Bose symmetry and chiral decomposition of 2D fermionic determinants
NASA Astrophysics Data System (ADS)
Abreu, E. M. C.; Banerjee, R.; Wotzasek, C.
1998-01-01
We show in a precise way, either in the fermionic or its bosonized version, that Bose symmetry provides a systematic way to carry out the chiral decomposition of the two-dimensional fermionic determinant. Interpreted properly, we show that there is no obstruction of this decomposition to gauge invariance, as is usually claimed. Finally, a new way of interpreting the Polyakov-Wiegman identity is proposed.
Viscous dissipation in 2D fluid dynamics as a symplectic process and its metriplectic representation
NASA Astrophysics Data System (ADS)
Blender, Richard; Badin, Gualtiero
2017-03-01
Dissipation can be represented in Hamiltonian mechanics in an extended phase space as a symplectic process. The method uses an auxiliary variable which represents the excitation of unresolved dynamics and a Hamiltonian for the interaction between the resolved dynamics and the auxiliary variable. This method is applied to viscous dissipation (including hyper-viscosity) in a two-dimensional fluid, for which the dynamics is non-canonical. We derive a metriplectic representation and suggest a measure for the entropy of the system.
Chiral fermions on 2D curved space-times
NASA Astrophysics Data System (ADS)
Loran, Farhang
2017-06-01
The theory of free Majorana-Weyl spinors is the prototype of conformal field theory in two dimensions in which the gravitational anomaly and the Weyl anomaly obstruct extending the flat space-time results to curved backgrounds. In this paper, we investigate a quantization scheme in which the short distance singularity in the two-point function of chiral fermions on a two-dimensional curved space-time is given by the Green’s function corresponding to the classical field equation. We compute the singular term in the Green’s function explicitly and observe that the short distance limit is not well-defined in general. We identify constraints on the geometry which are necessary to resolve this problem. On such special backgrounds, the theory has locally c = 1 2 conformal symmetry.
Long-lived magnetoexcitons in 2D-fermion system
NASA Astrophysics Data System (ADS)
Kulik, L. V.; Zhuravlev, A. S.; Gorbunov, A. V.; Timofeev, V. B.; Kukushkin, I. V.
2017-01-01
The paper addresses the experimental technique that, when applied to a 2D-electron system in the integer quantum Hall regime with filling factor ν = 2 (the Hall insulating state), allows resonant excitation of magnetoexcitons, their detection, control of an ensemble of long-lived triplet excitons and investigation of their radiationless decay related to exciton spin relaxation into the ground state. The technique proposed enables independent control of photoexcited electrons and Fermi-holes using photoinduced resonance reflection spectra as well as estimate with a reasonable degree of accuracy the resulting density of photoinduced electron-hole pairs bound into magnetoexcitons. The mere existence of triplet excitons was directly established by inelastic light scattering spectra which were analyzed to determine the value of singlet-triplet exciton splitting. It was found that the lifetimes of triplet excitons conditioned by electron spin relaxation in highly perfect GaAs/AlGaAs heterostructures with highly mobile 2D electrons are extremely long exceeding 100 μs at T < 1 K. The paper presents a qualitative explanation of the long-spin relaxation lifetimes which are unprecedented for translation-invariant 2D systems. This enabled us to create sufficiently high concentrations of triplet magnetoexcitons, electrically neutral excitations following Bose-Einstein statistics, in a Fermi electron system and investigate their collective properties. At sufficiently high densities of triplet magnetoexcitons and low temperatures, T < 1 K, the degenerate magnetofermionic system exhibits condensation of the triplet magnetoexcitons into a qualitatively new collective state with unusual properties which occurs in the space of generalized moments (magnetic translation vectors). The occurrence of a condensed phase is accompanied with a significant decrease in the viscosity of the photoexcited system, which is responsible for electron spin transport at macroscopic distances, as well
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.
Blue Phosphorene Oxide: Strain-Tunable Quantum Phase Transitions and Novel 2D Emergent Fermions
NASA Astrophysics Data System (ADS)
Zhu, Liyan; Wang, Shan-Shan; Guan, Shan; Liu, Ying; Zhang, Tingting; Chen, Guibin; Yang, Shengyuan A.
2016-10-01
Tunable quantum phase transitions and novel emergent fermions in solid state materials are fascinating subjects of research. Here, we propose a new stable two-dimensional (2D) material, the blue phosphorene oxide (BPO), which exhibits both. Based on first-principles calculations, we show that its equilibrium state is a narrow-bandgap semiconductor with three bands at low energy. Remarkably, a moderate strain can drive a semiconductor-to-semimetal quantum phase transition in BPO. At the critical transition point, the three bands cross at a single point at Fermi level, around which the quasiparticles are a novel type of 2D pseudospin-1 fermions. Going beyond the transition, the system becomes a symmetry-protected semimetal, for which the conduction and valence bands touch quadratically at a single Fermi point that is protected by symmetry, and the low-energy quasiparticles become another novel type of 2D double Weyl fermions. We construct effective models characterizing the phase transition and these novel emergent fermions, and we point out several exotic effects, including super Klein tunneling, supercollimation, and universal optical absorbance. Our result reveals BPO as an intriguing platform for the exploration of fundamental properties of quantum phase transitions and novel emergent fermions, and also suggests its great potential in nanoscale device applications.
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.
Chiral fermion dynamics in 2d magnetic vortices: Manifestation of momentum-spin-locking
NASA Astrophysics Data System (ADS)
Pötz, W.; Hammer, René
2016-11-01
The electronic surface-states of a topological insulator in the presence of an in-plane magnetization vortex M (ϕ)=M (cos(Φ+νϕ), sin(Φ+νϕ)) are investigated theoretically. For a general angle of magnetization Φ∈[0 ,2 π) and topological charge ν = 1, the modifications to the zero-mass single Dirac cone dispersion are treated exactly and the spectrum of bound eigenstates which forms in the energy window ±M cos(Φ) is derived. The space-time resolved dynamics of Dirac fermions in the presence of such vortices is studied numerically using a single-cone (2 + 1)D finite-difference scheme. In the continuous spectral region, Φ-dependent scattering of Dirac fermions at the vortex is observed. Depending on the type of vortex ( Φ, ν) and the impact parameter, the propagation direction of the Dirac fermion is changed: the magnetization of the vortex exerts a torque onto the fermion spin which, by momentum-spin locking associated with the helical Dirac states, results in an in-plane rotation of the propagation direction of the scattered Dirac fermion. In head-on collisions of a Gaussian wave-packet with ν = 1 vortices a Φ-dependent lensing effect is seen in our simulations. Depending on the direction of incidence, the vortex Φ=-π/2 , ν = 2 is identified as a coherent particle-beam splitter or "condenser" in head-on collisions.
Tunable Majorana fermion from Landau quantization in 2D topological superconductors
NASA Astrophysics Data System (ADS)
Akzyanov, R. S.; Rakhmanov, A. L.; Rozhkov, A. V.; Nori, Franco
2016-09-01
We study Majorana fermions in a two-dimensional topological superconductor placed in a transverse magnetic-field B . We consider a topological insulator/superconductor heterostructure and a two-dimensional p -wave superconductor. A single field-generated vortex creates two Majorana fermions, one of which is hosted at the vortex core. The wave function of the second Majorana state is localized in the superconductor volume along a circle with a radius of r*∝B-1 centered at the vortex core. In the case of many vortices, the sensitivity of r* to the magnetic field B may be used to control the coupling between the Majorana fermions. The latter property could be an asset for quantum computations.
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.
Double valley Dirac fermions for 3D and 2D Hg1-x Cd x Te with strong asymmetry
NASA Astrophysics Data System (ADS)
Marchewka, M.
2017-04-01
In this paper the possibility to bring about the double-valley Dirac fermions in some quantum structures is predicted. These quantum structures are: strained 3D Hg1-x Cd x Te topological insulator (TI) with strong interface inversion asymmetry and the asymmetric Hg1-x Cd x Te double quantum wells (DQW). The numerical analysis of the dispersion relation for 3D TI Hg1-x Cd x Te for the proper Cd (x)-content of the Hg1-x Cd x Te compound clearly shows that the inversion symmetry breaking together with the unaxial tensile strain causes the splitting of each of the Dirac nodes (two belonging to two interfaces) into two in the proximity of the Γ-point. Similar effects can be obtained for asymmetric Hg1-x Cd x Te DQW with the proper content of Cd and proper width of the quantum wells. The aim of this work is to explore the inversion symmetry breaking in 3D TI and 2D DQW mixed HgCdTe systems. It is shown that this symmetry breaking leads to the dependence of carriers energy on quasi-momentum similar to that of Weyl fermions.
Composite Fermion States near 3/2 Hosted by a High-Mobility 2D Hole System
NASA Astrophysics Data System (ADS)
Zhang, Po; Liu, Ruiyuan; Wang, Jianli; Zhang, Chi; Yang, Changli; Lu, Li; Pfeiffer, Loren; West, Ken; Du, Rui-Rui
Magnetotransport experiments of Carbon-doped GaAs/AlGaAs 2D hole gas (2DHG) have revealed a variety of interesting phenomena previous not seen in the 2DEG counterpart. For example, it was found that the effective g -factor of 2DHG is large enough to cause Landau level crossing even at ~1 T, and the product of gm* (where m* is the hole effective mass) increases with total magnetic field. Such level crossings could have profound influences on the fractional quantum Hall states in the relevant magnetic fields. We systematically investigate the composite fermion states near 3/2 in C-doped high-mobility 2DHG by tilted-magnetic field experiments, and map out the Landau levels and composite fermion spectra as a function of hole density and tilt angles. Preliminary results and brief discussions will be presented. The work at Peking University were supported by National Basic Research Program of China Grants 2012CB921301 and 2014CB920901, and by Collaborative Innovation Center of Quantum Matter.
Fermi-to-Bose crossover in a trapped quasi-2D gas of fermionic atoms
NASA Astrophysics Data System (ADS)
Turlapov, A. V.; Kagan, M. Yu
2017-09-01
The physics of many-body systems where particles are restricted to move in two spatial dimensions is challenging and even controversial: on one hand, neither long-range order nor Bose condensation may appear in infinite uniform 2D systems at finite temperature, on the other hand this does not prohibit superfluidity or superconductivity. Moreover, 2D superconductors, such as cuprates, are among the systems with the highest critical temperatures. Ultracold atoms are a platform for studying 2D physics. Unique from other physical systems, quantum statistics may be completely changed in an ultracold gas: an atomic Fermi gas may be smoothly crossed over into a gas of Bose molecules (or dimers) by tuning interatomic interactions. We review recent experiments where such crossover has been demonstrated, as well as critical phenomena in the Fermi-to-Bose crossover. We also present simple theoretical models describing the gas at different points of the crossover and compare the data to these and more advanced models.
Functional renormalization group and bosonization as a solver for 2D fermionic Hubbard models
NASA Astrophysics Data System (ADS)
Schuetz, Florian; Marston, Brad
2007-03-01
The functional renormalization group (fRG) provides an unbiased framework to analyze competing instabilities in two-dimensional electron systems and has been used extensively over the past decade [1]. In order to obtain an equally unbiased tool to interprete the flow, we investigate the combination of a many-patch, one-loop calculation with higher dimensional bosonization [2] of the resulting low-energy action. Subsequently a semi-classical approximation [3] can be used to describe the resulting phases. The spinless Hubbard model on a square lattice with nearest neighbor repulsion is investigated as a test case. [1] M. Salmhofer and C. Honerkamp, Prog. Theor. Phys. 105, 1 (2001). [2] A. Houghton, H.-J. Kwon, J. B. Marston, Adv.Phys. 49, 141 (2000); P. Kopietz, Bosonization of interacting fermions in arbitrary dimensions, (Springer, Berlin, 1997). [3] H.-H. Lin, L. Balents, M. P. A. Fisher, Phys. Rev. B 56, 6569 6593 (1997); J. O. Fjaerestad, J. B. Marston, U. Schollwoeck, Ann. Phys. (N.Y.) 321, 894 (2006).
Izawa, K; Yamaguchi, H; Matsuda, Y; Shishido, H; Settai, R; Onuki, Y
2001-07-30
The thermal conductivity of the heavy-fermion superconductor CeCoIn5 has been studied in a magnetic field rotating within the 2D planes. A clear fourfold symmetry of the thermal conductivity which is characteristic of a superconducting gap with nodes along the ( +/- pi,+/- pi) directions is resolved. The thermal conductivity measurement also reveals a first-order transition at H(c2), indicating a Pauli limited superconducting state. These results indicate that the symmetry most likely belongs to d(x(2)-y(2)), implying that the anisotropic antiferromagnetic fluctuation is relevant to the superconductivity.
Exponentially fitted symplectic integrator
NASA Astrophysics Data System (ADS)
Simos, T. E.; Vigo-Aguiar, Jesus
2003-01-01
In this paper a procedure for constructing efficient symplectic integrators for Hamiltonian problems is introduced. This procedure is based on the combination of the exponential fitting technique and symplecticness conditions. Based on this procedure, a simple modified Runge-Kutta-Nyström second-order algebraic exponentially fitted method is developed. We give explicitly the symplecticness conditions for the modified Runge-Kutta-Nyström method. We also give the exponential fitting and trigonometric fitting conditions. Numerical results indicate that the present method is much more efficient than the “classical” symplectic Runge-Kutta-Nyström second-order algebraic method introduced by M.P. Calvo and J.M. Sanz-Serna [J. Sci. Comput. (USA) 14, 1237 (1993)]. We note that the present procedure is appropriate for all near-unimodal systems.
Symplectic Clifford Algebraic Field Theory.
NASA Astrophysics Data System (ADS)
Dixon, Geoffrey Moore
We develop a mathematical framework on which is built a theory of fermion, scalar, and gauge vector fields. This field theory is shown to be equivalent to the original Weinberg-Salam model of weak and electromagnetic interactions, but since the new framework is more rigid than that on which the original Weinberg-Salam model was built, a concomitant reduction in the number of assumptions lying outside of the framework has resulted. In particular, parity violation is actually hiding within our framework, and with little difficulty we are able to manifest it. The mathematical framework upon which we build our field theory is arrived at along two separate paths. The first is by the marriage of a Clifford algebra and a Lie superalgebra, the result being called a super Clifford algebra. The second is by providing a new characterization for a Clifford algebra employing its generators and a symmetric array of metric coefficients. Subsequently we generalize this characterization to the case of an antisymmetric array of metric coefficients, and we call the algebra which results a symplectic Clifford algebra. It is upon one of these that we build our field theory, and it is shown that this symplectic Clifford algebra is a particular subalgebra of a super Clifford algebra. The final ingredient is the operation of bracketing which involves treating the elements of our algebra as endomorphisms of a particular inner product space, and employing this space and its inner product to provide us with maps from our algebra to the reals. It is this operation which enables us to manifest the parity violation hiding in our algebra.
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.
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.
NASA Astrophysics Data System (ADS)
Ohsawa, Tomoki
2015-09-01
We show that the Siegel upper half space is identified with the Marsden-Weinstein quotient obtained by symplectic reduction of the cotangent bundle with O(2 d)-symmetry. The reduced symplectic form on corresponding to the standard symplectic form on turns out to be a constant multiple of the symplectic form on obtained by Siegel. Our motivation is to understand the geometry behind two different formulations of the Gaussian wave packet dynamics commonly used in semiclassical mechanics. Specifically, we show that the two formulations are related via the symplectic reduction.
NASA Astrophysics Data System (ADS)
Hairer, Ernst; Zbinden, Christophe J.
2012-09-01
For the long-time integration of Hamiltonian differential equations the use of symplectic methods is recommended. In practice it is often sufficient to apply a method that is conjugate (up to a sufficiently high order) to a symplectic integrator. This article gives a criterion on the conjugate symplecticity of methods that can be represented as a B-series. It allows to characterize the conjugate symplecticity of a large class of numerical integrators including Lobatto IIIA and Lobatto IIIB methods, as well as energy-preserving collocation methods.
Partial dynamical symmetry in a fermion system
Escher; Leviatan
2000-02-28
The relevance of the partial dynamical symmetry concept for an interacting fermion system is demonstrated. Hamiltonians with partial SU(3) symmetry are presented in the framework of the symplectic shell model of nuclei and shown to be closely related to the quadrupole-quadrupole interaction. Implications are discussed for the deformed light nucleus 20Ne.
NASA Astrophysics Data System (ADS)
Slagle, Kevin
2015-03-01
Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions, each with connections to symmetry protected topological states. 1) The first is a continuous phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase. Because there is no spontaneous symmetry breaking, this transition cannot be described by the standard Gross-Neveu model. We argue that this phase transition is related to the Z16 classification of the topological superconductor 3He-B phase with interactions. 2) The second is a quantum critical point between a quantum spin Hall insulator with spin Sz conservation and the previously mentioned strongly interacting gapped phase. At the critical point the single particle excitations remain gapped, while spin and charge gaps close. We argue that this transition is described by a bosonic O(4) nonlinear sigma model field theory with a topological Θ-term.
Pre-symplectic algebroids and their applications
NASA Astrophysics Data System (ADS)
Liu, Jiefeng; Sheng, Yunhe; Bai, Chengming
2017-06-01
In this paper, we introduce the notion of a pre-symplectic algebroid and show that there is a one-to-one correspondence between pre-symplectic algebroids and symplectic Lie algebroids. This result is the geometric generalization of the relation between left-symmetric algebras and symplectic (Frobenius) Lie algebras. Although pre-symplectic algebroids are not left-symmetric algebroids, they still can be viewed as the underlying structures of symplectic Lie algebroids. Then we study exact pre-symplectic algebroids and show that they are classified by the third cohomology group of a left-symmetric algebroid. Finally, we study para-complex pre-symplectic algebroids. Associated with a para-complex pre-symplectic algebroid, there is a pseudo-Riemannian Lie algebroid. The multiplication in a para-complex pre-symplectic algebroid characterizes the restriction to the Lagrangian subalgebroids of the Levi-Civita connection in the corresponding pseudo-Riemannian Lie algebroid.
Symplectic integrators for spin systems
NASA Astrophysics Data System (ADS)
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 R3. 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.
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.
The symplectic group and classical mechanics.
Dragt, Alex J
2005-06-01
The symplectic group is the underlying symmetry group for Hamiltonian dynamics. Yet relatively little is commonly known about its properties including its Lie structure and representations. This paper describes and summarizes some of these properties; and, as a first application of symplectic group theory, provides a symplectic classification of all first-order differential equations in an even number of variables.
Symplecticity in Beam Dynamics: An Introduction
Rees, John R
2003-06-10
A particle in a particle accelerator can often be considered a Hamiltonian system, and when that is the case, its motion obeys the constraints of the Symplectic Condition. This tutorial monograph derives the condition from the requirement that a canonical transformation must yield a new Hamiltonian system from an old one. It then explains some of the consequences of symplecticity and discusses examples of its applications, touching on symplectic matrices, phase space and Liouville's Theorem, Lagrange and Poisson brackets, Lie algebra, Lie operators and Lie transformations, symplectic maps and symplectic integrators.
A pseudo third order symplectic integrator
NASA Astrophysics Data System (ADS)
Liu, Fu-Yao; Wu, Xin; Lu, Ben-Kui
2005-01-01
The symplectic integrator has been regarded as one of the optimal tools for research on qualitative secular evolution of Hamiltonian systems in solar system dynamics. An integrable and separate Hamiltonian system H = H0 + Σi=1NɛiHi (ɛi ≪ 1) forms a pseudo third order symplectic integrator, whose accuracy is approximately equal to that of the first order corrector of the Wisdom-Holman second order symplectic integrator or that of the Forest-Ruth fourth order symplectic integrator. In addition, the symplectic algorithm with force gradients is also suited to the treatment of the Hamiltonian system H = H0(q,p) + ɛH1(q), with accuracy better than that of the original symplectic integrator but not superior to that of the corresponding pseudo higher order symplectic integrator.
Symplectic time integrators for numerical general relativity
Richter, Ronny
2009-05-01
We describe how we use symplectic time integrators in numerical general relativity. Of particular interest is the free symplectic Stoermer-Verlet method and its application to the dynamical part of ADM-like equations.The behavior of this scheme is illustrated on an effectively 1+1-dimensional version of Einstein's equations that we apply to a perturbed Minkowski problem. We discuss differences between symplectic and non-symplectic integrators, showing favorable evolution properties of the symplectic Stoermer-Verlet method in this example.To handle the constraint part of the equations with a symplectic integrator one can use a partially constrained scheme that applies the RATTLE method, a modification of the Stoermer-Verlet method for holonomic constraints.
Nonlinear Symplectic Attitude Estimation for Small Satellites
2006-08-01
accuracy and constants of motion accuracy when applied to standard EKF theory for satellite attitude estimation (symplectic EKF, or SKF ). This...determine the source of the performance difference between the IEKF and the SF, the SF is compared to the symplectic EKF ( SKF ) in Ref 17. The SF is...contrast, the SKF combines a symplectic dynamical model with the standard EKF algorithm. Figure 4 illustrates that, given the same initial conditions
Majorana fermions in vortex lattices
NASA Astrophysics Data System (ADS)
Biswas, Rudro
2013-03-01
We consider Majorana fermions tunneling between vortices, within an array of such vortices in a 2D chiral p-wave superconductor. We calculate that the tunneling amplitude for Majorana fermions in a pair of vortices is proportional to the sine of half the difference between the global order parameter phases at the two vortices. Using this result we study tight-binding models of Majorana fermions in vortices arranged in a triangular or square lattice. In both cases we find that this phase-tunneling relationship leads to the creation of superlattices where the Majorana fermions form macroscopically degenerate `flat' bands at zero energy, in addition to other dispersive bands. This finding suggests that in vortex arrays tunneling processes do not change the energies of a finite fraction of Majorana fermions and hence brighten the prospects of topological quantum computing with a large number of Majorana states.
On Lorentz Transformations in Symplectic Deformations
Cuesta, R.; Sabido, M.; Guzman, W.
2010-07-12
In this paper we study noncommutative Lorentz transformations using symplectic deformations. In this framework we define an infinitesimal line element that is invariant under this noncommutative Lorentz transformations. Using the symplectic geometry formalism, we find that noncommutative Lorentz transformations intertwine the canonical momentums with canonical position coordinates.
On symplectic and symmetric ARKN methods
NASA Astrophysics Data System (ADS)
Shi, Wei; Wu, Xinyuan
2012-06-01
Symplecticness and symmetry are favorable properties for solving Hamiltonian systems. For the oscillatory second-order initial value problems of the form q+ωq=f(q,q), adapted Runge-Kutta-Nyström methods (ARKN methods, in short notation) were investigated by several authors. In a wide range of physical applications from molecular dynamics to nonlinear wave propagation, an important class of the problems is Hamiltonian systems for which symplectic methods should be preferred. Hence it is quite natural to raise a question of the symplecticness for ARKN methods. In this paper we investigate the symplecticness conditions of ARKN methods for separable Hamiltonian systems. We conclude that there exist only one-stage explicit symplectic ARKN (SARKN, in short notation) methods under the symplecticness conditions of ARKN methods. The SARKN methods have a special form and the algebraic order cannot exceed 2. We also point out that no ARKN method can be symmetric. An explicit SARKN method of order two is proposed with the analysis of phase and stability properties. The numerical results accompanied show good performance for the new explicit symplectic algorithm in comparison with the popular symplectic methods in the scientific literature.
On local invariants of singular symplectic forms
NASA Astrophysics Data System (ADS)
Domitrz, Wojciech
2017-04-01
We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a 2 n-dimensional manifold. In the C-analytic category this set consists of the Martinet hypersurface Σ2, the restriction of the singular symplectic form ω to TΣ2 and the kernel of ω n - 1 at the point p ∈Σ2. In the R-analytic and smooth categories this set contains one more invariant: the canonical orientation of Σ2. We find the conditions to determine the kernel of ω n - 1 at p by the other invariants. In dimension 4 we find sufficient conditions to determine the equivalence class of a singular symplectic form-germ with the structurally smooth Martinet hypersurface by the Martinet hypersurface and the restriction of the singular symplectic form to it. We also study the singular symplectic forms with singular Martinet hypersurfaces. We prove that the equivalence class of such singular symplectic form-germ is determined by the Martinet hypersurface, the canonical orientation of its regular part and the restriction of the singular symplectic form to its regular part if the Martinet hypersurface is a quasi-homogeneous hypersurface with an isolated singularity.
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 Technical Reports Server (NTRS)
Wilczek, Frank
1987-01-01
A simple heuristic proof of the Nielsen-Ninomaya theorem is given. A method is proposed whereby the multiplication of fermion species on a lattice is reduced to the minimal doubling, in any dimension, with retention of appropriate chiral symmetries. Also, it is suggested that use of spatially thinned fermion fields is likely to be a useful and appropriate approximation in QCD - in any case, it is a self-checking one.
Composite fermion-boson mapping for fermionic lattice models.
Zhao, J; Jiménez-Hoyos, C A; Scuseria, G E; Huerga, D; Dukelsky, J; Rombouts, S M A; Ortiz, G
2014-11-12
We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic cluster operators. The mapping is an exact isomorphism as long as the physical constraint of one composite particle per cluster is satisfied. This condition is treated on average in a composite particle mean-field approach, which consists of an ansatz that decouples the composite fermionic and bosonic sectors. The theory is tested on the 1D and 2D Hubbard models. Using a Bogoliubov determinant for the composite fermions and either a coherent or Bogoliubov state for the bosons, we obtain a simple and accurate procedure for treating the Mott insulating phase of the Hubbard model with mean-field computational cost.
Symplectic Attitude Estimation for Small Satellites
2006-01-01
give the SKF , which outperforms the standard EKF in the presence of nonlinearity and low measurement noise in the 1-D case. Building on this result, a...six-state SKF is compared to an EKF of the same order for satellite attitude estimation. Simulation of a stan- dard small satellite mission...1-D case, a symplectic propagator is com- bined with Extended Kalman Filter (EKF) equations to give a symplectic Kalman Filter ( SKF ). The SKF’s
Spin Tqfts and Fermionic Phases of Matter
NASA Astrophysics Data System (ADS)
Gaiotto, Davide; Kapustin, Anton
We study lattice constructions of gapped fermionic phases of matter. We show that the construction of fermionic Symmetry Protected Topological orders by Gu and Wen has a hidden dependence on a discrete spin structure on the Euclidean space-time. The spin structure is needed to resolve ambiguities which are otherwise present. An identical ambiguity is shown to arise in the fermionic analog of the string-net construction of 2D topological orders. We argue that the need for a spin structure is a general feature of lattice models with local fermionic degrees of freedom and is a lattice analog of the spinstatistics relation.
Georgi, Howard; Kats, Yevgeny
2008-09-26
We discuss what can be learned about unparticle physics by studying simple quantum field theories in one space and one time dimension. We argue that the exactly soluble 2D theory of a massless fermion coupled to a massive vector boson, the Sommerfield model, is an interesting analog of a Banks-Zaks model, approaching a free theory at high energies and a scale-invariant theory with nontrivial anomalous dimensions at low energies. We construct a toy standard model coupling to the fermions in the Sommerfield model and study how the transition from unparticle behavior at low energies to free particle behavior at high energies manifests itself in interactions with the toy standard model particles.
Symplectic method in quantum cosmology
Silva, E. V. Correa; Monerat, G. A.; Oliveira-Neto, G.; Neves, C.; Ferreira Filho, L. G.
2009-08-15
In the present work, we study the quantum cosmology description of Friedmann-Robertson-Walker models in the presence of a generic perfect fluid and a cosmological constant, which may be positive or negative. We work in Schutz's variational formalism and the three-dimensional spatial sections may have positive, negative, or zero constant curvature. If one uses the scale factor and its canonically conjugated momentum as the phase space variables that describe the geometrical sector of these models, one obtains Wheeler-DeWitt equations with operator ordering ambiguities. In order to avoid those ambiguities and simplify the quantum treatment of the models, we follow references [Edesio M. Barbosa, Jr. and Nivaldo A. Lemos, Gen. Relativ. Gravit. 38, 1609 (2006).][Edesio M. Barbosa, Jr. and Nivaldo A. Lemos, Phys. Rev. D 78, 023504 (2008).] and introduce new phase space variables. We explicitly demonstrate, using the symplectic method, that the transformation leading from the old set of variables to the new one is canonical.
On the symplectic structure of harmonic superspace
Kachkachi, M.; Saidi, E.H. )
1992-11-10
In this paper, the symplectic properties of harmonic superspace are studied. It is shown that Diff(S[sup 2]) is isomorphic to Diff[sub 0](S[sup 3])/Ab(Diff[sub 0](S[sup 3])), where Diff[sub 0](S[sup 3]) is the group of the diffeomorphisms of S[sup 3] preserving the Cartan charge operator D[sup 0] and Ab(Diff[sub 0](S[sup 3])) is its Abelian subgroup generated by the Cartan vectors L[sub 0] = w[sup 0]D[sup 0]. The authors show also that the eigenvalue equation D[sup 0] [lambda](z) = 0 defines a symplectic structure in harmonic superspace, and the authors calculate the corresponding algebra. The general symplectic invariant coupling of the Maxwell prepotential is constructed in both flat and curved harmonic superspace. Other features are discussed.
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.
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.
Fermion masses through four-fermion condensates
Ayyar, Venkitesh; Chandrasekharan, Shailesh
2016-10-12
Fermion masses can be generated through four-fermion condensates when symmetries prevent fermion bilinear condensates from forming. This less explored mechanism of fermion mass generation is responsible for making four reduced staggered lattice fermions massive at strong couplings in a lattice model with a local four-fermion coupling. The model has a massless fermion phase at weak couplings and a massive fermion phase at strong couplings. In particular there is no spontaneous symmetry breaking of any lattice symmetries in both these phases. Recently it was discovered that in three space-time dimensions there is a direct second order phase transition between the two phases. Here we study the same model in four space-time dimensions and find results consistent with the existence of a narrow intermediate phase with fermion bilinear condensates, that separates the two asymptotic phases by continuous phase transitions.
Fermion masses through four-fermion condensates
Ayyar, Venkitesh; Chandrasekharan, Shailesh
2016-10-12
Fermion masses can be generated through four-fermion condensates when symmetries prevent fermion bilinear condensates from forming. This less explored mechanism of fermion mass generation is responsible for making four reduced staggered lattice fermions massive at strong couplings in a lattice model with a local four-fermion coupling. The model has a massless fermion phase at weak couplings and a massive fermion phase at strong couplings. In particular there is no spontaneous symmetry breaking of any lattice symmetries in both these phases. Recently it was discovered that in three space-time dimensions there is a direct second order phase transition between the twomore » phases. Here we study the same model in four space-time dimensions and find results consistent with the existence of a narrow intermediate phase with fermion bilinear condensates, that separates the two asymptotic phases by continuous phase transitions.« less
A possible symplectic framework for Radon-type transforms
NASA Astrophysics Data System (ADS)
Cahen, Michel; Grouy, Thibaut; Gutt, Simone
2016-07-01
Our project is to define Radon-type transforms in symplectic geometry. The chosen framework consists of symplectic symmetric spaces whose canonical connection is of Ricci-type. They can be considered as symplectic analogues of the spaces of constant holomorphic curvature in Kählerian Geometry. They are characterized amongst a class of symplectic manifolds by the existence of many totally geodesic symplectic submanifolds. We present a particular class of Radon type transforms, associating to a smooth compactly supported function on a homogeneous manifold M, a function on a homogeneous space N of totally geodesic submanifolds of M, and vice versa. We describe some spaces M and N in such Radon-type duality with M a model of symplectic symmetric space with Ricci-type canonical connection and N an orbit of totally geodesic symplectic submanifolds.
On the Langlands correspondence for symplectic motives
NASA Astrophysics Data System (ADS)
Gross, B. H.
2016-08-01
We present a refinement of the global Langlands correspondence for symplectic motives. Using the local theory of generic representations of odd orthogonal groups, we define a new vector in the associated automorphic representation, which is the tensor product of test vectors for the Whittaker functionals.
Hamiltonian vector fields on almost symplectic manifolds
NASA Astrophysics Data System (ADS)
Vaisman, Izu
2013-09-01
Let (M, ω) be an almost symplectic manifold (ω is a nondegenerate, not closed, 2-form). We say that a vector field X of M is locally Hamiltonian if LXω = 0, d(i(X)ω) = 0, and it is Hamiltonian if, furthermore, the 1-form i(X)ω is exact. Such vector fields were considered in Fassò and Sansonetto ["Integrable almost-symplectic Hamiltonian systems," J. Math. Phys. 48, 092902 (2007)], 10.1063/1.2783937, under the name of strongly Hamiltonian, and a corresponding action-angle theorem was proven. Almost symplectic manifolds may have few, nonzero, Hamiltonian vector fields, or even none. Therefore, it is important to have examples and it is our aim to provide such examples here. We also obtain some new general results. In particular, we show that the locally Hamiltonian vector fields generate a Dirac structure on M and we state a reduction theorem of the Marsden-Weinstein type. A final section is dedicated to almost symplectic structures on tangent bundles.
Symplectic integration approach for metastable systems
NASA Astrophysics Data System (ADS)
Klotins, E.
2006-03-01
Nonadiabatic behavior of metastable systems modeled by anharmonic Hamiltonians is reproduced by the Fokker-Planck and imaginary time Schrödinger equation scheme with subsequent symplectic integration. Example solutions capture ergodicity breaking, reassure the H-theorem of global stability [M. Shiino, Phys. Rev. A 36, 2393 (1987)], and reproduce spatially extended response under alternate source fields.
Majorana Fermions in Vortex Lattices
NASA Astrophysics Data System (ADS)
Biswas, Rudro R.
2013-09-01
We consider Majorana fermions tunneling among an array of vortices in a 2D chiral p-wave superconductor or equivalent material. The amplitude for Majorana fermions to tunnel between a pair of vortices is found to necessarily depend on the background superconducting phase profile; it is found to be proportional to the sine of half the difference between the phases at the two vortices. Using this result we study tight-binding models of Majorana fermions in vortices arranged in triangular or square lattices. In both cases we find that the aforementioned phase-tunneling relationship leads to the creation of superlattices where the Majorana fermions form macroscopically degenerate localizable flat bands at zero energy, in addition to other dispersive bands. This finding suggests that tunneling processes in these vortex arrays do not change the energies of a finite fraction of Majorana fermions, contrary to previous expectation. The presence of flat Majorana bands, and hence less-than-expected decoherence in these vortex arrays, bodes well for the prospects of topological quantum computation with large numbers of Majorana states.
Majorana fermions in vortex lattices.
Biswas, Rudro R
2013-09-27
We consider Majorana fermions tunneling among an array of vortices in a 2D chiral p-wave superconductor or equivalent material. The amplitude for Majorana fermions to tunnel between a pair of vortices is found to necessarily depend on the background superconducting phase profile; it is found to be proportional to the sine of half the difference between the phases at the two vortices. Using this result we study tight-binding models of Majorana fermions in vortices arranged in triangular or square lattices. In both cases we find that the aforementioned phase-tunneling relationship leads to the creation of superlattices where the Majorana fermions form macroscopically degenerate localizable flat bands at zero energy, in addition to other dispersive bands. This finding suggests that tunneling processes in these vortex arrays do not change the energies of a finite fraction of Majorana fermions, contrary to previous expectation. The presence of flat Majorana bands, and hence less-than-expected decoherence in these vortex arrays, bodes well for the prospects of topological quantum computation with large numbers of Majorana states.
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.
The Categorification of Fermions
NASA Astrophysics Data System (ADS)
Wang, Na; Wang, Rui; Wang, Zhi-Xi; Wu, Ke; Yang, Jie; Yang, Zi-Feng
2015-02-01
In this paper, we lift Fermions to functors acting on some homotopy category by the Boson-Fermion correspondence and get the categorified relations of Fermions. In this way, both the categorified Bosons and the categorified Fermions can be viewed as functors on the same category. We also give actions of these functors on the charged Young diagrams (or equivalently Maya diagrams), so that the classical theory of Boson-Fermion correspondence is very well recovered as a result of such a categorification.
Symplectic integrator for molecular dynamics of a protein in water
NASA Astrophysics Data System (ADS)
Ishida, Hisashi; Nagai, Yoshinori; Kidera, Akinori
1998-01-01
The symplectic integrator is an algorithm for solving equations of motion, preserving the volume in phase space and ensuring a stable simulation. We carried out molecular dynamics simulations of liquid water and a protein in water using several variations of symplectic integrators. It was found that a fourth-order symplectic integrator of Calvo and Sanz-Serna generated a trajectory of much higher accuracy than the conventional Verlet and Gear methods with the same requirements for CPU time.
Symplectic discretization for spectral element solution of Maxwell's equations
NASA Astrophysics Data System (ADS)
Zhao, Yanmin; Dai, Guidong; Tang, Yifa; Liu, Qinghuo
2009-08-01
Applying the spectral element method (SEM) based on the Gauss-Lobatto-Legendre (GLL) polynomial to discretize Maxwell's equations, we obtain a Poisson system or a Poisson system with at most a perturbation. For the system, we prove that any symplectic partitioned Runge-Kutta (PRK) method preserves the Poisson structure and its implied symplectic structure. Numerical examples show the high accuracy of SEM and the benefit of conserving energy due to the use of symplectic methods.
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.
Comparison of several symplectic and quasi-symplectic methods in solar system dynamics
NASA Astrophysics Data System (ADS)
Wan, Xiaosheng; Huang, Tianyi
2002-07-01
Symplectic methods are so far the best numerical methods for qualitative exploration in solar system dynamics. They maintain the symplectic structure and key properties of Hamiltonian systems and do not bring in any artificial dissipation, making possible long-term numerical integrations with a large step size. The symplectic method that has been widely adopted in references on qualitative studies of solar system dynamics is the method worked out by Wisdom and Holman (SYA). It is built in the Jacobian coordinate system and takes an approximation of the Hamiltonian. The Wisdom and Holman's method for an exact Hamiltonian is abbreviated as SYP. Actually a symplectic integrator can be built in the barycentric coordinate system (SYS), which separates the Hamiltonian into two parts, the potential energy and the kinetic energy. Here we propose a quasi-symplectic method SYQ in the barycentric coordinate system. An extensive comparative study of these four types of methods is given, especially on their computation efficiency and error accumulation. This research draws the following conclusion. Considering that symplectic integrators are mainly used in exploring the qualitative evolution of dynamical systems and a high precision is not required, SYS should not be recommended in solar system dynamics for its low efficiency. During a 108 years integration, SYP methods cause almost the same errors on the positions of the planets but they take about 40% more computing time. We thus believe that SYP cannot compete with SYA or SYQ, but it is hard to tell SYA or SYQ is better. Our research has also shown that resonances play a role in keeping the orbit configuration of a planetary system during long-term numerical integrations.
Semiclassical approach to dynamics of interacting fermions
NASA Astrophysics Data System (ADS)
Davidson, Shainen M.; Sels, Dries; Polkovnikov, Anatoli
2017-09-01
Understanding the behaviour of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of this. Already in equilibrium, fermions are notoriously hard to handle due to the sign problem. Out of equilibrium, an important outstanding problem is the efficient numerical simulation of the dynamics of these systems. In this work we develop a new semiclassical phase-space approach (a.k.a. the truncated Wigner approximation) for simulating the dynamics of interacting fermions in arbitrary dimensions. As fermions are essentially non-classical objects, a phase-space is constructed out of all fermionic bilinears. Classical phase-space is thus comprised of highly non-local (hidden) variables representing these bilinears, and the cost of the method is that it scales quadratic rather than linear with system size. We demonstrate the strength of the method by comparing the results to the exact quantum dynamics of fermion expansion in the Hubbard model and quantum thermalization in the Sachdev-Ye-Kitaev (SYK) model for small systems, where the semiclassics nearly perfectly reproduces correct results. We furthermore analyse fermion expansion in a larger, intractable by exact methods, 2D Hubbard model, which is directly relevant to recent cold atom experiments.
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.
A Symplectic Integrator for Hill's Equations
NASA Astrophysics Data System (ADS)
Quinn, Thomas; Perrine, Randall P.; Richardson, Derek C.; Barnes, Rory
2010-02-01
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.
Higher-order force gradient symplectic algorithms
NASA Astrophysics Data System (ADS)
Chin, Siu A.; Kidwell, Donald W.
2000-12-01
We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to similarly iterated higher order algorithms based on the standard Forest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the step-size independent error functions associated with energy conservation and the rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric Kepler problem. For orders 6, 8, 10, and 12, the new algorithms are approximately a factor of 103, 104, 104, and 105 better.
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.
Reduced dynamics and Lagrangian submanifolds of symplectic manifolds
NASA Astrophysics Data System (ADS)
García-Toraño Andrés, E.; Guzmán, E.; Marrero, J. C.; Mestdag, T.
2014-06-01
In this paper, we will see that the symplectic creed by Weinstein ‘everything is a Lagrangian submanifold’ also holds for Hamilton-Poincaré and Lagrange-Poincaré reduction. In fact, we show that solutions of the Hamilton-Poincaré equations and of the Lagrange-Poincaré equations are in one-to-one correspondence with distinguished curves in a Lagrangian submanifold of a symplectic manifold. For this purpose, we will combine the concept of a Tulczyjew triple with Marsden-Weinstein symplectic reduction.
Heavy fermion quantum criticality.
Nazario, Zaira; Santiago, David I
2008-09-26
During the last few years, investigations of rare-earth materials have made clear that heavy fermion quantum criticality exhibits novel physics not fully understood. In this work, we write for the first time the effective action describing the low energy physics of the system. The f fermions are replaced by a dynamical scalar field whose nonzero expected value corresponds to the heavy fermion phase. The effective theory is amenable to numerical studies as it is bosonic, circumventing the fermion sign problem. Via effective action techniques, renormalization group studies, and Callan-Symanzik resummations, we describe the heavy fermion criticality and predict the heavy fermion critical dynamical susceptibility and critical specific heat. The specific heat coefficient exponent we obtain (0.39) is in excellent agreement with the experimental result at low temperatures (0.4).
Unity of quark and lepton interactions with symplectic gauge symmetry
Rajpoot, S.
1982-07-01
Properties of symplectic groups are reviewed and the gauge structure of Sp(2n) derived. The electroweak unification of leptons within Sp(8) gauge symmetry and grand unification of quarks and leptons within Sp(10) gauge symmetry are discussed.
Poisson and symplectic structures on Lie algebras. I
NASA Astrophysics Data System (ADS)
Alekseevsky, D. V.; Perelomov, A. M.
1997-06-01
The purpose of this paper is to describe a new class of Poisson and symplectic structures on Lie algebras. This gives a new class of solutions of the classical Yang-Baxter equation. The class of elementary Lie algebras is defined and the Poisson and symplectic structures for them are described. The algorithm is given for description of all closed 2-forms and of symplectic structures on any Lie algebra G, which is decomposed into semidirect sum of elementary subalgebras. Using these results we obtain the description of closed 2-forms and symplectic forms (if they exist) on the Borel subalgebra B(G) of semisimple Lie algebra G. As a byproduct, we get description of the second cohomology group H2( B( G)).
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.
k-Symplectic Lie systems: theory and applications
NASA Astrophysics Data System (ADS)
de Lucas, J.; Vilariño, S.
2015-03-01
A Lie system is a system of first-order ordinary differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional real Lie algebra of vector fields: a so-called Vessiot-Guldberg Lie algebra. We suggest the definition of a particular class of Lie systems, the k-symplectic Lie systems, admitting a Vessiot-Guldberg Lie algebra of Hamiltonian vector fields with respect to the presymplectic forms of a k-symplectic structure. We devise new k-symplectic geometric methods to study their superposition rules, t-independent constants of motion and general properties. Our results are illustrated through examples of physical and mathematical interest. As a byproduct, we find a new interesting setting of application of the k-symplectic geometry: systems of first-order ordinary differential equations.
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.
Symplectic test particle encounters: a comparison of methods
NASA Astrophysics Data System (ADS)
Wisdom, Jack
2017-01-01
A new symplectic method for handling encounters of test particles with massive bodies is presented. The new method is compared with several popular methods (RMVS3, SYMBA, and MERCURY). The new method compares favourably.
On the n-symplectic structure of faithful irreducible representations
NASA Astrophysics Data System (ADS)
Norris, L. K.
2017-04-01
Each faithful irreducible representation of an N-dimensional vector space V1 on an n-dimensional vector space V2 is shown to define a unique irreducible n-symplectic structure on the product manifold V1×V2 . The basic details of the associated Poisson algebra are developed for the special case N = n2, and 2n-dimensional symplectic submanifolds are shown to exist.
A modified symplectic PRK scheme for seismic wave modeling
NASA Astrophysics Data System (ADS)
Liu, Shaolin; Yang, Dinghui; Ma, Jian
2017-02-01
A new scheme for the temporal discretization of the seismic wave equation is constructed based on symplectic geometric theory and a modified strategy. The ordinary differential equation in terms of time, which is obtained after spatial discretization via the spectral-element method, is transformed into a Hamiltonian system. A symplectic partitioned Runge-Kutta (PRK) scheme is used to solve the Hamiltonian system. A term related to the multiplication of the spatial discretization operator with the seismic wave velocity vector is added into the symplectic PRK scheme to create a modified symplectic PRK scheme. The symplectic coefficients of the new scheme are determined via Taylor series expansion. The positive coefficients of the scheme indicate that its long-term computational capability is more powerful than that of conventional symplectic schemes. An exhaustive theoretical analysis reveals that the new scheme is highly stable and has low numerical dispersion. The results of three numerical experiments demonstrate the high efficiency of this method for seismic wave modeling.
Symmetries of the Space of Linear Symplectic Connections
NASA Astrophysics Data System (ADS)
Fox, Daniel J. F.
2017-01-01
There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt moment map, the Ricci tensor, and a translational term. The critical points of a functional constructed from it interpolate between the equations for preferred symplectic connections and the equations for critical symplectic connections. The commutative algebra of formal sums of symmetric tensors on a symplectic manifold carries a pair of compatible Poisson structures, one induced from the canonical Poisson bracket on the space of functions on the cotangent bundle polynomial in the fibers, and the other induced from the algebraic fiberwise Schouten bracket on the symmetric algebra of each fiber of the cotangent bundle. These structures are shown to be compatible, and the required Lie algebras are constructed as central extensions of their! linear combinations restricted to formal sums of symmetric tensors whose first order term is a multiple of the differential of its zeroth order term.
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.
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
A symplectic coherent beam-beam model
Furman, M.A.
1989-05-01
We consider a simple one-dimensional model to study the effects of the beam-beam force on the coherent dynamics of colliding beams. The key ingredient is a linearized beam-beam kick. We study only the quadrupole modes, with the dynamical variables being the 2nd-order moments of the canonical variables q, p. Our model is self-consistent in the sense that no higher order moments are generated by the linearized beam-beam kicks, and that the only source of violation of symplecticity is the radiation. We discuss the round beam case only, in which vertical and horizontal quantities are assumed to be equal (though they may be different in the two beams). Depending on the values of the tune and beam intensity, we observe steady states in which otherwise identical bunches have sizes that are equal, or unequal, or periodic, or behave chaotically from turn to turn. Possible implications of luminosity saturation with increasing beam intensity are discussed. Finally, we present some preliminary applications to an asymmetric collider. 8 refs., 8 figs.
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.
Iliesiu, Luca; Kos, Filip; Poland, David; ...
2016-03-17
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 CT. We observe features in our bounds that coincide with scaling dimensions in the GrossNeveu models at large N. Finally, we also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.
Iliesiu, Luca; Kos, Filip; Poland, David; Pufu, Silviu S.; Simmons-Duffin, David; Yacoby, Ran
2016-03-17
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. Finally, we also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.
DPI: Symplectic mapping for binary star systems for the Mercury software package
NASA Astrophysics Data System (ADS)
Turrini, D.
2015-04-01
DPI is a FORTRAN77 library that supplies the symplectic mapping method for binary star systems for the Mercury N-Body software package (ascl:1201.008). The binary symplectic mapping is implemented as a hybrid symplectic method that allows close encounters and collisions between massive bodies and is therefore suitable for planetary accretion simulations.
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 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).
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.
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.
Explicit K-symplectic algorithms for charged particle dynamics
NASA Astrophysics Data System (ADS)
He, Yang; Zhou, Zhaoqi; Sun, Yajuan; Liu, Jian; Qin, Hong
2017-02-01
We study the Lorentz force equation of charged particle dynamics by considering its K-symplectic structure. As the Hamiltonian of the system can be decomposed as four parts, we are able to construct the numerical methods that preserve the K-symplectic structure based on Hamiltonian splitting technique. The newly derived numerical methods are explicit, and are shown in numerical experiments to be stable over long-term simulation. The error convergency as well as the long term energy conservation of the numerical solutions is also analyzed by means of the Darboux transformation.
Symmetric and symplectic ERKN methods for oscillatory Hamiltonian systems
NASA Astrophysics Data System (ADS)
Chen, Zhaoxia; You, Xiong; Shi, Wei; Liu, Zhongli
2012-01-01
The ERKN methods proposed by H. Yang et al. [Comput. Phys. Comm. 180 (2009) 1777] are an important improvement of J.M. Franco's ARKN methods for perturbed oscillators [J.M. Franco, Comput. Phys. Comm. 147 (2002) 770]. This paper focuses on the symmetry and symplecticity conditions for ERKN methods solving oscillatory Hamiltonian systems. Two examples of symmetric and symplectic ERKN (SSERKN) methods of orders two and four respectively are constructed. The phase and stability properties of the new methods are analyzed. The results of numerical experiments show the robustness and competence of the SSERKN methods compared with some well-known methods in the literature.
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 and multisymplectic Lobatto methods for the ``good'' Boussinesq equation
NASA Astrophysics Data System (ADS)
Aydın, A.; Karasözen, B.
2008-08-01
In this paper, we construct second order symplectic and multisymplectic integrators for the "good" Boussineq equation using the two-stage Lobatto IIIA-IIIB partitioned Runge-Kutta method, which yield an explicit scheme and is equivalent to the classical central difference approximation to the second order spatial derivative. Numerical dispersion properties and the stability of both integrators are investigated. Numerical results for different solitary wave solutions confirm the excellent long time behavior of symplectic and multisymplectic integrators by preserving local and global energy and momentum.
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.
Triplet fermions and Dirac fermions in borophene
NASA Astrophysics Data System (ADS)
Ezawa, Motohiko
2017-07-01
Borophene is a monolayer materials made of boron. A perfect planar boropehene called β12 borophene has Dirac cones and they are well reproduced by a tight-binding model according to recent experimental and first-principles calculation results. We explicitly derive a Dirac theory for β12 borophene. Dirac cones are gapless when the inversion symmetry exists, while they are gapped when it is broken. In addition, three-band touching points emerge together with pseudospin triplet fermions when all transfer energy is equal and all onsite energy is equal. The three-band touching is slightly resolved otherwise. We construct effective three-band theories for triplet fermions. We also study the edge states of borophene nanoribbons, which show various behaviors depending on the way of edge terminations.
2D semiconductor optoelectronics
NASA Astrophysics Data System (ADS)
Novoselov, Kostya
The advent of graphene and related 2D materials has recently led to a new technology: heterostructures based on these atomically thin crystals. The paradigm proved itself extremely versatile and led to rapid demonstration of tunnelling diodes with negative differential resistance, tunnelling transistors, photovoltaic devices, etc. By taking the complexity and functionality of such van der Waals heterostructures to the next level we introduce quantum wells engineered with one atomic plane precision. Light emission from such quantum wells, quantum dots and polaritonic effects will be discussed.
Highly Anisotropic Dirac Fermions in Square Graphynes.
Zhang, L Z; Wang, Z F; Wang, Zhiming M; Du, S X; Gao, H-J; Liu, Feng
2015-08-06
We predict a family of 2D carbon (C) allotropes, square graphynes (S-graphynes) that exhibit highly anisotropic Dirac fermions, using first-principle calculations within density functional theory. They have a square unit-cell containing two sizes of square C rings. The equal-energy contour of their 3D band structure shows a crescent shape, and the Dirac crescent has varying Fermi velocities from 0.6 × 10(5) to 7.2 × 10(5) 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. S-graphynes may be used to build new 2D electronic devices taking advantages of their highly directional charge transport.
Critical exponents from infinite-dimensional symplectic algebras
NASA Astrophysics Data System (ADS)
Altschüler, D.
1985-11-01
Unitary representations of the Virasoro algebra with centrala c = 1 - 6/(n + 2) are important in the study of two-dimensional models in statistical mechanics. It is shown that they can be constructed using Kac-Moody algebras of symplectic type. At the same time, this provides a simple derivation of the critical exponents.
Lorentzian affine hypersurfaces with an almost symplectic form
NASA Astrophysics Data System (ADS)
Szancer, Michal
2017-09-01
In this paper, we study affine hypersurfaces with a Lorentzian second fundamental form additionally equipped with an almost symplectic structure ω. We prove that the rank of the shape operator is at most one if the hypersurface is of dimension at least 6 and Rk ṡ ω = 0 or ∇k ω = 0 for some positive integer k.
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.
Singularly Weighted Symplectic Forms and Applications to Asteroid Motion
NASA Astrophysics Data System (ADS)
Varadi, F.; de La Barre, C. M.; Kaula, W. M.; Ghil, M.
1995-05-01
New techniques to study Hamiltonian systems with Hamiltonian forcing are proposed. They are based on singularly weighted symplectic forms and transformations which preserve these forms. Applications pertaining to asteroid motion are outlined. These involve the presence of both Jupiter and Saturn.
Polygon sign rules of Majorana fermions in two-dimensional topological superconductors
NASA Astrophysics Data System (ADS)
Cheng, Qiu-Bo; He, Jing; Yu, Jing; Zhao, Xiao-Ming; Kou, Su-Peng
2016-09-01
Recently, Majorana fermions (MFs) have attracted intensive attention due to their exotic statistics and possible applications in topological quantum computation. They are proposed to exist in various two-dimensional (2D) topological systems, such as px + ipy topological superconductor (SC) and nanowire-superconducting hybridization system. In this paper, we point out that Majorana fermions in different topological systems obey different types of polygon sign rules. A numerical approach is described to identify the type of polygon sign rule of the Majorana fermions. Applying the approach to study two 2D topological systems, we find that vortex-induced Majorana fermions obey topological polygon sign rule and line-defect-induced Majorana fermions obey normal polygon sign rule.
Scattering of fermions by gravitons
NASA Astrophysics Data System (ADS)
Ulhoa, S. C.; Santos, A. F.; Khanna, Faqir C.
2017-04-01
The interaction between gravitons and fermions is investigated in the teleparallel gravity. The scattering of fermions and gravitons in the weak field approximation is analyzed. The transition amplitudes of M\\varnothing ller, Compton and new gravitational scattering are calculated.
Kalos, M. H.; Pederiva, F.
1998-12-01
We review the fundamental challenge of fermion Monte Carlo for continuous systems, the "sign problem". We seek that eigenfunction of the many-body Schriodinger equation that is antisymmetric under interchange of the coordinates of pairs of particles. We describe methods that depend upon the use of correlated dynamics for pairs of correlated walkers that carry opposite signs. There is an algorithmic symmetry between such walkers that must be broken to create a method that is both exact and as effective as for symmetric functions, In our new method, it is broken by using different "guiding" functions for walkers of opposite signs, and a geometric correlation between steps of their walks, With a specific process of cancellation of the walkers, overlaps with antisymmetric test functions are preserved. Finally, we describe the progress in treating free-fermion systems and a fermion fluid with 14 ^{3}He atoms.
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.
NASA Astrophysics Data System (ADS)
Tsekov, R.
2017-04-01
Thermodynamically, bosons and fermions differ by their statistics only. A general entropy functional is proposed by superposition of entropic terms, typical for different quantum gases. The statistical properties of the corresponding Janus particles are derived by variation of the weight of the boson/fermion fraction. It is shown that di-bosons and anti-fermions separate in gas and liquid phases, while three-phase equilibrium appears for poly-boson/fermion Janus particles.
Bipartite Composite Fermion States
NASA Astrophysics Data System (ADS)
Sreejith, G. J.; Tőke, C.; Wójs, A.; Jain, J. K.
2011-08-01
We study a class of ansatz wave functions in which composite fermions form two correlated “partitions.” These “bipartite” composite fermion states are demonstrated to be very accurate for electrons in a strong magnetic field interacting via a short-range 3-body interaction potential over a broad range of filling factors. Furthermore, this approach gives accurate approximations for the exact Coulomb ground state at 2+3/5 and 2+4/7 and is thus a promising candidate for the observed fractional quantum Hall states at the hole conjugate fractions at 2+2/5 and 2+3/7.
Bipartite composite fermion States.
Sreejith, G J; Toke, C; Wójs, A; Jain, J K
2011-08-19
We study a class of ansatz wave functions in which composite fermions form two correlated "partitions." These "bipartite" composite fermion states are demonstrated to be very accurate for electrons in a strong magnetic field interacting via a short-range 3-body interaction potential over a broad range of filling factors. Furthermore, this approach gives accurate approximations for the exact Coulomb ground state at 2+3/5 and 2+4/7 and is thus a promising candidate for the observed fractional quantum Hall states at the hole conjugate fractions at 2+2/5 and 2+3/7.
Interacting fermionic symmetry-protected topological phases in two dimensions
NASA Astrophysics Data System (ADS)
Wang, Chenjie; Lin, Chien-Hung; Gu, Zheng-Cheng
2017-05-01
We classify and construct models for two-dimensional (2D) interacting fermionic symmetry-protected topological (FSPT) phases with general finite Abelian unitary symmetry Gf. To obtain the classification, we couple the FSPT system to a dynamical discrete gauge field with gauge group Gf and study braiding statistics in the resulting gauge theory. Under reasonable assumptions, the braiding statistics data allows us to infer a potentially complete classification of 2D FSPT phases with Abelian symmetry. The FSPT models that we construct are simple stacks of the following two kinds of existing models: (i) free-fermion models and (ii) models obtained through embedding of bosonic symmetry-protected topological (BSPT) phases. Interestingly, using these two kinds of models, we are able to realize almost all FSPT phases in our classification, except for one class. We argue that this exceptional class of FSPT phases can never be realized through models (i) and (ii), and therefore can be thought of as intrinsically interacting and intrinsically fermionic. The simplest example of this class is associated with Z4f×Z4×Z4 symmetry. In addition, we show that all 2D FSPT phases with a finite Abelian symmetry of the form Z2f×G can be realized through the above models (i), (ii), or a simple stack of them. Finally, we study the stability of BSPT phases when they are embedded into fermionic systems.
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.
Fermionic T-duality in fermionic double space
NASA Astrophysics Data System (ADS)
Nikolić, B.; Sazdović, B.
2017-04-01
In this article we offer the interpretation of the fermionic T-duality of the type II superstring theory in double space. We generalize the idea of double space doubling the fermionic sector of the superspace. In such doubled space fermionic T-duality is represented as permutation of the fermionic coordinates θα and θbarα with the corresponding fermionic T-dual ones, ϑα and ϑbarα, respectively. Demanding that T-dual transformation law has the same form as initial one, we obtain the known form of the fermionic T-dual NS-R and R-R background fields. Fermionic T-dual NS-NS background fields are obtained under some assumptions. We conclude that only symmetric part of R-R field strength and symmetric part of its fermionic T-dual contribute to the fermionic T-duality transformation of dilaton field and analyze the dilaton field in fermionic double space. As a model we use the ghost free action of type II superstring in pure spinor formulation in approximation of constant background fields up to the quadratic terms.
Notes on spinning operators in fermionic CFT
NASA Astrophysics Data System (ADS)
Giombi, S.; Kirilin, V.; Skvortsov, E.
2017-05-01
The Gross-Neveu model defines a unitary CFT of interacting fermions in 2 < d < 4 which has perturbative descriptions in the 1 /N expansion and in the epsilon-expansion near two and four dimensions. In each of these descriptions, the CFT has an infinite tower of nearly conserved currents of all spins. We determine the structure of the non-conservation equations both at large N and in the epsilon-expansion, and use it to find the leading order anomalous dimensions of the broken currents. Similarly, we use the fact that the CFT spectrum includes a nearly free fermion to fix the leading anomalous dimensions of a few scalar composite operators. We also compute the scaling dimensions of double-trace spinning operators in the large N expansion, which correspond to interaction energies of two-particle states in the AdS dual higher-spin theory. We first derive these anomalous dimensions by a direct Feynman diagram calculation, and then show that the result can be exactly reproduced by analytic bootstrap methods, provided the sum over the tower of weakly broken higher-spin currents is suitably regularized. Finally, we apply the analytic bootstrap approach to derive the anomalous dimensions of the double-trace spinning operators in the 3d bosonic and fermion vector models coupled to Chern-Simons theory, to leading order in 1 /N but exactly in the `t Hooft coupling.
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.
Second-order evaluations of orthogonal and symplectic Yangians
NASA Astrophysics Data System (ADS)
Karakhanyan, D. R.; Kirschner, R.
2017-08-01
Orthogonal or symplectic Yangians are defined by the Yang-Baxter RLL relation involving the fundamental R-matrix with the corresponding so( n) or sp(2 m) symmetry. We investigate the second-order solution conditions, where the expansion of L( u) in u -1 is truncated at the second power, and we derive the relations for the two nontrivial terms in L( u).
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.
Trees, B-series and G-symplectic methods
NASA Astrophysics Data System (ADS)
Butcher, J. C.
2017-07-01
The order conditions for Runge-Kutta methods are intimately connected with the graphs known as rooted trees. The conditions can be expressed in terms of Taylor expansions written as weighted sums of elementary differentials, that is as B-series. Polish notation provides a unifying structure for representing many of the quantities appearing in this theory. Applications include the analysis of general linear methods with special reference to G-symplectic methods. A new order 6 method has recently been constructed.
Aubry-Mather Theory for Conformally Symplectic Systems
NASA Astrophysics Data System (ADS)
Marò, Stefano; Sorrentino, Alfonso
2017-09-01
In this article we develop an analogue of Aubry-Mather theory for a class of dissipative systems, namely conformally symplectic systems, and prove the existence of interesting invariant sets, which, in analogy to the conservative case, will be called the Aubry and the Mather sets. Besides describing their structure and their dynamical significance, we shall analyze their attracting/repelling properties, as well as their noteworthy role in driving the asymptotic dynamics of the system.
Splitting K-symplectic methods for non-canonical separable Hamiltonian problems
NASA Astrophysics Data System (ADS)
Zhu, Beibei; Zhang, Ruili; Tang, Yifa; Tu, Xiongbiao; Zhao, Yue
2016-10-01
Non-canonical Hamiltonian systems have K-symplectic structures which are preserved by K-symplectic numerical integrators. There is no universal method to construct K-symplectic integrators for arbitrary non-canonical Hamiltonian systems. However, in many cases of interest, by using splitting, we can construct explicit K-symplectic methods for separable non-canonical systems. In this paper, we identify situations where splitting K-symplectic methods can be constructed. Comparative numerical experiments in three non-canonical Hamiltonian problems show that symmetric/non-symmetric splitting K-symplectic methods applied to the non-canonical systems are more efficient than the same-order Gauss' methods/non-symmetric symplectic methods applied to the corresponding canonicalized systems; for the non-canonical Lotka-Volterra model, the splitting algorithms behave better in efficiency and energy conservation than the K-symplectic method we construct via generating function technique. In our numerical experiments, the favorable energy conservation property of the splitting K-symplectic methods is apparent.
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.
Gauge properties of the guiding center variational symplectic integrator
NASA Astrophysics Data System (ADS)
Squire, J.; Qin, H.; Tang, W. M.
2012-05-01
Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008); H. Qin, X. Guan, and W. Tang, Phys. Plasmas (2009); J. Li, H. Qin, Z. Pu, L. Xie, and S. Fu, Phys. Plasmas 18, 052902 (2011)]. 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 φ 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 law [J. Squire, H. Qin, and W. Tang (to be published)].
Multi-symplectic, Lagrangian, one-dimensional gas dynamics
NASA Astrophysics Data System (ADS)
Webb, G. M.
2015-05-01
The equations of Lagrangian, ideal, one-dimensional, compressible gas dynamics are written in a multi-symplectic form using the Lagrangian mass coordinate m and time t as independent variables, and in which the Eulerian position of the fluid element x = x(m, t) is one of the dependent variables. This approach differs from the Eulerian, multi-symplectic approach using Clebsch variables. Lagrangian constraints are used to specify equations for xm, xt, and St consistent with the Lagrangian map, where S is the entropy of the gas. We require St = 0 corresponding to advection of the entropy S with the flow. We show that the Lagrangian Hamiltonian equations are related to the de Donder-Weyl multi-momentum formulation. The pullback conservation laws and the symplecticity conservation laws are discussed. The pullback conservation laws correspond to invariance of the action with respect to translations in time (energy conservation) and translations in m in Noether's theorem. The conservation law due to m-translation invariance gives rise to a novel nonlocal conservation law involving the Clebsch variable r used to impose ∂S(m, t)/∂t = 0. Translation invariance with respect to x in Noether's theorem is associated with momentum conservation. We obtain the Cartan-Poincaré form for the system, and use it to obtain a closed ideal of two-forms representing the equation system.
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.
A two-dimensional Dirac fermion microscope
NASA Astrophysics Data System (ADS)
Bøggild, Peter; Caridad, José M.; Stampfer, Christoph; Calogero, Gaetano; Papior, Nick Rübner; Brandbyge, Mads
2017-06-01
The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.
A two-dimensional Dirac fermion microscope
Bøggild, Peter; Caridad, José M.; Stampfer, Christoph; Calogero, Gaetano; Papior, Nick Rübner; Brandbyge, Mads
2017-01-01
The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots. PMID:28598421
A two-dimensional Dirac fermion microscope.
Bøggild, Peter; Caridad, José M; Stampfer, Christoph; Calogero, Gaetano; Papior, Nick Rübner; Brandbyge, Mads
2017-06-09
The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.
Fermion number anomaly with the fluffy mirror fermion
NASA Astrophysics Data System (ADS)
Okumura, Ken-ichi; Suzuki, Hiroshi
2016-12-01
Quite recently, Grabowska and Kaplan presented a 4-dimensional lattice formulation of chiral gauge theories based on the chiral overlap operator. We study this formulation from the perspective of the fermion number anomaly and possible associated phenomenology. A simple argument shows that the consistency of the formulation implies that the fermion with the opposite chirality to the physical one, the "fluffy mirror fermion" or "fluff", suffers from the fermion number anomaly in the same magnitude (with the opposite sign) as the physical fermion. This immediately shows that if at least one of the fluff quarks is massless, the formulation provides a simple viable solution to the strong CP problem. Also, if the fluff interacts with gravity essentially in the same way as the physical fermion, the formulation can realize the asymmetric dark matter scenario.
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
Leptogenesis from split fermions
Nagatani, Yukinori; Perez, Gilad
2004-01-11
We present a new type of leptogenesis mechanism based on a two-scalar split-fermions framework. At high temperatures the bulk scalar vacuum expectation values (VEVs) vanish and lepton number is strongly violated. Below some temperature, T{sub c}, the scalars develop extra dimension dependent VEVs. This transition is assumed to proceed via a first order phase transition. In the broken phase the fermions are localized and lepton number violation is negligible. The lepton-bulk scalar Yukawa couplings contain sizable CP phases which induce lepton production near the interface between the two phases. We provide a qualitative estimation of the resultant baryon asymmetry which agrees with current observation. The neutrino flavor parameters are accounted for by the above model with an additional approximate U(1) symmetry.
(Strongly interacting fermion system)
Not Available
1990-01-01
Research has been concentrated primarily in three areas: heavy fermions, physics of high-temperature superconductivity, and electronic properties. In heavy fermions a peak in the attenuation coefficient of ultrasound just below the superconducting transition temperature can be explained in the context of conventional (BCS) superconductivity theory by recognizing how profoundly that theory is reorganized in heavy fermion systems in which the sound velocity is comparable to electron Fermi velocity. In high-temperature superconductors there have been development of a model for magnetism in one alloy which shows unusual first-order phase transitions in a magnetic field, a possible mechanism for high-temperature superconductivity based on an electric quadrupole moment of Cu in tetragonal crystal geometry, and a neat resolution of a paradox between a theory connecting gaps in spectrum with the degeneracy of the system and a prominent current theoretical view that there is a gap and no degeneracy. It turns out there is a topological degeneracy that had not been previously recognized. In electronic structure we have shown that the finite element approach can be used for electronic systems with an efficient code using more than a half-million local basis functions. In addition, we have developed a variational principle for determining optimal meshes for solving differential equations --- such as the Schroedinger equation.
Tripartite composite fermion states
NASA Astrophysics Data System (ADS)
Sreejith, G. J.; Wu, Ying-Hai; Wójs, A.; Jain, J. K.
2013-06-01
The Read-Rezayi wave function is one of the candidates for the fractional quantum Hall effect at filling fraction ν=2+⅗, and thereby also its hole conjugate at 2+⅖. We study a general class of tripartite composite fermion wave functions, which reduce to the Rezayi-Read ground state and quasiholes for appropriate quantum numbers, but also allow a construction of wave functions for quasiparticles and neutral excitations by analogy to the standard composite fermion theory. We present numerical evidence in finite systems that these trial wave functions capture well the low energy physics of a four-body model interaction. We also compare the tripartite composite fermion wave functions with the exact Coulomb eigenstates at 2+⅗, and find reasonably good agreement. The ground state as well as several excited states of the four-body interaction are seen to evolve adiabatically into the corresponding Coulomb states for N=15 particles. These results support the plausibility of the Read-Rezayi proposal for the 2+⅖ and 2+⅗ fractional quantum Hall effect. However, certain other proposals also remain viable, and further study of excitations and edge states will be necessary for a decisive establishment of the physical mechanism of these fractional quantum Hall states.
Topology and Fermionic Condensate
NASA Astrophysics Data System (ADS)
Kulikov, I.; Pronin, P.
The purpose of this paper is to investigate an influence of a space-time topology on the formation of fermionic condensate in the model with four-fermion interaction ()2. The value for the space-time with topology of R1 × R1 × S1 is found. Moreover a relation of the value of fermionic condensate to a periodic length is studied. In this connection the possibility of a relation of the topologic deposits to structure of hadrons is discussed.
NASA Astrophysics Data System (ADS)
Obuse, H.; Subramaniam, A. R.; Furusaki, A.; Gruzberg, I. A.; Ludwig, A. W. W.
2007-04-01
We study the multifractality (MF) of critical wave functions at boundaries and corners at the metal-insulator transition (MIT) for noninteracting electrons in the two-dimensional (2D) spin-orbit (symplectic) universality class. We find that the MF exponents near a boundary are different from those in the bulk. The exponents at a corner are found to be directly related to those at a straight boundary through a relation arising from conformal invariance. This provides direct numerical evidence for conformal invariance at the 2D spin-orbit MIT. The presence of boundaries modifies the MF of the whole sample even in the thermodynamic limit.
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.
Fermion mass without symmetry breaking
NASA Astrophysics Data System (ADS)
Catterall, Simon
2016-01-01
We examine a model of reduced staggered fermions in three dimensions interacting through an SO (4) invariant four fermion interaction. The model is similar to that considered in a recent paper by Ayyer and Chandrasekharan [1]. We present theoretical arguments and numerical evidence which support the idea that the system develops a mass gap for sufficiently strong four fermi coupling without producing a symmetry breaking fermion bilinear condensate. Massless and massive phases appear to be separated by a continuous phase transition.
Fermion mass without symmetry breaking
Catterall, Simon
2016-01-20
We examine a model of reduced staggered fermions in three dimensions interacting through an SO (4) invariant four fermion interaction. The model is similar to that considered in a recent paper by Ayyer and Chandrasekharan. We present theoretical arguments and numerical evidence which support the idea that the system develops a mass gap for sufficiently strong four fermi coupling without producing a symmetry breaking fermion bilinear condensate. As a result, massless and massive phases appear to be separated by a continuous phase transition.
Cloaking two-dimensional fermions
Lin, De-Hone
2011-09-15
A cloaking theory for a two-dimensional spin-(1/2) fermion is proposed. It is shown that the spinor of the two-dimensional fermion can be cloaked perfectly through controlling the fermion's energy and mass in a specific manner moving in an effective vector potential inside a cloaking shell. Different from the cloaking of three-dimensional fermions, the scaling function that determines the invisible region is uniquely determined by a nonlinear equation. It is also shown that the efficiency of the cloaking shell is unaltered under the Aharonov-Bohm effect.
Global phase diagram of two-dimensional Dirac fermions in random potentials
NASA Astrophysics Data System (ADS)
Ryu, S.; Mudry, C.; Ludwig, A. W. W.; Furusaki, A.
2012-06-01
Anderson localization is studied for two flavors of massless Dirac fermions in two-dimensional space perturbed by static disorder that is invariant under a chiral symmetry (chS) and a time-reversal symmetry (TRS) operation which, when squared, is equal either to plus or minus the identity. The former TRS (symmetry class BDI) can, for example, be realized when the Dirac fermions emerge from spinless fermions hopping on a two-dimensional lattice with a linear energy dispersion such as the honeycomb lattice (graphene) or the square lattice with π flux per plaquette. The latter TRS is realized by the surface states of three-dimensional Z2-topological band insulators in symmetry class CII. In the phase diagram parametrized by the disorder strengths, there is an infrared stable line of critical points for both symmetry classes BDI and CII. Here we discuss a “global phase diagram” in which disordered Dirac fermion systems in all three chiral symmetry classes, AIII, CII, and BDI, occur in four quadrants, sharing one corner which represents the clean Dirac fermion limit. This phase diagram also includes symmetry classes AII [e.g., appearing at the surface of a disordered three-dimensional Z2-topological band insulator in the spin-orbit (symplectic) symmetry class] and D (e.g., the random bond Ising model in two dimensions) as boundaries separating regions of the phase diagram belonging to the three chS classes AIII, BDI, and CII. Moreover, we argue that physics of Anderson localization in the CII phase can be presented in terms of a non-linear-σ model (NLσM) with a Z2-topological term. We thereby complete the derivation of topological or Wess-Zumino-Novikov-Witten terms in the NLσM description of disordered fermionic models in all ten symmetry classes relevant to Anderson localization in two spatial dimensions.
Modified symplectic schemes with nearly-analytic discrete operators for acoustic wave simulations
NASA Astrophysics Data System (ADS)
Liu, Shaolin; Yang, Dinghui; Lang, Chao; Wang, Wenshuai; Pan, Zhide
2017-04-01
Using a structure-preserving algorithm significantly increases the computational efficiency of solving wave equations. However, only a few explicit symplectic schemes are available in the literature, and the capabilities of these symplectic schemes have not been sufficiently exploited. Here, we propose a modified strategy to construct explicit symplectic schemes for time advance. The acoustic wave equation is transformed into a Hamiltonian system. The classical symplectic partitioned Runge-Kutta (PRK) method is used for the temporal discretization. Additional spatial differential terms are added to the PRK schemes to form the modified symplectic methods and then two modified time-advancing symplectic methods with all of positive symplectic coefficients are then constructed. The spatial differential operators are approximated by nearly-analytic discrete (NAD) operators, and we call the fully discretized scheme modified symplectic nearly analytic discrete (MSNAD) method. Theoretical analyses show that the MSNAD methods exhibit less numerical dispersion and higher stability limits than conventional methods. Three numerical experiments are conducted to verify the advantages of the MSNAD methods, such as their numerical accuracy, computational cost, stability, and long-term calculation capability.
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.
Covariant differential calculi on quantum symplectic superspace S Pq 1 | 2
NASA Astrophysics Data System (ADS)
Celik, Salih
2017-02-01
A unitary orthosymplectic quantum supergroup is introduced. Two covariant differential calculi on the quantum superspace S Pq 1 | 2 are presented. The h-deformed symplectic superspaces via a contraction of the q-deformed symplectic superspaces are obtained. A new h-deformation of the Heisenberg superalgebra is given.
Search for Majorana Fermions in S-Wave Fermionic Superfluids
2016-04-01
Atomic and molecular physics Objectives and research goals Majorana fermions were envisioned by E. Majorana in 1935 to describe neutrinos . The Majorana...were initially conceived to describe neutrinos in particle physics. Recently, Weyl fermions have been widely examined in a class of solid-state
Dynamics of Quarks in a 2D Flux Tube
Koshelkin, Andrey V.; Wong, Cheuk-Yin
2015-01-01
On the basis of a compactification of the (3+1) into (1+1) dimensional space-time [1], the quark states inside the 2D flux tube are studied for the case of a linear transverse confining potential. The derived states are classified by both the projections of the orbital momentum and the spin along the tube direction. The spectrum of the fermion states is evaluated. It is found that the energy eigenvalues of the quarks appear to be approximately related to the square root of the eigenvalues of the two-dimensional harmonic oscillator.
Heavy fermion superconductivity
NASA Astrophysics Data System (ADS)
Brison, Jean-Pascal; Glémot, Loı̈c; Suderow, Hermann; Huxley, Andrew; Kambe, Shinsaku; Flouquet, Jacques
2000-05-01
The quest for a precise identification of the symmetry of the order parameter in heavy fermion systems has really started with the discovery of the complex superconducting phase diagram in UPt 3. About 10 years latter, despite numerous experiments and theoretical efforts, this is still not achieved, and we will quickly review the present status of knowledge and the main open question. Actually, the more forsaken issue of the nature of the pairing mechanism has been recently tackled by different groups with macroscopic or microscopic measurement, and significant progress have been obtained. We will discuss the results emerging from these recent studies which all support non-phonon-mediated mechanisms.
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
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.
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.
Canonical and symplectic analysis for three dimensional gravity without dynamics
NASA Astrophysics Data System (ADS)
Escalante, Alberto; Osmart Ochoa-Gutiérrez, H.
2017-03-01
In this paper a detailed Hamiltonian analysis of three-dimensional gravity without dynamics proposed by V. Hussain is performed. We report the complete structure of the constraints and the Dirac brackets are explicitly computed. In addition, the Faddeev-Jackiw symplectic approach is developed; we report the complete set of Faddeev-Jackiw constraints and the generalized brackets, then we show that the Dirac and the generalized Faddeev-Jackiw brackets coincide to each other. Finally, the similarities and advantages between Faddeev-Jackiw and Dirac's formalism are briefly discussed.
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
Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules
Cooper, N. R.; Shlyapnikov, G. V.
2009-10-09
We show that single-component fermionic polar molecules confined to a 2D geometry and dressed by a microwave field may acquire an attractive 1/r{sup 3} dipole-dipole interaction leading to superfluid p-wave pairing at sufficiently low temperatures even in the BCS regime. The emerging state is the topological p{sub x}+ip{sub y} phase promising for topologically protected quantum information processing. The main decay channel is via collisional transitions to dressed states with lower energies and is rather slow, setting a lifetime of the order of seconds at 2D densities approx10{sup 8} cm{sup -2}.
NASA Astrophysics Data System (ADS)
Zhang, Shuangxi; Jia, Yuesong; Sun, Qizhi
2015-02-01
Webb [1] proposed a method to get symplectic integrators of magnetic systems by Taylor expanding the discrete Euler-Lagrangian equations (DEL) which resulted from variational symplectic method by making the variation of the discrete action [2], and approximating the results to the order of O (h2), where h is the time step. And in that paper, Webb thought that the integrators obtained by that method are symplectic ones, especially, he treated Boris integrator (BI) as the symplectic one. However, we have questions about Webb's results. Theoretically the transformation of phase-space coordinates between two adjacent points induced by symplectic algorithm should conserve a symplectic 2-form [2-5]. As proved in Refs. [2,3], the transformations induced by the standard symplectic integrator derived from Hamilton and the variational symplectic integrator (VSI) [2,6] from Lagrangian should conserve a symplectic 2-forms. But the approximation of VSI to O (h2) obtained by that paper is hard to conserve a symplectic 2-form, contrary to the claim of [1]. In the next section, we will use BI as an example to support our point and will prove BI not to be a symplectic one but an integrator conserving discrete phase-space volume.
Several fourth-order force gradient symplectic algorithms
NASA Astrophysics Data System (ADS)
Xu, Jia; Wu, Xin
2010-02-01
By adding force gradient operators to symmetric compositions, we build a set of explicit fourth-order force gradient symplectic algorithms, including those of Chin and coworkers, for a separable Hamiltonian system with quadratic kinetic energy T and potential energy V. They are extended to solve a gravitational n-body Hamiltonian system that can be split into a Keplerian part H0 and a perturbation part H1 in Jacobi coordinates. It is found that the accuracy of each gradient scheme is greatly superior to that of the standard fourth-order Forest-Ruth symplectic integrator in T + V-type Hamiltonian decomposition, but they are both almost equivalent in the mean longitude and the relative position for H0 + H1-type decomposition. At the same time, there are no typical differences between the numerical performances of these gradient algorithms, either in the splitting of T + V or in the splitting of H0 + H1. In particular, compared with the former decomposition, the latter can dramatically improve the numerical accuracy. Because this extension provides a fast and high-precision method to simulate various orbital motions of n-body problems, it is worth recommending for practical computation.
An hp symplectic pseudospectral method for nonlinear optimal control
NASA Astrophysics Data System (ADS)
Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong
2017-01-01
An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.
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.
Relativistic space-charge-limited current for massive Dirac fermions
NASA Astrophysics Data System (ADS)
Ang, Y. S.; Zubair, M.; Ang, L. K.
2017-04-01
A theory of relativistic space-charge-limited current (SCLC) is formulated to determine the SCLC scaling, J ∝Vα/Lβ , for a finite band-gap Dirac material of length L biased under a voltage V . In one-dimensional (1D) bulk geometry, our model allows (α ,β ) to vary from (2,3) for the nonrelativistic model in traditional solids to (3/2,2) for the ultrarelativistic model of massless Dirac fermions. For 2D thin-film geometry we obtain α =β , which varies between 2 and 3/2, respectively, at the nonrelativistic and ultrarelativistic limits. We further provide rigorous proof based on a Green's-function approach that for a uniform SCLC model described by carrier-density-dependent mobility, the scaling relations of the 1D bulk model can be directly mapped into the case of 2D thin film for any contact geometries. Our simplified approach provides a convenient tool to obtain the 2D thin-film SCLC scaling relations without the need of explicitly solving the complicated 2D problems. Finally, this work clarifies the inconsistency in using the traditional SCLC models to explain the experimental measurement of a 2D Dirac semiconductor. We conclude that the voltage scaling 3 /2 <α <2 is a distinct signature of massive Dirac fermions in a Dirac semiconductor and is in agreement with experimental SCLC measurements in MoS2.
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.
Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems
NASA Astrophysics Data System (ADS)
Mei, Lijie; Wu, Xinyuan
2017-06-01
Symplecticity is also an important property for exponential Runge-Kutta (ERK) methods in the sense of structure preservation once the underlying problem is a Hamiltonian system, though ERK methods provide a good performance of higher accuracy and better efficiency than classical Runge-Kutta (RK) methods in dealing with stiff problems: y‧ (t) = My + f (y). On account of this observation, the main theme of this paper is to derive and analyze the symplectic conditions for ERK methods. Using the fundamental analysis of geometric integrators, we first establish one class of sufficient conditions for symplectic ERK methods. It is shown that these conditions will reduce to the conventional ones when M → 0, and this means that these conditions of symplecticity are extensions of the conventional ones in the literature. Furthermore, we also present a new class of structure-preserving ERK methods possessing the remarkable property of symplecticity. Meanwhile, the revised stiff order conditions are proposed and investigated in detail. Since the symplectic ERK methods are implicit and iterative solutions are required in practice, we also investigate the convergence of the corresponding fixed-point iterative procedure. Finally, the numerical experiments, including a nonlinear Schrödinger equation, a sine-Gordon equation, a nonlinear Klein-Gordon equation, and the well-known Fermi-Pasta-Ulam problem, are implemented in comparison with the corresponding symplectic RK methods and the prominent numerical results definitely coincide with the theories and conclusions made in this paper.
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.
Explicit symplectic algorithms based on generating functions for charged particle dynamics
NASA Astrophysics Data System (ADS)
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 ) =pif (x ) or H (x ,p ) =xig (p ) . Applied to the simulations of charged particle dynamics, the explicit symplectic algorithms based on generating functions demonstrate superiorities in conservation and efficiency.
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.
Feng, Baojie; Sugino, Osamu; Liu, Ro-Ya; Zhang, Jin; Yukawa, Ryu; Kawamura, Mitsuaki; Iimori, Takushi; Kim, Howon; Hasegawa, Yukio; Li, Hui; Chen, Lan; Wu, Kehui; Kumigashira, Hiroshi; Komori, Fumio; Chiang, Tai-Chang; Meng, Sheng; Matsuda, Iwao
2017-03-03
Honeycomb structures of group IV elements can host massless Dirac fermions with nontrivial Berry phases. Their potential for electronic applications has attracted great interest and spurred a broad search for new Dirac materials especially in monolayer structures. We present a detailed investigation of the β_{12} sheet, which is a borophene structure that can form spontaneously on a Ag(111) surface. Our tight-binding analysis revealed that the lattice of the β_{12} sheet could be decomposed into two triangular sublattices in a way similar to that for a honeycomb lattice, thereby hosting Dirac cones. Furthermore, each Dirac cone could be split by introducing periodic perturbations representing overlayer-substrate interactions. These unusual electronic structures were confirmed by angle-resolved photoemission spectroscopy and validated by first-principles calculations. Our results suggest monolayer boron as a new platform for realizing novel high-speed low-dissipation devices.
NASA Astrophysics Data System (ADS)
Feng, Baojie; Sugino, Osamu; Liu, Ro-Ya; Zhang, Jin; Yukawa, Ryu; Kawamura, Mitsuaki; Iimori, Takushi; Kim, Howon; Hasegawa, Yukio; Li, Hui; Chen, Lan; Wu, Kehui; Kumigashira, Hiroshi; Komori, Fumio; Chiang, Tai-Chang; Meng, Sheng; Matsuda, Iwao
2017-03-01
Honeycomb structures of group IV elements can host massless Dirac fermions with nontrivial Berry phases. Their potential for electronic applications has attracted great interest and spurred a broad search for new Dirac materials especially in monolayer structures. We present a detailed investigation of the β12 sheet, which is a borophene structure that can form spontaneously on a Ag(111) surface. Our tight-binding analysis revealed that the lattice of the β12 sheet could be decomposed into two triangular sublattices in a way similar to that for a honeycomb lattice, thereby hosting Dirac cones. Furthermore, each Dirac cone could be split by introducing periodic perturbations representing overlayer-substrate interactions. These unusual electronic structures were confirmed by angle-resolved photoemission spectroscopy and validated by first-principles calculations. Our results suggest monolayer boron as a new platform for realizing novel high-speed low-dissipation devices.
Fermions in worldline holography
NASA Astrophysics Data System (ADS)
Dietrich, Dennis D.; Koenigstein, Adrian
2017-09-01
We analyze the worldline holographic framework for fermions. Worldline holography is based on the observation that in the worldline approach to quantum field theory, sources of a quantum field theory over Mink4 naturally form a field theory over AdS5 to all orders in the elementary fields and in the sources. Schwinger's proper time of the worldline formalism automatically appears with the physical four spacetime dimensions in an AdS5 geometry. The worldline holographic effective action in general and the proper-time profiles of the sources in particular solve a renormalization group equation. By taking into account sources up to spin one, we reconstruct seminal holographic models. Considering spin two confirms AdS5 as a consistent background.
Fermion mass without symmetry breaking
Catterall, Simon
2016-01-20
We examine a model of reduced staggered fermions in three dimensions interacting through an SO (4) invariant four fermion interaction. The model is similar to that considered in a recent paper by Ayyer and Chandrasekharan. We present theoretical arguments and numerical evidence which support the idea that the system develops a mass gap for sufficiently strong four fermi coupling without producing a symmetry breaking fermion bilinear condensate. As a result, massless and massive phases appear to be separated by a continuous phase transition.
Majorana fermions in condensed matter: An outlook
NASA Astrophysics Data System (ADS)
Ma, Ning
2017-05-01
The Majorana fermions (MFs) were firstly envisioned by Majorana in 1937 as fundamental constituents of nature, whereas experimentally thus far unobserved in the realm of fundamental particles. More recent studies have revealed that the MFs could occur in condensed matter physics as emergent quasiparticle excitations in effectively spinless p-wave topological superconductors (TS). They are shown to behave as effectively fractionalized anyons following non-Abelian braiding statistics rather than the usual Fermi or Bose exchange statistics. This extraordinary property would directly lead to a perpetually coherent and fault tolerant topological quantum computation in 2D systems. Currently the experiments searching for MFs on much more special systems are ongoing and the investigations of MFs' behavior in TS-coupled systems are also been actively pursued, with the goal of deeply understanding the fundamental physics of fractional statistics in nature, and further paving more feasible ways toward a working universal topological quantum computer.
Symplectic multiparticle tracking model for self-consistent space-charge simulation
NASA Astrophysics Data System (ADS)
Qiang, Ji
2017-01-01
Symplectic tracking is important in accelerator beam dynamics simulation. So far, to the best of our knowledge, there is no self-consistent symplectic space-charge tracking model available in the accelerator community. In this paper, we present a two-dimensional and a three-dimensional symplectic multiparticle spectral model for space-charge tracking simulation. This model includes both the effect from external fields and the effect of self-consistent space-charge fields using a split-operator method. Such a model preserves the phase space structure and shows much less numerical emittance growth than the particle-in-cell model in the illustrative examples.
Optoelectronics with 2D semiconductors
NASA Astrophysics Data System (ADS)
Mueller, Thomas
2015-03-01
Two-dimensional (2D) atomic crystals, such as graphene and layered transition-metal dichalcogenides, are currently receiving a lot of attention for applications in electronics and optoelectronics. In this talk, I will review our research activities on electrically driven light emission, photovoltaic energy conversion and photodetection in 2D semiconductors. In particular, WSe2 monolayer p-n junctions formed by electrostatic doping using a pair of split gate electrodes, type-II heterojunctions based on MoS2/WSe2 and MoS2/phosphorene van der Waals stacks, 2D multi-junction solar cells, and 3D/2D semiconductor interfaces will be presented. Upon optical illumination, conversion of light into electrical energy occurs in these devices. If an electrical current is driven, efficient electroluminescence is obtained. I will present measurements of the electrical characteristics, the optical properties, and the gate voltage dependence of the device response. In the second part of my talk, I will discuss photoconductivity studies of MoS2 field-effect transistors. We identify photovoltaic and photoconductive effects, which both show strong photoconductive gain. A model will be presented that reproduces our experimental findings, such as the dependence on optical power and gate voltage. We envision that the efficient photon conversion and light emission, combined with the advantages of 2D semiconductors, such as flexibility, high mechanical stability and low costs of production, could lead to new optoelectronic technologies.
Bipartite entanglement in fermion systems
NASA Astrophysics Data System (ADS)
Gigena, N.; Rossignoli, R.
2017-06-01
We discuss the relation between fermion entanglement and bipartite entanglement. We first show that an exact correspondence between them arises when the states are constrained to have a definite local number parity. Moreover, for arbitrary states in a four-dimensional single-particle Hilbert space, the fermion entanglement is shown to measure the entanglement between two distinguishable qubits defined by a suitable partition of this space. Such entanglement can be used as a resource for tasks like quantum teleportation. On the other hand, this fermionic entanglement provides a lower bound to the entanglement of an arbitrary bipartition, although in this case the local states involved will generally have different number parities. Finally, the fermionic implementation of the teleportation and superdense coding protocols based on qubits with odd and even number parity is discussed, together with the role of the previous types of entanglement.
Spontaneous compactification and chiral fermions
NASA Astrophysics Data System (ADS)
Frampton, Paul H.; Yamamoto, Katsuji
The question is addressed of which chiral fermions survive in spontaneously compactified solutions of the generalized Einstein-Yang-Mills field equations for higher even space-time dimensions. First, we study the allowed fermion representations of SU( N) which have no gauge or gravitational chiral anomalies in arbitrary even dimension and show how to find all such representations for the case of totally antisymmetric SU( N) tensors. Second, we look explicitly at monopole-induced spontaneous compactification in six dimensions; here, interesting chiral fermions in four dimensions do not occur easily but instead require highly artificial assignments of quantum numbers under the U(1) gauge group associated with the monopole. Finally, we consider instanton-induced spontaneous compactification in eight dimensions; for this case, we may readily obtain acceptable chiral fermions in four dimensions, including Georgi's three-family SU(11) model.
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.
Fermions as generalized Ising models
NASA Astrophysics Data System (ADS)
Wetterich, C.
2017-04-01
We establish a general map between Grassmann functionals for fermions and probability or weight distributions for Ising spins. The equivalence between the two formulations is based on identical transfer matrices and expectation values of products of observables. The map preserves locality properties and can be realized for arbitrary dimensions. We present a simple example where a quantum field theory for free massless Dirac fermions in two-dimensional Minkowski space is represented by an asymmetric Ising model on a euclidean square lattice.
NASA Astrophysics Data System (ADS)
Al-Hashimi, M. H.; Shalaby, A. M.; Wiese, U.-J.
2017-03-01
Motivated by potential applications to ultracold matter, we perform a theoretical study of Majorana fermions confined to a finite volume, whose boundary conditions are characterized by self-adjoint extension parameters. While the boundary conditions for Dirac fermions in (1 +1 )-d are characterized by a 1-parameter family, λ =-λ*, of self-adjoint extensions, for Majorana fermions λ is restricted to ±i . Based on this result, we compute the frequency spectrum of Majorana fermions confined to a 1-d interval. The boundary conditions for Dirac fermions confined to a 3-d region of space are characterized by a 4-parameter family of self-adjoint extensions, which is reduced to two distinct 1-parameter families for Majorana fermions. We also consider the problems related to the quantum mechanical interpretation of the Majorana equation as a single-particle equation. Furthermore, the equation is related to a relativistic Schrödinger equation that does not suffer from these problems. Here we restrict ourselves to theoretical considerations without yet focusing on concrete cold matter applications.
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.
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
Multipole Vortex Blobs (MVB): Symplectic Geometry and Dynamics.
Holm, Darryl D; Jacobs, Henry O
2017-01-01
Vortex blob methods are typically characterized by a regularization length scale, below which the dynamics are trivial for isolated blobs. In this article, we observe that the dynamics need not be trivial if one is willing to consider distributional derivatives of Dirac delta functionals as valid vorticity distributions. More specifically, a new singular vortex theory is presented for regularized Euler fluid equations of ideal incompressible flow in the plane. We determine the conditions under which such regularized Euler fluid equations may admit vorticity singularities which are stronger than delta functions, e.g., derivatives of delta functions. We also describe the symplectic geometry associated with these augmented vortex structures, and we characterize the dynamics as Hamiltonian. Applications to the design of numerical methods similar to vortex blob methods are also discussed. Such findings illuminate the rich dynamics which occur below the regularization length scale and enlighten our perspective on the potential for regularized fluid models to capture multiscale phenomena.
Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform
NASA Astrophysics Data System (ADS)
Hausel, Tamás
2006-04-01
A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This technique in turn gives information on Betti numbers of holomorphic symplectic quotients. As a consequence, simple unified proofs are obtained for formulas of Poincaré polynomials of toric hyperkähler varieties (recovering results of Bielawski-Dancer and Hausel-Sturmfels), Poincaré polynomials of Hilbert schemes of points and twisted Atiyah-Drinfeld-Hitchin-Manin (ADHM) spaces of instantons on 2 (recovering results of Nakajima-Yoshioka), and Poincaré polynomials of all Nakajima quiver varieties. As an application, a proof of a conjecture of Kac on the number of absolutely indecomposable representations of a quiver is announced. quiver varieties | Weyl-Kac character formula
Symplectic molecular dynamics simulations on specially designed parallel computers.
Borstnik, Urban; Janezic, Dusanka
2005-01-01
We have developed a computer program for molecular dynamics (MD) simulation that implements the Split Integration Symplectic Method (SISM) and is designed to run on specialized parallel computers. The MD integration is performed by the SISM, which analytically treats high-frequency vibrational motion and thus enables the use of longer simulation time steps. The low-frequency motion is treated numerically on specially designed parallel computers, which decreases the computational time of each simulation time step. The combination of these approaches means that less time is required and fewer steps are needed and so enables fast MD simulations. We study the computational performance of MD simulation of molecular systems on specialized computers and provide a comparison to standard personal computers. The combination of the SISM with two specialized parallel computers is an effective way to increase the speed of MD simulations up to 16-fold over a single PC processor.
Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform
Hausel, Tamás
2006-01-01
A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This technique in turn gives information on Betti numbers of holomorphic symplectic quotients. As a consequence, simple unified proofs are obtained for formulas of Poincaré polynomials of toric hyperkähler varieties (recovering results of Bielawski–Dancer and Hausel–Sturmfels), Poincaré polynomials of Hilbert schemes of points and twisted Atiyah–Drinfeld–Hitchin–Manin (ADHM) spaces of instantons on ℂ2 (recovering results of Nakajima–Yoshioka), and Poincaré polynomials of all Nakajima quiver varieties. As an application, a proof of a conjecture of Kac on the number of absolutely indecomposable representations of a quiver is announced. PMID:16606857
Explicit symplectic methods for solving charged particle trajectories
NASA Astrophysics Data System (ADS)
Zhou, Zhaoqi; He, Yang; Sun, Yajuan; Liu, Jian; Qin, Hong
2017-05-01
In this paper, we consider the Lorentz force system based on its Hamiltonian formulation. We decompose the Lorentz force system into four subsystems which can be solved with the help of coordinate transformations. Via the coordinate transformations, three kinds of explicit symplectic numerical methods have been established for simulating the motion of charged particles under the time-independent electromagnetic field. We generalize our methods to solve the system with time-dependent external electromagnetic fields, and also the system with a relativistic effect. In numerical experiments, the computing efficiency and accuracy over a long time for the newly derived methods are demonstrated. Also, the long-term simulation for the dynamics of runaway electrons is performed.
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.
Relational symplectic groupoid quantization for constant poisson structures
NASA Astrophysics Data System (ADS)
Cattaneo, Alberto S.; Moshayedi, Nima; Wernli, Konstantin
2017-09-01
As a detailed application of the BV-BFV formalism for the quantization of field theories on manifolds with boundary, this note describes a quantization of the relational symplectic groupoid for a constant Poisson structure. The presence of mixed boundary conditions and the globalization of results are also addressed. In particular, the paper includes an extension to space-times with boundary of some formal geometry considerations in the BV-BFV formalism, and specifically introduces into the BV-BFV framework a "differential" version of the classical and quantum master equations. The quantization constructed in this paper induces Kontsevich's deformation quantization on the underlying Poisson manifold, i.e., the Moyal product, which is known in full details. This allows focussing on the BV-BFV technology and testing it. For the inexperienced reader, this is also a practical and reasonably simple way to learn it.
Multipole Vortex Blobs (MVB): Symplectic Geometry and Dynamics
NASA Astrophysics Data System (ADS)
Holm, Darryl D.; Jacobs, Henry O.
2017-03-01
Vortex blob methods are typically characterized by a regularization length scale, below which the dynamics are trivial for isolated blobs. In this article, we observe that the dynamics need not be trivial if one is willing to consider distributional derivatives of Dirac delta functionals as valid vorticity distributions. More specifically, a new singular vortex theory is presented for regularized Euler fluid equations of ideal incompressible flow in the plane. We determine the conditions under which such regularized Euler fluid equations may admit vorticity singularities which are stronger than delta functions, e.g., derivatives of delta functions. We also describe the symplectic geometry associated with these augmented vortex structures, and we characterize the dynamics as Hamiltonian. Applications to the design of numerical methods similar to vortex blob methods are also discussed. Such findings illuminate the rich dynamics which occur below the regularization length scale and enlighten our perspective on the potential for regularized fluid models to capture multiscale phenomena.
Symplectic maps and chromatic optics in particle accelerators
NASA Astrophysics Data System (ADS)
Cai, Yunhai
2015-10-01
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. As a result, the cell becomes nearly perfect up to the third-order of the momentum deviation.
The Symplectic Evans Matrix and Solitary Wave Instability
NASA Astrophysics Data System (ADS)
Bridges, Thomas J.; Derks, Gianne
2001-10-01
Many models for physical phenomena in oceanography, atmospheric dynamics, optical fibre transmission, nerve conduction, acoustical and gas dynamic flows are conservative translation-invariant evolution equations with a Hamiltonian structure. Solitary waves and fronts form an important class of solutions of such equations and the calculus of variations, critical point theory and symplectic structure have played a major role in the analysis of their stability and instability. For example, the characterisation of solitary waves as critical points of the Hamiltonian (energy) constrained to level sets of the momentum (or momentum and other constants of motion) leads to a powerful framework for proving nonlinear Lyapunov stability - when the second variation, evaluated at the constrained critical point, has a finite number of negative eigenvalues (e.g. BENJAMIN2, BONA3, HOLM ET AL14, GRILLAKIS ET AL12, 13, MADDOCKS & SACHS16 and references therein)...
Relational symplectic groupoid quantization for constant poisson structures
NASA Astrophysics Data System (ADS)
Cattaneo, Alberto S.; Moshayedi, Nima; Wernli, Konstantin
2017-04-01
As a detailed application of the BV-BFV formalism for the quantization of field theories on manifolds with boundary, this note describes a quantization of the relational symplectic groupoid for a constant Poisson structure. The presence of mixed boundary conditions and the globalization of results are also addressed. In particular, the paper includes an extension to space-times with boundary of some formal geometry considerations in the BV-BFV formalism, and specifically introduces into the BV-BFV framework a "differential" version of the classical and quantum master equations. The quantization constructed in this paper induces Kontsevich's deformation quantization on the underlying Poisson manifold, i.e., the Moyal product, which is known in full details. This allows focussing on the BV-BFV technology and testing it. For the inexperienced reader, this is also a practical and reasonably simple way to learn it.
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.
Multipole Vortex Blobs (MVB): Symplectic Geometry and Dynamics
NASA Astrophysics Data System (ADS)
Holm, Darryl D.; Jacobs, Henry O.
2017-06-01
Vortex blob methods are typically characterized by a regularization length scale, below which the dynamics are trivial for isolated blobs. In this article, we observe that the dynamics need not be trivial if one is willing to consider distributional derivatives of Dirac delta functionals as valid vorticity distributions. More specifically, a new singular vortex theory is presented for regularized Euler fluid equations of ideal incompressible flow in the plane. We determine the conditions under which such regularized Euler fluid equations may admit vorticity singularities which are stronger than delta functions, e.g., derivatives of delta functions. We also describe the symplectic geometry associated with these augmented vortex structures, and we characterize the dynamics as Hamiltonian. Applications to the design of numerical methods similar to vortex blob methods are also discussed. Such findings illuminate the rich dynamics which occur below the regularization length scale and enlighten our perspective on the potential for regularized fluid models to capture multiscale phenomena.
Sevrin, A.
1993-06-01
After reviewing some aspects of gravity in two dimensions, I show that non-trivial embeddings of sl(2) in a semi-simple (super) Lie algebra give rise to a very large class of extensions of 2D gravity. The induced action is constructed as a gauged WZW model and an exact expression for the effective action is given.
Highly crystalline 2D superconductors
NASA Astrophysics Data System (ADS)
Saito, Yu; Nojima, Tsutomu; Iwasa, Yoshihiro
2017-02-01
Recent advances in materials fabrication have enabled the manufacturing of ordered 2D electron systems, such as heterogeneous interfaces, atomic layers grown by molecular beam epitaxy, exfoliated thin flakes and field-effect devices. These 2D electron systems are highly crystalline, and some of them, despite their single-layer thickness, exhibit a sheet resistance more than an order of magnitude lower than that of conventional amorphous or granular thin films. In this Review, we explore recent developments in the field of highly crystalline 2D superconductors and highlight the unprecedented physical properties of these systems. In particular, we explore the quantum metallic state (or possible metallic ground state), the quantum Griffiths phase observed in out-of-plane magnetic fields and the superconducting state maintained in anomalously large in-plane magnetic fields. These phenomena are examined in the context of weakened disorder and/or broken spatial inversion symmetry. We conclude with a discussion of how these unconventional properties make highly crystalline 2D systems promising platforms for the exploration of new quantum physics and high-temperature superconductors.
Highly crystalline 2D superconductors
NASA Astrophysics Data System (ADS)
Saito, Yu; Nojima, Tsutomu; Iwasa, Yoshihiro
2016-12-01
Recent advances in materials fabrication have enabled the manufacturing of ordered 2D electron systems, such as heterogeneous interfaces, atomic layers grown by molecular beam epitaxy, exfoliated thin flakes and field-effect devices. These 2D electron systems are highly crystalline, and some of them, despite their single-layer thickness, exhibit a sheet resistance more than an order of magnitude lower than that of conventional amorphous or granular thin films. In this Review, we explore recent developments in the field of highly crystalline 2D superconductors and highlight the unprecedented physical properties of these systems. In particular, we explore the quantum metallic state (or possible metallic ground state), the quantum Griffiths phase observed in out-of-plane magnetic fields and the superconducting state maintained in anomalously large in-plane magnetic fields. These phenomena are examined in the context of weakened disorder and/or broken spatial inversion symmetry. We conclude with a discussion of how these unconventional properties make highly crystalline 2D systems promising platforms for the exploration of new quantum physics and high-temperature superconductors.
Orbifold symmetry reductions of massive boson-fermion degeneracy
NASA Astrophysics Data System (ADS)
Florakis, Ioannis; Kounnas, Costas
2009-10-01
We investigate the existence of string vacua with Massive Spectrum Degeneracy Symmetry ( MSDS) in Heterotic and Type II orbifold constructions. We present a classification of all possible Z2N-orbifolds with MSDS symmetry that can be constructed in the formalism of the 2d free fermionic construction. We explicitly construct several two-dimensional models whose Reduced Massive Spectrum Degeneracy Symmetry ( RMSDS) is due to a set of Z-orbifold projections induced naturally in the framework of the free fermionic construction. In all proposed models the massive boson and fermion degrees of freedom exhibit Massive Spectrum Degeneracy Symmetry while the number of massless bosons n(b) and massless fermions n(f) are different; n(b)≠n(f). This property distinguishes the MSDSZ-twisted theories from ordinary supersymmetric ones. Some comments are stated concerning the large marginal JJ¯-deformations of the proposed models connecting them to higher-dimensional gauged-supergravity theories with non-trivial geometrical fluxes.
Symplectic Partitioned Runge-Kutta Methods with Minimum Phase Lag - Case of 5 Stages
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.
2010-09-30
In this work we consider explicit Symplectic Partitioned Runge-Kutta methods (SPRK) with five stages for problems with separable Hamiltonian. We construct a new method with constant coefficients third algebraic order and eighth phase-lag order.
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".
E-2D Advanced Hawkeye Aircraft (E-2D AHE)
2015-12-01
and Homeland Defense. As a part of the E-2D AHE radar modernization effort, the Navy also invested in integrating a full glass cockpit and full...Communication Navigation Surveillance/Air Traffic Management capability. The glass cockpit will also provide the capability for the pilot or co-pilot to...hours at a station distance of 200nm Flat Turn Service Ceiling =>25,000 feet above MSL at mission profile =>25,000 feet above MSL at mission
A symplectic Runge Kutta Nyström method with minimal phase-lag
NASA Astrophysics Data System (ADS)
van de Vyver, H.
2007-07-01
In this Letter we introduce a symplectic explicit RKN method for Hamiltonian systems with periodical solutions. The method has algebraic order three and phase-lag order six at a cost of three function evaluations per step. Numerical experiments show the relevance of the developed algorithm. It is found that the new method is much more efficient than the standard symplectic fourth-order method [M.P. Calvo, J.M. Sanz-Serna, SIAM J. Sci. Comput. 14 (1993) 936].
Multi-symplectic method for the coupled Schrödinger—KdV equations
NASA Astrophysics Data System (ADS)
Zhang, Hong; Song, Song-He; Zhou, Wei-En; Chen, Xu-Dong
2014-08-01
In this paper, we present a multi-symplectic Hamiltonian formulation of the coupled Schrödinger-KdV equations (CSKE) with periodic boundary conditions. Then we develop a novel multi-symplectic Fourier pseudospectral (MSFP) scheme for the CSKE. In numerical experiments, we compare the MSFP method with the Crank—Nicholson (CN) method. Our results show high accuracy, effectiveness, and good ability of conserving the invariants of the MSFP method.
Practical Symplectic Methods with Time Transformation for the Few-Body Problem
NASA Astrophysics Data System (ADS)
Mikkola, Seppo
1997-02-01
The use of the extended phase space and time transformations for constructing efficient symplectic algorithms for the investigation of long term behavior of hierarchical few-body systems is discussed. Numerical experiments suggest that the time-transformed generalized leap-frog, combined with symplectic correctors, is one of the most efficient methods for such studies. Applications extend from perturbed two-body motion to hierarchical many-body systems with large eccentricities.
Fermions and gravitational gyrotropy
NASA Astrophysics Data System (ADS)
Helfer, Adam D.
2016-12-01
In conventional general relativity without torsion, high-frequency gravitational waves couple to the chiral number density of spin one-half quanta: the polarization of the waves is rotated by 2 π N5ℓPl2, where N5 is the chiral column density and ℓPl is the Planck length. This means that if a primordial distribution of gravitational waves with E-E or B-B correlations passed through a chiral density of fermions in the very early Universe, an E-B correlation will be generated. This in turn will give rise to E-B and T-B correlations in the cosmic microwave background (CMB). Less obviously but more primitively, the condition Albrecht called "cosmic coherence" would be violated, changing the restrictions on the class of admissible cosmological gravitational waves. This altered class of waves would, generally speaking, probe earlier physics than do the conventional waves; their effects on the CMB would be most pronounced for low (≲100 ) multipoles. Rough estimates indicate that if the tensor-to-scalar ratio is less than about 10-2, it will be hard to constrain a spatially homogeneous primordial N5 by present data.
Parzen, G.
1993-06-01
In order to study long term stability, it appears desirable that the particle tracking by symplectic. One way to achieve symplectic tracking is to replace the magnets by a series of point magnets and drift spaces. This approach is modified here by using a reference orbit that is made up of arcs of circles and straight lines which join smoothly with each other. This make sthe symplecticity more evident, and simplifies in some way the particle tracking, as the coordinate system based on this reference orbit is not changing discontinuously between elements. It also allows the use of transfer matrices to find the linear orbit parameters. For this choice of reference orbit, the required ersults are obtained to track particles, which are the transfer functions, the transer matrices and the transfer time, for the different elements present in the accelerator. It is shown that, in the absence of longitudinal magnetic fields these results provide a symplectic, second order itnegrator. Existing tracking programs that use a reference orbit, made up of arcs of circles and straight lines, can be modified, using the results given here to do symplectic tracking with point magnets. The results have been used to modify the ORBIT tracking program. The ORBIT program will now, by changing an indicator, either track using the usual large accelerator approximation for the transfer functions or do symplectic tracking with ponit magnets, and will use the same reference orbit in both cases.
Variational symplectic algorithm for guiding center dynamics and its application in tokamak geometry
Qin Hong; Guan Xiaoyin; Tang, William M.
2009-04-15
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.
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.
Studying fermionic ghost imaging with independent photons
NASA Astrophysics Data System (ADS)
Liu, Jianbin; Zhou, Yu; Zheng, Huaibin; Chen, Hui; Li, Fu-li; Xu, Zhuo
2016-12-01
Ghost imaging with thermal fermions is calculated based on two-particle interference in Feynman's path integral theory. It is found that ghost imaging with thermal fermions can be simulated by ghost imaging with thermal bosons and classical particles. Photons in pseudothermal light are employed to experimentally study fermionic ghost imaging. Ghost imaging with thermal bosons and fermions is discussed based on the point-to-point (spot) correlation between the object and image planes. The employed method offers an efficient guidance for future ghost imaging with real thermal fermions, which may also be generalized to study other second-order interference phenomena with fermions.
Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model
Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; Neupert, Titus; Maciejko, Joseph
2016-08-25
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.
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.
Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model
NASA Astrophysics Data System (ADS)
Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; Neupert, Titus; Maciejko, Joseph
2016-08-01
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.
Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model
Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; Neupert, Titus; Maciejko, Joseph
2016-08-25
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.
NASA Astrophysics Data System (ADS)
Tarantino, Nicolas; Fidkowski, Lukasz
2016-09-01
We construct exactly solved commuting projector Hamiltonian lattice models for all known (2+1)-dimensional (2+1D) fermionic symmetry protected topological phases (SPTs) with on-site unitary symmetry group Gf=G ×Z2f , where G is finite and Z2f is the fermion parity symmetry. In particular, our models transcend the class of group supercohomology models, which realize some, but not all, fermionic SPTs in 2+1D. A natural ingredient in our construction is a discrete form of the spin structure of the 2D spatial surface M on which our model is defined, namely a "Kasteleyn" orientation of a certain graph associated with the lattice. As a special case, our construction yields commuting projector models for all eight members of the Z8 classification of 2D fermionic SPTs with G =Z2 .
PT-Symmetric Real Dirac Fermions and Semimetals.
Zhao, Y X; Lu, Y
2017-02-03
Recently, Weyl fermions have attracted increasing interest in condensed matter physics due to their rich phenomenology originated from their nontrivial monopole charges. Here, we present a theory of real Dirac points that can be understood as real monopoles in momentum space, serving as a real generalization of Weyl fermions with the reality being endowed by the PT symmetry. The real counterparts of topological features of Weyl semimetals, such as Nielsen-Ninomiya no-go theorem, 2D subtopological insulators, and Fermi arcs, are studied in the PT symmetric Dirac semimetals and the underlying reality-dependent topological structures are discussed. In particular, we construct a minimal model of the real Dirac semimetals based on recently proposed cold atom experiments and quantum materials about PT symmetric Dirac nodal line semimetals.
Anatomy of fermionic entanglement and criticality in Kitaev spin liquids
NASA Astrophysics Data System (ADS)
Meichanetzidis, K.; Cirio, M.; Pachos, J. K.; Lahtinen, V.
2016-09-01
We analyze in detail the effect of nontrivial band topology on the area-law behavior of the entanglement entropy in Kitaev's honeycomb model. By mapping the translationally invariant 2D spin model onto 1D fermionic subsystems, we identify those subsystems responsible for universal entanglement contributions in the gapped phases and those responsible for critical entanglement scaling in the gapless phases. For the gapped phases, we analytically show how the topological edge states contribute to the entanglement entropy and provide a universal lower bound for it. For the gapless semimetallic phases and topological phase transitions, the identification of the critical subsystems shows that they fall always into the Ising or the XY universality classes. As our study concerns the fermionic degrees of freedom in the honeycomb model, qualitatively similar results are expected to apply also to generic topological insulators and superconductors.
P T -Symmetric Real Dirac Fermions and Semimetals
NASA Astrophysics Data System (ADS)
Zhao, Y. X.; Lu, Y.
2017-02-01
Recently, Weyl fermions have attracted increasing interest in condensed matter physics due to their rich phenomenology originated from their nontrivial monopole charges. Here, we present a theory of real Dirac points that can be understood as real monopoles in momentum space, serving as a real generalization of Weyl fermions with the reality being endowed by the P T symmetry. The real counterparts of topological features of Weyl semimetals, such as Nielsen-Ninomiya no-go theorem, 2D subtopological insulators, and Fermi arcs, are studied in the P T symmetric Dirac semimetals and the underlying reality-dependent topological structures are discussed. In particular, we construct a minimal model of the real Dirac semimetals based on recently proposed cold atom experiments and quantum materials about P T symmetric Dirac nodal line semimetals.
Dual-fermion approach to interacting disordered fermion systems
NASA Astrophysics Data System (ADS)
Yang, S.-X.; Haase, P.; Terletska, H.; Meng, Z. Y.; Pruschke, T.; Moreno, J.; Jarrell, M.
2014-05-01
We generalize the recently introduced dual-fermion (DF) formalism for disordered fermion systems by including the effect of interactions. For an interacting disordered system the contributions to the full vertex function have to be separated into crossing-asymmetric and crossing-symmetric scattering processes, and addressed differently when constructing the DF diagrams. By applying our approach to the Anderson-Falicov-Kimball model and systematically restoring the nonlocal correlations in the DF lattice calculation, we show a significant improvement over the dynamical mean-field theory and the coherent potential approximation for both one-particle and two-particle quantities.
Dual-fermion approach to interacting disordered fermion systems
NASA Astrophysics Data System (ADS)
Yang, Shuxiang; Haase, Patrick; Terletska, Hanna; Meng, Zi Yang; Pruschke, Thomas; Moreno, Juana; Jarrell, Mark
2014-03-01
We generalize the recently introduced dual fermion (DF) formalism for disordered fermion systems by including the effect of interactions. For an interacting disordered system the contributions to the full vertex function have to be separated into elastic and inelastic scattering processes, and addressed differently when constructing the DF diagrams. By applying our approach to the Anderson-Falicov-Kimball model and systematically restoring the nonlocal correlations in the DF lattice calculation, we show a significant improvement over the Dynamical Mean-Field Theory and the Coherent Potential Approximation for both one-particle and two-particle quantities.
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.
Fermion production during and after axion inflation
Adshead, Peter; Sfakianakis, Evangelos I. E-mail: esfaki@illinois.edu
2015-11-01
We study derivatively coupled fermions in axion-driven inflation, specifically m{sub φ}{sup 2φ2} 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.
Local spin operators for fermion simulations
NASA Astrophysics Data System (ADS)
Whitfield, James D.; Havlíček, Vojtěch; Troyer, Matthias
2016-09-01
Digital quantum simulation of fermionic systems is important in the context of chemistry and physics. Simulating fermionic models on general purpose quantum computers requires imposing a fermionic algebra on qubits. The previously studied Jordan-Wigner and Bravyi-Kitaev transformations are two techniques for accomplishing this task. Here, we reexamine an auxiliary fermion construction which maps fermionic operators to local operators on qubits. The local simulation is performed by relaxing the requirement that the number of qubits should match the number of single-particle states. Instead, auxiliary sites are introduced to enable nonconsecutive fermionic couplings to be simulated with constant low-rank tensor products on qubits. The additional number of auxiliary qubits required per fermionic degree of freedom depends only on the degree of connectivity of the Hamiltonian. We connect the auxiliary fermion construction to topological models and give examples of the construction.
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.
Fast evaluation and locality of overlap fermions
NASA Astrophysics Data System (ADS)
Bietenholz, W.; Hip, I.; Schilling, K.
2002-03-01
In order to construct improved overlap fermions, we start from a short ranged approximate Ginsparg-Wilson fermion and insert it into the overlap formula. We show that its polynomial evaluation is accelerated considerably compared to the standard Neuberger fermion. In addition the degree of locality is strongly improved.
Fast evaluation and locality of overlap fermions
NASA Astrophysics Data System (ADS)
Bietenholz, W.; Hip, I.; Schilling, K.
In order to construct improved overlap fermions, we start from a short ranged approximate Ginsparg-Wilson fermion and insert it into the overlap formula. We show that its polynomial evaluation is accelerated considerably compared to the standard Neuberger fermion. In addition the degree of locality is strongly improved.
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
Configurations of Points and the Symplectic Berry-Robbins Problem
NASA Astrophysics Data System (ADS)
Malkoun, Joseph
2014-12-01
We present a new problem on configurations of points, which is a new version of a similar problem by Atiyah and Sutcliffe, except it is related to the Lie group operatorname{Sp}(n), instead of the Lie group operatorname{U}(n). Denote by h a Cartan algebra of operatorname{Sp}(n), and Δ the union of the zero sets of the roots of operatorname{Sp}(n) tensored with R^3, each being a map from h otimes R^3 to R^3. We wish to construct a map (h otimes R^3) backslash Δ to operatorname{Sp}(n)/T^n which is equivariant under the action of the Weyl group W_n of operatorname{Sp}(n) (the symplectic Berry-Robbins problem). Here, the target space is the flag manifold of operatorname{Sp}(n), and T^n is the diagonal n-torus. The existence of such a map was proved by Atiyah and Bielawski in a more general context. We present an explicit smooth candidate for such an equivaria! nt map, which would be a genuine map provided a certain linear independence conjecture holds. We prove the linear independence conjecture for n=2.
A Green's function decoupling scheme for the Edwards fermion-boson model.
Edwards, D M; Ejima, S; Alvermann, A; Fehske, H
2010-11-03
Holes in a Mott insulator are represented by spinless fermions in the fermion-boson model introduced by Edwards. Although the physically interesting regime is for low to moderate fermion density, the model has interesting properties over the whole density range. It has previously been studied at half-filling in the one-dimensional (1D) case by numerical methods, in particular using exact diagonalization and the density matrix renormalization group (DMRG). In the present study the one-particle Green's function is calculated analytically by means of a decoupling scheme for the equations of motion, valid for arbitrary density in 1D, 2D and 3D with fairly large boson energy and zero boson relaxation parameter. The Green's function is used to compute some ground state properties, and the one-fermion spectral function, for fermion densities n = 0.1, 0.5 and 0.9 in the 1D case. The results are generally in good agreement with numerical results obtained using the DMRG and dynamical DMRG, and new light is shed on the nature of the ground state at different fillings. The Green's function approximation is sufficiently successful in 1D to justify future application to the 2D and 3D cases.
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.
Symplectic and Killing symmetries of AdS3 gravity: holographic vs boundary gravitons
NASA Astrophysics Data System (ADS)
Compère, G.; Mao, P.; Seraj, A.; Sheikh-Jabbari, M. M.
2016-01-01
The set of solutions to the AdS3 Einstein gravity with Brown-Henneaux boundary conditions is known to be a family of metrics labeled by two arbitrary periodic functions, respectively left and right-moving. It turns out that there exists an appropriate presymplectic form which vanishes on-shell. This promotes this set of metrics to a phase space in which the Brown-Henneaux asymptotic symmetries become symplectic symmetries in the bulk of spacetime. Moreover, any element in the phase space admits two global Killing vectors. We show that the conserved charges associated with these Killing vectors commute with the Virasoro symplectic symmetry algebra, extending the Virasoro symmetry algebra with two U(1) generators. We discuss that any element in the phase space falls into the coadjoint orbits of the Virasoro algebras and that each orbit is labeled by the U(1) Killing charges. Upon setting the right-moving function to zero and restricting the choice of orbits, one can take a near-horizon decoupling limit which preserves a chiral half of the symplectic symmetries. Here we show two distinct but equivalent ways in which the chiral Virasoro symplectic symmetries in the near-horizon geometry can be obtained as a limit of the bulk symplectic symmetries.
Explicit Symplectic-like Integrators with Midpoint Permutations for Spinning Compact Binaries
NASA Astrophysics Data System (ADS)
Luo, Junjie; Wu, Xin; Huang, Guoqing; Liu, Fuyao
2017-01-01
We refine the recently developed fourth-order extended phase space explicit symplectic-like methods for inseparable Hamiltonians using Yoshida’s triple product combined with a midpoint permuted map. The midpoint between the original variables and their corresponding extended variables at every integration step is readjusted as the initial values of the original variables and their corresponding extended ones at the next step integration. The triple-product construction is apparently superior to the composition of two triple products in computational efficiency. Above all, the new midpoint permutations are more effective in restraining the equality of the original variables and their corresponding extended ones at each integration step than the existing sequent permutations of momenta and coordinates. As a result, our new construction shares the benefit of implicit symplectic integrators in the conservation of the second post-Newtonian Hamiltonian of spinning compact binaries. Especially for the chaotic case, it can work well, but the existing sequent permuted algorithm cannot. When dissipative effects from the gravitational radiation reaction are included, the new symplectic-like method has a secular drift in the energy error of the dissipative system for the orbits that are regular in the absence of radiation, as an implicit symplectic integrator does. In spite of this, it is superior to the same-order implicit symplectic integrator in accuracy and efficiency. The new method is particularly useful in discussing the long-term evolution of inseparable Hamiltonian problems.
NASA Astrophysics Data System (ADS)
Li, Yuyin; Zhang, Yahui; Kennedy, David
2017-10-01
A random vibration analysis of an axially compressed cylindrical shell under a turbulent boundary layer (TBL) is presented in the symplectic duality system. By expressing the cross power spectral density (PSD) of the TBL as a Fourier series in the axial and circumferential directions, the problem of structures excited by a random distributed pressure due to the TBL is reduced to solving the harmonic response function, which is the response of structures to a spatial and temporal harmonic pressure of unit magnitude. The governing differential equations of the axially compressed cylindrical shell are derived in the symplectic duality system, and then a symplectic eigenproblem is formed by using the method of separation of variables. Expanding the excitation vector and unknown state vector in symplectic space, decoupled governing equations are derived, and then the analytical solution can be obtained. In contrast to the modal decomposition method (MDM), the present method is formulated in the symplectic duality system and does not need modal truncation, and hence the computations are of high precision and efficiency. In numerical examples, harmonic response functions for the axially compressed cylindrical shell are studied, and a comparison is made with the MDM to verify the present method. Then, the random responses of the shell to the TBL are obtained by the present method, and the convergence problems induced by Fourier series expansion are discussed. Finally, influences of the axial compression on random responses are investigated.
Gravitational contribution to fermion masses
NASA Astrophysics Data System (ADS)
Tiemblo, A.; Tresguerres, R.
2005-08-01
In the context of a non-linear gauge theory of the Poincaré group, we show that covariant derivatives of Dirac fields include a coupling to the translational connections, manifesting itself in the matter action as a universal background mass contribution to fermions.
Nonlinear fermions and coherent states
NASA Astrophysics Data System (ADS)
Trifonov, D. A.
2012-06-01
Nonlinear fermions of degree n (n-fermions) are introduced as particles with creation and annihilation operators obeying the simple nonlinear anticommutation relation AA† + A†nAn = 1. The (n + 1)th-order nilpotency of these operators follows from the existence of unique A-vacuum. Supposing appropriate (n + 1)th-order nilpotent para-Grassmann variables and integration rules the sets of n-fermion number states, ‘right’ and ‘left’ ladder operator coherent states (CS) and displacement-operator-like CS are constructed. The (n + 1) × (n + 1) matrix realization of the related para-Grassmann algebra is provided. General (n + 1)th-order nilpotent ladder operators of finite-dimensional systems are expressed as polynomials in terms of n-fermion operators. Overcomplete sets of (normalized) ‘right’ and ‘left’ eigenstates of such general ladder operators are constructed and their properties are briefly discussed. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.
Wilson fermions at finite temperature
Creutz, M.
1996-09-17
The author conjectures on the phase structure expected for lattice gauge theory with two flavors of Wilson fermions, concentrating on large values of the hopping parameter. Numerous phases are expected, including the conventional confinement and deconfinement phases, as well as an Aoki phase with spontaneous breaking of flavor and parity and a large hopping phase corresponding to negative quark masses.
Constructing entanglement measures for fermions
NASA Astrophysics Data System (ADS)
Johansson, Markus; Raissi, Zahra
2016-10-01
In this paper we describe a method for finding polynomial invariants under stochastic local operations and classical communication (SLOCC) for a system of delocalized fermions shared between different parties, with global particle-number conservation as the only constraint. These invariants can be used to construct entanglement measures for different types of entanglement in such a system. It is shown that the invariants, and the measures constructed from them, take a nonzero value only if the state of the system allows for the observation of Bell-nonlocal correlations. Invariants of this kind are constructed for systems of two and three spin-1/2 fermions and examples of maximally entangled states are given that illustrate the different types of entanglement distinguished by the invariants. A general condition for the existence of SLOCC invariants and their associated measures is given as a relation between the number of fermions, their spin, and the number of spatial modes of the system. In addition, the effect of further constraints on the system, including the localization of a subset of the fermions, is discussed. Finally, a hybrid Ising-Hubbard Hamiltonian is constructed for which the ground state of a three-site chain exhibits a high degree of entanglement at the transition between a regime dominated by on-site interaction and a regime dominated by Ising interaction. This entanglement is well described by a measure constructed by the introduced method.
Chronometric cosmology and fundamental fermions
Segal, I. E.
1982-01-01
It is proposed that the fundamental fermions of nature are modeled by fields on the chronometric cosmos that are not precisely spinors but become such only in the nonchronometric limit. The imbedding of the scale-extended Poincaré group in the linearizer of the Minkowskian conformal group defines such fields, by induction. PMID:16593266
2D quasiperiodic plasmonic crystals
Bauer, Christina; Kobiela, Georg; Giessen, Harald
2012-01-01
Nanophotonic structures with irregular symmetry, such as quasiperiodic plasmonic crystals, have gained an increasing amount of attention, in particular as potential candidates to enhance the absorption of solar cells in an angular insensitive fashion. To examine the photonic bandstructure of such systems that determines their optical properties, it is necessary to measure and model normal and oblique light interaction with plasmonic crystals. We determine the different propagation vectors and consider the interaction of all possible waveguide modes and particle plasmons in a 2D metallic photonic quasicrystal, in conjunction with the dispersion relations of a slab waveguide. Using a Fano model, we calculate the optical properties for normal and inclined light incidence. Comparing measurements of a quasiperiodic lattice to the modelled spectra for angle of incidence variation in both azimuthal and polar direction of the sample gives excellent agreement and confirms the predictive power of our model. PMID:23209871
NASA Astrophysics Data System (ADS)
Schaibley, John R.; Yu, Hongyi; Clark, Genevieve; Rivera, Pasqual; Ross, Jason S.; Seyler, Kyle L.; Yao, Wang; Xu, Xiaodong
2016-11-01
Semiconductor technology is currently based on the manipulation of electronic charge; however, electrons have additional degrees of freedom, such as spin and valley, that can be used to encode and process information. Over the past several decades, there has been significant progress in manipulating electron spin for semiconductor spintronic devices, motivated by potential spin-based information processing and storage applications. However, experimental progress towards manipulating the valley degree of freedom for potential valleytronic devices has been limited until very recently. We review the latest advances in valleytronics, which have largely been enabled by the isolation of 2D materials (such as graphene and semiconducting transition metal dichalcogenides) that host an easily accessible electronic valley degree of freedom, allowing for dynamic control.
2D quasiperiodic plasmonic crystals.
Bauer, Christina; Kobiela, Georg; Giessen, Harald
2012-01-01
Nanophotonic structures with irregular symmetry, such as quasiperiodic plasmonic crystals, have gained an increasing amount of attention, in particular as potential candidates to enhance the absorption of solar cells in an angular insensitive fashion. To examine the photonic bandstructure of such systems that determines their optical properties, it is necessary to measure and model normal and oblique light interaction with plasmonic crystals. We determine the different propagation vectors and consider the interaction of all possible waveguide modes and particle plasmons in a 2D metallic photonic quasicrystal, in conjunction with the dispersion relations of a slab waveguide. Using a Fano model, we calculate the optical properties for normal and inclined light incidence. Comparing measurements of a quasiperiodic lattice to the modelled spectra for angle of incidence variation in both azimuthal and polar direction of the sample gives excellent agreement and confirms the predictive power of our model.
Quantum coherence selective 2D Raman-2D electronic spectroscopy
NASA Astrophysics Data System (ADS)
Spencer, Austin P.; Hutson, William O.; Harel, Elad
2017-03-01
Electronic and vibrational correlations report on the dynamics and structure of molecular species, yet revealing these correlations experimentally has proved extremely challenging. Here, we demonstrate a method that probes correlations between states within the vibrational and electronic manifold with quantum coherence selectivity. Specifically, we measure a fully coherent four-dimensional spectrum which simultaneously encodes vibrational-vibrational, electronic-vibrational and electronic-electronic interactions. By combining near-impulsive resonant and non-resonant excitation, the desired fifth-order signal of a complex organic molecule in solution is measured free of unwanted lower-order contamination. A critical feature of this method is electronic and vibrational frequency resolution, enabling isolation and assignment of individual quantum coherence pathways. The vibronic structure of the system is then revealed within an otherwise broad and featureless 2D electronic spectrum. This method is suited for studying elusive quantum effects in which electronic transitions strongly couple to phonons and vibrations, such as energy transfer in photosynthetic pigment-protein complexes.
Quantum coherence selective 2D Raman–2D electronic spectroscopy
Spencer, Austin P.; Hutson, William O.; Harel, Elad
2017-01-01
Electronic and vibrational correlations report on the dynamics and structure of molecular species, yet revealing these correlations experimentally has proved extremely challenging. Here, we demonstrate a method that probes correlations between states within the vibrational and electronic manifold with quantum coherence selectivity. Specifically, we measure a fully coherent four-dimensional spectrum which simultaneously encodes vibrational–vibrational, electronic–vibrational and electronic–electronic interactions. By combining near-impulsive resonant and non-resonant excitation, the desired fifth-order signal of a complex organic molecule in solution is measured free of unwanted lower-order contamination. A critical feature of this method is electronic and vibrational frequency resolution, enabling isolation and assignment of individual quantum coherence pathways. The vibronic structure of the system is then revealed within an otherwise broad and featureless 2D electronic spectrum. This method is suited for studying elusive quantum effects in which electronic transitions strongly couple to phonons and vibrations, such as energy transfer in photosynthetic pigment–protein complexes. PMID:28281541
Quantum coherence selective 2D Raman-2D electronic spectroscopy.
Spencer, Austin P; Hutson, William O; Harel, Elad
2017-03-10
Electronic and vibrational correlations report on the dynamics and structure of molecular species, yet revealing these correlations experimentally has proved extremely challenging. Here, we demonstrate a method that probes correlations between states within the vibrational and electronic manifold with quantum coherence selectivity. Specifically, we measure a fully coherent four-dimensional spectrum which simultaneously encodes vibrational-vibrational, electronic-vibrational and electronic-electronic interactions. By combining near-impulsive resonant and non-resonant excitation, the desired fifth-order signal of a complex organic molecule in solution is measured free of unwanted lower-order contamination. A critical feature of this method is electronic and vibrational frequency resolution, enabling isolation and assignment of individual quantum coherence pathways. The vibronic structure of the system is then revealed within an otherwise broad and featureless 2D electronic spectrum. This method is suited for studying elusive quantum effects in which electronic transitions strongly couple to phonons and vibrations, such as energy transfer in photosynthetic pigment-protein complexes.
High-performance functional Renormalization Group calculations for interacting fermions
NASA Astrophysics Data System (ADS)
Lichtenstein, J.; Sánchez de la Peña, D.; Rohe, D.; Di Napoli, E.; Honerkamp, C.; Maier, S. A.
2017-04-01
We derive a novel computational scheme for functional Renormalization Group (fRG) calculations for interacting fermions on 2D lattices. The scheme is based on the exchange parametrization fRG for the two-fermion interaction, with additional insertions of truncated partitions of unity. These insertions decouple the fermionic propagators from the exchange propagators and lead to a separation of the underlying equations. We demonstrate that this separation is numerically advantageous and may pave the way for refined, large-scale computational investigations even in the case of complex multiband systems. Furthermore, on the basis of speedup data gained from our implementation, it is shown that this new variant facilitates efficient calculations on a large number of multi-core CPUs. We apply the scheme to the t ,t‧ Hubbard model on a square lattice to analyze the convergence of the results with the bond length of the truncation of the partition of unity. In most parameter areas, a fast convergence can be observed. Finally, we compare to previous results in order to relate our approach to other fRG studies.
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.
NASA Astrophysics Data System (ADS)
Cui-Cui, Liao; Jin-Chao, Cui; Jiu-Zhen, Liang; Xiao-Hua, Ding
2016-01-01
In this paper, we propose a variational integrator for nonlinear Schrödinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrödinger equations with variable coefficients, cubic nonlinear Schrödinger equations and Gross-Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space. Project supported by the National Natural Science Foundation of China (Grant No. 11401259) and the Fundamental Research Funds for the Central Universities, China (Grant No. JUSRR11407).
Conjugate symplecticity of second-order linear multi-step methods
NASA Astrophysics Data System (ADS)
Feng, Quan-Dong; Jiao, Yan-Dong; Tang, Yi-Fa
2007-06-01
We review the two different approaches for symplecticity of linear multi-step methods (LMSM) by Eirola and Sanz-Serna, Ge and Feng, and by Feng and Tang, Hairer and Leone, respectively, and give a numerical example between these two approaches. We prove that in the conjugate relation with and being LMSMs, if is symplectic, then the B-series error expansions of , and of the form are equal to those of trapezoid, mid-point and Euler forward schemes up to a parameter [theta] (completely the same when [theta]=1), respectively, this also partially solves a problem due to Hairer. In particular we indicate that the second-order symmetric leap-frog scheme Z2=Z0+2[tau]J-1[backward difference]H(Z1) cannot be conjugate-symplectic via another LMSM.
Yangians and Yang-Baxter R-operators for ortho-symplectic superalgebras
NASA Astrophysics Data System (ADS)
Fuksa, J.; Isaev, A. P.; Karakhanyan, D.; Kirschner, R.
2017-04-01
Yang-Baxter relations symmetric with respect to the ortho-symplectic superalgebras are studied. We start with the formulation of graded algebras and the linear superspace carrying the vector (fundamental) representation of the ortho-symplectic supergroup. On this basis we study the analogy of the Yang-Baxter operators considered earlier for the cases of orthogonal and symplectic symmetries: the vector (fundamental) R-matrix, the L-operator defining the Yangian algebra and its first and second order evaluations. We investigate the condition for L (u) in the case of the truncated expansion in inverse powers of u and give examples of Lie algebra representations obeying these conditions. We construct the R-operator intertwining two superspinor representations and study the fusion of L-operators involving the tensor product of such representations.
NASA Astrophysics Data System (ADS)
Geiser, Jürgen
2017-07-01
In this paper, we present splitting methods which are based on iterative schemes and applied to stochastic nonlinear Schrödinger equation. We will design stochastic integrators which almost conserve the symplectic structure. The idea is based on rewriting an iterative splitting approach as a successive approximation method based on a contraction mapping principle and that we have an almost symplectic scheme. We apply a stochastic differential equation, that we can decouple into deterministic and stochastic parts, while each part can be solved analytically. Such decompositions allow accelerating the methods and preserving, under suitable conditions, the symplecticity of the schemes. A numerical analysis and application to the stochastic Schrödunger equation are presented.
A Family of Hierarchical Symplectic Maps for N-body Simulations with Post-Newtonian Corrections
NASA Astrophysics Data System (ADS)
Ferrari, Guilherme Gonçalves
Symplectic maps are well known for preserving the phase-space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times, such as the N-body problem. However, when combined with a varying time-step scheme, they end up losing its symplecticity and become numerically inefficient. We address this problem by using a recursive Hamiltonian splitting based on the time-symmetric value of the individual time-steps required by the particles in the system. We present a family of 48 quasi-symplectic maps with different orders of convergence (2nd-, 4th- & 6th-order) and three time-stepping schemes: i) 16 using constant time-steps, ii) 16 using shared adaptive time-steps, and iii) 16 using hierarchical (individual) time-steps. All maps include post-Newtonian corrections up to order 3.5PN. We describe the method and present some details of the implementation.
Petrera, Matteo; Suris, Yuri B
2017-02-01
We give a construction of completely integrable four-dimensional Hamiltonian systems with cubic Hamilton functions. Applying to the corresponding pairs of commuting quadratic Hamiltonian vector fields the so called Kahan-Hirota-Kimura discretization scheme, we arrive at pairs of birational four-dimensional maps. We show that these maps are symplectic with respect to a symplectic structure that is a perturbation of the standard symplectic structure on [Formula: see text], and possess two independent integrals of motion, which are perturbations of the original Hamilton functions and which are in involution with respect to the perturbed symplectic structure. Thus, these maps are completely integrable in the Liouville-Arnold sense. Moreover, under a suitable normalization of the original pairs of vector fields, the pairs of maps commute and share the invariant symplectic structure and the two integrals of motion.
Xiao, Jianyuan; Liu, Jian; Qin, Hong; 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 fractionalization to Majorana fermions in a dimerized Kitaev superconductor
NASA Astrophysics Data System (ADS)
Wakatsuki, Ryohei; Ezawa, Motohiko; Tanaka, Yukio; Nagaosa, Naoto
2014-07-01
We study theoretically a one-dimensional dimerized Kitaev superconductor model which belongs to BDI class with time-reversal, particle-hole, and chiral symmetries. There are two sources of the particle-hole symmetry, i.e., the sublattice symmetry and superconductivity. Accordingly, we define two types of topological numbers with respect to the chiral indices of normal and Majorana fermions, which offers an ideal laboratory to examine the interference between the two different physics within the same symmetry class. Phase diagram, zero-energy bound states, and conductance at normal metal/superconductor junction of this model are unveiled from this viewpoint. Especially, the electron fractionalization to the Majorana fermions showing the splitting of the local density of states is realized at the soliton of the dimerization in this model.
Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
NASA Astrophysics Data System (ADS)
Wakatsuki, Ryohei; Ezawa, Motohiko; Tanaka, Yukio; Nagaosa, Naoto
2015-03-01
We study theoretically a one-dimensional dimerized Kitaev superconductor model which belongs to BDI class with time-reversal, particle-hole, and chiral symmetries. There are two sources of the particle-hole symmetry, i.e., the sublattice symmetry and superconductivity. Accordingly, we define two types of topological numbers with respect to the chiral indices of normal and Majorana fermions, which offers an ideal laboratory to examine the interference between the two different physics within the same symmetry class. Phase diagram, zero-energy bound states, and conductance at normal metal/superconductor junction of this model are unveiled from this viewpoint. Especially, the electron fractionalization to the Majorana fermions showing the splitting of the local density of states is realized at the soliton of the dimerization in this model.
NASA Astrophysics Data System (ADS)
Obuse, Hideaki; Subramaniam, Arvind; Furusaki, Akira; Gruzberg, Ilya; Ludwig, Andreas
2007-03-01
We study the multifractality of critical wave functions at boundaries and corners at the Anderson metal-insulator transition for noninteracting electrons in the two-dimensional (2D) spin-orbit (symplectic) universality class. We find that the multifractal exponents near a boundary are different from those in the bulk. The exponents at a corner are found to be directly related to those at a straight boundary through a relation arising from conformal invariance. This provides direct numerical evidence for conformal invariance at the 2D spin-orbit metal-insulator transition. We also show that the presence of boundaries modifies the multifractality of the whole sample even in the thermodynamic limit.
2D transition metal dichalcogenides
NASA Astrophysics Data System (ADS)
Manzeli, Sajedeh; Ovchinnikov, Dmitry; Pasquier, Diego; Yazyev, Oleg V.; Kis, Andras
2017-08-01
Graphene is very popular because of its many fascinating properties, but its lack of an electronic bandgap has stimulated the search for 2D materials with semiconducting character. Transition metal dichalcogenides (TMDCs), which are semiconductors of the type MX2, where M is a transition metal atom (such as Mo or W) and X is a chalcogen atom (such as S, Se or Te), provide a promising alternative. Because of its robustness, MoS2 is the most studied material in this family. TMDCs exhibit a unique combination of atomic-scale thickness, direct bandgap, strong spin-orbit coupling and favourable electronic and mechanical properties, which make them interesting for fundamental studies and for applications in high-end electronics, spintronics, optoelectronics, energy harvesting, flexible electronics, DNA sequencing and personalized medicine. In this Review, the methods used to synthesize TMDCs are examined and their properties are discussed, with particular attention to their charge density wave, superconductive and topological phases. The use of TMCDs in nanoelectronic devices is also explored, along with strategies to improve charge carrier mobility, high frequency operation and the use of strain engineering to tailor their properties.
Explicit high-order symplectic integrators for charged particles in general electromagnetic fields
NASA Astrophysics Data System (ADS)
Tao, Molei
2016-12-01
This article considers non-relativistic charged particle dynamics in both static and non-static electromagnetic fields, which are governed by nonseparable, possibly time-dependent Hamiltonians. For the first time, explicit symplectic integrators of arbitrary high-orders are constructed for accurate and efficient simulations of such mechanical systems. Performances superior to the standard non-symplectic method of Runge-Kutta are demonstrated on two examples: the first is on the confined motion of a particle in a static toroidal magnetic field used in tokamak; the second is on how time-periodic perturbations to a magnetic field inject energy into a particle via parametric resonance at a specific frequency.
Constrained Galerkin variational integrators and modified constrained symplectic Runge-Kutta methods
NASA Astrophysics Data System (ADS)
Wenger, Theresa; Ober-Blöbaum, Sina; Leyendecker, Sigrid
2017-07-01
The presented constrained Galerkin variational integrators base on the higher order variational integrators in [1], now applied to holonomically constrained systems and are an extension of the constrained Galerkin methods in [2]. Sufficient conditions are given to obtain a stiffly accurate integration scheme, its structure preserving properties are analysed and the convergence order as well as the computational efficiency are investigated numerically. The equivalence to constrained symplectic Runge-Kutta methods is shown, with focus on a modified constrained symplectic Runge-Kutta method, that was first introduced in [3], there for the unconstrained case.
NASA Astrophysics Data System (ADS)
Wang, Dongling; Xiao, Aiguo; Li, Xueyang
2013-02-01
Based on W-transformation, some parametric symplectic partitioned Runge-Kutta (PRK) methods depending on a real parameter α are developed. For α=0, the corresponding methods become the usual PRK methods, including Radau IA-IA¯ and Lobatto IIIA-IIIB methods as examples. For any α≠0, the corresponding methods are symplectic and there exists a value α∗ such that energy is preserved in the numerical solution at each step. The existence of the parameter and the order of the numerical methods are discussed. Some numerical examples are presented to illustrate these results.
Complete characterization of fourth-order symplectic integrators with extended-linear coefficients.
Chin, Siu A
2006-02-01
The structure of symplectic integrators up to fourth order can be completely and analytically understood when the factorization (split) coefficients are related linearly but with a uniform nonlinear proportional factor. The analytic form of these extended-linear symplectic integrators greatly simplified proofs of their general properties and allowed easy construction of both forward and nonforward fourth-order algorithms with an arbitrary number of operators. Most fourth-order forward integrators can now be derived analytically from this extended-linear formulation without the use of symbolic algebra.
Chang, P
2004-09-15
A differential algebraic integration algorithm is developed for symplectic mapping through a three-dimensional (3-D) magnetic field. The self-consistent reference orbit in phase space is obtained by making a canonical transformation to eliminate the linear part of the Hamiltonian. Transfer maps from the entrance to the exit of any 3-D magnetic field are then obtained through slice-by-slice symplectic integration. The particle phase-space coordinates are advanced by using the integrable polynomial procedure. This algorithm is a powerful tool to attain nonlinear maps for insertion devices in synchrotron light source or complicated magnetic field in the interaction region in high energy colliders.
GENERAL: Symplectic-energy-first integrators of discrete mechanico-electrical dynamical systems
NASA Astrophysics Data System (ADS)
Fu, Jing-Li; Chen, Ben-Yong; Tang, Yi-Fa; Fu, Hao
2008-11-01
A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler-Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.
Landau quantization of Dirac fermions in graphene and its multilayers
NASA Astrophysics Data System (ADS)
Yin, Long-Jing; Bai, Ke-Ke; Wang, Wen-Xiao; Li, Si-Yu; Zhang, Yu; He, Lin
2017-08-01
When electrons are confined in a two-dimensional (2D) system, typical quantum-mechanical phenomena such as Landau quantization can be detected. Graphene systems, including the single atomic layer and few-layer stacked crystals, are ideal 2D materials for studying a variety of quantum-mechanical problems. In this article, we review the experimental progress in the unusual Landau quantized behaviors of Dirac fermions in monolayer and multilayer graphene by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Through STS measurement of the strong magnetic fields, distinct Landau-level spectra and rich level-splitting phenomena are observed in different graphene layers. These unique properties provide an effective method for identifying the number of layers, as well as the stacking orders, and investigating the fundamentally physical phenomena of graphene. Moreover, in the presence of a strain and charged defects, the Landau quantization of graphene can be significantly modified, leading to unusual spectroscopic and electronic properties.
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.
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.
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.
Quantum Algorithms for Fermionic Simulations
NASA Astrophysics Data System (ADS)
Ortiz, Gerardo
2001-06-01
The probabilistic simulation of quantum systems in classical computers is known to be limited by the so-called sign or phase problem, a problem believed to be of exponential complexity. This ``disease" manifests itself by the exponentially hard task of estimating the expectation value of an observable with a given error. Therefore, probabilistic simulations on a classical computer do not seem to qualify as a practical computational scheme for general quantum many-body problems. The limiting factors, for whatever reasons, are negative or complex-valued probabilities whether the simulations are done in real or imaginary time. In 1981 Richard Feynman raised some provocative questions in connection to the ``exact imitation'' of such systems using a special device named a ``quantum computer.'' Feynman hesitated about the possibility of imitating fermion systems using such a device. Here we address some of his concerns and, in particular, investigate the simulation of fermionic systems. We show how quantum algorithms avoid the sign problem by reducing the complexity from exponential to polynomial. Our demonstration is based upon the use of isomorphisms of *-algebras (spin-particle transformations) which connect different models of quantum computation. In particular, we present fermionic models (the fabled ``Grassmann Chip''); but, of course, these models are not the only ones since our spin-particle connections allow us to introduce more ``esoteric'' models of computation. We present specific quantum algorithms that illustrate the main points of our algebraic approach.
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
Topological superfluid state of fermions on a p-band optical square lattice
NASA Astrophysics Data System (ADS)
Wu, Ya-Jie; He, Jing; Zang, Chun-Li; Kou, Su-Peng
2012-08-01
In this paper we study an interacting mixture of ultracold spinless fermions on the s band and bosons on the p band in a 2D square optical lattice, of which the effective model is reduced to a p-band fermionic system with nearest-neighbor attractive interaction. From this effective p-band model, we find a translation symmetry protected Z2 topological superfluid that is characterized by a special fermion parity pattern at high-symmetry points in momentum space k=(0,0), (0,π), (π,0), (π,π). Such Z2 topological superfluid supports the robust Majorana edge modes and a new type of low-energy excitation—(supersymmetric) Z2 link excitation.
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
Tuning of Fermi contour anisotropy in GaAs (001) 2D holes via strain
NASA Astrophysics Data System (ADS)
Jo, Insun; Mueed, M. A.; Pfeiffer, L. N.; West, K. W.; Baldwin, K. W.; Winkler, R.; Padmanabhan, Medini; Shayegan, M.
2017-06-01
We demonstrate tuning of the Fermi contour anisotropy of two-dimensional (2D) holes in a symmetric GaAs (001) quantum well via the application of in-plane strain. The ballistic transport of high-mobility hole carriers allows us to measure the Fermi wavevector of 2D holes via commensurability oscillations as a function of strain. Our results show that a small amount of in-plane strain, on the order of 10-4, can induce significant Fermi wavevector anisotropy as large as 3.3, equivalent to a mass anisotropy of 11 in a parabolic band. Our method to tune the anisotropy in situ provides a platform to study the role of anisotropy in phenomena such as the fractional quantum Hall effect and composite fermions in interacting 2D systems.
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.
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.
Multipartite concurrence for identical-fermion systems
NASA Astrophysics Data System (ADS)
Majtey, A. P.; Bouvrie, P. A.; Valdés-Hernández, A.; Plastino, A. R.
2016-03-01
We study the problem of detecting multipartite entanglement among indistinguishable fermionic particles. A multipartite concurrence for pure states of N identical fermions, each one having a d -dimensional single-particle Hilbert space, is introduced. Such an entanglement measure, in particular, is optimized for maximally entangled states of three identical fermions that play a role analogous to the usual (qubit) Greenberger-Horne-Zeilinger state. In addition, it is shown that the fermionic multipartite concurrence can be expressed as the mean value of an observable, provided two copies of the composite state are available.
An optimized formulation for Deprit-type Lie transformations of Taylor maps for symplectic systems
Shi, Jicong; Yan, Yiton T.
1993-06-01
An optimized iterative formulation is presented for directly transforming a Taylor map of a symplectic system into a Deprit-type Lie transformation, which is a composition of a linear transfer matrix and a single Lie transformation, to an arbitrary order.
A fourth order modified trigonometrically fitted symplectic Runge-Kutta-Nyström method
NASA Astrophysics Data System (ADS)
Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E.
2013-10-01
In this work we construct a modified trigonometrically fitted symplectic Runge Kutta Nyström method based on the forth order five stages method of Calvo and Sanz-Serna. We apply the new method on the numerical integration of the two-body problem.
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
Symplectic and antiplectic waves in an array of beating cilia attached to a closed body
NASA Astrophysics Data System (ADS)
Ghorbani, Aref; Najafi, Ali
2017-05-01
By taking into account the hydrodynamic interactions in a one dimensional array of model cilia attached to a no-slip cylinderical surface, we investigate their synchronized motion. We show how the emergence of metachronal waves depends on the initial state of the system and investigate the conditions under which the formation of symplectic and antiplectic waves are possible.
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.
NASA Astrophysics Data System (ADS)
Guzzo, Massimiliano
2001-07-01
I have improved the precision of the leap-frog symplectic integrators for perturbed Kepler problems at small eccentricities, without significant loss of CPU time. The integration scheme proposed is competitive, in some situations, with the so-called mixed variable integrators.
NASA Astrophysics Data System (ADS)
Canoglu, Ahmet; Güldogan, Bahri; Salihoglu, Selâmi
We obtain new integrable coupled nonlinear partial differential equations by assuming the soliton connection having values in orthogonal-symplectic Lie superalgebras [B(m, n), C(n), D(m, n)]. These equations are coupled Nonlinear Schrödinger equations on various super symmetric spaces.
Observation of spatial charge and spin correlations in the 2D Fermi-Hubbard model.
Cheuk, Lawrence W; Nichols, Matthew A; Lawrence, Katherine R; Okan, Melih; Zhang, Hao; Khatami, Ehsan; Trivedi, Nandini; Paiva, Thereza; Rigol, Marcos; Zwierlein, Martin W
2016-09-16
Strong electron correlations lie at the origin of high-temperature superconductivity. Its essence is believed to be captured by the Fermi-Hubbard model of repulsively interacting fermions on a lattice. Here we report on the site-resolved observation of charge and spin correlations in the two-dimensional (2D) Fermi-Hubbard model realized with ultracold atoms. Antiferromagnetic spin correlations are maximal at half-filling and weaken monotonically upon doping. At large doping, nearest-neighbor correlations between singly charged sites are negative, revealing the formation of a correlation hole, the suppressed probability of finding two fermions near each other. As the doping is reduced, the correlations become positive, signaling strong bunching of doublons and holes, in agreement with numerical calculations. The dynamics of the doublon-hole correlations should play an important role for transport in the Fermi-Hubbard model. Copyright © 2016, American Association for the Advancement of Science.
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.
Is the Composite Fermion a Dirac Particle?
NASA Astrophysics Data System (ADS)
Son, Dam Thanh
2015-07-01
We propose a particle-hole symmetric theory of the Fermi-liquid ground state of a half-filled Landau level. This theory should be applicable for a Dirac fermion in the magnetic field at charge neutrality, as well as for the ν =1/2 quantum Hall ground state of nonrelativistic fermions in the limit of negligible inter-Landau-level mixing. We argue that when particle-hole symmetry is exact, the composite fermion is a massless Dirac fermion, characterized by a Berry phase of π around the Fermi circle. We write down a tentative effective field theory of such a fermion and discuss the discrete symmetries, in particular, C P . The Dirac composite fermions interact through a gauge, but non-Chern-Simons, interaction. The particle-hole conjugate pair of Jain-sequence states at filling factors n /(2 n +1 ) and (n +1 )/(2 n +1 ) , which in the conventional composite fermion picture corresponds to integer quantum Hall states with different filling factors, n and n +1 , is now mapped to the same half-integer filling factor n +1/2 of the Dirac composite fermion. The Pfaffian and anti-Pfaffian states are interpreted as d -wave Bardeen-Cooper-Schrieffer paired states of the Dirac fermion with orbital angular momentum of opposite signs, while s -wave pairing would give rise to a particle-hole symmetric non-Abelian gapped phase. When particle-hole symmetry is not exact, the Dirac fermion has a C P -breaking mass. The conventional fermionic Chern-Simons theory is shown to emerge in the nonrelativistic limit of the massive 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
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.
Dipole oscillations in fermionic mixtures
Chiacchiera, S.; Macri, T.; Trombettoni, A.
2010-03-15
We study dipole oscillations in a general fermionic mixture. Starting from the Boltzmann equation, we classify the different solutions in the parameter space through the number of real eigenvalues of the small oscillations matrix. We discuss how this number can be computed using the Sturm algorithm and its relation with the properties of the Laplace transform of the experimental quantities. After considering two components in harmonic potentials having different trapping frequencies, we study dipole oscillations in three-component mixtures. Explicit computations are done for realistic experimental setups using the classical Boltzmann equation without intraspecies interactions. A brief discussion of the application of this classification to general collective oscillations is also presented.
Chiral 2D "strange metals" from SYM
NASA Astrophysics Data System (ADS)
Berkooz, Micha; Narayan, Prithvi; Zait, Amir
2015-01-01
Familiar field theories may contain closed subsectors made out of only fermions, which can be used to explore new and unusual phases of matter in lower dimensions. We focus on the fermionic su(1, 1) sector in SYM and on its ground states, which are Fermi surface states/operators. By computing their spectrum to order ( g {YM/2} N)2, we argue that fluctuations around this Fermi surface, within the sector and in the limit k F → ∞, are governed by a chiral 1+1 dimensional sector of the "strange metal" coset SU( N ) N ⊗ SU( N ) N /SU( N )2 N . On the gravity side, the conjectured dual configuration is an S = 0 degeneration of a rotating black hole. On general grounds we expect that the near horizon excitations of ( S = 0, Ω = 1, J → ∞) degenerations of black holes will be governed by a chiral sector of a 1+1 CFT.
Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model
Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; ...
2016-08-25
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 fermionicmore » symmetry-protected topological phase. This state—protected by time-reversal and reflection symmetries—cannot be connected adiabatically to a free-fermion topological phase.« less
Quantitative 2D liquid-state NMR.
Giraudeau, Patrick
2014-06-01
Two-dimensional (2D) liquid-state NMR has a very high potential to simultaneously determine the absolute concentration of small molecules in complex mixtures, thanks to its capacity to separate overlapping resonances. However, it suffers from two main drawbacks that probably explain its relatively late development. First, the 2D NMR signal is strongly molecule-dependent and site-dependent; second, the long duration of 2D NMR experiments prevents its general use for high-throughput quantitative applications and affects its quantitative performance. Fortunately, the last 10 years has witnessed an increasing number of contributions where quantitative approaches based on 2D NMR were developed and applied to solve real analytical issues. This review aims at presenting these recent efforts to reach a high trueness and precision in quantitative measurements by 2D NMR. After highlighting the interest of 2D NMR for quantitative analysis, the different strategies to determine the absolute concentrations from 2D NMR spectra are described and illustrated by recent applications. The last part of the manuscript concerns the recent development of fast quantitative 2D NMR approaches, aiming at reducing the experiment duration while preserving - or even increasing - the analytical performance. We hope that this comprehensive review will help readers to apprehend the current landscape of quantitative 2D NMR, as well as the perspectives that may arise from it.
Coherent states in the fermionic Fock space
NASA Astrophysics Data System (ADS)
Oeckl, Robert
2015-01-01
We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing kernel Hilbert space of continuous holomorphic functions.
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
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.
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.
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.
Causal fermions in discrete space-time
NASA Astrophysics Data System (ADS)
Farrelly, Terence C.; Short, Anthony J.
2014-01-01
In this paper, we consider fermionic systems in discrete space-time evolving with a strict notion of causality, meaning they evolve unitarily and with a bounded propagation speed. First, we show that the evolution of these systems has a natural decomposition into a product of local unitaries, which also holds if we include bosons. Next, we show that causal evolution of fermions in discrete space-time can also be viewed as the causal evolution of a lattice of qubits, meaning these systems can be viewed as quantum cellular automata. Following this, we discuss some examples of causal fermionic models in discrete space-time that become interesting physical systems in the continuum limit: Dirac fermions in one and three spatial dimensions, Dirac fields, and briefly the Thirring model. Finally, we show that the dynamics of causal fermions in discrete space-time can be efficiently simulated on a quantum computer.
Tunable Dirac Fermion Dynamics in Topological Insulators
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.
2013-01-01
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. PMID:23934507
Tunable Dirac fermion dynamics in topological insulators.
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
2013-01-01
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.
Evidence for Symplectic Symmetry in AbInitio No-Core Shell Model Results for Light Nuclei
NASA Astrophysics Data System (ADS)
Dytrych, Tomáš; Sviratcheva, Kristina D.; Bahri, Chairul; Draayer, Jerry P.; Vary, James P.
2007-04-01
Clear evidence for symplectic symmetry in low-lying states of C12 and O16 is reported. Eigenstates of C12 and O16, determined within the framework of the no-core shell model using the J-matrix inverse scattering potential with A≤16 (JISP16) nucleon-nucleon (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.
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
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.
Bosonization of free Weyl fermions
NASA Astrophysics Data System (ADS)
Marino, E. C.
2017-03-01
We generalize the method of bosonization, in its complete form, to a spacetime with 3 + 1 dimensions, and apply it to free Weyl fermion fields, which thereby, can be expressed in terms of a boson field, namely the Kalb-Ramond anti-symmetric tensor gauge field. The result may have interesting consequences both in condensed matter and in particle physics. In the former, the bosonized form of the Weyl chiral currents provides a simple explanation for the angle-dependent magneto-conductance recently observed in materials known as Weyl semimetals. In the latter, conversely, since electrons can be thought of as a combination of left and right Weyl fermions, our result suggests the possibility of a unified description of the elementary particles, which undergo the fundamental interactions, with the mediators of such interactions, namely, the gauge fields. This would fulfill the pioneering attempt of Skyrme, to unify the particles with their interaction mediators (Skyrme 1962 Nucl. Phys. 31 556).
Cosmology of fermionic dark matter
Boeckel, Tillmann; Schaffner-Bielich, Juergen
2007-11-15
We explore a model for a fermionic dark matter particle family which decouples from the rest of the particles when at least all standard model particles are in equilibrium. We calculate the allowed ranges for mass and chemical potential to be compatible with big bang nucleosynthesis (BBN) calculations and WMAP data for a flat universe with dark energy ({omega}{sub {lambda}}{sup 0}=0.72, {omega}{sub M}{sup 0}=0.27, h=0.7). Futhermore we estimate the free streaming length for fermions and antifermions to allow comparison to large scale structure data (LSS). We find that for dark matter decoupling when all standard model particles are present even the least restrictive combined BBN calculation and WMAP results allow us to constrain the initial dark matter chemical potential to a highest value of 6.3 times the dark matter temperature. In this case, the resulting mass range is at most 1.8 eV{<=}m{<=}53 eV, where the upper bound scales linearly with g{sub eff}{sup s}(T{sub Dec}). From LSS we find that, similar to ordinary warm dark matter models, the particle mass has to be larger than {approx}500 eV [meaning g{sub eff}{sup s}(T{sub Dec})>10{sup 3}] to be compatible with observations of the Ly {alpha} forest at high redshift, but still the dark matter chemical potential over temperature ratio can exceed unity.
Thermalization of Fermionic Quantum Walkers
NASA Astrophysics Data System (ADS)
Hamza, Eman; Joye, Alain
2017-03-01
We consider the discrete time dynamics of an ensemble of fermionic quantum walkers moving on a finite discrete sample, interacting with a reservoir of infinitely many quantum particles on the one dimensional lattice. The reservoir is given by a fermionic quasifree state, with free discrete dynamics given by the shift, whereas the free dynamics of the non-interacting quantum walkers in the sample is defined by means of a unitary matrix. The reservoir and the sample exchange particles at specific sites by a unitary coupling and we study the discrete dynamics of the coupled system defined by the iteration of the free discrete dynamics acting on the unitary coupling, in a variety of situations. In particular, in absence of correlation within the particles of the reservoir and under natural assumptions on the sample's dynamics, we prove that the one- and two-body reduced density matrices of the sample admit large times limits characterized by the state of the reservoir which are independent of the free dynamics of the quantum walkers and of the coupling strength. Moreover, the corresponding asymptotic density profile in the sample is flat and the correlations of number operators have no structure, a manifestation of thermalization.
Fermion condensation and gapped domain walls in topological orders
NASA Astrophysics Data System (ADS)
Wan, Yidun; Wang, Chenjie
2017-03-01
We study fermion condensation in bosonic topological orders in two spatial dimensions. Fermion condensation may be realized as gapped domain walls between bosonic and fermionic topological orders, which may be thought of as real-space phase transitions from bosonic to fermionic topological orders. This picture generalizes the previous idea of understanding boson condensation as gapped domain walls between bosonic topological orders. While simple-current fermion condensation was considered before, we systematically study general fermion condensation and show that it obeys a Hierarchy Principle: a general fermion condensation can always be decomposed into a boson condensation followed by a minimal fermion condensation. The latter involves only a single self-fermion that is its own anti-particle and that has unit quantum dimension. We develop the rules of minimal fermion condensation, which together with the known rules of boson condensation, provides a full set of rules for general fermion condensation.
Two-Dimensional Massless Dirac Fermions in Antiferromagnetic A Fe2As2 (A =Ba ,Sr )
NASA Astrophysics Data System (ADS)
Chen, Zhi-Guo; Wang, Luyang; Song, Yu; Lu, Xingye; Luo, Huiqian; Zhang, Chenglin; Dai, Pengcheng; Yin, Zhiping; Haule, Kristjan; Kotliar, Gabriel
2017-09-01
We report infrared studies of A Fe2As2 (A =Ba , Sr), two representative parent compounds of iron-arsenide superconductors, at magnetic fields (B ) up to 17.5 T. Optical transitions between Landau levels (LLs) were observed in the antiferromagnetic states of these two parent compounds. Our observation of a √{B } dependence of the LL transition energies, the zero-energy intercepts at B =0 T under the linear extrapolations of the transition energies and the energy ratio (˜2.4 ) between the observed LL transitions, combined with the linear band dispersions in two-dimensional (2D) momentum space obtained by theoretical calculations, demonstrates the existence of massless Dirac fermions in the antiferromagnet BaFe2 As2 . More importantly, the observed dominance of the zeroth-LL-related absorption features and the calculated bands with extremely weak dispersions along the momentum direction kz indicate that massless Dirac fermions in BaFe2 As2 are 2D. Furthermore, we find that the total substitution of the barium atoms in BaFe2 As2 by strontium atoms not only maintains 2D massless Dirac fermions in this system, but also enhances their Fermi velocity, which supports that the Dirac points in iron-arsenide parent compounds are topologically protected.
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
2016-07-28
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.
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
Two-Dimensional Massless Dirac Fermions in Antiferromagnetic AFe_{2}As_{2} (A=Ba,Sr).
Chen, Zhi-Guo; Wang, Luyang; Song, Yu; Lu, Xingye; Luo, Huiqian; Zhang, Chenglin; Dai, Pengcheng; Yin, Zhiping; Haule, Kristjan; Kotliar, Gabriel
2017-09-01
We report infrared studies of AFe_{2}As_{2} (A=Ba, Sr), two representative parent compounds of iron-arsenide superconductors, at magnetic fields (B) up to 17.5 T. Optical transitions between Landau levels (LLs) were observed in the antiferromagnetic states of these two parent compounds. Our observation of a sqrt[B] dependence of the LL transition energies, the zero-energy intercepts at B=0 T under the linear extrapolations of the transition energies and the energy ratio (∼2.4) between the observed LL transitions, combined with the linear band dispersions in two-dimensional (2D) momentum space obtained by theoretical calculations, demonstrates the existence of massless Dirac fermions in the antiferromagnet BaFe_{2}As_{2}. More importantly, the observed dominance of the zeroth-LL-related absorption features and the calculated bands with extremely weak dispersions along the momentum direction k_{z} indicate that massless Dirac fermions in BaFe_{2}As_{2} are 2D. Furthermore, we find that the total substitution of the barium atoms in BaFe_{2}As_{2} by strontium atoms not only maintains 2D massless Dirac fermions in this system, but also enhances their Fermi velocity, which supports that the Dirac points in iron-arsenide parent compounds are topologically protected.
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.
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.
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.
Dual fermion approach for disordered interacting fermion systems
NASA Astrophysics Data System (ADS)
Yang, Shuxiang; Haase, Patrick; Terletska, Hanna; Meng, Ziyang; Moreno, Juana; Jarrell, Mark; Pruschke, Thomas
2013-03-01
Understanding the combined effect of electron-electron interaction and disorder is one of the crucial questions in condensed matter physics. There is an obvious need of theoretical tools which allow to treat both these effects on equal footing. To study the intricate interplay of these effects, we generalize our recently proposed dual fermion approach to include both electron-electron interaction and disorder. Since the constraint imposed on the dual-space Feynman diagrams in the disordered case does not apply to those generated due to interactions, it is essential to treat elastic scattering processes due to the disorder separately from the inelastic scattering processes due to the pure interaction and mixed contributions. I will discuss the resulting diagrammatic formalism and an algorithm for its implementation. The possible applications for the Anderson Falicov-Kimball and the Anderson-Hubbard models are also discussed.
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.
Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
Hong Jialin . E-mail: lichun@lsec.cc.ac.cn
2006-01-20
In this paper, we consider the multi-symplectic Runge-Kutta (MSRK) methods applied to the nonlinear Dirac equation in relativistic quantum physics, based on a discovery of the multi-symplecticity of the equation. In particular, the conservation of energy, momentum and charge under MSRK discretizations is investigated by means of numerical experiments and numerical comparisons with non-MSRK methods. Numerical experiments presented reveal that MSRK methods applied to the nonlinear Dirac equation preserve exactly conservation laws of charge and momentum, and conserve the energy conservation in the corresponding numerical accuracy to the method utilized. It is verified numerically that MSRK methods are stable and convergent with respect to the conservation laws of energy, momentum and charge, and MSRK methods preserve not only the inner geometric structure of the equation, but also some crucial conservative properties in quantum physics. A remarkable advantage of MSRK methods applied to the nonlinear Dirac equation is the precise preservation of charge conservation law.
NASA Astrophysics Data System (ADS)
Peng, Haijun; Wang, Xinwei; Zhang, Sheng; Chen, Biaosong
2017-07-01
Nonlinear state-delayed optimal control problems have complex nonlinear characters. To solve this complex nonlinear problem, an iterative symplectic pseudospectral method based on quasilinearization techniques, the dual variational principle and pseudospectral methods is proposed in this paper. First, the proposed method transforms the original nonlinear optimal control problem into a series of linear quadratic optimal control problems. Then, a symplectic pseudospectral method is developed to solve these converted linear quadratic state-delayed optimal control problems. Coefficient matrices in the proposed method are sparse and symmetric since the dual variational principle is used, which makes the proposed method highly efficient. Converged numerical solutions with high precision can be obtained after a few iterations due to the benefit of the local pseudospectral method and quasilinearization techniques. In the numerical simulations, other numerical methods were used for comparisons. The numerical simulation results show that the proposed method is highly accurate, efficient and robust.
A reciprocity law and the skew Pieri rule for the symplectic group
NASA Astrophysics Data System (ADS)
Howe, Roger; Lávička, Roman; Lee, Soo Teck; Souček, Vladimír
2017-03-01
We use the theory of skew duality to show that decomposing the tensor product of k irreducible representations of the symplectic group Sp2 m=Sp2 m(ℂ ) is equivalent to branching from Sp2n to Sp2 n1×⋯ ×Sp2 nk , where n ,n1,… ,nk are positive integers such that n =n1+⋯ +nk and the njs depend on m as well as the representations in the tensor product. Using this result and a work of Lepowsky, we obtain a skew Pieri rule for Sp2m, i.e., a description of the irreducible decomposition of the tensor product of an irreducible representation of the symplectic group Sp2m with a fundamental representation.
A new family of four-dimensional symplectic and integrable mappings
NASA Astrophysics Data System (ADS)
Capel, H. W.; Sahadevan, R.
2001-01-01
We investigate the generalisations of the Quispel, Roberts and Thompson (QRT) family of mappings in the plane leaving a rational quadratic expression invariant to the case of four variables. We assume invariance of the rational expression under a cyclic permutation of variables and we impose a symplectic structure with Poisson brackets of the Weyl type. All mappings satisfying these conditions are shown to be integrable either as four-dimensional mappings with two explicit integrals which are in involution with respect to the symplectic structure and which can also be inferred from the periodic reductions of the double-discrete versions of the modified Korteweg-deVries ( ΔΔMKdV) and sine-Gordon ( ΔΔsG) equations or by reduction to two-dimensional mappings with one integral of the symmetric QRT family.
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.
Ab initio calculations in the symplectic no-core configuration interaction framework
NASA Astrophysics Data System (ADS)
McCoy, Anna; Caprio, Mark; Dytrych, Tomas
2016-09-01
A major challenge in quantitatively predicting nuclear structure directly from realistic nucleon-nucleon interactions, i.e., ab initio, arises due to an explosion in the dimension of the traditional Slater determinant basis as the number of nucleons and included shells increases. The need for including highly excited configurations arises, in large part, because the kinetic energy induces strong coupling across shells. However, the kinetic energy conserves symplectic symmetry. By combining this symplectic symmetry with the no-core configuration interaction (NCCI) framework, we reduce the size of basis necessary to obtain accurate results for p-shell nuclei. Supported by the US DOE under Grants DE-AC05-06OR23100 and DE-FG02-95ER-40934, and the Czech Science Foundation under Grant No. 16-16772S.
Transference of Fermi Contour Anisotropy to Composite Fermions
NASA Astrophysics Data System (ADS)
Jo, Insun; Rosales, K. A. Villegas; Mueed, M. A.; Pfeiffer, L. N.; West, K. W.; Baldwin, K. W.; Winkler, R.; Padmanabhan, Medini; Shayegan, M.
2017-07-01
There has been a surge of recent interest in the role of anisotropy in interaction-induced phenomena in two-dimensional (2D) charged carrier systems. A fundamental question is how an anisotropy in the energy-band structure of the carriers at zero magnetic field affects the properties of the interacting particles at high fields, in particular of the composite fermions (CFs) and the fractional quantum Hall states (FQHSs). We demonstrate here tunable anisotropy for holes and hole-flux CFs confined to GaAs quantum wells, via applying in situ in-plane strain and measuring their Fermi wave vector anisotropy through commensurability oscillations. For strains on the order of 10-4 we observe significant deformations of the shapes of the Fermi contours for both holes and CFs. The measured Fermi contour anisotropy for CFs at high magnetic field (αCF) is less than the anisotropy of their low-field hole (fermion) counterparts (αF), and closely follows the relation αCF=√{αF}. The energy gap measured for the ν =2 /3 FQHS, on the other hand, is nearly unaffected by the Fermi contour anisotropy up to αF˜3.3 , the highest anisotropy achieved in our experiments.
NASA Astrophysics Data System (ADS)
de Brito, K. P. S.; da Rocha, Roldão
2016-10-01
The spinor fields on 5-dimensional Lorentzian manifolds are classified according to the geometric Fierz identities, which involve their bilinear covariants. Based upon this classification, which generalises the celebrated 4-dimensional Lounesto classification of spinor fields, new non-trivial classes of 5-dimensional spinor fields are hence found, with important potential applications regarding bulk fermions and their subsequent localisation on brane-worlds. In addition, quaternionic bilinear covariants are used to derive the quaternionic spin density through the truncated exterior bundle. In order to accomplish the realisation of these new spinors, a Killing vector field is constructed on the horizon of a 5-dimensional Kerr black hole. This Killing vector field is shown to reach the time-like Killing vector field at spatial infinity through a current 1-form density, constructed with the new derived spinor fields. The current density is, moreover, expressed as the fünfbein component, assuming a condensed form.
Noncommutativity Parameter and Composite Fermions
NASA Astrophysics Data System (ADS)
Jellal, Ahmed
We determine some particular values of the noncommutativity parameter θ and show that the Murthy Shankar approach is in fact a particular case of a more general one. Indeed, using the fractional quantum Hall effect (FQHE) experimental data, we give a measurement of θ. This measurement can be obtained by considering some values of the filling factor ν and other ingredients, magnetic field B and electron density ρ. Moreover, it is found that θ can be quantized either fractionally or integrally in terms of the magnetic length l0 and the quantization is exactly what Murthy and Shankar formulated recently for the FQHE. On the other hand, we show that the mapping of the FQHE in terms of the composite fermion basis has a noncommutative geometry nature and therefore there is a more general way than the Murthy Shankar method to do this mapping.
Flavor symmetries and fermion masses
Rasin, Andrija
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_{ub}/V_{cb} = √m_{u}/m_{c} and V_{td}/V_{ts} = √m_{d}/m_{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 β → sγ constrains the parameter space when the ratio of the vacuum expectation values of the two Higgs doublets, tanβ, 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.
Symes, L M; Blakie, P B
2017-01-01
We develop numerical methods for solving the spin-2 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of this evolution equation that leads to two exactly solvable subsystems. Utilizing second-order and fourth-order composition schemes we realize two fully symplectic integration algorithms, the first such algorithms for evolving spin-2 condensates. We demonstrate the accuracy of these algorithms against other methods on application to an exact continuous wave solution that we derive.
A fourth order modified trigonometrically fitted symplectic Runge-Kutta-Nyström method
NASA Astrophysics Data System (ADS)
Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E.
2014-12-01
In this work we construct a modified trigonometrically fitted symplectic Runge Kutta Nyström method based on the fourth order five stages method of Calvo and Sanz-Serna (1994). We apply the new method on the numerical integration of the two-dimensional harmonic oscillator, the two-body problem, a perturbed two-body problem and two two-dimensional nonlinear oscillatory Hamiltonian systems.
Characteristic classes of star products on Marsden-Weinstein reduced symplectic manifolds
NASA Astrophysics Data System (ADS)
Reichert, Thorsten
2017-04-01
In this note we consider a quantum reduction scheme in deformation quantization on symplectic manifolds proposed by Bordemann, Herbig and Waldmann based on BRST cohomology. We explicitly construct the induced map on equivalence classes of star products which will turn out to be an analogue to the Kirwan map in the Cartan model of equivariant cohomology. As a byproduct, we shall see that every star product on a (suitable) reduced manifold is equivalent to a reduced star product.
Characteristic classes of star products on Marsden-Weinstein reduced symplectic manifolds
NASA Astrophysics Data System (ADS)
Reichert, Thorsten
2016-12-01
In this note we consider a quantum reduction scheme in deformation quantization on symplectic manifolds proposed by Bordemann, Herbig and Waldmann based on BRST cohomology. We explicitly construct the induced map on equivalence classes of star products which will turn out to be an analogue to the Kirwan map in the Cartan model of equivariant cohomology. As a byproduct, we shall see that every star product on a (suitable) reduced manifold is equivalent to a reduced star product.
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.
NASA Astrophysics Data System (ADS)
Symes, L. M.; Blakie, P. B.
2017-01-01
We develop numerical methods for solving the spin-2 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of this evolution equation that leads to two exactly solvable subsystems. Utilizing second-order and fourth-order composition schemes we realize two fully symplectic integration algorithms, the first such algorithms for evolving spin-2 condensates. We demonstrate the accuracy of these algorithms against other methods on application to an exact continuous wave solution that we derive.
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.
Entanglement in fermion systems and quantum metrology
NASA Astrophysics Data System (ADS)
Benatti, F.; Floreanini, R.; Marzolino, U.
2014-03-01
Entanglement in fermion many-body systems is studied using a generalized definition of separability based on partitions of the set of observables, rather than on particle tensor products. In this way, the characterizing properties of nonseparable fermion states can be explicitly analyzed, allowing a precise description of the geometric structure of the corresponding state space. These results have direct applications in fermion quantum metrology: Sub-shot-noise accuracy in parameter estimation can be obtained without the need of a preliminary state entangling operation.
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.
Two-dimensional fermionic Hong-Ou-Mandel interference with massless Dirac fermions
NASA Astrophysics Data System (ADS)
Khan, M. A.; Leuenberger, Michael N.
2014-08-01
We propose a two-dimensional Hong-Ou-Mandel (HOM) type interference experiment for massless Dirac fermions in graphene and 3D topological insulators. Since massless Dirac fermions exhibit linear dispersion, similar to photons in vacuum, they can be used to obtain the HOM interference intensity pattern as a function of the delay time between two massless Dirac fermions. We show that while the Coulomb interaction leads to a significant change in the angle dependence of the tunneling of two identical massless Dirac fermions incident from opposite sides of a potential barrier, it does not affect the HOM interference pattern. We apply our formalism to develop a massless Dirac fermion beam splitter (BS) for controlling the transmission and reflection coefficients. We calculate the resulting time-resolved correlation function for two identical massless Dirac fermions scattering off the BS.
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.
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.
Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation
NASA Astrophysics Data System (ADS)
Su, Bo; Tuo, Xianguo; Xu, Ling
2017-08-01
Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.
Modification of logarithmic Hamiltonians and application of explicit symplectic-like integrators
NASA Astrophysics Data System (ADS)
Li, Dan; Wu, Xin
2017-08-01
We modify the logarithmic Hamiltonian of Mikkola and Tanikawa by adding a constant (or function) to both the kinetic energy and the force function. Explicit symplectic algorithms are available when the logarithmic Hamiltonian has two separable parts of coordinates and momenta. However, they are not if the logarithmic Hamiltonian is inseparable. Fortunately, they are still efficient by manipulating the logarithmic Hamiltonian as a new separable Hamiltonian in an extended phase space. In fact, they belong to symplectic-like integrators. The choice of mixing maps affects the performance of the considered symplectic-like integrators. It is shown that two maps about sequent permutations of coordinates and momenta are inferior to a map with mid-point permutations in some cases. The choice of the constant (or function) added also exerts some influence on the performance of the algorithms. As a result, with the help of the mid-point permutations and a suitable choice for the constant (or function) included, the logarithmic Hamiltonian methods bring an increase in accuracy compared to the non-logarithmic ones, particularly for highly eccentric orbits.
Conservation Laws in Fluids and MHD: MultiSymplectic and Hamiltonian Approaches
NASA Astrophysics Data System (ADS)
Hu, Q.; Webb, G. M.; Zank, G. P.
2015-12-01
We discuss conservation laws in ideal fluids and in magneto-hydrodynamics (MHD) using Eulerian, Lagrangian and Multi-Symplectic approaches. We show how the fluid and MHD equations can be written in multi-symplectic form using multi-momenta (the de Donder Weyl approach) in which both space and time are placed on an equal footing. We illustrate how this approach gives rise to both local and non-local conservation laws for both barotropic and non-barotropic gases. We obtain the symplecticity and pullback conservation laws for 1D gas dynamics and for the multi-dimensional gas and MHD equations. For the case of a non-barotropic gas, the helicity and cross helicity conservation laws are nonlocal conservation laws. A similar nonlocal conservation law also applies for 1D, non-barotropic gas dynamics, in which a nonlocal variable corresponding to the integral of the temperature back along the fluid path, keeps track of the history of the fluid element.
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).
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.
NASA Astrophysics Data System (ADS)
Dekker, T.; de Zwart, S. T.; Willemsen, O. H.; Hiddink, M. G. H.; IJzerman, W. L.
2006-02-01
A prerequisite for a wide market acceptance of 3D displays is the ability to switch between 3D and full resolution 2D. In this paper we present a robust and cost effective concept for an auto-stereoscopic switchable 2D/3D display. The display is based on an LCD panel, equipped with switchable LC-filled lenticular lenses. We will discuss 3D image quality, with the focus on display uniformity. We show that slanting the lenticulars in combination with a good lens design can minimize non-uniformities in our 20" 2D/3D monitors. Furthermore, we introduce fractional viewing systems as a very robust concept to further improve uniformity in the case slanting the lenticulars and optimizing the lens design are not sufficient. We will discuss measurements and numerical simulations of the key optical characteristics of this display. Finally, we discuss 2D image quality, the switching characteristics and the residual lens effect.
2-d Finite Element Code Postprocessor
Sanford, L. A.; Hallquist, J. O.
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 forces 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.
General form of the boson-fermion interaction in the interacting boson-fermion model-2
NASA Astrophysics Data System (ADS)
Matus, F. A.; Barea, J.
2017-03-01
The boson-fermion interaction in the interacting boson-fermion model-2 (IBFM-2) is derived in a systematic and general form from a quadrupole-quadrupole force using several nondegenerate levels. The boson-fermion quadrupole operator employed is obtained from the boson-fermion image of the one nucleon transfer operator which in turn can be calculated following two alternative schemes: the Otsuka-Arima-Iachello and generalized Holstein-Primakoff schemes. Four different terms (two quadrupole and two exchange) were obtained. Application of the new expressions to a single-j model is studied and analyzed.
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.
Amplified fermion production from overpopulated Bose fields
NASA Astrophysics Data System (ADS)
Berges, J.; Gelfand, D.; Sexty, D.
2014-01-01
We study the real-time dynamics of fermions coupled to scalar fields in a linear sigma model, which is often employed in the context of preheating after inflation or as a low-energy effective model for quantum chromodynamics. We find a dramatic amplification of fermion production in the presence of highly occupied bosonic quanta for weak as well as strong effective couplings. For this we consider the range of validity of different methods: lattice simulations with male/female fermions, the mode functions approach and the quantum 2PI effective action with its associated kinetic theory. For strongly coupled fermions we find a rapid approach to a Fermi-Dirac distribution with time-dependent temperature and chemical potential parameters, while the bosons are still far from equilibrium.
Fermionic Orbital Optimization in Tensor Network States
NASA Astrophysics Data System (ADS)
Krumnow, C.; Veis, L.; Legeza, Ö.; Eisert, J.
2016-11-01
Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin models. Recently, they have also been applied to interacting fermionic problems, specifically in the context of quantum chemistry. A new freedom arising in such nonlocal fermionic systems is the choice of orbitals, it being far from clear what choice of fermionic orbitals to make. In this Letter, we propose a way to overcome this challenge. We suggest a method intertwining the optimization over matrix product states with suitable fermionic Gaussian mode transformations. The described algorithm generalizes basis changes in the spirit of the Hartree-Fock method to matrix-product states, and provides a black box tool for basis optimization in tensor network methods.
Thermostatistics of bosonic and fermionic Fibonacci oscillators
NASA Astrophysics Data System (ADS)
Algin, Abdullah; Arik, Metin; Senay, Mustafa; Topcu, Gozde
2017-01-01
In this work, we first introduce some new properties concerning the Fibonacci calculus. We then discuss the thermostatistics of gas models of two-parameter deformed oscillators, called bosonic and fermionic Fibonacci oscillators, in the thermodynamical limit. In this framework, we analyze the behavior of two-parameter deformed mean occupation numbers describing the Fibonacci-type bosonic and fermionic intermediate-statistics particles. A virial expansion of the equation of state for the bosonic Fibonacci oscillators’ gas model is obtained in both two and three dimensions, and the first five virial coefficients are derived in terms of the real independent deformation parameters p and q. The effect of bosonic and fermionic p, q-deformation on the thermostatistical properties of Fibonacci-type p, q-boson and p, q-fermion gas models are also discussed. The results obtained in this work can be useful for investigating some exotic quasiparticle states encountered in condensed matter systems.
Chiral fermions in asymptotically safe quantum gravity.
Meibohm, J; Pawlowski, J M
2016-01-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
Quantum-Gas Microscope for Fermionic Atoms
NASA Astrophysics Data System (ADS)
Cheuk, Lawrence W.; Nichols, Matthew A.; Okan, Melih; Gersdorf, Thomas; Ramasesh, Vinay V.; Bakr, Waseem S.; Lompe, Thomas; Zwierlein, Martin W.
2015-05-01
We realize a quantum-gas microscope for fermionic 40K atoms trapped in an optical lattice, which allows one to probe strongly correlated fermions at the single-atom level. We combine 3D Raman sideband cooling with high-resolution optics to simultaneously cool and image individual atoms with single-lattice-site resolution at a detection fidelity above 95%. The imaging process leaves the atoms predominantly in the 3D motional ground state of their respective lattice sites, inviting the implementation of a Maxwell's demon to assemble low-entropy many-body states. Single-site-resolved imaging of fermions enables the direct observation of magnetic order, time-resolved measurements of the spread of particle correlations, and the detection of many-fermion entanglement.
Fermion localization in a backreacted warped spacetime
NASA Astrophysics Data System (ADS)
Paul, Tanmoy; SenGupta, Soumitra
2017-06-01
We consider a five dimensional anti-de Sitter (AdS) warped spacetime in presence of a massive scalar field in the bulk. The scalar field potential fulfills the requirement of modulus stabilization even when the effect of backreaction of the stabilizing field is taken into account. In such a scenario, we explore the role of backreaction on the localization of bulk fermions which in turn determines the effective radion-fermion coupling on the brane. Our result reveals that both the chiral modes of the zeroth Kaluza-Klein (KK) fermions get localized near TeV brane as the backreaction of the scalar field increases. We also show that the profile of massive KK fermions shifts towards the Planck brane with an increasing backreaction parameter. Some implications in the context of LHC physics are discussed.
Factorization of fermion doubles on the lattice
NASA Astrophysics Data System (ADS)
de A. Bicudo, P. J.
2000-04-01
We address the problem of the fermion species doubling on the Lattice. Our strategy is to factorize the fermion doubles from the action. The mass term of the Dirac-Wilson action is changed. In this case the extra roots which appear in the action of free fermions in the moment representation are independent of the mass and can be factorized from the fermion propagator. However the gauge couplings suffer from the pathological ghost poles which are common to non-local actions. This action can be used to find a solution of the Ginsparg Wilson relation, which is cured from the non-local pathology. Finally we compare this factorized action with solutions of The Ginsparg Wilson relation. We find that the present is equivalent to the Zenkin action, and that it is not exponentially local, in contrast with Neuberger's action.
Chiral fermions in asymptotically safe quantum gravity
NASA Astrophysics Data System (ADS)
Meibohm, J.; Pawlowski, J. M.
2016-05-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
Majorana Fermions and Topology in Superconductors
NASA Astrophysics Data System (ADS)
Sato, Masatoshi; Fujimoto, Satoshi
2016-07-01
Topological superconductors are novel classes of quantum condensed phases, characterized by topologically nontrivial structures of Cooper pairing states. On the surfaces of samples and in vortex cores of topological superconductors, Majorana fermions, which are particles identified with their own anti-particles, appear as Bogoliubov quasiparticles. The existence and stability of Majorana fermions are ensured by bulk topological invariants constrained by the symmetries of the systems. Majorana fermions in topological superconductors obey a new type of quantum statistics referred to as non-Abelian statistics, which is distinct from bose and fermi statistics, and can be utilized for application to topological quantum computation. Also, Majorana fermions give rise to various exotic phenomena such as "fractionalization", non-local correlation, and "teleportation". A pedagogical review of these subjects is presented. We also discuss interaction effects on topological classification of superconductors, and the basic properties of Weyl superconductors.
Bilinear forms on fermionic Novikov algebras
NASA Astrophysics Data System (ADS)
Chen, Zhiqi; Zhu, Fuhai
2007-05-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in formal variational calculus. Fermionic Novikov algebras correspond to a certain Hamiltonian super-operator in a super-variable. In this paper, we show that there is a remarkable geometry on fermionic Novikov algebras with non-degenerate invariant symmetric bilinear forms, which we call pseudo-Riemannian fermionic Novikov algebras. They are related to pseudo-Riemannian Lie algebras. Furthermore, we obtain a procedure to classify pseudo-Riemannian fermionic Novikov algebras. As an application, we give the classification in dimension <=4. Motivated by the one in dimension 4, we construct some examples in high dimensions.
Two-photon interactions with Majorana fermions
NASA Astrophysics Data System (ADS)
Latimer, David C.
2016-11-01
Because Majorana fermions are their own antiparticles, their electric and magnetic dipole moments must vanish, leaving the anapole moment as their only static electromagnetic property. But the existence of induced dipole moments is not necessarily prohibited. Through a study of real Compton scattering, we explore the constraints that the Majorana fermion's self-conjugate nature has on induced moments. In terms of the Compton amplitude, we find no constraints if the interactions are separately invariant under charge conjugation, parity, and time reversal. However, if the interactions are odd under parity and even under time reversal, then these contributions to the Compton amplitude must vanish. We employ a simple model to confirm these general findings via explicit calculation of the Majorana fermion's polarizabilities. We then use these polarizabilities to estimate the cross section for s -wave annihilation of two Majorana fermions into photons. The cross section is larger than a naive estimate might suggest.
Canonical approach to Ginsparg-Wilson fermions
Matsui, Kosuke; Okamoto, Tomohito; Fujiwara, Takanori
2005-06-01
Based upon the lattice Dirac operator satisfying the Ginsparg-Wilson relation, we investigate canonical formulation of massless fermion on the spatial lattice. For free fermion system exact chiral symmetry can be implemented without species doubling. In the presence of gauge couplings the chiral symmetry is violated. We show that the divergence of the axial vector current is related to the chiral anomaly in the classical continuum limit.
Superfluid response in heavy fermion superconductors
NASA Astrophysics Data System (ADS)
Zhong, Yin; Zhang, Lan; Shao, Can; Luo, Hong-Gang
2017-10-01
Motivated by a recent London penetration depth measurement [H. Kim, et al., Phys. Rev. Lett. 114, 027003 (2015)] and novel composite pairing scenario [O. Erten, R. Flint, and P. Coleman, Phys. Rev. Lett. 114, 027002 (2015)] of the Yb-doped heavy fermion superconductor CeCoIn5, we revisit the issue of superfluid response in the microscopic heavy fermion lattice model. However, from the literature, an explicit expression for the superfluid response function in heavy fermion superconductors is rare. In this paper, we investigate the superfluid density response function in the celebrated Kondo-Heisenberg model. To be specific, we derive the corresponding formalism from an effective fermionic large- N mean-field pairing Hamiltonian whose pairing interaction is assumed to originate from the effective local antiferromagnetic exchange interaction. Interestingly, we find that the physically correct, temperature-dependent superfluid density formula can only be obtained if the external electromagnetic field is directly coupled to the heavy fermion quasi-particle rather than the bare conduction electron or local moment. Such a unique feature emphasizes the key role of the Kondo-screening-renormalized heavy quasi-particle for low-temperature/energy thermodynamics and transport behaviors. As an important application, the theoretical result is compared to an experimental measurement in heavy fermion superconductors CeCoIn5 and Yb-doped Ce1- x Yb x CoIn5 with fairly good agreement and the transition of the pairing symmetry in the latter material is explained as a simple doping effect. In addition, the requisite formalism for the commonly encountered nonmagnetic impurity and non-local electrodynamic effect are developed. Inspired by the success in explaining classic 115-series heavy fermion superconductors, we expect the present theory will be applied to understand other heavy fermion superconductors such as CeCu2Si2 and more generic multi-band superconductors.
Evolution of boson-fermion stars
NASA Astrophysics Data System (ADS)
Valdez-Alvarado, Susana; Palenzuela, Carlos; Alic, Daniela; Ureña-López, L. Arturo; Becerril, Ricardo
2012-08-01
The boson-fermion stars can be modeled with a complex scalar field coupled minimally to a perfect fluid (i.e., without viscosity and non-dissipative). We present a study of these solutions and their dynamical evolution by solving numerically the Einstein-Klein-Gordon-Hydrodynamic (EKGHD) system. It is shown that stable configurations exist, but stability of general configurations depends finely upon the number of bosons and fermions.
The physics and chemistry of heavy fermions.
Fisk, Z; Sarrao, J L; Smith, J L; Thompson, J D
1995-01-01
The heavy fermions are a subset of the f-electron intermetallic compounds straddling the magnetic/nonmagnetic boundary. Their low-temperature properties are characterized by an electronic energy scale of order 1-10 K. Among the low-temperature ground states observed in heavy fermion compounds are exotic superconductors and magnets, as well as unusual semiconductors. We review here the current experimental and theoretical understanding of these systems. PMID:11607558
Inhomogeneous state of few-fermion superfluids.
Bugnion, P O; Lofthouse, J A; Conduit, G J
2013-07-26
The few-fermion atomic gas is an ideal setting to explore inhomogeneous superfluid pairing analogous to the Larkin-Ovchinnikov state. Two up and one down-spin atom is the minimal configuration that displays an inhomogeneous pairing density, whereas imbalanced systems containing more fermions present a more complex pairing topology. With more than eight atoms trapped the system approaches the macroscopic superfluid limit. An oblate trap with a central barrier offers a direct experimental probe of pairing inhomogeneity.
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).
Fermionic topological quantum states as tensor networks
NASA Astrophysics Data System (ADS)
Wille, C.; Buerschaper, O.; Eisert, J.
2017-06-01
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.
Fermion-induced quantum critical points.
Li, Zi-Xiang; Jiang, Yi-Fan; Jian, Shao-Kai; Yao, Hong
2017-08-22
A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points. We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a fermion-induced quantum critical points for N = 2, 3, 4, 5 and 6, consistent with the renormalization group analysis. We finally discuss possible experimental realizations of the fermion-induced quantum critical points in graphene and graphene-like materials.Quantum phase transitions are governed by Landau-Ginzburg theory and the exceptions are rare. Here, Li et al. propose a type of Landau-forbidden quantum critical points induced by gapless fermions in two-dimensional Dirac semimetals.
Quantum Gas Microscope for Fermionic Atoms
NASA Astrophysics Data System (ADS)
Okan, Melih; Cheuk, Lawrence; Nichols, Matthew; Lawrence, Katherine; Zhang, Hao; Zwierlein, Martin
2016-05-01
Strongly interacting fermions define the properties of complex matter throughout nature, from atomic nuclei and modern solid state materials to neutron stars. Ultracold atomic Fermi gases have emerged as a pristine platform for the study of many-fermion systems. In this poster we demonstrate the realization of a quantum gas microscope for fermionic 40 K atoms trapped in an optical lattice and the recent experiments which allows one to probe strongly correlated fermions at the single atom level. We combine 3D Raman sideband cooling with high- resolution optics to simultaneously cool and image individual atoms with single lattice site resolution at a detection fidelity above 95%. The imaging process leaves the atoms predominantly in the 3D motional ground state of their respective lattice sites, inviting the implementation of a Maxwell's demon to assemble low-entropy many-body states. Single-site resolved imaging of fermions enables the direct observation of magnetic order, time resolved measurements of the spread of particle correlations, and the detection of many-fermion entanglement. NSF, AFOSR-PECASE, AFOSR-MURI on Exotic Phases of Matter, ARO-MURI on Atomtronics, ONR, a Grant from the Army Research Office with funding from the DARPA OLE program, and the David and Lucile Packard Foundation.
Isotropic Landau levels of relativistic and non-relativistic fermions in 3D flat space
NASA Astrophysics Data System (ADS)
Li, Yi; Wu, Congjun
2012-02-01
The usual Landau level quantization, as demonstrated in the 2D quantum Hall effect, is crucially based on the planar structure. In this talk, we explore its 3D counterpart possessing the full 3D rotational symmetry as well as the time reversal symmetry. We construct the Landau level Hamiltonians in 3 and higher dimensional flat space for both relativistic and non-relativistic fermions. The 3D cases with integer fillings are Z2 topological insulators. The non-relativistic version describes spin-1/2 fermions coupling to the Aharonov-Casher SU(2) gauge field. This system exhibits flat Landau levels in which the orbital angular momentum and the spin are coupled with a fixed helicity. Each filled Landau level contributes one 2D helical Dirac Fermi surface at an open boundary, which demonstrates the Z2 topological nature. A natural generalization to Dirac fermions is found as a square root problem of the above non-relativistic version, which can also be viewed as the Dirac equation defined on the phase space. All these Landau level problems can be generalized to arbitrary high dimensions systematically. [4pt] [1] Yi Li and Congjun Wu, arXiv:1103.5422.[0pt] [2] Yi Li, Ken Intriligator, Yue Yu and Congjun Wu, arXiv:1108.5650.
NASA Astrophysics Data System (ADS)
Das, Joy Prakash; Setlur, Girish S.
2017-10-01
The one step fermionic ladder refers to two parallel Luttinger Liquids (poles of the ladder) placed such that there is a finite probability of electrons hopping between the two poles at a pair of opposing points along each of the poles. The many-body Green function for such a system is calculated in presence of forward scattering interactions using the powerful non-chiral bosonization technique (NCBT). This technique is based on a non-standard harmonic analysis of the rapidly varying parts of the density fields appropriate for the study of strongly inhomogeneous ladder systems. The closed analytical expression for the correlation function obtained from NCBT is nothing but the series involving the RPA (Random Phase Approximation) diagrams in powers of the forward scattering coupling strength resummed to include only the most singular terms with the source of inhomogeneities treated exactly. Finally the correlation functions are used to study physical phenomena such as Friedel oscillations and the conductance of such systems with the potential difference applied across various ends.
Iterants, Fermions and Majorana Operators
NASA Astrophysics Data System (ADS)
Kauffman, Louis H.
Beginning with an elementary, oscillatory discrete dynamical system associated with the square root of minus one, we study both the foundations of mathematics and physics. Position and momentum do not commute in our discrete physics. Their commutator is related to the diffusion constant for a Brownian process and to the Heisenberg commutator in quantum mechanics. We take John Wheeler's idea of It from Bit as an essential clue and we rework the structure of that bit to a logical particle that is its own anti-particle, a logical Marjorana particle. This is our key example of the amphibian nature of mathematics and the external world. We show how the dynamical system for the square root of minus one is essentially the dynamics of a distinction whose self-reference leads to both the fusion algebra and the operator algebra for the Majorana Fermion. In the course of this, we develop an iterant algebra that supports all of matrix algebra and we end the essay with a discussion of the Dirac equation based on these principles.
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.
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.
Orthotropic Piezoelectricity in 2D Nanocellulose
NASA Astrophysics Data System (ADS)
García, Y.; Ruiz-Blanco, Yasser B.; Marrero-Ponce, Yovani; Sotomayor-Torres, C. M.
2016-10-01
The control of electromechanical responses within bonding regions is essential to face frontier challenges in nanotechnologies, such as molecular electronics and biotechnology. Here, we present Iβ-nanocellulose as a potentially new orthotropic 2D piezoelectric crystal. The predicted in-layer piezoelectricity is originated on a sui-generis hydrogen bonds pattern. Upon this fact and by using a combination of ab-initio and ad-hoc models, we introduce a description of electrical profiles along chemical bonds. Such developments lead to obtain a rationale for modelling the extended piezoelectric effect originated within bond scales. The order of magnitude estimated for the 2D Iβ-nanocellulose piezoelectric response, ~pm V‑1, ranks this material at the level of currently used piezoelectric energy generators and new artificial 2D designs. Such finding would be crucial for developing alternative materials to drive emerging nanotechnologies.
Orthotropic Piezoelectricity in 2D Nanocellulose
García, Y.; Ruiz-Blanco, Yasser B.; Marrero-Ponce, Yovani; Sotomayor-Torres, C. M.
2016-01-01
The control of electromechanical responses within bonding regions is essential to face frontier challenges in nanotechnologies, such as molecular electronics and biotechnology. Here, we present Iβ-nanocellulose as a potentially new orthotropic 2D piezoelectric crystal. The predicted in-layer piezoelectricity is originated on a sui-generis hydrogen bonds pattern. Upon this fact and by using a combination of ab-initio and ad-hoc models, we introduce a description of electrical profiles along chemical bonds. Such developments lead to obtain a rationale for modelling the extended piezoelectric effect originated within bond scales. The order of magnitude estimated for the 2D Iβ-nanocellulose piezoelectric response, ~pm V−1, ranks this material at the level of currently used piezoelectric energy generators and new artificial 2D designs. Such finding would be crucial for developing alternative materials to drive emerging nanotechnologies. PMID:27708364
Orthotropic Piezoelectricity in 2D Nanocellulose.
García, Y; Ruiz-Blanco, Yasser B; Marrero-Ponce, Yovani; Sotomayor-Torres, C M
2016-10-06
The control of electromechanical responses within bonding regions is essential to face frontier challenges in nanotechnologies, such as molecular electronics and biotechnology. Here, we present Iβ-nanocellulose as a potentially new orthotropic 2D piezoelectric crystal. The predicted in-layer piezoelectricity is originated on a sui-generis hydrogen bonds pattern. Upon this fact and by using a combination of ab-initio and ad-hoc models, we introduce a description of electrical profiles along chemical bonds. Such developments lead to obtain a rationale for modelling the extended piezoelectric effect originated within bond scales. The order of magnitude estimated for the 2D Iβ-nanocellulose piezoelectric response, ~pm V(-1), ranks this material at the level of currently used piezoelectric energy generators and new artificial 2D designs. Such finding would be crucial for developing alternative materials to drive emerging nanotechnologies.
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.
Assessing 2D electrophoretic mobility spectroscopy (2D MOSY) for analytical applications.
Fang, Yuan; Yushmanov, Pavel V; Furó, István
2016-12-08
Electrophoretic displacement of charged entity phase modulates the spectrum acquired in electrophoretic NMR experiments, and this modulation can be presented via 2D FT as 2D mobility spectroscopy (MOSY) spectra. We compare in various mixed solutions the chemical selectivity provided by 2D MOSY spectra with that provided by 2D diffusion-ordered spectroscopy (DOSY) spectra and demonstrate, under the conditions explored, a superior performance of the former method. 2D MOSY compares also favourably with closely related LC-NMR methods. The shape of 2D MOSY spectra in complex mixtures is strongly modulated by the pH of the sample, a feature that has potential for areas such as in drug discovery and metabolomics. Copyright © 2016 The Authors. Magnetic Resonance in Chemistry published by John Wiley & Sons Ltd. StartCopTextCopyright © 2016 The Authors. Magnetic Resonance in Chemistry published by John Wiley & Sons Ltd.
Adams, David H.
2008-05-15
To investigate the viability of the 4th root trick for the staggered fermion determinant in a simpler setting, we consider a 2-taste (flavor) lattice fermion formulation with no taste mixing but with exact taste-nonsinglet chiral symmetries analogous to the taste-nonsinglet U(1){sub A} symmetry of staggered fermions. Creutz's objections to the rooting trick apply just as much in this setting. To counter them we show that the formulation has robust would-be zero modes in topologically nontrivial gauge backgrounds, and that these manifest themselves in a viable way in the rooted fermion determinant and also in the disconnected piece of the pseudoscalar meson propagator as required to solve the U(1) problem. Also, our rooted theory is heuristically seen to be in the right universality class for QCD if the same is true for an unrooted mixed fermion action theory.
2D Distributed Sensing Via TDR
2007-11-02
plate VEGF CompositeSensor Experimental Setup Air 279 mm 61 78 VARTM profile: slope RTM profile: rectangle 22 1 Jul 2003© 2003 University of Delaware...2003 University of Delaware All rights reserved Vision: Non-contact 2D sensing ü VARTM setup constructed within TL can be sensed by its EM field: 2D...300.0 mm/ns. 1 2 1 Jul 2003© 2003 University of Delaware All rights reserved Model Validation “ RTM Flow” TDR Response to 139 mm VEGC
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.
Heavy fermion behavior explained by bosons
NASA Technical Reports Server (NTRS)
Kallio, A.; Poykko, S.; Apaja, V.
1995-01-01
Conventional heavy fermion (HF) theories require existence of massive fermions. We show that heavy fermion phenomena can also be simply explained by existence of bosons with moderate mass but temperature dependent concentration below the formation temperature T(sub B), which in turn is close to room temperature. The bosons B(++) are proposed to be in chemical equilibrium with a system of holes h(+): B(++) = h(+) + h(+). This equilibrium is governed by a boson breaking function f(T), which determines the decreasing boson density and the increasing fermion density with increasing temperature. Since HF-compounds are hybridized from minimum two elements, we assume in addition existence of another fermion component h(sub s)(+) with temperature independent density. This spectator component is thought to be the main agent in binding the bosons in analogy with electronic or muonic molecules. Using a linear boson breaking function we can explain temperature dependence of the giant linear specific heat coefficient gamma(T) coming essentially from bosons. The maxima in resistivity, Hall coefficient, and susceptibility are explained by boson localization effects due to the Wigner crystallization. The antiferromagnetic transitions in turn are explained by similar localization of the pairing fermion system when their density n(sub h)(T(sub FL)) becomes lower than n(sub WC), the critical density of Wigner crystallization. The model applies irrespective whether a compound is superconducting or not. The same model explains the occurrence of low temperature antiferromagnetism also in high-T(sub c) superconductors. The double transition in UPt3 is proposed to be due to the transition of the pairing fermion liquid from spin polarized to unpolarized state.
NASA Astrophysics Data System (ADS)
Bian, Guang; Chung, Ting-Fung; Chen, Chaoyu; Liu, Chang; Chang, Tay-Rong; Wu, Tailung; Belopolski, Ilya; Zheng, Hao; Xu, Su-Yang; Sanchez, Daniel S.; Alidoust, Nasser; Pierce, Jonathan; Quilliams, Bryson; Barletta, Philip P.; Lorcy, Stephane; Avila, José; Chang, Guoqing; Lin, Hsin; Jeng, Horng-Tay; Asensio, Maria-Carmen; Chen, Yong P.; Zahid Hasan, M.
2016-06-01
Graphene and topological insulators (TI) possess two-dimensional (2D) Dirac fermions with distinct physical properties. Integrating these two Dirac materials in a single device creates interesting opportunities for exploring new physics of interacting massless Dirac fermions. Here we report on a practical route to experimental fabrication of graphene-Sb2Te3 heterostructure. The graphene-TI heterostructures are prepared by using a dry transfer of chemical-vapor-deposition grown graphene film. ARPES measurements confirm the coexistence of topological surface states of Sb2Te3 and Dirac π bands of graphene, and identify the twist angle in the graphene-TI heterostructure. The results suggest a potential tunable electronic platform in which two different Dirac low-energy states dominate the transport behavior.
She, Jian-Huang; Balatsky, Alexander V
2012-08-17
We propose an explanation of the superconducting transitions discovered in the heavy-fermion superlattices by Mizukami et al. [Nature Phys. 7, 849 (2011)] in terms of Berezinskii-Kosterlitz-Thouless (BKT) transition. We observe that the effective mass mismatch between the heavy-fermion superconductor and the normal metal regions provides an effective barrier that enables quasi-2D superconductivity in such systems. We show that the resistivity data, both with and without magnetic field, are consistent with BKT transition. Furthermore, we study the influence of a nearby magnetic quantum critical point on the vortex system and find that the vortex core energy can be significantly reduced due to magnetic fluctuations. Further reduction of the gap with decreasing number of layers is understood as a result of pair breaking effect of Yb ions at the interface.
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
2016-03-23
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.
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; Hsu, Allen L.; Bie, Yaqing; Lee, Yi -Hsien; Zhu, Yimei; Li, Ju; Jarillo-Herrero, Pablo; Dresselhaus, Mildred; Palacios, Tomas; Kong, Jing
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.
Beckett, Phil
2012-01-01
The technique of two-dimensional (2D) gel electrophoresis is a powerful tool for separating complex mixtures of proteins, but since its inception in the mid 1970s, it acquired the stigma of being a very difficult application to master and was generally used to its best effect by experts. The introduction of commercially available immobilized pH gradients in the early 1990s provided enhanced reproducibility and easier protocols, leading to a pronounced increase in popularity of the technique. However gel-to-gel variation was still difficult to control without the use of technical replicates. In the mid 1990s (at the same time as the birth of "proteomics"), the concept of multiplexing fluorescently labeled proteins for 2D gel separation was realized by Jon Minden's group and has led to the ability to design experiments to virtually eliminate gel-to-gel variation, resulting in biological replicates being used for statistical analysis with the ability to detect very small changes in relative protein abundance. This technology is referred to as 2D difference gel electrophoresis (2D DIGE).
Parallel stitching of 2D materials
Ling, Xi; Wu, Lijun; Lin, Yuxuan; ...
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.
Fermionic entanglement that survives a black hole
Martin-Martinez, Eduardo; Leon, Juan
2009-10-15
We introduce an arbitrary number of accessible modes when analyzing bipartite entanglement degradation due to Unruh effect between two partners Alice and Rob. Under the single mode approximation (SMA) a fermion field only had a few accessible levels due to Pauli exclusion principle conversely to bosonic fields which had an infinite number of excitable levels. This was argued to justify entanglement survival in the fermionic case in the SMA infinite acceleration limit. Here we relax SMA. Hence, an infinite number of modes are excited as the observer Rob accelerates, even for a fermion field. We will prove that, despite this analogy with the bosonic case, entanglement loss is limited. We will show that this comes from fermionic statistics through the characteristic structure it imposes on the infinite dimensional density matrix for Rob. Surprisingly, the surviving entanglement is independent of the specific maximally entangled state chosen, the kind of fermionic field analyzed, and the number of accessible modes considered. We shall discuss whether this surviving entanglement goes beyond the purely statistical correlations, giving insight concerning the black hole information paradox.
Analysis of quantum error-correcting codes: Symplectic lattice codes and toric codes
NASA Astrophysics Data System (ADS)
Harrington, James William
Quantum information theory is concerned with identifying how quantum mechanical resources (such as entangled quantum states) can be utilized for a number of information processing tasks, including data storage, computation, communication, and cryptography. Efficient quantum algorithms and protocols have been developed for performing some tasks (e.g. , factoring large numbers, securely communicating over a public channel, and simulating quantum mechanical systems) that appear to be very difficult with just classical resources. In addition to identifying the separation between classical and quantum computational power, much of the theoretical focus in this field over the last decade has been concerned with finding novel ways of encoding quantum information that are robust against errors, which is an important step toward building practical quantum information processing devices. In this thesis I present some results on the quantum error-correcting properties of oscillator codes (also described as symplectic lattice codes) and toric codes. Any harmonic oscillator system (such as a mode of light) can be encoded with quantum information via symplectic lattice codes that are robust against shifts in the system's continuous quantum variables. I show the existence of lattice codes whose achievable rates match the one-shot coherent information over the Gaussian quantum channel. Also, I construct a family of symplectic self-dual lattices and search for optimal encodings of quantum information distributed between several oscillators. Toric codes provide encodings of quantum information into two-dimensional spin lattices that are robust against local clusters of errors and which require only local quantum operations for error correction. Numerical simulations of this system under various error models provide a calculation of the accuracy threshold for quantum memory using toric codes, which can be related to phase transitions in certain condensed matter models. I also present
Evidence of Topological Nodal-Line Fermions in ZrSiSe and ZrSiTe
NASA Astrophysics Data System (ADS)
Hu, Jin; Tang, Zhijie; Liu, Jinyu; Liu, Xue; Zhu, Yanglin; Graf, David; Myhro, Kevin; Tran, Son; Lau, Chun Ning; Wei, Jiang; Mao, Zhiqiang
2016-07-01
A Dirac nodal-line semimetal phase, which represents a new quantum state of topological materials, has been experimentally realized only in a few systems, including PbTaSe2 , PtSn4 , and ZrSiS. In this Letter, we report evidence of nodal-line fermions in ZrSiSe and ZrSiTe probed in de Haas-van Alphen quantum oscillations. Although ZrSiSe and ZrSiTe share a similar layered structure with ZrSiS, our studies show the Fermi surface (FS) enclosing a Dirac nodal line has a 2D character in ZrSiTe, in contrast with 3D-like FS in ZrSiSe and ZrSiS. Another important property revealed in our experiment is that the nodal-line fermion density in this family of materials (˜1020 cm-3 ) is much higher than the Dirac fermion density of other topological materials with discrete nodes. In addition, we have demonstrated ZrSiSe and ZrSiTe single crystals can be thinned down to 2D atomic thin layers through microexfoliation, which offers the first platform to explore exotic properties of topological nodal-line fermions in low dimensions.
Evidence of Topological Nodal-Line Fermions in ZrSiSe and ZrSiTe.
Hu, Jin; Tang, Zhijie; Liu, Jinyu; Liu, Xue; Zhu, Yanglin; Graf, David; Myhro, Kevin; Tran, Son; Lau, Chun Ning; Wei, Jiang; Mao, Zhiqiang
2016-07-01
A Dirac nodal-line semimetal phase, which represents a new quantum state of topological materials, has been experimentally realized only in a few systems, including PbTaSe_{2}, PtSn_{4}, and ZrSiS. In this Letter, we report evidence of nodal-line fermions in ZrSiSe and ZrSiTe probed in de Haas-van Alphen quantum oscillations. Although ZrSiSe and ZrSiTe share a similar layered structure with ZrSiS, our studies show the Fermi surface (FS) enclosing a Dirac nodal line has a 2D character in ZrSiTe, in contrast with 3D-like FS in ZrSiSe and ZrSiS. Another important property revealed in our experiment is that the nodal-line fermion density in this family of materials (∼10^{20} cm^{-3}) is much higher than the Dirac fermion density of other topological materials with discrete nodes. In addition, we have demonstrated ZrSiSe and ZrSiTe single crystals can be thinned down to 2D atomic thin layers through microexfoliation, which offers the first platform to explore exotic properties of topological nodal-line fermions in low dimensions.
A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation
NASA Technical Reports Server (NTRS)
Jones, Brandon A.; Anderson, Rodney L.
2012-01-01
Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.
NASA Astrophysics Data System (ADS)
Brizard, Alain J.
2017-08-01
The nonlinear (full-f) electromagnetic gyrokinetic Vlasov-Maxwell equations are derived in the parallel-symplectic representation from an Eulerian gyrokinetic variational principle. The gyrokinetic Vlasov-Maxwell equations are shown to possess an exact energy conservation law, which is derived by the Noether method from the gyrokinetic variational principle. Here, the gyrocenter Poisson bracket and the gyrocenter Jacobian contain contributions from the perturbed magnetic field. In the full-f formulation of the gyrokinetic Vlasov-Maxwell theory presented here, the gyrocenter parallel-Ampère equation contains a second-order contribution to the gyrocenter current density that is derived from the second-order gyrocenter ponderomotive Hamiltonian.
A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation
NASA Technical Reports Server (NTRS)
Jones, Brandon A.; Anderson, Rodney L.
2012-01-01
Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.
The gauge sector of the SME with Lorentz-symmetry violation by symplectic projector method
NASA Astrophysics Data System (ADS)
Belich, H.; Santos, M. A.; Orlando, M. T. D.
2015-09-01
We propose to analyze a modified electromagnetism inspired from the gauge sector of the Standard Model extension (SME). From the point of view of a canonical formulation, we carried out the usual analysis on the constraints structure of the odd sector (Carroll-Field-Jackiw term) and a Maxwell term with an effective metric. This effective metric is obtained by a vectorial decomposition of the CPT-even term, that is absorbed in the ordinary Maxwell term. Using symplectic projector method (SPM), we obtain the dispersions relations and we have verified conditions of stability to determine the valid spectrum.
Teichmüller spaces as degenerated symplectic leaves in Dubrovin-Ugaglia Poisson manifolds
NASA Astrophysics Data System (ADS)
Chekhov, Leonid; Mazzocco, Marta
2012-12-01
In this paper, we study the Goldman bracket between geodesic length functions both on a Riemann surface Σg,s,0 of genus g with s=1,2 holes and on a Riemann sphere Σ0,1,n with one hole and n orbifold points of order two. We show that the corresponding Teichmüller spaces Tg,s,0 and T0,1,n are realised as real slices of degenerated symplectic leaves in the Dubrovin-Ugaglia Poisson algebra of upper-triangular matrices S with 1 on the diagonal.
Explicit symplectic orbit and spin tracking method for electric storage ring
Hwang, Kilean; Lee, S. Y.
2016-08-18
We develop a symplectic charged particle tracking method for phase space coordinates and polarization in all electric storage rings. Near the magic energy, the spin precession tune is proportional to the fractional momentum deviation δm from the magic energy, and the amplitude of the radial and longitudinal spin precession is proportional to η/δm, where η is the electric dipole moment for an initially vertically polarized beam. As a result, the method can be used to extract the electron electric dipole moment of a charged particle by employing narrow band frequency analysis of polarization around the magic energy.
NASA Astrophysics Data System (ADS)
Georgieva, A. I.; Ganev, H. G.; Draayer, J. P.; Garistov, V. P.
2009-07-01
In the algebraic Interacting Vector Boson Model (IVBM) it is assumed that the nuclear dynamics can be described by means of two types of vector “quasiparticles,” which are also characterized by another quantum number—a “T-spin” (an analogue to the F-spin). The non-compact symplectic group Sp(12, R) appears as the group of dynamical symmetry for the problem of two interacting vector bosons. The symplectic structure allows the change in the number of phonons, needed to build the collective states, that results in larger model spaces, which can accommodate the more complex structural effects as observed in the contemporary experiment. The applications of the IVBM are extended by exploiting three new subgroup chains in the reduction of Sp(12, R) to the physical angular momentum subgroup SO(3). The corresponding exactly solvable limiting cases are applied to achieve a description of complex nuclear collective spectra of even-even nuclei in the rare earth and actinide regions up to states of very high angular momentum. The first reduction that we exploit is one that extends the rotational limit of the number preserving version of the model; namely, Sp(12, R) ⊃ U(6) ⊃ U(2) ⊗ SU(3). Another limit of the symplectic IVBM, Sp(12, R) ⊃ Sp(2, R) ⊗ SO(6), contains in a natural way the 6-dimensional Davidson potential. In both of these cases, because collective modes can be mixed, we obtain successful descriptions of both positive and negative parity band configurations. The structure of band-head configurations, whose importance is established in the first two limits, is also examined in a third reduction, Sp(12, R) ⊃ Sp(4, R) ⊗ SO(3). The distributions of energies that are obtained in this limit with respect to the number of bosons that build each of the states with fixed angular momentum, enables one to distinguish typical collective vibrational and rotational spectra. This algebraic chain also provides important links between the subgroups of the other
Quantization of a symplectic manifold associated to a manifold with projective structure
Biswas, Indranil
2009-07-15
Let X be a complex manifold equipped with a projective structure P. There is a holomorphic principal C*-bundle L{sub P}{sup '} over X associated with P. We show that the holomorphic cotangent bundle of the total space of L{sub P}{sup '} equipped with the Liouville symplectic form has a canonical deformation quantization. This generalizes the construction in the work of and Ben-Zvi and Biswas [''A quantization on Riemann surfaces with projective structure,'' Lett. Math. Phys. 54, 73 (2000)] done under the assumption that dim{sub C} X=1.
NASA Astrophysics Data System (ADS)
Blanes, Sergio; Budd, Chris J.
2004-05-01
We present a generalisation of the Levi-Civita and Kustaanheimo-Stiefel regularisation. This allows the use of more general time rescalings. In particular, it is possible to find a regularisation which removes the singularity of the equations and preserves scaling invariance. In addition, these equations can, in certain cases, be integrated with explicit symplectic Runge-Kutta-Nyström methods. The combination of both techniques gives an explicit adaptive symplectic (EASY) integrator. We apply those methods to some perturbations of the Kepler problem and illustrate, by means of some numerical examples, when scaling invariant regularisations are more efficient that the LC/KS regularisation.
NASA Astrophysics Data System (ADS)
Ikeda, Noriaki; Xu, Xiaomeng
2014-11-01
Consistent boundary conditions for Alexandrov-Kontsevich-Schwartz-Zaboronsky (AKSZ) sigma models and the corresponding boundary theories are analyzed. As their mathematical structures, we introduce a generalization of differential graded symplectic manifolds, called twisted QP manifolds, in terms of graded symplectic geometry, canonical functions, and QP pairs. We generalize the AKSZ construction of topological sigma models to sigma models with Wess-Zumino terms and show that all the twisted Poisson-like structures known in the literature can actually be naturally realized as boundary conditions for AKSZ sigma models.
Dias, Nuno Costa; de Gosson, Maurice; Luef, Franz; Prata, João Nuno
2011-11-01
The usual Weyl calculus is intimately associated with the choice of the standard symplectic structure on [Formula: see text]. In this paper we will show that the replacement of this structure by an arbitrary symplectic structure leads to a pseudo-differential calculus of operators acting on functions or distributions defined, not on [Formula: see text] but rather on [Formula: see text]. These operators are intertwined with the standard Weyl pseudo-differential operators using an infinite family of partial isometries of [Formula: see text] indexed by [Formula: see text]. This allows us to obtain spectral and regularity results for our operators using Shubin's symbol classes and Feichtinger's modulation spaces.
Spectrum structure of a fermion on Bloch branes with two scalar-fermion couplings
NASA Astrophysics Data System (ADS)
Xie, Qun-Ying; Guo, Heng; Zhao, Zhen-Hua; Du, Yun-Zhi; Zhang, Yu-Peng
2017-03-01
It is known that the Bloch brane is generated by an odd scalar field ϕ and an even one χ. In order to localize a bulk fermion on the Bloch brane, the coupling between the fermion and scalars should be introduced. There are two localization mechanisms in the literature, the Yukawa coupling -η \\bar{\\Psi}{{F}1}≤ft(φ,χ \\right) \\Psi and non-Yukawa coupling λ \\bar{\\Psi}{ΓM}{{\\partial}M}{{F}2}≤ft(φ,χ \\right){γ5} \\Psi . The Yukawa coupling has been considered. In this paper, we consider both couplings between the fermion and the scalars with {{F}1}={χm}{φ2p+1} and {{F}2}={χn}{φ2q} , and investigate the localization and spectrum structure of the fermion on the Bloch brane. It is found that the left-handed fermion zero mode can be localized on the Bloch brane under some conditions, and the effective potentials have rich structure and may be volcano-like, finite square well-like, and infinite potentials. As a result, the spectrum consists of a series of resonant Kaluza-Klein fermions, finite or infinite numbers of bound Kaluza-Klein fermions. Especially, we find a new feature of the introduction of both couplings: the spectrum for the case of finite square well-like potentials contains discrete quasi-localized and localized massive KK modes simultaneously.
NASA Astrophysics Data System (ADS)
Corboz, Philippe; Orús, Román; Bauer, Bela; Vidal, Guifré
2010-04-01
We explain how to implement, in the context of projected entangled-pair states (PEPSs), the general procedure of fermionization of a tensor network introduced in P. Corboz and G. Vidal, Phys. Rev. B 80, 165129 (2009). The resulting fermionic PEPS, similar to previous proposals, can be used to study the ground state of interacting fermions on a two-dimensional lattice. As in the bosonic case, the cost of simulations depends on the amount of entanglement in the ground state and not directly on the strength of interactions. The present formulation of fermionic PEPS leads to a straightforward numerical implementation that allowed us to recycle much of the code for bosonic PEPS. We demonstrate that fermionic PEPS are a useful variational ansatz for interacting fermion systems by computing approximations to the ground state of several models on an infinite lattice. For a model of interacting spinless fermions, ground state energies lower than Hartree-Fock results are obtained, shifting the boundary between the metal and charge-density wave phases. For the t-J model, energies comparable with those of a specialized Gutzwiller-projected ansatz are also obtained.
Quantum Phases of Fermionic Cold Atoms Through Pairing and Dissociation
NASA Astrophysics Data System (ADS)
Lopez, Nicolas; Tsai, Shan-Wen; Timmermans, E.; Lin, Chi-Yong
2011-03-01
Cold atom experiments have realized molecule creation consisting of paired fermions and dissociation of weakly bound molecules into correlated fermions by tuning of the interactions with external fields [1,2]. We study many-body correlations in such system where molecules are weakly bound and therefore pairs of fermionic atoms convert into and dissociate from the bound molecule state. This exchange mediates a long-range interaction between the fermions. We consider a simple many-body Hamiltonian that includes the destruction of fermionic atom pairs to form single bosonic molecules and vice versa. We employ a functional renormalization-group approach to search for instabilities from the disordered quantum liquid phase that may arise from a boson mediated fermion-fermion interaction. We calculate the renormalized frequency-dependent fermion interactions vertices and renormalized molecular binding energy.
Plaquette boson-fermion model of cuprates
NASA Astrophysics Data System (ADS)
Altman, Ehud; Auerbach, Assa
2002-03-01
The strongly interacting Hubbard model on the square lattice is reduced to the low energy plaquette boson fermion model (PBFM). The four bosons (an antiferromagnon triplet and a d-wave hole pair), and the fermions are defined by the lowest plaquette eigenstates. We apply the contractor renormalization method of Morningstar and Weinstein to compute the boson effective interactions. The range-3 truncation error is found to be very small, signaling short hole-pair and magnon coherence lengths. The pair-hopping and magnon interactions are comparable, which explains the rapid destruction of antiferromagnetic order with emergence of superconductivity, and validates a key assumption of the projected SO(5) theory. A vacuum crossing at larger doping marks a transition into the overdoped regime. With hole fermions occupying small Fermi pockets and Andreev coupled to hole pair bosons, the PBFM yields several testable predictions for photoemission, tunneling asymmetry, and entropy measurements.
Fermionic light in common optical media.
Novoa, David; Michinel, Humberto; Tommasini, Daniele
2010-11-12
Recent experiments have proved that the response to short laser pulses of common optical media, such as air or oxygen, can be described by focusing Kerr and higher order nonlinearities of alternating signs. Such media support the propagation of steady solitary waves. We argue by both numerical and analytical computations that the low-power fundamental bright solitons satisfy an equation of state which is similar to that of a degenerate gas of fermions at zero temperature. Considering, in particular, the propagation in both O2 and air, we also find that the high-power solutions behave like droplets of ordinary liquids. We then show how a grid of the fermionic light bubbles can be generated and forced to merge in a liquid droplet. This leads us to propose a set of experiments aimed at the production of both the fermionic and liquid phases of light, and at the demonstration of the transition from the former to the latter.
Quantum Theory of Fermion Production after Inflation
NASA Astrophysics Data System (ADS)
Berges, Jürgen; Gelfand, Daniil; Pruschke, Jens
2011-08-01
We show that quantum effects dramatically enhance the production of fermions following preheating after inflation in the early Universe in the presence of high excitations of bosonic quanta. As a consequence, fermions rapidly approach a quasistationary distribution with a thermal occupancy in the infrared, while the inflaton enters a turbulent scaling regime. The failure of standard semiclassical descriptions based on the Dirac equation with a homogeneous background field is caused by nonperturbatively high boson occupation numbers. During preheating the inflaton occupation number increases, thus leading to a dynamical mechanism for the enhanced production of fermions from the rescattering of the inflaton quanta. We comment on related phenomena in heavy-ion collisions for the production of quark matter fields from highly occupied gauge bosons.
Dirac fermions in an antiferromagnetic semimetal
Tang, Peizhe; Zhou, Quan; Xu, Gang; Zhang, Shou-Cheng
2016-08-08
Analogues of the elementary particles have been extensively searched for in condensed-matter systems for both scientific interest and technological applications. Recently, massless Dirac fermions were found to emerge as low-energy excitations in materials now known as Dirac semimetals. All of the currently known Dirac semimetals are non-magnetic with both time-reversal symmetry and inversion symmetry. Here in this paper, we show that Dirac fermions can exist in one type of antiferromagnetic system, where both and are broken but their combination is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate, analyse the robustness of the Dirac points under symmetry protections and demonstrate its distinctive bulk dispersions, as well as the corresponding surface states, by ab initio calculations. Our results provide a possible platform to study the interplay of Dirac fermion physics and magnetism.
Plutonium-Based Heavy-Fermion Systems
NASA Astrophysics Data System (ADS)
Bauer, E. D.; Thompson, J. D.
2015-03-01
An effective mass of charge carriers that is significantly larger than the mass of a free electron develops at low temperatures in certain lanthanide- and actinide-based metals, including those formed with plutonium, owing to strong electron-electron interactions. This heavy-fermion mass is reflected in a substantially enhanced electronic coefficient of specific heat Î³, which for elemental Pu is much larger than that of normal metals. By our definition, there are twelve Pu-based heavy-fermion compounds, most discovered recently, whose basic properties are known and discussed. Relative to other examples, these Pu-based heavy-fermion systems are particularly complex owing in part to the possible simultaneous presence of multiple, nearly degenerate 5fn configurations. This complexity poses significant opportunities as well as challenges, including understanding the origin of unconventional superconductivity in some of these materials.
Fermions on one or fewer kinks
Chu Yizen; Vachaspati, Tanmay
2008-01-15
We find the full spectrum of fermion bound states on a Z{sub 2} kink. In addition to the zero mode, there are int[2m{sub f}/m{sub s}] bound states, where m{sub f} is the fermion and m{sub s} the scalar mass. We also study fermion modes on the background of a well-separated kink-antikink pair. Using a variational argument, we prove that there is at least one bound state in this background, and that the energy of this bound state goes to zero with increasing kink-antikink separation, 2L, and faster than e{sup -a2L} where a=min(m{sub s},2m{sub f}). By numerical evaluation, we find some of the low lying bound states explicitly.
Ladder physics in the spin fermion model
Tsvelik, A. M.
2017-05-01
A link is established between the spin fermion (SF) model of the cuprates and the approach based on the analogy between the physics of doped Mott insulators in two dimensions and the physics of fermionic ladders. This enables one to use nonperturbative results derived for fermionic ladders to move beyond the large-N approximation in the SF model. Here, it is shown that the paramagnon exchange postulated in the SF model has exactly the right form to facilitate the emergence of the fully gapped d-Mott state in the region of the Brillouin zone at the hot spots of the Fermi surface.more » Hence, the SF model provides an adequate description of the pseudogap.« less
Dirac fermions in an antiferromagnetic semimetal
Tang, Peizhe; Zhou, Quan; Xu, Gang; ...
2016-08-08
Analogues of the elementary particles have been extensively searched for in condensed-matter systems for both scientific interest and technological applications. Recently, massless Dirac fermions were found to emerge as low-energy excitations in materials now known as Dirac semimetals. All of the currently known Dirac semimetals are non-magnetic with both time-reversal symmetry and inversion symmetry. Here in this paper, we show that Dirac fermions can exist in one type of antiferromagnetic system, where both and are broken but their combination is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate, analyse the robustness of the Dirac points under symmetry protections andmore » demonstrate its distinctive bulk dispersions, as well as the corresponding surface states, by ab initio calculations. Our results provide a possible platform to study the interplay of Dirac fermion physics and magnetism.« less
Dirac fermions in an antiferromagnetic semimetal
NASA Astrophysics Data System (ADS)
Tang, Peizhe; Zhou, Quan; Xu, Gang; Zhang, Shou-Cheng
2016-12-01
Analogues of the elementary particles have been extensively searched for in condensed-matter systems for both scientific interest and technological applications. Recently, massless Dirac fermions were found to emerge as low-energy excitations in materials now known as Dirac semimetals. All of the currently known Dirac semimetals are non-magnetic with both time-reversal symmetry and inversion symmetry . Here we show that Dirac fermions can exist in one type of antiferromagnetic system, where both and are broken but their combination is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate, analyse the robustness of the Dirac points under symmetry protections and demonstrate its distinctive bulk dispersions, as well as the corresponding surface states, by ab initio calculations. Our results provide a possible platform to study the interplay of Dirac fermion physics and magnetism.
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
2016-02-06
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.
Fermion boson metamorphosis in field theory
Ha, Y.K.
1982-01-01
In two-dimensional field theories many features are especially transparent if the Fermi fields are represented by non-local expressions of the Bose fields. Such a procedure is known as boson representation. Bilinear quantities appear in the Lagrangian of a fermion theory transform, however, as simple local expressions of the bosons so that the resulting theory may be written as a theory of bosons. Conversely, a theory of bosons may be transformed into an equivalent theory of fermions. Together they provide a basis for generating many interesting equivalences between theories of different types. In the present work a consistent scheme for constructing a canonical Fermi field in terms of a real scalar field is developed and such a procedure is valid and consistent with the tenets of quantum field theory is verified. A boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. The nature of dynamical generation of mass when the theory undergoes boson transmutation and the preservation of continuous chiral symmetry in the massive case are examined. The dynamics of the system depends to a great extent on the specific number of fermions and different models of the same system can have very different properties. Many unusual symmetries of the fermion theory, such as hidden symmetry, duality and triality symmetries, are only manifest in the boson formulation. The underlying connections between some models with U(N) internal symmetry and another class of fermion models built with Majorana fermions which have O(2N) internal symmetry are uncovered.
Scaling of fat-link irrelevant-clover fermions
Zanotti, J.M.; Lasscock, B.; Leinweber, D.B.; Williams, A.G.
2005-02-01
Hadron masses are calculated in quenched lattice QCD on a variety of lattices in order to probe the scaling behavior of the Fat-Link Irrelevant Clover (FLIC) fermion action, a fat-link clover fermion action in which the purely irrelevant operators of the fermion action are constructed using APE-smeared links. 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.
Topological susceptibility in staggered fermion chiral perturbation theory
Billeter, Brian; DeTar, Carleton; Osborn, James
2004-10-01
The topological susceptibility of the vacuum in quantum chromodynamics has been simulated numerically using the Asqtad improved staggered fermion formalism. At nonzero lattice spacing, the residual fermion doublers (fermion tastes) in the staggered fermion formalism give contributions to the susceptibility that deviate from conventional continuum chiral perturbation theory. In this brief report, we estimate the taste-breaking artifact and compare it with results of recent simulations, finding that it accounts for roughly half of the scaling violation.
Fermion-fermion scattering in quantum field theory with superconducting circuits.
García-Álvarez, L; Casanova, J; Mezzacapo, A; Egusquiza, I L; Lamata, L; Romero, G; Solano, E
2015-02-20
We propose an analog-digital quantum simulation of fermion-fermion scattering mediated by a continuum of bosonic modes within a circuit quantum electrodynamics scenario. This quantum technology naturally provides strong coupling of superconducting qubits with a continuum of electromagnetic modes in an open transmission line. In this way, we propose qubits to efficiently simulate fermionic modes via digital techniques, while we consider the continuum complexity of an open transmission line to simulate the continuum complexity of bosonic modes in quantum field theories. Therefore, we believe that the complexity-simulating-complexity concept should become a leading paradigm in any effort towards scalable quantum simulations.
Gradient terms in quantum-critical theories of itinerant fermions
NASA Astrophysics Data System (ADS)
Maslov, Dmitrii L.; Sharma, Prachi; Torbunov, Dmitrii; Chubukov, Andrey V.
2017-08-01
We investigate the origin and renormalization of the gradient (Q2) term in the propagator of soft bosonic fluctuations in theories of itinerant fermions near a quantum critical point (QCP) with ordering wavevector Q0=0 . A common belief is that (i) the Q2 term comes from fermions with high energies (roughly of order of the bandwidth) and, as such, should be included into the bare bosonic propagator of the effective low-energy model, and (ii) fluctuations within the low-energy model generate Landau damping of soft bosons, but affect the Q2 term only weakly. We argue that the situation is in fact more complex. First, we found that the high- and low-energy contributions to the Q2 term are of the same order. Second, we computed the high-energy contributions to the Q2 term in two microscopic models (a Fermi gas with Coulomb interaction and the Hubbard model) and found that in all cases these contributions are numerically much smaller than the low-energy ones, especially in 2D. This last result is relevant for the behavior of observables at low energies, because the low-energy part of the Q2 term is expected to flow when the effective mass diverges near QCP. If this term is the dominant one, its flow has to be computed self-consistently, which gives rise to a novel quantum-critical behavior. Following up on these results, we discuss two possible ways of formulating the theory of a QCP with Q0=0 .
Floquet Majorana Fermions for Topological Qubits
NASA Astrophysics Data System (ADS)
Liu, D. E.; Levchenko, A.; Baranger, H. U.
2013-03-01
We develop an approach to realizing a topological phase transition and non-Abelian statistics with dynamically induced Floquet Majorana Fermions (FMFs). When the periodic driving potential does not break fermion parity conservation, FMFs can encode quantum information. Quasi-energy analysis shows that a stable FMF zero mode and two other satellite modes exist in a wide parameter space with large quasi-energy gaps, which prevents transitions to other Floquet states under adiabatic driving. We also show that in the asymptotic limit FMFs preserve non-Abelian statistics and, thus, behave like their equilibrium counterparts.
Cosmic expansion from boson and fermion fields
NASA Astrophysics Data System (ADS)
de Souza, Rudinei C.; Kremer, Gilberto M.
2011-06-01
This paper consists in analyzing an action that describes boson and fermion fields minimally coupled to the gravity and a common matter field. The self-interaction potentials of the fields are not chosen a priori but from the Noether symmetry approach. The Noether forms of the potentials allow the boson field to play the role of dark energy and matter and the fermion field to behave as standard matter. The constant of motion and the cyclic variable associated with the Noether symmetry allow the complete integration of the field equations, whose solution produces a universe with alternated periods of accelerated and decelerated expansion.
Residual entanglement of accelerated fermions is useful
NASA Astrophysics Data System (ADS)
Farahmand, Mehrnoosh; Mohammadzadeh, Hosein; Rahimi, Robabeh; Mehri-Dehnavi, Hossein
2017-08-01
The non-vanishing residual entanglement, between the fermionic modes in the infinite acceleration limit, does not violate CHSH inequality, therefore it is not non-local. In this paper, we study the usefulness of the residual fermionic entanglement in single mode approximation and beyond single mode approximation. It is shown that there are some cases where the CHSH inequality is not violated by the residual entanglement, but the state is useful for quantum teleportation. Conditions for the violation of the CHSH inequality in terms of the ;presence probability; of the particle in different Rindler regions are given for the state to be useful for teleportation and superdense coding.
Massless rotating fermions inside a cylinder
Ambruş, Victor E.; Winstanley, Elizabeth
2015-12-07
We study rotating thermal states of a massless quantum fermion field inside a cylinder in Minkowski space-time. Two possible boundary conditions for the fermion field on the cylinder are considered: the spectral and MIT bag boundary conditions. If the radius of the cylinder is sufficiently small, rotating thermal expectation values are finite everywhere inside the cylinder. We also study the Casimir divergences on the boundary. The rotating thermal expectation values and the Casimir divergences have different properties depending on the boundary conditions applied at the cylinder. This is due to the local nature of the MIT bag boundary condition, while the spectral boundary condition is nonlocal.
Novel Fat-Link Fermion Actions
J. M. Zanotti; S. Bilson-Thompson; F. D. R. Bonnet; P. D. Coddington; D. B. Leinweber; A. G. Williams; J. B. Zhang; W. Melnitchouk; F. X. Lee
2001-07-01
The hadron mass spectrum is calculated in lattice QCD using a novel fat-link clover fermion action in which only the irrelevant operators in the fermion action are constructed using smeared links. The simulations are performed on a 16{sup 3} x 32 lattice with a lattice spacing of a=0.125 fm. We compare actions with n=4 and 12 smearing sweeps with a smearing fraction of 0.7. The n=4 Fat-Link Irrelevant Clover (FLIC) action provides scaling which is superior to mean-field improvement, and offers advantages over nonperturbative 0(a) improvement.
Chiral gravitational waves from chiral fermions
NASA Astrophysics Data System (ADS)
Anber, Mohamed M.; Sabancilar, Eray
2017-07-01
We report on a new mechanism that leads to the generation of primordial chiral gravitational waves, and hence, the violation of the parity symmetry in the Universe. We show that nonperturbative production of fermions with a definite helicity is accompanied by the generation of chiral gravitational waves. This is a generic and model-independent phenomenon that can occur during inflation, reheating and radiation eras, and can leave imprints in the cosmic microwave background polarization and may be observed in future ground- and space-based interferometers. We also discuss a specific model where chiral gravitational waves are generated via the production of light chiral fermions during pseudoscalar inflation.
Eigenenergies of fermions bound in Skyrme fields
Zhao, M. ); Hiller, J.R.
1989-08-15
A numerical method is applied to the calculation of bound-state energies of fermions in Skyrme fields. The models considered for the field are smoothed one- and two-step wells and a numerical approximation to the exact hedgehog soliton. The results for the smoothed wells confirm earlier work that showed the fermion spectrum to be sensitive to local variations in the Skyrme field. The spectrum for the hedgehog Skyrmion is similar to the spectra obtained by others for linear and exponential models.
Global analysis of fermion mixing with exotics
NASA Technical Reports Server (NTRS)
Nardi, Enrico; Roulet, Esteban; Tommasini, Daniele
1991-01-01
The limits are analyzed on deviation of the lepton and quark weak-couplings from their standard model values in a general class of models where the known fermions are allowed to mix with new heavy particles with exotic SU(2) x U(1) quantum number assignments (left-handed singlets or right-handed doublets). These mixings appear in many extensions of the electroweak theory such as models with mirror fermions, E(sub 6) models, etc. The results update previous analyses and improve considerably the existing bounds.
Extrinsic Cation Selectivity of 2D Membranes
2017-01-01
From a systematic study of the concentration driven diffusion of positive and negative ions across porous 2D membranes of graphene and hexagonal boron nitride (h-BN), we prove their cation selectivity. Using the current–voltage characteristics of graphene and h-BN monolayers separating reservoirs of different salt concentrations, we calculate the reversal potential as a measure of selectivity. We tune the Debye screening length by exchanging the salt concentrations and demonstrate that negative surface charge gives rise to cation selectivity. Surprisingly, h-BN and graphene membranes show similar characteristics, strongly suggesting a common origin of selectivity in aqueous solvents. For the first time, we demonstrate that the cation flux can be increased by using ozone to create additional pores in graphene while maintaining excellent selectivity. We discuss opportunities to exploit our scalable method to use 2D membranes for applications including osmotic power conversion. PMID:28157333
Schottky diodes from 2D germanane
NASA Astrophysics Data System (ADS)
Sahoo, Nanda Gopal; Esteves, Richard J.; Punetha, Vinay Deep; Pestov, Dmitry; Arachchige, Indika U.; McLeskey, James T.
2016-07-01
We report on the fabrication and characterization of a Schottky diode made using 2D germanane (hydrogenated germanene). When compared to germanium, the 2D structure has higher electron mobility, an optimal band-gap, and exceptional stability making germanane an outstanding candidate for a variety of opto-electronic devices. One-atom-thick sheets of hydrogenated puckered germanium atoms have been synthesized from a CaGe2 framework via intercalation and characterized by XRD, Raman, and FTIR techniques. The material was then used to fabricate Schottky diodes by suspending the germanane in benzonitrile and drop-casting it onto interdigitated metal electrodes. The devices demonstrate significant rectifying behavior and the outstanding potential of this material.
Schottky diodes from 2D germanane
Sahoo, Nanda Gopal; Punetha, Vinay Deep; Esteves, Richard J; Arachchige, Indika U.; Pestov, Dmitry; McLeskey, James T.
2016-07-11
We report on the fabrication and characterization of a Schottky diode made using 2D germanane (hydrogenated germanene). When compared to germanium, the 2D structure has higher electron mobility, an optimal band-gap, and exceptional stability making germanane an outstanding candidate for a variety of opto-electronic devices. One-atom-thick sheets of hydrogenated puckered germanium atoms have been synthesized from a CaGe{sub 2} framework via intercalation and characterized by XRD, Raman, and FTIR techniques. The material was then used to fabricate Schottky diodes by suspending the germanane in benzonitrile and drop-casting it onto interdigitated metal electrodes. The devices demonstrate significant rectifying behavior and the outstanding potential of this material.
Compatible embedding for 2D shape animation.
Baxter, William V; Barla, Pascal; Anjyo, Ken-Ichi
2009-01-01
We present new algorithms for the compatible embedding of 2D shapes. Such embeddings offer a convenient way to interpolate shapes having complex, detailed features. Compared to existing techniques, our approach requires less user input, and is faster, more robust, and simpler to implement, making it ideal for interactive use in practical applications. Our new approach consists of three parts. First, our boundary matching algorithm locates salient features using the perceptually motivated principles of scale-space and uses these as automatic correspondences to guide an elastic curve matching algorithm. Second, we simplify boundaries while maintaining their parametric correspondence and the embedding of the original shapes. Finally, we extend the mapping to shapes' interiors via a new compatible triangulation algorithm. The combination of our algorithms allows us to demonstrate 2D shape interpolation with instant feedback. The proposed algorithms exhibit a combination of simplicity, speed, and accuracy that has not been achieved in previous work.
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
Lin, Jerry
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 surface 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.
Explicit 2-D Hydrodynamic FEM Program
Lin, Jerry
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. The 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.
2D Metals by Repeated Size Reduction.
Liu, Hanwen; Tang, Hao; Fang, Minghao; Si, Wenjie; Zhang, Qinghua; Huang, Zhaohui; Gu, Lin; Pan, Wei; Yao, Jie; Nan, Cewen; Wu, Hui
2016-10-01
A general and convenient strategy for manufacturing freestanding metal nanolayers is developed on large scale. By the simple process of repeatedly folding and calendering stacked metal sheets followed by chemical etching, free-standing 2D metal (e.g., Ag, Au, Fe, Cu, and Ni) nanosheets are obtained with thicknesses as small as 1 nm and with sizes of the order of several micrometers.
Realistic and efficient 2D crack simulation
NASA Astrophysics Data System (ADS)
Yadegar, Jacob; Liu, Xiaoqing; Singh, Abhishek
2010-04-01
Although numerical algorithms for 2D crack simulation have been studied in Modeling and Simulation (M&S) and computer graphics for decades, realism and computational efficiency are still major challenges. In this paper, we introduce a high-fidelity, scalable, adaptive and efficient/runtime 2D crack/fracture simulation system by applying the mathematically elegant Peano-Cesaro triangular meshing/remeshing technique to model the generation of shards/fragments. The recursive fractal sweep associated with the Peano-Cesaro triangulation provides efficient local multi-resolution refinement to any level-of-detail. The generated binary decomposition tree also provides efficient neighbor retrieval mechanism used for mesh element splitting and merging with minimal memory requirements essential for realistic 2D fragment formation. Upon load impact/contact/penetration, a number of factors including impact angle, impact energy, and material properties are all taken into account to produce the criteria of crack initialization, propagation, and termination leading to realistic fractal-like rubble/fragments formation. The aforementioned parameters are used as variables of probabilistic models of cracks/shards formation, making the proposed solution highly adaptive by allowing machine learning mechanisms learn the optimal values for the variables/parameters based on prior benchmark data generated by off-line physics based simulation solutions that produce accurate fractures/shards though at highly non-real time paste. Crack/fracture simulation has been conducted on various load impacts with different initial locations at various impulse scales. The simulation results demonstrate that the proposed system has the capability to realistically and efficiently simulate 2D crack phenomena (such as window shattering and shards generation) with diverse potentials in military and civil M&S applications such as training and mission planning.
Quasiparticle interference in unconventional 2D systems
NASA Astrophysics Data System (ADS)
Chen, Lan; Cheng, Peng; Wu, Kehui
2017-03-01
At present, research of 2D systems mainly focuses on two kinds of materials: graphene-like materials and transition-metal dichalcogenides (TMDs). Both of them host unconventional 2D electronic properties: pseudospin and the associated chirality of electrons in graphene-like materials, and spin-valley-coupled electronic structures in the TMDs. These exotic electronic properties have attracted tremendous interest for possible applications in nanodevices in the future. Investigation on the quasiparticle interference (QPI) in 2D systems is an effective way to uncover these properties. In this review, we will begin with a brief introduction to 2D systems, including their atomic structures and electronic bands. Then, we will discuss the formation of Friedel oscillation due to QPI in constant energy contours of electron bands, and show the basic concept of Fourier-transform scanning tunneling microscopy/spectroscopy (FT-STM/STS), which can resolve Friedel oscillation patterns in real space and consequently obtain the QPI patterns in reciprocal space. In the next two parts, we will summarize some pivotal results in the investigation of QPI in graphene and silicene, in which systems the low-energy quasiparticles are described by the massless Dirac equation. The FT-STM experiments show there are two different interference channels (intervalley and intravalley scattering) and backscattering suppression, which associate with the Dirac cones and the chirality of quasiparticles. The monolayer and bilayer graphene on different substrates (SiC and metal surfaces), and the monolayer and multilayer silicene on a Ag(1 1 1) surface will be addressed. The fifth part will introduce the FT-STM research on QPI in TMDs (monolayer and bilayer of WSe2), which allow us to infer the spin texture of both conduction and valence bands, and present spin-valley coupling by tracking allowed and forbidden scattering channels.
Compact 2-D graphical representation of DNA
NASA Astrophysics Data System (ADS)
Randić, Milan; Vračko, Marjan; Zupan, Jure; Novič, Marjana
2003-05-01
We present a novel 2-D graphical representation for DNA sequences which has an important advantage over the existing graphical representations of DNA in being very compact. It is based on: (1) use of binary labels for the four nucleic acid bases, and (2) use of the 'worm' curve as template on which binary codes are placed. The approach is illustrated on DNA sequences of the first exon of human β-globin and gorilla β-globin.
2D materials: Graphene and others
Bansal, Suneev Anil Singh, Amrinder Pal; Kumar, Suresh
2016-05-06
Present report reviews the recent advancements in new atomically thick 2D materials. Materials covered in this review are Graphene, Silicene, Germanene, Boron Nitride (BN) and Transition metal chalcogenides (TMC). These materials show extraordinary mechanical, electronic and optical properties which make them suitable candidates for future applications. Apart from unique properties, tune-ability of highly desirable properties of these materials is also an important area to be emphasized on.
NASA Astrophysics Data System (ADS)
Smith, Greg; Lankshear, Allan
1998-07-01
2dF is a multi-object instrument mounted at prime focus at the AAT capable of spectroscopic analysis of 400 objects in a single 2 degree field. It also prepares a second 2 degree 400 object field while the first field is being observed. At its heart is a high precision robotic positioner that places individual fiber end magnetic buttons on one of two field plates. The button gripper is carried on orthogonal gantries powered by linear synchronous motors and contains a TV camera which precisely locates backlit buttons to allow placement in user defined locations to 10 (mu) accuracy. Fiducial points on both plates can also be observed by the camera to allow repeated checks on positioning accuracy. Field plates rotate to follow apparent sky rotation. The spectrographs both analyze light from the 200 observing fibers each and back- illuminate the 400 fibers being re-positioned during the observing run. The 2dF fiber position and spectrograph system is a large and complex instrument located at the prime focus of the Anglo Australian Telescope. The mechanical design has departed somewhat from the earlier concepts of Gray et al, but still reflects the audacity of those first ideas. The positioner is capable of positioning 400 fibers on a field plate while another 400 fibers on another plate are observing at the focus of the telescope and feeding the twin spectrographs. When first proposed it must have seemed like ingenuity unfettered by caution. Yet now it works, and works wonderfully well. 2dF is a system which functions as the result of the combined and coordinated efforts of the astronomers, the mechanical designers and tradespeople, the electronic designers, the programmers, the support staff at the telescope, and the manufacturing subcontractors. The mechanical design of the 2dF positioner and spectrographs was carried out by the mechanical engineering staff of the AAO and the majority of the manufacture was carried out in the AAO workshops.
Engineering light outcoupling in 2D materials.
Lien, Der-Hsien; Kang, Jeong Seuk; Amani, Matin; Chen, Kevin; Tosun, Mahmut; Wang, Hsin-Ping; Roy, Tania; Eggleston, Michael S; Wu, Ming C; Dubey, Madan; Lee, Si-Chen; He, Jr-Hau; Javey, Ali
2015-02-11
When light is incident on 2D transition metal dichalcogenides (TMDCs), it engages in multiple reflections within underlying substrates, producing interferences that lead to enhancement or attenuation of the incoming and outgoing strength of light. Here, we report a simple method to engineer the light outcoupling in semiconducting TMDCs by modulating their dielectric surroundings. We show that by modulating the thicknesses of underlying substrates and capping layers, the interference caused by substrate can significantly enhance the light absorption and emission of WSe2, resulting in a ∼11 times increase in Raman signal and a ∼30 times increase in the photoluminescence (PL) intensity of WSe2. On the basis of the interference model, we also propose a strategy to control the photonic and optoelectronic properties of thin-layer WSe2. This work demonstrates the utilization of outcoupling engineering in 2D materials and offers a new route toward the realization of novel optoelectronic devices, such as 2D LEDs and solar cells.
Irreversibility-inversions in 2D turbulence
NASA Astrophysics Data System (ADS)
Bragg, Andrew; de Lillo, Filippo; Boffetta, Guido
2016-11-01
We consider a recent theoretical prediction that for inertial particles in 2D turbulence, the nature of the irreversibility of their pair dispersion inverts when the particle inertia exceeds a certain value. In particular, when the particle Stokes number, St , is below a certain value, the forward-in-time (FIT) dispersion should be faster than the backward-in-time (BIT) dispersion, but for St above this value, this should invert so that BIT becomes faster than FIT dispersion. This non-trivial behavior arises because of the competition between two physically distinct irreversibility mechanisms that operate in different regimes of St . In 3D turbulence, both mechanisms act to produce faster BIT than FIT dispersion, but in 2D, the two mechanisms have opposite effects because of the inverse energy cascade in the turbulent velocity field. We supplement the qualitative argument given by Bragg et al. by deriving quantitative predictions of this effect in the short-time dispersion limit. These predictions are then confirmed by results of inertial particle dispersion in a direct numerical simulation of 2D turbulence.
MAGNUM-2D computer code: user's guide
England, R.L.; Kline, N.W.; Ekblad, K.J.; Baca, R.G.
1985-01-01
Information relevant to the general use of the MAGNUM-2D computer code is presented. This computer code was developed for the purpose of modeling (i.e., simulating) the thermal and hydraulic conditions in the vicinity of a waste package emplaced in a deep geologic repository. The MAGNUM-2D computer computes (1) the temperature field surrounding the waste package as a function of the heat generation rate of the nuclear waste and thermal properties of the basalt and (2) the hydraulic head distribution and associated groundwater flow fields as a function of the temperature gradients and hydraulic properties of the basalt. MAGNUM-2D is a two-dimensional numerical model for transient or steady-state analysis of coupled heat transfer and groundwater flow in a fractured porous medium. The governing equations consist of a set of coupled, quasi-linear partial differential equations that are solved using a Galerkin finite-element technique. A Newton-Raphson algorithm is embedded in the Galerkin functional to formulate the problem in terms of the incremental changes in the dependent variables. Both triangular and quadrilateral finite elements are used to represent the continuum portions of the spatial domain. Line elements may be used to represent discrete conduits. 18 refs., 4 figs., 1 tab.
Su, Hongling; Li, Shengtai
2016-02-03
In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete versionmore » of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less
Variational symplectic algorithm for guiding center dynamics in the inner magnetosphere
Li Jinxing; Pu Zuyin; Xie Lun; Fu Suiyan; Qin Hong
2011-05-15
Charged particle dynamics in magnetosphere has temporal and spatial multiscale; therefore, numerical accuracy over a long integration time is required. A variational symplectic integrator (VSI) [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008) and H. Qin, X. Guan, and W. M. Tang, Phys. Plasmas 16, 042510 (2009)] for the guiding-center motion of charged particles in general magnetic field is applied to study the dynamics of charged particles in magnetosphere. 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 VSI conserves exactly a discrete Lagrangian symplectic structure and has better numerical properties over a long integration time, compared with standard integrators, such as the standard and adaptive fourth order Runge-Kutta (RK4) methods. Applying the VSI method to guiding-center dynamics in the inner magnetosphere, we can accurately calculate the particles'orbits for an arbitrary long simulating time with good conservation property. When a time-independent convection and corotation electric field is considered, the VSI method can give the accurate single particle orbit, while the RK4 method gives an incorrect orbit due to its intrinsic error accumulation over a long integrating time.
Boundaries, mirror symmetry, and symplectic duality in 3d N=4 gauge theory
NASA Astrophysics Data System (ADS)
Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide; Hilburn, Justin
2016-10-01
We introduce several families of N=(2, 2) UV boundary conditions in 3d N=4 gaugetheoriesandstudytheirIRimagesinsigma-modelstotheHiggsandCoulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respec-tively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studying two-dimensional compactifications of 3d N=4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality — an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.
Construction of symplectic maps for nonlinear motion of particles in accelerators
NASA Astrophysics Data System (ADS)
Berg, J. S.; Warnock, R. L.; Ruth, R. D.; Forest, É.
1994-01-01
We explore an algorithm for the construction of symplectic maps to describe nonlinear particle motion in circular accelerators. We emphasize maps for motion over one or a few full turns, which may provide an economical way of studying long-term stability in large machines such as the Superconducting Super Collider (SSC). The map is defined implicitly by a mixed-variable generating function, represented as a Fourier series in betatron angle variables, with coefficients given as B-spline functions of action variables and the total energy. Despite the implicit definition, iteration of the map proves to be a fast process. The method is illustrated with a realistic model of the SSC. We report extensive tests of accuracy and iteration time in various regions of phase space, and demonstrate the results by using single-turn maps to follow trajectories symplectically for 107 turns on a workstation computer. The same method may be used to construct the Poincaré map of Hamiltonian systems in other fields of physics.
Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
NASA Astrophysics Data System (ADS)
Xiao, Jianyuan; Qin, Hong; Morrison, Philip J.; Liu, Jian; Yu, Zhi; Zhang, Ruili; He, Yang
2016-11-01
An explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed. The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as discrete differential form fields on a fixed mesh. With the assistance of Whitney interpolating forms [H. Whitney, Geometric Integration Theory (Princeton University Press, 1957); M. Desbrun et al., Discrete Differential Geometry (Springer, 2008); J. Xiao et al., Phys. Plasmas 22, 112504 (2015)], this scheme preserves the gauge symmetry of the electromagnetic field, and the pressure field is naturally derived from the discrete internal energy. The whole system is solved using the Hamiltonian splitting method discovered by He et al. [Phys. Plasmas 22, 124503 (2015)], which was been successfully adopted in constructing symplectic particle-in-cell schemes [J. Xiao et al., Phys. Plasmas 22, 112504 (2015)]. Because of its structure preserving and explicit nature, this algorithm is especially suitable for large-scale simulations for physics problems that are multi-scale and require long-term fidelity and accuracy. The algorithm is verified via two tests: studies of the dispersion relation of waves in a two-fluid plasma system and the oscillating two-stream instability.
Symplectic analysis of vertical random vibration for coupled vehicle track systems
NASA Astrophysics Data System (ADS)
Lu, F.; Kennedy, D.; Williams, F. W.; Lin, J. H.
2008-10-01
A computational model for random vibration analysis of vehicle-track systems is proposed and solutions use the pseudo excitation method (PEM) and the symplectic method. The vehicle is modelled as a mass, spring and damping system with 10 degrees of freedom (dofs) which consist of vertical and pitching motion for the vehicle body and its two bogies and vertical motion for the four wheelsets. The track is treated as an infinite Bernoulli-Euler beam connected to sleepers and hence to ballast and is regarded as a periodic structure. Linear springs couple the vehicle and the track. Hence, the coupled vehicle-track system has only 26 dofs. A fixed excitation model is used, i.e. the vehicle does not move along the track but instead the track irregularity profile moves backwards at the vehicle velocity. This irregularity is assumed to be a stationary random process. Random vibration theory is used to obtain the response power spectral densities (PSDs), by using PEM to transform this random multiexcitation problem into a deterministic harmonic excitation one and then applying symplectic solution methodology. Numerical results for an example include verification of the proposed method by comparing with finite element method (FEM) results; comparison between the present model and the traditional rigid track model and; discussion of the influences of track damping and vehicle velocity.
Symplectic random vibration analysis of a vehicle moving on an infinitely long periodic track
NASA Astrophysics Data System (ADS)
Zhang, You-Wei; Lin, Jia-Hao; Zhao, Yan; Howson, W. P.; Williams, F. W.
2010-10-01
Based on the pseudo-excitation method (PEM), symplectic mathematical scheme and Schur decomposition, the random responses of coupled vehicle-track systems are analyzed. The vehicle is modeled as a spring-mass-damper system and the track is regarded as an infinitely long substructural chain consisting of three layers, i.e. the rails, sleepers and ballast. The vehicle and track are coupled via linear springs and the "moving-vehicle model" is adopted. The latter assumes that the vehicle moves along a static track for which the rail irregularity is further assumed to be a zero-mean valued stationary Gaussian random process. The problem is then solved efficiently as follows. Initially, PEM is used to transform the rail random excitations into deterministic harmonic excitations. The symplectic mathematical scheme is then applied to establish a low degree of freedom equation of motion with periodic coefficients. In turn these are transformed into a linear equation set whose upper triangular coefficient matrix is established using the Schur decomposition scheme. Finally, the frequency-dependent terms are separated from the load vector to avoid repeated computations for different frequencies associated with the pseudo-excitations. The proposed method is subsequently justified by comparison with a Monte-Carlo simulation; the fixed-vehicle model and the moving-vehicle model are compared and the influences of vehicle velocity and class of track on system responses are also discussed.
Su, Hongling; Li, Shengtai
2016-02-03
In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete version of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.
Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 gauge theory
Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide; ...
2016-10-20
We introduce several families of N = (2, 2) UV boundary conditions in 3d N=4 gauge theories and study their IR images in sigma-models to the Higgs and Coulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respectively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studyingmore » two-dimensional compactifications of 3d N = 4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality $-$ an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.« less
Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 gauge theory
Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide; Hilburn, Justin
2016-10-20
We introduce several families of N = (2, 2) UV boundary conditions in 3d N=4 gauge theories and study their IR images in sigma-models to the Higgs and Coulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respectively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studying two-dimensional compactifications of 3d N = 4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality $-$ an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.
Wang, Xinwei; Peng, Haijun; Zhang, Sheng; Chen, Biaosong; Zhong, Wanxie
2017-03-16
A symplectic pseudospectral method based on the dual variational principle and the quasilinearization method is proposed and is successfully applied to solve nonlinear optimal control problems with inequality constraints in this paper. Nonlinear optimal control problem is firstly converted into a series of constraint linear-quadratic optimal control problems with the help of quasilinearization techniques. Then a symplectic pseudospectral method based on dual variational principle for solving the converted constrained linear-quadratic optimal control problems is developed. In the proposed method, inequality constraints which can be functions of pure state, pure control and mixed state-control are transformed into equality constraints with the help of parameteric variables. After that, state variables, costate variables and parametric variables are interpolated locally at Legendre-Gauss-Lobatto points. Finally, based on the parametric variational principle and complementary conditions, the converted problem is transformed into a standard linear complementary problem which can be solved easily. Numerical examples show that the proposed method is of high accuracy and efficiency.
NASA Astrophysics Data System (ADS)
Su, Hongling; Li, Shengtai
2016-04-01
In this paper, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete version of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. We also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.
Implicit - symplectic partitioned (IMSP) Runge-Kutta schemes for predator-prey dynamics
NASA Astrophysics Data System (ADS)
Diele, F.; Marangi, C.; Ragni, S.
2012-09-01
In the study of the effects of habitat fragmentation on biodiversity the role of spatial processes reveals of great interest since both the variation of size of the domains as well as their heterogeneity largely affects the dynamics of species. In order to begin a preliminary study about the effects of habitat fragmentation on wolf - wild boar pair populating the Italian "Alta Murgia" Natura 2000 site, object of interest for FP7 project BIOSOS, (BIOdiversity multi-SOurce Monitoring System: from Space TO Species), spatially explicit models described by reaction-diffusion partial differential equations are considered. Numerical methods based on partitioned Runge-Kutta schemes which use an implicit scheme for the stiff diffusive term and a partitioned symplectic scheme for the reaction function are here proposed. We are motivated by the classical results about Lotka-Volterra model described by ordinary differential equations to which the spatially explicit model reduces for diffusion coefficients tending to zero: for their accurate solution symplectic schemes have to be used for an optimal long run preservation of the dynamics invariant. Moreover, for models based on logistic growth and Holling type II functional predator response we verify the better performance of our schemes when compared with classical implicit-explicit (IMEX) schemes on chaotic dynamics given in literature.
Variational symplectic algorithm for guiding center dynamics in the inner magnetosphere
NASA Astrophysics Data System (ADS)
Li, Jinxing; Qin, Hong; Pu, Zuyin; Xie, Lun; Fu, Suiyan
2011-05-01
Charged particle dynamics in magnetosphere has temporal and spatial multiscale; therefore, numerical accuracy over a long integration time is required. A variational symplectic integrator (VSI) [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008) and H. Qin, X. Guan, and W. M. Tang, Phys. Plasmas 16, 042510 (2009)] for the guiding-center motion of charged particles in general magnetic field is applied to study the dynamics of charged particles in magnetosphere. 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 VSI conserves exactly a discrete Lagrangian symplectic structure and has better numerical properties over a long integration time, compared with standard integrators, such as the standard and adaptive fourth order Runge-Kutta (RK4) methods. Applying the VSI method to guiding-center dynamics in the inner magnetosphere, we can accurately calculate the particles'orbits for an arbitrary long simulating time with good conservation property. When a time-independent convection and corotation electric field is considered, the VSI method can give the accurate single particle orbit, while the RK4 method gives an incorrect orbit due to its intrinsic error accumulation over a long integrating time.
2D superconductivity by ionic gating
NASA Astrophysics Data System (ADS)
Iwasa, Yoshi
2D superconductivity is attracting a renewed interest due to the discoveries of new highly crystalline 2D superconductors in the past decade. Superconductivity at the oxide interfaces triggered by LaAlO3/SrTiO3 has become one of the promising routes for creation of new 2D superconductors. Also, the MBE grown metallic monolayers including FeSe are also offering a new platform of 2D superconductors. In the last two years, there appear a variety of monolayer/bilayer superconductors fabricated by CVD or mechanical exfoliation. Among these, electric field induced superconductivity by electric double layer transistor (EDLT) is a unique platform of 2D superconductivity, because of its ability of high density charge accumulation, and also because of the versatility in terms of materials, stemming from oxides to organics and layered chalcogenides. In this presentation, the following issues of electric filed induced superconductivity will be addressed; (1) Tunable carrier density, (2) Weak pinning, (3) Absence of inversion symmetry. (1) Since the sheet carrier density is quasi-continuously tunable from 0 to the order of 1014 cm-2, one is able to establish an electronic phase diagram of superconductivity, which will be compared with that of bulk superconductors. (2) The thickness of superconductivity can be estimated as 2 - 10 nm, dependent on materials, and is much smaller than the in-plane coherence length. Such a thin but low resistance at normal state results in extremely weak pinning beyond the dirty Boson model in the amorphous metallic films. (3) Due to the electric filed, the inversion symmetry is inherently broken in EDLT. This feature appears in the enhancement of Pauli limit of the upper critical field for the in-plane magnetic fields. In transition metal dichalcogenide with a substantial spin-orbit interactions, we were able to confirm the stabilization of Cooper pair due to its spin-valley locking. This work has been supported by Grant-in-Aid for Specially
NASA Astrophysics Data System (ADS)
Gordillo, M. C.; De Soto, F.
2017-07-01
The behavior of small clusters of one spin-up and two spin-down fermions with unlike-spin repulsive interactions in one-dimensional optical lattices was calculated using a diffusion Monte Carlo technique. We considered also a harmonic potential in the longitudinal direction to make our system resemble the standard experimental setups. When the interparticle repulsion is strong enough, the onset of fermionization is observed irrespective of the optical lattice parameters considered, in line with previous results for pure harmonic confinement. However, fermionization can also be seen even for small interparticle couplings if the optical potential is deep enough. In addition, for certain values of the wavelengths and the potential depths defining the lattice, Mott insulators in the fermionization limit with only three atoms were found.
2D non-separable linear canonical transform (2D-NS-LCT) based cryptography
NASA Astrophysics Data System (ADS)
Zhao, Liang; Muniraj, Inbarasan; Healy, John J.; Malallah, Ra'ed; Cui, Xiao-Guang; Ryle, James P.; Sheridan, John T.
2017-05-01
The 2D non-separable linear canonical transform (2D-NS-LCT) can describe a variety of paraxial optical systems. Digital algorithms to numerically evaluate the 2D-NS-LCTs are not only important in modeling the light field propagations but also of interest in various signal processing based applications, for instance optical encryption. Therefore, in this paper, for the first time, a 2D-NS-LCT based optical Double-random- Phase-Encryption (DRPE) system is proposed which offers encrypting information in multiple degrees of freedom. Compared with the traditional systems, i.e. (i) Fourier transform (FT); (ii) Fresnel transform (FST); (iii) Fractional Fourier transform (FRT); and (iv) Linear Canonical transform (LCT), based DRPE systems, the proposed system is more secure and robust as it encrypts the data with more degrees of freedom with an augmented key-space.
Composite fermions and the field-tuned superconductor-insulator transition
NASA Astrophysics Data System (ADS)
Raghu, Srinivas; Mulligan, Michael
In several two-dimensional films that exhibit a magnetic field-tuned superconductor to insulator transition (SIT), stable metallic phases have been observed. Building on the `dirty boson' description of the SIT, we suggest that the metallic region is analogous to the composite Fermi liquid observed about half-filled Landau levels of the two-dimensional electron gas. The composite fermions here are mobile vortices attached to one flux quantum of an emergent gauge field. The composite vortex liquid is a 2D non-Fermi liquid metal, which we argue is stable to weak quenched disorder. We describe several experimental consequences of the emergent composite vortex liquid.
Composite fermions and the field-tuned superconductor-insulator transition
NASA Astrophysics Data System (ADS)
Mulligan, Michael; Raghu, S.
2016-05-01
In several two-dimensional films that exhibit a magnetic field-tuned superconductor to insulator transition (SIT), stable metallic phases have been observed. Building on the `dirty boson' description of the SIT, we suggest that the metallic region is analogous to the composite Fermi liquid observed about half-filled Landau levels of the two-dimensional electron gas. The composite fermions here are mobile vortices attached to one flux quantum of an emergent gauge field. The composite vortex liquid is a 2D non-Fermi liquid metal, which we argue is stable to weak quenched disorder. We describe several experimental consequences of the emergent composite vortex liquid.
Demonstrating non-Abelian statistics of Majorana fermions using twist defects
NASA Astrophysics Data System (ADS)
Zheng, Huaixiu; Dua, Arpit; Jiang, Liang
We study the twist defects in the toric code model introduced by Bombin [Phys. Rev. Lett.105, 030403 (2010)]. Using a generalized 2D Jordan-Wigner transformation and a projective construction, we show explicitly the twist defects carry unpaired Majorana zero modes. In addition, we propose a quantum non-demolition measurement scheme of the parity of Majorana modes. Such a scheme provides an alternative avenue to demonstrate the non-Abelian statistics of Majorana fermions. The braiding operation is simulated by an efficient measurement-based approach that removes the uncertainty associated with the previous forced measurement scheme.
Non-perturbative renormalisation of left left four-fermion operators with Neuberger fermions
NASA Astrophysics Data System (ADS)
Dimopoulos, P.; Giusti, L.; Hernández, P.; Palombi, F.; Pena, C.; Vladikas, A.; Wennekers, J.; Wittig, H.
2006-09-01
We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the ΔS = 1 and ΔS = 2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays.
Odd frequency pairing of interacting Majorana fermions
NASA Astrophysics Data System (ADS)
Huang, Zhoushen; Woelfle, Peter; Balatsky, Alexandar
Majorana fermions are rising as a promising key component in quantum computation. While the prevalent approach is to use a quadratic (i.e. non-interacting) Majorana Hamiltonian, when expressed in terms of Dirac fermions, generically the Hamiltonian involves interaction terms. Here we focus on the possible pair correlations in a simple model system. We study a model of Majorana fermions coupled to a boson mode and show that the anomalous correlator between different Majorana fermions, located at opposite ends of a topological wire, exhibits odd frequency behavior. It is stabilized when the coupling strength g is above a critical value gc. We use both, conventional diagrammatic theory and a functional integral approach, to derive the gap equation, the critical temperature, the gap function, the critical coupling, and a Ginzburg-Landau theory allowing to discuss a possible subleading admixture of even-frequency pairing. Work supported by USDOE DE-AC52-06NA25396 E304, Knut and Alice Wallenberg Foundation, and ERC DM-321031.
Axial gravity, massless fermions and trace anomalies
NASA Astrophysics Data System (ADS)
Bonora, L.; Cvitan, M.; Prester, P. Dominis; Pereira, A. Duarte; Giaccari, S.; Štemberga, T.
2017-08-01
This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms and using dimensional regularization, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones.
Finite volume renormalization scheme for fermionic operators
Monahan, Christopher; Orginos, Kostas
2013-11-01
We propose a new finite volume renormalization scheme. Our scheme is based on the Gradient Flow applied to both fermion and gauge fields and, much like the Schr\\"odinger functional method, allows for a nonperturbative determination of the scale dependence of operators using a step-scaling approach. We give some preliminary results for the pseudo-scalar density in the quenched approximation.
Observation of Weyl fermions in condensed matter
NASA Astrophysics Data System (ADS)
Ding, Hong
In 1929, a German mathematician and physicist Hermann Weyl proposed that a massless solution of the Dirac equation represents a pair of new type of particles, the so-called Weyl fermions. However, their existence in particle physics remains elusive after more than eight decades, e.g., neutrino has been regarded as a Weyl fermion in the Standard Model until it was found to have mass. Recently, significant advances in topological materials have provided an alternative way to realize Weyl fermions in condensed matter as an emergent phenomenon. Weyl semimetals are predicted as a class of topological materials that can be regarded as three-dimensional analogs of graphene breaking time reversal or inversion symmetry. Electrons in a Weyl semimetal behave exactly as Weyl fermions, which have many exotic properties, such as chiral anomaly, magnetic monopoles in the crystal momentum space, and open Fermi arcs on the surface. In this talk I will report our experimental discovery of a Weyl semimetal in TaAs by observing Fermi arcs with a characteristic spin texture in the surface states and Weyl nodes in the bulk states using angle-resolved photoemission spectroscopy.
Unorthodox lattice fermion derivatives and their shortcomings
Bodwin, G.T.; Kovacs, E.V.
1987-03-10
We discuss the DWY (Lagrangian), Quinn-Weinstein, and Rebbi proposals for incorporating fermions into lattice gauge theory and analyze them in the context of weak coupling perturbation theory. We find that none of these proposals leads to a completely satisfactory lattice transcription of fully-interacting gauge theory.
On the decoupling of mirror fermions
NASA Astrophysics Data System (ADS)
Chen, Chen; Giedt, Joel; Poppitz, Erich
2013-04-01
An approach to the formulation of chiral gauge theories on the lattice is to start with a vector-like theory, but decouple one chirality (the "mirror" fermions) using strong Yukawa interactions with a chirally coupled "Higgs" field. While this is an attractive idea, its viability needs to be tested with nonperturbative studies. The model that we study here, the so-called "3-4-5" model, is anomaly free and the presence of massless states in the mirror sector is not required by anomaly matching arguments, in contrast to the "1-0" model that was studied previously. We have computed the polarization tensor in this theory and find a directional discontinuity that appears to be nonzero in the limit of an infinite lattice, which is equivalent to the continuum limit at fixed physical volume. We show that a similar behavior occurs for the free massless Ginsparg-Wilson fermion, where the polarization tensor is known to have a directional discontinuity in the continuum limit. We thus find support for the conclusion that in the continuum limit of the 3-4-5 model, there are massless charged modes in the mirror sector so that it does not decouple from the light sector. The value of the discontinuity we obtain allows for two interpretations: either a chiral gauge theory does not emerge and mirror-sector fermions in a chiral anomaly free representation remain massless, or a massless vectorlike mirror fermion appears. We end by discussing some questions for future study.
Entanglement of several blocks in fermionic chains
NASA Astrophysics Data System (ADS)
Ares, Filiberto; Esteve, José G.; Falceto, Fernando
2014-12-01
In this paper we propose an expression for the entanglement entropy of several intervals in a stationary state of a free, translational invariant Hamiltonian in a fermionic chain. We check numerically the accuracy of our proposal and conjecture a formula for the asymptotic behavior of principal submatrices of a Toeplitz matrix.
Fermionic entanglement ambiguity in noninertial frames
Montero, Miguel; Martin-Martinez, Eduardo
2011-06-15
We analyze an ambiguity in previous works on entanglement of fermionic fields in noninertial frames. This ambiguity, related to the anticommutation properties of field operators, leads to nonunique results when computing entanglement measures for the same state. We show that the ambiguity disappears when we introduce detectors, which are in any case necessary as a means to probe the field entanglement.
Quantization of gravitation with Weyl fermions
Schaposnik, F.A.; Vucetich, H.
1987-12-01
It is shown that quantization of gravitation consistent with the presence of Weyl fermions is possible, in spite of the existence of Lorentz anomalies; the group of local Lorentz transformations is quantized becoming a physical field and the anomaly is absorbed.
Precision constraints on extra fermion generations.
Erler, Jens; Langacker, Paul
2010-07-16
There has been recent renewed interest in the possibility of additional fermion generations. At the same time there have been significant changes in the relevant electroweak precision constraints, in particular, in the interpretation of several of the low energy experiments. We summarize the various motivations for extra families and analyze them in view of the latest electroweak precision data.
Fermions Living in a Flat World
Jesus Anguiano-Galicia, Ma. de; Bashir, A.
2006-09-25
In a plane, parity transformation, which changes the sign of only one spatial coordinate, swaps the fermion fields living in two inequivalent representations. A parity invariant Lagrangian thus contains fields corresponding to both the representations. For such a Lagrangian, we show that we can also define a chiral symmetry.
NASA Astrophysics Data System (ADS)
Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto
2005-05-01
The first aim of this paper is to extend the Skinner-Rusk formalism on classical mechanics for first-order field theories. The second is to generalize the definition and properties of the evolution K-operator on classical mechanics for first-order field theories using in both cases Günther's formalism (k-symplectic formalism).
NASA Astrophysics Data System (ADS)
Marrero, Juan Carlos; Padrón, Edith; Rodríguez-Olmos, Miguel
2012-04-01
This paper addresses the problem of developing an extension of the Marsden-Weinstein reduction process to symplectic-like Lie algebroids, and in particular to the case of the canonical cover of a fiberwise linear Poisson structure, whose reduction process is the analog to cotangent bundle reduction in the context of Lie algebroids. Dedicated to the memory of Jerrold E Marsden
NASA Astrophysics Data System (ADS)
Ma, Xiao; Yang, Dinghui
2017-06-01
The finite-difference method, which is an important numerical tool for solving seismic wave equations, is widely applied in simulation, wave-equation-based migration and inversion. As the seismic wave phase plays a critical role in forward simulation and inversion, it should be preserved during wavefield simulation. In this paper, we propose a type of phase-preserving stereomodelling method, which is simultaneously symplectic and low numerical dispersive. First, we propose three new time-marching schemes for solving wave equations that are optimal symplectic partitioned Runge-Kutta schemes with minimized phase errors. Relevant simulations on a harmonic oscillator show that even after 200 000 temporal iterations, our schemes can still avoid the phase drifting issue that appears in other symplectic schemes. We use these symplectic schemes as time integrators, and a numerically low dispersive operator called the stereomodelling discrete operator as a spatial discretization approach to solve seismic wave equations. Theoretical analysis on the stability conditions shows that the new methods are more stable than previous methods. We also investigate the numerical dispersion relations of the methods proposed in this study. To further investigate phase accuracy, we compare the numerical solutions generated by the proposed methods with analytic solutions. Several numerical experiments indicate that our proposed methods are efficient for various models and perform well with perfectly matched layer boundary conditions.
NASA Astrophysics Data System (ADS)
Ma, Xiao; Yang, Dinghui
2017-03-01
The finite-difference method, which is an important numerical tool for solving seismic wave equations, is widely applied in wavefield simulation, wave-equation-based migration and inversion. As the seismic wave phase plays a critical role in forward simulation and inversion, it should be preserved during wavefield simulation. In this paper, we propose a type of phase-preserving stereomodelling method, which is simultaneously symplectic and low numerical dispersive. First, we propose three new time-marching schemes for solving wave equations that are optimal symplectic partitioned Runge-Kutta schemes with minimized phase errors. Relevant simulations on a harmonic oscillator show that even after 200,000 temporal iterations, our schemes can still avoid the phase drifting issue that appears in other symplectic schemes. We use these symplectic schemes as time integrators, and a numerically low dispersive operator called the stereomodelling discrete operator as a spatial discretization approach to solve seismic wave equations. Theoretical analysis on the stability conditions shows that the new methods are more stable than previous methods. We also investigate the numerical dispersion relations of the methods proposed in this study. To further investigate phase accuracy, we compare the numerical solutions generated by the proposed methods with analytic solutions. Several numerical experiments indicate that our proposed methods are efficient for various models and perform well with perfectly matched layer boundary conditions.
NASA Astrophysics Data System (ADS)
Wang, Yue; Wang, Jianguo; Chen, Zaigao; Cheng, Guoxin; Wang, Pan
2016-08-01
To overcome the staircase error in the traditional particle-in-cell (PIC) method, a three dimensional (3D) simple conformal (SC) symplectic PIC method is presented in this paper. The SC symplectic finite integration technique (FIT) scheme is used to advance the electromagnetic fields without reduction of the time step. Particles are emitted from conformal boundaries with the charge conserving emission scheme and moved by using the relativistic Newton-Lorentz force equation. The symplectic formulas of auxiliary-differential equation, complex frequency shifted perfectly matched layer (ADE-CFS-PML) are given for truncating the open boundaries, numerical results show that the maximum relative error of truncation is less than 90 dB. Based on the surface equivalence theorem, the computing algorithms of conformal signals' injection are given, numerical results show that the algorithms can give the right mode patterns and the errors of cutoff frequencies could be as low as 0.1%. To verify the conformal algorithms, a magnetically insulated line oscillator is simulated, and the results are compared to those provided by using the 2.5D UNIPIC code, which show that they agree well. The results also show that the high order symplectic integration method can suppress the numerical Cherenkov radiation.
Ghost free systems with coexisting bosons and fermions
NASA Astrophysics Data System (ADS)
Kimura, Rampei; Sakakihara, Yuki; Yamaguchi, Masahide
2017-08-01
We study the coexistence system of both bosonic and fermionic degrees of freedom. Even if a Lagrangian does not include higher derivatives, fermionic ghosts exist. For a Lagrangian with up to first derivatives, we find the fermionic ghost free condition in Hamiltonian analysis, which is found to be the same as requiring that the equations of motion of fermions be first order in Lagrangian formulation. When fermionic degrees of freedom are present, the uniqueness of time evolution is not guaranteed a priori because of the Grassmann property. We confirm that the additional condition, which is introduced to close Hamiltonian analysis, also ensures the uniqueness of the time evolution of the system.
Effect of Fermion Velocity on Phase Structure of QED3
NASA Astrophysics Data System (ADS)
Li, Jian-Feng; Feng, Hong-Tao; Zong, Hong-Shi
2016-11-01
Dynamical chiral symmetry breaking (DCSB) in thermal QED3 with fermion velocity is studied in the framework of Dyson-Schwinger equations. By adopting instantaneous approximation and neglecting the transverse component of gauge boson propagator at finite temperature, we numerically solve the fermion self-energy equation in the rainbow approximation. It is found that both DCSB and fermion chiral condensate are suppressed by fermion velocity. Moreover, the critical temperature decreases as fermion velocity increases. Supported in part by the National Natural Science Foundation of China under Grant No. 11535005 and the Natural Science Foundation of Jiangsu Province under Grant No. BK20130387
Codon Constraints on Closed 2D Shapes,
2014-09-26
19843$ CODON CONSTRAINTS ON CLOSED 2D SHAPES Go Whitman Richards "I Donald D. Hoffman’ D T 18 Abstract: Codons are simple primitives for describing plane...RSONAL AUT"ORtIS) Richards, Whitman & Hoffman, Donald D. 13&. TYPE OF REPORT 13b. TIME COVERED N/A P8 AT F RRrT t~r. Ago..D,) is, PlE COUNT Reprint...outlines, if figure and ground are ignored. Later, we will address the problem of indexing identical codon descriptors that have different figure
ENERGY LANDSCAPE OF 2D FLUID FORMS
Y. JIANG; ET AL
2000-04-01
The equilibrium states of 2D non-coarsening fluid foams, which consist of bubbles with fixed areas, correspond to local minima of the total perimeter. (1) The authors find an approximate value of the global minimum, and determine directly from an image how far a foam is from its ground state. (2) For (small) area disorder, small bubbles tend to sort inwards and large bubbles outwards. (3) Topological charges of the same sign repel while charges of opposite sign attract. (4) They discuss boundary conditions and the uniqueness of the pattern for fixed topology.
Periodically sheared 2D Yukawa systems
Kovács, Anikó Zsuzsa; Hartmann, Peter; Donkó, Zoltán
2015-10-15
We present non-equilibrium molecular dynamics simulation studies on the dynamic (complex) shear viscosity of a 2D Yukawa system. We have identified a non-monotonic frequency dependence of the viscosity at high frequencies and shear rates, an energy absorption maximum (local resonance) at the Einstein frequency of the system at medium shear rates, an enhanced collective wave activity, when the excitation is near the plateau frequency of the longitudinal wave dispersion, and the emergence of significant configurational anisotropy at small frequencies and high shear rates.
Fermions in hybrid loop quantum cosmology
NASA Astrophysics Data System (ADS)
Elizaga Navascués, Beatriz; Mena Marugán, Guillermo A.; Martín-Benito, Mercedes
2017-08-01
This work pioneers the quantization of primordial fermion perturbations in hybrid loop quantum cosmology (LQC). We consider a Dirac field coupled to a spatially flat, homogeneous, and isotropic cosmology, sourced by a scalar inflaton, and treat the Dirac field as a perturbation. We describe the inhomogeneities of this field in terms of creation and annihilation variables, chosen to admit a unitary evolution if the Dirac fermion were treated as a test field. Considering instead the full system, we truncate its action at quadratic perturbative order and construct a canonical formulation. In particular this implies that, in the global Hamiltonian constraint of the model, the contribution of the homogeneous sector is corrected with a quadratic perturbative term. We then adopt the hybrid LQC approach to quantize the full model, combining the loop representation of the homogeneous geometry with the Fock quantization of the inhomogeneities. We assume a Born-Oppenheimer ansatz for physical states and show how to obtain a Schrödinger equation for the quantum evolution of the perturbations, where the role of time is played by the homogeneous inflaton. We prove that the resulting quantum evolution of the Dirac field is indeed unitary, despite the fact that the underlying homogeneous geometry has been quantized as well. Remarkably, in such evolution, the fermion field couples to an infinite sequence of quantum moments of the homogeneous geometry. Moreover, the evolved Fock vacuum of our fermion perturbations is shown to be an exact solution of the Schrödinger equation. Finally, we discuss in detail the quantum backreaction that the fermion field introduces in the global Hamiltonian constraint. For completeness, our quantum study includes since the beginning (gauge-invariant) scalar and tensor perturbations, that were studied in previous works.
The tensor hierarchies of pure N = 2, d = 4, 5, 6 supergravities
NASA Astrophysics Data System (ADS)
Hübscher, M.; Ortín, T.; Shahbazi, C. S.
2010-11-01
We study the supersymmetric tensor hierarchy of pure (gauged) N = 2, d = 4 , 5 , 6 supergravity and compare them with those of the pure, ungauged, theories (worked out in ref. [1] for d = 5) and the predictions of the Kač-Moody approach made in ref. [2]. We find complete agreement in the ungauged case but we also find that, after gauging, new Stückelberg symmetries reduce the number of independent physical top-forms. The analysis has to be performed to all orders in fermion fields. We discuss the construction of the worldvolume effective actions for the p-branes which are charged with respect to the ( p + 1)-form potentials and the relations between the tensor hierarchies and p-branes upon dimensional reduction.
Fermionic-mode entanglement in non-Markovian environment
Cheng, Jiong; Han, Yan; An, Qing-zhi; Zhou, Ling
2015-03-15
We evaluate the non-Markovian effects on the entanglement dynamics of a fermionic system interacting with two dissipative vacuum reservoirs. The exact solution of density matrix is derived by utilizing the Feynman–Vernon influence functional theory in the fermionic coherent state representation and the Grassmann calculus, which are valid for both the fermionic and bosonic baths, and their difference lies in the dependence of the parity of the initial states. The fermionic entanglement dynamics is presented by adding an additional restriction to the density matrix known as the superselection rules. Our analysis shows that the usual decoherence suppression schemes implemented in qubits systems can also be achieved for systems of identical fermions, and the initial state proves its importance in the evolution of fermionic entanglement. Our results provide a potential way to decoherence controlling of identical fermions.
H. Qin and X. Guan
2008-02-11
A variational symplectic integrator for the guiding-center motion of charged particles in general magnetic fields is developed for 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 has better numerical properties over long integration time, compared with standard integrators, such as the standard and variable time-step fourth order Runge-Kutta methods.
Qin Hong; Guan Xiaoyin
2008-01-25
A variational symplectic integrator for the guiding-center motion of charged particles in general magnetic fields is developed for 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 has better numerical properties over long integration time, compared with standard integrators, such as the standard and variable time-step fourth order Runge-Kutta methods.
Remarks on thermalization in 2D CFT
NASA Astrophysics Data System (ADS)
de Boer, Jan; Engelhardt, Dalit
2016-12-01
We revisit certain aspects of thermalization in 2D conformal field theory (CFT). In particular, we consider similarities and differences between the time dependence of correlation functions in various states in rational and non-rational CFTs. We also consider the distinction between global and local thermalization and explain how states obtained by acting with a diffeomorphism on the ground state can appear locally thermal, and we review why the time-dependent expectation value of the energy-momentum tensor is generally a poor diagnostic of global thermalization. Since all 2D CFTs have an infinite set of commuting conserved charges, generic initial states might be expected to give rise to a generalized Gibbs ensemble rather than a pure thermal ensemble at late times. We construct the holographic dual of the generalized Gibbs ensemble and show that, to leading order, it is still described by a Banados-Teitelboim-Zanelli black hole. The extra conserved charges, while rendering c <1 theories essentially integrable, therefore seem to have little effect on large-c conformal field theories.
NASA Astrophysics Data System (ADS)
Yang, Shengxue; Jiang, Chengbao; Wei, Su-huai
2017-06-01
Two-dimensional (2D) layered inorganic nanomaterials have attracted huge attention due to their unique electronic structures, as well as extraordinary physical and chemical properties for use in electronics, optoelectronics, spintronics, catalysts, energy generation and storage, and chemical sensors. Graphene and related layered inorganic analogues have shown great potential for gas-sensing applications because of their large specific surface areas and strong surface activities. This review aims to discuss the latest advancements in the 2D layered inorganic materials for gas sensors. We first elaborate the gas-sensing mechanisms and introduce various types of gas-sensing devices. Then, we describe the basic parameters and influence factors of the gas sensors to further enhance their performance. Moreover, we systematically present the current gas-sensing applications based on graphene, graphene oxide (GO), reduced graphene oxide (rGO), functionalized GO or rGO, transition metal dichalcogenides, layered III-VI semiconductors, layered metal oxides, phosphorene, hexagonal boron nitride, etc. Finally, we conclude the future prospects of these layered inorganic materials in gas-sensing applications.
2D packing using the Myriad framework
NASA Astrophysics Data System (ADS)
Chatburn, Luke T.; Batchelor, Bruce G.
2004-02-01
Myriad is a framework for building networked and distributed vision systems and is described in a companion paper in this conference. Myriad allows the components of a multi-camera, multi-user vision system (web-cameras, image processing engines, intelligent device controllers, databases and the user interface terminals) to be interconnected and operated together, even if they are physically separated by many hundreds, or thousands, of kilometres. This is achieved by operating them as Internet services. The principal objective in this article is to illustrate the simplicity of harmonising visual control with an existing system using Myriad. However, packing of 2-dimensional blob-like objects is of considerable commercial importance in some industries and involves robotic handling and/or cutting. The shapes to be packed may be cut from sheet metal, glass, cloth, leather, wood, card, paper, composite board, or flat food materials. In addition, many 3D packing applications can realistically be tackled only by regarding them as multi-layer 2D applications. Using Myriad to perform 2D packing, a set of blob-like input objects ("shapes") can be digitised using a standard camera (e.g. a "webcam"). The resulting digital images are then analysed, using a separate processing engine, perhaps located on a different continent. The packing is planned by another processing system, perhaps on a third continent. Finally, the assembly is performed using a robot, usually but not necessarily, located close to the camera.
Microwave Assisted 2D Materials Exfoliation
NASA Astrophysics Data System (ADS)
Wang, Yanbin
Two-dimensional materials have emerged as extremely important materials with applications ranging from energy and environmental science to electronics and biology. Here we report our discovery of a universal, ultrafast, green, solvo-thermal technology for producing excellent-quality, few-layered nanosheets in liquid phase from well-known 2D materials such as such hexagonal boron nitride (h-BN), graphite, and MoS2. We start by mixing the uniform bulk-layered material with a common organic solvent that matches its surface energy to reduce the van der Waals attractive interactions between the layers; next, the solutions are heated in a commercial microwave oven to overcome the energy barrier between bulk and few-layers states. We discovered the minutes-long rapid exfoliation process is highly temperature dependent, which requires precise thermal management to obtain high-quality inks. We hypothesize a possible mechanism of this proposed solvo-thermal process; our theory confirms the basis of this novel technique for exfoliation of high-quality, layered 2D materials by using an as yet unknown role of the solvent.
Analysis of the antiferromagnetic phase transitions of the 2D Kondo lattice
NASA Astrophysics Data System (ADS)
Jones, Barbara
2010-03-01
The Kondo lattice continues to present an interesting and relevant challenge, with its interactions between Kondo, RKKY, and coherent order. We present our study[1] of the antiferromagnetic quantum phase transitions of a 2D Kondo-Heisenberg square lattice. Starting from the nonlinear sigma model as a model of antiferromagnetism, we carry out a renormalization group analysis of the competing Kondo-RKKY interaction to one-loop order in an ɛ-expansion. We find a new quantum critical point (QCP) strongly affected by Kondo fluctuations. Near this QCP, there is a breakdown of hydrodynamic behavior, and the spin waves are logarithmically frozen out. The renormalization group results allow us to propose a new phase diagram near the antiferromagnetic fixed point of this 2D Kondo lattice model. The T=0 phase diagram contains four phases separated by a tetracritical point, the new QCP. For small spin fluctuations, we find a stable local magnetic moment antiferromagnet. For stronger coupling, region II is a metallic quantum disordered paramagnet. We find in region III a paramagnetic phase driven by Kondo interactions, with possible ground states of a heavy fermion liquid or a Kondo driven spin-liquid. The fourth phase is a spiral phase, or a large-Fermi-surface antiferromagnetic phase. We will describe these phases in more detail, including possible experimental confirmation of the spiral phase. The existence of the tetracritical point found here would be expected to affect the phase diagram at finite temperatures as well. In addition, It is hoped that these results, and particularly the Kondo interaction paramagnetic phase, will serve to bridge to solutions starting from the opposite limit, of a Kondo effect leading to a heavy fermion ground state. Work in collaboration with T. Tzen Ong. [4pt] [1] T. Ong and B. A. Jones, Phys. Rev. Lett. 103, 066405 (2009).
WFR-2D: an analytical model for PWAS-generated 2D ultrasonic guided wave propagation
NASA Astrophysics Data System (ADS)
Shen, Yanfeng; Giurgiutiu, Victor
2014-03-01
This paper presents WaveFormRevealer 2-D (WFR-2D), an analytical predictive tool for the simulation of 2-D ultrasonic guided wave propagation and interaction with damage. The design of structural health monitoring (SHM) systems and self-aware smart structures requires the exploration of a wide range of parameters to achieve best detection and quantification of certain types of damage. Such need for parameter exploration on sensor dimension, location, guided wave characteristics (mode type, frequency, wavelength, etc.) can be best satisfied with analytical models which are fast and efficient. The analytical model was constructed based on the exact 2-D Lamb wave solution using Bessel and Hankel functions. Damage effects were inserted in the model by considering the damage as a secondary wave source with complex-valued directivity scattering coefficients containing both amplitude and phase information from wave-damage interaction. The analytical procedure was coded with MATLAB, and a predictive simulation tool called WaveFormRevealer 2-D was developed. The wave-damage interaction coefficients (WDICs) were extracted from harmonic analysis of local finite element model (FEM) with artificial non-reflective boundaries (NRB). The WFR-2D analytical simulation results were compared and verified with full scale multiphysics finite element models and experiments with scanning laser vibrometer. First, Lamb wave propagation in a pristine aluminum plate was simulated with WFR-2D, compared with finite element results, and verified by experiments. Then, an inhomogeneity was machined into the plate to represent damage. Analytical modeling was carried out, and verified by finite element simulation and experiments. This paper finishes with conclusions and suggestions for future work.
NASA Astrophysics Data System (ADS)
Khisina, N. R.; Wirth, R.; Abart, R.; Rhede, D.; Heinrich, W.
2013-03-01
Calcium-chromium rich lamellae in olivine grain No. 1611 from the Luna-24 regolith were studied with FEG-EMPA and TEM. The lamellae consist of a worm-like intergrowth of FeCr2O4 chromite (Chr) and CaMgSi2O6 diopside (Di), with a Chr:Di modal proportion of 1:3. The linear extension of the lamellae and crystallographic orientation relationships among the symplectite phases and the olivine suggest that the lamellae nucleated at deformation defects in the olivine host. Calcium depletion haloes surrounding the lamellae amount to about 75 μm and indicate that the chromite + diopside lamellae were formed by segregation of calcium and chromium from the host olivine into the lamellae without addition of calcium and/or chromium from outside the olivine. The segregation of calcium and chromium and, consequently, the growth of the symplectic lamellae were diffusion-controlled. The segregation of a calcium-chromium component from the host olivine was associated with oxidation of divalent to trivalent chromium. Oxidation was facilitated by dehydrogenation, which was driven by decompression and/or a change in redox potential. Hydrogen point defects in the original olivine with H+ substituting for divalent cations on the M-sites provided the necessary electron acceptors for the oxidation of chromium and after electron transfer left olivine as molecular H2. The internal microstructure of the lamellae suggests that exsolution of the calcium-chromium rich lamellae from the host olivine and formation of the chromite-diopside symplectic intergrowth occurred simultaneously. The time scale derived from diffusion modeling of the calcium depletion haloes around the lamellae indicates a thermal event on the order of several months to several hundred years at most. Symplectic inclusions found in olivine from lunar, martian and terrestrial rocks are similar with respect to their shape, crystallographic orientation relationships, and internal microstructure of the spinel
2-D or not 2-D, that is the question: A Northern California test
Mayeda, K; Malagnini, L; Phillips, W S; Walter, W R; Dreger, D
2005-06-06
Reliable estimates of the seismic source spectrum are necessary for accurate magnitude, yield, and energy estimation. In particular, how seismic radiated energy scales with increasing earthquake size has been the focus of recent debate within the community and has direct implications on earthquake source physics studies as well as hazard mitigation. The 1-D coda methodology of Mayeda et al. has provided the lowest variance estimate of the source spectrum when compared against traditional approaches that use direct S-waves, thus making it ideal for networks that have sparse station distribution. The 1-D coda methodology has been mostly confined to regions of approximately uniform complexity. For larger, more geophysically complicated regions, 2-D path corrections may be required. The complicated tectonics of the northern California region coupled with high quality broadband seismic data provides for an ideal ''apples-to-apples'' test of 1-D and 2-D path assumptions on direct waves and their coda. Using the same station and event distribution, we compared 1-D and 2-D path corrections and observed the following results: (1) 1-D coda results reduced the amplitude variance relative to direct S-waves by roughly a factor of 8 (800%); (2) Applying a 2-D correction to the coda resulted in up to 40% variance reduction from the 1-D coda results; (3) 2-D direct S-wave results, though better than 1-D direct waves, were significantly worse than the 1-D coda. We found that coda-based moment-rate source spectra derived from the 2-D approach were essentially identical to those from the 1-D approach for frequencies less than {approx}0.7-Hz, however for the high frequencies (0.7{le} f {le} 8.0-Hz), the 2-D approach resulted in inter-station scatter that was generally 10-30% smaller. For complex regions where data are plentiful, a 2-D approach can significantly improve upon the simple 1-D assumption. In regions where only 1-D coda correction is available it is still preferable over 2
Jiao, Yalong; Ma, Fengxian; Bell, John; Bilic, Ante; Du, Aijun
2016-08-22
Two-dimensional (2D) boron sheets have been successfully synthesized in recent experiments, however, some important issues remain, including the dynamical instability, high energy, and the active surface of the sheets. In an attempt to stabilize 2D boron layers, we have used density functional theory and global minimum search with the particle-swarm optimization method to predict four stable 2D boron hydride layers, namely the C2/m, Pbcm, Cmmm, and Pmmn sheets. The vibrational normal mode calculations reveal all these structures are dynamically stable, indicating potential for successful experimental synthesis. The calculated Young's modulus indicates a high mechanical strength for the C2/m and Pbcm phases. Most importantly, the C2/m, Pbcm, and Pmmn structures exhibit Dirac cones with massless Dirac fermions and the Fermi velocities for the Pbcm and Cmmm structures are even higher than that of graphene. The Cmmm phase is reported as the first discovery of Dirac ring material among boron-based 2D structures. The unique electronic structure of the 2D boron hydride sheets makes them ideal for nanoelectronics applications. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Metal-insulator transition in two-dimensional random fermion systems of chiral symmetry classes
NASA Astrophysics Data System (ADS)
König, E. J.; Ostrovsky, P. M.; Protopopov, I. V.; Mirlin, A. D.
2012-05-01
Field-theoretical approach to Anderson localization in 2D disordered fermionic systems of chiral symmetry classes (BDI, AIII, CII) is developed. Important representatives of these symmetry classes are random hopping models on bipartite lattices at the band center. As was found by Gade and Wegner two decades ago within the sigma-model formalism, quantum interference effects in these classes are absent to all orders of perturbation theory. We demonstrate that the quantum localization effects emerge when the theory is treated nonperturbatively. Specifically, they are controlled by topological vortexlike excitations of the sigma models. We derive renormalization-group equations including these nonperturbative contributions. Analyzing them, we find that the 2D disordered systems of chiral classes undergo a metal-insulator transition driven by topologically induced Anderson localization. We also show that the Wess-Zumino and Z2 θ terms on surfaces of 3D topological insulators (in classes AIII and CII, respectively) overpower the vortex-induced localization.
Simulation of Yeast Cooperation in 2D.
Wang, M; Huang, Y; Wu, Z
2016-03-01
Evolution of cooperation has been an active research area in evolutionary biology in decades. An important type of cooperation is developed from group selection, when individuals form spatial groups to prevent them from foreign invasions. In this paper, we study the evolution of cooperation in a mixed population of cooperating and cheating yeast strains in 2D with the interactions among the yeast cells restricted to their small neighborhoods. We conduct a computer simulation based on a game theoretic model and show that cooperation is increased when the interactions are spatially restricted, whether the game is of a prisoner's dilemma, snow drifting, or mutual benefit type. We study the evolution of homogeneous groups of cooperators or cheaters and describe the conditions for them to sustain or expand in an opponent population. We show that under certain spatial restrictions, cooperator groups are able to sustain and expand as group sizes become large, while cheater groups fail to expand and keep them from collapse.
Variational regularized 2-D nonnegative matrix factorization.
Gao, Bin; Woo, W L; Dlay, S S
2012-05-01
A novel approach for adaptive regularization of 2-D nonnegative matrix factorization is presented. The proposed matrix factorization is developed under the framework of maximum a posteriori probability and is adaptively fine-tuned using the variational approach. The method enables: (1) a generalized criterion for variable sparseness to be imposed onto the solution; and (2) prior information to be explicitly incorporated into the basis features. The method is computationally efficient and has been demonstrated on two applications, that is, extracting features from image and separating single channel source mixture. In addition, it is shown that the basis features of an information-bearing matrix can be extracted more efficiently using the proposed regularized priors. Experimental tests have been rigorously conducted to verify the efficacy of the proposed method.
Graphene suspensions for 2D printing
NASA Astrophysics Data System (ADS)
Soots, R. A.; Yakimchuk, E. A.; Nebogatikova, N. A.; Kotin, I. A.; Antonova, I. V.
2016-04-01
It is shown that, by processing a graphite suspension in ethanol or water by ultrasound and centrifuging, it is possible to obtain particles with thicknesses within 1-6 nm and, in the most interesting cases, 1-1.5 nm. Analogous treatment of a graphite suspension in organic solvent yields eventually thicker particles (up to 6-10 nm thick) even upon long-term treatment. Using the proposed ink based on graphene and aqueous ethanol with ethylcellulose and terpineol additives for 2D printing, thin (~5 nm thick) films with sheet resistance upon annealing ~30 MΩ/□ were obtained. With the ink based on aqueous graphene suspension, the sheet resistance was ~5-12 kΩ/□ for 6- to 15-nm-thick layers with a carrier mobility of ~30-50 cm2/(V s).