest-fire and slider-block models. Each of these models can be associated with a serious natural hazard: the sandpile model with landslides, the forest-fire model with actual forest fires, and the slider-block model with earthquakes. We examine the noncumulative frequency-area statistics for each natural hazard, and show that each has a robust power-law (fractal) distribution. We propose an inverse-cascade model as a general explanation for the power-law frequency-area statistics of the three cellular-automata models and their ‘associated’ natural hazards.
Model with a gauged lepton flavor SU(2) symmetry
NASA Astrophysics Data System (ADS)
Chiang, Cheng-Wei; Tsumura, Koji
2018-05-01
We propose a model having a gauged SU(2) symmetry associated with the second and third generations of leptons, dubbed SU(2) μτ , of which U{(1)}_{L_{μ }-L_{τ }} is an Abelian subgroup. In addition to the Standard Model fields, we introduce two types of scalar fields. One exotic scalar field is an SU(2) μτ doublet and SM singlet that develops a nonzero vacuum expectation value at presumably multi-TeV scale to completely break the SU(2) μτ symmetry, rendering three massive gauge bosons. At the same time, the other exotic scalar field, carrying electroweak as well as SU(2) μτ charges, is induced to have a nonzero vacuum expectation value as well and breaks mass degeneracy between the muon and tau. We examine how the new particles in the model contribute to the muon anomalous magnetic moment in the parameter space compliant with the Michel decays of tau.
On the tensionless limit of gauged WZW models
NASA Astrophysics Data System (ADS)
Bakas, I.; Sourdis, C.
2004-06-01
The tensionless limit of gauged WZW models arises when the level of the underlying Kac-Moody algebra assumes its critical value, equal to the dual Coxeter number, in which case the central charge of the Virasoro algebra becomes infinite. We examine this limit from the world-sheet and target space viewpoint and show that gravity decouples naturally from the spectrum. Using the two-dimensional black-hole coset SL(2,Bbb R)k/U(1) as illustrative example, we find for k = 2 that the world-sheet symmetry is described by a truncated version of Winfty generated by chiral fields with integer spin s geq 3, whereas the Virasoro algebra becomes abelian and it can be consistently factored out. The geometry of target space looks like an infinitely curved hyperboloid, which invalidates the effective field theory description and conformal invariance can no longer be used to yield reliable space-time interpretation. We also compare our results with the null gauging of WZW models, which correspond to infinite boost in target space and they describe the Liouville mode that decouples in the tensionless limit. A formal BRST analysis of the world-sheet symmetry suggests that the central charge of all higher spin generators should be fixed to a critical value, which is not seen by the contracted Virasoro symmetry. Generalizations to higher dimensional coset models are also briefly discussed in the tensionless limit, where similar observations are made.
Goldstone models of modified gravity
NASA Astrophysics Data System (ADS)
Brax, Philippe; Valageas, Patrick
2017-02-01
We investigate scalar-tensor theories where matter couples to the scalar field via a kinetically dependent conformal coupling. These models can be seen as the low-energy description of invariant field theories under a global Abelian symmetry. The scalar field is then identified with the Goldstone mode of the broken symmetry. It turns out that the properties of these models are very similar to the ones of ultralocal theories where the scalar-field value is directly determined by the local matter density. This leads to a complete screening of the fifth force in the Solar System and between compact objects, through the ultralocal screening mechanism. On the other hand, the fifth force can have large effects in extended structures with large-scale density gradients, such as galactic halos. Interestingly, it can either amplify or damp Newtonian gravity, depending on the model parameters. We also study the background cosmology and the linear cosmological perturbations. The background cosmology is hardly different from its Λ -CDM counterpart while cosmological perturbations crucially depend on whether the coupling function is convex or concave. For concave functions, growth is hindered by the repulsiveness of the fifth force while it is enhanced in the convex case. In both cases, the departures from the Λ -CDM cosmology increase on smaller scales and peak for galactic structures. For concave functions, the formation of structure is largely altered below some characteristic mass, as smaller structures are delayed and would form later through fragmentation, as in some warm dark matter scenarios. For convex models, small structures form more easily than in the Λ -CDM scenario. This could lead to an over-abundance of small clumps. We use a thermodynamic analysis and show that although convex models have a phase transition between homogeneous and inhomogeneous phases, on cosmological scales the system does not enter the inhomogeneous phase. On the other hand, for galactic
The Kroll-Lee-Zumino Model and Pion Form Factors
Dominguez, C. A.; Loewe, M.
2010-08-04
At the one loop level, we make use of the renormalizable Abelian quantum field theory model of Kroll, Lee, and Zumino (KLZ) in order to compute the vertex corrections to the tree-level, Vector Meson Dominance (VMD) electromagnetic pion form factor. This result, together with the one-loop vacuum polarization contribution, implies an electromagnetic pion form factor which is in outstanding agreement with data in the whole range of accessible momentum transfers in the space-like region. The time-like form factor, which reproduces the Gounaris-Sakurai formula at and near the rho-meson peak, remains unaffected by the vertex correction at order O(g{sup 2}). Wemore » also use the KLZ model to compute the pion scalar radius at the one loop level, finding
Supersymmetric solutions of the cosmological, gauged, ℂ magic model
NASA Astrophysics Data System (ADS)
Chimento, Samuele; Ortín, Tomás; Ruipérez, Alejandro
2018-05-01
We construct supersymmetric solutions of theories of gauged N = 1 , d = 5 supergravity coupled to vector multiplets with a U(1)R Abelian (Fayet-Iliopoulos) gauging and an independent SU(2) gauging associated to an SU(2) isometry group of the Real Special scalar manifold. These theories provide minimal supersymmetrizations of 5-dimensional SU(2) Einstein-Yang-Mills theories with negative cosmological constant. We consider a minimal model with these gauge groups and the "magic model" based on the Jordan algebra J 3 ℂ with gauge group SU(3) × U(1)R, which is a consistent truncation of maximal SO(6)-gauged supergravity in d = 5 and whose solutions can be embedded in Type IIB Superstring Theory. We find several solutions containing selfdual SU(2) instantons, some of which asymptote to AdS5 and some of which are very small, supersymmetric, deformations of AdS5. We also show how some of those solutions can be embedded in Romans' SU(2) × U(1)-gauged half-maximal supergravity, which was obtained by Lu, Pope and Tran by compactification of the Type IIB Superstring effective action. This provides another way of uplifting those solutions to 10 dimensions.
Non-Abelian Bosonization and Fractional Quantum Hall Transitions
NASA Astrophysics Data System (ADS)
Hui, Aaron; Mulligan, Michael; Kim, Eun-Ah
A fully satisfying theoretical description for the quantum phase transition between fractional quantum Hall plateaus remains an outstanding problem. Experiments indicate scaling exponents that are not readily obtained in conventional theories. Using insights from duality, we describe a class of quantum critical effective theories that produce qualitatively realistic scaling exponents for the transition. We discuss the implications of our results for the physically-relevant interactions controlling this broad class of quantum critical behavior. Supported by National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1650441.
A Non-Abelian Geometric Phase for Spin Systems
NASA Astrophysics Data System (ADS)
H M, Bharath; Boguslawski, Matthew; Barrios, Maryrose; Chapman, Michael
Berry's geometric phase has been used to characterize topological phase transitions. Recent works have addressed the question of whether generalizations of Berry's phase to mixed states can be used to characterize topological phase transitions. Berry's phase is essentially the geometric information stored in the overall phase of a quantum system. Here, we show that geometric information is also stored in the higher order spin moments of a quantum spin system. In particular, we show that when the spin vector of a quantum spin system with a spin 1 or higher is transported along a closed path inside the Bloch ball, the tensor of second moments picks up a geometric phase in the form of an SO(3) operator. Geometrically interpreting this phase is tantamount to defining a steradian angle for closed paths inside the Bloch ball. Typically the steradian angle is defined by projecting the path onto the surface of the Bloch ball. However, paths that pass through the center cannot be projected onto the surface. We show that the steradian angles of all paths, including those that pass through the center can be defined by projecting them onto a real projective plane, instead of a sphere. This steradian angle is equal to the geometric phase picked up by a spin system.
Non-Abelian fermionization and fractional quantum Hall transitions
Hui, Aaron; Mulligan, Michael; Kim, Eun-Ah
There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall interplateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall inter-plateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponentmore » $$\
Non-Abelian fermionization and fractional quantum Hall transitions
Hui, Aaron; Mulligan, Michael; Kim, Eun-Ah
2018-02-08
There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall interplateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall inter-plateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponentmore » $$\
Simulation of Non-Abelian Braiding in Majorana Time Crystals
NASA Astrophysics Data System (ADS)
Bomantara, Raditya Weda; Gong, Jiangbin
2018-06-01
Discrete time crystals have attracted considerable theoretical and experimental studies but their potential applications have remained unexplored. A particular type of discrete time crystals, termed "Majorana time crystals," is found to emerge in a periodically driven superconducting wire accommodating two different species of topological edge modes. It is further shown that one can manipulate different Majorana edge modes separated in the time lattice, giving rise to an unforeseen scenario for topologically protected gate operations mimicking braiding. The proposed protocol can also generate a magic state that is important for universal quantum computation. This study thus advances the quantum control in discrete time crystals and reveals their great potential arising from their time-domain properties.
Infrared problem in non-Abelian gauge theory
Yao, Y.
1976-03-22
I extend the Bloch--Nordsieck idea to show that in the lowest nontrivial order of radiative correction the fermion--fermion and gauge-meson--fermion scattering rates are finite, provided that they are averaged over the initial and summed over the final internal spin states. Questions of the physical gauge coupling and infrared slavery are discussed. (AIP)
Non-locality of non-Abelian anyons
NASA Astrophysics Data System (ADS)
Brennen, G. K.; Iblisdir, S.; Pachos, J. K.; Slingerland, J. K.
2009-10-01
Entangled states of quantum systems can give rise to measurement correlations of separated observers that cannot be described by local hidden variable theories. Usually, it is assumed that entanglement between particles is generated due to some distance-dependent interaction. Yet anyonic particles in two dimensions have a nontrivial interaction that is purely topological in nature. In other words, it does not depend on the distance between two particles, but rather on their exchange history. The information encoded in anyons is inherently non-local even in the single subsystem level making the treatment of anyons non-conventional. We describe a protocol to reveal the non-locality of anyons in terms of correlations in the outcomes of measurements in two separated regions. This gives a clear operational measure of non-locality for anyonic states and it opens up the possibility to test Bell inequalities in quantum Hall liquids or spin lattices.
Non-Abelian vortices of higher winding numbers
Eto, Minoru; Konishi, Kenichi; Vinci, Walter
2006-09-15
We make a detailed study of the moduli space of winding number two (k=2) axially symmetric vortices (or equivalently, of coaxial composite of two fundamental vortices), occurring in U(2) gauge theory with two flavors in the Higgs phase, recently discussed by Hashimoto and Tong and by Auzzi, Shifman, and Yung. We find that it is a weighted projective space WCP{sub (2,1,1)}{sup 2}{approx_equal}CP{sup 2}/Z{sub 2}. This manifold contains an A{sub 1}-type (Z{sub 2}) orbifold singularity even though the full moduli space including the relative position moduli is smooth. The SU(2) transformation properties of such vortices are studied. Our results are thenmore » generalized to U(N) gauge theory with N flavors, where the internal moduli space of k=2 axially symmetric vortices is found to be a weighted Grassmannian manifold. It contains singularities along a submanifold.« less
BRST Quantization of the Proca Model Based on the BFT and the BFV Formalism
NASA Astrophysics Data System (ADS)
Kim, Yong-Wan; Park, Mu-In; Park, Young-Jai; Yoon, Sean J.
The BRST quantization of the Abelian Proca model is performed using the Batalin-Fradkin-Tyutin and the Batalin-Fradkin-Vilkovisky formalism. First, the BFT Hamiltonian method is applied in order to systematically convert a second class constraint system of the model into an effectively first class one by introducing new fields. In finding the involutive Hamiltonian we adopt a new approach which is simpler than the usual one. We also show that in our model the Dirac brackets of the phase space variables in the original second class constraint system are exactly the same as the Poisson brackets of the corresponding modified fields in the extended phase space due to the linear character of the constraints comparing the Dirac or Faddeev-Jackiw formalisms. Then, according to the BFV formalism we obtain that the desired resulting Lagrangian preserving BRST symmetry in the standard local gauge fixing procedure naturally includes the Stückelberg scalar related to the explicit gauge symmetry breaking effect due to the presence of the mass term. We also analyze the nonstandard nonlocal gauge fixing procedure.
Towards an M5-brane model I: A 6d superconformal field theory
NASA Astrophysics Data System (ADS)
Sämann, Christian; Schmidt, Lennart
2018-04-01
We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the string Lie 2-algebra as a gauge structure, which we motivated in previous work. The kinematical data contains a connection on a categorified principal bundle, which is the appropriate mathematical description of the parallel transport of self-dual strings. Our action can be written down for each of the simply laced Dynkin diagrams, and each case reduces to a four-dimensional supersymmetric Yang-Mills theory with corresponding gauge Lie algebra. Our action also reduces nicely to an M2-brane model which is a deformation of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model. While this action is certainly not the desired M5-brane model, we regard it as a key stepping stone towards a potential construction of the (2, 0)-theory.
Ultraviolet properties of the Higgs sector in the Lee-Wick standard model
Espinosa, Jose R.; Grinstein, Benjamin
2011-04-01
The Lee-Wick (LW) standard model (SM) offers a new solution to the hierarchy problem. We discuss, using effective potential techniques, its peculiar UV behavior. We show how quadratic divergences in the Higgs mass M{sub h} cancel as a result of the unusual dependence of LW fields on the Higgs background (in a manner reminiscent of little Higgses). We then extract from the effective potential the renormalization group evolution of the Higgs quartic coupling {lambda} above the LW scale. After clarifying an apparent discrepancy with previous results for the LW Abelian Higgs model, we focus on the LWSM. In contrast withmore » the SM case, for any M{sub h}, {lambda} grows monotonically and hits a Landau pole at a fixed trans-Planckian scale (never turning negative in the UV). Then, the perturbativity and stability bounds on M{sub h} disappear. We identify a cutoff {approx}10{sup 16} GeV for the LWSM due to the hypercharge gauge coupling hitting a Landau pole. Finally, we also discuss briefly the possible impact of the UV properties of the LW models on their behavior at finite temperature, in particular, regarding symmetry nonrestoration.« less
An asymptotic safety scenario for gauged chiral Higgs-Yukawa models
NASA Astrophysics Data System (ADS)
Gies, Holger; Rechenberger, Stefan; Scherer, Michael M.; Zambelli, Luca
2013-12-01
We investigate chiral Higgs-Yukawa models with a non-abelian gauged left-handed sector reminiscent to a sub-sector of the standard model. We discover a new weak-coupling fixed-point behavior that allows for ultraviolet complete RG trajectories which can be connected with a conventional long-range infrared behavior in the Higgs phase. This non-trivial ultraviolet behavior is characterized by asymptotic freedom in all interaction couplings, but a quasi conformal behavior in all mass-like parameters. The stable microscopic scalar potential asymptotically approaches flatness in the ultraviolet, however, with a non-vanishing minimum increasing inversely proportional to the asymptotically free gauge coupling. This gives rise to non-perturbative—though weak-coupling—threshold effects which induce ultraviolet stability along a line of fixed points. Despite the weak-coupling properties, the system exhibits non-Gaußian features which are distinctly different from its standard perturbative counterpart: e.g., on a branch of the line of fixed points, we find linear instead of quadratically running renormalization constants. Whereas the Fermi constant and the top mass are naturally of the same order of magnitude, our model generically allows for light Higgs boson masses. Realistic mass ratios are related to particular RG trajectories with a "walking" mid-momentum regime.
GUT models at current and future hadron colliders and implications to dark matter searches
NASA Astrophysics Data System (ADS)
Arcadi, Giorgio; Lindner, Manfred; Mambrini, Yann; Pierre, Mathias; Queiroz, Farinaldo S.
2017-08-01
Grand Unified Theories (GUT) offer an elegant and unified description of electromagnetic, weak and strong interactions at high energy scales. A phenomenological and exciting possibility to grasp GUT is to search for TeV scale observables arising from Abelian groups embedded in GUT constructions. That said, we use dilepton data (ee and μμ) that has been proven to be a golden channel for a wide variety of new phenomena expected in theories beyond the Standard Model to probe GUT-inspired models. Since heavy dilepton resonances feature high signal selection efficiencies and relatively well-understood backgrounds, stringent and reliable bounds can be placed on the mass of the Z‧ gauge boson arising in such theories. In this work, we obtain 95% C.L. limits on the Z‧ mass for several GUT-models using current and future proton-proton colliders with √{ s} = 13 TeV , 33 TeV ,and 100 TeV, and put them into perspective with dark matter searches in light of the next generation of direct detection experiments.
N = 1 supersymmetric indices and the four-dimensional A-model
NASA Astrophysics Data System (ADS)
Closset, Cyril; Kim, Heeyeon; Willett, Brian
2017-08-01
We compute the supersymmetric partition function of N = 1 supersymmetric gauge theories with an R-symmetry on M_4\\cong M_{g,p}× {S}^1 , a principal elliptic fiber bundle of degree p over a genus- g Riemann surface, Σ g . Equivalently, we compute the generalized supersymmetric index I_{M}{_{g,p}, with the supersymmetric three-manifold M_{g,p} as the spatial slice. The ordinary N = 1 supersymmetric index on the round three-sphere is recovered as a special case. We approach this computation from the point of view of a topological A-model for the abelianized gauge fields on the base Σ g . This A-model — or A-twisted two-dimensional N = (2 , 2) gauge theory — encodes all the information about the generalized indices, which are viewed as expectations values of some canonically-defined surface defects wrapped on T 2 inside Σ g × T 2. Being defined by compactification on the torus, the A-model also enjoys natural modular properties, governed by the four-dimensional 't Hooft anomalies. As an application of our results, we provide new tests of Seiberg duality. We also present a new evaluation formula for the three-sphere index as a sum over two-dimensional vacua.
NASA Astrophysics Data System (ADS)
Borah, Debasish; Dasgupta, Arnab; Adhikari, Rathin
2015-10-01
We attempt to simultaneously explain the recently observed 3.55 keV x-ray line in the analysis of XMM-Newton telescope data and the Galactic Center gamma ray excess observed by the Fermi Gamma Ray Space Telescope within an Abelian gauge extension of the standard model. We consider a two component dark matter scenario with tree level mass difference 3.55 keV such that the heavier one can decay into the lighter one and a photon with energy 3.55 keV. The lighter dark matter candidate is protected from decaying into the standard model particles by a remnant Z2 symmetry into which the Abelian gauge symmetry gets spontaneously broken. If the mass of the dark matter particle is chosen to be within 31-40 GeV, then this model can also explain the Galactic Center gamma ray excess if the dark matter annihilation into b b ¯ pairs has a cross section of ⟨σ v ⟩≃(1.4 -2.0 )×1 0-26 cm3/s . We constrain the model from the requirement of producing correct dark matter relic density, 3.55 keV x-ray line flux, and Galactic Center gamma ray excess. We also impose the bounds coming from dark matter direct detection experiments as well as collider limits on additional gauge boson mass and gauge coupling. We also briefly discuss how this model can give rise to subelectron volt neutrino masses at tree level as well as the one-loop level while keeping the dark matter mass at a few tens of giga-electron volts. We also constrain the model parameters from the requirement of keeping the one-loop mass difference between two dark matter particles below a kilo-electron volt. We find that the constraints from light neutrino mass and kilo-electron volt mass splitting between two dark matter components show more preference for opposite C P eigenvalues of the two fermion singlet dark matter candidates in the model.
Azaria, P.; Konik, R. M.; Lecheminant, P.; ...
2016-08-03
In our paper we study a (1+1)-dimensional version of the famous Nambu–Jona-Lasinio model of quantum chromodynamics (QCD2) both at zero and at finite baryon density. We use nonperturbative techniques (non-Abelian bosonization and the truncated conformal spectrum approach). When the baryon chemical potential, μ, is zero, we describe the formation of fermion three-quark (nucleons and Δ baryons) and boson (two-quark mesons, six-quark deuterons) bound states. We also study at μ=0 the formation of a topologically nontrivial phase. When the chemical potential exceeds the critical value and a finite baryon density appears, the model has a rich phase diagram which includes phasesmore » with a density wave and superfluid quasi-long-range (QLR) order, as well as a phase of a baryon Tomonaga-Luttinger liquid (strange metal). Finally, the QLR order results in either a condensation of scalar mesons (the density wave) or six-quark bound states (deuterons).« less
Basic Brackets of a 2D Model for the Hodge Theory Without its Canonical Conjugate Momenta
NASA Astrophysics Data System (ADS)
Kumar, R.; Gupta, S.; Malik, R. P.
2016-06-01
We deduce the canonical brackets for a two (1+1)-dimensional (2D) free Abelian 1-form gauge theory by exploiting the beauty and strength of the continuous symmetries of a Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density that respects, in totality, six continuous symmetries. These symmetries entail upon this model to become a field theoretic example of Hodge theory. Taken together, these symmetries enforce the existence of exactly the same canonical brackets amongst the creation and annihilation operators that are found to exist within the standard canonical quantization scheme. These creation and annihilation operators appear in the normal mode expansion of the basic fields of this theory. In other words, we provide an alternative to the canonical method of quantization for our present model of Hodge theory where the continuous internal symmetries play a decisive role. We conjecture that our method of quantization is valid for a class of field theories that are tractable physical examples for the Hodge theory. This statement is true in any arbitrary dimension of spacetime.
Ko, P.; Tang, Yong
We show that hidden sector dark matter (DM) models with local dark gauge symmetries make a natural playground for the possible γ-ray excess from the galactic center (GC). We first discuss in detail the GC γ-ray excess in a scalar dark matter (DM) model with local Z{sub 3} symmetry which was recently proposed by the present authors. Within this model, scalar DM with mass 30–70 GeV is allowed due to the newly-opened (semi-)annihilation channels of a DM pair into dark Higgs ϕ and/or dark photon Z′ pair, and the γ-ray spectrum from the GC can be fit within this model.more » Then we argue that the GC gamma ray excess can be easily accommodated within hidden sector dark matter models where DM is stabilized by local gauge symmetries, due to the presence of dark Higgs (and also dark photon for Abelian dark gauge symmetry)« less
A unified model of quarks and leptons with a universal texture zero
NASA Astrophysics Data System (ADS)
de Medeiros Varzielas, Ivo; Ross, Graham G.; Talbert, Jim
2018-03-01
We show that a universal texture zero in the (1,1) position of all fermionic mass matrices, including heavy right-handed Majorana neutrinos driving a type-I see-saw mechanism, can lead to a viable spectrum of mass, mixing and CP violation for both quarks and leptons, including (but not limited to) three important postdictions: the Cabibbo angle, the charged lepton masses, and the leptonic `reactor' angle. We model this texture zero with a non-Abelian discrete family symmetry that can easily be embedded in a grand unified framework, and discuss the details of the phenomenology after electroweak and family symmetry breaking. We provide an explicit numerical fit to the available data and obtain excellent agreement with the 18 observables in the charged fermion and neutrino sectors with just 9 free parameters. We further show that the vacua of our new scalar familon fields are readily aligned along desired directions in family space, and also demonstrate discrete gauge anomaly freedom at the relevant scale of our effective theory.
New simple A{sub 4} neutrino model for nonzero {theta}{sub 13} and large {delta}{sub CP}
Ishimori, Hajime
In a new simple application of the non-Abelian discrete symmetry A{sub 4} to charged-lepton and neutrino mass matrices, we show that for the current experimental central value of sin{sup 2} 2{theta}{sub 13} Asymptotically-Equal-To 0.1, leptonic CP violation is necessarily large, i.e. Double-Vertical-Line tan{delta}{sub CP} Double-Vertical-Line > 1.3. We also consider T{sub 7} model with one parameter to be complex, thus allowing for one Dirac CP phase {delta}{sub CP} and two Majorana CP phases {alpha}{sub 1,2}. We find a slight modification to this correlation as a function of {delta}{sub CP}. For a given set of input values of {Delta}m{sup 2}{sub 21},more » {Delta}m{sup 2}{sub 32}, {theta}{sub 12}, and {theta}{sub 13}, we obtain sin{sup 2} 2{theta}{sub 23} and m{sub ee} (the effective Majorana neutrino mass in neutrinoless double beta decay) as functions of tan {delta}{sub CP}. We find that the structure of this model always yields small Double-Vertical-Line tan {delta}{sub CP} Double-Vertical-Line .« less
Nehaniv, Chrystopher L; Rhodes, John; Egri-Nagy, Attila; Dini, Paolo; Morris, Eric Rothstein; Horváth, Gábor; Karimi, Fariba; Schreckling, Daniel; Schilstra, Maria J
2015-07-28
Interaction computing is inspired by the observation that cell metabolic/regulatory systems construct order dynamically, through constrained interactions between their components and based on a wide range of possible inputs and environmental conditions. The goals of this work are to (i) identify and understand mathematically the natural subsystems and hierarchical relations in natural systems enabling this and (ii) use the resulting insights to define a new model of computation based on interactions that is useful for both biology and computation. The dynamical characteristics of the cellular pathways studied in systems biology relate, mathematically, to the computational characteristics of automata derived from them, and their internal symmetry structures to computational power. Finite discrete automata models of biological systems such as the lac operon, the Krebs cycle and p53-mdm2 genetic regulation constructed from systems biology models have canonically associated algebraic structures (their transformation semigroups). These contain permutation groups (local substructures exhibiting symmetry) that correspond to 'pools of reversibility'. These natural subsystems are related to one another in a hierarchical manner by the notion of 'weak control'. We present natural subsystems arising from several biological examples and their weak control hierarchies in detail. Finite simple non-Abelian groups are found in biological examples and can be harnessed to realize finitary universal computation. This allows ensembles of cells to achieve any desired finitary computational transformation, depending on external inputs, via suitably constrained interactions. Based on this, interaction machines that grow and change their structure recursively are introduced and applied, providing a natural model of computation driven by interactions.
Unified models of neutrinos, flavour and CP Violation
NASA Astrophysics Data System (ADS)
King, S. F.
2017-05-01
Recent data from neutrino experiments gives intriguing hints about the mass ordering, the CP violating phase and non-maximal atmospheric mixing. There seems to be a (one sigma) preference for a normal ordered (NO) neutrino mass pattern, with a CP phase δ = - 100 ° ± 50 °, and (more significantly) non-maximal atmospheric mixing. Global fits for the NO case yield lepton mixing angle one sigma ranges: θ23 ≈ 41.4 ° ± 1.6 °, θ12 ≈ 33.2 ° ± 1.2 °, θ13 ≈ 8.45 ° ± 0.15 °. Cosmology gives a limit on the total of the three masses to be below about 0.23 eV, favouring hierarchical neutrino masses over quasi-degenerate masses. Given such experimental advances, it seems an opportune moment to review the theoretical status of attempts to explain such a pattern of neutrino masses and lepton mixing, focusing on approaches based on the four pillars of: predictivity, minimality, robustness and unification. Predictivity can result from various mixing sum rules whose status is reviewed. Minimality can follow from the type I seesaw mechanism, including constrained sequential dominance of right-handed (RH) neutrinos, and the littlest seesaw model. Robustness requires enforcing a discrete CP and non-Abelian family symmetry, spontaneously broken by flavons with the symmetry preserved in a semi-direct way. Unification can account for all lepton and quark masses, mixing angles and CP phases, as in Supersymmetric Grand Unified Theories of Flavour, with possible string theory origin.
Fuentes-Martín, J.
2016-01-22
It is well known that non-abelian Yang-Mills theories present non-trivial minima of the action, the so-called instantons. In the context of electroweak theories these instanton solutions may induce violations of baryon and lepton number of the form ΔB = ΔL = n{sub f}, with n{sub f} being the number of families coupled to the gauge group. An interesting feature of these violations is that the flavor structure of the gauge couplings is inherited by the instanton transitions. This effect is generally neglected in the literature. We will show that the inclusion of flavor interactions in the instanton solutions may bemore » interesting in certain theoretical frameworks and will provide an approach to include these effects. In particular we will perform this implementation in the non-universal SU (2){sub l} ⊗SU (2){sub h} ⊗U (1){sub Y} model that singularizes the third family. Within this framework, we will use the instanton transitions to set a bound on the SU (2){sub h} gauge coupling.« less
The Dualized Standard Model and its Applications — AN Interim Report
NASA Astrophysics Data System (ADS)
Chan, Hong-Mo; Tsou, Sheung Tsun
Based on a non-Abelian generalization of electric-magnetic duality, the Dualized Standard Model (DSM) suggests a natural explanation for exactly three generations of fermions as the "dual colour" widetilde SU (3) symmetry broken in a particular manner. The resulting scheme then offers on the one hand a fermion mass hierarchy and a perturbative method for calculating the mass and mixing parameters of the Standard Model fermions, and on the other hand testable predictions for new phenomena ranging from rare meson decays to ultra-high energy cosmic rays. Calculations to one-loop order gives, at the cost of adjusting only three real parameters, values for the following quantities all (except one) in very good agreement with experiment: the quark CKM matrix elements dvbr Vrsdvbr , the lepton CKM matrix elements dvbr Ursdvbr, and the second generation masses mc, ms, mμ. This means, in particular, that it gives near maximal mixing Uμ3 between νμ and ντ as observed by SuperKamiokande, Kamiokande and Soudan, while keeping small the corresponding quark angles Vcb, Vts. In addition, the scheme gives (i) rough order-of-magnitude estimates for the masses of the lowest generation, (ii) predictions for low energy FCNC effects such as KL→ eμ, and (iii) a possible explanation for the long-standing puzzle of air showers beyond the GZK cut-off. All these together, however, still represent but a portion of the possible physical consequences derivable from the DSM scheme, the majority of which are yet to be explored.
Topological vortices in gauge models of graphene
NASA Astrophysics Data System (ADS)
Zhang, Xin-Hui; Li, Xueqin; Hao, Jin-Bo
2018-06-01
Graphene-like structure possessing the topological vortices and knots, and the magnetic flux of the vortices configuration quantized, are proposed in this paper. The topological charges of the vortices are characterized by Hopf indices and Brower degrees. The Abelian background field action (BF action) is a topological invariant for the knot family, which is just the total sum of all the self-linking numbers and all the linking numbers. Flux quantization opens the possibility of having Aharonov-Bohm-type effects in graphene without external electromagnetic field.
ERIC Educational Resources Information Center
Freeman, Thomas J.
This paper discusses six different models of organizational structure and leadership, including the scalar chain or pyramid model, the continuum model, the grid model, the linking pin model, the contingency model, and the circle or democratic model. Each model is examined in a separate section that describes the model and its development, lists…
ten Cate, Jacob M
2015-01-01
Developing experimental models to understand dental caries has been the theme in our research group. Our first, the pH-cycling model, was developed to investigate the chemical reactions in enamel or dentine, which lead to dental caries. It aimed to leverage our understanding of the fluoride mode of action and was also utilized for the formulation of oral care products. In addition, we made use of intra-oral (in situ) models to study other features of the oral environment that drive the de/remineralization balance in individual patients. This model addressed basic questions, such as how enamel and dentine are affected by challenges in the oral cavity, as well as practical issues related to fluoride toothpaste efficacy. The observation that perhaps fluoride is not sufficiently potent to reduce dental caries in the present-day society triggered us to expand our knowledge in the bacterial aetiology of dental caries. For this we developed the Amsterdam Active Attachment biofilm model. Different from studies on planktonic ('single') bacteria, this biofilm model captures bacteria in a habitat similar to dental plaque. With data from the combination of these models, it should be possible to study separate processes which together may lead to dental caries. Also products and novel agents could be evaluated that interfere with either of the processes. Having these separate models in place, a suggestion is made to design computer models to encompass the available information. Models but also role models are of the utmost importance in bringing and guiding research and researchers. 2015 S. Karger AG, Basel
Quantum Engineering of Dynamical Gauge Fields on Optical Lattices
2016-07-08
opens the door for exciting new research directions, such as quantum simulation of the Schwinger model and of non-Abelian models. (a) Papers...exact blocking formulas from the TRG formulation of the transfer matrix. The second is a worm algorithm. The particle number distributions obtained...a fact that can be explained by an approximate particle- hole symmetry. We have also developed a computer code suite for simulating the Abelian
Cvetic, Mirjam; Klevers, Denis; Piragua, Hernan; ...
2015-11-30
We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier F-theory constructions with U(1)×U(1) gauge symmetry. Generic U(1)×U(1) models can be related to a Higgsed non-Abelian model with gauge group SU(2)×SU(2)×SU(3), SU(2) 3×SU(3), or a subgroup thereof. The nonlocal horizontal divisors of the Mordell-Weil group are replaced with local vertical divisors associated with the Cartan generators of non-Abelian gauge groups from Kodaira singularities. Wemore » give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed non-Abelian model. The non-Abelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first explicit construction of matter in the symmetric representation of SU(3). This matter is realized on double point singularities of the discriminant locus. In conclusion, the construction suggests a generalization to U(1) k factors with k > 2, which can be studied by Higgsing theories with larger non-Abelian gauge groups.« less
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.
The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states
NASA Astrophysics Data System (ADS)
Finster, Felix; Smoller, Joel; Yau, Shing-Tung
2000-09-01
We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.
On the 4D generalized Proca action for an Abelian vector field
Allys, Erwan; Almeida, Juan P. Beltrán; Peter, Patrick
We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated StÃ¼ckelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the StÃ¼ckelberg field describing the longitudinal mode, which is in agreement with the results of http://dx.doi.org/10.1088/1475-7516/2014/05/015 and http://dx.doi.org/10.1016/j.physletb.2016.04.017 and complements those of http://dx.doi.org/10.1088/1475-7516/2016/02/004.more » We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field A{sub μ}, the Faraday tensor F{sub μν} and its Hodge dual F-tilde{sub μν}.« less
On the 4D generalized Proca action for an Abelian vector field
NASA Astrophysics Data System (ADS)
Allys, Erwan; Beltrán Almeida, Juan P.; Peter, Patrick; Rodríguez, Yeinzon
2016-09-01
We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated Stückelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the Stückelberg field describing the longitudinal mode, which is in agreement with the results of JCAP 05 (2014) 015 and Phys. Lett. B 757 (2016) 405 and complements those of JCAP 02 (2016) 004. We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field Aμ, the Faraday tensor Fμν and its Hodge dual tilde Fμν.
On Pauli's Invention of Non-Abelian Kaluza-Klein Theory in 1953
NASA Astrophysics Data System (ADS)
Straumann, N.
2002-12-01
There are documents which show that Wolfgang Pauli developed in 1953 the first consistent generalization of the five-dimensional theory of Kaluza, Klein, Fock and others to a higher dimensional internal space. Because he saw no way to give masses to the gauge bosons, he refrained from publishing his results formally.
Fermionic vacuum polarization by an Abelian magnetic tube in the cosmic string spacetime
NASA Astrophysics Data System (ADS)
Maior de Sousa, M. S.; Ribeiro, R. F.; Bezerra de Mello, E. R.
2017-02-01
In this paper, we consider a charged massive fermionic quantum field in the idealized cosmic string spacetime and in the presence of a magnetic field confined in a cylindrical tube of finite radius. Three distinct configurations for the magnetic fields are taken into account: (i) a cylindrical shell of radius a , (ii) a magnetic field proportional to 1 /r , and (iii) a constant magnetic field. In these three cases, the axis of the infinitely long tube of radius a coincides with the cosmic string. Our main objectives in this paper are to analyze the fermionic condensate (FC) and the vacuum expectation value (VEV) of the fermionic energy-momentum tensor. In order to do that, we explicitly construct the complete set of normalized wave functions for each configuration of the magnetic field. We show that in the region outside the tube, the FC and the VEV of the energy-momentum tensor are decomposed into two parts: The first ones correspond to the zero-thickness magnetic flux contributions, and the second ones are induced by the nontrivial structure of the magnetic field, named core-induced contributions. The latter present specific forms depending on the magnetic field configuration considered. We also show that the VEV of the energy-momentum tensor is diagonal and obeys the conservation condition, and its trace is expressed in terms of the fermionic condensate. The zero-thickness contributions to the FC and VEV of the energy-momentum tensor depend only on the fractional part of the ration of the magnetic flux inside the tube by the quantum one. As to the core-induced contributions, they depend on the total magnetic flux inside the tube and, consequently, in general, are not a periodic function of the magnetic flux.
Disassembling the clockwork mechanism
NASA Astrophysics Data System (ADS)
Craig, Nathaniel; Garcia Garcia, Isabel; Sutherland, Dave
2017-10-01
The clockwork mechanism is a means of naturally generating exponential hierarchies in theories without significant hierarchies among fundamental parameters. We emphasize the role of interactions in the clockwork mechanism, demonstrating that clockwork is an intrinsically abelian phenomenon precluded in non-abelian theories such as Yang-Mills, non-linear sigma models, and gravity. We also show that clockwork is not realized in extra-dimensional theories through purely geometric effects, but may be generated by appropriate localization of zero modes.
Deformations of vector-scalar models
NASA Astrophysics Data System (ADS)
Barnich, Glenn; Boulanger, Nicolas; Henneaux, Marc; Julia, Bernard; Lekeu, Victor; Ranjbar, Arash
2018-02-01
Abelian vector fields non-minimally coupled to uncharged scalar fields arise in many contexts. We investigate here through algebraic methods their consistent deformations ("gaugings"), i.e., the deformations that preserve the number (but not necessarily the form or the algebra) of the gauge symmetries. Infinitesimal consistent deformations are given by the BRST cohomology classes at ghost number zero. We parametrize explicitly these classes in terms of various types of global symmetries and corresponding Noether currents through the characteristic cohomology related to antifields and equations of motion. The analysis applies to all ghost numbers and not just ghost number zero. We also provide a systematic discussion of the linear and quadratic constraints on these parameters that follow from higher-order consistency. Our work is relevant to the gaugings of extended supergravities.
Healy, Richard W.; Scanlon, Bridget R.
2010-01-01
Simulation models are widely used in all types of hydrologic studies, and many of these models can be used to estimate recharge. Models can provide important insight into the functioning of hydrologic systems by identifying factors that influence recharge. The predictive capability of models can be used to evaluate how changes in climate, water use, land use, and other factors may affect recharge rates. Most hydrological simulation models, including watershed models and groundwater-flow models, are based on some form of water-budget equation, so the material in this chapter is closely linked to that in Chapter 2. Empirical models that are not based on a water-budget equation have also been used for estimating recharge; these models generally take the form of simple estimation equations that define annual recharge as a function of precipitation and possibly other climatic data or watershed characteristics.Model complexity varies greatly. Some models are simple accounting models; others attempt to accurately represent the physics of water movement through each compartment of the hydrologic system. Some models provide estimates of recharge explicitly; for example, a model based on the Richards equation can simulate water movement from the soil surface through the unsaturated zone to the water table. Recharge estimates can be obtained indirectly from other models. For example, recharge is a parameter in groundwater-flow models that solve for hydraulic head (i.e. groundwater level). Recharge estimates can be obtained through a model calibration process in which recharge and other model parameter values are adjusted so that simulated water levels agree with measured water levels. The simulation that provides the closest agreement is called the best fit, and the recharge value used in that simulation is the model-generated estimate of recharge.
Computational studies of model disordered and strongly correlated electronic systems
NASA Astrophysics Data System (ADS)
Johri, Sonika
cannot be achieved perfectly in experiments. A chapter of this thesis is devoted to studying signatures of incomplete localization in a disordered system with interacting particles which is coupled to a bath. . Strongly interacting particles can also give rise to topological phases of matter that have exotic emergent properties, such as quasiparticles with fractional charges and anyonic, or perhaps even non-Abelian statistics. In addition to their intrinsic novelty, these particles (e.g. Majorana fermions) may be the building blocks of future quantum computers. The third part of my thesis focuses on the best experimentally known realizations of such systems - the fractional quantum Hall effect (FQHE) which occurs in two-dimensional electron gases in a strong perpendicular magnetic field. It has been observed in systems such as semiconductor heterostructures and, more recently, graphene. I have developed software for exact diagonalization of the many-body FQHE problem on the surface of a cylinder, a hitherto unstudied type of geometry. This geometry turns out to be optimal for the DMRG algorithm. Using this new geometry, I have studied properties of various fractionally-filled states, computing the overlap between exact ground states and model wavefunctions, their edge excitations, and entanglement spectra. I have calculated the sizes and tunneling amplitudes of quasiparticles, information which is needed to design the interferometers used to experimentally measure their Aharanov-Bohm phase. I have also designed numerical probes of the recently discovered geometric degree of freedom of FQHE states.
This presentation presented information on entrainment models. Entrainment models use entrainment hypotheses to express the continuity equation. The advantage is that plume boundaries are known. A major disadvantage is that the problems that can be solved are rather simple. The ...
ERIC Educational Resources Information Center
James, W. G. G.
1970-01-01
Discusses the historical development of both the wave and the corpuscular photon model of light. Suggests that students should be informed that the two models are complementary and that each model successfully describes a wide range of radiation phenomena. Cites 19 references which might be of interest to physics teachers and students. (LC)
Phoenix (formerly referred to as the Second Generation Model or SGM) is a global general equilibrium model designed to analyze energy-economy-climate related questions and policy implications in the medium- to long-term. This model disaggregates the global economy into 26 industr...
NASA Technical Reports Server (NTRS)
Druyan, Leonard M.
2012-01-01
Climate models is a very broad topic, so a single volume can only offer a small sampling of relevant research activities. This volume of 14 chapters includes descriptions of a variety of modeling studies for a variety of geographic regions by an international roster of authors. The climate research community generally uses the rubric climate models to refer to organized sets of computer instructions that produce simulations of climate evolution. The code is based on physical relationships that describe the shared variability of meteorological parameters such as temperature, humidity, precipitation rate, circulation, radiation fluxes, etc. Three-dimensional climate models are integrated over time in order to compute the temporal and spatial variations of these parameters. Model domains can be global or regional and the horizontal and vertical resolutions of the computational grid vary from model to model. Considering the entire climate system requires accounting for interactions between solar insolation, atmospheric, oceanic and continental processes, the latter including land hydrology and vegetation. Model simulations may concentrate on one or more of these components, but the most sophisticated models will estimate the mutual interactions of all of these environments. Advances in computer technology have prompted investments in more complex model configurations that consider more phenomena interactions than were possible with yesterday s computers. However, not every attempt to add to the computational layers is rewarded by better model performance. Extensive research is required to test and document any advantages gained by greater sophistication in model formulation. One purpose for publishing climate model research results is to present purported advances for evaluation by the scientific community.
NASA Technical Reports Server (NTRS)
Tao, Wei-Kuo; Moncrieff, Mitchell; Einaud, Franco (Technical Monitor)
2001-01-01
Numerical cloud models have been developed and applied extensively to study cloud-scale and mesoscale processes during the past four decades. The distinctive aspect of these cloud models is their ability to treat explicitly (or resolve) cloud-scale dynamics. This requires the cloud models to be formulated from the non-hydrostatic equations of motion that explicitly include the vertical acceleration terms since the vertical and horizontal scales of convection are similar. Such models are also necessary in order to allow gravity waves, such as those triggered by clouds, to be resolved explicitly. In contrast, the hydrostatic approximation, usually applied in global or regional models, does allow the presence of gravity waves. In addition, the availability of exponentially increasing computer capabilities has resulted in time integrations increasing from hours to days, domain grids boxes (points) increasing from less than 2000 to more than 2,500,000 grid points with 500 to 1000 m resolution, and 3-D models becoming increasingly prevalent. The cloud resolving model is now at a stage where it can provide reasonably accurate statistical information of the sub-grid, cloud-resolving processes poorly parameterized in climate models and numerical prediction models.
NASA Technical Reports Server (NTRS)
Bardina, Jorge E.
1995-01-01
The objective of this work is to develop, verify, and incorporate the baseline two-equation turbulence models which account for the effects of compressibility into the three-dimensional Reynolds averaged Navier-Stokes (RANS) code and to provide documented descriptions of the models and their numerical procedures so that they can be implemented into 3-D CFD codes for engineering applications.
ERIC Educational Resources Information Center
Lawler, Robert W.
1996-01-01
Argues that the organization of cognitive structures for technical domains can be visualized as a network of connected thinkable models. Describes a taxonomy of models that has been developed and discusses the issue of how representations relate to human modes of perception and action. Contains 25 references. (DDR)
ERIC Educational Resources Information Center
Ballard, W.L.
1968-01-01
The article discusses models of synchronic and diachronic phonology and suggests changes in them. The basic generative model of phonology is outlined with the author's reinterpretations. The systematic phonemic level is questioned in terms of its unreality with respect to linguistic performance and its lack of validity with respect to historical…
ERIC Educational Resources Information Center
Oh, Phil Seok; Oh, Sung Jin
2013-01-01
Modeling in science has been studied by education researchers for decades and is now being applied broadly in school. It is among the scientific practices featured in the "Next Generation Science Standards" ("NGSS") (Achieve Inc. 2013). This article describes modeling activities in an extracurricular science club in a high…
Nonlinear Dynamics, Chaotic and Complex Systems
NASA Astrophysics Data System (ADS)
Infeld, E.; Zelazny, R.; Galkowski, A.
2011-04-01
Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet
Modeling complexes of modeled proteins.
Anishchenko, Ivan; Kundrotas, Petras J; Vakser, Ilya A
2017-03-01
Structural characterization of proteins is essential for understanding life processes at the molecular level. However, only a fraction of known proteins have experimentally determined structures. This fraction is even smaller for protein-protein complexes. Thus, structural modeling of protein-protein interactions (docking) primarily has to rely on modeled structures of the individual proteins, which typically are less accurate than the experimentally determined ones. Such "double" modeling is the Grand Challenge of structural reconstruction of the interactome. Yet it remains so far largely untested in a systematic way. We present a comprehensive validation of template-based and free docking on a set of 165 complexes, where each protein model has six levels of structural accuracy, from 1 to 6 Å C α RMSD. Many template-based docking predictions fall into acceptable quality category, according to the CAPRI criteria, even for highly inaccurate proteins (5-6 Å RMSD), although the number of such models (and, consequently, the docking success rate) drops significantly for models with RMSD > 4 Å. The results show that the existing docking methodologies can be successfully applied to protein models with a broad range of structural accuracy, and the template-based docking is much less sensitive to inaccuracies of protein models than the free docking. Proteins 2017; 85:470-478. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
ERIC Educational Resources Information Center
Lin, Tony; Erfan, Sasan
2016-01-01
Mathematical modeling is an open-ended research subject where no definite answers exist for any problem. Math modeling enables thinking outside the box to connect different fields of studies together including statistics, algebra, calculus, matrices, programming and scientific writing. As an integral part of society, it is the foundation for many…
Exact results for the star lattice chiral spin liquid
NASA Astrophysics Data System (ADS)
Kells, G.; Mehta, D.; Slingerland, J. K.; Vala, J.
2010-03-01
We examine the star lattice Kitaev model whose ground state is a chiral spin liquid. We fermionize the model such that the fermionic vacua are toric-code states on an effective Kagome lattice. This implies that the Abelian phase of the system is inherited from the fermionic vacua and that time-reversal symmetry is spontaneously broken at the level of the vacuum. In terms of these fermions we derive the Bloch-matrix Hamiltonians for the vortex-free sector and its time-reversed counterpart and illuminate the relationships between the sectors. The phase diagram for the model is shown to be a sphere in the space of coupling parameters around the triangles of the lattices. The Abelian phase lies inside the sphere and the critical boundary between topologically distinct Abelian and non-Abelian phases lies on the surface. Outside the sphere the system is generically gapped except in the planes where the coupling parameters between the vertices on triangles are zero. These cases correspond to bipartite lattice structures and the dispersion relations are similar to that of the original Kitaev honeycomb model. In a further analysis we demonstrate the threefold non-Abelian ground-state degeneracy on a torus by explicit calculation.
EPA's modeling community is working to gain insights into certain parts of a physical, biological, economic, or social system by conducting environmental assessments for Agency decision making to complex environmental issues.
Energy models characterize the energy system, its evolution, and its interactions with the broader economy. The energy system consists of primary resources, including both fossil fuels and renewables; power plants, refineries, and other technologies to process and convert these r...
NASA Technical Reports Server (NTRS)
Guillet, J. E.
1984-01-01
A reaction kinetics based model of the photodegradation process, which measures all important rate constants, and a computerized model capable of predicting the photodegradation rate and failure modes of a 30 year period, were developed. It is shown that the computerized photodegradation model for polyethylene correctly predicts failure of ELVAX 15 and cross linked ELVAX 150 on outdoor exposure. It is indicated that cross linking ethylene vinyl acetate (EVA) does not significantly change its degradation rate. It is shown that the effect of the stabilizer package is approximately equivalent on both polymers. The computerized model indicates that peroxide decomposers and UV absorbers are the most effective stabilizers. It is found that a combination of UV absorbers and a hindered amine light stabilizer (HALS) is the most effective stabilizer system.
NASA Astrophysics Data System (ADS)
Regardt, Olle; Rönnbäck, Lars; Bergholtz, Maria; Johannesson, Paul; Wohed, Petia
Maintaining and evolving data warehouses is a complex, error prone, and time consuming activity. The main reason for this state of affairs is that the environment of a data warehouse is in constant change, while the warehouse itself needs to provide a stable and consistent interface to information spanning extended periods of time. In this paper, we propose a modeling technique for data warehousing, called anchor modeling, that offers non-destructive extensibility mechanisms, thereby enabling robust and flexible management of changes in source systems. A key benefit of anchor modeling is that changes in a data warehouse environment only require extensions, not modifications, to the data warehouse. This ensures that existing data warehouse applications will remain unaffected by the evolution of the data warehouse, i.e. existing views and functions will not have to be modified as a result of changes in the warehouse model.
NASA Technical Reports Server (NTRS)
Denning, Peter J.
1990-01-01
Although powerful computers have allowed complex physical and manmade hardware systems to be modeled successfully, we have encountered persistent problems with the reliability of computer models for systems involving human learning, human action, and human organizations. This is not a misfortune; unlike physical and manmade systems, human systems do not operate under a fixed set of laws. The rules governing the actions allowable in the system can be changed without warning at any moment, and can evolve over time. That the governing laws are inherently unpredictable raises serious questions about the reliability of models when applied to human situations. In these domains, computers are better used, not for prediction and planning, but for aiding humans. Examples are systems that help humans speculate about possible futures, offer advice about possible actions in a domain, systems that gather information from the networks, and systems that track and support work flows in organizations.
NASA Technical Reports Server (NTRS)
Kallman, T.
2010-01-01
Warm absorber spectra are characterized by the many lines from partially ionized intermediate-Z elements, and iron, detected with the grating instruments on Chandra and XMM-Newton. If these ions are formed in a gas which is in photoionization equilibrium, they correspond to a broad range of ionization parameters, although there is evidence for certain preferred values. A test for any dynamical model for these outflows is to reproduce these properties, at some level of detail. In this paper we present a statistical analysis of the ionization distribution which can be applied both the observed spectra and to theoretical models. As an example, we apply it to our dynamical models for warm absorber outflows, based on evaporation from the molecular torus.
NASA Technical Reports Server (NTRS)
Smith, J. A. (Principal Investigator)
1985-01-01
The overall goal of this work has been to develop a set of computational tools and media abstractions for the terrain bidirectional reflectance problem. The modeling of soil and vegetation surfaces has been emphasized with a gradual increase in the complexity of the media geometries treated. Pragmatic problems involved in the combined modeling of soil, vegetation, and atmospheric effects have been of interest and one of the objectives has been to describe the canopy reflectance problem in a classical radiative transfer sense permitting easier inclusion of our work by other workers in the radiative transfer field.
ERIC Educational Resources Information Center
Ebert, James R.; Elliott, Nancy A.; Hurteau, Laura; Schulz, Amanda
2004-01-01
Students must understand the fundamental process of convection before they can grasp a wide variety of Earth processes, many of which may seem abstract because of the scales on which they operate. Presentation of a very visual, concrete model prior to instruction on these topics may facilitate students' understanding of processes that are largely…
Ensemble forecasting has been used for operational numerical weather prediction in the United States and Europe since the early 1990s. An ensemble of weather or climate forecasts is used to characterize the two main sources of uncertainty in computer models of physical systems: ...
NASA Astrophysics Data System (ADS)
Baart, F.; Donchyts, G.; van Dam, A.; Plieger, M.
2015-12-01
The emergence of interactive art has blurred the line between electronic, computer graphics and art. Here we apply this art form to numerical models. Here we show how the transformation of a numerical model into an interactive painting can both provide insights and solve real world problems. The cases that are used as an example include forensic reconstructions, dredging optimization, barrier design. The system can be fed using any source of time varying vector fields, such as hydrodynamic models. The cases used here, the Indian Ocean (HYCOM), the Wadden Sea (Delft3D Curvilinear), San Francisco Bay (3Di subgrid and Delft3D Flexible Mesh), show that the method used is suitable for different time and spatial scales. High resolution numerical models become interactive paintings by exchanging their velocity fields with a high resolution (>=1M cells) image based flow visualization that runs in a html5 compatible web browser. The image based flow visualization combines three images into a new image: the current image, a drawing, and a uv + mask field. The advection scheme that computes the resultant image is executed in the graphics card using WebGL, allowing for 1M grid cells at 60Hz performance on mediocre graphic cards. The software is provided as open source software. By using different sources for a drawing one can gain insight into several aspects of the velocity fields. These aspects include not only the commonly represented magnitude and direction, but also divergence, topology and turbulence .
Although air quality models have been applied historically to address issues specific to ambient air quality standards (i.e., one criteria pollutant at a time) or welfare (e.g.. acid deposition or visibility impairment). they are inherently multipollutant based. Therefore. in pri...
ERIC Educational Resources Information Center
Goodwyn, Lauren; Salm, Sarah
2007-01-01
Teaching the anatomy of the muscle system to high school students can be challenging. Students often learn about muscle anatomy by memorizing information from textbooks or by observing plastic, inflexible models. Although these mediums help students learn about muscle placement, the mediums do not facilitate understanding regarding integration of…
1975-01-01
thai h’liathe0in antd is finaull’ %IIIrd alt %tramlit And drohlttle. Mike aplpars Ito inua•,e upward in outler a rei and dowoi. ward it %iunr areli, Oil...fiducial marks should be constant and the edges phobic nor hydrophilic is better for routine sharpl ) defined. model testing. Before each launching in
Figures 1-10 and Table 1This dataset is associated with the following publication:Chang, S.Y., S. Arunachalam, A. Valencia, B. Naess, V. Isakov , M. Breen , T. Palma , and W. Vizuete. A modeling framework for characterizing near-road air pollutant concentration at community scales. SCIENCE OF THE TOTAL ENVIRONMENT. Elsevier BV, AMSTERDAM, NETHERLANDS, 538: 905-921, (2015).
(Super)symmetries of semiclassical models in theoretical and condensed matter physics
NASA Astrophysics Data System (ADS)
Ngome, J.-P.
2011-03-01
Van Holten's covariant algorithm for deriving conserved quantities is presented, with particular attention paid to Runge-Lenz-type vectors. The classical dynamics of isospin-carrying particles is reviewed. Physical applications including non-Abelian monopole-type systems in diatoms, introduced by Moody, Shapere and Wilczek, are considered. Applied to curved space, the formalism of van Holten allows us to describe the dynamical symmetries of generalized Kaluza-Klein monopoles. The framework is extended to supersymmetry and applied to the SUSY of the monopoles. Yet another application concerns the three-dimensional non-commutative oscillator.
Anyonic braiding in optical lattices
Zhang, Chuanwei; Scarola, V. W.; Tewari, Sumanta; Das Sarma, S.
2007-01-01
Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo nontrivial statistical transformations as one excitation is moved (braided) around another. Topological quantum computation proposes to use the topological protection and the braiding statistics of a non-Abelian topological state to perform quantum computation. The enormous technological prospect of topological quantum computation provides new motivation for experimentally observing a topological state. Here, we explicitly work out a realistic experimental scheme to create and braid the Abelian topological excitations in the Kitaev model built on a tunable robust system, a cold atom optical lattice. We also demonstrate how to detect the key feature of these excitations: their braiding statistics. Observation of this statistics would directly establish the existence of anyons, quantum particles that are neither fermions nor bosons. In addition to establishing topological matter, the experimental scheme we develop here can also be adapted to a non-Abelian topological state, supported by the same Kitaev model but in a different parameter regime, to eventually build topologically protected quantum gates. PMID:18000038
NASA Astrophysics Data System (ADS)
Günther, Uwe; Kuzhel, Sergii
2010-10-01
Gauged \\ {P}\\ {T} quantum mechanics (PTQM) and corresponding Krein space setups are studied. For models with constant non-Abelian gauge potentials and extended parity inversions compact and noncompact Lie group components are analyzed via Cartan decompositions. A Lie-triple structure is found and an interpretation as \\ {P}\\ {T}-symmetrically generalized Jaynes-Cummings model is possible with close relation to recently studied cavity QED setups with transmon states in multilevel artificial atoms. For models with Abelian gauge potentials a hidden Clifford algebra structure is found and used to obtain the fundamental symmetry of Krein space-related J-self-adjoint extensions for PTQM setups with ultra-localized potentials.
Models, Part V: Composition Models.
ERIC Educational Resources Information Center
Callison, Daniel
2003-01-01
Describes four models: The Authoring Cycle, a whole language approach that reflects the inquiry process; I-Search, an approach to research that uses the power of student interests; Cultural Celebration, using local heritage topics; and Science Lab Report, for the composition of a lab report. (LRW)
NASA Technical Reports Server (NTRS)
2000-01-01
The molecule modeling method known as Multibody Order (N) Dynamics, or MBO(N)D, was developed by Moldyn, Inc. at Goddard Space Flight Center through funding provided by the SBIR program. The software can model the dynamics of molecules through technology which stimulates low-frequency molecular motions and properties, such as movements among a molecule's constituent parts. With MBO(N)D, a molecule is substructured into a set of interconnected rigid and flexible bodies. These bodies replace the computation burden of mapping individual atoms. Moldyn's technology cuts computation time while increasing accuracy. The MBO(N)D technology is available as Insight II 97.0 from Molecular Simulations, Inc. Currently the technology is used to account for forces on spacecraft parts and to perform molecular analyses for pharmaceutical purposes. It permits the solution of molecular dynamics problems on a moderate workstation, as opposed to on a supercomputer.
NASA Technical Reports Server (NTRS)
1999-01-01
Dr. Donald Gilles, the Discipline Scientist for Materials Science in NASA's Microgravity Materials Science and Applications Department, demonstrates to Carl Dohrman a model of dendrites, the branch-like structures found in many metals and alloys. Dohrman was recently selected by the American Society for Metals International as their 1999 ASM International Foundation National Merit Scholar. The University of Illinois at Urbana-Champaign freshman recently toured NASA's materials science facilities at the Marshall Space Flight Center.
Walker, Ellen A
2010-01-01
As clinical studies reveal that chemotherapeutic agents may impair several different cognitive domains in humans, the development of preclinical animal models is critical to assess the degree of chemotherapy-induced learning and memory deficits and to understand the underlying neural mechanisms. In this chapter, the effects of various cancer chemotherapeutic agents in rodents on sensory processing, conditioned taste aversion, conditioned emotional response, passive avoidance, spatial learning, cued memory, discrimination learning, delayed-matching-to-sample, novel-object recognition, electrophysiological recordings and autoshaping is reviewed. It appears at first glance that the effects of the cancer chemotherapy agents in these many different models are inconsistent. However, a literature is emerging that reveals subtle or unique changes in sensory processing, acquisition, consolidation and retrieval that are dose- and time-dependent. As more studies examine cancer chemotherapeutic agents alone and in combination during repeated treatment regimens, the animal models will become more predictive tools for the assessment of these impairments and the underlying neural mechanisms. The eventual goal is to collect enough data to enable physicians to make informed choices about therapeutic regimens for their patients and discover new avenues of alternative or complementary therapies that reduce or eliminate chemotherapy-induced cognitive deficits.
NASA Astrophysics Data System (ADS)
Ausloos, Marcel; Vandewalle, Nicolas; Ivanova, Kristinka
Specialized topics on financial data analysis from a numerical and physical point of view are discussed when pertaining to the analysis of coherent and random sequences in financial fluctuations within (i) the extended detrended fluctuation analysis method, (ii) multi-affine analysis technique, (iii) mobile average intersection rules and distributions, (iv) sandpile avalanches models for crash prediction, (v) the (m,k)-Zipf method and (vi) the i-variability diagram technique for sorting out short range correlations. The most baffling result that needs further thought from mathematicians and physicists is recalled: the crossing of two mobile averages is an original method for measuring the "signal" roughness exponent, but why it is so is not understood up to now.
Pattern formation with proportionate growth
NASA Astrophysics Data System (ADS)
Dhar, Deepak
It is a common observation that as baby animals grow, different body parts grow approximately at same rate. This property, called proportionate growth is remarkable in that it is not encountered easily outside biology. The models of growth that have been studied in Physics so far, e.g diffusion -limited aggregation, surface deposition, growth of crystals from melt etc. involve only growth at the surface, with the inner structure remaining frozen. Interestingly, patterns formed in growing sandpiles provide a very wide variety of patterns that show proportionate growth. One finds patterns with different features, with sharply defined boundaries. In particular, even with very simple rules, one can produce patterns that show striking resemblance to those seen in nature. We can characterize the asymptotic pattern exactly in some special cases. I will discuss in particular the patterns grown on noisy backgrounds. Supported by J. C. Bose fellowship from DST (India).
Non-fixation for Conservative Stochastic Dynamics on the Line
NASA Astrophysics Data System (ADS)
Basu, Riddhipratim; Ganguly, Shirshendu; Hoffman, Christopher
2018-03-01
We consider activated random walk (ARW), a model which generalizes the stochastic sandpile, one of the canonical examples of self organized criticality. Informally ARW is a particle system on Z with mass conservation. One starts with a mass density {μ > 0} of initially active particles, each of which performs a symmetric random walk at rate one and falls asleep at rate {λ > 0}. Sleepy particles become active on coming in contact with other active particles. We investigate the question of fixation/non-fixation of the process and show for small enough {λ} the critical mass density for fixation is strictly less than one. Moreover, the critical density goes to zero as {λ} tends to zero. This settles a long standing open question.
Spreading granular material with a blade
NASA Astrophysics Data System (ADS)
Dressaire, Emilie; Singh, Vachitar; Grimaldi, Emma; Sauret, Alban
2015-11-01
The spreading of a complex fluid with a blade is encountered in applications that range from the bulldozing of granular material in construction projects to the coating of substrates with fluids in industrial applications. This spreading process is also present in everyday life, when we use a knife to turn a lump of peanut butter into a thin layer over our morning toast. In this study, we rely on granular media in a model experiment to describe the three-dimensional spreading of the material. Our experimental set-up allows tracking the spreading of a sandpile on a translating flat surface as the blade remains fixed. We characterize the spreading dynamics and the shape of the spread fluid layer when varying the tilt of the blade, its spacing with the surface and its speed. Our findings suggest that it is possible to tune the spreading parameters to optimize the coating.
Duality, marginal perturbations, and gauging
Henningson, M.; Nappi, C.R.
1993-07-15
We study duality transformations for two-dimensional [sigma] models with Abelian chiral isometries and prove that generic such transformations are equivalent to integrated marginal perturbations by bilinears in the chiral currents, thus confirming a recent conjecture by Hassan and Sen formulated in the context of Wess-Zumino-Witten models. Specific duality transformations instead give rise to coset models plus free bosons.
Vincent, Julian F V
2003-01-01
Biomimetics is seen as a path from biology to engineering. The only path from engineering to biology in current use is the application of engineering concepts and models to biological systems. However, there is another pathway: the verification of biological mechanisms by manufacture, leading to an iterative process between biology and engineering in which the new understanding that the engineering implementation of a biological system can bring is fed back into biology, allowing a more complete and certain understanding and the possibility of further revelations for application in engineering. This is a pathway as yet unformalized, and one that offers the possibility that engineers can also be scientists. PMID:14561351
Students' Models of Curve Fitting: A Models and Modeling Perspective
ERIC Educational Resources Information Center
Gupta, Shweta
2010-01-01
The Models and Modeling Perspectives (MMP) has evolved out of research that began 26 years ago. MMP researchers use Model Eliciting Activities (MEAs) to elicit students' mental models. In this study MMP was used as the conceptual framework to investigate the nature of students' models of curve fitting in a problem-solving environment consisting of…
10. MOVABLE BED SEDIMENTATION MODELS. DOGTOOTH BEND MODEL (MODEL SCALE: ...
10. MOVABLE BED SEDIMENTATION MODELS. DOGTOOTH BEND MODEL (MODEL SCALE: 1' = 400' HORIZONTAL, 1' = 100' VERTICAL), AND GREENVILLE BRIDGE MODEL (MODEL SCALE: 1' = 360' HORIZONTAL, 1' = 100' VERTICAL). - Waterways Experiment Station, Hydraulics Laboratory, Halls Ferry Road, 2 miles south of I-20, Vicksburg, Warren County, MS
Neutrino mixing in SO(10) GUTs with a non-Abelian flavor symmetry in the hidden sector
NASA Astrophysics Data System (ADS)
Smirnov, Alexei Yu.; Xu, Xun-Jie
2018-05-01
The relation between the mixing matrices of leptons and quarks, UPMNS≈VCKM†U0 , where U0 is a matrix of special forms [e.g., bimaximal (BM) and tribimaximal], can be a clue for understanding the lepton mixing and neutrino masses. It may imply the grand unification and the existence of a hidden sector with certain symmetry that generates U0 and leads to the smallness of neutrino masses. We apply the residual symmetry approach to obtain U0. The residual symmetries of both the visible and hidden sectors are Z2×Z2 . Their embedding in a unified flavor group is considered. We find that there are only several possible structures of U0, including the BM mixing and matrices with elements determined by the golden ratio. Realization of the BM scenario based on the SO(10) grand unified theory with the S4 flavor group is presented. Generic features of this scenario are discussed, in particular, the prediction of C P phase 14 4 ° ≲δCP≲21 0 ° in the minimal version.
NASA Astrophysics Data System (ADS)
Jurco, B.; Schraml, S.; Schupp, P.; Wess, J.
2000-11-01
An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces.
NASA Astrophysics Data System (ADS)
Georgiev, Lachezar S.
2006-12-01
We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma , in a way that might potentially allow for the topologically protected construction of a universal set of quantum gates. We construct, for the first time, a topologically protected controlled-NOT gate, which is entirely based on quasihole braidings of Pfaffian qubits. All single-qubit gates, except for the π/8 gate, are also explicitly implemented by quasihole braidings. Instead of the π/8 gate we try to construct a topologically protected Toffoli gate, in terms of the controlled-phase gate and CNOT or by a braid-group-based controlled-controlled- Z precursor. We also give a topologically protected realization of the Bravyi-Kitaev two-qubit gate g3 .
Sumner, Walton; Xu, Jin Zhong
2002-01-01
The American Board of Family Practice is developing a patient simulation program to evaluate diagnostic and management skills. The simulator must give temporally and physiologically reasonable answers to symptom questions such as "Have you been tired?" A three-step process generates symptom histories. In the first step, the simulator determines points in time where it should calculate instantaneous symptom status. In the second step, a Bayesian network implementing a roughly physiologic model of the symptom generates a value on a severity scale at each sampling time. Positive, zero, and negative values represent increased, normal, and decreased status, as applicable. The simulator plots these values over time. In the third step, another Bayesian network inspects this plot and reports how the symptom changed over time. This mechanism handles major trends, multiple and concurrent symptom causes, and gradually effective treatments. Other temporal insights, such as observations about short-term symptom relief, require complimentary mechanisms.
Modeling uncertainty: quicksand for water temperature modeling
Bartholow, John M.
2003-01-01
Uncertainty has been a hot topic relative to science generally, and modeling specifically. Modeling uncertainty comes in various forms: measured data, limited model domain, model parameter estimation, model structure, sensitivity to inputs, modelers themselves, and users of the results. This paper will address important components of uncertainty in modeling water temperatures, and discuss several areas that need attention as the modeling community grapples with how to incorporate uncertainty into modeling without getting stuck in the quicksand that prevents constructive contributions to policy making. The material, and in particular the reference, are meant to supplement the presentation given at this conference.
Comparative Protein Structure Modeling Using MODELLER
Webb, Benjamin; Sali, Andrej
2016-01-01
Comparative protein structure modeling predicts the three-dimensional structure of a given protein sequence (target) based primarily on its alignment to one or more proteins of known structure (templates). The prediction process consists of fold assignment, target-template alignment, model building, and model evaluation. This unit describes how to calculate comparative models using the program MODELLER and how to use the ModBase database of such models, and discusses all four steps of comparative modeling, frequently observed errors, and some applications. Modeling lactate dehydrogenase from Trichomonas vaginalis (TvLDH) is described as an example. The download and installation of the MODELLER software is also described. PMID:27322406
Magnetic monopole versus vortex as gauge-invariant topological objects for quark confinement
NASA Astrophysics Data System (ADS)
Kondo, Kei-Ichi; Sasago, Takaaki; Shinohara, Toru; Shibata, Akihiro; Kato, Seikou
2017-12-01
First, we give a gauge-independent definition of chromomagnetic monopoles in SU(N) Yang-Mills theory which is derived through a non-Abelian Stokes theorem for the Wilson loop operator. Then we discuss how such magnetic monopoles can give a nontrivial contribution to the Wilson loop operator for understanding the area law of the Wilson loop average. Next, we discuss how the magnetic monopole condensation picture are compatible with the vortex condensation picture as another promising scenario for quark confinement. We analyze the profile function of the magnetic flux tube as the non-Abelian vortex solution of U(N) gauge-Higgs model, which is to be compared with numerical simulations of the SU(N) Yang-Mills theory on a lattice. This analysis gives an estimate of the string tension based on the vortex condensation picture, and possible interactions between two non-Abelian vortices.
Pre-Modeling Ensures Accurate Solid Models
ERIC Educational Resources Information Center
Gow, George
2010-01-01
Successful solid modeling requires a well-organized design tree. The design tree is a list of all the object's features and the sequential order in which they are modeled. The solid-modeling process is faster and less prone to modeling errors when the design tree is a simple and geometrically logical definition of the modeled object. Few high…
Einstein-Yang-Mills-Dirac systems from the discretized Kaluza-Klein theory
NASA Astrophysics Data System (ADS)
Wali, Kameshwar; Viet, Nguyen Ali
2017-01-01
A unified theory of the non-Abelian gauge interactions with gravity in the framework of a discretized Kaluza-Klein theory is constructed with a modified Dirac operator and wedge product. All the couplings of chiral spinors to the non-Abelian gauge fields emerge naturally as components of the coupling of the chiral spinors in the generalized gravity together with some new interactions. In particular, the currently prevailing gravity-QCD quark and gravity-electroweak-quark and lepton models are shown to follow as special cases of the general framework.
Geometric Defects in Quantum Hall States
NASA Astrophysics Data System (ADS)
Gromov, Andrey
I will describe a geometric analogue of Laughlin quasiholes in fractional quantum Hall (FQH) states. These ``quasiholes'' are generated by an insertion of quantized fluxes of curvature - which can be modeled by branch points of a certain Riemann surface - and, consequently, are related to genons. Unlike quasiholes, the genons are not excitations, but extrinsic defects. Fusion of genons describes the response of an FQH state to a process that changes (effective) topology of the physical space. These defects are abelian for IQH states and non-abelian for FQH states. I will explain how to calculate an electric charge, geometric spin and adiabatic mutual statistics of the these defects. Leo Kadanoff Fellowship.
Vector models and generalized SYK models
Peng, Cheng
2017-05-23
Here, we consider the relation between SYK-like models and vector models by studying a toy model where a tensor field is coupled with a vector field. By integrating out the tensor field, the toy model reduces to the Gross-Neveu model in 1 dimension. On the other hand, a certain perturbation can be turned on and the toy model flows to an SYK-like model at low energy. Furthermore, a chaotic-nonchaotic phase transition occurs as the sign of the perturbation is altered. We further study similar models that possess chaos and enhanced reparameterization symmetries.
Frequentist Model Averaging in Structural Equation Modelling.
Jin, Shaobo; Ankargren, Sebastian
2018-06-04
Model selection from a set of candidate models plays an important role in many structural equation modelling applications. However, traditional model selection methods introduce extra randomness that is not accounted for by post-model selection inference. In the current study, we propose a model averaging technique within the frequentist statistical framework. Instead of selecting an optimal model, the contributions of all candidate models are acknowledged. Valid confidence intervals and a [Formula: see text] test statistic are proposed. A simulation study shows that the proposed method is able to produce a robust mean-squared error, a better coverage probability, and a better goodness-of-fit test compared to model selection. It is an interesting compromise between model selection and the full model.
NASA Astrophysics Data System (ADS)
Burger, M. H.; Killen, R. M.; M, N.; Sarantos, M.; Crider, D. H.; Vervak, R. J.
2009-04-01
Mercury has a tenuous exosphere created by the combined effects of solar radiation and micrometeoroid bombardment on the surface and the interaction of the solar wind with Mercury's magnetic field and surface. Observations of this exosphere provide essential data necessary for understanding the composition and evolution of Mercury's surface, as well as the interaction between Mercury's magnetosphere with the solar wind. The sodium component of the exosphere has been well observed from the ground (see review by Killen et al., 2007). These observations have revealed a highly variable and inhomogeneous exosphere with emission often peaking in the polar regions. Radiation acceleration drives exospheric escape producing a sodium tail pointing away from the sun which has been detected up to 1400 Mercury radii from the planet (Potter et al. 2002; Baumgardner et al. 2008). Calcium has also been observed in Mercury's exosphere showing a distribution distinct from sodium, although also variable (Killen et al. 2005). During the first two encounters with Mercury by MESSENGER, observations of the exosphere were made by the UltraViolet and Visible Spectrometer (UVVS) channel of the Mercury Atmospheric and Surface Composition Spectrometer (MASCS). Sodium and calcium emission were detected during both flybys, and magnesium was detected for the first time in Mercury's exosphere during the second flyby. The spatial distributions of these species showed significant, unexpected differences which suggest differences in the mechanisms responsible for releasing them from the surface. We present a Monte-Carlo model of sodium, magnesium, and calcium in Mercury's exosphere. The important source mechanisms for ejecting these species from the surface are sputtering by solar wind ions, photon-stimulated desorption, and micrometeoroid impact vaporization. Thermal desorption on the dayside does not supply enough energy to significantly populate the exosphere, although it does play a role in
Building Mental Models by Dissecting Physical Models
ERIC Educational Resources Information Center
Srivastava, Anveshna
2016-01-01
When students build physical models from prefabricated components to learn about model systems, there is an implicit trade-off between the physical degrees of freedom in building the model and the intensity of instructor supervision needed. Models that are too flexible, permitting multiple possible constructions require greater supervision to…
Target Scattering Metrics: Model-Model and Model Data comparisons
2017-12-13
measured synthetic aperture sonar (SAS) data or from numerical models is investigated. Metrics are needed for quantitative comparisons for signals...candidate metrics for model-model comparisons are examined here with a goal to consider raw data prior to its reduction to data products, which may...be suitable for input to classification schemes. The investigated metrics are then applied to model-data comparisons. INTRODUCTION Metrics for
Metabolic network modeling with model organisms.
Yilmaz, L Safak; Walhout, Albertha Jm
2017-02-01
Flux balance analysis (FBA) with genome-scale metabolic network models (GSMNM) allows systems level predictions of metabolism in a variety of organisms. Different types of predictions with different accuracy levels can be made depending on the applied experimental constraints ranging from measurement of exchange fluxes to the integration of gene expression data. Metabolic network modeling with model organisms has pioneered method development in this field. In addition, model organism GSMNMs are useful for basic understanding of metabolism, and in the case of animal models, for the study of metabolic human diseases. Here, we discuss GSMNMs of most highly used model organisms with the emphasis on recent reconstructions. Published by Elsevier Ltd.
Metabolic network modeling with model organisms
Yilmaz, L. Safak; Walhout, Albertha J.M.
2017-01-01
Flux balance analysis (FBA) with genome-scale metabolic network models (GSMNM) allows systems level predictions of metabolism in a variety of organisms. Different types of predictions with different accuracy levels can be made depending on the applied experimental constraints ranging from measurement of exchange fluxes to the integration of gene expression data. Metabolic network modeling with model organisms has pioneered method development in this field. In addition, model organism GSMNMs are useful for basic understanding of metabolism, and in the case of animal models, for the study of metabolic human diseases. Here, we discuss GSMNMs of most highly used model organisms with the emphasis on recent reconstructions. PMID:28088694
Air Quality Dispersion Modeling - Alternative Models
Models, not listed in Appendix W, that can be used in regulatory applications with case-by-case justification to the Reviewing Authority as noted in Section 3.2, Use of Alternative Models, in Appendix W.
Model selection for logistic regression models
NASA Astrophysics Data System (ADS)
Duller, Christine
2012-09-01
Model selection for logistic regression models decides which of some given potential regressors have an effect and hence should be included in the final model. The second interesting question is whether a certain factor is heterogeneous among some subsets, i.e. whether the model should include a random intercept or not. In this paper these questions will be answered with classical as well as with Bayesian methods. The application show some results of recent research projects in medicine and business administration.
[Bone remodeling and modeling/mini-modeling.
Hasegawa, Tomoka; Amizuka, Norio
Modeling, adapting structures to loading by changing bone size and shapes, often takes place in bone of the fetal and developmental stages, while bone remodeling-replacement of old bone into new bone-is predominant in the adult stage. Modeling can be divided into macro-modeling(macroscopic modeling)and mini-modeling(microscopic modeling). In the cellular process of mini-modeling, unlike bone remodeling, bone lining cells, i.e., resting flattened osteoblasts covering bone surfaces will become active form of osteoblasts, and then, deposit new bone onto the old bone without mediating osteoclastic bone resorption. Among the drugs for osteoporotic treatment, eldecalcitol(a vitamin D3 analog)and teriparatide(human PTH[1-34])could show mini-modeling based bone formation. Histologically, mature, active form of osteoblasts are localized on the new bone induced by mini-modeling, however, only a few cell layer of preosteoblasts are formed over the newly-formed bone, and accordingly, few osteoclasts are present in the region of mini-modeling. In this review, histological characteristics of bone remodeling and modeling including mini-modeling will be introduced.
ERIC Educational Resources Information Center
Willden, Jeff
2001-01-01
"Bohr's Atomic Model" is a small interactive multimedia program that introduces the viewer to a simplified model of the atom. This interactive simulation lets students build an atom using an atomic construction set. The underlying design methodology for "Bohr's Atomic Model" is model-centered instruction, which means the central model of the…
ERIC Educational Resources Information Center
Frees, Edward W.; Kim, Jee-Seon
2006-01-01
Multilevel models are proven tools in social research for modeling complex, hierarchical systems. In multilevel modeling, statistical inference is based largely on quantification of random variables. This paper distinguishes among three types of random variables in multilevel modeling--model disturbances, random coefficients, and future response…
Haiganoush Preisler; Alan Ager
2013-01-01
For applied mathematicians forest fire models refer mainly to a non-linear dynamic system often used to simulate spread of fire. For forest managers forest fire models may pertain to any of the three phases of fire management: prefire planning (fire risk models), fire suppression (fire behavior models), and postfire evaluation (fire effects and economic models). In...
Building mental models by dissecting physical models.
Srivastava, Anveshna
2016-01-01
When students build physical models from prefabricated components to learn about model systems, there is an implicit trade-off between the physical degrees of freedom in building the model and the intensity of instructor supervision needed. Models that are too flexible, permitting multiple possible constructions require greater supervision to ensure focused learning; models that are too constrained require less supervision, but can be constructed mechanically, with little to no conceptual engagement. We propose "model-dissection" as an alternative to "model-building," whereby instructors could make efficient use of supervisory resources, while simultaneously promoting focused learning. We report empirical results from a study conducted with biology undergraduate students, where we demonstrate that asking them to "dissect" out specific conceptual structures from an already built 3D physical model leads to a significant improvement in performance than asking them to build the 3D model from simpler components. Using questionnaires to measure understanding both before and after model-based interventions for two cohorts of students, we find that both the "builders" and the "dissectors" improve in the post-test, but it is the latter group who show statistically significant improvement. These results, in addition to the intrinsic time-efficiency of "model dissection," suggest that it could be a valuable pedagogical tool. © 2015 The International Union of Biochemistry and Molecular Biology.
NASA Astrophysics Data System (ADS)
Cheng, Meng; Tantivasadakarn, Nathanan; Wang, Chenjie
2018-01-01
We study Abelian braiding statistics of loop excitations in three-dimensional gauge theories with fermionic particles and the closely related problem of classifying 3D fermionic symmetry-protected topological (FSPT) phases with unitary symmetries. It is known that the two problems are related by turning FSPT phases into gauge theories through gauging the global symmetry of the former. We show that there exist certain types of Abelian loop braiding statistics that are allowed only in the presence of fermionic particles, which correspond to 3D "intrinsic" FSPT phases, i.e., those that do not stem from bosonic SPT phases. While such intrinsic FSPT phases are ubiquitous in 2D systems and in 3D systems with antiunitary symmetries, their existence in 3D systems with unitary symmetries was not confirmed previously due to the fact that strong interaction is necessary to realize them. We show that the simplest unitary symmetry to support 3D intrinsic FSPT phases is Z2×Z4. To establish the results, we first derive a complete set of physical constraints on Abelian loop braiding statistics. Solving the constraints, we obtain all possible Abelian loop braiding statistics in 3D gauge theories, including those that correspond to intrinsic FSPT phases. Then, we construct exactly soluble state-sum models to realize the loop braiding statistics. These state-sum models generalize the well-known Crane-Yetter and Dijkgraaf-Witten models.
Geologic Framework Model Analysis Model Report
R. Clayton
2000-12-19
The purpose of this report is to document the Geologic Framework Model (GFM), Version 3.1 (GFM3.1) with regard to data input, modeling methods, assumptions, uncertainties, limitations, and validation of the model results, qualification status of the model, and the differences between Version 3.1 and previous versions. The GFM represents a three-dimensional interpretation of the stratigraphy and structural features of the location of the potential Yucca Mountain radioactive waste repository. The GFM encompasses an area of 65 square miles (170 square kilometers) and a volume of 185 cubic miles (771 cubic kilometers). The boundaries of the GFM were chosen to encompassmore » the most widely distributed set of exploratory boreholes (the Water Table or WT series) and to provide a geologic framework over the area of interest for hydrologic flow and radionuclide transport modeling through the unsaturated zone (UZ). The depth of the model is constrained by the inferred depth of the Tertiary-Paleozoic unconformity. The GFM was constructed from geologic map and borehole data. Additional information from measured stratigraphy sections, gravity profiles, and seismic profiles was also considered. This interim change notice (ICN) was prepared in accordance with the Technical Work Plan for the Integrated Site Model Process Model Report Revision 01 (CRWMS M&O 2000). The constraints, caveats, and limitations associated with this model are discussed in the appropriate text sections that follow. The GFM is one component of the Integrated Site Model (ISM) (Figure l), which has been developed to provide a consistent volumetric portrayal of the rock layers, rock properties, and mineralogy of the Yucca Mountain site. The ISM consists of three components: (1) Geologic Framework Model (GFM); (2) Rock Properties Model (RPM); and (3) Mineralogic Model (MM). The ISM merges the detailed project stratigraphy into model stratigraphic units that are most useful for the primary downstream models
Photochemical Modeling Applications
Provides access to modeling applications involving photochemical models, including modeling of ozone, particulate matter (PM), and mercury for national and regional EPA regulations such as the Clean Air Interstate Rule (CAIR) and the Clean Air Mercury Rule
DOT National Transportation Integrated Search
1977-10-01
This report describes an operational, though preliminary, version of the Railroad Performance Model, which is a computer simulation model of the nation's railroad system. The ultimate purpose of this model is to predict the effect of changes in gover...
NASA Astrophysics Data System (ADS)
Brimicombe, N. W.
1991-07-01
Hot air balloons can be modelled in a number of different ways. The most satisfactory, but least useful model is at a microscopic level. Macroscopic models are easier to use but can be very misleading.
Contains WASP tutorial videos. WASP Command Line, WASP, Modeling Dissolved Oxygen, Building a Steady State Example, Modeling Nutrients in Rivers, Nutrient Cycles, Interpreting Water Quality Models, Linking with LSPC, WRDB, BASINS, WCS, WASP Network Tool
Analytic Modeling of Insurgencies
2014-08-01
Counterinsurgency, Situational Awareness, Civilians, Lanchester 1. Introduction Combat modeling is one of the oldest areas of operations research, dating...Army. The ground-breaking work of Lanchester in 1916 [1] marks the beginning of formal models of conflicts, where mathematical formulas and, later...Warfare model [3], which is a Lanchester - based mathematical model (see more details about this model later on), and McCormick’s Magic Diamond model [4
NASA Technical Reports Server (NTRS)
Liou, J. C.
2012-01-01
Presentation outlne: (1) The NASA Orbital Debris (OD) Engineering Model -- A mathematical model capable of predicting OD impact risks for the ISS and other critical space assets (2) The NASA OD Evolutionary Model -- A physical model capable of predicting future debris environment based on user-specified scenarios (3) The NASA Standard Satellite Breakup Model -- A model describing the outcome of a satellite breakup (explosion or collision)
Comparative Protein Structure Modeling Using MODELLER.
Webb, Benjamin; Sali, Andrej
2014-09-08
Functional characterization of a protein sequence is one of the most frequent problems in biology. This task is usually facilitated by accurate three-dimensional (3-D) structure of the studied protein. In the absence of an experimentally determined structure, comparative or homology modeling can sometimes provide a useful 3-D model for a protein that is related to at least one known protein structure. Comparative modeling predicts the 3-D structure of a given protein sequence (target) based primarily on its alignment to one or more proteins of known structure (templates). The prediction process consists of fold assignment, target-template alignment, model building, and model evaluation. This unit describes how to calculate comparative models using the program MODELLER and discusses all four steps of comparative modeling, frequently observed errors, and some applications. Modeling lactate dehydrogenase from Trichomonas vaginalis (TvLDH) is described as an example. The download and installation of the MODELLER software is also described. Copyright © 2014 John Wiley & Sons, Inc.
NASA Technical Reports Server (NTRS)
Cellier, Francois E.
1991-01-01
A comprehensive and systematic introduction is presented for the concepts associated with 'modeling', involving the transition from a physical system down to an abstract description of that system in the form of a set of differential and/or difference equations, and basing its treatment of modeling on the mathematics of dynamical systems. Attention is given to the principles of passive electrical circuit modeling, planar mechanical systems modeling, hierarchical modular modeling of continuous systems, and bond-graph modeling. Also discussed are modeling in equilibrium thermodynamics, population dynamics, and system dynamics, inductive reasoning, artificial neural networks, and automated model synthesis.
Models of ovarian cancer metastasis: Murine models
Šale, Sanja; Orsulic, Sandra
2008-01-01
Mice have mainly been used in ovarian cancer research as immunodeficient hosts for cell lines derived from the primary tumors and ascites of ovarian cancer patients. These xenograft models have provided a valuable system for pre-clinical trials, however, the genetic complexity of human tumors has precluded the understanding of key events that drive metastatic dissemination. Recently developed immunocompetent, genetically defined mouse models of epithelial ovarian cancer represent significant improvements in the modeling of metastatic disease. PMID:19337569
Integrity modelling of tropospheric delay models
NASA Astrophysics Data System (ADS)
Rózsa, Szabolcs; Bastiaan Ober, Pieter; Mile, Máté; Ambrus, Bence; Juni, Ildikó
2017-04-01
The effect of the neutral atmosphere on signal propagation is routinely estimated by various tropospheric delay models in satellite navigation. Although numerous studies can be found in the literature investigating the accuracy of these models, for safety-of-life applications it is crucial to study and model the worst case performance of these models using very low recurrence frequencies. The main objective of the INTegrity of TROpospheric models (INTRO) project funded by the ESA PECS programme is to establish a model (or models) of the residual error of existing tropospheric delay models for safety-of-life applications. Such models are required to overbound rare tropospheric delays and should thus include the tails of the error distributions. Their use should lead to safe error bounds on the user position and should allow computation of protection levels for the horizontal and vertical position errors. The current tropospheric model from the RTCA SBAS Minimal Operational Standards has an associated residual error that equals 0.12 meters in the vertical direction. This value is derived by simply extrapolating the observed distribution of the residuals into the tail (where no data is present) and then taking the point where the cumulative distribution has an exceedance level would be 10-7.While the resulting standard deviation is much higher than the estimated standard variance that best fits the data (0.05 meters), it surely is conservative for most applications. In the context of the INTRO project some widely used and newly developed tropospheric delay models (e.g. RTCA MOPS, ESA GALTROPO and GPT2W) were tested using 16 years of daily ERA-INTERIM Reanalysis numerical weather model data and the raytracing technique. The results showed that the performance of some of the widely applied models have a clear seasonal dependency and it is also affected by a geographical position. In order to provide a more realistic, but still conservative estimation of the residual
New 3D model for dynamics modeling
NASA Astrophysics Data System (ADS)
Perez, Alain
1994-05-01
The wrist articulation represents one of the most complex mechanical systems of the human body. It is composed of eight bones rolling and sliding along their surface and along the faces of the five metacarpals of the hand and the two bones of the arm. The wrist dynamics are however fundamental for the hand movement, but it is so complex that it still remains incompletely explored. This work is a part of a new concept of computer-assisted surgery, which consists in developing computer models to perfect surgery acts by predicting their consequences. The modeling of the wrist dynamics are based first on the static model of its bones in three dimensions. This 3D model must optimise the collision detection procedure which is the necessary step to estimate the physical contact constraints. As many other possible computer vision models do not fit with enough precision to this problem, a new 3D model has been developed thanks to the median axis of the digital distance map of the bones reconstructed volume. The collision detection procedure is then simplified for contacts are detected between spheres. The experiment of this original 3D dynamic model products realistic computer animation images of solids in contact. It is now necessary to detect ligaments on digital medical images and to model them in order to complete a wrist model.
Better models are more effectively connected models
NASA Astrophysics Data System (ADS)
Nunes, João Pedro; Bielders, Charles; Darboux, Frederic; Fiener, Peter; Finger, David; Turnbull-Lloyd, Laura; Wainwright, John
2016-04-01
The concept of hydrologic and geomorphologic connectivity describes the processes and pathways which link sources (e.g. rainfall, snow and ice melt, springs, eroded areas and barren lands) to accumulation areas (e.g. foot slopes, streams, aquifers, reservoirs), and the spatial variations thereof. There are many examples of hydrological and sediment connectivity on a watershed scale; in consequence, a process-based understanding of connectivity is crucial to help managers understand their systems and adopt adequate measures for flood prevention, pollution mitigation and soil protection, among others. Modelling is often used as a tool to understand and predict fluxes within a catchment by complementing observations with model results. Catchment models should therefore be able to reproduce the linkages, and thus the connectivity of water and sediment fluxes within the systems under simulation. In modelling, a high level of spatial and temporal detail is desirable to ensure taking into account a maximum number of components, which then enables connectivity to emerge from the simulated structures and functions. However, computational constraints and, in many cases, lack of data prevent the representation of all relevant processes and spatial/temporal variability in most models. In most cases, therefore, the level of detail selected for modelling is too coarse to represent the system in a way in which connectivity can emerge; a problem which can be circumvented by representing fine-scale structures and processes within coarser scale models using a variety of approaches. This poster focuses on the results of ongoing discussions on modelling connectivity held during several workshops within COST Action Connecteur. It assesses the current state of the art of incorporating the concept of connectivity in hydrological and sediment models, as well as the attitudes of modellers towards this issue. The discussion will focus on the different approaches through which connectivity
ERIC Educational Resources Information Center
Clancey, William J.
The concept of a qualitative model is used as the focus of this review of qualitative student models in order to compare alternative computational models and to contrast domain requirements. The report is divided into eight sections: (1) Origins and Goals (adaptive instruction, qualitative models of processes, components of an artificial…
Models of Counselling Centres.
ERIC Educational Resources Information Center
Calgary Univ. (Alberta).
University counseling centers usually follow one of a variety of themes or "models," although not in pure form. Perhaps the oldest is the vocational counseling model, which concentrates on helping students find suitable careers. In the psychotherapy model, most student concerns are seen for their personal content. Another model, student affairs…
ERIC Educational Resources Information Center
Yeates, Devin Rodney
2011-01-01
The goal of this dissertation is to enable better predictive models by engaging raw experimental data through the Instrumental Model. The Instrumental Model captures the protocols and procedures of experimental data analysis. The approach is formalized by encoding the Instrumental Model in an XML record. Decoupling the raw experimental data from…
NASA Astrophysics Data System (ADS)
Wenger, Trey V.; Kepley, Amanda K.; Balser, Dana S.
2017-07-01
HII Region Models fits HII region models to observed radio recombination line and radio continuum data. The algorithm includes the calculations of departure coefficients to correct for non-LTE effects. HII Region Models has been used to model star formation in the nucleus of IC 342.
NASA Astrophysics Data System (ADS)
Rahmani, Fouad Lazhar
2010-11-01
The aim of this paper is to present mathematical modelling of the spread of infection in the context of the transmission of the human immunodeficiency virus (HIV) and the acquired immune deficiency syndrome (AIDS). These models are based in part on the models suggested in the field of th AIDS mathematical modelling as reported by ISHAM [6].
Generative Models of Disfluency
ERIC Educational Resources Information Center
Miller, Timothy A.
2010-01-01
This thesis describes a generative model for representing disfluent phenomena in human speech. This model makes use of observed syntactic structure present in disfluent speech, and uses a right-corner transform on syntax trees to model this structure in a very natural way. Specifically, the phenomenon of speech repair is modeled by explicitly…
Efficient polarimetric BRDF model.
Renhorn, Ingmar G E; Hallberg, Tomas; Boreman, Glenn D
2015-11-30
The purpose of the present manuscript is to present a polarimetric bidirectional reflectance distribution function (BRDF) model suitable for hyperspectral and polarimetric signature modelling. The model is based on a further development of a previously published four-parameter model that has been generalized in order to account for different types of surface structures (generalized Gaussian distribution). A generalization of the Lambertian diffuse model is presented. The pBRDF-functions are normalized using numerical integration. Using directional-hemispherical reflectance (DHR) measurements, three of the four basic parameters can be determined for any wavelength. This simplifies considerably the development of multispectral polarimetric BRDF applications. The scattering parameter has to be determined from at least one BRDF measurement. The model deals with linear polarized radiation; and in similarity with e.g. the facet model depolarization is not included. The model is very general and can inherently model extreme surfaces such as mirrors and Lambertian surfaces. The complex mixture of sources is described by the sum of two basic models, a generalized Gaussian/Fresnel model and a generalized Lambertian model. Although the physics inspired model has some ad hoc features, the predictive power of the model is impressive over a wide range of angles and scattering magnitudes. The model has been applied successfully to painted surfaces, both dull and glossy and also on metallic bead blasted surfaces. The simple and efficient model should be attractive for polarimetric simulations and polarimetric remote sensing.
Molenaar, Peter C M
2017-01-01
Equivalences of two classes of dynamic models for weakly stationary multivariate time series are discussed: dynamic factor models and autoregressive models. It is shown that exploratory dynamic factor models can be rotated, yielding an infinite set of equivalent solutions for any observed series. It also is shown that dynamic factor models with lagged factor loadings are not equivalent to the currently popular state-space models, and that restriction of attention to the latter type of models may yield invalid results. The known equivalent vector autoregressive model types, standard and structural, are given a new interpretation in which they are conceived of as the extremes of an innovating type of hybrid vector autoregressive models. It is shown that consideration of hybrid models solves many problems, in particular with Granger causality testing.
WASP TRANSPORT MODELING AND WASP ECOLOGICAL MODELING
A combination of lectures, demonstrations, and hands-on excercises will be used to introduce pollutant transport modeling with the U.S. EPA's general water quality model, WASP (Water Quality Analysis Simulation Program). WASP features include a user-friendly Windows-based interfa...
Introduction to Adjoint Models
NASA Technical Reports Server (NTRS)
Errico, Ronald M.
2015-01-01
In this lecture, some fundamentals of adjoint models will be described. This includes a basic derivation of tangent linear and corresponding adjoint models from a parent nonlinear model, the interpretation of adjoint-derived sensitivity fields, a description of methods of automatic differentiation, and the use of adjoint models to solve various optimization problems, including singular vectors. Concluding remarks will attempt to correct common misconceptions about adjoint models and their utilization.
Trapped Radiation Model Uncertainties: Model-Data and Model-Model Comparisons
NASA Technical Reports Server (NTRS)
Armstrong, T. W.; Colborn, B. L.
2000-01-01
The standard AP8 and AE8 models for predicting trapped proton and electron environments have been compared with several sets of flight data to evaluate model uncertainties. Model comparisons are made with flux and dose measurements made on various U.S. low-Earth orbit satellites (APEX, CRRES, DMSP, LDEF, NOAA) and Space Shuttle flights, on Russian satellites (Photon-8, Cosmos-1887, Cosmos-2044), and on the Russian Mir Space Station. This report gives the details of the model-data comparisons-summary results in terms of empirical model uncertainty factors that can be applied for spacecraft design applications are given in a combination report. The results of model-model comparisons are also presented from standard AP8 and AE8 model predictions compared with the European Space Agency versions of AP8 and AE8 and with Russian-trapped radiation models.
Trapped Radiation Model Uncertainties: Model-Data and Model-Model Comparisons
NASA Technical Reports Server (NTRS)
Armstrong, T. W.; Colborn, B. L.
2000-01-01
The standard AP8 and AE8 models for predicting trapped proton and electron environments have been compared with several sets of flight data to evaluate model uncertainties. Model comparisons are made with flux and dose measurements made on various U.S. low-Earth orbit satellites (APEX, CRRES, DMSP. LDEF, NOAA) and Space Shuttle flights, on Russian satellites (Photon-8, Cosmos-1887, Cosmos-2044), and on the Russian Mir space station. This report gives the details of the model-data comparisons -- summary results in terms of empirical model uncertainty factors that can be applied for spacecraft design applications are given in a companion report. The results of model-model comparisons are also presented from standard AP8 and AE8 model predictions compared with the European Space Agency versions of AP8 and AE8 and with Russian trapped radiation models.
Modeling for Battery Prognostics
NASA Technical Reports Server (NTRS)
Kulkarni, Chetan S.; Goebel, Kai; Khasin, Michael; Hogge, Edward; Quach, Patrick
2017-01-01
For any battery-powered vehicles (be it unmanned aerial vehicles, small passenger aircraft, or assets in exoplanetary operations) to operate at maximum efficiency and reliability, it is critical to monitor battery health as well performance and to predict end of discharge (EOD) and end of useful life (EOL). To fulfil these needs, it is important to capture the battery's inherent characteristics as well as operational knowledge in the form of models that can be used by monitoring, diagnostic, and prognostic algorithms. Several battery modeling methodologies have been developed in last few years as the understanding of underlying electrochemical mechanics has been advancing. The models can generally be classified as empirical models, electrochemical engineering models, multi-physics models, and molecular/atomist. Empirical models are based on fitting certain functions to past experimental data, without making use of any physicochemical principles. Electrical circuit equivalent models are an example of such empirical models. Electrochemical engineering models are typically continuum models that include electrochemical kinetics and transport phenomena. Each model has its advantages and disadvantages. The former type of model has the advantage of being computationally efficient, but has limited accuracy and robustness, due to the approximations used in developed model, and as a result of such approximations, cannot represent aging well. The latter type of model has the advantage of being very accurate, but is often computationally inefficient, having to solve complex sets of partial differential equations, and thus not suited well for online prognostic applications. In addition both multi-physics and atomist models are computationally expensive hence are even less suited to online application An electrochemistry-based model of Li-ion batteries has been developed, that captures crucial electrochemical processes, captures effects of aging, is computationally efficient
Model Validation Status Review
E.L. Hardin
The primary objective for the Model Validation Status Review was to perform a one-time evaluation of model validation associated with the analysis/model reports (AMRs) containing model input to total-system performance assessment (TSPA) for the Yucca Mountain site recommendation (SR). This review was performed in response to Corrective Action Request BSC-01-C-01 (Clark 2001, Krisha 2001) pursuant to Quality Assurance review findings of an adverse trend in model validation deficiency. The review findings in this report provide the following information which defines the extent of model validation deficiency and the corrective action needed: (1) AMRs that contain or support models are identified,more » and conversely, for each model the supporting documentation is identified. (2) The use for each model is determined based on whether the output is used directly for TSPA-SR, or for screening (exclusion) of features, events, and processes (FEPs), and the nature of the model output. (3) Two approaches are used to evaluate the extent to which the validation for each model is compliant with AP-3.10Q (Analyses and Models). The approaches differ in regard to whether model validation is achieved within individual AMRs as originally intended, or whether model validation could be readily achieved by incorporating information from other sources. (4) Recommendations are presented for changes to the AMRs, and additional model development activities or data collection, that will remedy model validation review findings, in support of licensing activities. The Model Validation Status Review emphasized those AMRs that support TSPA-SR (CRWMS M&O 2000bl and 2000bm). A series of workshops and teleconferences was held to discuss and integrate the review findings. The review encompassed 125 AMRs (Table 1) plus certain other supporting documents and data needed to assess model validity. The AMRs were grouped in 21 model areas representing the modeling of processes affecting the natural
Modeling volatility using state space models.
Timmer, J; Weigend, A S
1997-08-01
In time series problems, noise can be divided into two categories: dynamic noise which drives the process, and observational noise which is added in the measurement process, but does not influence future values of the system. In this framework, we show that empirical volatilities (the squared relative returns of prices) exhibit a significant amount of observational noise. To model and predict their time evolution adequately, we estimate state space models that explicitly include observational noise. We obtain relaxation times for shocks in the logarithm of volatility ranging from three weeks (for foreign exchange) to three to five months (for stock indices). In most cases, a two-dimensional hidden state is required to yield residuals that are consistent with white noise. We compare these results with ordinary autoregressive models (without a hidden state) and find that autoregressive models underestimate the relaxation times by about two orders of magnitude since they do not distinguish between observational and dynamic noise. This new interpretation of the dynamics of volatility in terms of relaxators in a state space model carries over to stochastic volatility models and to GARCH models, and is useful for several problems in finance, including risk management and the pricing of derivative securities. Data sets used: Olsen & Associates high frequency DEM/USD foreign exchange rates (8 years). Nikkei 225 index (40 years). Dow Jones Industrial Average (25 years).
Modeling Guru: Knowledge Base for NASA Modelers
NASA Astrophysics Data System (ADS)
Seablom, M. S.; Wojcik, G. S.; van Aartsen, B. H.
2009-05-01
Modeling Guru is an on-line knowledge-sharing resource for anyone involved with or interested in NASA's scientific models or High End Computing (HEC) systems. Developed and maintained by the NASA's Software Integration and Visualization Office (SIVO) and the NASA Center for Computational Sciences (NCCS), Modeling Guru's combined forums and knowledge base for research and collaboration is becoming a repository for the accumulated expertise of NASA's scientific modeling and HEC communities. All NASA modelers and associates are encouraged to participate and provide knowledge about the models and systems so that other users may benefit from their experience. Modeling Guru is divided into a hierarchy of communities, each with its own set forums and knowledge base documents. Current modeling communities include those for space science, land and atmospheric dynamics, atmospheric chemistry, and oceanography. In addition, there are communities focused on NCCS systems, HEC tools and libraries, and programming and scripting languages. Anyone may view most of the content on Modeling Guru (available at http://modelingguru.nasa.gov/), but you must log in to post messages and subscribe to community postings. The site offers a full range of "Web 2.0" features, including discussion forums, "wiki" document generation, document uploading, RSS feeds, search tools, blogs, email notification, and "breadcrumb" links. A discussion (a.k.a. forum "thread") is used to post comments, solicit feedback, or ask questions. If marked as a question, SIVO will monitor the thread, and normally respond within a day. Discussions can include embedded images, tables, and formatting through the use of the Rich Text Editor. Also, the user can add "Tags" to their thread to facilitate later searches. The "knowledge base" is comprised of documents that are used to capture and share expertise with others. The default "wiki" document lets users edit within the browser so others can easily collaborate on the
Program management model study
NASA Technical Reports Server (NTRS)
Connelly, J. J.; Russell, J. E.; Seline, J. R.; Sumner, N. R., Jr.
1972-01-01
Two models, a system performance model and a program assessment model, have been developed to assist NASA management in the evaluation of development alternatives for the Earth Observations Program. Two computer models were developed and demonstrated on the Goddard Space Flight Center Computer Facility. Procedures have been outlined to guide the user of the models through specific evaluation processes, and the preparation of inputs describing earth observation needs and earth observation technology. These models are intended to assist NASA in increasing the effectiveness of the overall Earth Observation Program by providing a broader view of system and program development alternatives.
Modeling the transition region
NASA Technical Reports Server (NTRS)
Singer, Bart A.
1993-01-01
The current status of transition-region models is reviewed in this report. To understand modeling problems, various flow features that influence the transition process are discussed first. Then an overview of the different approaches to transition-region modeling is given. This is followed by a detailed discussion of turbulence models and the specific modifications that are needed to predict flows undergoing laminar-turbulent transition. Methods for determining the usefulness of the models are presented, and an outlook for the future of transition-region modeling is suggested.
NASA Astrophysics Data System (ADS)
Geller, Michael; Telem, Ofri
2015-05-01
We present the first realization of a "twin Higgs" model as a holographic composite Higgs model. Uniquely among composite Higgs models, the Higgs potential is protected by a new standard model (SM) singlet elementary "mirror" sector at the sigma model scale f and not by the composite states at mKK , naturally allowing for mKK beyond the LHC reach. As a result, naturalness in our model cannot be constrained by the LHC, but may be probed by precision Higgs measurements at future lepton colliders, and by direct searches for Kaluza-Klein excitations at a 100 TeV collider.
Geller, Michael; Telem, Ofri
2015-05-15
We present the first realization of a "twin Higgs" model as a holographic composite Higgs model. Uniquely among composite Higgs models, the Higgs potential is protected by a new standard model (SM) singlet elementary "mirror" sector at the sigma model scale f and not by the composite states at m_{KK}, naturally allowing for m_{KK} beyond the LHC reach. As a result, naturalness in our model cannot be constrained by the LHC, but may be probed by precision Higgs measurements at future lepton colliders, and by direct searches for Kaluza-Klein excitations at a 100 TeV collider.
Orthogonal Gaussian process models
Plumlee, Matthew; Joseph, V. Roshan
2017-01-01
Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads to poor estimation of the coefficients in the mean model, and thus the estimated mean model loses interpretability. This paper introduces a new Gaussian process model whose stochastic part is orthogonal to the mean part to address this issue. As a result, this paper also discusses applications to multi-fidelity simulations using data examples.
Orthogonal Gaussian process models
Plumlee, Matthew; Joseph, V. Roshan
Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads to poor estimation of the coefficients in the mean model, and thus the estimated mean model loses interpretability. This paper introduces a new Gaussian process model whose stochastic part is orthogonal to the mean part to address this issue. As a result, this paper also discusses applications to multi-fidelity simulations using data examples.
NASA Technical Reports Server (NTRS)
Cohen, Gerald C. (Inventor); McMann, Catherine M. (Inventor)
1991-01-01
An improved method and system for automatically generating reliability models for use with a reliability evaluation tool is described. The reliability model generator of the present invention includes means for storing a plurality of low level reliability models which represent the reliability characteristics for low level system components. In addition, the present invention includes means for defining the interconnection of the low level reliability models via a system architecture description. In accordance with the principles of the present invention, a reliability model for the entire system is automatically generated by aggregating the low level reliability models based on the system architecture description.
NASA Technical Reports Server (NTRS)
Peabody, Hume L.
2017-01-01
This presentation is meant to be an overview of the model building process It is based on typical techniques (Monte Carlo Ray Tracing for radiation exchange, Lumped Parameter, Finite Difference for thermal solution) used by the aerospace industry This is not intended to be a "How to Use ThermalDesktop" course. It is intended to be a "How to Build Thermal Models" course and the techniques will be demonstrated using the capabilities of ThermalDesktop (TD). Other codes may or may not have similar capabilities. The General Model Building Process can be broken into four top level steps: 1. Build Model; 2. Check Model; 3. Execute Model; 4. Verify Results.
Entanglement from topology in Chern-Simons theory
NASA Astrophysics Data System (ADS)
Salton, Grant; Swingle, Brian; Walter, Michael
2017-05-01
The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where topology alone determines the quantum states of the theory. In this work, we study the set of quantum states that can be prepared by the Euclidean path integral in three-dimensional Chern-Simons theory. Specifically, we consider arbitrary three-manifolds with a fixed number of torus boundaries in both Abelian U (1 ) and non-Abelian S O (3 ) Chern-Simons theory. For the Abelian theory, we find that the states that can be prepared coincide precisely with the set of stabilizer states from quantum information theory. This constrains the multipartite entanglement present in this theory, but it also reveals that stabilizer states can be described by topology. In particular, we find an explicit expression for the entanglement entropy of a many-torus subsystem using only a single replica, as well as a concrete formula for the number of GHZ states that can be distilled from a tripartite state prepared through path integration. For the non-Abelian theory, we find a notion of "state universality," namely that any state can be prepared to an arbitrarily good approximation. The manifolds we consider can also be viewed as toy models of multiboundary wormholes in AdS/CFT.
NASA Technical Reports Server (NTRS)
Ensey, Tyler S.
2013-01-01
During my internship at NASA, I was a model developer for Ground Support Equipment (GSE). The purpose of a model developer is to develop and unit test model component libraries (fluid, electrical, gas, etc.). The models are designed to simulate software for GSE (Ground Special Power, Crew Access Arm, Cryo, Fire and Leak Detection System, Environmental Control System (ECS), etc. .) before they are implemented into hardware. These models support verifying local control and remote software for End-Item Software Under Test (SUT). The model simulates the physical behavior (function, state, limits and 110) of each end-item and it's dependencies as defined in the Subsystem Interface Table, Software Requirements & Design Specification (SRDS), Ground Integrated Schematic (GIS), and System Mechanical Schematic.(SMS). The software of each specific model component is simulated through MATLAB's Simulink program. The intensiv model development life cycle is a.s follows: Identify source documents; identify model scope; update schedule; preliminary design review; develop model requirements; update model.. scope; update schedule; detailed design review; create/modify library component; implement library components reference; implement subsystem components; develop a test script; run the test script; develop users guide; send model out for peer review; the model is sent out for verifictionlvalidation; if there is empirical data, a validation data package is generated; if there is not empirical data, a verification package is generated; the test results are then reviewed; and finally, the user. requests accreditation, and a statement of accreditation is prepared. Once each component model is reviewed and approved, they are intertwined together into one integrated model. This integrated model is then tested itself, through a test script and autotest, so that it can be concluded that all models work conjointly, for a single purpose. The component I was assigned, specifically, was a
Aerosol Modeling for the Global Model Initiative
NASA Technical Reports Server (NTRS)
Weisenstein, Debra K.; Ko, Malcolm K. W.
2001-01-01
The goal of this project is to develop an aerosol module to be used within the framework of the Global Modeling Initiative (GMI). The model development work will be preformed jointly by the University of Michigan and AER, using existing aerosol models at the two institutions as starting points. The GMI aerosol model will be tested, evaluated against observations, and then applied to assessment of the effects of aircraft sulfur emissions as needed by the NASA Subsonic Assessment in 2001. The work includes the following tasks: 1. Implementation of the sulfur cycle within GMI, including sources, sinks, and aqueous conversion of sulfur. Aerosol modules will be added as they are developed and the GMI schedule permits. 2. Addition of aerosol types other than sulfate particles, including dust, soot, organic carbon, and black carbon. 3. Development of new and more efficient parameterizations for treating sulfate aerosol nucleation, condensation, and coagulation among different particle sizes and types.
Nonlinear Modeling by Assembling Piecewise Linear Models
NASA Technical Reports Server (NTRS)
Yao, Weigang; Liou, Meng-Sing
2013-01-01
To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.
Traffic & safety statewide model and GIS modeling.
DOT National Transportation Integrated Search
2012-07-01
Several steps have been taken over the past two years to advance the Utah Department of Transportation (UDOT) safety initiative. Previous research projects began the development of a hierarchical Bayesian model to analyze crashes on Utah roadways. De...
METEOROLOGICAL AND TRANSPORT MODELING
Advanced air quality simulation models, such as CMAQ, as well as other transport and dispersion models, require accurate and detailed meteorology fields. These meteorology fields include primary 3-dimensional dynamical and thermodynamical variables (e.g., winds, temperature, mo...
NASA Technical Reports Server (NTRS)
Agena, S. M.; Pusey, M. L.; Bogle, I. D.
1999-01-01
A thermodynamic framework (UNIQUAC model with temperature dependent parameters) is applied to model the salt-induced protein crystallization equilibrium, i.e., protein solubility. The framework introduces a term for the solubility product describing protein transfer between the liquid and solid phase and a term for the solution behavior describing deviation from ideal solution. Protein solubility is modeled as a function of salt concentration and temperature for a four-component system consisting of a protein, pseudo solvent (water and buffer), cation, and anion (salt). Two different systems, lysozyme with sodium chloride and concanavalin A with ammonium sulfate, are investigated. Comparison of the modeled and experimental protein solubility data results in an average root mean square deviation of 5.8%, demonstrating that the model closely follows the experimental behavior. Model calculations and model parameters are reviewed to examine the model and protein crystallization process. Copyright 1999 John Wiley & Sons, Inc.
Bounding species distribution models
Stohlgren, T.J.; Jarnevich, C.S.; Esaias, W.E.; Morisette, J.T.
2011-01-01
Species distribution models are increasing in popularity for mapping suitable habitat for species of management concern. Many investigators now recognize that extrapolations of these models with geographic information systems (GIS) might be sensitive to the environmental bounds of the data used in their development, yet there is no recommended best practice for "clamping" model extrapolations. We relied on two commonly used modeling approaches: classification and regression tree (CART) and maximum entropy (Maxent) models, and we tested a simple alteration of the model extrapolations, bounding extrapolations to the maximum and minimum values of primary environmental predictors, to provide a more realistic map of suitable habitat of hybridized Africanized honey bees in the southwestern United States. Findings suggest that multiple models of bounding, and the most conservative bounding of species distribution models, like those presented here, should probably replace the unbounded or loosely bounded techniques currently used. ?? 2011 Current Zoology.
Bounding Species Distribution Models
NASA Technical Reports Server (NTRS)
Stohlgren, Thomas J.; Jarnevich, Cahterine S.; Morisette, Jeffrey T.; Esaias, Wayne E.
2011-01-01
Species distribution models are increasing in popularity for mapping suitable habitat for species of management concern. Many investigators now recognize that extrapolations of these models with geographic information systems (GIS) might be sensitive to the environmental bounds of the data used in their development, yet there is no recommended best practice for "clamping" model extrapolations. We relied on two commonly used modeling approaches: classification and regression tree (CART) and maximum entropy (Maxent) models, and we tested a simple alteration of the model extrapolations, bounding extrapolations to the maximum and minimum values of primary environmental predictors, to provide a more realistic map of suitable habitat of hybridized Africanized honey bees in the southwestern United States. Findings suggest that multiple models of bounding, and the most conservative bounding of species distribution models, like those presented here, should probably replace the unbounded or loosely bounded techniques currently used [Current Zoology 57 (5): 642-647, 2011].
ERIC Educational Resources Information Center
Bennett, Joan
1998-01-01
Recommends the use of a model of DNA made out of Velcro to help students visualize the steps of DNA replication. Includes a materials list, construction directions, and details of the demonstration using the model parts. (DDR)
NASA Technical Reports Server (NTRS)
Holland, L. D.; Walsh, J. R., Jr.; Wetherington, R. D.
1971-01-01
This report presents the results of work on communications systems modeling and covers three different areas of modeling. The first of these deals with the modeling of signals in communication systems in the frequency domain and the calculation of spectra for various modulations. These techniques are applied in determining the frequency spectra produced by a unified carrier system, the down-link portion of the Command and Communications System (CCS). The second modeling area covers the modeling of portions of a communication system on a block basis. A detailed analysis and modeling effort based on control theory is presented along with its application to modeling of the automatic frequency control system of an FM transmitter. A third topic discussed is a method for approximate modeling of stiff systems using state variable techniques.
NASA Technical Reports Server (NTRS)
Butler, Thomas G.
1987-01-01
Methods of modeling mass for bars are surveyed. A method for extending John Archer's concept of consistent mass beyond just translational inertia effects is included. Recommendations are given for various types of modeling situations.
DOT National Transportation Integrated Search
1995-02-01
This report annotates the cold regions mobility prediction routines included in the CAAMS/ALBE mobility models. It further explains the development of the algorithms that are used in these models to describe the interaction of a vehicle with terrain ...
DOT National Transportation Integrated Search
2014-01-01
This study developed a new snow model and a database which warehouses geometric, weather and traffic : data on New Jersey highways. The complexity of the model development lies in considering variable road : width, different spreading/plowing pattern...
We developed a simplified spreadsheet modeling approach for characterizing and prioritizing sources of sediment loadings from watersheds in the United States. A simplified modeling approach was developed to evaluate sediment loadings from watersheds and selected land segments. ...
Consistent model driven architecture
NASA Astrophysics Data System (ADS)
Niepostyn, Stanisław J.
2015-09-01
The goal of the MDA is to produce software systems from abstract models in a way where human interaction is restricted to a minimum. These abstract models are based on the UML language. However, the semantics of UML models is defined in a natural language. Subsequently the verification of consistency of these diagrams is needed in order to identify errors in requirements at the early stage of the development process. The verification of consistency is difficult due to a semi-formal nature of UML diagrams. We propose automatic verification of consistency of the series of UML diagrams originating from abstract models implemented with our consistency rules. This Consistent Model Driven Architecture approach enables us to generate automatically complete workflow applications from consistent and complete models developed from abstract models (e.g. Business Context Diagram). Therefore, our method can be used to check practicability (feasibility) of software architecture models.
Modeling Philosophies and Applications
All models begin with a framework and a set of assumptions and limitations that go along with that framework. In terms of fracing and RA, there are several places where models and parameters must be chosen to complete hazard identification.
DOT National Transportation Integrated Search
1976-04-01
This report describes the development of a model and companion data base for evaluating levels and qualities of service provided to the public by Air Carrier Airports. The model is designed to translate changes in airport capabilities into public ser...
Until recently, sediment geochemical models (diagenetic models) have been only able to explain sedimentary flux and concentration profiles for a few simplified geochemical cycles (e.g., nitrogen, carbon and sulfur). However with advances in numerical methods, increased accuracy ...
ERIC Educational Resources Information Center
Brinner, Bonnie
1992-01-01
Presents an activity in which models help students visualize both the DNA process and transcription. After constructing DNA, RNA messenger, and RNA transfer molecules; students model cells, protein synthesis, codons, and RNA movement. (MDH)
PARTICIPANT MODELING IN STUTTERING
Bhargava, S.C.
1988-01-01
SUMMARY Participant modeling was tried in twenty five stutterers; auditory feedback of modelled speech and guided exposure were also done along with. The patients were able to have a fluent stuttering free speech in most situations. PMID:21927289
Green Infrastructure Modeling Toolkit
EPA's Green Infrastructure Modeling Toolkit is a toolkit of 5 EPA green infrastructure models and tools, along with communication materials, that can be used as a teaching tool and a quick reference resource when making GI implementation decisions.
Mathematical circulatory system model
NASA Technical Reports Server (NTRS)
Lakin, William D. (Inventor); Stevens, Scott A. (Inventor)
2010-01-01
A system and method of modeling a circulatory system including a regulatory mechanism parameter. In one embodiment, a regulatory mechanism parameter in a lumped parameter model is represented as a logistic function. In another embodiment, the circulatory system model includes a compliant vessel, the model having a parameter representing a change in pressure due to contraction of smooth muscles of a wall of the vessel.
NASA Astrophysics Data System (ADS)
Tashiro, Tohru
2014-03-01
We propose a new model about diffusion of a product which includes a memory of how many adopters or advertisements a non-adopter met, where (non-)adopters mean people (not) possessing the product. This effect is lacking in the Bass model. As an application, we utilize the model to fit the iPod sales data, and so the better agreement is obtained than the Bass model.
Cancer Model Development Centers
The Cancer Model Development Centers (CMDCs) are the NCI-funded contributors to the HCMI. They are tasked with producing next-generation cancer models from clinical samples. The cancer models will encompass tumor types that are rare, originate from patients from underrepresented populations, or lack precision therapy. These models will be annotated with clinical and genomic data and will become a community resource.
Modeling of spacecraft charging
NASA Technical Reports Server (NTRS)
Whipple, E. C., Jr.
1977-01-01
Three types of modeling of spacecraft charging are discussed: statistical models, parametric models, and physical models. Local time dependence of circuit upset for DoD and communication satellites, and electron current to a sphere with an assumed Debye potential distribution are presented. Four regions were involved in spacecraft charging: (1) undisturbed plasma, (2) plasma sheath region, (3) spacecraft surface, and (4) spacecraft equivalent circuit.
Modeling individual tree survial
Quang V. Cao
2016-01-01
Information provided by growth and yield models is the basis for forest managers to makeÂ decisions on how to manage their forests. Among different types of growth models, whole-stand models offerÂ predictions at stand level, whereas individual-tree models give detailed information at tree level. The well-knownÂ logistic regression is commonly used to predict tree...
NASA Technical Reports Server (NTRS)
Mueller, A. C.
1977-01-01
An atmospheric model developed by Jacchia, quite accurate but requiring a large amount of computer storage and execution time, was found to be ill-suited for the space shuttle onboard program. The development of a simple atmospheric density model to simulate the Jacchia model was studied. Required characteristics including variation with solar activity, diurnal variation, variation with geomagnetic activity, semiannual variation, and variation with height were met by the new atmospheric density model.
NASA Technical Reports Server (NTRS)
Hildreth, W. W.
1978-01-01
A determination of the state of the art in soil moisture transport modeling based on physical or physiological principles was made. It was found that soil moisture models based on physical principles have been under development for more than 10 years. However, these models were shown to represent infiltration and redistribution of soil moisture quite well. Evapotranspiration has not been as adequately incorporated into the models.
Modelling MIZ dynamics in a global model
NASA Astrophysics Data System (ADS)
Rynders, Stefanie; Aksenov, Yevgeny; Feltham, Daniel; Nurser, George; Naveira Garabato, Alberto
2016-04-01
Exposure of large, previously ice-covered areas of the Arctic Ocean to the wind and surface ocean waves results in the Arctic pack ice cover becoming more fragmented and mobile, with large regions of ice cover evolving into the Marginal Ice Zone (MIZ). The need for better climate predictions, along with growing economic activity in the Polar Oceans, necessitates climate and forecasting models that can simulate fragmented sea ice with a greater fidelity. Current models are not fully fit for the purpose, since they neither model surface ocean waves in the MIZ, nor account for the effect of floe fragmentation on drag, nor include sea ice rheology that represents both the now thinner pack ice and MIZ ice dynamics. All these processes affect the momentum transfer to the ocean. We present initial results from a global ocean model NEMO (Nucleus for European Modelling of the Ocean) coupled to the Los Alamos sea ice model CICE. The model setup implements a novel rheological formulation for sea ice dynamics, accounting for ice floe collisions, thus offering a seamless framework for pack ice and MIZ simulations. The effect of surface waves on ice motion is included through wave pressure and the turbulent kinetic energy of ice floes. In the multidecadal model integrations we examine MIZ and basin scale sea ice and oceanic responses to the changes in ice dynamics. We analyse model sensitivities and attribute them to key sea ice and ocean dynamical mechanisms. The results suggest that the effect of the new ice rheology is confined to the MIZ. However with the current increase in summer MIZ area, which is projected to continue and may become the dominant type of sea ice in the Arctic, we argue that the effects of the combined sea ice rheology will be noticeable in large areas of the Arctic Ocean, affecting sea ice and ocean. With this study we assert that to make more accurate sea ice predictions in the changing Arctic, models need to include MIZ dynamics and physics.
Retrofitted supersymmetric models
NASA Astrophysics Data System (ADS)
Bose, Manatosh
This thesis explores several models of metastable dynamic supersymmetry breaking (MDSB) and a supersymmetric model of hybrid inflation. All of these models possess discrete R-symmetries. We specially focus on the retrofitted models for supersymmetry breaking models. At first we construct retrofitted models of gravity mediation. In these models we explore the genericity of the so-called "split supersymmetry." We show that with the simplest models, where the goldstino multiplet is neutral under the discrete R-symmetry, a split spectrum is not generic. However if the goldstino superfield is charged under some symmetry other than the R-symmetry, then a split spectrum is achievable but not generic. We also present a gravity mediated model where the fine tuning of the Z-boson mass is dictated by a discrete choice rather than a continuous tuning. Then we construct retrofitted models of gauge mediated SUSY breaking. We show that, in these models, if the approximate R-symmetry of the theory is spontaneously broken, the messenger scale is fixed; if explicitly broken by retrofitted couplings, a very small dimensionless number is required; if supergravity corrections are responsible for the symmetry breaking, at least two moderately small couplings are required, and that there is a large range of possible messenger scales. Finally we switch our attention to small field hybrid inflation. We construct a model that yields a spectral index ns = 0.96. Here, we also briefly discuss the possibility of relating the scale of inflation with the dynamics responsible for supersymmetry breaking.
ERIC Educational Resources Information Center
Fedorov, Alexander
2011-01-01
The author supposed that media education models can be divided into the following groups: (1) educational-information models (the study of the theory, history, language of media culture, etc.), based on the cultural, aesthetic, semiotic, socio-cultural theories of media education; (2) educational-ethical models (the study of moral, religions,…
ERIC Educational Resources Information Center
Speiser, Bob; Walter, Chuck
2011-01-01
This paper explores how models can support productive thinking. For us a model is a "thing", a tool to help make sense of something. We restrict attention to specific models for whole-number multiplication, hence the wording of the title. They support evolving thinking in large measure through the ways their users redesign them. They assume new…
ESPC Common Model Architecture
2014-09-30
1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. ESPC Common Model Architecture Earth System Modeling...Operational Prediction Capability (NUOPC) was established between NOAA and Navy to develop common software architecture for easy and efficient...development under a common model architecture and other software-related standards in this project. OBJECTIVES NUOPC proposes to accelerate
Open Source Molecular Modeling
Pirhadi, Somayeh; Sunseri, Jocelyn; Koes, David Ryan
2016-01-01
The success of molecular modeling and computational chemistry efforts are, by definition, dependent on quality software applications. Open source software development provides many advantages to users of modeling applications, not the least of which is that the software is free and completely extendable. In this review we categorize, enumerate, and describe available open source software packages for molecular modeling and computational chemistry. PMID:27631126
Modeling Applications and Tools
The U.S. EPA's Air Quality Modeling Group (AQMG) conducts modeling analyses to support policy and regulatory decisions in OAR and provides leadership and direction on the full range of air quality models and other mathematical simulation techniques used in
E. Gregory McPherson; Paula J. Peper
2012-01-01
This paper describes three long-term tree growth studies conducted to evaluate tree performance because repeated measurements of the same trees produce critical data for growth model calibration and validation. Several empirical and process-based approaches to modeling tree growth are reviewed. Modeling is more advanced in the fields of forestry and...
ERIC Educational Resources Information Center
Fitzsimmons, Charles P.
1986-01-01
Points out the instructional applications and program possibilities of a unit on model rocketry. Describes the ways that microcomputers can assist in model rocket design and in problem calculations. Provides a descriptive listing of model rocket software for the Apple II microcomputer. (ML)
1960-05-14
Project: Wing Sweep Range Series TAC Variable Sweep Model configure 8 A. Taken at 8 foot tunnels building 641. L60-3412 through 3416 Model of proposed military supersonic attack airplane shows wing sweep range. TAC Models taken at the 8 Foot Tunnel. Photograph published in Sixty Years of Aeronautical Research 1917-1977 By David A. Anderton. A NASA publication. Page 53.
Richard Haynes; Darius Adams; Peter Ince; John Mills; Ralph Alig
2006-01-01
The United States has a century of experience with the development of models that describe markets for forest products and trends in resource conditions. In the last four decades, increasing rigor in policy debates has stimulated the development of models to support policy analysis. Increasingly, research has evolved (often relying on computer-based models) to increase...
2017-03-01
models of software execution, for example memory access patterns, to check for security intrusions. Additional research was performed to tackle the...considered using indirect models of software execution, for example memory access patterns, to check for security intrusions. Additional research ...deterioration for example , no longer corresponds to the model used during verification time. Finally, the research looked at ways to combine hybrid systems
Elementary Teacher Training Models.
ERIC Educational Resources Information Center
Blewett, Evelyn J., Ed.
This collection of articles contains descriptions of nine elementary teacher training program models conducted at universities throughout the United States. The articles include the following: (a) "The University of Toledo Model Program," by George E. Dickson; (b) "The Florida State University Model Program," by G. Wesley Sowards; (c) "The…
USDA-ARS?s Scientific Manuscript database
Adsorption-desorption reactions are important processes that affect the transport of contaminants in the environment. Surface complexation models are chemical models that can account for the effects of variable chemical conditions, such as pH, on adsorption reactions. These models define specific ...
Model Breaking Points Conceptualized
ERIC Educational Resources Information Center
Vig, Rozy; Murray, Eileen; Star, Jon R.
2014-01-01
Current curriculum initiatives (e.g., National Governors Association Center for Best Practices and Council of Chief State School Officers 2010) advocate that models be used in the mathematics classroom. However, despite their apparent promise, there comes a point when models break, a point in the mathematical problem space where the model cannot,…
ERIC Educational Resources Information Center
Thornton, Bradley D.; Smalley, Robert A.
2008-01-01
Building information modeling (BIM) uses three-dimensional modeling concepts, information technology and interoperable software to design, construct and operate a facility. However, BIM can be more than a tool for virtual modeling--it can provide schools with a 3-D walkthrough of a project while it still is on the electronic drawing board. BIM can…
ERIC Educational Resources Information Center
Summerlin, Lee; Borgford, Christie
1989-01-01
Described is an activity which uses a 96-well reaction plate and soda straws to construct a model of the periodic table of the elements. The model illustrates the ionization energies of the various elements. Construction of the model and related concepts are discussed. (CW)
ERIC Educational Resources Information Center
Walsh, Jim; McGehee, Richard
2013-01-01
A dynamical systems approach to energy balance models of climate is presented, focusing on low order, or conceptual, models. Included are global average and latitude-dependent, surface temperature models. The development and analysis of the differential equations and corresponding bifurcation diagrams provides a host of appropriate material for…
ERIC Educational Resources Information Center
Bogiages, Christopher A.; Lotter, Christine
2011-01-01
In their research, scientists generate, test, and modify scientific models. These models can be shared with others and demonstrate a scientist's understanding of how the natural world works. Similarly, students can generate and modify models to gain a better understanding of the content, process, and nature of science (Kenyon, Schwarz, and Hug…
NASA Astrophysics Data System (ADS)
Marion, Giles M.; Kargel, Jeffrey S.
Implementation of the Pitzer approach is through the FREZCHEM (FREEZING CHEMISTRY) model, which is at the core of this work. This model was originally designed to simulate salt chemistries and freezing processes at low temperatures (-54 to 25°C) and 1 atm pressure. Over the years, this model has been broadened to include more chemistries (from 16 to 58 solid phases), a broader temperature range for some chemistries (to 113°C), and incorporation of a pressure dependence (1 to 1000 bars) into the model. Implementation, parameterization, validation, and limitations of the FREZCHEM model are extensively discussed in Chapter 3.
Ritchie, L.T.; Alpert, D.J.; Burke, R.P.
1984-03-01
The CRAC2 computer code is a revised version of CRAC (Calculation of Reactor Accident Consequences) which was developed for the Reactor Safety Study. This document provides an overview of the CRAC2 code and a description of each of the models used. Significant improvements incorporated into CRAC2 include an improved weather sequence sampling technique, a new evacuation model, and new output capabilities. In addition, refinements have been made to the atmospheric transport and deposition model. Details of the modeling differences between CRAC2 and CRAC are emphasized in the model descriptions.
NASA Astrophysics Data System (ADS)
Blackman, Jonathan; Field, Scott; Galley, Chad; Scheel, Mark; Szilagyi, Bela; Tiglio, Manuel
2015-04-01
With the advanced detector era just around the corner, there is a strong need for fast and accurate models of gravitational waveforms from compact binary coalescence. Fast surrogate models can be built out of an accurate but slow waveform model with minimal to no loss in accuracy, but may require a large number of evaluations of the underlying model. This may be prohibitively expensive if the underlying is extremely slow, for example if we wish to build a surrogate for numerical relativity. We examine alternate choices to building surrogate models which allow for a more sparse set of input waveforms. Research supported in part by NSERC.
Johnson, Douglas H.; Cook, R.D.
2013-01-01
In her AAAS News & Notes piece "Can the Southwest manage its thirst?" (26 July, p. 362), K. Wren quotes Ajay Kalra, who advocates a particular method for predicting Colorado River streamflow "because it eschews complex physical climate models for a statistical data-driven modeling approach." A preference for data-driven models may be appropriate in this individual situation, but it is not so generally, Data-driven models often come with a warning against extrapolating beyond the range of the data used to develop the models. When the future is like the past, data-driven models can work well for prediction, but it is easy to over-model local or transient phenomena, often leading to predictive inaccuracy (1). Mechanistic models are built on established knowledge of the process that connects the response variables with the predictors, using information obtained outside of an extant data set. One may shy away from a mechanistic approach when the underlying process is judged to be too complicated, but good predictive models can be constructed with statistical components that account for ingredients missing in the mechanistic analysis. Models with sound mechanistic components are more generally applicable and robust than data-driven models.
Collins, Lisa M.; Part, Chérie E.
2013-01-01
Simple Summary In this review paper we discuss the different modeling techniques that have been used in animal welfare research to date. We look at what questions they have been used to answer, the advantages and pitfalls of the methods, and how future research can best use these approaches to answer some of the most important upcoming questions in farm animal welfare. Abstract The use of models in the life sciences has greatly expanded in scope and advanced in technique in recent decades. However, the range, type and complexity of models used in farm animal welfare is comparatively poor, despite the great scope for use of modeling in this field of research. In this paper, we review the different modeling approaches used in farm animal welfare science to date, discussing the types of questions they have been used to answer, the merits and problems associated with the method, and possible future applications of each technique. We find that the most frequently published types of model used in farm animal welfare are conceptual and assessment models; two types of model that are frequently (though not exclusively) based on expert opinion. Simulation, optimization, scenario, and systems modeling approaches are rarer in animal welfare, despite being commonly used in other related fields. Finally, common issues such as a lack of quantitative data to parameterize models, and model selection and validation are discussed throughout the review, with possible solutions and alternative approaches suggested. PMID:26487411
NASA Technical Reports Server (NTRS)
Tijidjian, Raffi P.
2010-01-01
The TEAMS model analyzer is a supporting tool developed to work with models created with TEAMS (Testability, Engineering, and Maintenance System), which was developed by QSI. In an effort to reduce the time spent in the manual process that each TEAMS modeler must perform in the preparation of reporting for model reviews, a new tool has been developed as an aid to models developed in TEAMS. The software allows for the viewing, reporting, and checking of TEAMS models that are checked into the TEAMS model database. The software allows the user to selectively model in a hierarchical tree outline view that displays the components, failure modes, and ports. The reporting features allow the user to quickly gather statistics about the model, and generate an input/output report pertaining to all of the components. Rules can be automatically validated against the model, with a report generated containing resulting inconsistencies. In addition to reducing manual effort, this software also provides an automated process framework for the Verification and Validation (V&V) effort that will follow development of these models. The aid of such an automated tool would have a significant impact on the V&V process.
Making ecological models adequate
Getz, Wayne M.; Marshall, Charles R.; Carlson, Colin J.; Giuggioli, Luca; Ryan, Sadie J.; Romañach, Stephanie; Boettiger, Carl; Chamberlain, Samuel D.; Larsen, Laurel; D'Odorico, Paolo; O'Sullivan, David
2018-01-01
Critical evaluation of the adequacy of ecological models is urgently needed to enhance their utility in developing theory and enabling environmental managers and policymakers to make informed decisions. Poorly supported management can have detrimental, costly or irreversible impacts on the environment and society. Here, we examine common issues in ecological modelling and suggest criteria for improving modelling frameworks. An appropriate level of process description is crucial to constructing the best possible model, given the available data and understanding of ecological structures. Model details unsupported by data typically lead to over parameterisation and poor model performance. Conversely, a lack of mechanistic details may limit a model's ability to predict ecological systems’ responses to management. Ecological studies that employ models should follow a set of model adequacy assessment protocols that include: asking a series of critical questions regarding state and control variable selection, the determinacy of data, and the sensitivity and validity of analyses. We also need to improve model elaboration, refinement and coarse graining procedures to better understand the relevancy and adequacy of our models and the role they play in advancing theory, improving hind and forecasting, and enabling problem solving and management.
Spanagel, Rainer
2017-01-01
In recent years, animal models in psychiatric research have been criticized for their limited translational value to the clinical situation. Failures in clinical trials have thus often been attributed to the lack of predictive power of preclinical animal models. Here, I argue that animal models of voluntary drug intake—under nonoperant and operant conditions—and addiction models based on the Diagnostic and Statistical Manual of Mental Disorders are crucial and informative tools for the identification of pathological mechanisms, target identification, and drug development. These models provide excellent face validity, and it is assumed that the neurochemical and neuroanatomical substrates involved in drug-intake behavior are similar in laboratory rodents and humans. Consequently, animal models of drug consumption and addiction provide predictive validity. This predictive power is best illustrated in alcohol research, in which three approved medications—acamprosate, naltrexone, and nalmefene—were developed by means of animal models and then successfully translated into the clinical situation. PMID:29302222
NASA Astrophysics Data System (ADS)
Horstemeyer, M. F.
This review of multiscale modeling covers a brief history of various multiscale methodologies related to solid materials and the associated experimental influences, the various influence of multiscale modeling on different disciplines, and some examples of multiscale modeling in the design of structural components. Although computational multiscale modeling methodologies have been developed in the late twentieth century, the fundamental notions of multiscale modeling have been around since da Vinci studied different sizes of ropes. The recent rapid growth in multiscale modeling is the result of the confluence of parallel computing power, experimental capabilities to characterize structure-property relations down to the atomic level, and theories that admit multiple length scales. The ubiquitous research that focus on multiscale modeling has broached different disciplines (solid mechanics, fluid mechanics, materials science, physics, mathematics, biological, and chemistry), different regions of the world (most continents), and different length scales (from atoms to autos).
Physical modelling in biomechanics.
Koehl, M A R
2003-01-01
Physical models, like mathematical models, are useful tools in biomechanical research. Physical models enable investigators to explore parameter space in a way that is not possible using a comparative approach with living organisms: parameters can be varied one at a time to measure the performance consequences of each, while values and combinations not found in nature can be tested. Experiments using physical models in the laboratory or field can circumvent problems posed by uncooperative or endangered organisms. Physical models also permit some aspects of the biomechanical performance of extinct organisms to be measured. Use of properly scaled physical models allows detailed physical measurements to be made for organisms that are too small or fast to be easily studied directly. The process of physical modelling and the advantages and limitations of this approach are illustrated using examples from our research on hydrodynamic forces on sessile organisms, mechanics of hydraulic skeletons, food capture by zooplankton and odour interception by olfactory antennules. PMID:14561350
NASA Technical Reports Server (NTRS)
Guenther, D. B.; Demarque, P.; Kim, Y.-C.; Pinsonneault, M. H.
1992-01-01
A set of solar models have been constructed, each based on a single modification to the physics of a reference solar model. In addition, a model combining several of the improvements has been calculated to provide a best solar model. Improvements were made to the nuclear reaction rates, the equation of state, the opacities, and the treatment of the atmosphere. The impact on both the structure and the frequencies of the low-l p-modes of the model to these improvements are discussed. It is found that the combined solar model, which is based on the best physics available (and does not contain any ad hoc assumptions), reproduces the observed oscillation spectrum (for low-l) within the errors associated with the uncertainties in the model physics (primarily opacities).
Toward Scientific Numerical Modeling
NASA Technical Reports Server (NTRS)
Kleb, Bil
2007-01-01
Ultimately, scientific numerical models need quantified output uncertainties so that modeling can evolve to better match reality. Documenting model input uncertainties and verifying that numerical models are translated into code correctly, however, are necessary first steps toward that goal. Without known input parameter uncertainties, model sensitivities are all one can determine, and without code verification, output uncertainties are simply not reliable. To address these two shortcomings, two proposals are offered: (1) an unobtrusive mechanism to document input parameter uncertainties in situ and (2) an adaptation of the Scientific Method to numerical model development and deployment. Because these two steps require changes in the computational simulation community to bear fruit, they are presented in terms of the Beckhard-Harris-Gleicher change model.
NASA Technical Reports Server (NTRS)
Schoeberl, Mark; Rood, Richard B.; Hildebrand, Peter; Raymond, Carol
2003-01-01
The Earth System Model is the natural evolution of current climate models and will be the ultimate embodiment of our geophysical understanding of the planet. These models are constructed from components - atmosphere, ocean, ice, land, chemistry, solid earth, etc. models and merged together through a coupling program which is responsible for the exchange of data from the components. Climate models and future earth system models will have standardized modules, and these standards are now being developed by the ESMF project funded by NASA. The Earth System Model will have a variety of uses beyond climate prediction. The model can be used to build climate data records making it the core of an assimilation system, and it can be used in OSSE experiments to evaluate. The computing and storage requirements for the ESM appear to be daunting. However, the Japanese ES theoretical computing capability is already within 20% of the minimum requirements needed for some 2010 climate model applications. Thus it seems very possible that a focused effort to build an Earth System Model will achieve succcss.
Quantitative Rheological Model Selection
NASA Astrophysics Data System (ADS)
Freund, Jonathan; Ewoldt, Randy
2014-11-01
The more parameters in a rheological the better it will reproduce available data, though this does not mean that it is necessarily a better justified model. Good fits are only part of model selection. We employ a Bayesian inference approach that quantifies model suitability by balancing closeness to data against both the number of model parameters and their a priori uncertainty. The penalty depends upon prior-to-calibration expectation of the viable range of values that model parameters might take, which we discuss as an essential aspect of the selection criterion. Models that are physically grounded are usually accompanied by tighter physical constraints on their respective parameters. The analysis reflects a basic principle: models grounded in physics can be expected to enjoy greater generality and perform better away from where they are calibrated. In contrast, purely empirical models can provide comparable fits, but the model selection framework penalizes their a priori uncertainty. We demonstrate the approach by selecting the best-justified number of modes in a Multi-mode Maxwell description of PVA-Borax. We also quantify relative merits of the Maxwell model relative to powerlaw fits and purely empirical fits for PVA-Borax, a viscoelastic liquid, and gluten.
Chen, Changyou; Buntine, Wray; Ding, Nan; Xie, Lexing; Du, Lan
2015-02-01
In applications we may want to compare different document collections: they could have shared content but also different and unique aspects in particular collections. This task has been called comparative text mining or cross-collection modeling. We present a differential topic model for this application that models both topic differences and similarities. For this we use hierarchical Bayesian nonparametric models. Moreover, we found it was important to properly model power-law phenomena in topic-word distributions and thus we used the full Pitman-Yor process rather than just a Dirichlet process. Furthermore, we propose the transformed Pitman-Yor process (TPYP) to incorporate prior knowledge such as vocabulary variations in different collections into the model. To deal with the non-conjugate issue between model prior and likelihood in the TPYP, we thus propose an efficient sampling algorithm using a data augmentation technique based on the multinomial theorem. Experimental results show the model discovers interesting aspects of different collections. We also show the proposed MCMC based algorithm achieves a dramatically reduced test perplexity compared to some existing topic models. Finally, we show our model outperforms the state-of-the-art for document classification/ideology prediction on a number of text collections.
Models as Relational Categories
NASA Astrophysics Data System (ADS)
Kokkonen, Tommi
2017-11-01
Model-based learning (MBL) has an established position within science education. It has been found to enhance conceptual understanding and provide a way for engaging students in authentic scientific activity. Despite ample research, few studies have examined the cognitive processes regarding learning scientific concepts within MBL. On the other hand, recent research within cognitive science has examined the learning of so-called relational categories. Relational categories are categories whose membership is determined on the basis of the common relational structure. In this theoretical paper, I argue that viewing models as relational categories provides a well-motivated cognitive basis for MBL. I discuss the different roles of models and modeling within MBL (using ready-made models, constructive modeling, and generative modeling) and discern the related cognitive aspects brought forward by the reinterpretation of models as relational categories. I will argue that relational knowledge is vital in learning novel models and in the transfer of learning. Moreover, relational knowledge underlies the coherent, hierarchical knowledge of experts. Lastly, I will examine how the format of external representations may affect the learning of models and the relevant relations. The nature of the learning mechanisms underlying students' mental representations of models is an interesting open question to be examined. Furthermore, the ways in which the expert-like knowledge develops and how to best support it is in need of more research. The discussion and conceptualization of models as relational categories allows discerning students' mental representations of models in terms of evolving relational structures in greater detail than previously done.
Turbulence modeling and experiments
NASA Technical Reports Server (NTRS)
Shabbir, Aamir
1992-01-01
The best way of verifying turbulence is to do a direct comparison between the various terms and their models. The success of this approach depends upon the availability of the data for the exact correlations (both experimental and DNS). The other approach involves numerically solving the differential equations and then comparing the results with the data. The results of such a computation will depend upon the accuracy of all the modeled terms and constants. Because of this it is sometimes difficult to find the cause of a poor performance by a model. However, such a calculation is still meaningful in other ways as it shows how a complete Reynolds stress model performs. Thirteen homogeneous flows are numerically computed using the second order closure models. We concentrate only on those models which use a linear (or quasi-linear) model for the rapid term. This, therefore, includes the Launder, Reece and Rodi (LRR) model; the isotropization of production (IP) model; and the Speziale, Sarkar, and Gatski (SSG) model. Which of the three models performs better is examined along with what are their weaknesses, if any. The other work reported deal with the experimental balances of the second moment equations for a buoyant plume. Despite the tremendous amount of activity toward the second order closure modeling of turbulence, very little experimental information is available about the budgets of the second moment equations. Part of the problem stems from our inability to measure the pressure correlations. However, if everything else appearing in these equations is known from the experiment, pressure correlations can be obtained as the closing terms. This is the closest we can come to in obtaining these terms from experiment, and despite the measurement errors which might be present in such balances, the resulting information will be extremely useful for the turbulence modelers. The purpose of this part of the work was to provide such balances of the Reynolds stress and heat
Manpower Planning Models. 5. Optimization Models
1975-10-01
aide 11 neceaaary and Identity by block number) Manpower Planning \\ \\ X Modelling Optimization 20. ABS emry and Identity by block number...notation resulting from the previous maximum M. We exploit the probabilistic interpretation of the flow process whenever it eases the exposi - tion
Teaching macromolecular modeling.
Harvey, S C; Tan, R K
1992-01-01
Training newcomers to the field of macromolecular modeling is as difficult as is training beginners in x-ray crystallography, nuclear magnetic resonance, or other methods in structural biology. In one or two lectures, the most that can be conveyed is a general sense of the relationship between modeling and other structural methods. If a full semester is available, then students can be taught how molecular structures are built, manipulated, refined, and analyzed on a computer. Here we describe a one-semester modeling course that combines lectures, discussions, and a laboratory using a commercial modeling package. In the laboratory, students carry out prescribed exercises that are coordinated to the lectures, and they complete a term project on a modeling problem of their choice. The goal is to give students an understanding of what kinds of problems can be attacked by molecular modeling methods and which problems are beyond the current capabilities of those methods. PMID:1489919
Probabilistic Mesomechanical Fatigue Model
NASA Technical Reports Server (NTRS)
Tryon, Robert G.
1997-01-01
A probabilistic mesomechanical fatigue life model is proposed to link the microstructural material heterogeneities to the statistical scatter in the macrostructural response. The macrostructure is modeled as an ensemble of microelements. Cracks nucleation within the microelements and grow from the microelements to final fracture. Variations of the microelement properties are defined using statistical parameters. A micromechanical slip band decohesion model is used to determine the crack nucleation life and size. A crack tip opening displacement model is used to determine the small crack growth life and size. Paris law is used to determine the long crack growth life. The models are combined in a Monte Carlo simulation to determine the statistical distribution of total fatigue life for the macrostructure. The modeled response is compared to trends in experimental observations from the literature.
2013-01-01
Animal models of disease states are valuable tools for developing new treatments and investigating underlying mechanisms. They should mimic the symptoms and pathology of the disease and importantly be predictive of effective treatments. Fibromyalgia is characterized by chronic widespread pain with associated co-morbid symptoms that include fatigue, depression, anxiety and sleep dysfunction. In this review, we present different animal models that mimic the signs and symptoms of fibromyalgia. These models are induced by a wide variety of methods that include repeated muscle insults, depletion of biogenic amines, and stress. All potential models produce widespread and long-lasting hyperalgesia without overt peripheral tissue damage and thus mimic the clinical presentation of fibromyalgia. We describe the methods for induction of the model, pathophysiological mechanisms for each model, and treatment profiles. PMID:24314231
Zhou, Yongquan; Xie, Jian; Li, Liangliang; Ma, Mingzhi
2014-01-01
Bat algorithm (BA) is a novel stochastic global optimization algorithm. Cloud model is an effective tool in transforming between qualitative concepts and their quantitative representation. Based on the bat echolocation mechanism and excellent characteristics of cloud model on uncertainty knowledge representation, a new cloud model bat algorithm (CBA) is proposed. This paper focuses on remodeling echolocation model based on living and preying characteristics of bats, utilizing the transformation theory of cloud model to depict the qualitative concept: “bats approach their prey.” Furthermore, Lévy flight mode and population information communication mechanism of bats are introduced to balance the advantage between exploration and exploitation. The simulation results show that the cloud model bat algorithm has good performance on functions optimization. PMID:24967425
Macklin, Paul; Cristini, Vittorio
2013-01-01
Simulating cancer behavior across multiple biological scales in space and time, i.e., multiscale cancer modeling, is increasingly being recognized as a powerful tool to refine hypotheses, focus experiments, and enable more accurate predictions. A growing number of examples illustrate the value of this approach in providing quantitative insight on the initiation, progression, and treatment of cancer. In this review, we introduce the most recent and important multiscale cancer modeling works that have successfully established a mechanistic link between different biological scales. Biophysical, biochemical, and biomechanical factors are considered in these models. We also discuss innovative, cutting-edge modeling methods that are moving predictive multiscale cancer modeling toward clinical application. Furthermore, because the development of multiscale cancer models requires a new level of collaboration among scientists from a variety of fields such as biology, medicine, physics, mathematics, engineering, and computer science, an innovative Web-based infrastructure is needed to support this growing community. PMID:21529163
Inverse and Predictive Modeling
Syracuse, Ellen Marie
The LANL Seismo-Acoustic team has a strong capability in developing data-driven models that accurately predict a variety of observations. These models range from the simple – one-dimensional models that are constrained by a single dataset and can be used for quick and efficient predictions – to the complex – multidimensional models that are constrained by several types of data and result in more accurate predictions. Team members typically build models of geophysical characteristics of Earth and source distributions at scales of 1 to 1000s of km, the techniques used are applicable for other types of physical characteristics at an evenmore » greater range of scales. The following cases provide a snapshot of some of the modeling work done by the Seismo- Acoustic team at LANL.« less
NASA Technical Reports Server (NTRS)
North, G. R.; Cahalan, R. F.; Coakley, J. A., Jr.
1981-01-01
An introductory survey of the global energy balance climate models is presented with an emphasis on analytical results. A sequence of increasingly complicated models involving ice cap and radiative feedback processes are solved, and the solutions and parameter sensitivities are studied. The model parameterizations are examined critically in light of many current uncertainties. A simple seasonal model is used to study the effects of changes in orbital elements on the temperature field. A linear stability theorem and a complete nonlinear stability analysis for the models are developed. Analytical solutions are also obtained for the linearized models driven by stochastic forcing elements. In this context the relation between natural fluctuation statistics and climate sensitivity is stressed.
NASA Technical Reports Server (NTRS)
1985-01-01
The outside users payload model which is a continuation of documents and replaces and supersedes the July 1984 edition is presented. The time period covered by this model is 1985 through 2000. The following sections are included: (1) definition of the scope of the model; (2) discussion of the methodology used; (3) overview of total demand; (4) summary of the estimated market segmentation by launch vehicle; (5) summary of the estimated market segmentation by user type; (6) details of the STS market forecast; (7) summary of transponder trends; (8) model overview by mission category; and (9) detailed mission models. All known non-NASA, non-DOD reimbursable payloads forecast to be flown by non-Soviet-block countries are included in this model with the exception of Spacelab payloads and small self contained payloads. Certain DOD-sponsored or cosponsored payloads are included if they are reimbursable launches.
Extended frequency turbofan model
NASA Technical Reports Server (NTRS)
Mason, J. R.; Park, J. W.; Jaekel, R. F.
1980-01-01
The fan model was developed using two dimensional modeling techniques to add dynamic radial coupling between the core stream and the bypass stream of the fan. When incorporated into a complete TF-30 engine simulation, the fan model greatly improved compression system frequency response to planar inlet pressure disturbances up to 100 Hz. The improved simulation also matched engine stability limits at 15 Hz, whereas the one dimensional fan model required twice the inlet pressure amplitude to stall the simulation. With verification of the two dimensional fan model, this program formulated a high frequency F-100(3) engine simulation using row by row compression system characteristics. In addition to the F-100(3) remote splitter fan, the program modified the model fan characteristics to simulate a proximate splitter version of the F-100(3) engine.
Global Atmospheric Aerosol Modeling
NASA Technical Reports Server (NTRS)
Hendricks, Johannes; Aquila, Valentina; Righi, Mattia
2012-01-01
Global aerosol models are used to study the distribution and properties of atmospheric aerosol particles as well as their effects on clouds, atmospheric chemistry, radiation, and climate. The present article provides an overview of the basic concepts of global atmospheric aerosol modeling and shows some examples from a global aerosol simulation. Particular emphasis is placed on the simulation of aerosol particles and their effects within global climate models.
NASA Technical Reports Server (NTRS)
2000-01-01
Dr. Marc Pusey (seated) and Dr. Craig Kundrot use computers to analyze x-ray maps and generate three-dimensional models of protein structures. With this information, scientists at Marshall Space Flight Center can learn how proteins are made and how they work. The computer screen depicts a proten structure as a ball-and-stick model. Other models depict the actual volume occupied by the atoms, or the ribbon-like structures that are crucial to a protein's function.
Atmospheric prediction model survey
NASA Technical Reports Server (NTRS)
Wellck, R. E.
1976-01-01
As part of the SEASAT Satellite program of NASA, a survey of representative primitive equation atmospheric prediction models that exist in the world today was written for the Jet Propulsion Laboratory. Seventeen models developed by eleven different operational and research centers throughout the world are included in the survey. The surveys are tutorial in nature describing the features of the various models in a systematic manner.
Cultural Resource Predictive Modeling
2017-10-01
property to manage ? a. Yes 2) Do you use CRPM (Cultural Resource Predictive Modeling) No, but I use predictive modelling informally . For example...resource program and provide support to the test ranges for their missions. This document will provide information such as lessons learned, points...of contact, and resources to the range cultural resource managers . Objective/Scope: Identify existing cultural resource predictive models and
NASA Technical Reports Server (NTRS)
Levison, W. H.; Baron, S.
1984-01-01
Preliminary results in the application of a closed loop pilot/simulator model to the analysis of some simulator fidelity issues are discussed in the context of an air to air target tracking task. The closed loop model is described briefly. Then, problem simplifications that are employed to reduce computational costs are discussed. Finally, model results showing sensitivity of performance to various assumptions concerning the simulator and/or the pilot are presented.
NASA Technical Reports Server (NTRS)
Hsu, H. M.
1980-01-01
A mesoscale numerical model of the Florida peninsula was formulated and applied to a dry, neutral atmosphere. The prospective use of the STAR-100 computer for the submesoscale model is discussed. The numerical model presented is tested under synoptically undisturbed conditions. Two cases, differing only in the direction of the prevailing geostrophic wind, are examined: a prevailing southwest wind and a prevailing southeast wind, both 6 m/sec at all levels initially.
2014-08-01
ER D C/ CE RL S R- 14 -7 Optimal Allocation of Land for Training and Non-training Uses OPAL Land Condition Model Co ns tr uc tio n En...Optimal Allocation of Land for Training and Non-training Uses ERDC/CERL SR-14-7 August 2014 OPAL Land Condition Model Daniel Koch, Scott Tweddale...programmer information supporting the Op- timal Programming of Army Lands ( OPAL ) model, which was designed for use by trainers, Integrated Training