Lorentz symmetric quantum field theory for symplectic fermions
Robinson, Dean J.; Kapit, Eliot; LeClair, Andre
2009-11-15
A free quantum field theory with Lorentz symmetry is derived for spin-half symplectic fermions in 2+1 dimensions. In particular, we show that fermionic spin-half fields may be canonically quantized in a free theory with a Klein-Gordon Lagrangian. This theory is shown to have all the required properties of a consistent free quantum field theory, namely, causality, unitarity, adherence to the spin-statistics theorem, CPT symmetry, and the Hermiticity and positive definiteness of the Hamiltonian. The global symmetry of the free theory is Sp(4){approx_equal}SO(5). Possible interacting theories of both the pseudo-Hermitian and Hermitian variety are then examined briefly.
Symplectically invariant flow equations for N = 2, D = 4 gauged supergravity with hypermultiplets
NASA Astrophysics Data System (ADS)
Klemm, Dietmar; Petri, Nicolò; Rabbiosi, Marco
2016-04-01
We consider N = 2 supergravity in four dimensions, coupled to an arbitrary number of vector- and hypermultiplets, where abelian isometries of the quaternionic hyperscalar target manifold are gauged. Using a static and spherically or hyperbolically symmetric ansatz for the fields, a one-dimensional effective action is derived whose variation yields all the equations of motion. By imposing a sort of Dirac charge quantization condition, one can express the complete scalar potential in terms of a superpotential and write the action as a sum of squares. This leads to first-order flow equations, that imply the second-order equations of motion. The first-order flow turns out to be driven by Hamilton's characteristic function in the Hamilton-Jacobi formalism, and contains among other contributions the superpotential of the scalars. We then include also magnetic gaugings and generalize the flow equations to a symplectically covariant form. Moreover, by rotating the charges in an appropriate way, an alternative set of non-BPS first-order equations is obtained that corresponds to a different squaring of the action. Finally, we use our results to derive the attractor equations for near-horizon geometries of extremal black holes.
Magnetotransport properties of 2D fermionic systems with k-cubic Rashba spin-orbit interaction
NASA Astrophysics Data System (ADS)
Mawrie, Alestin; Biswas, Tutul; Kanti Ghosh, Tarun
2014-10-01
The spin-orbit interaction in heavy hole gas formed at p-doped semiconductor heterojunctions and electron gas at SrTiO3 surfaces is cubic in momentum. Here we report magnetotransport properties of k-cubic Rashba spin-orbit coupled 2D fermionic systems. We study longitudinal and Hall components of the resistivity tensor analytically as well as numerically. The longitudinal resistivity shows a beating pattern due to different Shubnikov-de Haas (SdH) oscillation frequencies f± for spin-up and spin-down fermions. We propose empirical forms of f± as exact expressions are not available, which are being used to find locations of the beating nodes. The beating nodes and the number of oscillations between any two successive nodes obtained from exact numerical results are in excellent agreement with those calculated from the proposed empirical formula. In the Hall resistivity, an additional Hall plateau appears between the two conventional ones as the spin-orbit coupling constant increases. The width of this additional plateau increases with spin-orbit coupling constant.
NASA Astrophysics Data System (ADS)
Volčko, Dušan; Quader, Khandker F.
2012-12-01
We consider fermions on a 2D square lattice with a finite-range pairing interaction, and obtain signatures for unconventional pair-symmetry states, dx2-y2 and extended-s (s*), in the Bardeen-Cooper-Schrieffer-Bose-Einstein Condensation crossover region. We find that the fermion momentum distribution function, vk2, the ratio of the Bogoliubov coefficients, vk/uk, and the Fourier transform of vk2 are strikingly different for d and s* symmetries in the crossover region. The chemical potential and the gap functions for both pairing symmetries show several interesting features as a function of interaction. Fermionic atoms in 2D optical lattices may provide a way to test these signatures. We discuss current generation cold atom experiments that may be utilized.
Counter-Ions Between or at Asymmetrically Charged Walls: 2D Free-Fermion Point
NASA Astrophysics Data System (ADS)
Šamaj, Ladislav; Trizac, Emmanuel
2014-09-01
This work contributes to the problem of determining effective interaction between asymmetrically (likely or oppositely) charged objects whose total charge is neutralized by mobile pointlike counter-ions of the same charge, the whole system being in thermal equilibrium. The problem is formulated in two spatial dimensions with logarithmic Coulomb interactions. The charged objects correspond to two parallel lines at distance , with fixed line charge densities. Two versions of the model are considered: the standard "unconstrained" one with particles moving freely between the lines and the "constrained" one with particles confined to the lines. We solve exactly both systems at the free-fermion coupling and compare the results for the pressure (i.e. the force between the lines per unit length of one of the lines) with the mean-field Poisson-Boltzmann solution. For the unconstrained model, the large- asymptotic behaviour of the free-fermion pressure differs from that predicted by the mean-field theory. For the constrained model, the asymptotic pressure coincides with the attractive van der Waals-Casimir fluctuational force. For both models, there are fundamental differences between the cases of likely-charged and oppositely-charged lines, the latter case corresponding at large distances to a capacitor.
Equation of state of ultracold fermions in the 2D BEC-BCS crossover
NASA Astrophysics Data System (ADS)
Boettcher, Igor; Bayha, Luca; Kedar, Dhruv; Murthy, Puneet; Neidig, Mathias; Ries, Martin; Wenz, Andre; Zuern, Gerhard; Jochim, Selim; Enss, Tilman
We report the experimental measurement of the equation of state of a two-dimensional Fermi gas with attractive s-wave interactions throughout the crossover from a weakly coupled Fermi gas to a Bose gas of tightly bound dimers as the interaction strength is varied. We demonstrate that interactions lead to a renormalization of the density of the Fermi gas by several orders of magnitude. We compare our data near the ground state and at finite temperature to predictions for both fermions and bosons from Quantum Monte Carlo simulations and Luttinger-Ward theory. Our results serve as input for investigations of close-to-equilibrium dynamics and transport in the two-dimensional system.
Equation of State of Ultracold Fermions in the 2D BEC-BCS Crossover Region.
Boettcher, I; Bayha, L; Kedar, D; Murthy, P A; Neidig, M; Ries, M G; Wenz, A N; Zürn, G; Jochim, S; Enss, T
2016-01-29
We report the experimental measurement of the equation of state of a two-dimensional Fermi gas with attractive s-wave interactions throughout the crossover from a weakly coupled Fermi gas to a Bose gas of tightly bound dimers as the interaction strength is varied. We demonstrate that interactions lead to a renormalization of the density of the Fermi gas by several orders of magnitude. We compare our data near the ground state and at finite temperature with predictions for both fermions and bosons from quantum Monte Carlo simulations and Luttinger-Ward theory. Our results serve as input for investigations of close-to-equilibrium dynamics and transport in the two-dimensional system. PMID:26871341
Equation of State of Ultracold Fermions in the 2D BEC-BCS Crossover Region
NASA Astrophysics Data System (ADS)
Boettcher, I.; Bayha, L.; Kedar, D.; Murthy, P. A.; Neidig, M.; Ries, M. G.; Wenz, A. N.; Zürn, G.; Jochim, S.; Enss, T.
2016-01-01
We report the experimental measurement of the equation of state of a two-dimensional Fermi gas with attractive s -wave interactions throughout the crossover from a weakly coupled Fermi gas to a Bose gas of tightly bound dimers as the interaction strength is varied. We demonstrate that interactions lead to a renormalization of the density of the Fermi gas by several orders of magnitude. We compare our data near the ground state and at finite temperature with predictions for both fermions and bosons from quantum Monte Carlo simulations and Luttinger-Ward theory. Our results serve as input for investigations of close-to-equilibrium dynamics and transport in the two-dimensional system.
Anisotropic Dirac Fermions in Novel 2D Carbon and Silicon Allotropes
NASA Astrophysics Data System (ADS)
Wang, Zhenhai; Zhao, Mingwen; Zhou, Xiang-Feng; Zhu, Qiang; Zhang, Xiaoming; Dong, Huafeng; Oganov, Artem R.; He, Shumin; Grünberg, Peter
Graphene, due to its unique Dirac cones with linear dispersion, exhibits a number of novel physics, such as high carrier mobility and quantum hall effect. Successful preparation of graphene in 2004 has inspired further searches for other 2D Dirac materials. Using systematic evolutionary structure searching, here we proposed one interesting type of 2D Dirac allotropes, which were named as `phagraphene' [Nano. Lett. 15, 6182 (2015)] and `siliconeet' respectively. Compared with the isotropic energy dispersion in graphene, the Dirac cones in these samples are direction-dependent. Further investigations proved that such anisotropic behaviors and the distorted Dirac cones are robust against external strain with tunable Fermi velocities. These predictions pave a new way to construct novel functional Dirac materials that might have potential applications in future.
MACKAY, W.W.; LUCCIO, A.U.
2006-06-23
It is important to have symplectic maps for the various electromagnetic elements in an accelerator ring. For some tracking problems we must consider elements which evolve during a ramp. Rather than performing a computationally intensive numerical integration for every turn, it should be possible to integrate the trajectory for a few sets of parameters, and then interpolate the transport map as a function of one or more parameters, such as energy. We present two methods for interpolation of symplectic matrices as a function of parameters: one method is based on the calculation of a representation in terms of a basis of group generators [2, 3] and the other is based on the related but simpler symplectification method of Healy [1]. Both algorithms guarantee a symplectic result.
NASA Astrophysics Data System (ADS)
Metlitski, Max; Vishwanath, Ashvin
Particle-vortex duality is a powerful theoretical tool that has been used to study systems of bosons. In arXiv:1505.05142, we propose an analogous duality for Dirac fermions in 2+1 dimensions. The physics of a single Dirac cone is proposed to be described by a dual theory, QED3 with a dual Dirac fermion coupled to a u(1) gauge field. This duality is established by considering two alternate descriptions of the 3d topological insulator (TI) surface. The first description is the usual Dirac cone surface state. The second description is accessed via an electric-magnetic duality of the bulk TI coupled to a gauge field, which maps it to a gauged topological superconductor. This alternate description ultimately leads to a new surface theory - dual QED3. The dual theory provides an explicit derivation of the T-Pfaffian state, a proposed surface topological order of the TI, which is simply the paired superfluid state of the dual fermions. The roles of time reversal and particle-hole symmetry are exchanged by the duality, which connects some of our results to a recent conjecture by Son on particle-hole symmetric quantum Hall states at ν = 1 / 2 .
Chuang, Wu-yen; Kachru, Shamit; Tomasiello, Alessandro; /Stanford U., ITP
2005-10-28
We construct a class of symplectic non-Kaehler and complex non-Kaehler string theory vacua, extending and providing evidence for an earlier suggestion by Polchinski and Strominger. The class admits a mirror pairing by construction. Comparing hints from a variety of sources, including ten-dimensional supergravity and KK reduction on SU(3)-structure manifolds, suggests a picture in which string theory extends Reid's fantasy to connect classes of both complex non-Kaehler and symplectic non-Kaehler manifolds.
Multi-symplectic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Webb, G. M.; McKenzie, J. F.; Zank, G. P.; Zank
2014-10-01
A multi-symplectic formulation of ideal magnetohydrodynamics (MHD) is developed based on the Clebsch variable variational principle in which the Lagrangian consists of the kinetic minus the potential energy of the MHD fluid modified by constraints using Lagrange multipliers that ensure mass conservation, entropy advection with the flow, the Lin constraint, and Faraday's equation (i.e. the magnetic flux is Lie dragged with the flow). The analysis is also carried out using the magnetic vector potential Ã where α=Ã. d x is Lie dragged with the flow, and B=∇×Ã. The multi-symplectic conservation laws give rise to the Eulerian momentum and energy conservation laws. The symplecticity or structural conservation laws for the multi-symplectic system corresponds to the conservation of phase space. It corresponds to taking derivatives of the momentum and energy conservation laws and combining them to produce n(n-1)/2 extra conservation laws, where n is the number of independent variables. Noether's theorem for the multi-symplectic MHD system is derived, including the case of non-Cartesian space coordinates, where the metric plays a role in the equations.
Symplectic wavelet transformation.
Fan, Hong-Yi; Lu, Hai-Liang
2006-12-01
Usually a wavelet transform is based on dilated-translated wavelets. We propose a symplectic-transformed-translated wavelet family psi(*)(r,s)(z-kappa) (r,s are the symplectic transform parameters, |s|(2)-|r|(2)=1, kappa is a translation parameter) generated from the mother wavelet psi and the corresponding wavelet transformation W(psi)f(r,s;kappa)=integral(infinity)(-infinity)(d(2)z/pi)f(z)psi(*)(r,s)(z-kappa). This new transform possesses well-behaved properties and is related to the optical Fresnel transform in quantum mechanical version. PMID:17099740
Carvalho, Vanuildo S de; Freire, Hermann
2014-09-15
The two-loop renormalization group (RG) calculation is considerably extended here for the two-dimensional (2D) fermionic effective field theory model, which includes only the so-called “hot spots” that are connected by the spin-density-wave (SDW) ordering wavevector on a Fermi surface generated by the 2D t−t{sup ′} Hubbard model at low hole doping. We compute the Callan–Symanzik RG equation up to two loops describing the flow of the single-particle Green’s function, the corresponding spectral function, the Fermi velocity, and some of the most important order-parameter susceptibilities in the model at lower energies. As a result, we establish that–in addition to clearly dominant SDW correlations–an approximate (pseudospin) symmetry relating a short-range incommensurated-wave charge order to the d-wave superconducting order indeed emerges at lower energy scales, which is in agreement with recent works available in the literature addressing the 2D spin-fermion model. We derive implications of this possible electronic phase in the ongoing attempt to describe the phenomenology of the pseudogap regime in underdoped cuprates.
Infinitesimal affine automorphisms of symplectic connections
NASA Astrophysics Data System (ADS)
Fox, Daniel J. F.
2016-08-01
Conditions are given under which an infinitesimal automorphism of a torsion-free connection preserving a symplectic form is necessarily a symplectic vector field. An example is given of a compact symplectic nilmanifold admitting a flat symplectic connection and an infinitesimal automorphism that is not symplectic.
Spectral geometry of symplectic spinors
NASA Astrophysics Data System (ADS)
Vassilevich, Dmitri
2015-10-01
Symplectic spinors form an infinite-rank vector bundle. Dirac operators on this bundle were constructed recently by Habermann, K. ["The Dirac operator on symplectic spinors," Ann. Global Anal. Geom. 13, 155-168 (1995)]. Here we study the spectral geometry aspects of these operators. In particular, we define the associated distance function and compute the heat trace asymptotics.
Symplectic integrators for spin systems.
McLachlan, Robert I; Modin, Klas; Verdier, Olivier
2014-06-01
We present a symplectic integrator, based on the implicit midpoint method, for classical spin systems where each spin is a unit vector in R{3}. Unlike splitting methods, it is defined for all Hamiltonians and is O(3)-equivariant, i.e., coordinate-independent. It is a rare example of a generating function for symplectic maps of a noncanonical phase space. It yields a new integrable discretization of the spinning top. PMID:25019718
Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms
NASA Astrophysics Data System (ADS)
Xin-Lei, Kong; Hui-Bin, Wu; Feng-Xiang, Mei
2016-01-01
In this paper, we focus on the construction of structure preserving algorithms for Birkhoffian systems, based on existing symplectic schemes for the Hamiltonian equations. The key of the method is to seek an invertible transformation which drives the Birkhoffian equations reduce to the Hamiltonian equations. When there exists such a transformation, applying the corresponding inverse map to symplectic discretization of the Hamiltonian equations, then resulting difference schemes are verified to be Birkhoffian symplectic for the original Birkhoffian equations. To illustrate the operation process of the method, we construct several desirable algorithms for the linear damped oscillator and the single pendulum with linear dissipation respectively. All of them exhibit excellent numerical behavior, especially in preserving conserved quantities. Project supported by the National Natural Science Foundation of China (Grant No. 11272050), the Excellent Young Teachers Program of North China University of Technology (Grant No. XN132), and the Construction Plan for Innovative Research Team of North China University of Technology (Grant No. XN129).
Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics
NASA Astrophysics Data System (ADS)
Webb, G. M.; Anco, S. C.
2016-02-01
The Lagrangian, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, m i (the Lagrangian mass coordinates) and time t are the independent variables, and in which the Eulerian position of the fluid element {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the Lagrangian map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the Lagrangian map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The Lagrangian is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the Lagrangian energy conservation law with respect to the Lagrangian mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.
Folded Symplectic Toric Four-Manifolds
ERIC Educational Resources Information Center
Lee, Christopher R.
2009-01-01
A folded symplectic form on an even-dimensional manifold is a closed two-form that degenerates in a suitably controlled way along a smooth hypersurface. When a torus having half the dimension of the manifold acts in a way preserving the folded symplectic form and admitting a moment map, the manifold is called a folded symplectic toric manifold.…
Symplectic homology product via Legendrian surgery.
Bourgeois, Frédéric; Ekholm, Tobias; Eliashberg, Yakov
2011-05-17
This research announcement continues the study of the symplectic homology of Weinstein manifolds undertaken by the authors [Bourgeois F, Ekholm T, Eliashberg Y (2009) arXiv:0911.0026] where the symplectic homology, as a vector space, was expressed in terms of the Legendrian homology algebra of the attaching spheres of critical handles. Here, we express the product and Batalin-Vilkovisky operator of symplectic homology in that context. PMID:21518898
Clifford Algebras in Symplectic Geometry and Quantum Mechanics
NASA Astrophysics Data System (ADS)
Binz, Ernst; de Gosson, Maurice A.; Hiley, Basil J.
2013-04-01
The necessary appearance of Clifford algebras in the quantum description of fermions has prompted us to re-examine the fundamental role played by the quaternion Clifford algebra, C 0,2. This algebra is essentially the geometric algebra describing the rotational properties of space. Hidden within this algebra are symplectic structures with Heisenberg algebras at their core. This algebra also enables us to define a Poisson algebra of all homogeneous quadratic polynomials on a two-dimensional sub-space, {F}a of the Euclidean three-space. This enables us to construct a Poisson Clifford algebra, ℍ F , of a finite dimensional phase space which will carry the dynamics. The quantum dynamics appears as a realisation of ℍ F in terms of a Clifford algebra consisting of Hermitian operators.
Rozansky-Witten-Type Invariants from Symplectic Lie Pairs
NASA Astrophysics Data System (ADS)
Voglaire, Yannick; Xu, Ping
2015-05-01
We introduce symplectic structures on "Lie pairs" of (real or complex) Lie algebroids as studied by Chen et al. (From Atiyah classes to homotopy Leibniz algebras. arXiv:1204.1075, 2012), encompassing homogeneous symplectic spaces, symplectic manifolds with a -action, and holomorphic symplectic manifolds. We show that to each such symplectic Lie pair are associated Rozansky-Witten-type invariants of three-manifolds and knots, given respectively by weight systems on trivalent and chord diagrams.
Local Physical Coordinates from Symplectic Projector Method
NASA Astrophysics Data System (ADS)
de Andrade, M. A.; Santos, M. A.; Vancea, I. V.
The basic arguments underlying the symplectic projector method are presented. By this method, local free coordinates on the constraint surface can be obtained for a broader class of constrained systems. Some interesting examples are analyzed.
On Orbifold Criteria for Symplectic Toric Quotients
NASA Astrophysics Data System (ADS)
Farsi, Carla; Herbig, Hans-Christian; Seaton, Christopher
2013-04-01
We introduce the notion of regular symplectomorphism and graded regular symplectomorphism between singular phase spaces. Our main concern is to exhibit examples of unitary torus representations whose symplectic quotients cannot be graded regularly symplectomorphic to the quotient of a symplectic representation of a finite group, while the corresponding GIT quotients are smooth. Additionally, we relate the question of simplicialness of a torus representation to Gaussian elimination.
NASA Technical Reports Server (NTRS)
Strecker, Kevin; Truscott, Andrew; Partridge, Guthrie; Chen, Ying-Cheng
2003-01-01
Dual evaporation gives 50 million fermions at T = 0.1 T(sub F). Demonstrated suppression of interactions by coherent superposition - applicable to atomic clocks. Looking for evidence of Cooper pairing and superfluidity.
NASA Astrophysics Data System (ADS)
Javarone, Marco Alberto
2016-08-01
We study the structure of fermionic networks, i.e. a model of networks based on the behavior of fermionic gases, and we analyze dynamical processes over them. In this model, particle dynamics have been mapped to the domain of networks, hence a parameter representing the temperature controls the evolution of the system. In doing so, it is possible to generate adaptive networks, i.e. networks whose structure varies over time. As shown in previous works, networks generated by quantum statistics can undergo critical phenomena as phase transitions and, moreover, they can be considered as thermodynamic systems. In this study, we analyze fermionic networks and opinion dynamics processes over them, framing this network model as a computational model useful to represent complex and adaptive systems. Results highlight that a strong relation holds between the gas temperature and the structure of the achieved networks. Notably, both the degree distribution and the assortativity vary as the temperature varies, hence we can state that fermionic networks behave as adaptive networks. On the other hand, it is worth to highlight that we did not finding relation between outcomes of opinion dynamics processes and the gas temperature. Therefore, although the latter plays a fundamental role in gas dynamics, on the network domain, its importance is related only to structural properties of fermionic networks.
q-Deformation of symplectic dynamical symmetries in algebraic models of nuclear structure
Georgieva, A. I.; Sviratcheva, K. D.; Ivanov, M. I.; Draayer, J. P.
2011-06-15
With a view toward further nuclear structure applications of approaches based on quantum-deformed (or q-deformed) algebras, introduced to the authors by Yu.F. Smirnov, we construct a q analog of a boson realization of the symplectic noncompact sp(4, R) algebra together with a q analog of a fermion realization of the symplectic compact sp(4) algebra. The first study, on the q-deformed Sp(4,R) symmetry, is applied to the development of a q analog of the two-dimensional Interacting Boson Model with q-deformed SU(3) the underpinning dynamical symmetry group. An explicit realization in terms of q-tensor operators with respect to the standard su{sub q}(2) algebra is given. The group-subgroup structure of this framework yields the physical interpretation of the generators of the groups under consideration. The second symplectic algebra, the q-deformed sp(4), is applied to studying isovector pairing correlations in atomic nuclei. A specific q deformation of the sp(4) algebra is realized in terms of q deformed fermion creation and annihilation operators of the shell model. The generators of the algebra close on four distinct realizations of the u{sub q}(2) subalgebra. These reductions, which correspond to different types of pairing interactions, yield a complete classification of the basis states. An analysis of the role of the q deformation is based on a comparison of the results for energies of the lowest isovector-paired 0{sup +} states in the deformed and nondeformed cases.
k-symplectic structures and absolutely trianalytic subvarieties in hyperkähler manifolds
NASA Astrophysics Data System (ADS)
Soldatenkov, Andrey; Verbitsky, Misha
2015-06-01
Let (M, I, J, K) be a hyperkähler manifold, and Z ⊂(M, I) a complex subvariety in (M, I) . We say that Z is trianalytic if it is complex analytic with respect to J and K, and absolutely trianalytic if it is trianalytic with respect to any hyperkähler triple of complex structures (M, I, J‧, K‧) containing I. For a generic complex structure I on M, all complex subvarieties of (M, I) are absolutely trianalytic. It is known that the normalization Z‧ of a trianalytic subvariety is smooth; we prove that b2(Z‧) ⩾b2(M), when M has maximal holonomy (that is, M is IHS). To study absolutely trianalytic subvarieties further, we define a new geometric structure, called k-symplectic structure; this structure is a generalization of hypersymplectic structure. A k-symplectic structure on a 2 d-dimensional manifold X is a k-dimensional space R of closed 2-forms on X which all have rank 2 d or d. It is called non-degenerate if the set of all degenerate forms in R is a smooth, non-degenerate quadric hypersurface in R. We consider absolutely trianalytic tori in a hyperkähler manifold M of maximal holonomy. We prove that any such torus is equipped with a non-degenerate k-symplectic structure, where k =b2(M) . We show that the tangent bundle TX of a k-symplectic manifold is a Clifford module over a Clifford algebra Cl(k - 1) . Then an absolutely trianalytic torus in a hyperkähler manifold M with b2(M) ⩾ 2 r + 1 is at least 2 r - 1-dimensional.
NASA Astrophysics Data System (ADS)
Wang, Zhijun; Alexandradinata, A.; Cava, Robert J.; Bernevig, B. Andrei
Spatial symmetries in crystals are distinguished by whether they preserve the spatial origin. We show how this basic geometric property gives rise to a new topology in band insulators. We study spatial symmetries that translate the origin by a fraction of the lattice period, and find that these nonsymmorphic symmetries protect a novel surface fermion whose dispersion is shaped like an hourglass; surface bands connect one hourglass to the next in an unbreakable zigzag pattern. These exotic fermions are materialized in the large-gap insulators: KHg X (X = As,Sb,Bi), which we propose as the first material class whose topology relies on nonsymmorphic symmetries. Beside the hourglass fermion, a different surface of KHg X manifests a 3D generalization of the quantum spin Hall effect. To describe the bulk topology of nonsymmorphic crystals, we propose a non-Abelian generalization of the geometric theory of polarization. Our nontrivial topology originates not from an inversion of the parity quantum numbers, but rather of the rotational quantum numbers, which we propose as a fruitful in the search for topological materials. Finally, KHg X uniquely exemplifies a cohomological insulator, a concept that we will introduce in a companion work.
Wang, Zhijun; Alexandradinata, A; Cava, R J; Bernevig, B Andrei
2016-04-14
Spatial symmetries in crystals may be distinguished by whether they preserve the spatial origin. Here we study spatial symmetries that translate the origin by a fraction of the lattice period, and find that these non-symmorphic symmetries protect an exotic surface fermion whose dispersion relation is shaped like an hourglass; surface bands connect one hourglass to the next in an unbreakable zigzag pattern. These 'hourglass' fermions are formed in the large-gap insulators, KHgX (X = As, Sb, Bi), which we propose as the first material class whose band topology relies on non-symmorphic symmetries. Besides the hourglass fermion, another surface of KHgX manifests a three-dimensional generalization of the quantum spin Hall effect, which has previously been observed only in two-dimensional crystals. To describe the bulk topology of non-symmorphic crystals, we propose a non-Abelian generalization of the geometric theory of polarization. Our non-trivial topology originates from an inversion of the rotational quantum numbers, which we propose as a criterion in the search for topological materials. PMID:27075096
Natural cutoffs via compact symplectic manifolds
NASA Astrophysics Data System (ADS)
Nozari, K.; Gorji, M. A.; Hosseinzadeh, V.; Vakili, B.
2016-01-01
In the context of phenomenological models of quantum gravity, it is claimed that ultraviolet (UV) and infrared (IR) natural cutoffs can be realized from local deformations of the Hamiltonian systems. In this paper, we scrutinize this hypothesis and formulate a cutoff-regularized Hamiltonian system. The results show that while local deformations are necessary to have cutoffs, they are not sufficient. In fact, the cutoffs can be realized from globally-deformed Hamiltonian systems that are defined on compact symplectic manifolds. By taking the universality of quantum gravity effects into account, we then conclude that quantum gravity cutoffs are global (topological) properties of the symplectic manifolds. We justify our results by considering three well-known examples: the Moyal, Snyder and polymer-deformed Hamiltonian systems.
Microwave Realization of the Gaussian Symplectic Ensemble.
Rehemanjiang, A; Allgaier, M; Joyner, C H; Müller, S; Sieber, M; Kuhl, U; Stöckmann, H-J
2016-08-01
Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014)], a microwave graph with an antiunitary symmetry T obeying T^{2}=-1 is realized. The Kramers doublets expected for such systems are clearly identified and can be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level spacings distribution of the Kramers doublets is in agreement with the predictions from the Gaussian symplectic ensemble expected for chaotic systems with such a symmetry. PMID:27541466
Noncommutative scalar fields from symplectic deformation
Daoud, M.; Hamama, A.
2008-02-15
This paper is concerned with the quantum theory of noncommutative scalar fields in two dimensional space-time. It is shown that the noncommutativity originates from the the deformation of symplectic structures. The quantization is performed and the modes expansions of the fields, in the presence of an electromagnetic background, are derived. The Hamiltonian of the theory is given and the degeneracies lifting, induced by the deformation, is also discussed.
Microwave Realization of the Gaussian Symplectic Ensemble
NASA Astrophysics Data System (ADS)
Rehemanjiang, A.; Allgaier, M.; Joyner, C. H.; Müller, S.; Sieber, M.; Kuhl, U.; Stöckmann, H.-J.
2016-08-01
Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014)], a microwave graph with an antiunitary symmetry T obeying T2=-1 is realized. The Kramers doublets expected for such systems are clearly identified and can be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level spacings distribution of the Kramers doublets is in agreement with the predictions from the Gaussian symplectic ensemble expected for chaotic systems with such a symmetry.
QYMSYM: A GPU-accelerated hybrid symplectic integrator
NASA Astrophysics Data System (ADS)
Moore, Alexander; Quillen, Alice C.
2012-10-01
QYMSYM is a GPU accelerated 2nd order hybrid symplectic integrator that identifies close approaches between particles and switches from symplectic to Hermite algorithms for particles that require higher resolution integrations. This is a parallel code running with CUDA on a video card that puts the many processors on board to work while taking advantage of fast shared memory.
Anomalous Behavior in Ideal Fermion Gases Below 2D
NASA Astrophysics Data System (ADS)
Grether, M.; de Llano, M.; Solís, M. A.
2003-03-01
``Normal" thermodynamic properties of a ideal Fermi gas in d>2 dimensions, integer or not, is manifested by monotonically increasing or decreasing of its specific heat, chemical potential or isothermal sound velocity. However, for 0
Stochastic deformation of a thermodynamic symplectic structure
NASA Astrophysics Data System (ADS)
Kazinski, P. O.
2009-01-01
A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation is analogous to the deformation of an algebra of observables such as deformation quantization, but for an imaginary deformation parameter (the Planck constant). Gauge symmetries of thermodynamics and corresponding stochastic mechanics, which describes fluctuations of a thermodynamic system, are revealed and gauge fields are introduced. A physical interpretation to the gauge transformations and gauge fields is given. An application of the formalism to a description of systems with distributed parameters in a local thermodynamic equilibrium is considered.
Stochastic deformation of a thermodynamic symplectic structure.
Kazinski, P O
2009-01-01
A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation is analogous to the deformation of an algebra of observables such as deformation quantization, but for an imaginary deformation parameter (the Planck constant). Gauge symmetries of thermodynamics and corresponding stochastic mechanics, which describes fluctuations of a thermodynamic system, are revealed and gauge fields are introduced. A physical interpretation to the gauge transformations and gauge fields is given. An application of the formalism to a description of systems with distributed parameters in a local thermodynamic equilibrium is considered. PMID:19256999
A SYMPLECTIC INTEGRATOR FOR HILL'S EQUATIONS
Quinn, Thomas; Barnes, Rory; Perrine, Randall P.; Richardson, Derek C.
2010-02-15
Hill's equations are an approximation that is useful in a number of areas of astrophysics including planetary rings and planetesimal disks. We derive a symplectic method for integrating Hill's equations based on a generalized leapfrog. This method is implemented in the parallel N-body code, PKDGRAV, and tested on some simple orbits. The method demonstrates a lack of secular changes in orbital elements, making it a very useful technique for integrating Hill's equations over many dynamical times. Furthermore, the method allows for efficient collision searching using linear extrapolation of particle positions.
Gravitational Descendants in Symplectic Field Theory
NASA Astrophysics Data System (ADS)
Fabert, Oliver
2011-02-01
It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold is the prequantization space of a symplectic manifold. In this paper we generalize the definition of gravitational descendants in SFT from circle bundles in the Morse-Bott case to general contact manifolds. After we have shown using the ideas in Okounkov and Pandharipande (Ann Math 163(2):517-560, 2006) that for the basic examples of holomorphic curves in SFT, that is, branched covers of cylinders over closed Reeb orbits, the gravitational descendants have a geometric interpretation in terms of branching conditions, we follow the ideas in Cieliebak and Latschev (
Exponential estimates of symplectic slow manifolds
NASA Astrophysics Data System (ADS)
Kristiansen, K. U.; Wulff, C.
2016-07-01
In this paper we prove the existence of an almost invariant symplectic slow manifold for analytic Hamiltonian slow-fast systems with finitely many slow degrees of freedom for which the error field is exponentially small. We allow for infinitely many fast degrees of freedom. The method we use is motivated by a paper of MacKay from 2004. The method does not notice resonances, and therefore we do not pose any restrictions on the motion normal to the slow manifold other than it being fast and analytic. We also present a stability result and obtain a generalization of a result of Gelfreich and Lerman on an invariant slow manifold to (finitely) many fast degrees of freedom.
High-order control for symplectic maps
NASA Astrophysics Data System (ADS)
Sansottera, M.; Giorgilli, A.; Carletti, T.
2016-02-01
We revisit the problem of introducing an a priori control for devices that can be modeled via a symplectic map in a neighborhood of an elliptic equilibrium. Using a technique based on Lie transform methods we produce a normal form algorithm that avoids the usual step of interpolating the map with a flow. The formal algorithm is completed with quantitative estimates that bring into evidence the asymptotic character of the normal form transformation. Then we perform an heuristic analysis of the dynamical behavior of the map using the invariant function for the normalized map. Finally, we discuss how control terms of different orders may be introduced so as to increase the size of the stable domain of the map. The numerical examples are worked out on a two dimensional map of Hénon type.
Approach to combined-function magnets via symplectic slicing
NASA Astrophysics Data System (ADS)
Titze, M.
2016-05-01
In this article we describe how to obtain symplectic "slice" maps for combined-function magnets, by using a method of generating functions. A feature of this method is that one can use an unexpanded and unsplit Hamiltonian. From such a slice map we obtain a first-order map which is symplectic at the closed orbit. We also obtain a symplectic kick map. Both results were implemented into the widely used program MAD-X to regain, in particular, the twiss parameters for the sliced model of the Proton Synchrotron at CERN. In addition, we obtain recursion equations for symplectic maps of general time-dependent Hamiltonians, which might be useful even beyond the scope of accelerator physics.
A brief introduction to symplectic integrators and recent results
Channell, P.J.
1994-02-01
The author begins with a brief synopsis about Hamiltonian systems and symplectic maps. A symplectic integrator is a symplectic map {phi}(q,p;t) that systematically approximates the time t flow of a Hamiltonian system. Systematic means: (1) in time step, t, i.e. the error should vanish as some power of the time step, and (2) in order of approximation, i.e. one would like a hierarchy of such {phi} that have errors that vanish as successively higher powers of the time step. At present the authors known two general types of symplectic integrators: (1) implicit integrators that are derived from a generating function or from algebraic conditions on Runge-Kutta schemes, and (2) explicit integrators that are derived from integrable Hamiltonians or from algebraic conditions on Runge-Kutta schemes.
Symplectic integration for the collisional gravitational N-body problem
NASA Astrophysics Data System (ADS)
Hernandez, David M.; Bertschinger, Edmund
2015-09-01
We present a new symplectic integrator designed for collisional gravitational N-body problems which makes use of Kepler solvers. The integrator is also reversible and conserves nine integrals of motion of the N-body problem to machine precision. The integrator is second order, but the order can easily be increased by the method of Yoshida. We use fixed time step in all tests studied in this paper to ensure preservation of symplecticity. We study small N collisional problems and perform comparisons with typically used integrators. In particular, we find comparable or better performance when compared to the fourth-order Hermite method and much better performance than adaptive time step symplectic integrators introduced previously. We find better performance compared to SAKURA, a non-symplectic, non-time-reversible integrator based on a different two-body decomposition of the N-body problem. The integrator is a promising tool in collisional gravitational dynamics.
TOPICAL REVIEW: Ab initio symplectic no-core shell model
NASA Astrophysics Data System (ADS)
Dytrych, T.; Sviratcheva, K. D.; Draayer, J. P.; Bahri, C.; Vary, J. P.
2008-12-01
The no-core shell model (NCSM) is a prominent ab initio method that yields a good description of the low-lying states in few-nucleon systems as well as in more complex p-shell nuclei. Nevertheless, its applicability is limited by the rapid growth of the many-body basis with larger model spaces and increasing number of nucleons. The symplectic no-core shell model (Sp-NCSM) aspires to extend the scope of the NCSM beyond the p-shell region by augmenting the conventional spherical harmonic oscillator basis with the physically relevant symplectic \\SpR{3} symmetry-adapted configurations of the symplectic shell model that describe naturally the monopole-quadrupole vibrational and rotational modes, and also partially incorporate α-cluster correlations. In this review, the models underpinning the Sp-NCSM approach, namely, the NCSM, the Elliott SU(3) model and the symplectic shell model, are discussed. Following this, a prescription for constructing translationally invariant symplectic configurations in the spherical harmonic oscillator basis is given. This prescription is utilized to unveil the extent to which symplectic configurations enter into low-lying states in 12C and 16O nuclei calculated within the framework of the NCSM with the JISP16 realistic nucleon-nucleon interaction. The outcomes of this proof-of-principle study are presented in detail.
Fermionization and Hubbard models
NASA Astrophysics Data System (ADS)
Dargis, P.; Maassarani, Z.
1998-12-01
We introduce a transformation which allows the fermionization of operators of any one-dimensional spin-chain. This fermionization procedure is independent of any eventual integrable structure and is compatible with it. We illustrate this method on various integrable and non-integrable chains, and deduce some general results. In particular, we fermionize XXC spin-chains and study their symmetries. Fermionic realizations of certain Lie algebras and superalgebras appear naturally as symmetries of some models. We also fermionize recently obtained Hubbard models, and obtain for the first time multispecies analogues of the Hubbard model, in their fermionic form. We comment on the conflict between symmetry enhancement and integrability of these models. Finally, the fermionic versions of the non-integrable spin-1 and spin- {3}/{2} Heisenberg chains are obtained.
Energy Science and Technology Software Center (ESTSC)
2005-07-01
Aniso2d is a two-dimensional seismic forward modeling code. The earth is parameterized by an X-Z plane in which the seismic properties Can have monoclinic with x-z plane symmetry. The program uses a user define time-domain wavelet to produce synthetic seismograms anrwhere within the two-dimensional media.
High-order symplectic FDTD scheme for solving a time-dependent Schrödinger equation
NASA Astrophysics Data System (ADS)
Shen, Jing; Sha, Wei E. I.; Huang, Zhixiang; Chen, Mingsheng; Wu, Xianliang
2013-03-01
Using the three-order symplectic integrators and fourth-order collocated spatial differences, a high-order symplectic finite-difference time-domain (SFDTD) scheme is proposed to solve the time-dependent Schrödinger equation. First, the high-order symplectic framework for discretizing a Schrödinger equation is described. Then the numerical stability and dispersion analyses are provided for the FDTD(2, 2), higher-order FDTD(2, 4) and SFDTD(3, 4) schemes. Next, to implement the Dirichlet boundary condition encountered in the quantum eigenvalue problem, the image theory and one-sided difference technique are manipulated particularly for high-order collocated differences. Finally, a detailed numerical study on 1D and 2D quantum eigenvalue problems is carried out. The simulation results of quantum wells and harmonic oscillators strongly confirm the advantages of the SFDTD scheme over the traditional FDTD method and other high-order approaches. The explicit SFDTD scheme, which is high-order-accurate and energy-conserving, is well suited for a long-term simulation and can save computer resources with large time step and coarse spatial grids.
Greg Flach, Frank Smith
2011-12-31
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.
Energy Science and Technology Software Center (ESTSC)
2011-12-31
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assignsmore » an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.« less
NASA Astrophysics Data System (ADS)
Lotsch, Bettina V.
2015-07-01
Graphene's legacy has become an integral part of today's condensed matter science and has equipped a whole generation of scientists with an armory of concepts and techniques that open up new perspectives for the postgraphene area. In particular, the judicious combination of 2D building blocks into vertical heterostructures has recently been identified as a promising route to rationally engineer complex multilayer systems and artificial solids with intriguing properties. The present review highlights recent developments in the rapidly emerging field of 2D nanoarchitectonics from a materials chemistry perspective, with a focus on the types of heterostructures available, their assembly strategies, and their emerging properties. This overview is intended to bridge the gap between two major—yet largely disjunct—developments in 2D heterostructures, which are firmly rooted in solid-state chemistry or physics. Although the underlying types of heterostructures differ with respect to their dimensions, layer alignment, and interfacial quality, there is common ground, and future synergies between the various assembly strategies are to be expected.
Bifurcations of families of 1D-tori in 4D symplectic maps
NASA Astrophysics Data System (ADS)
Onken, Franziska; Lange, Steffen; Ketzmerick, Roland; Bäcker, Arnd
2016-06-01
The regular structures of a generic 4d symplectic map with a mixed phase space are organized by one-parameter families of elliptic 1d-tori. Such families show prominent bends, gaps, and new branches. We explain these features in terms of bifurcations of the families when crossing a resonance. For these bifurcations, no external parameter has to be varied. Instead, the longitudinal frequency, which varies along the family, plays the role of the bifurcation parameter. As an example, we study two coupled standard maps by visualizing the elliptic and hyperbolic 1d-tori in a 3d phase-space slice, local 2d projections, and frequency space. The observed bifurcations are consistent with the analytical predictions previously obtained for quasi-periodically forced oscillators. Moreover, the new families emerging from such a bifurcation form the skeleton of the corresponding resonance channel.
DECREASING COMPUTING TIME WITH SYMPLECTIC CORRECTORS IN ADAPTIVE TIMESTEPPING ROUTINES
Kaib, Nathan A.; Quinn, Thomas; Brasser, Ramon
2011-01-15
It has previously been shown that varying the numerical timestep during a symplectic orbital integration leads to a random walk in energy and angular momentum, destroying the phase space-conserving property of symplectic integrators. Here we show that when altering the timestep symplectic correctors can be used to reduce this error to a negligible level. Furthermore, these correctors can also be employed to avoid a large error introduction when changing the Hamiltonian's partitioning. We have constructed a numerical integrator using this technique that is nearly as accurate as widely used fixed-step routines. In addition, our algorithm is drastically faster for integrations of highly eccentricitic, large semimajor axis orbits, such as those found in the Oort Cloud.
Symplectic structures related with higher order variational problems
NASA Astrophysics Data System (ADS)
Kijowski, Jerzy; Moreno, Giovanni
2015-06-01
In this paper, we derive the symplectic framework for field theories defined by higher order Lagrangians. The construction is based on the symplectic reduction of suitable spaces of iterated jets. The possibility of reducing a higher order system of partial differential equations to a constrained first-order one, the symplectic structures naturally arising in the dynamics of a first-order Lagrangian theory, and the importance of the Poincaré-Cartan form for variational problems, are all well-established facts. However, their adequate combination corresponding to higher order theories is missing in the literature. Here we obtain a consistent and truly finite-dimensional canonical formalism, as well as a higher order version of the Poincaré-Cartan form. In our exposition, the rigorous global proofs of the main results are always accompanied by their local coordinate descriptions, indispensable to work out practical examples.
Symplectic representation of higher-order guiding-center theory
NASA Astrophysics Data System (ADS)
Brizard, Alain; Tronko, Natalia
2012-03-01
Two representations of guiding-center theory are possible depending on whether the guiding-center Poisson bracket (i.e., the symplectic structure) or the Hamiltonian contains higher-order corrections due to the nonuniformity of the magnetic field. By combining the guiding-center parallel hierarchy with the symplectic representation, the guiding-center equations of motion are derived with second-order corrections included in the symplectic structure without the need of carrying out the guiding-center transformation to second order. Guiding-center polarization and magnetization are thus shown to arise naturally from higher-order guiding-center theory within the context of a two-step derivation of nonlinear gyrokinetic theory.footnotetextA. J. Brizard and T. S. Hahm, Rev. Mod. Phys. 79, 421 (2007).
Symplectic geometry spectrum regression for prediction of noisy time series
NASA Astrophysics Data System (ADS)
Xie, Hong-Bo; Dokos, Socrates; Sivakumar, Bellie; Mengersen, Kerrie
2016-05-01
We present the symplectic geometry spectrum regression (SGSR) technique as well as a regularized method based on SGSR for prediction of nonlinear time series. The main tool of analysis is the symplectic geometry spectrum analysis, which decomposes a time series into the sum of a small number of independent and interpretable components. The key to successful regularization is to damp higher order symplectic geometry spectrum components. The effectiveness of SGSR and its superiority over local approximation using ordinary least squares are demonstrated through prediction of two noisy synthetic chaotic time series (Lorenz and Rössler series), and then tested for prediction of three real-world data sets (Mississippi River flow data and electromyographic and mechanomyographic signal recorded from human body).
Symplectic geometry spectrum regression for prediction of noisy time series.
Xie, Hong-Bo; Dokos, Socrates; Sivakumar, Bellie; Mengersen, Kerrie
2016-05-01
We present the symplectic geometry spectrum regression (SGSR) technique as well as a regularized method based on SGSR for prediction of nonlinear time series. The main tool of analysis is the symplectic geometry spectrum analysis, which decomposes a time series into the sum of a small number of independent and interpretable components. The key to successful regularization is to damp higher order symplectic geometry spectrum components. The effectiveness of SGSR and its superiority over local approximation using ordinary least squares are demonstrated through prediction of two noisy synthetic chaotic time series (Lorenz and Rössler series), and then tested for prediction of three real-world data sets (Mississippi River flow data and electromyographic and mechanomyographic signal recorded from human body). PMID:27300890
Fermionic Quantization and Configuration Spaces for the Skyrme and Faddeev-Hopf Models
NASA Astrophysics Data System (ADS)
Auckly, Dave; Speight, Martin
2006-04-01
The fundamental group and rational cohomology of the configuration spaces of the Skyrme and Faddeev-Hopf models are computed. Physical space is taken to be a compact oriented 3-manifold, either with or without a marked point representing an end at infinity. For the Skyrme model, the codomain is any Lie group, while for the Faddeev-Hopf model it is S 2. It is determined when the topology of configuration space permits fermionic and isospinorial quantization of the solitons of the model within generalizations of the frameworks of Finkelstein-Rubinstein and Sorkin. Fermionic quantization of Skyrmions is possible only if the target group contains a symplectic or special unitary factor, while fermionic quantization of Hopfions is always possible. Geometric interpretations of the results are given.
NASA Astrophysics Data System (ADS)
Gu, Zheng-Cheng; Wen, Xiao-Gang
2014-09-01
Symmetry-protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G, which can all be smoothly connected to the trivial product states if we break the symmetry. It has been shown that a large class of interacting bosonic SPT phases can be systematically described by group cohomology theory. In this paper, we introduce a (special) group supercohomology theory which is a generalization of the standard group cohomology theory. We show that a large class of short-range interacting fermionic SPT phases can be described by the group supercohomology theory. Using the data of supercocycles, we can obtain the ideal ground state wave function for the corresponding fermionic SPT phase. We can also obtain the bulk Hamiltonian that realizes the SPT phase, as well as the anomalous (i.e., non-onsite) symmetry for the boundary effective Hamiltonian. The anomalous symmetry on the boundary implies that the symmetric boundary must be gapless for (1+1)-dimensional [(1+1)D] boundary, and must be gapless or topologically ordered beyond (1+1)D. As an application of this general result, we construct a new SPT phase in three dimensions, for interacting fermionic superconductors with coplanar spin order (which have T2=1 time-reversal Z2T and fermion-number-parity Z2f symmetries described by a full symmetry group Z2T×Z2f). Such a fermionic SPT state can neither be realized by free fermions nor by interacting bosons (formed by fermion pairs), and thus are not included in the K-theory classification for free fermions or group cohomology description for interacting bosons. We also construct three interacting fermionic SPT phases in two dimensions (2D) with a full symmetry group Z2×Z2f. Those 2D fermionic SPT phases all have central-charge c =1 gapless edge excitations, if the symmetry is not broken.
Proton spin tracking with symplectic integration of orbit motion
Luo, Y.; Dutheil, Y.; Huang, H.; Meot, F.; Ranjbar, V.
2015-05-03
Symplectic integration had been adopted for orbital motion tracking in code SimTrack. SimTrack has been extensively used for dynamic aperture calculation with beam-beam interaction for the Relativistic Heavy Ion Collider (RHIC). Recently proton spin tracking has been implemented on top of symplectic orbital motion in this code. In this article, we will explain the implementation of spin motion based on Thomas-BMT equation, and the benchmarking with other spin tracking codes currently used for RHIC. Examples to calculate spin closed orbit and spin tunes are presented too.
Symplectic full-turn maps in a Fourier representation
Berg, J.S. . Dept. of Physics); Warnock, R.L. )
1991-05-01
We have developed a method that uses an arbitrary symplectic tracking code to generate an exactly symplectic full-turn or multi-turn map. The map is obtained from a generating function, which is a finite Fourier series in the final angle coordinates, the Fourier coefficients being represented as a B-spline series in the initial action coordinates. We achieve fast iteration of this implicitly defined map, and good accuracy. As a first application, we treat a simplified model of arcs of the SSC. 5 refs., 1 fig.
Entanglement in fermionic systems
Banuls, Mari-Carmen; Cirac, J. Ignacio; Wolf, Michael M.
2007-08-15
The anticommuting properties of fermionic operators, together with the presence of parity conservation, affect the concept of entanglement in a composite fermionic system. Hence different points of view can give rise to different reasonable definitions of separable and entangled states. Here we analyze these possibilities and the relationship between the different classes of separable states. The behavior of the various classes when taking multiple copies of a state is also studied, showing that some of the differences vanish in the asymptotic regime. In particular, in the case of only two fermionic modes all the classes become equivalent in this limit. We illustrate the differences and relations by providing a complete characterization of all the sets defined for systems of two fermionic modes. The results are applied to Gibbs states of infinite chains of fermions whose interaction corresponds to a XY Hamiltonian with transverse magnetic field.
A stochastic multi-symplectic scheme for stochastic Maxwell equations with additive noise
Hong, Jialin; Zhang, Liying
2014-07-01
In this paper we investigate a stochastic multi-symplectic method for stochastic Maxwell equations with additive noise. Based on the stochastic version of variational principle, we find a way to obtain the stochastic multi-symplectic structure of three-dimensional (3-D) stochastic Maxwell equations with additive noise. We propose a stochastic multi-symplectic scheme and show that it preserves the stochastic multi-symplectic conservation law and the local and global stochastic energy dissipative properties, which the equations themselves possess. Numerical experiments are performed to verify the numerical behaviors of the stochastic multi-symplectic scheme.
Bold Diagrammatic Monte Carlo for Fermionic and Fermionized Systems
NASA Astrophysics Data System (ADS)
Svistunov, Boris
2013-03-01
In three different fermionic cases--repulsive Hubbard model, resonant fermions, and fermionized spins-1/2 (on triangular lattice)--we observe the phenomenon of sign blessing: Feynman diagrammatic series features finite convergence radius despite factorial growth of the number of diagrams with diagram order. Bold diagrammatic Monte Carlo technique allows us to sample millions of skeleton Feynman diagrams. With the universal fermionization trick we can fermionize essentially any (bosonic, spin, mixed, etc.) lattice system. The combination of fermionization and Bold diagrammatic Monte Carlo yields a universal first-principle approach to strongly correlated lattice systems, provided the sign blessing is a generic fermionic phenomenon. Supported by NSF and DARPA
Heavy fermions: From nodal metals to super-spins
NASA Astrophysics Data System (ADS)
Ramires Neves de Oliveira, Aline
construction of supersymmetric spin representations in the large-N limit, now with symplectic symmetry, and explore its properties. We apply the supersymmetric symplectic-N spin representation to two toy models in Chapter 5, and find promising results for a future unified picture of heavy fermion systems.
The proton-neutron symplectic model of nuclear collective motions
NASA Astrophysics Data System (ADS)
Ganev, H. G.
2016-06-01
The proton-neutron symplectic model of nuclear collective motion is presented. It is shown that it appears as a natural multi-major-shell extension of the generalized proton- neutron SU(3) scheme which includes rotations with intrinsic vortex as well as monopole, quadrupole and dipole giant resonance vibrational degrees of freedom.
A survey of open problems in symplectic integration
McLachlan, R.I.; Scovel, C.
1993-10-15
In the past few years there has been a substantial amount of research on symplectic integration. The subject is only part of a program concerned with numerically preserving a system`s inherent geometrical structures. Volume preservation, reversibility, local conservation laws for elliptic equations, and systems with integral invariants are but a few examples of such invariant structures. In many cases one requires a numerical method to stay in the smallest possible appropriate group of phase space maps. It is not the authors` opinion that symplecticity, for example, automatically makes a numerical method superior to all others, but it is their opinion that it should be taken seriously and that a conscious, informed decision be made in that regard. The authors present here a survey of open problems in symplectic integration, including other problems from the larger program. This is not intended as a review of symplectic integration and is naturally derived from the authors` own research interests. At present, this survey is incomplete, but the authors hope the help of the colleagues to be able to include in the proceedings of this conference a more comprehensive survey. Many of the problems mentioned here call for numerical experimentation, some for application of suggested but untested methods, some for new methods, and some for theorems, Some envisage large research programs.
NASA Astrophysics Data System (ADS)
Iliesiu, Luca; Kos, Filip; Poland, David; Pufu, Silviu S.; Simmons-Duffin, David; Yacoby, Ran
2016-03-01
We study the conformal bootstrap for a 4-point function of fermions < ψψψψ> in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ × ψ OPE, and also on the central charge C T . We observe features in our bounds that coincide with scaling dimensions in the GrossNeveu models at large N . We also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.
NASA Astrophysics Data System (ADS)
Weiner, Richard M.
2010-05-01
It is conjectured that all known fermions are topological solitons. This could explain the non-observation of bosonic leptons and baryons and provide a physical mechanism for the Pauli exclusion principle.
Fermions from classical statistics
Wetterich, C.
2010-12-15
We describe fermions in terms of a classical statistical ensemble. The states {tau} of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability distribution can be associated to a quantum state for fermions. If the time evolution of the classical probabilities p{sub {tau}} amounts to a rotation of the wave function q{sub {tau}}(t)={+-}{radical}(p{sub {tau}}(t)), we infer the unitary time evolution of a quantum system of fermions according to a Schroedinger equation. We establish how such classical statistical ensembles can be mapped to Grassmann functional integrals. Quantum field theories for fermions arise for a suitable time evolution of classical probabilities for generalized Ising models.
Canonical gravity with fermions
Bojowald, Martin; Das, Rupam
2008-09-15
Canonical gravity in real Ashtekar-Barbero variables is generalized to allow for fermionic matter. The resulting torsion changes several expressions in Holst's original vacuum analysis, which are summarized here. This in turn requires adaptations to the known loop quantization of gravity coupled to fermions, which is discussed on the basis of the classical analysis. As a result, parity invariance is not manifestly realized in loop quantum gravity.
Global structure of regular tori in a generic 4D symplectic map
NASA Astrophysics Data System (ADS)
Lange, S.; Richter, M.; Onken, F.; Bäcker, A.; Ketzmerick, R.
2014-06-01
For the case of generic 4d symplectic maps with a mixed phase space, we investigate the global organization of regular tori. For this, we compute elliptic 1-tori of two coupled standard maps and display them in a 3d phase-space slice. This visualizes how all regular 2-tori are organized around a skeleton of elliptic 1-tori in the 4d phase space. The 1-tori occur in two types of one-parameter families: (α) Lyapunov families emanating from elliptic-elliptic periodic orbits, which are observed to exist even far away from them and beyond major resonance gaps, and (β) families originating from rank-1 resonances. At resonance gaps of both types of families either (i) periodic orbits exist, similar to the Poincaré-Birkhoff theorem for 2d maps, or (ii) the family may form large bends. In combination, these results allow for describing the hierarchical structure of regular tori in the 4d phase space analogously to the islands-around-islands hierarchy in 2d maps.
NASA Astrophysics Data System (ADS)
Sau, Jay; Tewari, Sumanta; Das Sarma, Sankar
2011-03-01
Majorana Fermions are hitherto unobserved exotic Fermionic excitations, which are their own anti-particles. Recently, a lot of excitement has been generated by proposals to realize Majorana fermions in topological superconductors in a rather general class of topological superconductors, some of which may be as simple as the interface 1D or 2D InAs and Al in the appropriate parameter regime might have exotic topological properties and Majorana Fermions. In my talk, I will discuss recent proposals for performing interferometry in 2D and 1D versions of such systems together with ideas for performing Quantum Computation using such robust Majorana fermion based qubits. This work is supported by DARPA-QuEST, JQI-NSF- PFC, and LPS-NSA.
Significance of Symplectic Symmetry in Many-nucleon Dynamics
Dytrych, T.; Sviratcheva, K. D.; Draayer, J. P.; Vary, J. P.
2009-01-28
Understanding the origin, structure, and phases of hadronic matter is a forefront research area in physics. An integral part of this challenge is to achieve realistic modeling of the complex dynamics of atomic nuclei, which is key to comprehending the evolution of the universe from a fundamental quark/gluon level. We recently demonstrated the potential power of an innovative concept, the ab initio symplectic no-core shell model (Sp-NCSM), based on expanding the conventional harmonic oscillator basis in terms of the symmetry-adapted and physically relevant symplectic basis, to reach new domains of nuclear structure. Using realistic interactions tied to Quantum Chromo-dynamics (QCD), the Sp-NCSM approach holds promise to build the bridge from QCD to measured properties of light nuclei, predict diverse features of unstable nuclei crucial for astrophysical processes, and provide nuclear structure information essential for cosmology and probing physics beyond the standard model.
Semi-global symplectic invariants of the spherical pendulum
NASA Astrophysics Data System (ADS)
Dullin, Holger R.
We compute the semi-global symplectic invariants near the focus-focus point of the spherical pendulum. A modified Birkhoff normal form procedure is presented to compute the expansion of the Hamiltonian near the focus-focus point in Eliasson-variables. Combining this with explicit formulas for the action we find the semi-global symplectic invariants near the focus-focus point introduced by Vũ Ngọc (2003) [32]. We show that the Birkhoff normal form at the focus-focus point is the inverse of a complete elliptic integral over a vanishing cycle. We close with some remarks about the pendulum, for which the invariants can be related to theta functions in a beautiful way.
Life on the Edge of Chaos: Orbital Mechanics and Symplectic Integration
NASA Astrophysics Data System (ADS)
Newman, William I.; Hyman, James M.
1998-09-01
Symplectic mapping techniques have become very popular among celestial mechanicians and molecular dynamicists. The word "symplectic" was coined by Hermann Weyl (1939), exploiting the Greek root for a word meaning "complex," to describe a Lie group with special geometric properties. A symplectic integration method is one whose time-derivative satisfies Hamilton's equations of motion (Goldstein, 1980). When due care is paid to the standard computational triad of consistency, accuracy, and stability, a numerical method that is also symplectic offers some potential advantages. Varadarajan (1974) at UCLA was the first to formally explore, for a very restrictive class of problems, the geometric implications of symplectic splittings through the use of Lie series and group representations. Over the years, however, a "mythology" has emerged regarding the nature of symplectic mappings and what features are preserved. Some of these myths have already been shattered by the computational mathematics community. These results, together with new ones we present here for the first time, show where important pitfalls and misconceptions reside. These misconceptions include that: (a) symplectic maps preserve conserved quantities like the energy; (b) symplectic maps are equivalent to the exact computation of the trajectory of a nearby, time-independent Hamiltonian; (c) complicated splitting methods (i.e., "maps in composition") are not symplectic; (d) symplectic maps preserve the geometry associated with separatrices and homoclinic points; and (e) symplectic maps possess artificial resonances at triple and quadruple frequencies. We verify, nevertheless, that using symplectic methods together with traditional safeguards, e.g. convergence and scaling checks using reduced step sizes for integration schemes of sufficient order, can provide an important exploratory and development tool for Solar System applications.
NASA Astrophysics Data System (ADS)
Munteanu, Florian
2016-01-01
In this paper, we will present Lagrangian and Hamiltonian k-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using symmetries and pseudosymmetries, without the help of a Noether type theorem, we will obtain new kinds of conservation laws for k-symplectic Hamiltonian systems and k-symplectic Lagrangian systems.
Symplectic ray-tracing: a new approach for nonlinear ray tracings by Hamiltonian dynamics
NASA Astrophysics Data System (ADS)
Satoh, Tetsu R.
2003-05-01
This paper describes a method of symplectic ray tracing for calculating the flows of non-linear dynamical systems. Symplectic ray tracing method traces the path of photons moving along the orbit calculated by using Hamilton's canonical equation. Using this method, we can simulate non-linear dynamical systems with various dimensions, accurate calculation, and quick implementation of scientif visualization system. This paper also demonstrates some visualization results of non-linear dynamical systems computed by using symplectic ray tracing method.
Finding four dimensional symplectic maps with reduced chaos: Preliminary results
Weishi Wan; Cary, J.R.; Shasharina, S.G.
1998-06-01
A method for finding integrable four-dimensional symplectic maps is outlined. The method relies on solving for parameter values at which the linear stability factors of the fixed points of the map have the values corresponding to integrability. This method is applied to accelerator lattices in order to increase dynamic aperture. Results show a increase of the dynamic aperture after correction, which implies the validity of the method.
Covariant Star Product for Exterior Differential Forms on Symplectic Manifolds
McCurdy, Shannon; Zumino, Bruno
2010-02-10
After a brief description of the Z-graded differential Poisson algebra, we introduce a covariant star product for exterior differential forms and give an explicit expression for it up to second order in the deformation parameter h, in the case of symplectic manifolds. The graded differential Poisson algebra endows the manifold with a connection, not necessarily torsion-free, and places upon the connection various constraints.
Tensor representation of color images and fast 2D quaternion discrete Fourier transform
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.; Agaian, Sos S.
2015-03-01
In this paper, a general, efficient, split algorithm to compute the two-dimensional quaternion discrete Fourier transform (2-D QDFT), by using the special partitioning in the frequency domain, is introduced. The partition determines an effective transformation, or color image representation in the form of 1-D quaternion signals which allow for splitting the N × M-point 2-D QDFT into a set of 1-D QDFTs. Comparative estimates revealing the efficiency of the proposed algorithms with respect to the known ones are given. In particular, a proposed method of calculating the 2r × 2r -point 2-D QDFT uses 18N2 less multiplications than the well-known column-row method and method of calculation based on the symplectic decomposition. The proposed algorithm is simple to apply and design, which makes it very practical in color image processing in the frequency domain.
NASA Astrophysics Data System (ADS)
Wang, Jin; Ma, Jianyong; Zhou, Changhe
2014-11-01
A 3×3 high divergent 2D-grating with period of 3.842μm at wavelength of 850nm under normal incidence is designed and fabricated in this paper. This high divergent 2D-grating is designed by the vector theory. The Rigorous Coupled Wave Analysis (RCWA) in association with the simulated annealing (SA) is adopted to calculate and optimize this 2D-grating.The properties of this grating are also investigated by the RCWA. The diffraction angles are more than 10 degrees in the whole wavelength band, which are bigger than the traditional 2D-grating. In addition, the small period of grating increases the difficulties of fabrication. So we fabricate the 2D-gratings by direct laser writing (DLW) instead of traditional manufacturing method. Then the method of ICP etching is used to obtain the high divergent 2D-grating.
Gauge Properties Of The Guiding Center Variational Symplectic Integrator
J. Squire, H. Qin and W. Tang
2012-03-05
Recently, variational symplectic algorithms have been developed for the long-time simulation of charged particles in magnetic fields1-3. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed for this type of system. It is found that for explicit algorithms an instability arises because the discrete symplectic structure does not become the continuous structure in the t → 0 limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the "antisymmetric discretization gauge," in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as A and are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss's law4.
Construction of Large Period Symplectic Maps by Interpolative Methods
Warnock, Robert; Cai, Yunhai; Ellison, James A.; /New Mexico U.
2009-12-17
The goal is to construct a symplectic evolution map for a large section of an accelerator, say a full turn of a large ring or a long wiggler. We start with an accurate tracking algorithm for single particles, which is allowed to be slightly non-symplectic. By tracking many particles for a distance S one acquires sufficient data to construct the mixed-variable generator of a symplectic map for evolution over S, given in terms of interpolatory functions. Two ways to find the generator are considered: (1) Find its gradient from tracking data, then the generator itself as a line integral. (2) Compute the action integral on many orbits. A test of method (1) has been made in a difficult example: a full turn map for an electron ring with strong nonlinearity near the dynamic aperture. The method succeeds at fairly large amplitudes, but there are technical difficulties near the dynamic aperture due to oddly shaped interpolation domains. For a generally applicable algorithm we propose method (2), realized with meshless interpolation methods.
An efficient symplectic approximation for fringe-field maps
NASA Astrophysics Data System (ADS)
Hoffstätter, G. H.; Berz, M.
1993-12-01
The fringe fields of particle optical elements have a strong effect on optical properties. In particular higher order aberrations are often dominated by fringe-field effects. So far their transfer maps can only be calculated accurately using numerical integrators, which is rather time consuming. Any alternative or approximate calculation scheme should be symplectic because of the importance of the symplectic symmetry for long term behavior. We introduce a method to approximate fringe-field maps of magnetic elements in a symplectic fashion which works extremely quickly and accurately. It is based on differential algebra (DA) techniques and was implemented in COSY INFINITY. The approximation exploits the advantages of Lie transformations, generating functions, scaling of the map with field strength and aperture, and the dependence of transfer maps on the ratio of magnetic rigidity to magnetic field strength. The results are compared to numerical integration and to the approximation via fringe-field integrals. The quality of the approximation will be illustrated on some examples including linear design, high order effects, and long term tracking.
Symplectic Symmetry and the Ab Initio No-Core Shell Model
Draayer, Jerry P.; Dytrych, Tomas; Sviratcheva, Kristina D.; Bahri, Chairul; Vary, James P.; /Iowa State U. /LLNL, Livermore /SLAC
2007-03-14
The symplectic symmetry of eigenstates for the 0{sub gs}{sup +} in {sup 16}O and the 0{sub gs}{sup +} and lowest 2{sup +} and 4{sup +} configurations of {sup 12}C that are well-converged within the framework of the no-core shell model with the JISP16 realistic interaction is examined. These states are found to project at the 85-90% level onto very few symplectic representations including the most deformed configuration, which confirms the importance of a symplectic no-core shell model and reaffirms the relevance of the Elliott SU(3) model upon which the symplectic scheme is built.
Multi-symplectic structure of fully nonlinear weakly dispersive internal gravity waves
NASA Astrophysics Data System (ADS)
Clamond, Didier; Dutykh, Denys
2016-08-01
In this short communication, we present the multi-symplectic structure for the two-layer Serre–Green–Naghdi equations describing the evolution of large amplitude internal gravity water waves when both layers are shallow. We consider only a two-layer stratification with rigid bottom and lid for simplicity, generalisations to several layers being conceivable. This multi-symplectic formulation allows the application of various multi-symplectic integrators (such as Euler or Preissman box schemes) that preserve exactly the multi-symplecticity at the discrete level.
NASA Astrophysics Data System (ADS)
Marino, Eduardo
The electron, discovered by Thomson by the end of the nineteenth century, was the first experimentally observed particle. The Weyl fermion, though theoretically predicted since a long time, was observed in a condensed matter environment in an experiment reported only a few weeks ago. Is there any linking thread connecting the first and the last observed fermion (quasi)particles? The answer is positive. By generalizing the method known as bosonization, the first time in its full complete form, for a spacetime with 3+1 dimensions, we are able to show that both electrons and Weyl fermions can be expressed in terms of the same boson field, namely the Kalb-Ramond anti-symmetric tensor gauge field. The bosonized form of the Weyl chiral currents lead to the angle-dependent magneto-conductance behavior observed in these systems.
Grossman, Yuval; Harnik, Roni; Perez, Gilad; Schwartz, MatthewD.; Surujon, Ze'ev
2004-07-30
The observed flavor structure of the standard model arises naturally in ''split fermion'' models which localize fermions at different places in an extra dimension. It has, until now, been assumed that the bulk masses for such fermions can be chosen to be flavor diagonal simultaneously at every point in the extra dimension, with all the flavor violation coming from the Yukawa couplings to the Higgs. We consider the more natural possibility in which the bulk masses cannot be simultaneously diagonalized, that is, that they are twisted in flavor space. We show that, in general, this does not disturb the natural generation of hierarchies in the flavor parameters. Moreover, it is conceivable that all the flavor mixing and CP-violation in the standard model may come only from twisting, with the five-dimensional Yukawa couplings taken to be universal.
Grossman, Y
2004-07-24
The observed flavor structure of the standard model arises naturally in ''split fermion'' models which localize fermions at different places in an extra dimension. It has, until now, been assumed that the bulk masses for such fermions can be chosen to be flavor diagonal simultaneously at every point in the extra dimension, with all the flavor violation coming from the Yukawa couplings to the Higgs. We consider the more natural possibility in which the bulk masses cannot be simultaneously diagonalized, that is, that they are twisted in flavor space. We show that, in general, this does not disturb the natural generation of hierarchies in the flavor parameters. Moreover, it is conceivable that all the flavor mixing and CP-violation in the standard model may come only from twisting, with the five-dimensional Yukawa couplings taken to be universal.
Punjabi, Alkesh; Ali, Halima
2011-02-15
Any canonical transformation of Hamiltonian equations is symplectic, and any area-preserving transformation in 2D is a symplectomorphism. Based on these, a discrete symplectic map and its continuous symplectic analog are derived for forward magnetic field line trajectories in natural canonical coordinates. The unperturbed axisymmetric Hamiltonian for magnetic field lines is constructed from the experimental data in the DIII-D [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The equilibrium Hamiltonian is a highly accurate, analytic, and realistic representation of the magnetic geometry of the DIII-D. These symplectic mathematical maps are used to calculate the magnetic footprint on the inboard collector plate in the DIII-D. Internal statistical topological noise and field errors are irreducible and ubiquitous in magnetic confinement schemes for fusion. It is important to know the stochasticity and magnetic footprint from noise and error fields. The estimates of the spectrum and mode amplitudes of the spatial topological noise and magnetic errors in the DIII-D are used as magnetic perturbation. The discrete and continuous symplectic maps are used to calculate the magnetic footprint on the inboard collector plate of the DIII-D by inverting the natural coordinates to physical coordinates. The combination of highly accurate equilibrium generating function, natural canonical coordinates, symplecticity, and small step-size together gives a very accurate calculation of magnetic footprint. Radial variation of magnetic perturbation and the response of plasma to perturbation are not included. The inboard footprint from noise and errors are dominated by m=3, n=1 mode. The footprint is in the form of a toroidally winding helical strip. The width of stochastic layer scales as (1/2) power of amplitude. The area of footprint scales as first power of amplitude. The physical parameters such as toroidal angle, length, and poloidal angle covered before striking, and the
Fermion actions extracted from lattice super Yang-Mills theories
NASA Astrophysics Data System (ADS)
Misumi, Tatsuhiro
2013-12-01
We revisit 2D = (2, 2) super Yang-Mills lattice formulation (Sugino model) to investigate its fermion action with two (Majorana) fermion flavors and exact chiral-U(1) R symmetry. We show that the reconcilement of chiral symmetry and absence of further species-doubling originates in the 4D clifford algebra structure of the action, where 2D two flavors are spuriously treated as a single 4D four-spinor with four 4D gamma matrices introduced into kinetic and Wilson terms. This fermion construction based on the higher-dimensional clifford algebra is extended to four dimensions in two manners: (1) pseudo-8D sixteen-spinor treatment of 4D four flavors with eight 8D gamma matrices, (2) pseudo-6D eight-spinor treatment of 4D two flavors with five out of six 6D gamma matrices. We obtain 4D four-species and two-species lattice fermions with unbroken subgroup of chiral symmetry and other essential properties. We discuss their relations to staggered and Wilson twisted-mass fermions. We also discuss their potential feedback to 4D super Yang-Mills lattice formulations.
Highly anisotropic Dirac fermions in square graphynes
NASA Astrophysics Data System (ADS)
Zhang, Lizhi; Wang, Zhengfei; Rao, Jiansheng; Li, Ziheng; Huang, Wulin; Wang, Zhiming; Du, Shixuan; Gao, Hongjun; Liu, Feng
Recently, there have been intense search of new 2D materials, and one especially appealing class of 2D materials is the all-carbon allotropes of Dirac materials. Here, we predict a new family of 2D carbon allotropes, square graphynes (S-graphynes) that exhibit highly anisotropic Dirac Fermions, using first-principle calculations within density functional theory. The equal-energy contour of their 3D band structure shows a crescent shape, and the Dirac crescent has varying Fermi velocities from 0.6 x 105 to 7.2 x 105 m/s along different k directions. Near the Fermi level, the Dirac crescent can be nicely expressed by an extended 2D Dirac model Hamiltonian. Furthermore, tight-binding band fitting reveals that the Dirac crescent originates from the next-nearest-neighbor interactions between C atoms. Our findings enrich the Dirac physics founded in other 2D Dirac systems, and offer a new design mechanism for creating Dirac band by tuning the interaction range. We envision that the highly anisotropic Dirac crescent may be exploited in all-carbon-based electronic devices for manipulating anisotropic electron propagation.
Highly anisotropic Dirac fermions in square graphynes
NASA Astrophysics Data System (ADS)
Zhang, Lizhi; Wang, Zhengfei; Rao, Jiansheng; Li, Ziheng; Huang, Wulin; Wang, Zhiming; Du, Shixuan; Gao, Hongjun; Liu, Feng
Recently, there have been intense search of new 2D materials, and one especially appealing class of 2D materials is the all-carbon allotropes of Dirac materials. Here, we predict a new family of 2D carbon allotropes, square graphynes (S-graphynes) that exhibit highly anisotropic Dirac Fermions, using first-principle calculations within density functional theory. The equal-energy contour of their 3D band structure shows a crescent shape, and the Dirac crescent has varying Fermi velocities from 0.6 ×105 to 7.2 ×105 m/s along different k directions. Near the Fermi level, the Dirac crescent can be nicely expressed by an extended 2D Dirac model Hamiltonian. Furthermore, tight-binding band fitting reveals that the Dirac crescent originates from the next-nearest-neighbor interactions between C atoms. Our findings enrich the Dirac physics founded in other 2D Dirac systems, and offer a new design mechanism for creating Dirac band by tuning the interaction range. We envision that the highly anisotropic Dirac crescent may be exploited in all-carbon-based electronic devices for manipulating anisotropic electron propagation.
2. QUANTUM HALL EFFECT: Magnetooptics of composite fermions
NASA Astrophysics Data System (ADS)
Kukushkin, I. V.; Smet, J. H.; von Klitzing, K.; Eberl, K.
2001-10-01
The Fermi energy and the Zeeman splitting of composite fermions are measured from the temperature dependence of the electron spin polarization at v = 1/2. We demonstrate that the Zeeman splitting of composite fermions is enhanced by a factor of 2.5 due to the interaction between CFs. The latter is very sensitive on the finite width of the 2D channel. The spin polarization at v = 1/3 and v = 2/3 displays an activated behavior and the derived spin-wave gaps are compared with simultaneously measured transport values.
A new multi-symplectic scheme for the generalized Kadomtsev-Petviashvili equation
NASA Astrophysics Data System (ADS)
Li, Haochen; Sun, Jianqiang
2012-09-01
We propose a new scheme for the generalized Kadomtsev-Petviashvili (KP) equation. The multi-symplectic conservation property of the new scheme is proved. Back error analysis shows that the new multi-symplectic scheme has second order accuracy in space and time. Numerical application on studying the KPI equation and the KPII equation are presented in detail.
A Family of Trigonometrically-fitted Partitioned Runge-Kutta Symplectic Methods
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.
2007-12-26
We are presenting a family of trigonometrically fitted partitioned Runge-Kutta symplectic methods of fourth order with six stages. The solution of the one dimensional time independent Schroedinger equation is considered by trigonometrically fitted symplectic integrators. The Schroedinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator and the exponential potential.
On the symplectic two-form of gravity in terms of Dirac eigenvalues
NASA Astrophysics Data System (ADS)
Abdalla, M. C. B.; De Andrade, M. A.; Santos, M. A.; Vancea, I. V.
2002-11-01
The Dirac eigenvalues form a subset of observables of the Euclidean gravity. The symplectic two-form in the covariant phase space could be expressed, in principle, in terms of the Dirac eigenvalues. We discuss the existence of the formal solution of the equations defining the components of the symplectic form in this framework.
Energy Science and Technology Software Center (ESTSC)
2004-08-01
AnisWave2D is a 2D finite-difference code for a simulating seismic wave propagation in fully anisotropic materials. The code is implemented to run in parallel over multiple processors and is fully portable. A mesh refinement algorithm has been utilized to allow the grid-spacing to be tailored to the velocity model, avoiding the over-sampling of high-velocity materials that usually occurs in fixed-grid schemes.
Higher-order symplectic Born-Oppenheimer molecular dynamics
Niklasson, Anders; Bock, Nicolas; Challacombe, Matt; Odell, Anders; Delin, Anna; Johansson, Borje
2009-01-01
The extended Lagrangian formulation of time-reversible Born-Oppenheimer molecular dynamics (TR-BOMD) enables the use of geometric integrators in the propagation of both the nuclear and the electronic degrees of freedom on the Born-Oppenheimer potential energy surface. Different symplectic integrators up to the 6th order have been adapted and optimized to TR-BOMD in the framework of ab initio self-consistent-field theory. It is shown how the accuracy can be significantly improved compared to a conventional Verlet integration at the same level of computational cost, in particular for the case of very high accuracy requirements.
Distribution of Transmission Eigenvalues in Disordered Wires with Symplectic Symmetry
NASA Astrophysics Data System (ADS)
Sakai, Hiroshi; Wakabayashi, Katsunori; Takane, Yositake
2007-03-01
We have numerically studied the electronic transport properties of quantum wires with symplectic symmetry based on the tight-binding model. The asymptotic behavior of the conductance crucially depends on the even-odd effect of the conducting channel, since one perfectly conducting channel exists only in the odd-channel system. The decay length of the conductance and the distribution of the largest transmission eigenvalues clearly show the even-odd difference. Our results are in excellent agreement with the random-matrix theory.
Method to render second order beam optics programs symplectic
Douglas, D.; Servranckx, R.V.
1984-10-01
We present evidence that second order matrix-based beam optics programs violate the symplectic condition. A simple method to avoid this difficulty, based on a generating function approach to evaluating transfer maps, is described. A simple example illustrating the non-symplectricity of second order matrix methods, and the effectiveness of our solution to the problem, is provided. We conclude that it is in fact possible to bring second order matrix optics methods to a canonical form. The procedure for doing so has been implemented in the program DIMAT, and could be implemented in programs such as TRANSPORT and TURTLE, making them useful in multiturn applications. 15 refs.
Contraction limits of the proton-neutron symplectic model
NASA Astrophysics Data System (ADS)
Ganev, H. G.
2016-01-01
The algebraic approach to nuclear structure physics allows a certain microscopic collective motion algebra to be also interpreted on macroscopic level which is achieved in the limit of large representation quantum numbers. Such limits are referred to as macroscopic or hydrodynamic limits and show how a given microscopic discrete system starts to behave like a continuous fluid. In the present paper, two contraction limits of the recently introduced fully microscopic proton-neutron symplectic model (PNSM) with the Sp(12; R) dynamical symmetry algebra are considered. As a result, two simplified macroscopic models of nuclear collective motion are obtained in simple geometrical terms. The first one is the U(6)-phonon model with the semi-direct product structure [HW(21)]U(6), which is shown to be actually an alternative formulation of the original proton-neutron symplectic model in the familiar IBM-terms. The second model which appears in double contraction limit is the two-rotor model with the ROTp(3) ⊗ ROTn(3) ⊃ ROT(3) algebraic structure. The latter, in contrast to the original two-rotor model, is not restricted to the case of two coupled axial rotors. In this way, the second contraction limit of the PNSM, provides the phenomenological two-rotor model with a simple microscopic foundation.
Gradient Symplectic Algorithms for Solving Quantum Dynamical Problems
NASA Astrophysics Data System (ADS)
Chin, Siu A.; Chen, C. R.; Auer, J.; Krotscheck, E.
2002-03-01
Recent advances[1] in factorizing the classical and quantum evolution operator to fourth order with purely positive coefficients have produce a new class of Monte Carlo[2,3] and quantum dynamical algorithms[4,5] that are at least two orders of magnitude better than existing algorithms of comparble order. This talk will focus on solving the Schrodinger equation in real and imaginary time for the extraction of dynamical information and for the determination of eigenvalue-function pairs from large 3-D grids. References: [1]S. A. Chin, ``Symplectic Integrators From Composite Operator Factorizations" Phys. Lett. A226, 344 (1997). [2]H. A. Forbert and S. A. Chin ``Fourth-order algorithms for solving the multivariable Langevin equation and the Kramers equation", Phys. Rev. E63, 016703 (2001). [3]H. A. Forbert and S. A. Chin, ``Fourth-order diffusion Monte Carlo algorithms for solving quantum many-body problems", Phys. Rev. B63, 144518 (2001). [4]S. A. Chin and C. R. Chen, ``Fourth order gradient symplectic integrator methods for solving the time-dependent Schrodinger equation", J. Chem. Phys. 114, 7338 (2001). [5]J. Auer, E. Krotscheck, and S. A. Chin, ``A fourth-order real-space algorithm for solving local Schrodinger equations", J. Chem. Phys. 115, 6841 (2001).
Hadron Properties with FLIC Fermions
James Zanotti; Wolodymyr Melnitchouk; Anthony Williams; J Zhang
2003-07-01
The Fat-Link Irrelevant Clover (FLIC) fermion action provides a new form of nonperturbative O(a)-improvement in lattice fermion actions offering near continuum results at finite lattice spacing. It provides computationally inexpensive access to the light quark mass regime of QCD where chiral nonanalytic behavior associated with Goldstone bosons is revealed. The motivation and formulation of FLIC fermions, its excellent scaling properties and its low-lying hadron mass phenomenology are presented.
A hybrid symplectic PIC/spectral scheme for one-dimensional electrostatic simulations
Doxas, I.; Cary, J.R.
1996-12-31
We develop a hybrid PIC/spectral integration scheme based on the explicit symplectic integrator of reference. We find that for low-accuracy short-term integration (5% accuracy over {omega}{sub p}t = 500) the second-order symplectic method is most efficient, outperforming the fourth-order method by 65% and non-symplectic methods such as Runge-Kutta, Bulirsch-Stoer and {open_quote}naive{close_quote} leap-frog by a factor of 3-10. For high-accuracy short-term integration (10{sup -4} over w{sub p}t = 500) the second-order symplectic method is 20% more efficient than both the fourth-order method and Bulirsch-Stoer, and a factor of 8-20 more efficient than Runge-Kutta and {open_quote}naive{close_quote} leap-frog. For long-term integration (w{sub p}t = 10{sup 5}) the second order symplectic method outperforms all non-symplectic methods by a factor of 8-20. We also show that the symplectic method is more robust to roundoff error than all other methods we tested, and that for simulations with a small number of particles per wavelength (usuall in plasma simulations) cubic spline interpolation is more efficient that linear interpolation.
Explicit symplectic algorithms based on generating functions for charged particle dynamics.
Zhang, Ruili; Qin, Hong; Tang, Yifa; Liu, Jian; He, Yang; Xiao, Jianyuan
2016-07-01
Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term accuracy and fidelity. For long-term simulations with high efficiency, explicit symplectic algorithms are desirable. However, it is generally believed that explicit symplectic algorithms are only available for sum-separable Hamiltonians, and this restriction limits the application of explicit symplectic algorithms to charged particle dynamics. To overcome this difficulty, we combine the familiar sum-split method and a generating function method to construct second- and third-order explicit symplectic algorithms for dynamics of charged particle. The generating function method is designed to generate explicit symplectic algorithms for product-separable Hamiltonian with form of H(x,p)=p_{i}f(x) or H(x,p)=x_{i}g(p). Applied to the simulations of charged particle dynamics, the explicit symplectic algorithms based on generating functions demonstrate superiorities in conservation and efficiency. PMID:27575228
Complete Boson-Fermion Model of Superconductivity
NASA Astrophysics Data System (ADS)
de Llano, Manuel
2003-03-01
The unification of the 1957 BCS theory with that of Bose-Einstein condensation (BEC) that gives roughly good first-principles transition temperature Tc predictions in either 2D or 3D for all of the ``Uemura plot'' ``exotic'' or conventional superconductors without abandoning the much-maligned phonon interaction mechanism has recently been achieved [1]-[3]. The same dynamical mechanism also allows for room-temperature superconductivity. The only condition is that one depart moderately from the perfect electron (e)-/hole (h)-Cooper-pair (CP) symmetry to which BCS (and indeed also the somewhat more general BCS-Bose crossover) theory are restricted by construction. It now becomes feasible to explain, among other things, why largely all superconductors empirically have substantially higher T_c's if their normal-state charge carriers are holes rather than electrons. A complete (in the sense that 2h-CPs are not ignored) boson-fermion model (CBFM) has been developed that reduces in the appropriate special cases to: a) ordinary BCS theory for weak boson-fermion coupling; b) the BCS-Bose ``crossover'' theory dating back to 1967; and, for no 2h-CPs to: c) the 1989 boson-fermion (BF) BEC model by T.D. Lee et al. of superconductors which without 2h-CPs is unrelated to BCS theory; d) an ideal BF binary-gas model [4] predicting nonzero BEC T_c's even in 2D; and finally to e) ordinary BEC (1925). The CBFM is a BF statistical model similar to those developed in the mid-50's by Schafroth, Blatt & Butler but which now includes 2h-CPs on an equal footing with 2e-CPs, and which unlike these models also contains the empirically well-established fermionic energy gap. [1] V.V. Tolmachev, Phys. Lett. A 266, 400 (2000). [2] M. Fortes, M.A. Solis, M. de Llano & V.V. Tolmachev, Physica C 364, 95 (2001). [3] M. de Llano & V.V. Tolmachev, Physica A 317, 546 (2003). [4] M. Casas, N.J. Davidson, M. de Llano, T.A. Mamedov, A. Puente, R.M. Quick, A. Rigo & M.A. Solis, Physica A 295, 146 (2001
NASA Astrophysics Data System (ADS)
Mayor, Louise
2016-05-01
Graphene might be the most famous example, but there are other 2D materials and compounds too. Louise Mayor explains how these atomically thin sheets can be layered together to create flexible “van der Waals heterostructures”, which could lead to a range of novel applications.
Novel p-wave superfluids of fermionic polar molecules
NASA Astrophysics Data System (ADS)
Fedorov, A. K.; Matveenko, S. I.; Yudson, V. I.; Shlyapnikov, G. V.
2016-06-01
Recently suggested subwavelength lattices offer remarkable prospects for the observation of novel superfluids of fermionic polar molecules. It becomes realistic to obtain a topological p-wave superfluid of microwave-dressed polar molecules in 2D lattices at temperatures of the order of tens of nanokelvins, which is promising for topologically protected quantum information processing. Another foreseen novel phase is an interlayer p-wave superfluid of polar molecules in a bilayer geometry.
Novel p-wave superfluids of fermionic polar molecules.
Fedorov, A K; Matveenko, S I; Yudson, V I; Shlyapnikov, G V
2016-01-01
Recently suggested subwavelength lattices offer remarkable prospects for the observation of novel superfluids of fermionic polar molecules. It becomes realistic to obtain a topological p-wave superfluid of microwave-dressed polar molecules in 2D lattices at temperatures of the order of tens of nanokelvins, which is promising for topologically protected quantum information processing. Another foreseen novel phase is an interlayer p-wave superfluid of polar molecules in a bilayer geometry. PMID:27278711
Novel p-wave superfluids of fermionic polar molecules
Fedorov, A. K.; Matveenko, S. I.; Yudson, V. I.; Shlyapnikov, G. V.
2016-01-01
Recently suggested subwavelength lattices offer remarkable prospects for the observation of novel superfluids of fermionic polar molecules. It becomes realistic to obtain a topological p-wave superfluid of microwave-dressed polar molecules in 2D lattices at temperatures of the order of tens of nanokelvins, which is promising for topologically protected quantum information processing. Another foreseen novel phase is an interlayer p-wave superfluid of polar molecules in a bilayer geometry. PMID:27278711
Nucleon Resonances from FLIC Fermions
Derek Leinweber; J. Hedditch; Wally Melnitchouk; Anthony Williams
2003-01-01
The Fat Link Irrelevant Glover (FL1C) fermion action and its associated phenomenology is described. The scaling analysis indicates FLIC fermions provide a new form of nonperturbative O(a) improvement where near-continuum results are obtained at finite lattice spacing spin-1/2 and spin-3/2 , even and odd parity nucleon resonances are investigated.
Symplectic maps and chromatic optics in particle accelerators
Cai, Yunhai
2015-07-06
Here, we have applied the nonlinear map method to comprehensively characterize the chromatic optics in particle accelerators. Our approach is built on the foundation of symplectic transfer maps of magnetic elements. The chromatic lattice parameters can be transported from one element to another by the maps. We also introduce a Jacobian operator that provides an intrinsic linkage between the maps and the matrix with parameter dependence. The link allows us to directly apply the formulation of the linear optics to compute the chromatic lattice parameters. As an illustration, we analyze an alternating-gradient cell with nonlinear sextupoles, octupoles, and decapoles and derive analytically their settings for the local chromatic compensation. Finally, the cell becomes nearly perfect up to the third-order of the momentum deviation.
Trigonometric Sutherland systems and their Ruijsenaars duals from symplectic reduction
Feher, L.; Ayadi, V.
2010-10-15
Beside its usual interpretation as a system of n indistinguishable particles moving on the circle, the trigonometric Sutherland system can be viewed alternatively as a system of distinguishable particles on the circle or on the line, and these three physically distinct systems are in duality with corresponding variants of the rational Ruijsenaars-Schneider system. We explain that the three duality relations, first obtained by Ruijsenaars in 1995, arise naturally from the Kazhdan-Kostant-Sternberg symplectic reductions of the cotangent bundles of the group U(n) and its covering groups U(1)xSU(n) and RxSU(n), respectively. This geometric interpretation enhances our understanding of the duality relations and simplifies Ruijsenaars' original direct arguments that led to their discovery.
Symplectic structure and monopole strength in {sup 12}C
Yoshida, T.; Itagaki, N.; Kato, K.
2011-02-15
The relation between the monopole transition strength and existence of cluster structure in the excited states is discussed based on an algebraic cluster model. The structure of {sup 12}C is studied with a 3{alpha} model, and the wave function for the relative motions between {alpha} clusters are described by the symplectic algebra Sp(2, R){sub z}, which corresponds to the linear combinations of SU(3) states with different multiplicities. Introducing Sp(2,R){sub z} algebra works well for reducing the number of the basis states, and it is also shown that states connected by the strong monopole transition are classified by a quantum number {Lambda} of the Sp(2,R){sub z} algebra.
Symplectic maps for the n-body problem - Stability analysis
NASA Technical Reports Server (NTRS)
Wisdom, Jack; Holman, Matthew
1992-01-01
The stability of new symplectic n-body maps is examined from the point of view of nonlinear dynamics. The resonances responsible for the principal artifacts are identified. These are resonances between the stepsize and the difference of mean motions between pairs of planets. For larger stepsizes resonant perturbations are evident in the variation of the energy of the system corresponding to these stepsize resonances. It is shown that the principal instability of the method can be predicted and corresponds to the overlap of the stepsize resonances. It is noted that the analysis suggests that other artifacts will occur. For example, the overlap of a stepsize resonance with a resonance of the actual system may also give a region of chaotic behavior that is an artifact. It is pointed out that the fact that the principal artifacts corresponds to a particular set of stepsize resonances suggests that it may be possible to perturbatively remove the effect when the stepsize resonances are nonoverlapping.
Symplectic maps for the n-body problem
NASA Technical Reports Server (NTRS)
Wisdom, Jack; Holman, Matthew
1991-01-01
The present study generalizes the mapping method of Wisdom (1982) to encompass all gravitational n-body problems with a dominant central mass. The rationale for the generalized mapping method is discussed as well as details for the mapping for the n-body problem. Some refinements of the method are considered, and the relationship of the mapping method to other symplectic integration methods is shown. The method is used to compute the evolution of the outer planets for a billion years. The resulting evolution is compared to the 845 million year evolution of the outer planets performed on the Digital Orerry using standard numerical integration techniques. This calculation provides independent numerical confirmation of the result of Sussman and Wisdom (1988) that the motion of the planet Pluto is chaotic.
A Unitary Transformation in the Contracted Symplectic Model Approach
NASA Astrophysics Data System (ADS)
Castaños, Octavio; López-Moreno, Enrique
1997-04-01
In the last years a contracted version of the Symplectic Shell Model scheme has been used to describe the energy spectra and electromagnetic transitions to describe light and heavy rotational nuclei. In these works a model hamiltonian that takes into account the shell structure, couplings to major shells through a quadrupole-quadrupole interaction, and a residual rotor term were used. In the present contribution a unitary transformation is introduced, which gives rise to a simpler hamiltonian and the matrix elements of its different component terms with respect to the Ub × U_s(3) basis states are easily calculated. Also the quadrupole electromagnetic transitions can be easily determined. At the same time this unitary transformation in the boson approximation limit yields new insights to the shell model interpretation of the quantum rotor hamiltonian.
Symplectic maps and chromatic optics in particle accelerators
Cai, Yunhai
2015-07-06
We have applied the nonlinear map method to comprehensively characterize the chromatic optics in particle accelerators. Our approach is built on the foundation of symplectic transfer maps of magnetic elements. The chromatic lattice parameters can be transported from one element to another by the maps. We introduce a Jacobian operator that provides an intrinsic linkage between the maps and the matrix with parameter dependence. The link allows us to directly apply the formulation of the linear optics to compute the chromatic lattice parameters. As an illustration, we analyze an alternating-gradient cell with nonlinear sextupoles, octupoles, and decapoles and derive analytically their settings for the local chromatic compensation. Lastly, the cell becomes nearly perfect up to the third-order of the momentum deviation.
The symplectic origin of conformal and Minkowski superspaces
NASA Astrophysics Data System (ADS)
Fioresi, R.; Latini, E.
2016-02-01
Supermanifolds provide a very natural ground to understand and handle supersymmetry from a geometric point of view; supersymmetry in d = 3, 4, 6, and 10 dimensions is also deeply related to the normed division algebras. In this paper we want to show the link between the conformal group and certain types of symplectic transformations over division algebras. Inspired by this observation we then propose a new realization of the real form of the 4 dimensional conformal and Minkowski superspaces we obtain, respectively, as a Lagrangian supermanifold over the twistor superspace ℂ4|1 and a big cell inside it. The beauty of this approach is that it naturally generalizes to the 6 dimensional case (and possibly also to the 10 dimensional one) thus providing an elegant and uniform characterization of the conformal superspaces.
Symplectic maps and chromatic optics in particle accelerators
Cai, Yunhai
2015-07-06
Here, we have applied the nonlinear map method to comprehensively characterize the chromatic optics in particle accelerators. Our approach is built on the foundation of symplectic transfer maps of magnetic elements. The chromatic lattice parameters can be transported from one element to another by the maps. We also introduce a Jacobian operator that provides an intrinsic linkage between the maps and the matrix with parameter dependence. The link allows us to directly apply the formulation of the linear optics to compute the chromatic lattice parameters. As an illustration, we analyze an alternating-gradient cell with nonlinear sextupoles, octupoles, and decapoles andmore » derive analytically their settings for the local chromatic compensation. Finally, the cell becomes nearly perfect up to the third-order of the momentum deviation.« less
Energy Science and Technology Software Center (ESTSC)
2001-01-31
This software reduces the data from two-dimensional kSA MOS program, k-Space Associates, Ann Arbor, MI. Initial MOS data is recorded without headers in 38 columns, with one row of data per acquisition per lase beam tracked. The final MOSS 2d data file is reduced, graphed, and saved in a tab-delimited column format with headers that can be plotted in any graphing software.
Composite Fermions and Quartets in Optical Traps and in High-Tc Superconductors
Kagan, M. Yu.; Brodsky, I. V.; Klaptsov, A. V.; Efremov, D. V.; Combescot, R.; Leyronas, X.
2006-09-07
We consider a possibility of the creation of composite fermions in optical traps and in high-Tc superconductors. For optical traps we study a model of Fermi-Bose mixture with resonant attraction between particles of different sorts. In this case a pairing between fermion and boson of the type bf is possible. This pairing corresponds to creation of composite fermions. At low temperatures and equal densities of fermions and bosons composite fermions are further paired in quartets. In the 2D case we exactly solve Skorniakov-Ter-Martirosian type of integral equations and find the binding energies of two bosons plus one fermion fbb and two bosons plus two fermions fbfb. For high-Tc superconductors we consider a quartet -- a bound state of two composite holes {delta} =< hh >, where each composite hole h = fb consists of a spinon and a holon bound by the stringlike potential. Our investigations are important for recent experiments on the observation of weakly bound composite fermions and bosons in optical traps in the regime of Feshbach resonance.
Fermi Blobs and the Symplectic Camel: A Geometric Picture of Quantum States
NASA Astrophysics Data System (ADS)
Gossona, Maurice A. De
We have explained in previous work the correspondence between the standard squeezed coherent states of quantum mechanics, and quantum blobs, which are the smallest phase space units compatible with the uncertainty principle of quantum mechanics and having the symplectic group as a group of symmetries. In this work, we discuss the relation between quantum blobs and a certain level set (which we call "Fermi blob") introduced by Enrico Fermi in 1930. Fermi blobs allows us to extend our previous results not only to the excited states of the generalized harmonic oscillator in n dimensions, but also to arbitrary quadratic Hamiltonians. As is the case for quantum blobs, we can evaluate Fermi blobs using a topological notion, related to the uncertainty principle, the symplectic capacity of a phase space set. The definition of this notion is made possible by Gromov's symplectic non-squeezing theorem, nicknamed the "principle of the symplectic camel".
Evidence for Symplectic Symmetry in Ab Initio No-Core Shell Model Results for Light Nuclei
Dytrych, Tomas; Sviratcheva, Kristina D.; Bahri, Chairul; Draayer, Jerry P.; Vary, James P.; /Iowa State U. /LLNL, Livermore /SLAC
2007-04-24
Clear evidence for symplectic symmetry in low-lying states of {sup 12}C and {sup 16}O is reported. Eigenstates of {sup 12}C and {sup 16}O, determined within the framework of the no-core shell model using the JISP16 NN realistic interaction, typically project at the 85-90% level onto a few of the most deformed symplectic basis states that span only a small fraction of the full model space. The results are nearly independent of whether the bare or renormalized effective interactions are used in the analysis. The outcome confirms Elliott's SU(3) model which underpins the symplectic scheme, and above all, points to the relevance of a symplectic no-core shell model that can reproduce experimental B(E2) values without effective charges as well as deformed spatial modes associated with clustering phenomena in nuclei.
Nanoimprint lithography: 2D or not 2D? A review
NASA Astrophysics Data System (ADS)
Schift, Helmut
2015-11-01
Nanoimprint lithography (NIL) is more than a planar high-end technology for the patterning of wafer-like substrates. It is essentially a 3D process, because it replicates various stamp topographies by 3D displacement of material and takes advantage of the bending of stamps while the mold cavities are filled. But at the same time, it keeps all assets of a 2D technique being able to pattern thin masking layers like in photon- and electron-based traditional lithography. This review reports about 20 years of development of replication techniques at Paul Scherrer Institut, with a focus on 3D aspects of molding, which enable NIL to stay 2D, but at the same time enable 3D applications which are "more than Moore." As an example, the manufacturing of a demonstrator for backlighting applications based on thermally activated selective topography equilibration will be presented. This technique allows generating almost arbitrary sloped, convex and concave profiles in the same polymer film with dimensions in micro- and nanometer scale.
Variational symplectic algorithm for guiding center dynamics and its application in tokamak geometry
NASA Astrophysics Data System (ADS)
Qin, Hong; Guan, Xiaoyin; Tang, William M.
2009-04-01
A variational symplectic integrator for the guiding center motion of charged particles in general magnetic fields is developed to enable accurate long-time simulation studies of magnetized plasmas. Instead of discretizing the differential equations of the guiding center motion, the action of the guiding center motion is discretized and minimized to obtain the iteration rules for advancing the dynamics. The variational symplectic integrator conserves exactly a discrete Lagrangian symplectic structure and globally bounds the numerical error in energy by a small number for all simulation time steps. Compared with standard integrators, such as the fourth order Runge-Kutta method, the variational symplectic integrator has superior numerical properties over long integration time. For example, in a two-dimensional tokamak geometry, the variational symplectic integrator is able to guarantee the accuracy for both the trapped and transit particle orbits for arbitrarily long simulation time. This is important for modern large-scale simulation studies of fusion plasmas where it is critical to use algorithms with long-term accuracy and fidelity. The variational symplectic integrator is expected to have a wide range of applications.
Open fermionic quantum systems
Artacho, E.; Falicov, L.M. Materials Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720 )
1993-01-15
A method to treat a quantum system in interaction with a fermionic reservoir is presented. Its most important feature is that the dynamics of the exchange of particles between the system and the reservoir is explicitly included via an effective interaction term in the Hamiltonian. This feature gives rise to fluctuations in the total number of particles in the system. The system is to be considered in its full structure, whereas the reservoir is described only in an effective way, as a source of particles characterized by a small set of parameters. Possible applications include surfaces, molecular clusters, and defects in solids, in particular in highly correlated electronic materials. Four examples are presented: a tight-binding model for an adsorbate on the surface of a one-dimensional lattice, the Anderson model of a magnetic impurity in a metal, a two-orbital impurity with interorbital hybridization (intermediate-valence center), and a two-orbital impurity with interorbital repulsive interactions.
Unlocking fermionic mode entanglement
NASA Astrophysics Data System (ADS)
Friis, Nicolai
2016-06-01
Aside from other puzzling features of entanglement, it has been debated whether a physically meaningful notion of entanglement requires two (or more) particles as carriers of the correlated degrees-of-freedom, or if a single particle could be considered to be entangled as well. While the usefulness of single-boson entanglement has been demonstrated some time ago, the restrictions of superselection rules have previously thwarted attempts at similar arguments for single fermions. In Dasenbrook et al (2016 New J. Phys. 18 043036) this obstacle is overcome. The authors propose a scheme for a Bell test on two copies of single-electron states whose entanglement is individually not accessible. The discussed scheme, which makes use of recent progress in electronic quantum optics, provides an experimentally viable and theoretically unambiguous way to assert that certain single-electron states can be considered to be entangled.
Dynamical symmetries for fermions
Guidry, M.
1989-01-01
An introduction is given to the Fermion Dynamical Symmetry Model (FDSM). The analytical symmetry limits of the model are then applied to the calculation of physical quantities such as ground-state masses and B(E{sub 2}) values in heavy nuclei. These comparisons with data provide strong support for a new principle of collective motion, the Dynamical Pauli Effect, and suggest that dynamical symmetries which properly account for the pauli principle are much more persistent in nuclear structure than the corresponding boson symmetries. Finally, we present an assessment of criticisms which have been voiced concerning the FDSM, and a discussion of new phenomena and exotic spectroscopy'' which may be suggested by the model. 14 refs., 8 figs., 4 tabs.
FLIC Fermions and Hadron Phenomenology
D. Leinweber; J.N. Hedditch; W. Melnitchouk; A.W. Thomas; A.G. Williams; R.D. Young; J.M. Zanotti; J.B. Zhang
2002-06-01
A pedagogical overview of the formulation of the Fat Link Irrelevant Clover (FLIC) fermion action and its associated phenomenology is described. The scaling analysis indicates FLIC fermions provide a new form of nonperturbative order (a) improvement where near-continuum results are obtained at finite lattice spacing. Spin-1/2 and spin-3/2, even and odd parity baryon resonances are investigated in quenched QCD, where the nature of the Roper resonance and Lambda (1405) are of particular interest. FLIC fermions allow efficient access to the light quark-mass regime, where evidence of chiral nonanalytic behavior in the Delta mass is observed.
Correlated Electron Phenomena in 2D Materials
NASA Astrophysics Data System (ADS)
Lambert, Joseph G.
In this thesis, I present experimental results on coherent electron phenomena in layered two-dimensional materials: single layer graphene and van der Waals coupled 2D TiSe2. Graphene is a two-dimensional single-atom thick sheet of carbon atoms first derived from bulk graphite by the mechanical exfoliation technique in 2004. Low-energy charge carriers in graphene behave like massless Dirac fermions, and their density can be easily tuned between electron-rich and hole-rich quasiparticles with electrostatic gating techniques. The sharp interfaces between regions of different carrier densities form barriers with selective transmission, making them behave as partially reflecting mirrors. When two of these interfaces are set at a separation distance within the phase coherence length of the carriers, they form an electronic version of a Fabry-Perot cavity. I present measurements and analysis of multiple Fabry-Perot modes in graphene with parallel electrodes spaced a few hundred nanometers apart. Transition metal dichalcogenide (TMD) TiSe2 is part of the family of materials that coined the term "materials beyond graphene". It contains van der Waals coupled trilayer stacks of Se-Ti-Se. Many TMD materials exhibit a host of interesting correlated electronic phases. In particular, TiSe2 exhibits chiral charge density waves (CDW) below TCDW ˜ 200 K. Upon doping with copper, the CDW state gets suppressed with Cu concentration, and CuxTiSe2 becomes superconducting with critical temperature of T c = 4.15 K. There is still much debate over the mechanisms governing the coexistence of the two correlated electronic phases---CDW and superconductivity. I will present some of the first conductance spectroscopy measurements of proximity coupled superconductor-CDW systems. Measurements reveal a proximity-induced critical current at the Nb-TiSe2 interfaces, suggesting pair correlations in the pure TiSe2. The results indicate that superconducting order is present concurrently with CDW in
Observing remnants by fermions' tunneling
Chen, D.Y.; Wu, H.W.; Yang, H. E-mail: iverwu@uestc.edu.cn
2014-03-01
The standard Hawking formula predicts the complete evaporation of black holes. In this paper, we introduce effects of quantum gravity into fermions' tunneling from Reissner-Nordstrom and Kerr black holes. The quantum gravity effects slow down the increase of Hawking temperatures. This property naturally leads to a residue mass in black hole evaporation. The corrected temperatures are affected by the quantum numbers of emitted fermions. Meanwhile, the temperature of the Kerr black hole is a function of θ due to the rotation.
Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model.
Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; Neupert, Titus; Maciejko, Joseph
2016-08-26
We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionic symmetry-protected topological phase. This state-protected by time-reversal and reflection symmetries-cannot be connected adiabatically to a free-fermion topological phase. PMID:27610869
Analytical and numerical manifolds in a symplectic 4-D map
NASA Astrophysics Data System (ADS)
Delis, N.; Contopoulos, G.
2016-05-01
We study analytically the orbits along the asymptotic manifolds from a complex unstable periodic orbit in a symplectic 4-D Froeschlé map. The orbits are given as convergent series. We compare the analytic results by truncating the series at various orders with the corresponding numerical results and we find agreement along a more extended length, as the order of truncation increases. The agreement is improved when the parameters approach those of the stability domain. Along the manifolds no terms with small divisors appear in the series. The same result is found if we use a parametrization method along the asymptotic curves. In the case of orbits starting close to the manifolds small divisors appear, but the orbits remain close to the manifolds for an extended period of time. If the parameters of the map are close to the stable domain the orbits recede and approach the origin several times and remain confined in a certain volume around the origin for a long time before escaping to large distances. For special sets of parameters we see resonance phenomena and the orbits take particular forms near every resonance.
High-order unified symplectic FDTD scheme for the metamaterials
NASA Astrophysics Data System (ADS)
Ren, Xingang; Huang, Zhixiang; Wu, Xianliang; Lu, Silong; Wang, Hui; Wu, Lei; Li, Shen
2012-06-01
A high-order unified symplectic finite-difference time-domain (US-FDTD) method, which is energy conserved, for modeling the metamaterials is proposed. The lossless Drude dispersive model is taken into account in US-FDTD scheme, and the detailed formulations of the proposed US-FDTD method are also provided. The high-order split perfectly matched layers (SPML) are used as the absorbing boundary conditions (ABCs) to terminate the computational domain. The analysis of Courant stability and numerical dispersion demonstrate that US-FDTD scheme is more efficient than the traditional time domain numerical methods. Focusing and refocusing of the electromagnetic wave in target detection is validated using the normal incident Gaussian beam with a matched slab. Oblique incidence results associated with the inverse Snell effect and the phase compensation effect of the composite slab further demonstrated the efficiency of the method. Numerical results for a more realistic structure are also included. All the results agree well with the theoretical prediction. The method proposed here can be directly put into using as a time-domain full-wave simulation tool for applications in metamaterials.
Star products on symplectic vector spaces: convergence, representations, and extensions
NASA Astrophysics Data System (ADS)
Soloviev, M. A.
2014-12-01
We briefly survey the general scheme of deformation quantization on symplectic vector spaces and analyze its functional analytic aspects. We treat different star products in a unified way by systematically using an appropriate space of analytic test functions for which the series expansions of the star products in powers of the deformation parameter converge absolutely. The star products are extendable by continuity to larger functional classes. The uniqueness of the extension is guaranteed by suitable density theorems. We show that the maximal star product algebra with the absolute convergence property, consisting of entire functions of an order at most 2 and minimal type, is nuclear. We obtain an integral representation for the star product corresponding to the Cahill-Glauber s-ordering, which connects the normal, symmetric, and antinormal orderings continuously as s varies from 1 to - 1. We exactly characterize those extensions of the Wick and anti-Wick correspondences that are in line with the known extension of the Weyl correspondence to tempered distributions.
Dirac Fermions in Nanoassembled Artificial Graphene
NASA Astrophysics Data System (ADS)
Gomes, Kenjiro K.; Ko, Wonhee; Mar, Warren; Manoharan, Hari C.
2011-03-01
In condensed matter, electronic properties derive from the energy band structure created by a periodic potential formed by the atoms that constitute a particular material. The power to design unique electronic states is ultimately tied to the power to design the atomic lattice. Utilizing the technique of atomic manipulation with a scanning tunneling microscope, we create an artificial lattice potential that reshapes the band structure of a normal 2D electron gas---found in the surface states of a normal metal---into a unique and distinct 2D gas of massless Dirac fermions. We present scanning tunneling spectroscopic measurements of nanoassembled honeycomb electron lattices, and we characterize their band structure through Fourier transform analysis of impurity scattering maps. The control of every atomic position in the lattice provides unprecedented control over physical parameters elusive in natural graphene systems. These abilities include atomically sharp doping configurations and the power to embed topological singularities, resulting in unique electronic states rarely encountered in natural systems. Supported by the DOE, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under contract DE-AC02-76SF00515.
Hubbard Model study of Off Diagonally Confined fermions in a 2D Optical Lattice
NASA Astrophysics Data System (ADS)
Cone, Dave; Chiesa, Simone; Scalettar, Richard; Batrouni, George
2010-03-01
We report Quantum Monte Carlo simulations of a Hubbard Hamiltonian which incorporates a proposed new method for confining atoms in an optical lattice employing an inhomogeneous array of hopping matrix elements which trap atoms by going to zero at the lattice edges. This has been termed ``Off Diagonal Confinement (ODC)'' [1] to distinguish it from the more conventional use of a parabolic trap coupling to (diagonal) density operators. It has the advantage of producing systems which, while still being inhomogeneous, are entirely in the Mott phase, and allow simulations which are free of the sign problem at low temperatures. We analyze the effects of using ODC traps on the local density, density fluctuation, spin, and pairing correlation functions. Finally, we will discuss the advantages and importance of this new confinement technique for modeling correlated systems. Research supported by the Department of Energy, Office of Science SCIDAC program, DOE-DE-FC0206ER25793. [1] V.G. Rousseau et al., arXiv:0909.3543
Observation of 2D Fermionic Mott Insulators of 40K with Single-Site Resolution
NASA Astrophysics Data System (ADS)
Cheuk, Lawrence W.; Nichols, Matthew A.; Lawrence, Katherine R.; Okan, Melih; Zhang, Hao; Zwierlein, Martin W.
2016-06-01
We report on the site-resolved observation of characteristic states of the two-dimensional repulsive Fermi-Hubbard model, using ultracold 40K atoms in an optical lattice. By varying the tunneling, interaction strength, and external confinement, we realize metallic, Mott-insulating, and band-insulating states. We directly measure the local moment, which quantifies the degree of on-site magnetization, as a function of temperature and chemical potential. Entropies per particle as low as 0.99 (6 )kB indicate that nearest-neighbor antiferromagnetic correlations should be detectable using spin-sensitive imaging.
Controlling the Properties of 2D Chiral Fermions and Local Moments in Graphene
NASA Astrophysics Data System (ADS)
Killi, Matthew P.
The primary subject of this thesis is graphene and how the rudimentary attributes of its charge carriers, and local moments on its surface, can be directly manipulated and controlled with electrostatic potentials. We first consider bilayer graphene subject to a spatially varying electrostatic potential that forms two neighbouring regions with opposite interlayer bias. Along the boundary, 1D chiral 'kink' states emerge. We find that these 1D modes behave as a strongly interacting Tomonaga-Luttinger liquid whose properties can be tuned via an external gate. Next, we consider superlattices in bilayer graphene. Superlattices are seen to have a more dramatic effect on bilayer graphene than monolayer graphene because the quasi-particles are changed in a fundamental way; the dispersion goes from a quadratic band touching point to linearly dispersing Dirac cones. We illustrate that a 1D superlattice of either the chemical potential or an interlayer bias generates multiple anisotropic Dirac cones. General arguments delineate how certain symmetries protect the Dirac points. We then map the Hamiltonian of an interlayer bias superlattice onto a coupled chain model comprised of 'topological' edge modes. We then discuss the relevance of spatially varying potentials to recent transport measurements. This is followed by another study that considers the effect of a magnetic field on graphene superlattices. We show that magnetotransport measurements in a weak perpendicular (orbital) magnetic field probe the number of emergent Dirac points and reveal further details about the dispersion. In the case of bilayer graphene, we also discuss the properties of kink states in an applied magnetic field. We then consider the implications of these results with regards to scanning tunnelling spectroscopy, valley filtering, and impurity induced breakdown of the quantum Hall effect. Finally, we investigate local moment formation of adatoms on bilayer graphene using an Anderson impurity model. We construct various phase diagrams and discuss their many unusual features. We identify regions where the local moments can be turned on or off by applying a external electric fields. Finally, we compute the RKKY interaction between local moments and show how it too can be controlled with electric fields.
Monte Carlo evaluation of a fermion-number-violating observable in 2D
Kikukawa, Y.; Narayanan, R.; Neuberger, H.
1998-01-01
We describe in some detail a computer evaluation of a {close_quote}t Hooft vertex in a two-dimensional model using the overlap. The computer result agrees with the known exact continuum value, and in this sense our work is the first successful fully dynamical simulation of a chiral gauge theory on the lattice. We add some new data to numbers obtained earlier and provide a self-contained description which should make it easy for others to reproduce and follow up on our work. {copyright} {ital 1997} {ital The American Physical Society}
NASA Astrophysics Data System (ADS)
Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing
2016-06-01
The symplectic integration method is popular in high-accuracy numerical simulations when discretizing temporal derivatives; however, it still suffers from time-dispersion error when the temporal interval is coarse, especially for long-term simulations and large-scale models. We employ the inverse time dispersion transform (ITDT) to the third-order symplectic integration method to reduce the time-dispersion error. First, we adopt the pseudospectral algorithm for the spatial discretization and the third-order symplectic integration method for the temporal discretization. Then, we apply the ITDT to eliminate time-dispersion error from the synthetic data. As a post-processing method, the ITDT can be easily cascaded in traditional numerical simulations. We implement the ITDT in one typical exiting third-order symplectic scheme and compare its performances with the performances of the conventional second-order scheme and the rapid expansion method. Theoretical analyses and numerical experiments show that the ITDT can significantly reduce the time-dispersion error, especially for long travel times. The implementation of the ITDT requires some additional computations on correcting the time-dispersion error, but it allows us to use the maximum temporal interval under stability conditions; thus, its final computational efficiency would be higher than that of the traditional symplectic integration method for long-term simulations. With the aid of the ITDT, we can obtain much more accurate simulation results but with a lower computational cost.
Kornilovitch, P E; Hague, J P
2015-02-25
Both FeSe and cuprate superconductors are quasi 2D materials with high transition temperatures and local fermion pairs. Motivated by such systems, we investigate real space pairing of fermions in an anisotropic lattice model with intersite attraction, V, and strong local Coulomb repulsion, U, leading to a determination of the optimal conditions for superconductivity from Bose-Einstein condensation. Our aim is to gain insight as to why high temperature superconductors tend to be quasi 2D. We make both analytically and numerically exact solutions for two body local pairing applicable to intermediate and strong V. We find that the Bose-Einstein condensation temperature of such local pairs pairs is maximal when hopping between layers is intermediate relative to in-plane hopping, indicating that the quasi 2D nature of unconventional superconductors has an important contribution to their high transition temperatures. PMID:25629425
Marginal fluctuations as instantons on M2/D2-branes
NASA Astrophysics Data System (ADS)
Naghdi, M.
2014-03-01
We introduce some (anti-) M/D-branes through turning on the corresponding field strengths of the 11- and 10-dimensional supergravity theories over spaces, where we use and for the internal spaces. Indeed, when we add M2/D2-branes on the same directions with the near horizon branes of the Aharony-Bergman-Jafferis-Maldacena model, all symmetries and supersymmetries are preserved trivially. In this case, we obtain a localized object just in the horizon. This normalizable bulk massless scalar mode is a singlet of and , and it agrees with a marginal boundary operator of the conformal dimension of . However, after performing a special conformal transformation, we see that the solution is localized in the Euclideanized space and is attributable to the included anti-M2/D2-branes, which are also necessary to ensure that there is no back-reaction. The resultant theory now breaks all supersymmetries to , while the other symmetries are so preserved. The dual boundary operator is then set up from the skew-whiffing of the representations and for the supercharges and scalars, respectively, while the fermions remain fixed in of the original theory. Besides, we also address another alternate bulk to boundary matching procedure through turning on one of the gauge fields of the full gauge group along the same lines with a similar situation to the one faced in the AdS/CFT correspondence. The latter approach covers the difficulty already faced with in the bulk-boundary matching procedure for as well.
Full-turn symplectic map from a generator in a Fourier-spline basis
Berg, J.S.; Warnock, R.L.; Ruth, R.D.; Forest, E.
1993-04-01
Given an arbitrary symplectic tracking code, one can construct a full-turn symplectic map that approximates the result of the code to high accuracy. The map is defined implicitly by a mixed-variable generating function. The implicit definition is no great drawback in practice, thanks to an efficient use of Newton`s method to solve for the explicit map at each iteration. The generator is represented by a Fourier series in angle variables, with coefficients given as B-spline functions of action variables. It is constructed by using results of single-turn tracking from many initial conditions. The method has been appliedto a realistic model of the SSC in three degrees of freedom. Orbits can be mapped symplectically for 10{sup 7} turns on an IBM RS6000 model 320 workstation, in a run of about one day.
Natural star-products on symplectic manifolds and related quantum mechanical operators
Błaszak, Maciej Domański, Ziemowit
2014-05-15
In this paper is considered a problem of defining natural star-products on symplectic manifolds, admissible for quantization of classical Hamiltonian systems. First, a construction of a star-product on a cotangent bundle to an Euclidean configuration space is given with the use of a sequence of pair-wise commuting vector fields. The connection with a covariant representation of such a star-product is also presented. Then, an extension of the construction to symplectic manifolds over flat and non-flat pseudo-Riemannian configuration spaces is discussed. Finally, a coordinate free construction of related quantum mechanical operators from Hilbert space over respective configuration space is presented. -- Highlights: •Invariant representations of natural star-products on symplectic manifolds are considered. •Star-products induced by flat and non-flat connections are investigated. •Operator representations in Hilbert space of considered star-algebras are constructed.
Low, Stephen G.
2014-02-15
A symmetry in quantum mechanics is described by the projective representations of a Lie symmetry group that transforms between physical quantum states such that the square of the modulus of the states is invariant. The Heisenberg commutation relations that are fundamental to quantum mechanics must be valid in all of these physical states. This paper shows that the maximal quantum symmetry group, whose projective representations preserve the Heisenberg commutation relations in this manner, is the inhomogeneous symplectic group. The projective representations are equivalent to the unitary representations of the central extension of the inhomogeneous symplectic group. This centrally extended group is the semidirect product of the cover of the symplectic group and the Weyl-Heisenberg group. Its unitary irreducible representations are computed explicitly using the Mackey representation theorems for semidirect product groups.
Electron motion in solenoidal magnetic fields using a first order symplectic integration algorithm
Fraser, J.S.
1984-05-07
The use of nonsymplectic procedures in particle tracing codes for relativistic electrons leads to errors that can be reduced only at the expense of using very small integration steps. More accurate results are obtained with symplectic transformations for position and momentum. A first-order symplectic integration procedure requires an iterative calculation of the new position coordinates using the old momenta, but the process usually converges in three or four steps. A first-order symplectic algorithm has been coded for cylindrical as well as Cartesian coordinates using the relativistic equations of motion with Hamiltonian variables. The procedure is applied to the steering of a beam of 80-keV electrons by a weak transverse magnetic field superposed on a strong magnetic field in the axial direction. The steering motion is shown to be parallel to the transverse field rather than perpendicular as would be the case without the strong axial field.
NASA Astrophysics Data System (ADS)
Yang, Xiao-Feng; Deng, Zi-Chen; Li, Qing-Jun; Wei, Yi
2016-07-01
The homogeneous balance of undetermined coefficients method (HBUCM) is firstly proposed to construct not only the exact traveling wave solutions, three-wave solutions, homoclinic solutions, N-soliton solutions, but also multi-symplectic structures of some nonlinear partial differential equations (NLPDEs). By applying the proposed method to the variant Boussinesq equations (VBEs), the exact combined traveling wave solutions and a multi-symplectic structure of the VBEs are obtained directly. Then, the definition and a multi-symplectic structure of the variant Boussinesq-Whitham-Broer-Kaup type equations (VBWBKTEs) which can degenerate to the VBEs, the Whitham-Broer-Kaup equations (WBKEs) and the Broer-Kaup equations (BKEs) are given in the multi-symplectic sense. The HBUCM is also a standard and computable method, which can be generalized to obtain the exact solutions and multi-symplectic structures for some types of NLPDEs.
Xiao, Jianyuan; Liu, Jian; Qin, Hong; Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 ; Yu, Zhi
2013-10-15
Smoothing functions are commonly used to reduce numerical noise arising from coarse sampling of particles in particle-in-cell (PIC) plasma simulations. When applying smoothing functions to symplectic algorithms, the conservation of symplectic structure should be guaranteed to preserve good conservation properties. In this paper, we show how to construct a variational multi-symplectic PIC algorithm with smoothing functions for the Vlasov-Maxwell system. The conservation of the multi-symplectic structure and the reduction of numerical noise make this algorithm specifically suitable for simulating long-term dynamics of plasmas, such as those in the steady-state operation or long-pulse discharge of a super-conducting tokamak. The algorithm has been implemented in a 6D large scale PIC code. Numerical examples are given to demonstrate the good conservation properties of the multi-symplectic algorithm and the reduction of the noise due to the application of smoothing function.
Fermion localization on thick branes
Melfo, Alejandra; Pantoja, Nelson; Tempo, Jose David
2006-02-15
We consider chiral fermion confinement in scalar thick branes, which are known to localize gravity, coupled through a Yukawa term. The conditions for the confinement and their behavior in the thin-wall limit are found for various different BPS branes, including double walls and branes interpolating between different AdS{sub 5} spacetimes. We show that only one massless chiral mode is localized in all these walls, whenever the wall thickness is keep finite. We also show that, independently of wall's thickness, chiral fermionic modes cannot be localized in dS{sub 4} walls embedded in a M{sub 5} spacetime. Finally, massive fermions in double wall spacetimes are also investigated. We find that, besides the massless chiral mode localization, these double walls support quasilocalized massive modes of both chiralities.
Fermion production during and after axion inflation
Adshead, Peter; Sfakianakis, Evangelos I.
2015-11-11
We study derivatively coupled fermions in axion-driven inflation, specifically m{sub ϕ}{sup 2}ϕ{sup 2} and monodromy inflation, and calculate particle production during the inflationary epoch and the post-inflationary axion oscillations. During inflation, the rolling axion acts as an effective chemical potential for helicity which biases the gravitational production of one fermion helicity over the other. This mechanism allows for efficient gravitational production of heavy fermion states that would otherwise be highly suppressed. Following inflation, the axion oscillates and fermions with both helicities are produced as the effective frequency of the fermion field changes non-adiabatically. For certain values of the fermion mass and axion-fermion coupling strength, the two helicity states are produced asymmetrically, resulting in unequal number-densities of left- and right-helicity fermions.
Fermionic influence on inflationary fluctuations
NASA Astrophysics Data System (ADS)
Boyanovsky, Daniel
2016-04-01
Motivated by apparent persistent large scale anomalies in the cosmic microwave background we study the influence of fermionic degrees of freedom on the dynamics of inflaton fluctuations as a possible source of violations of (nearly) scale invariance on cosmological scales. We obtain the nonequilibrium effective action of an inflaton-like scalar field with Yukawa interactions (YD ,M) to light fermionic degrees of freedom both for Dirac and Majorana fields in de Sitter space-time. The effective action leads to Langevin equations of motion for the fluctuations of the inflaton-like field, with self-energy corrections and a stochastic Gaussian noise. We solve the Langevin equation in the super-Hubble limit implementing a dynamical renormalization group resummation. For a nearly massless inflaton its power spectrum of super-Hubble fluctuations is enhanced, P (k ;η )=(H/2 π )2eγt[-k η ] with γt[-k η ]=1/6 π2 [∑i =1 NDYi,D 2+2 ∑j =1 NMYj,M 2]{ln2[-k η ]-2 ln [-k η ]ln [-k η0]} for ND Dirac and NM Majorana fermions, and η0 is the renormalization scale at which the inflaton mass vanishes. The full power spectrum is shown to be renormalization group invariant. These corrections to the super-Hubble power spectrum entail a violation of scale invariance as a consequence of the coupling to the fermionic fields. The effective action is argued to be exact in the limit of a large number of fermionic fields. A cancellation between the enhancement from fermionic degrees of freedom and suppression from light scalar degrees of freedom conformally coupled to gravity suggests the possibility of a finely tuned supersymmetry among these fields.
NKG2D ligands as therapeutic targets
Spear, Paul; Wu, Ming-Ru; Sentman, Marie-Louise; Sentman, Charles L.
2013-01-01
The Natural Killer Group 2D (NKG2D) receptor plays an important role in protecting the host from infections and cancer. By recognizing ligands induced on infected or tumor cells, NKG2D modulates lymphocyte activation and promotes immunity to eliminate ligand-expressing cells. Because these ligands are not widely expressed on healthy adult tissue, NKG2D ligands may present a useful target for immunotherapeutic approaches in cancer. Novel therapies targeting NKG2D ligands for the treatment of cancer have shown preclinical success and are poised to enter into clinical trials. In this review, the NKG2D receptor and its ligands are discussed in the context of cancer, infection, and autoimmunity. In addition, therapies targeting NKG2D ligands in cancer are also reviewed. PMID:23833565
Fermionic composite models from complementarity
NASA Astrophysics Data System (ADS)
Bordi, F.; Casalbuoni, R.; Dominici, D.; Gatto, R.
1982-08-01
Composite models for (in principle massless) quarks and leptons without fundamental scalars are constructed with the aim of providing for fermionic realizations of models which include elementary bosons (by Abbott and Farhi, Casalbuoni and Gatto and Barbieri, Mohapatra and Masiero). The models use one confining unitary (subcolor) group (with left-handed fermions in the fundamental, in its conjugate, and either in the adjoint, or in the symmetric, or in the antisymmetric representation of subcolor) or two confining groups. Families may arise from discrete symmetries.
NASA Astrophysics Data System (ADS)
Colangeli, Matteo; Pezzotti, Federica; Pulvirenti, Mario
2015-05-01
We introduce a stochastic N-particle system and show that, as N → ∞, an effective description ruled by the homogeneous fermionic Uehling-Uhlenbeck equation is recovered. The particle model we consider is the same as the Kac model for the homogeneous Boltzmann equation with an additional exclusion constraint taking into account the Pauli Exclusion Principle.
Perspectives for spintronics in 2D materials
NASA Astrophysics Data System (ADS)
Han, Wei
2016-03-01
The past decade has been especially creative for spintronics since the (re)discovery of various two dimensional (2D) materials. Due to the unusual physical characteristics, 2D materials have provided new platforms to probe the spin interaction with other degrees of freedom for electrons, as well as to be used for novel spintronics applications. This review briefly presents the most important recent and ongoing research for spintronics in 2D materials.
The Gaussian entropy of fermionic systems
Prokopec, Tomislav; Schmidt, Michael G.; Weenink, Jan
2012-12-15
We consider the entropy and decoherence in fermionic quantum systems. By making a Gaussian Ansatz for the density operator of a collection of fermions we study statistical 2-point correlators and express the entropy of a system fermion in terms of these correlators. In a simple case when a set of N thermalised environmental fermionic oscillators interacts bi-linearly with the system fermion we can study its time dependent entropy, which also represents a quantitative measure for decoherence and classicalization. We then consider a relativistic fermionic quantum field theory and take a mass mixing term as a simple model for the Yukawa interaction. It turns out that even in this Gaussian approximation, the fermionic system decoheres quite effectively, such that in a large coupling and high temperature regime the system field approaches the temperature of the environmental fields. - Highlights: Black-Right-Pointing-Pointer We construct the Gaussian density operator for relativistic fermionic systems. Black-Right-Pointing-Pointer The Gaussian entropy of relativistic fermionic systems is described in terms of 2-point correlators. Black-Right-Pointing-Pointer We explicitly show the growth of entropy for fermionic fields mixing with a thermal fermionic environment.
Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order
Cong, Y. H.; Jiang, C. X.
2014-01-01
The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type Runge-Kutta methods. PMID:24977178
Diagonally implicit symplectic Runge-Kutta methods with high algebraic and dispersion order.
Cong, Y H; Jiang, C X
2014-01-01
The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type Runge-Kutta methods. PMID:24977178
Physical Variables of d=3 Maxwell-Chern-Simons Theory by Symplectic Projector Method
NASA Astrophysics Data System (ADS)
Helayel-Neto, J. A.; Santos, M. A.; Vancea, I. V.
2006-12-01
The Symplectic Projector Method is applied to derive the local physical degrees of freedom and the physical Hamiltonian of the Maxwell-Chern-Simons theory in $d=1+2$. The results agree with the ones obtained in the literature through different approaches.
Zhang, Ruili; Tang, Yifa; Zhu, Beibei; Liu, Jian Xiao, Jianyuan; Qin, Hong
2014-03-15
The gyrocenter dynamics of charged particles in time-independent magnetic fields is a non-canonical Hamiltonian system. The canonical description of the gyrocenter has both theoretical and practical importance. We provide a general procedure of the gyrocenter canonicalization, which is expressed by the series of a small variable ϵ depending only on the parallel velocity u and can be expressed in a recursive manner. We prove that the truncation of the series to any given order generates a set of exact canonical coordinates for a system, whose Lagrangian approximates to that of the original gyrocenter system in the same order. If flux surfaces exist for the magnetic field, the series stops simply at the second order and an exact canonical form of the gyrocenter system is obtained. With the canonicalization schemes, the canonical symplectic simulation of gyrocenter dynamics is realized for the first time. The canonical symplectic algorithm has the advantage of good conservation properties and long-term numerical accuracy, while avoiding numerical instability. It is worth mentioning that explicitly expressing the canonical Hamiltonian in new coordinates is usually difficult and impractical. We give an iteration procedure that is easy to implement in the original coordinates associated with the coordinate transformation. This is crucial for modern large-scale simulation studies in plasma physics. The dynamics of gyrocenters in the dipole magnetic field and in the toroidal geometry are simulated using the canonical symplectic algorithm by comparison with the higher-order non symplectic Runge-Kutta scheme. The overwhelming superiorities of the symplectic method for the gyrocenter system are evidently exhibited.
Searches for Fourth Generation Fermions
Ivanov, A.; /Fermilab
2011-09-01
We present the results from searches for fourth generation fermions performed using data samples collected by the CDF II and D0 Detectors at the Fermilab Tevatron p{bar p} collider. Many of these results represent the most stringent 95% C. L. limits on masses of new fermions to-date. A fourth chiral generation of massive fermions with the same quantum numbers as the known fermions is one of the simplest extensions of the SM with three generations. The fourth generation is predicted in a number of theories, and although historically have been considered disfavored, stands in agreement with electroweak precision data. To avoid Z {yields} {nu}{bar {nu}} constraint from LEP I a fourth generation neutrino {nu}{sub 4} must be heavy: m({nu}{sub 4}) > m{sub Z}/2, where m{sub Z} is the mass of Z boson, and to avoid LEP II bounds a fourth generation charged lepton {ell}{sub 4} must have m({ell}{sub 4}) > 101 GeV/c{sup 2}. At the same time due to sizeable radiative corrections masses of fourth generation fermions cannot be much higher the current lower bounds and masses of new heavy quarks t' and b' should be in the range of a few hundred GeV/c{sup 2}. In the four-generation model the present bounds on the Higgs are relaxed: the Higgs mass could be as large as 1 TeV/c{sup 2}. Furthermore, the CP violation is significantly enhanced to the magnitude that might account for the baryon asymmetry in the Universe. Additional chiral fermion families can also be accommodated in supersymmetric two-Higgs-doublet extensions of the SM with equivalent effect on the precision fit to the Higgs mass. Another possibility is heavy exotic quarks with vector couplings to the W boson Contributions to radiative corrections from such quarks with mass M decouple as 1/M{sup 2} and easily evade all experimental constraints. At the Tevatron p{bar p} collider 4-th generation chiral or vector-like quarks can be either produced strongly in pairs or singly via electroweak production, where the latter can be
Annotated Bibliography of EDGE2D Use
J.D. Strachan and G. Corrigan
2005-06-24
This annotated bibliography is intended to help EDGE2D users, and particularly new users, find existing published literature that has used EDGE2D. Our idea is that a person can find existing studies which may relate to his intended use, as well as gain ideas about other possible applications by scanning the attached tables.
Staring 2-D hadamard transform spectral imager
Gentry, Stephen M.; Wehlburg, Christine M.; Wehlburg, Joseph C.; Smith, Mark W.; Smith, Jody L.
2006-02-07
A staring imaging system inputs a 2D spatial image containing multi-frequency spectral information. This image is encoded in one dimension of the image with a cyclic Hadamarid S-matrix. The resulting image is detecting with a spatial 2D detector; and a computer applies a Hadamard transform to recover the encoded image.
Transport of massless Dirac fermions in non-topological type edge states.
Latyshev, Yu I; Orlov, A P; Volkov, V A; Enaldiev, V V; Zagorodnev, I V; Vyvenko, O F; Petrov, Yu V; Monceau, P
2014-01-01
There are two types of intrinsic surface states in solids. The first type is formed on the surface of topological insulators. Recently, transport of massless Dirac fermions in the band of "topological" states has been demonstrated. States of the second type were predicted by Tamm and Shockley long ago. They do not have a topological background and are therefore strongly dependent on the properties of the surface. We study the problem of the conductivity of Tamm-Shockley edge states through direct transport experiments. Aharonov-Bohm magneto-oscillations of resistance are found on graphene samples that contain a single nanohole. The effect is explained by the conductivity of the massless Dirac fermions in the edge states cycling around the nanohole. The results demonstrate the deep connection between topological and non-topological edge states in 2D systems of massless Dirac fermions. PMID:25524881
Transport of Massless Dirac Fermions in Non-topological Type Edge States
Latyshev, Yu I.; Orlov, A. P.; Volkov, V. A.; Enaldiev, V. V.; Zagorodnev, I. V.; Vyvenko, O. F.; Petrov, Yu V.; Monceau, P.
2014-01-01
There are two types of intrinsic surface states in solids. The first type is formed on the surface of topological insulators. Recently, transport of massless Dirac fermions in the band of “topological” states has been demonstrated. States of the second type were predicted by Tamm and Shockley long ago. They do not have a topological background and are therefore strongly dependent on the properties of the surface. We study the problem of the conductivity of Tamm-Shockley edge states through direct transport experiments. Aharonov-Bohm magneto-oscillations of resistance are found on graphene samples that contain a single nanohole. The effect is explained by the conductivity of the massless Dirac fermions in the edge states cycling around the nanohole. The results demonstrate the deep connection between topological and non-topological edge states in 2D systems of massless Dirac fermions. PMID:25524881
Domain wall fermion quenched spectroscopy
NASA Astrophysics Data System (ADS)
Malureanu, Catalin Ionut
We measure y and the hadron spectrum on quenched ensembles using the domain wall fermion formulation. For the first time a 1/mf behavior of y for small valence masses has been observed. Our measurements of y on two different volumes of 83 x 32 and 163 x 32 at β = 5.85 suggest the behavior goes away on large enough volumes. Extensive spectrum calculations were done on 8 3 x 32 lattices at β = 5.7 and 5.85 corresponding roughly to a box size of 1.6 fm and 1.0 fm respectively. We have investigated five values of the extent of the fifth dimension Ls = 10, 16, 24, 32 and 48 with valence masses in the range 0.02 to 0.2 for the β = 5.7 ensemble and two values of Ls = 10 and 16 with valence masses in the range 0.02 to 0.08 for the β = 5.85 ensemble. Our pion remains massive in the infinite Ls extrapolation. This may be a finite volume effect. The nucleon to rho mass ratio stays constant at 1.4(1). Scaling violations for domain wall fermions are smaller roughly by a factor of four compared to the scaling violations in similar calculations done with staggered fermions.
Superdeformations and fermion dynamical symmetries
Wu, Cheng-Li . Dept. of Physics and Atmospheric Science Tennessee Univ., Knoxville, TN . Dept. of Physics and Astronomy Joint Inst. for Heavy Ion Research, Oak Ridge, TN )
1990-01-01
In this talk, I will present a link between nuclear collective motions and their underlying fermion dynamical symmetries. In particular, I will focus on the microscopic understanding of deformations. It is shown that the SU{sub 3} of the one major shell fermion dynamical symmetry model (FDSM) is responsible for the physics of low and high spins in normal deformation. For the recently observed phenomena of superdeformation, the physics of the problem dictates a generalization to a supershell structure (SFDSM), which also has an SU{sub 3} fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU{sub 3} symmetry. In both cases the dynamical Pauli effect plays a vital role. A particularly noteworthy discovery from this model is that the superdeformed ground band is not the usual unaligned band but the D-pair aligned (DPA) band, which sharply crosses the excited bands. The existence of such DPA band is a key point to understand many properties of superdeformation. Our studies also poses new experimental challenge. This is particularly interesting since there are now plans to build new and exciting {gamma}-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs.
Dephasing time of composite fermions
Lee, P.A.; Mucciolo, E.R.
1996-09-01
We study the dephasing of fermions interacting with a fluctuating transverse-gauge field. The divergence of the imaginary part of the fermion self-energy at finite temperatures is shown to result from a breakdown of Fermi{close_quote}s golden rule due to a faster than exponential decay in time. The strong dephasing affects experiments where phase coherence is probed. This result is used to describe the suppression of Shubnikov{endash}de Haas (SdH) oscillations of composite fermions (oscillations in the conductivity near the half-filled Landau level). We find that it is important to take into account both the effect of dephasing and the mass renormalization. We conclude that while it is possible to use the conventional theory to extract an effective mass from the temperature dependence of the SdH oscillations, the resulting effective mass differs from the {ital m}{sup {asterisk}} of the quasiparticle in Fermi-liquid theory. {copyright} {ital 1996 The American Physical Society.}
Light scattering of degenerate fermions
NASA Astrophysics Data System (ADS)
Aubin, S.; Leblanc, L. J.; Myrskog, S.; Extavour, M. H. T.; McKay, D.; Stummer, A.; Thywissen, J. H.
2006-05-01
We report on progress in measuring the suppression of resonant light scattering in a gas of degenerate fermions. A gas of trapped degenerate fermions is expected to exhibit narrower optical linewidths and longer excited state lifetimes than single atoms when the Fermi energy is larger than the photon recoil energy [1-3]. In this case, the number of available states into which a scattered atom can recoil is significantly reduced due to the filling of the Fermi sea. We produce a degenerate gas of 4x10^4 ultra-cold fermionic ^40K atoms by sympathetic cooling with bosonic ^87Rb in a micro-magnetic chip trap. The atoms can then be loaded into a tight dipole trap just above the surface of the chip and probed with a near resonance laser pulse. [1] Th. Busch, J. R. Anglin, J. I. Cirac, and P. Zoller, Europhys. Lett. 44, 1 (1998). [2] B. DeMarco and D. S. Jin, Phys. Rev. A 58, R4267 (1998). [3] J. Javanainen and J. Ruostekosky, Phys. Rev. A 52, 3033 (1995). Work supported by NSERC, CFI, OIT, Research Corporation, and PRO.
Inertial solvation in femtosecond 2D spectra
NASA Astrophysics Data System (ADS)
Hybl, John; Albrecht Ferro, Allison; Farrow, Darcie; Jonas, David
2001-03-01
We have used 2D Fourier transform spectroscopy to investigate polar solvation. 2D spectroscopy can reveal molecular lineshapes beneath ensemble averaged spectra and freeze molecular motions to give an undistorted picture of the microscopic dynamics of polar solvation. The transition from "inhomogeneous" to "homogeneous" 2D spectra is governed by both vibrational relaxation and solvent motion. Therefore, the time dependence of the 2D spectrum directly reflects the total response of the solvent-solute system. IR144, a cyanine dye with a dipole moment change upon electronic excitation, was used to probe inertial solvation in methanol and propylene carbonate. Since the static Stokes' shift of IR144 in each of these solvents is similar, differences in the 2D spectra result from solvation dynamics. Initial results indicate that the larger propylene carbonate responds more slowly than methanol, but appear to be inconsistent with rotational estimates of the inertial response. To disentangle intra-molecular vibrations from solvent motion, the 2D spectra of IR144 will be compared to the time-dependent 2D spectra of the structurally related nonpolar cyanine dye HDITCP.
Light field morphing using 2D features.
Wang, Lifeng; Lin, Stephen; Lee, Seungyong; Guo, Baining; Shum, Heung-Yeung
2005-01-01
We present a 2D feature-based technique for morphing 3D objects represented by light fields. Existing light field morphing methods require the user to specify corresponding 3D feature elements to guide morph computation. Since slight errors in 3D specification can lead to significant morphing artifacts, we propose a scheme based on 2D feature elements that is less sensitive to imprecise marking of features. First, 2D features are specified by the user in a number of key views in the source and target light fields. Then the two light fields are warped view by view as guided by the corresponding 2D features. Finally, the two warped light fields are blended together to yield the desired light field morph. Two key issues in light field morphing are feature specification and warping of light field rays. For feature specification, we introduce a user interface for delineating 2D features in key views of a light field, which are automatically interpolated to other views. For ray warping, we describe a 2D technique that accounts for visibility changes and present a comparison to the ideal morphing of light fields. Light field morphing based on 2D features makes it simple to incorporate previous image morphing techniques such as nonuniform blending, as well as to morph between an image and a light field. PMID:15631126
Internal Photoemission Spectroscopy of 2-D Materials
NASA Astrophysics Data System (ADS)
Nguyen, Nhan; Li, Mingda; Vishwanath, Suresh; Yan, Rusen; Xiao, Shudong; Xing, Huili; Cheng, Guangjun; Hight Walker, Angela; Zhang, Qin
Recent research has shown the great benefits of using 2-D materials in the tunnel field-effect transistor (TFET), which is considered a promising candidate for the beyond-CMOS technology. The on-state current of TFET can be enhanced by engineering the band alignment of different 2D-2D or 2D-3D heterostructures. Here we present the internal photoemission spectroscopy (IPE) approach to determine the band alignments of various 2-D materials, in particular SnSe2 and WSe2, which have been proposed for new TFET designs. The metal-oxide-2-D semiconductor test structures are fabricated and characterized by IPE, where the band offsets from the 2-D semiconductor to the oxide conduction band minimum are determined by the threshold of the cube root of IPE yields as a function of photon energy. In particular, we find that SnSe2 has a larger electron affinity than most semiconductors and can be combined with other semiconductors to form near broken-gap heterojunctions with low barrier heights which can produce a higher on-state current. The details of data analysis of IPE and the results from Raman spectroscopy and spectroscopic ellipsometry measurements will also be presented and discussed.
2D materials for nanophotonic devices
NASA Astrophysics Data System (ADS)
Xu, Renjing; Yang, Jiong; Zhang, Shuang; Pei, Jiajie; Lu, Yuerui
2015-12-01
Two-dimensional (2D) materials have become very important building blocks for electronic, photonic, and phononic devices. The 2D material family has four key members, including the metallic graphene, transition metal dichalcogenide (TMD) layered semiconductors, semiconducting black phosphorous, and the insulating h-BN. Owing to the strong quantum confinements and defect-free surfaces, these atomically thin layers have offered us perfect platforms to investigate the interactions among photons, electrons and phonons. The unique interactions in these 2D materials are very important for both scientific research and application engineering. In this talk, I would like to briefly summarize and highlight the key findings, opportunities and challenges in this field. Next, I will introduce/highlight our recent achievements. We demonstrated atomically thin micro-lens and gratings using 2D MoS2, which is the thinnest optical component around the world. These devices are based on our discovery that the elastic light-matter interactions in highindex 2D materials is very strong. Also, I would like to introduce a new two-dimensional material phosphorene. Phosphorene has strongly anisotropic optical response, which creates 1D excitons in a 2D system. The strong confinement in phosphorene also enables the ultra-high trion (charged exciton) binding energies, which have been successfully measured in our experiments. Finally, I will briefly talk about the potential applications of 2D materials in energy harvesting.
Duality Between Spin Networks and the 2D Ising Model
NASA Astrophysics Data System (ADS)
Bonzom, Valentin; Costantino, Francesco; Livine, Etera R.
2016-06-01
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.
Fermionic thermocoherent state: Efficiency of electron transport
NASA Astrophysics Data System (ADS)
Karmakar, Anirban; Gangopadhyay, Gautam
2016-02-01
On the basis of the fermionic coherent state of Cahill and Glauber [Phys. Rev. A 59, 1538 (1999)], 10.1103/PhysRevA.59.1538, we have introduced here the fermionic thermocoherent state in terms of the quasiprobability distribution which shows the appropriate thermal and coherent limits as in the bosonic case or the Glauber-Lachs state. It is shown that the fermionic thermocoherent state can be realized as a displaced thermal state of fermions. Its relation with the fermionic displaced number state and the fermion-added coherent state are explored in the spirit of the bosonic case. We have investigated the nature of the average current and the suppression of noise due to the thermocoherent character of the source. The theory is applied to the problem of electronic conduction. A modification of the Landauer conductance formula is suggested which reflects the role of nonzero coherence of the source in electron transport.
NASA Astrophysics Data System (ADS)
Rose, Danya; Dullin, Holger R.
2013-10-01
We construct an explicit reversible symplectic integrator for the planar 3-body problem with zero angular momentum. We start with a Hamiltonian of the planar 3-body problem that is globally regularised and fully symmetry reduced. This Hamiltonian is a sum of 10 polynomials each of which can be integrated exactly, and hence a symplectic integrator is constructed. The performance of the integrator is examined with three numerical examples: The figure eight, the Pythagorean orbit, and a periodic collision orbit.
Cold collisions between boson or fermion molecules
Kajita, Masatoshi
2004-01-01
We theoretically investigate collisions between electrostatically trapped cold polar molecules and compare boson and fermion isotopes. Evaporative cooling seems possible for fermion molecules as the ratio of the collision loss cross section to the elastic collision cross section (R) gets smaller as the molecular temperature T lowers. With boson molecules, R gets larger as T lowers, which makes evaporative cooling difficult. The elastic collision cross section between fermion molecules can be larger than that for boson molecules with certain conditions.
Fermion back reaction and the sphaleron
Roberge, A. )
1994-02-15
Using a simple model, a new sphaleron solution which incorporates finite fermionic density effects is obtained. The main result is that the height of the potential barrier (sphaleron energy) decreases as the fermion density increases. This suggests that the rate of sphaleron-induced transitions increases when the fermionic density increases. However the rate increase is not expected to change significantly the predictions from the standard sphaleron-induced baryogenesis scenarios.
Ginsparg, P.
1991-01-01
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Ginsparg, P.
1991-12-31
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Brittle damage models in DYNA2D
Faux, D.R.
1997-09-01
DYNA2D is an explicit Lagrangian finite element code used to model dynamic events where stress wave interactions influence the overall response of the system. DYNA2D is often used to model penetration problems involving ductile-to-ductile impacts; however, with the advent of the use of ceramics in the armor-anti-armor community and the need to model damage to laser optics components, good brittle damage models are now needed in DYNA2D. This report will detail the implementation of four brittle damage models in DYNA2D, three scalar damage models and one tensor damage model. These new brittle damage models are then used to predict experimental results from three distinctly different glass damage problems.
2-d Finite Element Code Postprocessor
Energy Science and Technology Software Center (ESTSC)
1996-07-15
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forcesmore » along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.« less
2D electronic materials for army applications
NASA Astrophysics Data System (ADS)
O'Regan, Terrance; Perconti, Philip
2015-05-01
The record electronic properties achieved in monolayer graphene and related 2D materials such as molybdenum disulfide and hexagonal boron nitride show promise for revolutionary high-speed and low-power electronic devices. Heterogeneous 2D-stacked materials may create enabling technology for future communication and computation applications to meet soldier requirements. For instance, transparent, flexible and even wearable systems may become feasible. With soldier and squad level electronic power demands increasing, the Army is committed to developing and harnessing graphene-like 2D materials for compact low size-weight-and-power-cost (SWAP-C) systems. This paper will review developments in 2D electronic materials at the Army Research Laboratory over the last five years and discuss directions for future army applications.
Quantum Hall effect in multilayered massless Dirac fermion systems with tilted cones
NASA Astrophysics Data System (ADS)
Tajima, Naoya; Yamauchi, Takahiro; Yamaguchi, Tatsuya; Suda, Masayuki; Kawasugi, Yoshitaka; Yamamoto, Hiroshi M.; Kato, Reizo; Nishio, Yutaka; Kajita, Koji
2013-08-01
A massless Dirac fermion ststem was realized in α-(BEDT-TTF)2I3 [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene] under high pressure. In contrast to graphene, this is the first bulk (multilayered) massless Dirac fermion material. Another important difference from graphene is that this system has highly tilted Dirac cones. In this case, conventional chiral symmetry is broken under a magnetic field. Here we experimentally addressed the following question: Is the Landau level structure of the system with tilted Dirac cones the same as that of graphene [conventional two-dimensional (2D) Dirac fermion system] under a magnetic field? The answer is yes. We succeeded in injecting holes into α-(BEDT-TTF)2I3 under high pressure. The detection of Shubnikov-de Haas oscillations whose phase was modified by Berry's phase π is direct evidence that this system is truly a 2D Dirac fermion system. In addition, we revealed the energy diagram of this device and characterized the multilayered quantum Hall effect.
Light quark simulations with FLIC fermions
J.M. Zanotti; D.B. Leinweber; W. Melnitchouk; A.G. Williams; J.B. Zhang
2002-06-01
Hadron masses are calculated in quenched lattice QCD in order to probe the scaling behavior of a novel fat-link clover fermion action in which only the irrelevant operators of the fermion action are constructed using APE-smeared links. Light quark masses corresponding to an m{sub pi}/m{sub p} ratio of 0.35 are considered to assess the exceptional configuration problem of clover-fermion actions. This Fat-Link Irrelevant Clover (FLIC) fermion action provides scaling which is superior to mean-field improvement and offers advantages over nonperturbative improvement, including reduced exceptional configurations.
Aharonov-Bohm radiation of fermions
Chu Yizen; Mathur, Harsh; Vachaspati, Tanmay
2010-09-15
We analyze Aharonov-Bohm radiation of charged fermions from oscillating solenoids and cosmic strings. We find that the angular pattern of the radiation has features that differ significantly from that for bosons. For example, fermionic radiation in the lowest harmonic is approximately isotropically distributed around an oscillating solenoid, whereas for bosons the radiation is dipolar. We also investigate the spin polarization of the emitted fermion-antifermion pair. Fermionic radiation from kinks and cusps on cosmic strings is shown to depend linearly on the ultraviolet cutoff, suggesting strong emission at an energy scale comparable to the string energy scale.
Chemical Approaches to 2D Materials.
Samorì, Paolo; Palermo, Vincenzo; Feng, Xinliang
2016-08-01
Chemistry plays an ever-increasing role in the production, functionalization, processing and applications of graphene and other 2D materials. This special issue highlights a selection of enlightening chemical approaches to 2D materials, which nicely reflect the breadth of the field and convey the excitement of the individuals involved in it, who are trying to translate graphene and related materials from the laboratory into a real, high-impact technology. PMID:27478083
Extended 2D generalized dilaton gravity theories
NASA Astrophysics Data System (ADS)
de Mello, R. O.
2008-09-01
We show that an anomaly-free description of matter in (1+1) dimensions requires a deformation of the 2D relativity principle, which introduces a non-trivial centre in the 2D Poincaré algebra. Then we work out the reduced phase space of the anomaly-free 2D relativistic particle, in order to show that it lives in a noncommutative 2D Minkowski space. Moreover, we build a Gaussian wave packet to show that a Planck length is well defined in two dimensions. In order to provide a gravitational interpretation for this noncommutativity, we propose to extend the usual 2D generalized dilaton gravity models by a specific Maxwell component, which guages the extra symmetry associated with the centre of the 2D Poincaré algebra. In addition, we show that this extension is a high energy correction to the unextended dilaton theories that can affect the topology of spacetime. Further, we couple a test particle to the general extended dilaton models with the purpose of showing that they predict a noncommutativity in curved spacetime, which is locally described by a Moyal star product in the low energy limit. We also conjecture a probable generalization of this result, which provides strong evidence that the noncommutativity is described by a certain star product which is not of the Moyal type at high energies. Finally, we prove that the extended dilaton theories can be formulated as Poisson Sigma models based on a nonlinear deformation of the extended Poincaré algebra.
Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation
Sha, Wei . E-mail: ws108@ahu.edu.cn; Huang, Zhixiang; Wu, Xianliang; Chen, Mingsheng
2007-07-01
An explicit fourth-order finite-difference time-domain (FDTD) scheme using the symplectic integrator is applied to electromagnetic simulation. A feasible numerical implementation of the symplectic FDTD (SFDTD) scheme is specified. In particular, new strategies for the air-dielectric interface treatment and the near-to-far-field (NFF) transformation are presented. By using the SFDTD scheme, both the radiation and the scattering of three-dimensional objects are computed. Furthermore, the energy-conserving characteristic hold for the SFDTD scheme is verified under long-term simulation. Numerical results suggest that the SFDTD scheme is more efficient than the traditional FDTD method and other high-order methods, and can save computational resources.
Orthogonal and symplectic Yangians and Yang-Baxter R-operators
NASA Astrophysics Data System (ADS)
Isaev, A. P.; Karakhanyan, D.; Kirschner, R.
2016-03-01
Yang-Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with the orthogonal or symplectic fundamental R matrix, are considered in the interesting cases, where their expansion in inverse powers of the spectral parameter is truncated. Unlike the case of special linear algebra symmetry the truncation results in additional conditions on the Lie algebra generators of which the L operators is built and which can be fulfilled in distinguished representations only. Further, generalized L operators, obeying the modified RLL relation with the fundamental R matrix replaced by the spinorial or metaplectic one, are considered in the particular case of linear dependence on the spectral parameter. It is shown how by fusion with respect to the spinorial or metaplectic representation these first order spinorial L operators reproduce the ordinary L operators with second order truncation.
The new integrable symplectic map and the symmetry of integrable nonlinear lattice equation
NASA Astrophysics Data System (ADS)
Dong, Huanhe; Zhang, Yong; Zhang, Xiaoen
2016-07-01
A discrete matrix spectral problem is presented and the hierarchy of discrete integrable systems is derived. Their Hamiltonian structures are established. As to the discrete integrable system, nonlinearization of the spatial parts of the Lax pairs and the adjoint Lax pairs generate a new integrable symplectic map. Based on the theory, a new integrable symplectic map and a family of finite-dimension completely integrable systems are given. Especially, two explicit equations are obtained under the Bargmann constraint. Finally, the symmetry of the discrete equation is provided according to the recursion operator and the seed symmetry. Although the solutions of the discrete equations have been gained by many methods, there are few articles that solving the discrete equation via the symmetry. So the solution of the discrete lattice equation is obtained through the symmetry theory.
STOUT SMEARING FOR TWISTED FERMIONS.
SCHOLZ,W.; JANSEN, K.; McNEILE, C.; MONTVAY, I.; RICHARDS, C.; URBACH, C.; WENGER, U.
2007-07-30
The effect of Stout smearing is investigated in numerical simulations with twisted mass Wilson quarks. The phase transition near zero quark mass is studied on 12{sup 3} x 24, 16{sup 3} x 32 and 24{sup 3} x 48 lattices at lattice spacings a {approx_equal} 0.1-0.125 fm. The phase structure of Wilson fermions with twisted mass ({mu}) has been investigated in [1,2]. As it is explained there, the observed first order phase transition limits the minimal pion mass which can be reached in simulations at a given lattice spacing: m{sub k}{sup min} {approx_equal} {theta}(a). The phase structure is schematically depicted in the left panel of Fig. I . The phase transition can be observed in simulations with twisted mass fermions, for instance, as a ''jump'' or even metastabilities in the average plaquette value as a function of the hopping parameter ({kappa}). One possibility to weaken the phase transition and therefore allow for lighter pion masses at a given lattice spacing is to use an improved gauge action like the DBW2, Iwasaki, or tree-level Symanzik (tlSym) improved gauge action instead of the simple Wilson gauge action. This has been successfully demonstrated in [3,4,5]. Here we report on our attempts to use a smeared gauge field in the fermion lattice Dirac operator to further reduce the strength of the phase transition. This is relevant in simulations with N{sub f} = 2 + 1 + 1 (u,d,s,c) quark flavors [6] where the first order phase transition becomes stronger compared to N{sub f} = 2 simulations. The main impact of the above mentioned improved gauge actions on the gauge fields occurring in simulations is to suppress short range fluctuations (''dislocations'') and the associated ''exceptionally small'' eigenvalues of the fermion matrix. The same effect is expected from smearing the gauge field links in the fermion action. The cumulated effect of the improved gauge action and smeared links should allow for a smaller pion mass at a given lattice spacing and volume. Our
Gao Yajun
2008-08-15
A previously established Hauser-Ernst-type extended double-complex linear system is slightly modified and used to develop an inverse scattering method for the stationary axisymmetric general symplectic gravity model. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method applied fine and effective. As an application, a concrete family of soliton double solutions for the considered theory is obtained.
Dirac method and symplectic submanifolds in the cotangent bundle of a factorizable Lie group
NASA Astrophysics Data System (ADS)
Capriotti, S.; Montani, H.
2011-07-01
We study some symplectic submanifolds in the cotangent bundle of a factorizable Lie group defined by second class constraints. By applying the Dirac method, we study many issues of these spaces as fundamental Dirac brackets, symmetries, and collective dynamics. As the main application, we study integrable systems on these submanifolds as inherited from a system on the whole cotangent bundle, meeting in a natural way with the Adler-Kostant-Symes theory of integrability.
Study of the asymptotic dynamic aperture in the NICA collider using symplectic tracking codes
NASA Astrophysics Data System (ADS)
Bolshakov, A. E.; Zenkevich, P. R.; Kozlov, O. S.
2015-12-01
The dependence of the dynamic aperture in the NICA collider on the number of turns has been calculated by MAD-X tracking code with the two independent algorithms: a program of symplectic tracking PTC (Polymorphic technology Tracking Code) and a program of the thin-lenses tracking method. The results of the numerical integration of particle motion forecast the asymptotic dynamic aperture and the possible losses of particles in the collider.
NASA Technical Reports Server (NTRS)
Garzia, M. R.; Loparo, K. A.; Martin, C. F.
1982-01-01
This paper looks at the structure of the solution of a matrix Riccati differential equation under a predefined group of transformations. The group of transformations used is an expanded form of the feedback group. It is shown that this group of transformations is a subgroup of the symplectic group. The orbits of the Riccati differential equation under the action of this group are studied and it is seen how these techniques apply to a decentralized optimal control problem.
Paired States of Composite Fermions
NASA Astrophysics Data System (ADS)
Bonesteel, N. E.
2002-03-01
There is compelling theoretical evidence(R. Morf, Phys. Rev. Lett. 80), 1505 (1998). that the ν=5/2 fractional quantum Hall state is a Moore-Read state(G. Moore and N. Read, Nucl. Phys. B 360), 362 (1991). -- a state which can be viewed as a spin-polarized p-wave `superconductor' of composite fermions. The question remains, how can one test this hypothesis experimentally? To address this we have developed a semi-phenomenological description of this state in which the Halperin-Lee-Read(B.I. Halperin, P.A. Lee, and N. Read, Phys. Rev. B 47), 7312 (1993). theory of the half-filled Landau level is modified by adding a p-wave pairing interaction between composite fermions by hand. The electromagnetic response functions for the resulting mean-field superconducting state are then calculated and used in an RPA calculation of the physical electronic response. For a clean enough sample, and for q << k_f, the transverse electromagnetic response function for composite fermions is governed by type-II coherence factors and shows a `Hebel-Slichter'-like peak as a function of temperature for low enough frequency. The possibility (and potential difficulties) of observing this peak indirectly in surface-acoustic-wave propagation experiments will be discussed. The observation of such a coherence peak would provide strong evidence of BCS pairing in the 5/2 state. Work supported by US DOE Grant No. DE-FG02-97ER45639. Work done in collaboration with K.C. Foster (FSU) and S.H. Simon (Lucent). note
Fermion dipole moment and holography
NASA Astrophysics Data System (ADS)
Kulaxizi, Manuela; Rahman, Rakibur
2015-12-01
In the background of a charged AdS black hole, we consider a Dirac particle endowed with an arbitrary magnetic dipole moment. For non-zero charge and dipole coupling of the bulk fermion, we find that the dual boundary theory can be plagued with superluminal modes. Requiring consistency of the dual CFT amounts to constraining the strength of the dipole coupling by an upper bound. We briefly discuss the implications of our results for the physics of holographic non-Fermi liquids.
Fermionic Quantization of Hopf Solitons
NASA Astrophysics Data System (ADS)
Krusch, S.; Speight, J. M.
2006-06-01
In this paper we show how to quantize Hopf solitons using the Finkelstein-Rubinstein approach. Hopf solitons can be quantized as fermions if their Hopf charge is odd. Symmetries of classical minimal energy configurations induce loops in configuration space which give rise to constraints on the wave function. These constraints depend on whether the given loop is contractible. Our method is to exploit the relationship between the configuration spaces of the Faddeev-Hopf and Skyrme models provided by the Hopf fibration. We then use recent results in the Skyrme model to determine whether loops are contractible. We discuss possible quantum ground states up to Hopf charge Q=7.
Coulomb interactions and fermion condensation
Capstick, S.; Cutkosky, R.E.; Joensen, M.A. ); Wang, K.C. )
1990-08-15
The influence of the Coulomb interaction in states containing massless and flavorless fermion-antifermion pairs is studied, using a continuum formulation within the finite volume {ital S}{sup 3}. Several different forms for the Coulomb interaction are examined, including confining potentials as well as nonconfining potentials. The calculations show that if the interaction is strong enough, the Coulomb interaction leads to condensation of pairs, and that this condensation has a chiral character. The condensation does not depend on whether the interaction is confining. It is found that simplified variational approximations are not accurate enough for an adequate description of the states.
Symplectic tracking using point magnets in the presence of a longitudinal magnetic field
Parzen, G.
1993-09-01
In the absence of a longitudinal magnetic field, symplectic tracking can be achieved by replacing the magnets by a series of point magnets and drift spaces. To treat the case when a longitudinal magnetic field is also present, this procedure is modified in this paper by replacing the drift space by a solenoidal drift, which is defined as the motion of a particle in a uniform longitudinal magnetic field. A symplectic integrator can be obtained by subdividing each magnet into pieces and replacing each magnet piece by point magnets, with only transverse fields, and solenoidal drift spaces. The reference orbit used here is made up of arcs of circles and straight lines which join smoothly with each other. For this choice of reference orbit, the required results are obtained to track particles, which are the transfer functions, and the transfer time for the different elements. It is shown that these results provide a symplectic integrator, and they are exact in the sense that as the number of magnet pieces is increased, the particle motion will converge to the particle motion of the exact equations of motion.
Light Nuclei in the Framework of the Symplectic No-Core Shell Model
Draayer, Jerry P.; Dytrych, Tomas; Sviratcheva, Kristina D.; Bahri, Chairul; Vary, James P.; /Iowa State U. /LLNL, Livermore /SLAC
2007-04-02
A symplectic no-core shell model (Sp-NCSM) is constructed with the goal of extending the ab-initio NCSM to include strongly deformed higher-oscillator-shell configurations and to reach heavier nuclei that cannot be studied currently because the spaces encountered are too large to handle, even with the best of modern-day computers. This goal is achieved by integrating two powerful concepts: the ab-initio NCSM with that of the Sp(3,R) {contains} SU(3) group-theoretical approach. The NCSM uses modern realistic nuclear interactions in model spaces that consists of many-body configurations up to a given number of {h_bar}{Upsilon} excitations together with modern high-performance parallel computing techniques. The symplectic theory extends this picture by recognizing that when deformed configurations dominate, which they often do, the model space can be better selected so less relevant low-lying {h_bar}{Upsilon} configurations yield to more relevant high-lying {h_bar}{Upsilon} configurations, ones that respect a near symplectic symmetry found in the Hamiltonian. Results from an application of the Sp-NCSM to light nuclei are compared with those for the NCSM and with experiment.
Fast and reliable symplectic integration for planetary system N-body problems
NASA Astrophysics Data System (ADS)
Hernandez, David M.
2016-06-01
We apply one of the exactly symplectic integrators, which we call HB15, of Hernandez & Bertschinger, along with the Kepler problem solver of Wisdom & Hernandez, to solve planetary system N-body problems. We compare the method to Wisdom-Holman (WH) methods in the MERCURY software package, the MERCURY switching integrator, and others and find HB15 to be the most efficient method or tied for the most efficient method in many cases. Unlike WH, HB15 solved N-body problems exhibiting close encounters with small, acceptable error, although frequent encounters slowed the code. Switching maps like MERCURY change between two methods and are not exactly symplectic. We carry out careful tests on their properties and suggest that they must be used with caution. We then use different integrators to solve a three-body problem consisting of a binary planet orbiting a star. For all tested tolerances and time steps, MERCURY unbinds the binary after 0 to 25 years. However, in the solutions of HB15, a time-symmetric HERMITE code, and a symplectic Yoshida method, the binary remains bound for >1000 years. The methods' solutions are qualitatively different, despite small errors in the first integrals in most cases. Several checks suggest that the qualitative binary behaviour of HB15's solution is correct. The Bulirsch-Stoer and Radau methods in the MERCURY package also unbind the binary before a time of 50 years, suggesting that this dynamical error is due to a MERCURY bug.
Teichmüller space for hyperkähler and symplectic structures
NASA Astrophysics Data System (ADS)
Amerik, Ekaterina; Verbitsky, Misha
2015-11-01
Let S be an infinite-dimensional manifold of all symplectic, or hyperkähler, structures on a compact manifold M, and Diff0 the connected component of its diffeomorphism group. The quotient S /Diff0 is called the Teichmüller space of symplectic (or hyperkähler) structures on M. MBM classes on a hyperkähler manifold M are cohomology classes which can be represented by a minimal rational curve on a deformation of M. We determine the Teichmüller space of hyperkähler structures on a hyperkähler manifold, identifying any of its connected components with an open subset of the Grassmannian variety SO(b2 - 3, 3) / SO(3) × SO(b2 - 3) consisting of all Beauville-Bogomolov positive 3-planes in H2(M, R) which are not orthogonal to any of the MBM classes. This is used to determine the Teichmüller space of symplectic structures of Kähler type on a hyperkähler manifold of maximal holonomy. We show that any connected component of this space is naturally identified with the space of cohomology classes v ∈H2(M, R) with q(v, v) > 0, where q is the Bogomolov-Beauville-Fujiki form on H2(M, R) .
Shell-model representations of the proton-neutron symplectic model
NASA Astrophysics Data System (ADS)
Ganev, H. G.
2015-07-01
The representation theory of the recently introduced proton-neutron symplectic model in the many-particle Hilbert space is considered. The relation of the Sp(12, R) irreducible representations (irreps) with the shell-model classification of the basis states is considered by extending of the state space to the direct product space of SU p (3) ⊗ SU n (3) irreps, generalizing in this way the Elliott's SU(3) model for the case of two-component system. The Sp(12, R) model appears then as a natural multi-major-shell extension of the generalized proton-neutron SU(3) scheme, which takes into account the core collective excitations of monopole and quadrupole, as well as dipole type associated with the giant resonance vibrational degrees of freedom. Each Sp(12, R) irreducible representation is determined by a symplectic bandhead or an intrinsic U(6) space which can be fixed by the underlying proton-neutron shell-model structure, so the theory becomes completely compatible with the Pauli principle. It is shown that this intrinsic U(6) structure is of vital importance for the appearance of the low-lying collective bands without involving a mixing of different symplectic irreps. The full range of low-lying collective states can then be described by the microscopically based intrinsic U(6) structure, renormalized by coupling to the giant resonance vibrations.
Nearly massless Dirac fermions hosted by Sb square net in BaMnSb2.
Liu, Jinyu; Hu, Jin; Cao, Huibo; Zhu, Yanglin; Chuang, Alyssa; Graf, D; Adams, D J; Radmanesh, S M A; Spinu, L; Chiorescu, I; Mao, Zhiqiang
2016-01-01
Layered compounds AMnBi2 (A = Ca, Sr, Ba, or rare earth element) have been established as Dirac materials. Dirac electrons generated by the two-dimensional (2D) Bi square net in these materials are normally massive due to the presence of a spin-orbital coupling (SOC) induced gap at Dirac nodes. Here we report that the Sb square net in an isostructural compound BaMnSb2 can host nearly massless Dirac fermions. We observed strong Shubnikov-de Haas (SdH) oscillations in this material. From the analyses of the SdH oscillations, we find key signatures of Dirac fermions, including light effective mass (~0.052m0; m0, mass of free electron), high quantum mobility (1280 cm(2)V(-1)S(-1)) and a π Berry phase accumulated along cyclotron orbit. Compared with AMnBi2, BaMnSb2 also exhibits much more significant quasi two-dimensional (2D) electronic structure, with the out-of-plane transport showing nonmetallic conduction below 120 K and the ratio of the out-of-plane and in-plane resistivity reaching ~670. Additionally, BaMnSb2 also exhibits a G-type antiferromagnetic order below 283 K. The combination of nearly massless Dirac fermions on quasi-2D planes with a magnetic order makes BaMnSb2 an intriguing platform for seeking novel exotic phenomena of massless Dirac electrons. PMID:27466151
Nearly massless Dirac fermions hosted by Sb square net in BaMnSb2
Liu, Jinyu; Hu, Jin; Cao, Huibo; Zhu, Yanglin; Chuang, Alyssa; Graf, D.; Adams, D. J.; Radmanesh, S. M. A.; Spinu, L.; Chiorescu, I.; Mao, Zhiqiang
2016-01-01
Layered compounds AMnBi2 (A = Ca, Sr, Ba, or rare earth element) have been established as Dirac materials. Dirac electrons generated by the two-dimensional (2D) Bi square net in these materials are normally massive due to the presence of a spin-orbital coupling (SOC) induced gap at Dirac nodes. Here we report that the Sb square net in an isostructural compound BaMnSb2 can host nearly massless Dirac fermions. We observed strong Shubnikov-de Haas (SdH) oscillations in this material. From the analyses of the SdH oscillations, we find key signatures of Dirac fermions, including light effective mass (~0.052m0; m0, mass of free electron), high quantum mobility (1280 cm2V−1S−1) and a π Berry phase accumulated along cyclotron orbit. Compared with AMnBi2, BaMnSb2 also exhibits much more significant quasi two-dimensional (2D) electronic structure, with the out-of-plane transport showing nonmetallic conduction below 120 K and the ratio of the out-of-plane and in-plane resistivity reaching ~670. Additionally, BaMnSb2 also exhibits a G-type antiferromagnetic order below 283 K. The combination of nearly massless Dirac fermions on quasi-2D planes with a magnetic order makes BaMnSb2 an intriguing platform for seeking novel exotic phenomena of massless Dirac electrons. PMID:27466151
Nearly massless Dirac fermions hosted by Sb square net in BaMnSb2
NASA Astrophysics Data System (ADS)
Liu, Jinyu; Hu, Jin; Cao, Huibo; Zhu, Yanglin; Chuang, Alyssa; Graf, D.; Adams, D. J.; Radmanesh, S. M. A.; Spinu, L.; Chiorescu, I.; Mao, Zhiqiang
2016-07-01
Layered compounds AMnBi2 (A = Ca, Sr, Ba, or rare earth element) have been established as Dirac materials. Dirac electrons generated by the two-dimensional (2D) Bi square net in these materials are normally massive due to the presence of a spin-orbital coupling (SOC) induced gap at Dirac nodes. Here we report that the Sb square net in an isostructural compound BaMnSb2 can host nearly massless Dirac fermions. We observed strong Shubnikov-de Haas (SdH) oscillations in this material. From the analyses of the SdH oscillations, we find key signatures of Dirac fermions, including light effective mass (~0.052m0 m0, mass of free electron), high quantum mobility (1280 cm2V‑1S‑1) and a π Berry phase accumulated along cyclotron orbit. Compared with AMnBi2, BaMnSb2 also exhibits much more significant quasi two-dimensional (2D) electronic structure, with the out-of-plane transport showing nonmetallic conduction below 120 K and the ratio of the out-of-plane and in-plane resistivity reaching ~670. Additionally, BaMnSb2 also exhibits a G-type antiferromagnetic order below 283 K. The combination of nearly massless Dirac fermions on quasi-2D planes with a magnetic order makes BaMnSb2 an intriguing platform for seeking novel exotic phenomena of massless Dirac electrons.
Superalgebra and fermion-boson symmetry
Miyazawa, Hironari
2010-01-01
Fermions and bosons are quite different kinds of particles, but it is possible to unify them in a supermultiplet, by introducing a new mathematical scheme called superalgebra. In this article we discuss the development of the concept of symmetry, starting from the rotational symmetry and finally arriving at this fermion-boson (FB) symmetry. PMID:20228617
Mass-induced transition in fermion number
Aragao de Carvalho, C.; Pureza, J. M.
1989-05-15
We show that if we increase the mass of fermions in interaction with a topological (kink) scalar background in 1+1 dimensions, the fractional fermion number of the system will eventually vanish. The transition is sharp and corresponds to the disappearance of localized states from the spectrum of a Dirac operator which is exactly solvable. Possible applications to different physical systems are discussed.
Quantum electrodynamics with complex fermion mass
McKellar, B.J.H. . School of Physics); Wu, D.D. . School of Physics Academia Sinica, Beijing, BJ . Inst. of High Energy Physics Superconducting Super Collider Lab., Dallas, TX )
1991-08-01
The quantum electrodynamics (QED) with a complex fermion mass -- that is, a fermion mass with a chiral phase -- is restudied, together with its chirally rotated version. We show how fake electric dipole moment can be obtained and how to avoid it. 10 refs.
Beyond Graphene: Electronic and Mechanical Properties of Defective 2-D Materials
NASA Astrophysics Data System (ADS)
Terrones, Humberto
One of the challenges in the production of 2-D materials is the synthesis of defect free systems which can achieve the desired properties for novel applications. However, the reality so far indicates that we need to deal with defective systems and understand their main features in order to perform defect engineering in such a way that we can engineer a new material. In this talk I discuss first, the introduction of defects in a hierarchic way starting from 2-D graphene to form giant Schwarzites or graphene foams, which also can exhibit further defects, thus we can have several levels of defectiveness. In this context, it will be shown that giant Schwarzites, depending on their symmetry, can exhibit Dirac-Fermion behavior and further, possess protected topological states as shown by other authors. Regarding the mechanical properties of these systems, it is possible to tune the Poisson Ratio by the addition of defects, thus shedding light to the explanation of the almost zero Poisson ratios in experimentally obtained graphene foams. Second, the idea of Haeckelites, a planar sp2 graphene-like structure with heptagons and pentagons, can be extended to transition metal dichalcogenides (TMDs) with square and octagonal-like defects, finding semi-metallic behaviors with Dirac-Fermions, and even topological insulating properties. National Science Foundation (EFRI-1433311).
2D-Crystal-Based Functional Inks.
Bonaccorso, Francesco; Bartolotta, Antonino; Coleman, Jonathan N; Backes, Claudia
2016-08-01
The possibility to produce and process graphene, related 2D crystals, and heterostructures in the liquid phase makes them promising materials for an ever-growing class of applications as composite materials, sensors, in flexible optoelectronics, and energy storage and conversion. In particular, the ability to formulate functional inks with on-demand rheological and morphological properties, i.e., lateral size and thickness of the dispersed 2D crystals, is a step forward toward the development of industrial-scale, reliable, inexpensive printing/coating processes, a boost for the full exploitation of such nanomaterials. Here, the exfoliation strategies of graphite and other layered crystals are reviewed, along with the advances in the sorting of lateral size and thickness of the exfoliated sheets together with the formulation of functional inks and the current development of printing/coating processes of interest for the realization of 2D-crystal-based devices. PMID:27273554
2D microwave imaging reflectometer electronics
Spear, A. G.; Domier, C. W. Hu, X.; Muscatello, C. M.; Ren, X.; Luhmann, N. C.; Tobias, B. J.
2014-11-15
A 2D microwave imaging reflectometer system has been developed to visualize electron density fluctuations on the DIII-D tokamak. Simultaneously illuminated at four probe frequencies, large aperture optics image reflections from four density-dependent cutoff surfaces in the plasma over an extended region of the DIII-D plasma. Localized density fluctuations in the vicinity of the plasma cutoff surfaces modulate the plasma reflections, yielding a 2D image of electron density fluctuations. Details are presented of the receiver down conversion electronics that generate the in-phase (I) and quadrature (Q) reflectometer signals from which 2D density fluctuation data are obtained. Also presented are details on the control system and backplane used to manage the electronics as well as an introduction to the computer based control program.
2D microwave imaging reflectometer electronics
NASA Astrophysics Data System (ADS)
Spear, A. G.; Domier, C. W.; Hu, X.; Muscatello, C. M.; Ren, X.; Tobias, B. J.; Luhmann, N. C.
2014-11-01
A 2D microwave imaging reflectometer system has been developed to visualize electron density fluctuations on the DIII-D tokamak. Simultaneously illuminated at four probe frequencies, large aperture optics image reflections from four density-dependent cutoff surfaces in the plasma over an extended region of the DIII-D plasma. Localized density fluctuations in the vicinity of the plasma cutoff surfaces modulate the plasma reflections, yielding a 2D image of electron density fluctuations. Details are presented of the receiver down conversion electronics that generate the in-phase (I) and quadrature (Q) reflectometer signals from which 2D density fluctuation data are obtained. Also presented are details on the control system and backplane used to manage the electronics as well as an introduction to the computer based control program.
Optical modulators with 2D layered materials
NASA Astrophysics Data System (ADS)
Sun, Zhipei; Martinez, Amos; Wang, Feng
2016-04-01
Light modulation is an essential operation in photonics and optoelectronics. With existing and emerging technologies increasingly demanding compact, efficient, fast and broadband optical modulators, high-performance light modulation solutions are becoming indispensable. The recent realization that 2D layered materials could modulate light with superior performance has prompted intense research and significant advances, paving the way for realistic applications. In this Review, we cover the state of the art of optical modulators based on 2D materials, including graphene, transition metal dichalcogenides and black phosphorus. We discuss recent advances employing hybrid structures, such as 2D heterostructures, plasmonic structures, and silicon and fibre integrated structures. We also take a look at the future perspectives and discuss the potential of yet relatively unexplored mechanisms, such as magneto-optic and acousto-optic modulation.
Large Area Synthesis of 2D Materials
NASA Astrophysics Data System (ADS)
Vogel, Eric
Transition metal dichalcogenides (TMDs) have generated significant interest for numerous applications including sensors, flexible electronics, heterostructures and optoelectronics due to their interesting, thickness-dependent properties. Despite recent progress, the synthesis of high-quality and highly uniform TMDs on a large scale is still a challenge. In this talk, synthesis routes for WSe2 and MoS2 that achieve monolayer thickness uniformity across large area substrates with electrical properties equivalent to geological crystals will be described. Controlled doping of 2D semiconductors is also critically required. However, methods established for conventional semiconductors, such as ion implantation, are not easily applicable to 2D materials because of their atomically thin structure. Redox-active molecular dopants will be demonstrated which provide large changes in carrier density and workfunction through the choice of dopant, treatment time, and the solution concentration. Finally, several applications of these large-area, uniform 2D materials will be described including heterostructures, biosensors and strain sensors.
2D microwave imaging reflectometer electronics.
Spear, A G; Domier, C W; Hu, X; Muscatello, C M; Ren, X; Tobias, B J; Luhmann, N C
2014-11-01
A 2D microwave imaging reflectometer system has been developed to visualize electron density fluctuations on the DIII-D tokamak. Simultaneously illuminated at four probe frequencies, large aperture optics image reflections from four density-dependent cutoff surfaces in the plasma over an extended region of the DIII-D plasma. Localized density fluctuations in the vicinity of the plasma cutoff surfaces modulate the plasma reflections, yielding a 2D image of electron density fluctuations. Details are presented of the receiver down conversion electronics that generate the in-phase (I) and quadrature (Q) reflectometer signals from which 2D density fluctuation data are obtained. Also presented are details on the control system and backplane used to manage the electronics as well as an introduction to the computer based control program. PMID:25430247
Fermionic T-Duality a Snapshot Review
NASA Astrophysics Data System (ADS)
Ó Colgáin, Eoin
2012-11-01
Through a self-dual mapping of the geometry AdS5 ×S5, fermionic T-duality provides a beautiful geometric interpretation of hidden symmetries for scattering amplitudes in N = 4 super-Yang-Mills. Starting with Green-Schwarz sigma-models, we consolidate developments in this area into this small review. In particular, we discuss the translation of fermionic T-duality into the supergravity fields via pure spinor formalism and show that a general class of fermionic transformations can be identified directly in the supergravity. In addition to discussing fermionic T-duality for the geometry AdS4 × ℂP3, dual to N = 6 ABJM theory, we review work on other self-dual geometries. Finally, we present a short round-up of studies with a formal interest in fermionic T-duality.
Tunable Dirac Fermion Dynamics in Topological Insulators
NASA Astrophysics Data System (ADS)
Chen, Chaoyu; Xie, Zhuojin; Feng, Ya; Yi, Hemian; Liang, Aiji; He, Shaolong; Mou, Daixiang; He, Junfeng; Peng, Yingying; Liu, Xu; Liu, Yan; Zhao, Lin; Liu, Guodong; Dong, Xiaoli; Zhang, Jun; Yu, Li; Wang, Xiaoyang; Peng, Qinjun; Wang, Zhimin; Zhang, Shenjin; Yang, Feng; Chen, Chuangtian; Xu, Zuyan; Zhou, X. J.
2013-08-01
Three-dimensional topological insulators are characterized by insulating bulk state and metallic surface state involving relativistic Dirac fermions which are responsible for exotic quantum phenomena and potential applications in spintronics and quantum computations. It is essential to understand how the Dirac fermions interact with other electrons, phonons and disorders. Here we report super-high resolution angle-resolved photoemission studies on the Dirac fermion dynamics in the prototypical Bi2(Te,Se)3 topological insulators. We have directly revealed signatures of the electron-phonon coupling and found that the electron-disorder interaction dominates the scattering process. The Dirac fermion dynamics in Bi2(Te3-xSex) topological insulators can be tuned by varying the composition, x, or by controlling the charge carriers. Our findings provide crucial information in understanding and engineering the electron dynamics of the Dirac fermions for fundamental studies and potential applications.
Fermion hierarchy from sfermion anarchy
Altmannshofer, Wolfgang; Frugiuele, Claudia; Harnik, Roni
2014-12-31
We present a framework to generate the hierarchical flavor structure of Standard Model quarks and leptons from loops of superpartners. The simplest model consists of the minimal supersymmetric standard model with tree level Yukawa couplings for the third generation only and anarchic squark and slepton mass matrices. Agreement with constraints from low energy flavor observables, in particular Kaon mixing, is obtained for supersymmetric particles with masses at the PeV scale or above. In our framework both the second and the first generation fermion masses are generated at 1-loop. Despite this, a novel mechanism generates a hierarchy among the first andmore » second generations without imposing a symmetry or small parameters. A second-to-first generation mass ratio of order 100 is typical. The minimal supersymmetric standard model thus includes all the necessary ingredients to realize a fermion spectrum that is qualitatively similar to observation, with hierarchical masses and mixing. The minimal framework produces only a few quantitative discrepancies with observation, most notably the muon mass is too low. Furthermore, we discuss simple modifications which resolve this and also investigate the compatibility of our model with gauge and Yukawa coupling Unification.« less
Fermion hierarchy from sfermion anarchy
NASA Astrophysics Data System (ADS)
Altmannshofer, Wolfgang; Frugiuele, Claudia; Harnik, Roni
2014-12-01
We present a framework to generate the hierarchical flavor structure of Standard Model quarks and leptons from loops of superpartners. The simplest model consists of the minimal supersymmetric standard model with tree level Yukawa couplings for the third generation only and anarchic squark and slepton mass matrices. Agreement with constraints from low energy flavor observables, in particular Kaon mixing, is obtained for supersymmetric particles with masses at the PeV scale or above. In our framework both the second and the first generation fermion masses are generated at 1-loop. Despite this, a novel mechanism generates a hierarchy among the first and second generations without imposing a symmetry or small parameters. A second-to-first generation mass ratio of order 100 is typical. The minimal supersymmetric standard model thus includes all the necessary ingredients to realize a fermion spectrum that is qualitatively similar to observation, with hierarchical masses and mixing. The minimal framework produces only a few quantitative discrepancies with observation, most notably the muon mass is too low. We discuss simple modifications which resolve this and also investigate the compatibility of our model with gauge and Yukawa coupling Unification.
Fermion hierarchy from sfermion anarchy
Altmannshofer, Wolfgang; Frugiuele, Claudia; Harnik, Roni
2014-12-31
We present a framework to generate the hierarchical flavor structure of Standard Model quarks and leptons from loops of superpartners. The simplest model consists of the minimal supersymmetric standard model with tree level Yukawa couplings for the third generation only and anarchic squark and slepton mass matrices. Agreement with constraints from low energy flavor observables, in particular Kaon mixing, is obtained for supersymmetric particles with masses at the PeV scale or above. In our framework both the second and the first generation fermion masses are generated at 1-loop. Despite this, a novel mechanism generates a hierarchy among the first and second generations without imposing a symmetry or small parameters. A second-to-first generation mass ratio of order 100 is typical. The minimal supersymmetric standard model thus includes all the necessary ingredients to realize a fermion spectrum that is qualitatively similar to observation, with hierarchical masses and mixing. The minimal framework produces only a few quantitative discrepancies with observation, most notably the muon mass is too low. Furthermore, we discuss simple modifications which resolve this and also investigate the compatibility of our model with gauge and Yukawa coupling Unification.
Inkjet printing of 2D layered materials.
Li, Jiantong; Lemme, Max C; Östling, Mikael
2014-11-10
Inkjet printing of 2D layered materials, such as graphene and MoS2, has attracted great interests for emerging electronics. However, incompatible rheology, low concentration, severe aggregation and toxicity of solvents constitute critical challenges which hamper the manufacturing efficiency and product quality. Here, we introduce a simple and general technology concept (distillation-assisted solvent exchange) to efficiently overcome these challenges. By implementing the concept, we have demonstrated excellent jetting performance, ideal printing patterns and a variety of promising applications for inkjet printing of 2D layered materials. PMID:25169938
Measurement of 2D birefringence distribution
NASA Astrophysics Data System (ADS)
Noguchi, Masato; Ishikawa, Tsuyoshi; Ohno, Masahiro; Tachihara, Satoru
1992-10-01
A new measuring method of 2-D birefringence distribution has been developed. It has not been an easy job to get a birefringence distribution in an optical element with conventional ellipsometry because of its lack of scanning means. Finding an analogy between the rotating analyzer method in ellipsometry and the phase-shifting method in recently developed digital interferometry, we have applied the phase-shifting algorithm to ellipsometry, and have developed a new method that makes the measurement of 2-D birefringence distribution easy and possible. The system contains few moving parts, assuring reliability, and measures a large area of a sample at one time, making the measuring time very short.
The 2D lingual appliance system.
Cacciafesta, Vittorio
2013-09-01
The two-dimensional (2D) lingual bracket system represents a valuable treatment option for adult patients seeking a completely invisible orthodontic appliance. The ease of direct or simplified indirect bonding of 2D lingual brackets in combination with low friction mechanics makes it possible to achieve a good functional and aesthetic occlusion, even in the presence of a severe malocclusion. The use of a self-ligating bracket significantly reduces chair-side time for the orthodontist, and the low-profile bracket design greatly improves patient comfort. PMID:24005953
Visco elasticity in 2D materials
NASA Astrophysics Data System (ADS)
Cortijo, Alberto; Ferreirós, Yago; Landsteiner, Karl; Vozmediano, María A. H.
2016-03-01
The combination of Dirac physics and elasticity has been explored at length in graphene where the so-called ‘elastic gauge fields’ have given rise to an entire new field of research and applications: straintronics. The fact that these elastic fields couple to fermions as the electromagnetic field, implies that many electromagnetic responses will have elastic counterparts not yet explored. In this work we will first show that the presence of elastic gauge fields is the rule rather than the exception in most of the topologically non-trivial materials in two- and three-dimensions. We will show that, associated to the physics of the anomalies, and as a counterpart of the Hall conductivity, elastic two-dimension materials will have a Hall viscosity with a coefficient orders of magnitude bigger than the previously studied response. The magnitude and generality of the new effect will greatly improve the chances for the experimental observation of this topological response.
Parallel stitching of 2D materials
Ling, Xi; Wu, Lijun; Lin, Yuxuan; Ma, Qiong; Wang, Ziqiang; Song, Yi; Yu, Lili; Huang, Shengxi; Fang, Wenjing; Zhang, Xu; et al
2016-01-27
Diverse parallel stitched 2D heterostructures, including metal–semiconductor, semiconductor–semiconductor, and insulator–semiconductor, are synthesized directly through selective “sowing” of aromatic molecules as the seeds in the chemical vapor deposition (CVD) method. Lastly, the methodology enables the large-scale fabrication of lateral heterostructures, which offers tremendous potential for its application in integrated circuits.
Parallel Stitching of 2D Materials.
Ling, Xi; Lin, Yuxuan; Ma, Qiong; Wang, Ziqiang; Song, Yi; Yu, Lili; Huang, Shengxi; Fang, Wenjing; Zhang, Xu; Hsu, Allen L; Bie, Yaqing; Lee, Yi-Hsien; Zhu, Yimei; Wu, Lijun; Li, Ju; Jarillo-Herrero, Pablo; Dresselhaus, Mildred; Palacios, Tomás; Kong, Jing
2016-03-01
Diverse parallel stitched 2D heterostructures, including metal-semiconductor, semiconductor-semiconductor, and insulator-semiconductor, are synthesized directly through selective "sowing" of aromatic molecules as the seeds in the chemical vapor deposition (CVD) method. The methodology enables the large-scale fabrication of lateral heterostructures, which offers tremendous potential for its application in integrated circuits. PMID:26813882
Baby universes in 2d quantum gravity
NASA Astrophysics Data System (ADS)
Ambjørn, Jan; Jain, Sanjay; Thorleifsson, Gudmar
1993-06-01
We investigate the fractal structure of 2d quantum gravity, both for pure gravity and for gravity coupled to multiple gaussian fields and for gravity coupled to Ising spins. The roughness of the surfaces is described in terms of baby universes and using numerical simulations we measure their distribution which is related to the string susceptibility exponent γstring.
NASA Astrophysics Data System (ADS)
Bahri, Yasaman; Vishwanath, Ashvin
2014-04-01
Topological phases which host Majorana fermions can not be identified via local order parameters. We give simple nonlocal order parameters to distinguish quasi-one-dimensional (1D) topological superconductors of spinless fermions, for any interacting model in the absence of time reversal symmetry. These string or "brane" order parameters are natural for measurements in cold atom systems using quantum gas microscopy. We propose them as a way to identify symmetry-protected topological phases of Majorana fermions in cold atom experiments via bulk rather than edge degrees of freedom. Subsequently, we study two-dimensional (2D) topological superconductors via the quasi-1D limit of coupling N identical chains on the cylinder. We classify the symmetric, interacting topological phases protected by the additional ZN translation symmetry. The phases include quasi-1D analogs of (i) the p +ip chiral topological superconductor, which can be distinguished up to the 2D Chern number mod 2, and (ii) the 2D weak topological superconductor. We devise general rules for constructing nonlocal order parameters which distinguish the phases. These rules encode the signature of the fermionic topological phase in the symmetry properties of the terminating operators of the nonlocal string or brane. The nonlocal order parameters for some of these phases simply involve a product of the string order parameters for the individual chains. Finally, we give a physical picture of one of the topological phases as a condensate of certain defects, which motivates the form of the nonlocal order parameter and is reminiscent of higher dimensional constructions of topological phases.
Fermion tunneling from dynamical horizons
NASA Astrophysics Data System (ADS)
Di Criscienzo, R.; Vanzo, L.
2008-06-01
The instability against emission of fermionic particles by the trapping horizon of an evolving black hole is analyzed and confirmed using the Hamilton-Jacobi tunneling method. This method automatically selects one special expression for the surface gravity of a changing horizon. The results also apply to point masses embedded in an expanding universe. As a bonus of the tunneling method, we gain the insight that the surface gravity still defines a temperature parameter as long as the evolution is sufficiently slow that the black-hole pass through a sequence of quasi-equilibrium states, and that black holes should be semi-classically unstable even in a hypothetical world without bosonic fields.
Green's functions for a CPn - 1 model with massless fermions
NASA Astrophysics Data System (ADS)
Schaposnik, F. A.
1983-07-01
We study the CPn - 1 model with massless fermions making a chiral change in the fermionic variables. We construct the generating functional and discuss relevant features of the theory. The factorization of a pure fermionic part shows a power law correction to the free fermion Green's function. The dynamical gauge field becomes massive and a screening phenomenon occurs. Member of CIC, Buenos Aires, Argentina
Flavor symmetries and fermion masses
Rasin, A.
1994-04-01
We introduce several ways in which approximate flavor symmetries act on fermions and which are consistent with observed fermion masses and mixings. Flavor changing interactions mediated by new scalars appear as a consequence of approximate flavor symmetries. We discuss the experimental limits on masses of the new scalars, and show that the masses can easily be of the order of weak scale. Some implications for neutrino physics are also discussed. Such flavor changing interactions would easily erase any primordial baryon asymmetry. We show that this situation can be saved by simply adding a new charged particle with its own asymmetry. The neutrality of the Universe, together with sphaleron processes, then ensures a survival of baryon asymmetry. Several topics on flavor structure of the supersymmetric grand unified theories are discussed. First, we show that the successful predictions for the Kobayashi-Maskawa mixing matrix elements, V{sub ub}/V{sub cb} = {radical}m{sub u}/m{sub c} and V{sub td}/V{sub ts} = {radical}m{sub d}/m{sub s}, are a consequence of a large class of models, rather than specific properties of a few models. Second, we discuss how the recent observation of the decay {beta} {yields} s{gamma} constrains the parameter space when the ratio of the vacuum expectation values of the two Higgs doublets, tan{Beta}, is large. Finally, we discuss the flavor structure of proton decay. We observe a surprising enhancement of the branching ratio for the muon mode in SO(10) models compared to the same mode in the SU(5) model.
Application of 2D Non-Graphene Materials and 2D Oxide Nanostructures for Biosensing Technology
Shavanova, Kateryna; Bakakina, Yulia; Burkova, Inna; Shtepliuk, Ivan; Viter, Roman; Ubelis, Arnolds; Beni, Valerio; Starodub, Nickolaj; Yakimova, Rositsa; Khranovskyy, Volodymyr
2016-01-01
The discovery of graphene and its unique properties has inspired researchers to try to invent other two-dimensional (2D) materials. After considerable research effort, a distinct “beyond graphene” domain has been established, comprising the library of non-graphene 2D materials. It is significant that some 2D non-graphene materials possess solid advantages over their predecessor, such as having a direct band gap, and therefore are highly promising for a number of applications. These applications are not limited to nano- and opto-electronics, but have a strong potential in biosensing technologies, as one example. However, since most of the 2D non-graphene materials have been newly discovered, most of the research efforts are concentrated on material synthesis and the investigation of the properties of the material. Applications of 2D non-graphene materials are still at the embryonic stage, and the integration of 2D non-graphene materials into devices is scarcely reported. However, in recent years, numerous reports have blossomed about 2D material-based biosensors, evidencing the growing potential of 2D non-graphene materials for biosensing applications. This review highlights the recent progress in research on the potential of using 2D non-graphene materials and similar oxide nanostructures for different types of biosensors (optical and electrochemical). A wide range of biological targets, such as glucose, dopamine, cortisol, DNA, IgG, bisphenol, ascorbic acid, cytochrome and estradiol, has been reported to be successfully detected by biosensors with transducers made of 2D non-graphene materials. PMID:26861346
Application of 2D Non-Graphene Materials and 2D Oxide Nanostructures for Biosensing Technology.
Shavanova, Kateryna; Bakakina, Yulia; Burkova, Inna; Shtepliuk, Ivan; Viter, Roman; Ubelis, Arnolds; Beni, Valerio; Starodub, Nickolaj; Yakimova, Rositsa; Khranovskyy, Volodymyr
2016-01-01
The discovery of graphene and its unique properties has inspired researchers to try to invent other two-dimensional (2D) materials. After considerable research effort, a distinct "beyond graphene" domain has been established, comprising the library of non-graphene 2D materials. It is significant that some 2D non-graphene materials possess solid advantages over their predecessor, such as having a direct band gap, and therefore are highly promising for a number of applications. These applications are not limited to nano- and opto-electronics, but have a strong potential in biosensing technologies, as one example. However, since most of the 2D non-graphene materials have been newly discovered, most of the research efforts are concentrated on material synthesis and the investigation of the properties of the material. Applications of 2D non-graphene materials are still at the embryonic stage, and the integration of 2D non-graphene materials into devices is scarcely reported. However, in recent years, numerous reports have blossomed about 2D material-based biosensors, evidencing the growing potential of 2D non-graphene materials for biosensing applications. This review highlights the recent progress in research on the potential of using 2D non-graphene materials and similar oxide nanostructures for different types of biosensors (optical and electrochemical). A wide range of biological targets, such as glucose, dopamine, cortisol, DNA, IgG, bisphenol, ascorbic acid, cytochrome and estradiol, has been reported to be successfully detected by biosensors with transducers made of 2D non-graphene materials. PMID:26861346
Instantons and Massless Fermions in Two Dimensions
DOE R&D Accomplishments Database
Callan, C. G. Jr.; Dashen, R.; Gross, D. J.
1977-05-01
The role of instantons in the breakdown of chiral U(N) symmetry is studied in a two dimensional model. Chiral U(1) is always destroyed by the axial vector anomaly. For N = 2 chiral SU(N) is also spontaneously broken yielding massive fermions and three (decoupled) Goldstone bosons. For N greater than or equal to 3 the fermions remain massless. Realistic four dimensional theories are believed to behave in a similar way but the critical N above which the fermions cease to be massive is not known in four dimensions.
Fermion localization on a split brane
Chumbes, A. E. R.; Vasquez, A. E. O.; Hott, M. B.
2011-05-15
In this work we analyze the localization of fermions on a brane embedded in five-dimensional, warped and nonwarped, space-time. In both cases we use the same nonlinear theoretical model with a nonpolynomial potential featuring a self-interacting scalar field whose minimum energy solution is a soliton (a kink) which can be continuously deformed into a two-kink. Thus a single brane splits into two branes. The behavior of spin 1/2 fermions wave functions on the split brane depends on the coupling of fermions to the scalar field and on the geometry of the space-time.
Fermionic quantum critical point of spinless fermions on a honeycomb lattice
NASA Astrophysics Data System (ADS)
Wang, Lei; Corboz, Philippe; Troyer, Matthias
2014-10-01
Spinless fermions on a honeycomb lattice provide a minimal realization of lattice Dirac fermions. Repulsive interactions between nearest neighbors drive a quantum phase transition from a Dirac semimetal to a charge-density-wave state through a fermionic quantum critical point, where the coupling of the Ising order parameter to the Dirac fermions at low energy drastically affects the quantum critical behavior. Encouraged by a recent discovery (Huffman and Chandrasekharan 2014 Phys. Rev. B 89 111101) of the absence of the fermion sign problem in this model, we study the fermionic quantum critical point using the continuous-time quantum Monte Carlo method with a worm-sampling technique. We estimate the transition point V/t=1.356(1) with the critical exponents ν =0.80(3) and η =0.302(7). Compatible results for the transition point are also obtained with infinite projected entangled-pair states.
Stochastic Inversion of 2D Magnetotelluric Data
Chen, Jinsong
2010-07-01
The algorithm is developed to invert 2D magnetotelluric (MT) data based on sharp boundary parametrization using a Bayesian framework. Within the algorithm, we consider the locations and the resistivity of regions formed by the interfaces are as unknowns. We use a parallel, adaptive finite-element algorithm to forward simulate frequency-domain MT responses of 2D conductivity structure. Those unknown parameters are spatially correlated and are described by a geostatistical model. The joint posterior probability distribution function is explored by Markov Chain Monte Carlo (MCMC) sampling methods. The developed stochastic model is effective for estimating the interface locations and resistivity. Most importantly, it provides details uncertainty information on each unknown parameter. Hardware requirements: PC, Supercomputer, Multi-platform, Workstation; Software requirements C and Fortan; Operation Systems/version is Linux/Unix or Windows
Static & Dynamic Response of 2D Solids
Energy Science and Technology Software Center (ESTSC)
1996-07-15
NIKE2D is an implicit finite-element code for analyzing the finite deformation, static and dynamic response of two-dimensional, axisymmetric, plane strain, and plane stress solids. The code is fully vectorized and available on several computing platforms. A number of material models are incorporated to simulate a wide range of material behavior including elasto-placicity, anisotropy, creep, thermal effects, and rate dependence. Slideline algorithms model gaps and sliding along material interfaces, including interface friction, penetration and single surfacemore » contact. Interactive-graphics and rezoning is included for analyses with large mesh distortions. In addition to quasi-Newton and arc-length procedures, adaptive algorithms can be defined to solve the implicit equations using the solution language ISLAND. Each of these capabilities and more make NIKE2D a robust analysis tool.« less
Stochastic Inversion of 2D Magnetotelluric Data
Energy Science and Technology Software Center (ESTSC)
2010-07-01
The algorithm is developed to invert 2D magnetotelluric (MT) data based on sharp boundary parametrization using a Bayesian framework. Within the algorithm, we consider the locations and the resistivity of regions formed by the interfaces are as unknowns. We use a parallel, adaptive finite-element algorithm to forward simulate frequency-domain MT responses of 2D conductivity structure. Those unknown parameters are spatially correlated and are described by a geostatistical model. The joint posterior probability distribution function ismore » explored by Markov Chain Monte Carlo (MCMC) sampling methods. The developed stochastic model is effective for estimating the interface locations and resistivity. Most importantly, it provides details uncertainty information on each unknown parameter. Hardware requirements: PC, Supercomputer, Multi-platform, Workstation; Software requirements C and Fortan; Operation Systems/version is Linux/Unix or Windows« less
Explicit 2-D Hydrodynamic FEM Program
Energy Science and Technology Software Center (ESTSC)
1996-08-07
DYNA2D* is a vectorized, explicit, two-dimensional, axisymmetric and plane strain finite element program for analyzing the large deformation dynamic and hydrodynamic response of inelastic solids. DYNA2D* contains 13 material models and 9 equations of state (EOS) to cover a wide range of material behavior. The material models implemented in all machine versions are: elastic, orthotropic elastic, kinematic/isotropic elastic plasticity, thermoelastoplastic, soil and crushable foam, linear viscoelastic, rubber, high explosive burn, isotropic elastic-plastic, temperature-dependent elastic-plastic. Themore » isotropic and temperature-dependent elastic-plastic models determine only the deviatoric stresses. Pressure is determined by one of 9 equations of state including linear polynomial, JWL high explosive, Sack Tuesday high explosive, Gruneisen, ratio of polynomials, linear polynomial with energy deposition, ignition and growth of reaction in HE, tabulated compaction, and tabulated.« less