Hamiltonian monodromy as lattice defect
Zhilinskii, B.
2003-01-01
The analogy between monodromy in dynamical (Hamiltonian) systems and defects in crystal lattices is used in order to formulate some general conjectures about possible types of qualitative features of quantum systems which can be interpreted as a manifestation of classical monodromy in quantum finite particle (molecular) problems.
Hamiltonian tomography of photonic lattices
Ma, Ruichao; Owens, Clai; LaChapelle, Aman; Schuster, David I.; Simon, Jonathan
2017-06-01
In this paper we introduce an approach to Hamiltonian tomography of noninteracting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites α and β may be obtained directly from Sα β(ω ) , the (suitably normalized) two-port measurement between sites α and β at frequency ω . This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band projectors in finite, disordered systems with good band flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in between.
Obtaining breathers in nonlinear Hamiltonian lattices
Flach, S
1995-01-01
Abstract We present a numerical method for obtaining high-accuracy numerical solutions of spatially localized time-periodic excitations on a nonlinear Hamiltonian lattice. We compare these results with analytical considerations of the spatial decay. We show that nonlinear contributions have to be considered, and obtain very good agreement between the latter and the numerical results. We discuss further applications of the method and results.
Noncommutative physics on Lie algebras, Z_2^n lattices and Clifford algebras
Majid, S
2004-01-01
We survey noncommutative spacetimes with coordinates being enveloping algebras of Lie algebras. We also explain how to do differential geometry on noncommutative spaces that are obtained from commutative ones via a Moyal-product type cocycle twist, such as the noncommutative torus, $\\theta$-spaces and Clifford algebras. The latter are noncommutative deformations of the finite lattice $(Z_2)^n$ and we compute their noncommutative de Rham cohomology and moduli of solutions of Maxwell's equations. We exactly quantize noncommutative U(1)-Yang-Mills theory on $Z_2\\times Z_2$ in a path integral approach.
Digital Quantum Simulation of Z2 Lattice Gauge Theories with Dynamical Fermionic Matter
Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio
2017-02-01
We propose a scheme for digital quantum simulation of lattice gauge theories with dynamical fermions. Using a layered optical lattice with ancilla atoms that can move and interact with the other atoms (simulating the physical degrees of freedom), we obtain a stroboscopic dynamics which yields the four-body plaquette interactions, arising in models with (2 +1 ) and higher dimensions, without the use of perturbation theory. As an example we show how to simulate a Z2 model in (2 +1 ) dimensions.
Z2 gauge theory for valence bond solids on the kagome lattice
Hwang, Kyusung; Huh, Yejin; Kim, Yong Baek
We present an effective Z2 gauge theory that captures various competing phases in spin-1/2 kagome lattice antiferromagnets: the topological Z2 spin liquid (SL) phase, and the 12-site and 36- site valence bond solid (VBS) phases. Our effective theory is a generalization of the recent Z2 gauge theory proposed for SL phases by Wan and Tchernyshyov. In particular, we investigate possible VBS phases that arise from vison condensations in the SL. In addition to the 12-site and 36-site VBS phases, there exists 6-site VBS that is closely related to the symmetry-breaking valence bond modulation patterns observed in the recent density matrix renormalization group simulations. We find that our results have remarkable consistency with a previous study using a different Z2 gauge theory. Motivated by the lattice geometry in the recently reported vanadium oxyfluoride kagome antiferromagnet, our gauge theory is extended to incorporate lowered symmetry by inequivalent up- and down-triangles. We investigate effects of this anisotropy on the 12-site, 36-site, and 6-site VBS phases. Particularly, interesting dimer melting effects are found in the 36-site VBS. We discuss the implications of our findings and also compare the results with a different type of Z2 gauge theory used in previous studies.
Digital quantum simulation of $\\mathbb{Z}_2$ lattice gauge theories with dynamical fermionic matter
Zohar, Erez; Reznik, Benni; Cirac, J Ignacio
2016-01-01
We propose a scheme for digital quantum simulation of lattice gauge theories with dynamical fermions. Using a layered optical lattice with ancilla atoms that can move and interact with the other atoms (simulating the physical degrees of freedom), we obtain a stroboscopic dynamics which yields the four-body plaquette interactions, arising in models with $2+1$ and higher dimensions, without the use of perturbation theory. As an example we show how to simulate a $\\mathbb{Z}_2$ model in $2+1$ dimensions.
Chirality and Z2 vortices in a Heisenberg spin model on the kagome lattice
Domenge, J.-C.; Lhuillier, C.; Messio, L.; Pierre, L.; Viot, P.
2008-05-01
The phase diagram of the classical J1-J2 model on the kagome lattice is investigated by using extensive Monte Carlo simulations. In a realistic range of parameters, this model has a low-temperature chiral-ordered phase without long-range spin order. We show that the critical transition marking the destruction of the chiral order is preempted by the first-order proliferation of Z2 point defects. The core energy of these vortices appears to vanish when approaching the T=0 phase boundary, where both Z2 defects and gapless magnons contribute to disordering the system at very low temperatures. This situation might be typical of a large class of frustrated magnets. Possible relevance for real materials is also discussed.
Monte Carlo methods in continuous time for lattice Hamiltonians
Huffman, Emilie
2016-01-01
We solve a variety of sign problems for models in lattice field theory using the Hamiltonian formulation, including Yukawa models and simple lattice gauge theories. The solutions emerge naturally in continuous time and use the dual representation for the bosonic fields. These solutions allow us to construct quantum Monte Carlo methods for these problems. The methods could provide an alternative approach to understanding non-perturbative dynamics of some lattice field theories.
Lattice effects on Laughlin wave functions and parent Hamiltonians
Glasser, Ivan; Cirac, J. Ignacio; Sierra, Germán; Nielsen, Anne E. B.
2016-12-01
We investigate lattice effects on wave functions that are lattice analogs of bosonic and fermionic Laughlin wave functions with number of particles per flux ν =1 /q in the Landau levels. These wave functions are defined analytically on lattices with μ particles per lattice site, where μ may be different than ν . We give numerical evidence that these states have the same topological properties as the corresponding continuum Laughlin states for different values of q and for different fillings μ . These states define, in particular, particle-hole symmetric lattice fractional quantum Hall states when the lattice is half filled. On the square lattice it is observed that for q ≤4 this particle-hole symmetric state displays the topological properties of the continuum Laughlin state at filling fraction ν =1 /q , while for larger q there is a transition towards long-range ordered antiferromagnets. This effect does not persist if the lattice is deformed from a square to a triangular lattice, or on the kagome lattice, in which case the topological properties of the state are recovered. We then show that changing the number of particles while keeping the expression of these wave functions identical gives rise to edge states that have the same correlations in the bulk as the reference lattice Laughlin states but a different density at the edge. We derive an exact parent Hamiltonian for which all these edge states are ground states with different number of particles. In addition this Hamiltonian admits the reference lattice Laughlin state as its unique ground state of filling factor 1 /q . Parent Hamiltonians are also derived for the lattice Laughlin states at other fillings of the lattice, when μ ≤1 /q or μ ≥1 -1 /q and when q =4 also at half filling.
Unification of bosonic and fermionic Z2 spin liquids on a rectangular lattice
Chatterjee, Shubhayu; Steinberg, Julia; Sachdev, Subir
Recent theories have postulated the presence of a fractionalized Fermi liquid (FL*) in the pseudogap metal phase of cuprates. The FL* phase can be described as a spin liquid co-existing with fermionic charge carrying quasiparticles. Underdoped cuprates also show a variety of competing orders, including nematic order which reduce the C4 symmetry of the square lattice to C2. Motivated by this, we classify mean-field bosonic spin liquids on a rectangular lattice using projective symmetry groups (PSG), and find equivalent descriptions in terms of fermionic partons. In particular, we find a fermionic spin liquid ansatz corresponding to a bosonic Z2 spin liquid with favorable mean field energy. The fermionic ansatz might be useful to investigate the transition from a FL* to a fermi liquid.
Rychkov, Slava; Vitale, Lorenzo G.
2016-03-01
The Fock-space Hamiltonian truncation method is developed further, paying particular attention to the treatment of the scalar field zero mode. This is applied to the two-dimensional ϕ4 theory in the phase where the Z2 -symmetry is spontaneously broken, complementing our earlier study of the Z2 -invariant phase and of the critical point. We also check numerically the weak/strong duality of this theory discussed long ago by Chang.
Geometry and dynamics in Hamiltonian lattices
Rink, B.W.
2003-01-01
E. Fermi, J. Pasta and S. Ulam introduced the Fermi-Pasta-Ulam lattice in the 1950s as a classical mechanical model for a mono-atomic crystal or a one-dimensional continuum. The model consisted of a discrete number of equal point masses that interact with their nearest neighbours only. On the basis
Yu, Pei; Han, Maoan
2013-04-01
In this paper, we show that a Z2-equivariant 3rd-order Hamiltonian planar vector fields with 3rd-order symmetric perturbations can have at least 10 limit cycles. The method combines the general perturbation to the vector field and the perturbation to the Hamiltonian function. The Melnikov function is evaluated near the center of vector field, as well as near homoclinic and heteroclinic orbits.
Localized Basis for Effective Lattice Hamiltonians Lattice Wannier Functions
Rabe, K M
1994-01-01
A systematic method is presented for constructing effective Hamiltonians for general phonon-related structural transitions. The key feature is the application of group theoretical methods to identify the subspace in which the effective Hamiltonian acts and construct for it localized basis vectors, which are the analogue of electronic Wannier functions. The results of the symmetry analysis for the perovskite, rocksalt, fluorite and A15 structures and the forms of effective Hamiltonians for the ferroelectric transition in $PbTiO_3$ and $BaTiO_3$, the oxygen-octahedron rotation transition in $SrTiO_3$, the Jahn-Teller instability in $La_{1-x}(Ca,Sr,Ba)_xMnO_3$ and the antiferroelectric transition in $PbZrO_3$ are discussed. For the oxygen- octahedron rotation transition in $SrTiO_3$, this method provides an alternative to the rotational variable approach which is well behaved throughout the Brillouin zone. The parameters appearing in the Wannier basis vectors and in the effective Hamiltonian, given by the corres...
On the existence of localized excitations in nonlinear hamiltonian lattices
Flach, S
1994-01-01
We consider time-periodic nonlinear localized excitations (NLEs) on one-dimensional translationally invariant Hamiltonian lattices with arbitrary finite interaction range and arbitrary finite number of degrees of freedom per unit cell. We analyse a mapping of the Fourier coefficients of the NLE solution. NLEs correspond to homoclinic points in the phase space of this map. Using dimensionality properties of separatrix manifolds of the mapping we show the persistence of NLE solutions under perturbations of the system, provided NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam chains we rigorously prove the existence of NLE solutions.
A Difference Hamiltonian Operator and a Hierarchy of Generalized Toda Lattice Equations
XU Xi-Xiang; YANG Hong-Xiang; DING Hai-Yong
2005-01-01
A difference Ha-miltonian operator with three arbitrary constants is presented. When the arbitrary constants -in the Hamiltonian operator are suitably chosen, a pair of Hamiltonian operators are given. The resulting Hamiltonian pair yields a difference hereditary operator. Using Magri scheme of bi-Hamiltonian formulation, a hierarchy of the generalized Toda lattice equations is constructed. Finally, the discrete zero curvature representation is given for the resulting hierarchy.
A Difference Hamiltonian Operator and a Hierarchy of Generalized Toda Lattice Equations
XUXi-Xiang; YANGHong-Xiang; DINGHai-Yong
2005-01-01
A difference Hamiltonian operator with three arbitrary constants is presented. When the arbitrary constants in the Hamiltonian operator are suitably chosen， a pair of Hamiltonian operators are given. The resulting Hamiltonian pair yields a difference hereditary operator. Using Magri scheme of bi-Hamiltonian formulations a hierarchy of the generalized Toda lattice equations is constructed. Finally, the discrete zero curvature representation is given for the resulting hierarchy.
Transverse Lattice Approach to Light-Front Hamiltonian QCD
Dalley, S
1999-01-01
We describe a non-perturbative procedure for solving from first principles the light-front Hamiltonian problem of SU(N) pure gauge theory in D spacetime dimensions (D>2), based on enforcing Lorentz covariance of observables. A transverse lattice regulator and colour-dielectric link fields are employed, together with an associated effective potential. We argue that the light-front vacuum is necessarily trivial for large enough lattice spacing, and clarify why this leads to an Eguchi-Kawai dimensional reduction of observables to 1+1-dimensions in the infinite N limit. The procedure is then tested by explicit calculations for 2+1-dimensional SU(infinity) gauge theory, within a first approximation to the lattice effective potential. We identify a scaling trajectory which produces Lorentz covariant behaviour for the lightest glueballs. The predicted masses, in units of the measured string tension, are in agreement with recent results from conventional Euclidean lattice simulations. In addition, we obtain the poten...
From lattice Hamiltonians to tunable band structures by lithographic design
Tadjine, Athmane; Allan, Guy; Delerue, Christophe
2016-08-01
Recently, new materials exhibiting exotic band structures characterized by Dirac cones, nontrivial flat bands, and band crossing points have been proposed on the basis of effective two-dimensional lattice Hamiltonians. Here, we show using atomistic tight-binding calculations that these theoretical predictions could be experimentally realized in the conduction band of superlattices nanolithographed in III-V and II-VI semiconductor ultrathin films. The lithographed patterns consist of periodic lattices of etched cylindrical holes that form potential barriers for the electrons in the quantum well. In the case of honeycomb lattices, the conduction minibands of the resulting artificial graphene host several Dirac cones and nontrivial flat bands. Similar features, but organized in different ways, in energy or in k -space are found in kagome, distorted honeycomb, and Lieb superlattices. Dirac cones extending over tens of meV could be obtained in superlattices with reasonable sizes of the lithographic patterns, for instance in InAs/AlSb heterostructures. Bilayer artificial graphene could be also realized by lithography of a double quantum-well heterostructure. These new materials should be interesting for the experimental exploration of Dirac-based quantum systems, for both fundamental and applied physics.
Ground states of fermionic lattice Hamiltonians with permutation symmetry
Kraus, Christina V.; Lewenstein, Maciej; Cirac, J. Ignacio
2013-08-01
We study the ground states of lattice Hamiltonians that are invariant under permutations, in the limit where the number of lattice sites N→∞. For spin systems, these are product states, a fact that follows directly from the quantum de Finetti theorem. For fermionic systems, however, the problem is very different, since mode operators acting on different sites do not commute, but anticommute. We construct a family of fermionic states, F, from which such ground states can be easily computed. They are characterized by few parameters whose number only depends on M, the number of modes per lattice site. We also give an explicit construction for M=1,2. In the first case, F is contained in the set of Gaussian states, whereas in the second it is not. Inspired by that construction, we build a set of fermionic variational wave functions, and apply it to the Fermi-Hubbard model in two spatial dimensions, obtaining results that go beyond the generalized Hartree-Fock theory.
Z2 topological liquid of hard-core bosons on a kagome lattice at 1 /3 filling
Roychowdhury, Krishanu; Bhattacharjee, Subhro; Pollmann, Frank
2015-08-01
We consider hard-core bosons on the kagome lattice in the presence of short-range repulsive interactions and focus particularly on the filling factor 1 /3 . In the strongly interacting limit, the low-energy excitations can be described by the quantum fully packed loop coverings on the triangular lattice. Using a combination of tensor product state based methods and exact diagonalization techniques, we show that the system has an extended Z2 topological liquid phase as well as a latti ce nematic phase. The latter breaks lattice rotational symmetry. By tuning appropriate parameters in the model, we study the quantum phase transition between the topological and the symmetry broken phases. We construct the critical theory for this transition using a mapping to an Ising gauge theory that predicts the transition to belong to the O (3 ) universality class.
Matrix product states for Hamiltonian lattice gauge theories
Buyens, Boye; Haegeman, Jutho; Verstraete, Frank
2014-01-01
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional systems. In [1] we considered the MPS formalism for the simulation of the Hamiltonian lattice gauge formulation of 1+1 dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model. We deduced the ground state and lowest lying excitations. Furthermore, we performed a full quantum real-time simulation for a quench with a uniform background electric field. In this proceeding we continue our work on the Schwinger model. We demonstrate the advantage of working with gauge invariant MPS by comparing with MPS simulations on the full Hilbert space, that includes numerous non-physical gauge variant states. Furthermore, we compute the chiral condensate and recover the predicted UV-divergent behavior.
Lie algebraic similarity transformed Hamiltonians for lattice model systems
Wahlen-Strothman, Jacob M.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E.
2015-01-01
We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site Hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor ni ↑ni ↓ , and two-site products of density (ni ↑+ni ↓) and spin (ni ↑-ni ↓) operators. The resulting non-Hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the one- and two-dimensional repulsive Hubbard model where it yields accurate results for small and medium sized interaction strengths.
Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices.
Miyake, Hirokazu; Siviloglou, Georgios A; Kennedy, Colin J; Burton, William Cody; Ketterle, Wolfgang
2013-11-01
We experimentally implement the Harper Hamiltonian for neutral particles in optical lattices using laser-assisted tunneling and a potential energy gradient provided by gravity or magnetic field gradients. This Hamiltonian describes the motion of charged particles in strong magnetic fields. Laser-assisted tunneling processes are characterized by studying the expansion of the atoms in the lattice. The band structure of this Hamiltonian should display Hofstadter's butterfly. For fermions, this scheme should realize the quantum Hall effect and chiral edge states.
Hamiltonian Effective Field Theory Study of the N^{*}(1535) Resonance in Lattice QCD.
Liu, Zhan-Wei; Kamleh, Waseem; Leinweber, Derek B; Stokes, Finn M; Thomas, Anthony W; Wu, Jia-Jun
2016-02-26
Drawing on experimental data for baryon resonances, Hamiltonian effective field theory (HEFT) is used to predict the positions of the finite-volume energy levels to be observed in lattice QCD simulations of the lowest-lying J^{P}=1/2^{-} nucleon excitation. In the initial analysis, the phenomenological parameters of the Hamiltonian model are constrained by experiment and the finite-volume eigenstate energies are a prediction of the model. The agreement between HEFT predictions and lattice QCD results obtained on volumes with spatial lengths of 2 and 3 fm is excellent. These lattice results also admit a more conventional analysis where the low-energy coefficients are constrained by lattice QCD results, enabling a determination of resonance properties from lattice QCD itself. Finally, the role and importance of various components of the Hamiltonian model are examined.
Finite-volume Hamiltonian method for $\\pi\\pi$ scattering in lattice QCD
Wu, Jia-Jun; Leinweber, Derek B; Thomas, A W; Young, Ross D
2015-01-01
Within a formulation of $\\pi\\pi$ scattering, we investigate the use of the finite-volume Hamiltonian approach to resolving scattering observables from lattice QCD spectra. We consider spectra in the centre-of-mass and moving frames for both S- and P-wave cases. Furthermore, we investigate the multi-channel case. Here we study the use of the Hamiltonian framework as a parametrization that can be fit directly to lattice spectra. Through this method, the hadron properties, such as mass, width and coupling, can be directly extracted from the lattice spectra.
Finite-volume Hamiltonian method for coupled channel interactions in lattice QCD
Wu, Jia-Jun; Thomas, A W; Young, R D
2014-01-01
Within a multi-channel formulation of $\\pi\\pi$ scattering, we investigate the use of the finite-volume Hamiltonian approach to relate lattice QCD spectra to scattering observables. The equivalence of the Hamiltonian approach and the coupled-channel extension of the well-known L\\"uscher formalism is established. Unlike the single channel system, the spectra at a single lattice volume in the coupled channel case do not uniquely determine the scattering parameters. We investigate the use of the Hamiltonian framework as a method to directly fit the lattice spectra and thereby extract the scattering phase shifts and inelasticities. We find that with a modest amount of lattice data, the scattering parameters can be reproduced rather well, with only a minor degree of model dependence.
Quantum search on the two-dimensional lattice using the staggered model with Hamiltonians
Portugal, R.; Fernandes, T. D.
2017-04-01
Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk models to provide efficient algorithms from the theoretical side and means to implement quantum walks in laboratories from the practical side. In this paper, we rigorously prove that the recent-proposed staggered quantum walk model provides an efficient quantum search on the two-dimensional lattice, if the reflection operators associated with the graph tessellations are used as Hamiltonians, which is an important theoretical result for validating the staggered model with Hamiltonians. Numerical results show that on the two-dimensional lattice staggered models without Hamiltonians are not as efficient as the one described in this paper and are, in fact, as slow as classical random-walk-based algorithms.
Dubček, Tena; Lelas, Karlo; Jukić, Dario; Pezer, Robert; Soljačić, Marin; Buljan, Hrvoje
2015-12-01
We propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one- and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k-space. We compare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper-Hofstadter Hamiltonian, and obtain excellent agreement.
周宏宪; 张燕
2011-01-01
This paper is concerned with the number and distributions of limit cycles of a cubic Z2-symmetry Hamiltonian system under quintic perturbation. By using qualitative analysis of differential equation, bifurcation theory of dynamical systems and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C91 (∪) [C11 + 2(C23 (∪) 2C21)].
Cold atoms in optical lattices a Hamiltonian ratchet
Monteiro, T S; Hutchings, N A C; Isherwood, M R
2002-01-01
We investigate a new type of quantum ratchet which may be realised by cold atoms in a double-well optical lattice which is pulsed with unequal periods. The classical dynamics is chaotic and we find the classical diffusion rate $D$ is asymmetric in momentum up to a finite time $t_r$. The quantum behaviour produces a corresponding asymmetry in the momentum distribution which is 'frozen-in' by Dynamical Localisation provided the break-time $t^* > t_r$. We conclude that the cold atom ratchets require $Db/ \\hbar \\sim 1$ where b is a small deviation from period-one pulses.
Compression of Hamiltonian matrix: Application to spin-1/2 Heisenberg square lattice
Seongsoo Choi
2016-09-01
Full Text Available We introduce a simple algorithm providing a compressed representation (∈ℝNorbits×Norbits×ℕNorbits of an irreducible Hamiltonian matrix (number of magnons M constrained, dimension: Nspins!M!(Nspins−M!>Norbits of the spin-1/2 Heisenberg antiferromagnet on the L×L non-periodic lattice, not looking for a good basis. As L increases, the ratio of the matrix dimension to Norbits converges to 8 (order of the symmetry group of square for the exact ground state computation. The sparsity of the Hamiltonian is retained in the compressed representation. Thus, the computational time and memory consumptions are reduced in proportion to the ratio.
Hamiltonian dynamics of the two-dimensional lattice {phi}{sup 4} model
Caiani, Lando [Scuola Internazionale Superiore di Studi Avanzati (SISSA/ISAS), Trieste (Italy); Casetti, Lapo [Istituto Nazionale di Fisica della Materia (INFM), Unita di Ricerca del Politecnico di Torino, Dipartimento di Fisica, Politecnico di Torino, Turin (Italy); Pettini, Marco [Osservatorio Astrofisico di Arcetri, Florence (Italy)
1998-04-17
The Hamiltonian dynamics of the classical {phi}{sup 4} model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the presence of the continuous phase transition at a finite energy density and are consistent both qualitatively and quantitatively with the predictions of equilibrium statistical mechanics. The Hamiltonian microscopic dynamics also exhibits critical slowing down close to the transition. Moreover, the relationship between chaos and the phase transition is considered, and interpreted in the light of a geometrization of dynamics. (author)
Hamiltonian chaos with a cold atom in an optical lattice
Prants, S V
2012-01-01
We consider a basic model of the lossless interaction between a moving two-level atom and a standing-wave single-mode laser field. Classical treatment of the translational atomic motion provides the semiclassical Hamilton-Schrodinger equations which are a 5D nonlinear dynamical system with two integrals of motion. The atomic dynamics can be regular or chaotic in dependence on values of the control parameters, the atom-field detuning and recoil frequency. We develop a semiclassical theory of the chaotic atomic transport in terms of a random walk of the atomic electric dipole moment $u$. Based on a jump-like behavior of this variable for atoms crossing nodes of the standing wave, we construct a stochastic map that specifies the center-of-mass motion. We find the relations between the detuning, recoil frequency and the atomic energy, under which atoms may move in a optical lattice in a chaotic way. We obtain the analytical conditions under which deterministic atomic transport has fractal properties and explain a...
Covariant hydrodynamic Lyapunov modes and strong stochasticity threshold in Hamiltonian lattices.
Romero-Bastida, M; Pazó, Diego; López, Juan M
2012-02-01
We scrutinize the reliability of covariant and Gram-Schmidt Lyapunov vectors for capturing hydrodynamic Lyapunov modes (HLMs) in one-dimensional Hamiltonian lattices. We show that, in contrast with previous claims, HLMs do exist for any energy density, so that strong chaos is not essential for the appearance of genuine (covariant) HLMs. In contrast, Gram-Schmidt Lyapunov vectors lead to misleading results concerning the existence of HLMs in the case of weak chaos.
Chandrashekar, C M
2013-10-03
From the unitary operator used for implementing two-state discrete-time quantum walk on one-, two- and three- dimensional lattice we obtain a two-component Dirac-like Hamiltonian. In particular, using different pairs of Pauli basis as position translation states we obtain three different form of Hamiltonians for evolution on one-dimensional lattice. We extend this to two- and three-dimensional lattices using different Pauli basis states as position translation states for each dimension and show that the external coin operation, which is necessary for one-dimensional walk is not a necessary requirement for a walk on higher dimensions but can serve as an additional resource to control the dynamics. The two-component Hamiltonian we present here for quantum walk on different lattices can serve as a general framework to simulate, control, and study the dynamics of quantum systems governed by Dirac-like Hamiltonian.
Realization of the Harper Hamiltonian with Artificial Gauge Fields in Optical Lattices
Miyake, Hirokazu; Siviloglou, Georgios; Kennedy, Colin; Burton, William Cody; Ketterle, Wolfgang
2014-03-01
Systems of charged particles in magnetic fields have led to many discoveries in science-such as the integer and fractional quantum Hall effects-and have become important paradigms of quantum many-body physics. We have proposed and implemented a scheme which realizes the Harper Hamiltonian, a lattice model for charged particles in magnetic fields, whose energy spectrum is the fractal Hofstadter butterfly. We experimentally realize this Hamiltonian for ultracold, charge neutral bosonic particles of 87Rb in a two-dimensional optical lattice by creating an artificial gauge field using laser-assisted tunneling and a potential energy gradient provided by gravity. Laser-assisted tunneling processes are characterized by studying the expansion of the atoms in the lattice. Furthermore, this scheme can be extended to realize spin-orbit coupling and the spin Hall effect for neutral atoms in optical lattices by modifying the motion of atoms in a spin-dependent way by laser recoil and Zeeman shifts created with a magnetic field gradient. Major advantages of our scheme are that it does not rely on near-resonant laser light to couple different spin states and should work even for fermionic particles. Our work is a step towards studying novel topological phenomena with ultracold atoms. Currently at the RAND Corporation.
A Few Discrete Lattice Systems and Their Hamiltonian Structures, Conservation Laws
Guo, Xiu-Rong; Zhang, Yu-Feng; Zhang, Xiang-Zhi; Yue, Rong
2017-04-01
With the help of three shift operators and r-matrix theory, a few discrete lattice systems are obtained which can be reduced to the well-known Toda lattice equation with a constraint whose Hamiltonian structures are generated by Poisson tensors of some induced Lie-Poisson bracket. The recursion operators of these lattice systems are constructed starting from Lax representations. Finally, reducing the given shift operators to get a simpler one and its expanding shift operators, we produce a lattice system with three vector fields whose recursion operator is given. Furthermore, we reduce the lattice system with three vector fields to get a lattice system whose Lax pair and conservation laws are obtained, respectively. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Innovation Team of Jiangsu Province Hosted by China University of Mining and Technology (2014), the the Key Discipline Construction by China University of Mining and Technology under Grant No. XZD201602, the Shandong Provincial Natural Science Foundation, China under Grant Nos. ZR2016AM31, ZR2016AQ19, ZR2015EM042, the Development of Science and Technology Plan Projects of TaiAn City under Grant No. 2015NS1048, National Social Science Foundation of China under Grant No. 13BJY026, and A Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J14LI58
Hamiltonian Study of Improved $U(1)_{2+1}$ Lattice Gauge Theory
Loan, M; Hamer, C; Loan, Mushtaq; Byrnes, Tim; Hamer, Chris
2003-01-01
Monte Carlo results are presented, in the Hamiltonian limit, for the string tension and antisymmetric mass gap for U(1) lattice gauge theory in (2+1) dimensions, using mean-field improved anisotropic Wilson action, are presented. Evidence of scaling in the string tension and antisymmetric mass gap is observed in the weak coupling regime of the theory. The results are compared to previous simulation data using the standard Wilson action and we find that a more accurate determination of the string tension and scalar glueball masses has been achieved. The scaling behaviour observed is in good agreement with the results from other numerical calculations. Finally comparisons are made with previous estimates obtained in the Hamiltonian limit by various other studies.
Compression of Hamiltonian matrix: Application to spin-1/2 Heisenberg square lattice
Choi, Seongsoo; Kim, Woohyun; Kim, Jongho
2016-09-01
We introduce a simple algorithm providing a compressed representation (∈ℝNorbits×Norbits×ℕNorbits ) of an irreducible Hamiltonian matrix (number of magnons M constrained, dimension: N/spins!M ! (N spins-M ) ! >Norbits ) of the spin-1/2 Heisenberg antiferromagnet on the L ×L non-periodic lattice, not looking for a good basis. As L increases, the ratio of the matrix dimension to Norbits converges to 8 (order of the symmetry group of square) for the exact ground state computation. The sparsity of the Hamiltonian is retained in the compressed representation. Thus, the computational time and memory consumptions are reduced in proportion to the ratio.
Mehta, Dhagash; Kastner, Michael
2011-06-01
We study the stationary points of what is known as the lattice Landau gauge fixing functional in one-dimensional compact U(1) lattice gauge theory, or as the Hamiltonian of the one-dimensional random phase XY model in statistical physics. An analytic solution of all stationary points is derived for lattices with an odd number of lattice sites and periodic boundary conditions. In the context of lattice gauge theory, these stationary points and their indices are used to compute the gauge fixing partition function, making reference in particular to the Neuberger problem. Interpreted as stationary points of the one-dimensional XY Hamiltonian, the solutions and their Hessian determinants allow us to evaluate a criterion which makes predictions on the existence of phase transitions and the corresponding critical energies in the thermodynamic limit.
De Lyra, J L; Foong, S K; Gallivan, T E; Harrington, R; Kapulkin, A; Myers, E; Polchinski, Joseph; Lyra, Jorge de; Witt, Bryce De; Foong, See Kit; Gallivan, Timothy; Harrington, Rob; Kapulkin, Arie; Myers, Eric; Polchinski, Joeseph
1992-01-01
A lattice formulation of the $O(1,2)/O(2)\\times Z_2$ sigma model is developed, based on the continuum theory presented in the preceding paper. Special attention is given to choosing a lattice action (the ``geodesic'' action) that is appropriate for fields having noncompact curved configuration spaces. A consistent continuum limit of the model exists only if the renormalized scale constant $\\beta_R$ vanishes for some value of the bare scale constant~$\\beta$. The geodesic action has a special form that allows direct access to the small-$\\beta$ limit. In this limit half of the degrees of freedom can be integrated out exactly. The remaining degrees of freedom are those of a compact model having a $\\beta$-independent action which is noteworthy in being unbounded from below yet yielding integrable averages. Both the exact action and the $\\beta$-independent action are used to obtain $\\beta_R$ from Monte Carlo computations of field-field averages (2-point functions) and current-current averages. Many consistency cros...
Berg, J. S. [Brookhaven National Lab. (BNL), Upton, NY (United States). Collider-Accelerator Dept.
2015-05-03
I describe a generic formulation for the evolution of emittances and lattice functions under arbitrary, possibly non-Hamiltonian, linear equations of motion. The average effect of stochastic processes, which would include ionization interactions and synchrotron radiation, is also included. I first compute the evolution of the covariance matrix, then the evolution of emittances and lattice functions from that. I examine the particular case of a cylindrically symmetric system, which is of particular interest for ionization cooling.
Reptation quantum Monte Carlo algorithm for lattice Hamiltonians with a directed-update scheme.
Carleo, Giuseppe; Becca, Federico; Moroni, Saverio; Baroni, Stefano
2010-10-01
We provide an extension to lattice systems of the reptation quantum Monte Carlo algorithm, originally devised for continuous Hamiltonians. For systems affected by the sign problem, a method to systematically improve upon the so-called fixed-node approximation is also proposed. The generality of the method, which also takes advantage of a canonical worm algorithm scheme to measure off-diagonal observables, makes it applicable to a vast variety of quantum systems and eases the study of their ground-state and excited-state properties. As a case study, we investigate the quantum dynamics of the one-dimensional Heisenberg model and we provide accurate estimates of the ground-state energy of the two-dimensional fermionic Hubbard model.
Stability and Clustering for Lattice Many-Body Quantum Hamiltonians with Multiparticle Potentials
Faria da Veiga, Paulo A.; O'Carroll, Michael
2015-11-01
We analyze a quantum system of N identical spinless particles of mass m, in the lattice Z^d, given by a Hamiltonian H_N=T_N+V_N, with kinetic energy T_N≥ 0 and potential V_N=V_{N,2}+V_{N,3} composed of attractive pair and repulsive 3-body contact-potentials. This Hamiltonian is motivated by the desire to understand the stability of quantum field theories, with massive single particles and bound states in the energy-momentum spectrum, in terms of an approximate Hamiltonian for their N-particle sector. We determine the role of the potentials V_{N,2} and V_{N,3} on the physical stability of the system, such as to avoid a collapse of the N particles. Mathematically speaking, stability is associated with an N-linear lower bound for the infimum of the H_N spectrum, \\underline{σ }(H_N)≥ -cN, for c>0 independent of N. For V_{N,3}=0, H_N is unstable, and the system collapses. If V_{N,3}not =0, H_N is stable and, for strong enough repulsion, we obtain \\underline{σ }(H_N)≥ -c' N, where c'N is the energy of ( N/2) isolated bound pairs. This result is physically expected. A much less trivial result is that, as N varies, we show [ \\underline{σ }(V_N)/N ] has qualitatively the same behavior as the well-known curve for minus the nuclear binding energy per nucleon. Moreover, it turns out that there exists a saturation value N_s of N at and above which the system presents a clustering: the N particles distributed in two fragments and, besides lattice translations of particle positions, there is an energy degeneracy of all two fragments with particle numbers N_r and N_s-N_r, with N_r=1,ldots ,N_s-1.
Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
Anna Hackenbroich
2017-03-01
Full Text Available We introduce a family of many-body quantum states that describe interacting spin one-half hard-core particles with bosonic or fermionic statistics on arbitrary one- and two-dimensional lattices. The wave functions at lattice filling fraction ν=2/(2m+1 are derived from deformations of the Wess–Zumino–Witten model su(31 and are related to the (m+1,m+1,m Halperin fractional quantum Hall states. We derive long-range SU(2 invariant parent Hamiltonians for these states which in two dimensions are chiral t–J–V models with additional three-body interaction terms. In one dimension we obtain a generalisation to open chains of a periodic inverse-square t–J–V model proposed in [25]. We observe that the gapless low-energy spectrum of this model and its open-boundary generalisation can be described by rapidity sets with the same generalised Pauli exclusion principle. A two-component compactified free boson conformal field theory is identified as the low-energy effective theory for the periodic inverse-square t–J–V model.
Z2 antiferromagnetic topological insulators with broken C4 symmetry
Bègue, Frédéric; Pujol, Pierre; Ramazashvili, Revaz
2017-04-01
A two-dimensional topological insulator may arise in a centrosymmetric commensurate Néel antiferromagnet (AF), where staggered magnetization breaks both the elementary translation and time reversal, but retains their product as a symmetry. Fang et al. [6] proposed an expression for a Z2 topological invariant to characterize such systems. Here, we show that this expression does not allow to detect all the existing phases if a certain lattice symmetry is lacking. We implement numerical techniques to diagnose topological phases of a toy Hamiltonian, and verify our results by computing the Chern numbers of degenerate bands, and also by explicitly constructing the edge states, thus illustrating the efficiency of the method.
Hamiltonian effective field theory study of the $\\mathbf{N^*(1440)}$ resonance in lattice QCD
Liu, Zhan-Wei; Leinweber, Derek B; Stokes, Finn M; Thomas, Anthony W; Wu, Jia-Jun
2016-01-01
We examine the phase shifts and inelasticities associated with the $N^*(1440)$ Roper resonance and connect these infinite-volume observables to the finite-volume spectrum of lattice QCD using Hamiltonian effective field theory. We explore three hypotheses for the structure of the Roper resonance. In the first scenario, the Roper is postulated to have a triquark-like bare or core component with a mass exceeding the resonance mass. This component mixes with attractive virtual meson-baryon contributions, including the $\\pi N$, $\\pi\\Delta$, and $\\sigma N$ channels, to reproduce the observed pole position. In the second hypothesis, the Roper resonance is dynamically generated purely from the meson-baryon channels. However, given the presence of a bare state associated with the ground state nucleon, we proceed to consider a third scenario incorporating the presence of this low-lying basis state. All three hypotheses are able to describe the scattering data well. However, the first hypothesis predicts a low-lying st...
Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G.; Vainchtein, Anna; Xu, Haitao
2017-09-01
In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One is as an eigenvalue problem for a stationary solution in a cotraveling frame, while the other is as a periodic orbit modulo shifts. We connect the eigenvalues of the former with the Floquet multipliers of the latter and using this formulation derive an energy-based spectral stability criterion. It states that a sufficient (but not necessary) condition for a change in the wave stability occurs when the functional dependence of the energy (Hamiltonian) H of the model on the wave velocity c changes its monotonicity. Moreover, near the critical velocity where the change of stability occurs, we provide an explicit leading-order computation of the unstable eigenvalues, based on the second derivative of the Hamiltonian H''(c0) evaluated at the critical velocity c0. We corroborate this conclusion with a series of analytically and numerically tractable examples and discuss its parallels with a recent energy-based criterion for the stability of discrete breathers.
Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions
Lloyd, Seth; Terhal, Barbara M.
2016-02-01
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates. The construction translates into a model for universal quantum computation with time-independent two-qubit ZZ and XX+YY interactions on an (almost) planar grid. The effective Hamiltonian is arrived at by a single use of first-order perturbation theory avoiding the use of perturbation gadgets. The dynamics and spectral properties of the effective Hamiltonian can be fully determined as it corresponds to a particular realization of a mapping between a quantum circuit and a Hamiltonian called the space-time circuit-to-Hamiltonian construction. Because of the simple interactions required, and because no higher-order perturbation gadgets are employed, our construction is potentially realizable using superconducting or other solid-state qubits.
Challifour, John L.; Timko, Edward J.
2016-06-01
Using a Krein indefinite metric in Fock space, the Hamiltonian for cut-off models of canonically quantized Higgs-Yang-Mills fields interpolating between the Gupta-Bleuler-Feynman and Landau gauges is shown to be essentially maximal accretive and essentially Krein selfadjoint.
Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
Hackenbroich, Anna
2016-01-01
We introduce a family of many-body quantum states that describe interacting spin one-half hard-core particles with bosonic or fermionic statistics on arbitrary one- and two-dimensional lattices. The wave functions at lattice filling fraction $\
Lattice Hamiltonian approach to the massless Schwinger model. Precise extraction of the mass gap
Cichy, Krzysztof [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Kujawa-Cichy, Agnieszka [Poznan Univ. (Poland). Faculty of Physics; Szyniszewski, Marcin [Poznan Univ. (Poland). Faculty of Physics; Manchester Univ. (United Kingdom). NOWNano DTC
2012-12-15
We present results of applying the Hamiltonian approach to the massless Schwinger model. A finite basis is constructed using the strong coupling expansion to a very high order. Using exact diagonalization, the continuum limit can be reliably approached. This allows to reproduce the analytical results for the ground state energy, as well as the vector and scalar mass gaps to an outstanding precision better than 10{sup -6} %.
Finite Lattice Hamiltonian Computations in the P-Representation the Schwinger Model
Aroca, J M; Alvarez-Campot, G; Alvarez-Campot, Gonzalo
1999-01-01
The Schwinger model is studied in a finite lattice by means of the P-representation. The vacuum energy, mass gap and chiral condensate are evaluated showing good agreement with the expected values in the continuum limit.
Finite Lattice Hamiltonian Computations in the P-Representation: the Schwinger Model
1997-01-01
The Schwinger model is studied in a finite lattice by means of the P-representation. The vacuum energy, mass gap and chiral condensate are evaluated showing good agreement with the expected values in the continuum limit.
Kennedy, Colin; Miyake, Hiro; Burton, Cody; Chung, Woo Chang; Siviloglou, Georgios; Ketterle, Wolfgang
2014-05-01
The study of charged particles in a magnetic field has led to paradigm shifts in condensed matter physics including the discovery of topologically ordered states like the quantum Hall and fractional quantum Hall states. Quantum simulation of such systems using neutral atoms has drawn much interest recently in the atomic physics community due to the versatility and defect-free nature of such systems. We discuss our recent experimental realization of the Harper Hamiltonian and strong, uniform effective magnetic fields for neutral particles in an optical lattice. Additionally, our scheme represents a promising system to realize spin-orbit coupling and the quantum spin Hall states without flipping atomic spin states and thus without the intrinsic heating that comes with near-resonant Raman lasers. We point out that our scheme can be implemented all optically through the use of a period-tripling superlattice, offering faster switching times and more precise control than with magnetic field gradients. Finally, we show that this method is very general for engineering novel single particle spectra in an optical lattice and can be used to map out Hofstadter's butterfly.
Chakrabarti, J; Bagchi, B; Chakrabarti, Jayprokas; Basu, Asis; Bagchi, Bijon
2000-01-01
Fermions on the lattice have bosonic excitations generated from the underlying periodic background. These, the lattice bosons, arise near the empty band or when the bands are nearly full. They do not depend on the nature of the interactions and exist for any fermion-fermion coupling. We discuss these lattice boson solutions for the Dirac Hamiltonian.
Exceptional (Z/2Z) x (Z/2Z)-symmetric spaces
2008-01-01
The notion of (Z/2Z) x (Z/2Z)-symmetric spaces is a generalization of classical symmetric spaces, where the group Z/2Z is replaced by (Z/2Z) x (Z/2Z). In this article, a classification is given of the (Z/2Z) x (Z/2Z)-symmetric spaces G/K where G is an exceptional compact Lie group or Spin(8), complementing recent results of Bahturin and Goze. Our results are equivalent to a classification of (Z/2Z) x (Z/2Z)-gradings on the exceptional simple Lie algebras e6, e7, e8, f4, g2 and so(8).
Ryan, M.
1972-01-01
The study of cosmological models by means of equations of motion in Hamiltonian form is considered. Hamiltonian methods applied to gravity seem to go back to Rosenfeld (1930), who constructed a quantum-mechanical Hamiltonian for linearized general relativity theory. The first to notice that cosmologies provided a simple model in which to demonstrate features of Hamiltonian formulation was DeWitt (1967). Applications of the ADM formalism to homogeneous cosmologies are discussed together with applications of the Hamiltonian formulation, giving attention also to Bianchi-type universes. Problems involving the concept of superspace and techniques of quantization are investigated.
Z(2) gauge neural network and its phase structure
Takafuji, Yusuke; Nakano, Yuki; Matsui, Tetsuo
2012-11-01
We study general phase structures of neural-network models that have Z(2) local gauge symmetry. The Z(2) spin variable Si=±1 on the i-th site describes a neuron state as in the Hopfield model, and the Z(2) gauge variable J=±1 describes a state of the synaptic connection between j-th and i-th neurons. The gauge symmetry allows for a self-coupling energy among J’s such as JJJ, which describes reverberation of signals. Explicitly, we consider the three models; (I) an annealed model with full and partial connections of J, (II) a quenched model with full connections where J is treated as a slow quenched variable, and (III) a quenched three-dimensional lattice model with the nearest-neighbor connections. By numerical simulations, we examine their phase structures paying attention to the effect of the reverberation term, and compare them with each other and with the annealed 3D lattice model which has been studied beforehand. By noting the dependence of thermodynamic quantities upon the total number of sites and the connectivity among sites, we obtain a coherent interpretation to understand these results. Among other things, we find that the Higgs phase of the annealed model is separated into two stable spin-glass phases in the quenched models (II) and (III).
环Z2+uZ2+u2Z2上的斜循环码%Skew cyclic codes over the ring Z2 +uZ2 +u2Z2
李锦; 朱士信
2011-01-01
文章研究的是环R=Z2 +uZ2 +u2Z2上一类广义的循环码——斜循环码；首先利用环R构造了一个非交换的多项式环R[x,θ],然后讨论了R上斜循环码与Rn=R[X,θ]/(Xn-1)左理想的关系,给出了斜循环码的生成多项式,以及环R上斜循环码是可逆码的充要条件,并考虑了斜循环码的对偶码.%This paper studies a class of generalized cyclic codes over the ring R=Z2+uZ2+m2Z2, which are called skew cyclic codes. The ring R is used to construct a noncommutative skew polynomial ring R[x,θ]. Then the relation between the skew cyclic codes over the ring R and the left ideal as Rn=R [X,θ]/(Xn - 1) is studied, and the generator polynomial of the skew cyclic codes is given. The necessary and sufficient condition for a skew cyclic code to be a reversible code is introduced,and the dual codes of the skew cyclic codes are discussed.
Orsucci, Davide [Scuola Normale Superiore, I-56126 Pisa (Italy); Burgarth, Daniel [Department of Mathematics, Aberystwyth University, Aberystwyth SY23 3BZ (United Kingdom); Facchi, Paolo; Pascazio, Saverio [Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Nakazato, Hiromichi; Yuasa, Kazuya [Department of Physics, Waseda University, Tokyo 169-8555 (Japan); Giovannetti, Vittorio [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy)
2015-12-15
The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.
Bountis, Tassos
2012-01-01
This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems. The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) res...
The Radiative Z2 Breaking Twin Higgs
Yu, Jiang-Hao
2016-01-01
In twin Higgs model, the Higgs boson mass is protected by a $Z_2$ symmetry. The $Z_2$ symmetry needs to be broken either explicitly or spontaneously to obtain misalignment between electroweak and new physics vacua. We propose a novel $Z_2$ breaking mechanism, in which the $Z_2$ is spontaneously broken by radiative corrections to the Higgs potential. Two twin Higgses with different vacua are needed, and vacuum misalignment is realized by opposite but comparable contributions from gauge and Yukawa interactions to the potential. Due to fully radiative symmetry breaking, the Higgs sector is completely determined by twin Higgs vacuum, Yukawa and gauge couplings. There are eight pseudo-Goldstone bosons: the Higgs boson, inert doublet Higgs, and three twin scalars. We show the 125 GeV Higgs mass and constraints from Higgs coupling measurements could be satisfied.
Z-2 Prototype Space Suit Development
Ross, Amy; Rhodes, Richard; Graziosi, David; Jones, Bobby; Lee, Ryan; Haque, Bazle Z.; Gillespie, John W., Jr.
2014-01-01
NASA's Z-2 prototype space suit is the highest fidelity pressure garment from both hardware and systems design perspectives since the Space Shuttle Extravehicular Mobility Unit (EMU) was developed in the late 1970's. Upon completion the Z-2 will be tested in the 11 foot human-rated vacuum chamber and the Neutral Buoyancy Laboratory (NBL) at the NASA Johnson Space Center to assess the design and to determine applicability of the configuration to micro-, low- (asteroid), and planetary- (surface) gravity missions. This paper discusses the 'firsts' that the Z-2 represents. For example, the Z-2 sizes to the smallest suit scye bearing plane distance for at least the last 25 years and is being designed with the most intensive use of human models with the suit model.
Meeds, E.; Leenders, R.; Welling, M.; Meila, M.; Heskes, T.
2015-01-01
Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively lowdimensional problems. We introduce Hamiltonian ABC (HABC), a set of lik
Minimal extension of tri-bimaximal mixing and generalized Z_2 X Z_2 symmetries
Gupta, Shivani; Patel, Ketan M
2011-01-01
We discuss consequences of combining the effective $Z_2\\times Z_2$ symmetry of the tri-bimaximal neutrino mass matrix with the CP symmetry. Imposition of such generalized $Z_2\\times Z_2$ symmetries leads to predictive neutrino mass matrices determined in terms of only four parameters and leads to non-zero $\\theta_{13}$ and maximal atmospheric mixing angle and CP violating phase. It is shown that an effective generalized $Z_2\\times Z_2$ symmetry of the mass matrix can arise from the $A_4$ symmetry with specific vacuum alignment. The neutrino mass matrix in the considered model has only three real parameters and leads to determination of the absolute neutrino mass scale as a function of the reactor angle $\\theta_{13}$.
Mochon, C
2006-01-01
Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In this limit, the problem of finding the optimal query algorithm can be mapped into the problem of finding shortest paths on a manifold. The study of these shortest paths leads to lower bounds of the original unitary oracle problem. A number of example Hamiltonian oracles are studied in this paper, including oracle interrogation and the problem of computing the XOR of the hidden bits. Both of these problems are related to the study of geodesics on spheres with non-round metrics. For the case of two hidden bits a complete description of the geodesics is given. For n hidden bits a simple lower bound is proven that shows the problems require a query time proportional to n, even in the continuum limit. Finally, the problem of continuous Grover search is reexamined leading to a modest improvement to the protocol of Farhi and Gutmann.
Vilasi, Gaetano
2001-01-01
This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a m
HOMOCLINIC TWIST BIFURCATIONS WITH Z(2) SYMMETRY
ARONSON, DG; VANGILS, SA; KRUPA, M
1994-01-01
We analyze bifurcations occurring in the vicinity of a homoclinic twist point for a generic two-parameter family of Z2 equivariant ODEs in four dimensions. The results are compared with numerical results for a system of two coupled Josephson junctions with pure capacitive load.
Han, Tianheng; Chu, Shaoyan; Lee, Young S
2012-04-13
We report thermodynamic measurements of the S=1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2, a promising candidate system with a spin-liquid ground state. Using single crystal samples, the magnetic susceptibility both perpendicular and parallel to the kagome plane has been measured. A small, temperature-dependent anisotropy has been observed, where χ(z)/χ(p)>1 at high temperatures and χ(z)/χ(p)kagome Heisenberg antiferromagnet model to the experiments on ZnCu3(OH)6Cl2.
Batı, Mehmet, E-mail: mehmet.bati@erdogan.edu.tr [Department of Physics, Recep Tayyip Erdoğan University, 53100 Rize (Turkey); Ertaş, Mehmet [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)
2017-05-15
The hysteresis properties of a kinetic mixed spin (1/2, 1) Ising ferrimagnetic system on a hexagonal lattice are studied by means of the dynamic mean field theory. In the present study, the effects of the nearest-neighbor interaction, temperature, frequency of oscillating magnetic field and the exchange anisotropy on the hysteresis properties of the kinetic system are discussed in detail. A number of interesting phenomena such as the shape of hysteresis loops with one, two, three and inverted-hysteresis/proteresis (butterfly shape hysteresis) have been obtained. Finally, the obtained results are compared with some experimental and theoretical results and a qualitatively good agreement is found.
Effective Hamiltonian of strained graphene.
Linnik, T L
2012-05-23
Based on the symmetry properties of the graphene lattice, we derive the effective Hamiltonian of graphene under spatially nonuniform acoustic and optical strains. Comparison with the published results of the first-principles calculations allows us to determine the values of some Hamiltonian parameters, and suggests the validity of the derived Hamiltonian for acoustical strain up to 10%. The results are generalized for the case of graphene with broken plane reflection symmetry, which corresponds, for example, to the case of graphene placed on a substrate. Here, essential modifications to the Hamiltonian give rise, in particular, to the gap opening in the spectrum in the presence of the out-of-plane component of optical strain, which is shown to be due to the lifting of the sublattice symmetry. The developed effective Hamiltonian can be used as a convenient tool for analysis of a variety of strain-related effects, including electron-phonon interaction or pseudo-magnetic fields induced by the nonuniform strain.
Lagrangian and Hamiltonian two-scale reduction
Giannoulis, Johannes; Mielke, Alexander
2008-01-01
Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dynamics on large spatial and temporal scales. This paper concerns the question how reasonable macroscopic Lagrangian and Hamiltonian structures can by derived from the microscopic system. In the first part we develop a general approach to this problem by considering non-canonical Hamiltonian structures on the tangent bundle. This approach can be applied to all Hamiltonian lattices (or Hamiltonian PDEs) and involves three building blocks: (i) the embedding of the microscopic system, (ii) an invertible two-scale transformation that encodes the underlying scaling of space and time, (iii) an elementary model reduction that is based on a Principle of Consistent Expansions. In the second part we exemplify the reduction approach and derive various reduced PDE models for the atomic chain. The reduced equations are either related to long wave...
Magnetic structures and Z_2 vortices in a non-Abelian gauge model
Cabra, Daniel; Schaposnik, Fidel A
2015-01-01
The magnetic order of the triangular lattice with antiferromagnetic interactions is described by an SO(3) field and allows for the presence of Z2 magnetic vortices as defects. In this work we show how these Z2 vortices can be fitted into a local SU(2) gauge theory. We propose simple Ansatzes for vortex configurations and calculate their energies using well-known results of the Abelian gauge model. We comment on how Dzyaloshinskii-Moriya interactions could be derived from a non-Abelian gauge theory and speculate on their effect on non trivial configurations.
On a general Heisenberg exchange effective Hamiltonian
Blanco, J.A.; Prida Pidal, V.M. [Dept. de Fisica, Oviedo Univ. (Spain)
1995-07-01
A general Heisenberg exchange effective Hamiltonian is deduced in a straightforward way from the elemental quantum mechanical principles for the case of magnetic ions with non-orbital degeneracy in a crystalline lattice. Expressions for the high order direct exchange coupling constants or parameters are presented. The meaning of this effective Hamiltonian is important because extracting information from the Heisenberg Hamiltonian is a difficult task and is however taken as the starting point for many quite profound investigations of magnetism in solids and therefore could play an important role in an introductory course to solid state physics. (author)
Indirect quantum tomography of quadratic Hamiltonians
Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)
2011-01-15
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
Scaling theory of {{{Z}}_{2}} topological invariants
Chen, Wei; Sigrist, Manfred; Schnyder, Andreas P.
2016-09-01
For inversion-symmetric topological insulators and superconductors characterized by {{{Z}}2} topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling schemes renormalize either the phase gradient or the second derivative of the Pfaffian of the time-reversal operator, through which the renormalization group flow of the driving energy parameter can be obtained. The Pfaffian near the time-reversal invariant momentum is revealed to display a universal critical behavior for a great variety of models examined.
Forming Compact Massive Galaxies at z~2
van Dokkum, Pieter G; Franx, Marijn; Momcheva, Ivelina; Brammer, Gabriel; Schreiber, Natascha M Forster; Skelton, Rosalind E; Whitaker, Katherine E; van der Wel, Arjen; Bezanson, Rachel; Fumagalli, Mattia; Kriek, Mariska; Leja, Joel; Wuyts, Stijn
2015-01-01
In this paper we study a key phase in the formation of massive galaxies: the transition of star forming galaxies into massive (M_stars~10^11 Msun), compact (r_e~1 kpc) quiescent galaxies, which takes place from z~3 to z~1.5. We use HST grism redshifts and extensive photometry in all five 3D-HST/CANDELS fields, more than doubling the area used previously for such studies, and combine these data with Keck MOSFIRE and NIRSPEC spectroscopy. We first confirm that a population of massive, compact, star forming galaxies exists at z~2, using K-band spectroscopy of 25 of these objects at 2.0<z<2.5. They have a median NII/Halpha ratio of 0.6, are highly obscured with SFR(tot)/SFR(Halpha)~10, and have a large range of observed velocity dispersions. We infer from the kinematics and spatial distribution of Halpha that the galaxies have rotating disks of ionized gas that are a factor of ~2 more extended than the stellar distribution. By combining measurements of individual galaxies, we find that the kinematics are co...
A Hamiltonian Formulation of Topological Gravity
Waelbroeck, Henri
2009-01-01
Topological gravity is the reduction of Einstein's theory to spacetimes with vanishing curvature, but with global degrees of freedom related to the topology of the universe. We present an exact Hamiltonian lattice theory for topological gravity, which admits translations of the lattice sites as a gauge symmetry. There are additional symmetries, not present in Einstein's theory, which kill the local degrees of freedom. We show that these symmetries can be fixed by choosing a gauge where the torsion is equal to zero. In this gauge, the theory describes flat space-times. We propose two methods to advance towards the holy grail of lattice gravity: A Hamiltonian lattice theory for curved space-times, with first-class translation constraints.
Derivation of Hamiltonians for accelerators
Symon, K.R.
1997-09-12
In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.
Thick brane solitons breaking $Z_2$ symmetry
Peyravi, Marzieh; Lobo, Francisco S N
2015-01-01
New soliton solutions for thick branes in 4 + 1 dimensions are considered in this article. In particular, brane models based on the sine-Gordon (SG), $\\varphi^{4}$ and $\\varphi^{6}$ scalar fields are investigated; in some cases $Z_{2}$ symmetry is broken. Besides, these soliton solutions are responsible for supporting and stabilizing the thick branes. In these models, the origin of the symmetry breaking resides in the fact that the modified scalar field potential may have non-degenerate vacuua and these non-degenerate vacuua determine the cosmological constant on both sides of the brane. At last, in order to explore the particle motion in the neighborhood of the brane, the geodesic equations along the fifth dimension are studied.
New integrable lattice hierarchies
Pickering, Andrew [Area de Matematica Aplicada, ESCET, Universidad Rey Juan Carlos, c/ Tulipan s/n, 28933 Mostoles, Madrid (Spain); Zhu Zuonong [Departamento de Matematicas, Universidad de Salamanca, Plaza de la Merced 1, 37008 Salamanca (Spain) and Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030 (China)]. E-mail: znzhu2@yahoo.com.cn
2006-01-23
In this Letter we give a new integrable four-field lattice hierarchy, associated to a new discrete spectral problem. We obtain our hierarchy as the compatibility condition of this spectral problem and an associated equation, constructed herein, for the time-evolution of eigenfunctions. We consider reductions of our hierarchy, which also of course admit discrete zero curvature representations, in detail. We find that our hierarchy includes many well-known integrable hierarchies as special cases, including the Toda lattice hierarchy, the modified Toda lattice hierarchy, the relativistic Toda lattice hierarchy, and the Volterra lattice hierarchy. We also obtain here a new integrable two-field lattice hierarchy, to which we give the name of Suris lattice hierarchy, since the first equation of this hierarchy has previously been given by Suris. The Hamiltonian structure of the Suris lattice hierarchy is obtained by means of a trace identity formula.
Hamiltonian Algorithm Sound Synthesis
大矢, 健一
2013-01-01
Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.
Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510 (Mexico)
2017-01-15
In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.
Excitation Potentials and Shell Corrections for the Elements Z2=20 to Z2=30
Andersen, H.H.; Sørensen, H.; Vadja, P.
1969-01-01
Excitation potentials and shell corrections for the elements Z 2=20 to Z2=30 are evaluated from experimental stopping-power data for 5-12-MeV protons and deuterons. Use is made of Walske's K- and L-shell corrections and shell corrections calculated by Bonderup (1967) on the basis of the Thomas-Fe...... are found by means of Bonderup's shell corrections. Within the Z2 interval treated here, it is found that I/Z2 increases with increasing Z2, contrary to the general trend through the periodic system of elements......Excitation potentials and shell corrections for the elements Z 2=20 to Z2=30 are evaluated from experimental stopping-power data for 5-12-MeV protons and deuterons. Use is made of Walske's K- and L-shell corrections and shell corrections calculated by Bonderup (1967) on the basis of the Thomas...
Konisi, G; Mäki, Z; Nakahara, M
1999-01-01
The left-right symmetric model (LRSM) with gauge group $SU(2)_{L} \\times SU(2)_{R} \\times U(1)_{B-L}$ is reconstructed from the geometric formulation of gauge theory in $M_4 \\times Z_2 \\times Z_2$ where $M_4$ is the four-dimensional Minkowski space and $Z_2 \\times Z_2$ the discrete space with four points. The geometrical structure of this model becomes clearer compared with other works based on noncommutative geometry. As a result, the Yukawa coupling terms and the Higgs potential are derived in more restricted forms than in the standard LRSM.
Quantum spin Hall and Z2 metallic states in an organic material
Zhao, Bao; Zhang, Jiayong; Feng, Wanxiang; Yao, Yugui; Yang, Zhongqin
2014-11-01
Motivated by recently searching for topological states in organic materials as well as successful experimental synthesis of a graphitelike metal-organic framework Ni3(C18H12N6 )2 [Sheberla et al., J. Am. Chem. Soc. 136, 8859 (2014), 10.1021/ja502765n], we systematically investigated the electronic and topological properties of the Ni3(C18H12N6 )2 monolayer using an ab initio method combined with a tight-binding model. Our calculations demonstrate that the material can be in a quantum spin Hall or Z2 metallic state in different electron-doped concentrations, which are experimentally accessible with currently electrostatic gating technologies. The tight-binding model also shows that the real next-nearest-neighbor interaction is essential to drive the Z2 metallic phase in Ni3(C18H12N6 )2-type lattices.
Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir;
2007-01-01
The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...... results in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We discuss some examples of unstable Hamiltonian systems in two dimensions....
T he Diophantine equation p x+ qy= z2%Diophantine方程px＋qy＝z2
李玲; 李小雪
2015-01-01
设 p和q是两个奇素数，且 p＜ q ．B ．Sroysang证明了如果（p ，q）＝（7，19）或（7，31），则方程 px＋ qy＝ z2没有正整数解（x ，y ，z）．为了研究这个问题，运用初等方法和指数Diophantine方程的一些性质，证明了一个一般结果，即如果 p＋ q≡2（mod4）和（q｜p）＝－1，则方程有唯一的正整数解（p ，q ，x ，y ，z）＝（3，11，5，4，122），其中（q｜p）表示Legendre符号．%Let p and q be two odd primes with p< q .Recently ,B .Sroysang proved that if (p ,q)= (7 ,19) or (7 ,31) ,then the equation px+ qy= z2 has no positive integer solutions (x ,y ,z) .In order to study this problem ,by using the elementary number theory methods and the properties of some exponential Diophantine equation ,a general result is proved that if p+ q≡2(mod4) and (q|p)= -1 ,w here (q|p) denotes the Legendre symbol ,then the equation has only the positive integer solution (p ,q ,x ,y ,z)= (3 ,11 ,5 ,4 ,122) .
Maxwell's Optics Symplectic Hamiltonian
Kulyabov, D S; Sevastyanov, L A
2015-01-01
The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and Hamiltonian in the case of hyperregular Lagrangian. It is impossible to do the same in gauge-invariant field theories. In the case of irregular Lagrangian the Dirac Hamiltonian formalism with constraints is usually used, and this leads to a number of certain difficulties. The paper proposes a reformulation of the problem to the case of a field without sources. This allows to use a symplectic Hamiltonian formalism. The proposed formalism will be used by the authors in the future to justify the methods of vector bundles (Hamiltonian bundles) in transformation optics.
Gastón Brasó, Bernat
2008-01-01
En aquest projecte es presenta el desenvolupament d'un paquet d'aplicacions en l'entorn de programació matemàtica Magma, per al tractament dels codis anomenats Z2Z4-additius. Els codis Z2Z4-additius permeten representar alguns codis binaris, com a codis lineals en l'espai dels codis Z2Z4-additius. Aquest fet permetrà l'estudi de tota una sèrie de codis binaris no lineals que fins ara eren intractables. En este proyecto se presenta el desarrollo de un paquete de aplicaciones en el entorno d...
Spectral analysis of tridiagonal Fibonacci Hamiltonians
Yessen, William
2011-01-01
We consider a family of discrete Jacobi operators on the one-dimensional integer lattice, with the diagonal and the off-diagonal entries given by two sequences generated by the Fibonacci substitution on two letters. We show that the spectrum is a Cantor set of zero Lebesgue measure, and discuss its fractal structure and Hausdorff dimension. We also extend some known results on the diagonal and the off-diagonal Fibonacci Hamiltonians.
Diagonalization of Hamiltonian; Diagonalization of Hamiltonian
Garrido, L. M.; Pascual, P.
1960-07-01
We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.
$Z_{2}$-Regge versus Standard Regge Calculus in two dimensions
Bittner, E R; Markum, H; Riedler, J; Holm, C; Janke, W
1999-01-01
We consider two versions of quantum Regge calculus. The Standard Regge Calculus where the quadratic link lengths of the simplicial manifold vary continuously and the Z_2-Regge Model where they are restricted to two possible values. The goal is to determine whether the computationally more easily accessible Z_2 model still retains the universal characteristics of standard Regge theory in two dimensions. In order to compare observables such as average curvature or Liouville field susceptibility, we use in both models the same functional integration measure, which is chosen to render the Z_2-Regge Model particularly simple. Expectation values are computed numerically and agree qualitatively for positive bare couplings. The phase transition within the Z_2-Regge Model is analyzed by mean-field theory.
Deforming D-brane models on $T^6/(\\mathbb{Z}_2 \\times \\mathbb{Z}_{2M})$ orbifolds
Koltermann, Isabel; Honecker, Gabriele
2015-01-01
We review the stabilisation of complex structure moduli in Type IIA orientifolds, especially on $T^6 / (\\mathbb{Z}_2 \\times \\mathbb{Z}_6^\\prime \\times \\Omega \\mathcal{R})$ with discrete torsion, via deformations of $\\mathbb{Z}_2 \\times \\mathbb{Z}_2$ orbifold singularities. While D6-branes in SO(2N) and USp(2N) models always preserve supersymmetry and thus give rise to flat directions, in an exemplary Pati-Salam model with only U(N) gauge groups ten out of the 15 deformation moduli can be stabilised at the orbifold point.
Hamiltonian Forms for a Hierarchy of Discrete Integrable Coupling Systems
XU Xi-Xiang; YANG Hong-Xiang; LU Rong-Wu
2008-01-01
A semi-direct sum of two Lie algebras of four-by-four matrices is presented, and a discrete four-by-fore matrix spectral problem is introduced. A hierarchy of discrete integrable coupling systems is derived. The obtained integrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity. Finally, we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discrete Hamiltonian systems.
Path Integrals and Hamiltonians
Baaquie, Belal E.
2014-03-01
1. Synopsis; Part I. Fundamental Principles: 2. The mathematical structure of quantum mechanics; 3. Operators; 4. The Feynman path integral; 5. Hamiltonian mechanics; 6. Path integral quantization; Part II. Stochastic Processes: 7. Stochastic systems; Part III. Discrete Degrees of Freedom: 8. Ising model; 9. Ising model: magnetic field; 10. Fermions; Part IV. Quadratic Path Integrals: 11. Simple harmonic oscillators; 12. Gaussian path integrals; Part V. Action with Acceleration: 13. Acceleration Lagrangian; 14. Pseudo-Hermitian Euclidean Hamiltonian; 15. Non-Hermitian Hamiltonian: Jordan blocks; 16. The quartic potential: instantons; 17. Compact degrees of freedom; Index.
Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
Callen, Benjamin D
2013-01-01
We present a generic Z_2 x Z_2-invariant scalar field theory with four real scalar fields in six-dimensional Minkowskian spacetime which yields solutions consisting of two intersecting domain-wall kinks which are each paired by fields with lump-like profiles. For a special parameter choice, analytic solutions can be obtained. We show that the Z_2 x Z_2 symmetry can be maintained while coupling fermions by introducing scalar Yukawa couplings to one kink-lump pair and six-dimensional pseudoscalar Yukawa couplings to the other, and we show that there exists a zero mode localized to the domain-wall junction in this case. We also show that scalar fields can be localized.
Mavrantzas, Vlasis G.; Beris, Antony N.; Leermakers, Frans; Fleer, Gerard J.
2005-11-01
Homopolymer adsorption from a dilute solution on an interacting (attractive) surface under static equilibrium conditions is studied in the framework of a Hamiltonian model. The model makes use of the density of chain ends n1,e and utilizes the concept of the propagator G describing conformational probabilities to locally define the polymer segment density or volume fraction φ; both n1,e and φ enter into the expression for the system free energy. The propagator G obeys the Edwards diffusion equation for walks in a self-consistent potential field. The equilibrium distribution of chain ends and, consequently, of chain conformational probabilities is found by minimizing the system free energy. This results in a set of model equations that constitute the exact continuum-space analog of the Scheutjens-Fleer (SF) lattice statistical theory for the adsorption of interacting chains. Since for distances too close to the surface the continuum formulation breaks down, the continuum model is here employed to describe the probability of chain configurations only for distances z greater than 2l, where l denotes the segment length, from the surface; instead, for distances z ⩽2l, the SF lattice model is utilized. Through this novel formulation, the lattice solution at z =2l provides the boundary condition for the continuum model. The resulting hybrid (lattice for distances z ⩽2l, continuum for distances z >2l) model is solved numerically through an efficient implementation of the pseudospectral collocation method. Representative results obtained with the new model and a direct application of the SF lattice model are extensively compared with each other and, in all cases studied, are found to be practically identical.
An effective Hamiltonian approach to quantum random walk
Sarkar, Debajyoti; Paul, Niladri; Bhattacharya, Kaushik; Ghosh, Tarun Kanti
2017-03-01
In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative (see Chandrashekar, Sci. Rep. 3, 2829 (18)). We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the graphene Hamiltonian, the walk has been studied on a graphene lattice and we conclude the preference of additive approach over the multiplicative one.
Running Couplings in Hamiltonians
Glazek, S D
2000-01-01
We describe key elements of the perturbative similarity renormalization group procedure for Hamiltonians using two, third-order examples: phi^3 interaction term in the Hamiltonian of scalar field theory in 6 dimensions and triple-gluon vertex counterterm in the Hamiltonian of QCD in 4 dimensions. These examples provide insight into asymptotic freedom in Hamiltonian approach to quantum field theory. The renormalization group procedure also suggests how one may obtain ultraviolet-finite effective Schrödinger equations that correspond to the asymptotically free theories, including transition from quark and gluon to hadronic degrees of freedom in case of strong interactions. The dynamics is invariant under boosts and allows simultaneous analysis of bound state structure in the rest and infinite momentum frames.
Covariant Hamiltonian field theory
Giachetta, G; Sardanashvily, G
1999-01-01
We study the relationship between the equations of first order Lagrangian field theory on fiber bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. The main peculiarity of these Hamilton equations lies in the fact that, for degenerate systems, they contain additional gauge fixing conditions. We develop the BRST extension of the covariant Hamiltonian formalism, characterized by a Lie superalgebra of BRST and anti-BRST symmetries.
The Z_2 -Orbifold of the W_3-Algebra
Al-Ali, Masoumah; Linshaw, Andrew R.
2016-12-01
The Zamolodchikov W_3-algebra W^c_3 with central charge c has full automorphism group Z_2. It was conjectured in the physics literature over 20 years ago that the orbifold (W^c_3)^{Z_2} is of type W(2,6,8,10,12) for generic values of c. We prove this conjecture for all c ≠ 559 ± 7 √{76657}/95, and we show that for these two values, the orbifold is of type W(2,6,8,10,12,14). This paper is part of a larger program of studying orbifolds and cosets of vertex algebras that depend continuously on a parameter. Minimal strong generating sets for orbifolds and cosets are often easy to find for generic values of the parameter, but determining which values are generic is a difficult problem. In the example of (W^c_3)^{Z_2} , we solve this problem using tools from algebraic geometry.
Topological classification with Z2Pack (Conference Presentation)
Gresch, Dominik; Soluyanov, Alexey A.; Autés, Gabriel; Yazyev, Oleg; Bernevig, Bogdan A.; Vanderbilt, David H.; Troyer, Matthias
2016-10-01
We present a general technique for capturing various non-trivial topologies in the band structure of materials, which often arise from spin-orbit coupling. The technique is aimed at insulators and semimetals. Of insulators, Chern, Z2, and crystalline topological insulators can be identified. Of semimetals, the technique captures non-trivial topologies associated with the presence of Weyl and Dirac points in the spectrum. A public software package - Z2Pack - based on this technique will be presented. Z2Pack is an easy-to-use, well documented Python package that computes topological invariants and illustrates non-trivial features of Berry curvature. It works as a post-processing tool with all major first-principles codes, as well as with tight-binding models. As such, it can be used to investigate materials with strong spin-orbit coupling.
Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices
Habib, K. M. Masum; Sajjad, Redwan N.; Ghosh, Avik W.
2016-03-01
Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.
${\\mathbb Z}_2\\times {\\mathbb Z}_2$-graded Lie Symmetries of the L\\'evy-Leblond Equations
Aizawa, N; Tanaka, H; Toppan, F
2016-01-01
The first-order differential L\\'evy-Leblond equations (LLE's) are the non-relativistic analogs of the Dirac equation, being square roots of ($1+d$)-dimensional Schr\\"odinger or heat equations. Just like the Dirac equation, the LLE's possess a natural supersymmetry. In previous works it was shown that non supersymmetric PDE's (notably, the Schr\\"odinger equations for free particles or in the presence of a harmonic potential), admit a natural ${\\mathbb Z}_2$-graded Lie symmetry. In this paper we show that, for a certain class of supersymmetric PDE's, a natural ${\\mathbb Z}_2\\times{\\mathbb Z}_2$-graded Lie symmetry appears. In particular, we exhaustively investigate the symmetries of the $(1+1)$-dimensional L\\'evy-Leblond Equations, both in the free case and for the harmonic potential. In the free case a ${\\mathbb Z}_2\\times{\\mathbb Z}_2$-graded Lie superalgebra, realized by first and second-order differential symmetry operators, is found. In the presence of a non-vanishing quadratic potential, the Schr\\"odinger...
Product Perfect Z2Z4-linear codes in Steganography
Rifa, J
2010-01-01
Product perfect codes have been proven to enhance the performance of the F5 steganographic method, whereas perfect Z2Z4-linear codes have been recently introduced as an efficient way to embed data, conforming to the +/-1-steganography. In this paper, we present two steganographic methods. On the one hand, a generalization of product perfect codes is made. On the other hand, this generalization is applied to perfect Z2Z4-linear codes. Finally, the performance of the proposed methods is evaluated and compared with those of the aforementioned schemes.
Excitability in optical systems close to Z2-symmetry
Beri, Stefano; Gelens, Lendert; Van der Sande, Guy; Mezosi, Gabor; Sorel, Marc; Danckaert, Jan; Verschaffelt, Guy; 10.1016/j.physleta.2009.11.070
2011-01-01
We report theoretically and experimentally on excitability in semiconductor ring lasers in order to reveal a mechanism of excitability, general for systems close to Z2-symmetry. The global shapes of the invariant manifolds of a saddle in the vicinity of a homoclinic loop determine the origin of excitability and the fea- tures of the excitable pulses. We show how to experimentally make a semiconductor ring laser excitable by breaking the Z2-symmetry in a controlled way. The experiments confirm the theoretical predictions.
Periodic solutions for second-order Hamiltonian systems with the p-Laplacian
Weigao Ge
2006-10-01
Full Text Available In this paper, we investigate the periodic solutions of Hamiltonian system with the p-Laplacian. By using Mountain Pass Theorem the existence of at least one periodic solution is obtained, Furthermore, under suitable assumptions, we obtain the existence of infinitely many solutions via $Z_2$-symmetric version of the Mountain Pass Theorem.
An effective Hamiltonian approach to quantum random walk
DEBAJYOTI SARKAR; NILADRI PAUL; KAUSHIK BHATTACHARYA; TARUN KANTI GHOSH
2017-03-01
In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamiltoniansare generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative (see Chandrashekar, $\\it{Sci. Rep}$. 3, 2829 (2013)). We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the graphene Hamiltonian, the walk has been studied on a graphene lattice and we conclude the preference of additive approach over the multiplicative one.
van Enter, A C; Fernández, R
1999-05-01
For classical lattice systems with finite (Ising) spins, we show that the implementation of momentum-space renormalization at the level of Hamiltonians runs into the same type of difficulties as found for real-space transformations: Renormalized Hamiltonians are ill-defined in certain regions of the phase diagram.
Enter, Aernout C.D. van; Fernández, Roberto
For classical lattice systems with finite (Ising) spins, we show that the implementation of momentum-space renormalization at the level of Hamiltonians runs into the same type of difficulties as found for real-space transformations: Renormalized Hamiltonians are ill-defined in certain regions of the
Multi-Hamiltonian structure of Lotka-Volterra and quantum Volterra models
Cronstroem, C. [Nordisk Inst. for Teoretisk Fysik (NORDITA), Copenhagen (Denmark); Noga, M. [Department of Theoretical Physics, Comenius University, Mlynska Dolina, Bratislava (Slovakia)
1995-07-10
We consider evolution equations of the Lotka-Volterra type, and elucidate especially their formulation as canonical Hamiltonian systems. The general conditions under which these equations admit several conserved quantities (multi-Hamiltonians) are analysed. A special case, which is related to the Liouville model on a lattice, is considered in detail, both as a classical and as a quantum system. (orig.).
Multi-hamiltonian structure of Lotka-Volterra and quantum Volterra models
Cronström, C; Cronström, C; Noga, M
1994-01-01
We consider evolution equations of the Lotka-Volterra type, and elucidate especially their formulation as canonical Hamiltonian systems. The general conditions under which these equations admit several conserved quantities (multi-Hamiltonians) are analysed. A special case, which is related to the Liouville model on a lattice, is considered in detail, both as aclassical and as aquantal system
Fermion zero modes in a $Z_2$ vortex background
Lozano, Gustavo; Schaposnik, Fidel A
2016-01-01
In this paper we study the zero energy solutions of the Dirac equation in the background of a $Z_2$ vortex of a non-Abelian gauge model with three charged scalar fields. We determine the number of the fermionic zero modes giving their explicit form for two specific Ansatze.
Kanchan Joshi
2012-12-01
Full Text Available In this paper we consider the group algebra R(C_2 ×D_infinity. It is shown that R(C_2 ×D_infinity can be represented by a 4 × 4 block circulant matrix. It is also shown that U(Z_2(C_2 × D_infinity isinfinitely generated
FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS
CHENG Daizhan; XI Zairong
2002-01-01
This paper investigates the relationship between state feedback and Hamiltonian realizatiou. First, it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization. Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural outpnt. Then some conditions for an affine nonlinear system to have a Hamiltonian realization arc given.For generalized outputs, the conditions of the feedback, keeping Hamiltonian, are discussed. Finally, the admissible feedback controls for generalized Hamiltonian systems are considered.
FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS
CHENGDaizhan; XIZairong
2002-01-01
This paper investigates the relationship between state feedback and Hamiltonican realization.Firest,it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization.Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural output.Then some conditions for an affine nonlinear system to have a Hamiltonian realization are given.some conditions for an affine nonlinear system to have a Hamiltonian realization are given.For generalized outputs,the conditions of the feedback,keeping Hamiltonian,are discussed.Finally,the admissible feedback controls for generalized Hamiltonian systems are considered.
Z-2 Architecture Description and Requirements Verification Results
Graziosi, Dave; Jones, Bobby; Ferl, Jinny; Scarborough, Steve; Hewes, Linda; Ross, Amy; Rhodes, Richard
2016-01-01
The Z-2 Prototype Planetary Extravehicular Space Suit Assembly is a continuation of NASA's Z series of spacesuits. The Z-2 is another step in NASA's technology development roadmap leading to human exploration of the Martian surface. The suit was designed for maximum mobility at 8.3 psid, reduced mass, and to have high fidelity life support interfaces. As Z-2 will be man-tested at full vacuum in NASA JSC's Chamber B, it was manufactured as Class II, making it the most flight-like planetary walking suit produced to date. The Z-2 suit architecture is an evolution of previous EVA suits, namely the ISS EMU, Mark III, Rear Entry I-Suit and Z-1 spacesuits. The suit is a hybrid hard and soft multi-bearing, rear entry spacesuit. The hard upper torso (HUT) is an all-composite structure and includes a 2-bearing rolling convolute shoulder with Vernier sizing mechanism, removable suit port interface plate (SIP), elliptical hemispherical helmet and self-don/doff shoulder harness. The hatch is a hybrid aluminum and composite construction with Apollo style gas connectors, custom water pass-thru, removable hatch cage and interfaces to primary and auxiliary life support feed water bags. The suit includes Z-1 style lower arms with cam brackets for Vernier sizing and government furnished equipment (GFE) Phase VI gloves. The lower torso includes a telescopic waist sizing system, waist bearing, rolling convolute waist joint, hard brief, 2 bearing soft hip thigh, Z-1 style legs with ISS EMU style cam brackets for sizing, and conformal walking boots with ankle bearings. The Z-2 Requirements Verification Plan includes the verification of more than 200 individual requirements. The verification methods include test, analysis, inspection, demonstration or a combination of methods. Examples of unmanned requirements include suit leakage, proof pressure testing, operational life, mass, isometric man-loads, sizing adjustment ranges, internal and external interfaces such as in-suit drink bag
Weakly deformed soliton lattices
Dubrovin, B. (Moskovskij Gosudarstvennyj Univ., Moscow (USSR). Dept. of Mechanics and Mathematics)
1990-12-01
In this lecture the author discusses periodic and quasiperiodic solutions of nonlinear evolution equations of phi{sub t}=K (phi, phi{sub x},..., phi{sup (n)}), the so-called soliton lattices. After introducing the theory of integrable systems of hydrodynamic type he discusses their Hamiltonian formalism, i.e. the theory of Poisson brackets of hydrodynamic type. Then he describes the application of algebraic geometry to the effective integration of such equations. (HSI).
Remarks on hamiltonian digraphs
Gutin, Gregory; Yeo, Anders
2001-01-01
This note is motivated by A.Kemnitz and B.Greger, Congr. Numer. 130 (1998)127-131. We show that the main result of the paper by Kemnitz and Greger is an easy consequence of the characterization of hamiltonian out-locally semicomplete digraphs by Bang-Jensen, Huang, and Prisner, J. Combin. Theory...... of Fan's su#cient condition [5] for an undirected graph to be hamiltonian. In this note we give another, more striking, example of this kind, which disproves a conjecture from [6]. We also show that the main result of [6] 1 is an easy consequence of the characterization of hamiltonian out......-tournaments by Bang-Jensen, Huang and Prisner [4]. For further information and references on hamiltonian digraphs, see e.g. the chapter on hamiltonicity in [1] as well as recent survey papers [2, 8]. We use the standard terminology and notation on digraphs as described in [1]. A digraph D has vertex set V (D) and arc...
Microscopic plasma Hamiltonian
Peng, Y.-K. M.
1974-01-01
A Hamiltonian for the microscopic plasma model is derived from the Low Lagrangian after the dual roles of the generalized variables are taken into account. The resulting Hamilton equations are shown to agree with the Euler-Lagrange equations of the Low Lagrangian.
Transformation design and nonlinear Hamiltonians
Brougham, Thomas; Jex, Igor
2009-01-01
We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple `beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons.
Grusdt, Fabian; Abanin, Dmitry; Demler, Eugene
2013-05-01
Recently experiments with ultracold atoms started to explore topological phases in 1D optical lattices. While transport measurements are challenging in these systems, ways to directly measure topological quantum numbers using a combination of Bloch oscillations and Ramsey interferometry have been explored (Atala et al., arXiv:1212.0572). In this talk I will present ways to measure the Z2 topological quantum numbers of two and three dimensional time-reversal invariant (TR) topological insulators. In this case non-Abelian Bloch oscillations can be combined with Ramsey interferometry to map out the topological properties of a given band-structure. Our method is very general and works even in the presence of accidental degeneracies. The applicability of the scheme is discussed for different theoretically proposed implementations of TR topological insulators using ultracold atoms. F. G. is grateful to Harvard University for hospitality and acknowledges financial support from Graduate School Materials Science in Mainz (MAINZ).
On the Erigone family and the $z_2$ secular resonance
Carruba, Valerio; Winter, Othon C
2015-01-01
The Erigone family is a C-type group in the inner main belt. Its age has been estimated by several researchers to be less then 300 My, so it is a relatively young cluster. Yarko-YORP Monte Carlo methods to study the chronology of the Erigone family confirm results obtained by other groups. The Erigone family, however, is also characterized by its interaction with the $z_2$ secular resonance. While less than 15% of its members are currently in librating states of this resonance, the number of objects, members of the dynamical group, in resonant states is high enough to allow to use the study of dynamics inside the $z_2$ resonance to set constraints on the family age. Like the ${\
Z2 Invariants of Topological Insulators as Geometric Obstructions
Fiorenza, Domenico; Monaco, Domenico; Panati, Gianluca
2016-05-01
We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to -1. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2 d, the obstruction to the existence of such a frame is shown to be encoded in a Z_2-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3 d, instead, four Z_2 invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones.
The Diophantine Equation 8x+py=z2
Lan Qi
2015-01-01
Full Text Available Let p be a fixed odd prime. Using certain results of exponential Diophantine equations, we prove that (i if p≡±3(mod 8, then the equation 8x+py=z2 has no positive integer solutions (x,y,z; (ii if p≡7(mod 8, then the equation has only the solutions (p,x,y,z=(2q-1,(1/3(q+2,2,2q+1, where q is an odd prime with q≡1(mod 3; (iii if p≡1(mod 8 and p≠17, then the equation has at most two positive integer solutions (x,y,z.
Analytic Torsion of Z_2-graded Elliptic Complexes
Mathai, Varghese
2010-01-01
We define analytic torsion of Z_2-graded elliptic complexes as an element in the graded determinant line of the cohomology of the complex, generalizing most of the variants of Ray-Singer analytic torsion in the literature. It applies to a myriad of new examples, including flat superconnection complexes, twisted analytic and twisted holomorphic torsions, etc. The definition uses pseudo-differential operators and residue traces. We also study properties of analytic torsion for Z_2-graded elliptic complexes, including the behavior under variation of the metric. For compact odd dimensional manifolds, the analytic torsion is independent of the metric, whereas for even dimensional manifolds, a relative version of the analytic torsion is independent of the metric. Finally, the relation to topological field theories is studied.
Stereoselective Synthesis of (Z)-2-Acylamido-4-phenylcrotonates
无
2000-01-01
Two practical methods for highly stereoselective synthesis of (Z)-2-acylamido-4-phenylcrotonates 2a～ b have been developed. The key step in the first route was how to control the acid-catalyzed isomerization of condensation mixtures of a -keto ester 5 with carbomite. In the second route the key step was reduction of oxime 8, derived from a -keto ester 5, with iron powder in the presence of acetic anhydride.
The Environmental Dependence of Galaxy Properties at z=2
Tanaka, Masayuki; Venemans, Bram; Kurk, Jaron
2010-01-01
We report on the environmental dependence of galaxy properties at z=2.15. We construct multi-band photometric data sets in the (proto-)cluster PKS1138-26 field and in the GOODS field. We then fit spectral energy distributions of the galaxies with model templates generated with the latest stellar population synthesis code and derive physical properties of galaxies from the fits. To quantify the environmental dependence of galaxy properties, a special care is taken of systematic errors -- we use data sets that have almost the same wavelength samplings, use the same code to fit SEDs with the same set of templates, and compare relative differences between the two samples. We find that the PKS1138 galaxies have similar ages, shorter star formation time scales, lower star formation rates, and weaker dust extinction compared to the GOODS galaxies at z~2. This trend is similar to that observed locally, suggesting that the environmental dependence of galaxy properties is already partly in place as early as z=2.15. We ...
Passive galaxies as tracers of cluster environments at z~2
Strazzullo, V; Gobat, R; Garilli, B; Mignoli, M; Valentino, F; Onodera, M; Renzini, A; Cimatti, A; Finoguenov, A; Arimoto, N; Cappellari, M; Carollo, C M; Feruglio, C; Floc'h, E Le; Lilly, S J; Maccagni, D; McCracken, H J; Moresco, M; Pozzetti, L; Zamorani, G
2015-01-01
Even 10 billion years ago, the cores of the first galaxy clusters are often found to host a characteristic population of massive galaxies with already suppressed star formation. Here we search for distant cluster candidates at z~2 using massive passive galaxies as tracers. With a sample of ~40 spectroscopically confirmed passive galaxies at 1.3<z<2.1, we tune photometric redshifts of several thousands passive sources in the full 2 sq.deg. COSMOS field. This allows us to map their density in redshift slices, probing the large scale structure in the COSMOS field as traced by passive sources. We report here on the three strongest passive galaxy overdensities that we identify in the redshift range 1.5<z<2.5. While the actual nature of these concentrations is still to be confirmed, we discuss their identification procedure, and the arguments supporting them as candidate galaxy clusters (likely mid-10^13 M_sun range). Although this search approach is likely biased towards more evolved structures, it has...
Wieland, Wolfgang M
2013-01-01
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
Quantum Hamiltonian Complexity
2014-01-01
Constraint satisfaction problems are a central pillar of modern computational complexity theory. This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems. Over the past decade and a half, this field has witnessed fundamental breakthroughs, ranging from the establishment of a "Quantum Cook-Levin Theorem" to deep insights into the structure of 1D low-temperature quantum systems via s...
GMASS Ultradeep Spectroscopy of Galaxies at z~2. III: The emergence of the color bimodality at z~2
Cassata, P; Kurk, J; Rodighiero, G; Pozzetti, L; Bolzonella, M; Daddi, E; Mignoli, M; Berta, S; Dickinson, M; Franceschini, A; Halliday, C; Renzini, A; Rosati, P; Zamorani, G
2008-01-01
The aim of this work is to study the evolution of the rest frame color distribution of galaxies with the redshift, in particular in the critical interval 1.410.1, and we study their morphological and spectro-photometric properties. We show that the contribution to this sample of early-type galaxies, defined as galaxies with a spheroidal morphology and no star formation, decreases from 60-70% at z2 we still find red galaxies in the mass complete sample, even if the bimodality is not seen any more. About 25% of these red galaxies at z>2 are passively evolving, with the bulk of their stars formed at redshift z>`3.
Exploring the Hamiltonian inversion landscape.
Donovan, Ashley; Rabitz, Herschel
2014-08-07
The identification of quantum system Hamiltonians through the use of experimental data remains an important research goal. Seeking a Hamiltonian that is consistent with experimental measurements constitutes an excursion over a Hamiltonian inversion landscape, which is the quality of reproducing the data as a function of the Hamiltonian parameters. Recent theoretical work showed that with sufficient experimental data there should be local convexity about the true Hamiltonian on the landscape. The present paper builds on this result and performs simulations to test whether such convexity is observed. A gradient-based Hamiltonian search algorithm is incorporated into an inversion routine as a means to explore the local inversion landscape. The simulations consider idealized noise-free as well as noise-ridden experimental data. The results suggest that a sizable convex domain exists about the true Hamiltonian, even with a modest amount of experimental data and in the presence of a reasonable level of noise.
Lattice Gauge Theories and Spin Models
Mathur, Manu
2016-01-01
The Wegner $Z_2$ gauge theory-$Z_2$ Ising spin model duality in $(2+1)$ dimensions is revisited and derived through a series of canonical transformations. These $Z_2$ results are directly generalized to SU(N) lattice gauge theory in $(2+1)$ dimensions to obtain a dual SU(N) spin model in terms of the SU(N) magnetic fields and electric scalar potentials. The gauge-spin duality naturally leads to a new gauge invariant disorder operator for SU(N) lattice gauge theory. A variational ground state of the dual SU(2) spin model with only nearest neighbour interactions is constructed to analyze SU(2) lattice gauge theory.
Bifurcation sequences in the symmetric 1:1 Hamiltonian resonance
Marchesiello, Antonella
2015-01-01
We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under $Z_2 \\times Z_2$ symmetry. The rich structure of these classical systems is investigated with geometric methods and the relation with the singularity theory approach is also highlighted. The geometric approach is the most straightforward way to obtain a general picture of the phase-space dynamics of the family as is defined by a complete subset in the space of control parameters complying with the symmetry constraint. It is shown how to find an energy-momentum map describing the phase space structure of each member of the family, a catastrophe map that captures its global features and formal expressions for action-angle variables. Several examples, mainly taken from astrodynamics, are used as applications.
A parity breaking Ising chain Hamiltonian as a Brownian motor
Cornu, F.; Hilhorst, H. J.
2014-10-01
We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonian {\\cal H} =-{U_2}\\sumk sksk+1 - {U_3}\\sumk sksk+1sk+3 and let this system evolve by Kawasaki spin exchange dynamics. Monte Carlo simulations show that perturbations forcing this system off equilibrium make it act as a Brownian molecular motor which, in the lattice gas interpretation, transports particles along the chain. We determine the particle current under various different circumstances, in particular as a function of the ratio {U_3}/{U_2} and of the conserved magnetization M=\\sum_ksk . The symmetry of the U3 term in the Hamiltonian is discussed.
Exotic Hadrons and Underlying Z_{2,3} Symmetries
Belhaj, Adil; Sedra, Moulay Brahim
2015-01-01
The recent observation of higher quark combinations, tetraquarks and pentaquarks, is a strong indication of more exotic hadrons. Using Z_{2} and Z_{3} symmetries and standard model data, a general quark combination producing new hadronic states is proposed in terms of polygon geometries according to the Dynkin diagrams of \\widehat{A}_{n} affine Lie algebras. It has been shown that Z_{\\mathbf{2,3}} invariance is crucial in the determination of the mesonic or the baryonic nature of these states. The hexagonal geometry is considered in some details producing both mesonic and baryonic states. A general class of this family is also presented.
Fring, Andreas; Frith, Thomas
2017-01-01
We propose a procedure to obtain exact analytical solutions to the time-dependent Schrödinger equations involving explicit time-dependent Hermitian Hamiltonians from solutions to time-independent non-Hermitian Hamiltonian systems and the time-dependent Dyson relation, together with the time-dependent quasi-Hermiticity relation. We illustrate the working of this method for a simple Hermitian Rabi-type model by relating it to a non-Hermitian time-independent system corresponding to the one-site lattice Yang-Lee model.
CANDELS: The progenitors of compact quiescent galaxies at z~2
Barro, Guillermo; Perez-Gonzalez, Pablo G; Koo, David C; Williams, Christina C; Kocevski, Dale D; Trump, Jonathan R; Mozena, Mark; McGrath, Elizabeth; van der Wel, Arjen; Wuyts, Stijn; Bell, Eric F; Croton, Darren J; Dekel, Avishai; Ashby, M L N; Ferguson, Henry C; Fontana, Adriano; Giavalisco, Mauro; Grogin, Norman A; Guo, Yicheng; Hathi, Nimish P; Hopkins, Philip F; Huang, Kuang-Han; Koekemoer, Anton M; Kartaltepe, Jeyhan S; Lee, Kyoung-Soo; Newman, Jeffrey A; Porter, Lauren A; Primack, Joel R; Ryan, Russell E; Rosario, David; Somerville, Rachel S
2012-01-01
We combine high-resolution HST/WFC3 images with multi-wavelength photometry to track the evolution of structure and activity of massive (log(M*) > 10) galaxies at redshifts z = 1.4 - 3 in two fields of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS). We detect compact, star-forming galaxies (cSFGs) whose number densities, masses, sizes, and star formation rates qualify them as likely progenitors of compact, quiescent, massive galaxies (cQGs) at z = 1.5 - 3. At z > 2 most cSFGs have specific star-formation rates (sSFR = 10^-9 yr^-1) half that of typical, massive SFGs at the same epoch, and host X-ray luminous AGN 30 times (~30%) more frequently. These properties suggest that cSFGs are formed by gas-rich processes (mergers or disk-instabilities) that induce a compact starburst and feed an AGN, which, in turn, quench the star formation on dynamical timescales (few 10^8 yr). The cSFGs are continuously being formed at z = 2 - 3 and fade to cQGs by z = 1.5. After this epoch, cSFGs are r...
Testing different stellar mass estimators at 1<z<2
Longhetti, Marcella; Mignano, Arturo
2008-01-01
Physical parameters of galaxies (as luminosity, stellar mass, age) are often derived by means of the model templates which best fit their spectro-photometric data. We have performed a quantitative test aimed at exploring the ability of this procedure in recovering the physical parameters of early-type galaxies at 1<z<2. A wide range of simulated SEDs, reproducing those of early-type galaxies at 1<z<2 with assigned age and mass, are used to build mock photometric catalogs with wavelength coverage and photometric uncertainties similar to those of two topical surveys (i.e. VVDS and GOODS). The best fitting analysis of the simulated photometric data allows to study the differences among the recovered parameters and the input ones. Results indicate that the stellar masses measured by means of optical bands are affected by larger uncertainties with respect to those obtained from near-IR bands, and they frequently underestimate the real values. The M/L ratio in the V band results strongly underestimated,...
Large scale structure around a z=2.1 cluster
Hung, Chao-Ling; Chiang, Yi-Kuan; Capak, Peter; Cowley, Michael J; Darvish, Behnam; Kacprzak, Glenn G; Kovac, K; Lilly, Simon J; Nanayakkara, Themiya; Spitler, Lee R; Tran, Kim-Vy H; Yuan, Tiantian
2016-01-01
The most prodigious starburst galaxies are absent in massive galaxy clusters today, but their connection with large scale environments is less clear at $z\\gtrsim2$. We present a search of large scale structure around a galaxy cluster core at $z=2.095$ using a set of spectroscopically confirmed galaxies. We find that both color-selected star-forming galaxies (SFGs) and dusty star-forming galaxies (DSFGs) show significant overdensities around the $z=2.095$ cluster. A total of 8 DSFGs (including 3 X-ray luminous active galactic nuclei, AGNs) and 34 SFGs are found within a 10 arcmin radius (corresponds to $\\sim$15 cMpc at $z\\sim2.1$) from the cluster center and within a redshift range of $\\Delta z=0.02$, which leads to galaxy overdensities of $\\delta_{\\rm DSFG}\\sim12.3$ and $\\delta_{\\rm SFG}\\sim2.8$. The cluster core and the extended DSFG- and SFG-rich structure together demonstrate an active cluster formation phase, in which the cluster is accreting a significant amount of material from large scale structure whi...
Classical Exchange Algebra of the Nonlinear Sigma Model on a Supercoset Target with Z2n Grading
KE San-Min; LI Xin-Ying; WANG Chun; YUE Rui-Hong
2011-01-01
The classical exchange algebra satisfied by the monodromy matrix of the nonlinear sigma model on a supercoset target with Z2n grading is derived using a first-order Hamiltonian formulation and by adding to the Lax connection terms proportional to constraints. This enables us to show that the conserved charges of the theory are in involution. When n = 2, our results coincide with the results given by Magro for the pure spinor description of AdS5 × S5 string theory (when the ghost terms are omitted).%The classical exchange algebra satisfied by the monodromy matrix of the nonlinear sigma model on a supercoset target with Z2n grading is derived using a first-order Hamiltonian formulation and by adding to the Lax connection terms proportional to constraints.This enables us to show that the conserved charges of the theory are in involution.When n =2,our results coincide with the results given by Magro for the pure spinor description of AdS5 × S5 string theory (when the ghost terms are omitted).Bena,Polchinski and Roiban[1] found an infinite number of non-local classically conserved charges for the Grecn-Schwarz superstring in AdS5 × S5 background.[2] Similar results were obtained for some other strings[3-9] that propagate in AdS space-time,as discussed in Refs.[7 9].Vallilo[10] showed that such charges also exist in the pure-spinor formalism of the superstring in AdS5 × S5.Bianchi and Klǔson[11] gave the current algebra of the pure-spinor superstring.Berkovits[12] proved that the nonlocal charges in the string theory are BRST-invariant and physical.
P.S. Vyas; FAN Hong-Yi; P.N. Gajjar; WU Hao; B.Y. Thakore; A.R. Jani
2008-01-01
We show that the recently proposed invariant eigen-operator (IEO) method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of compound lattice is also studied by IEO method.
A lattice approach to spinorial quantum gravity
Renteln, Paul; Smolin, Lee
1989-01-01
A new lattice regularization of quantum general relativity based on Ashtekar's reformulation of Hamiltonian general relativity is presented. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. Lattice versions of these constraints are constructed. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.
Towards a Precision Cosmology from Starburst Galaxies at z>2
Siegel, E R; Gallego, J P; López, M O; Hidalgo, P R; Gallego, Jorge P.
2004-01-01
This work investigates the use of a well-known empirical correlation between the velocity dispersion, metallicity, and luminosity in H beta of nearby HII galaxies to measure the distances to HII-like starburst galaxies at high redshifts. This correlation is applied to a sample of 15 starburst galaxies with redshifts between z=2.17 and z=3.39 to constrain Omega_m, using data available from the literature. A best-fit value of Omega_m = 0.21 +0.30 -0.12 in a Lambda-dominated universe and of Omega_m = 0.11 +0.37 -0.19 in an open universe is obtained. A detailed analysis of systematic errors, their causes, and their effects on the values derived for the distance moduli and Omega_m is carried out. A discussion of how future work will improve constraints on Omega_m by reducing the errors is also presented.
Perfect Z2Z4-linear codes in Steganography
Rifà, H; Ronquillo, L
2010-01-01
Steganography is an information hiding application which aims to hide secret data imperceptibly into a commonly used media. Unfortunately, the theoretical hiding asymptotical capacity of steganographic systems is not attained by algorithms developed so far. In this paper, we describe a novel coding method based on Z2Z4-linear codes that conforms to +/-1-steganography, that is secret data is embedded into a cover message by distorting each symbol by one unit at most. This method solves some problems encountered by the most efficient methods known today, based on ternary Hamming codes. Finally, the performance of this new technique is compared with that of the mentioned methods and with the well-known theoretical upper bound.
On the marginally relevant operator in z=2 Lifshitz holography
Holsheimer, Kristian [Institute of Physics, University of Amsterdam,Science Park 904, Postbus 94485, 1090 GL Amsterdam (Netherlands)
2014-03-19
We study holographic renormalization and RG flow in a strongly-coupled Lifshitz-type theory in 2+1 dimensions with dynamical exponent z=2. The bottom-up gravity dual we use is 3+1 dimensional Einstein gravity coupled to a massive vector field. This model contains a marginally relevant operator around the Lifshitz fixed point. We show how holographic renormalization works in the presence of this marginally relevant operator without the need to introduce explicitly cutoff-dependent counterterms. A simple closed-form expression is found for the renormalized on-shell action. We also discuss how asymptotically Lifshitz geometries flow to AdS in the interior due to the marginally relevant operator. We study the behavior of the renormalized entanglement entropy and confirm that it decreases monotonically along the Lifshitz-to-AdS RG flow.
Nechaev, I. A.; Krasovskii, E. E.
2016-11-01
We present a method to microscopically derive a small-size k .p Hamiltonian in a Hilbert space spanned by physically chosen ab initio spinor wave functions. Without imposing any complementary symmetry constraints, our formalism equally treats three- and two-dimensional systems and simultaneously yields the Hamiltonian parameters and the true Z2 topological invariant. We consider bulk crystals and thin films of Bi2Se3 , Bi2Te3 , and Sb2Te3 . It turns out that the effective continuous k .p models with open boundary conditions often incorrectly predict the topological character of thin films.
Chromatic roots and hamiltonian paths
Thomassen, Carsten
2000-01-01
We present a new connection between colorings and hamiltonian paths: If the chromatic polynomial of a graph has a noninteger root less than or equal to t(n) = 2/3 + 1/3 (3)root (26 + 6 root (33)) + 1/3 (3)root (26 - 6 root (33)) = 1.29559.... then the graph has no hamiltonian path. This result...
SPECTRAL CALCULATIONS OF HAMILTONIAN FOR A QUANTUM FRACTAL NETWORK
无
2000-01-01
A general formulation for the spectral calculations of the Hamiltonian operator of a Quantum Fractal Network(QFN) is presented. The QFN can be constructed by placing artificial neurons on each site of the fractal lattice. An artificial neuron may consist of a cell of a quantum cellular automaton or a quantum dot, which confines a single electron. The Coulomb interaction or the spin-spin interaction between neurons can be used to transmit signals and perform logic operations.The recursive formulas of the eigenvalues and eigenvectors between sub-lattices are obtained explicitly. As the application of the formulations,the eigenvalues and eigenvectors of the Hamiltonian operator for the Sierpinski gasket are calculated.
Quantization of noncommutative completely integrable Hamiltonian systems
Giachetta, G; Sardanashvily, G
2007-01-01
Integrals of motion of a Hamiltonian system need not be commutative. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as an abelian completely integrable Hamiltonian system.
An optical Hamiltonian experiment and the beam dynamics
Bazzani, A. [Department of Physics and CIG, University of Bologna, INFN sezione di Bologna (Italy)]. E-mail: bazzani@bo.infn.it; Freguglia, P. [Department of Pure and Applied Mathematics, University of L' Aquila (Italy); Fronzoni, L. [Department of Physics and CISC, University of Pisa (Italy); Turchetti, G. [Department of Physics and CIG, University of Bologna, INFN sezione di Bologna (Italy)
2006-06-01
The analogy between geometric optics and Hamiltonian mechanics is used to propose an experiment that simulates the beam propagation in a focusing magnetic lattice of a particle accelerator. A laser beam is reflected several times by a parabolic mirror and the resulting pattern is registered by a photo camera. This experiment allows to illustrate some aspects of nonlinear beam transport in presence of nonlinearities and stochastic perturbations. The experimental results are discussed and compared with computer simulations.
Ground State Properties of the 1/2 Flux Harper Hamiltonian
Kennedy, Colin; Burton, William Cody; Chung, Woo Chang; Ketterle, Wolfgang
2015-05-01
The Harper Hamiltonian describes the motion of charged particles in an applied magnetic field - the spectrum of which exhibits the famed Hofstadter's butterfly. Recent advances in driven optical lattices have made great strides in simulating nontrivial Hamiltonians, such as the Harper model, in the time-averaged sense. We report on the realization of the ground state of bosons in the Harper Hamiltonian for 1/2 flux per plaquette utilizing a tilted two-dimensional lattice with laser assisted tunneling. We detail progress in studying various ground state properties of the 1/2 flux Harper Hamiltonian including ground state degeneracies, gauge-dependent observables, effects of micromotion, adiabatic loading schemes, and emergence and decay of coherence. Additionally, we describe prospects for flux rectification using a period-tripled superlattice and generalizations to three dimensions. MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Department of Physics, Massachusetts Institute of Technology.
N=4 Supersymmetric Yang-Mills Theory on Orbifold-$T^4/{\\bf Z}_2$
Jinzenji, M; Jinzenji, Masao; Sasaki, Toru
2001-01-01
We derive the partition function of N=4 supersymmetric Yang-Mills theory on orbifold-$T^4/{\\bf Z}_2$. In classical geometry, K3 surface is constructed from the orbifold-$T^4/{\\bf Z}_2$. Along the same way as the orbifold construction, we construct the partition function of K3 surface from orbifold-$T^4/{\\bf Z}_2$. The partition function is given by the product of the contribution of the untwisted sector of $T^4/{\\bf Z}_2$, and that of the twisted sector of $T^4/{\\bf Z}_2$ i.e., ${\\cal O}(-2)$ curve blow-up formula.
A physical model for z ~ 2 dust-obscured galaxies
Narayanan, Desika; Dey, Arjun; Hayward, Christopher C.; Cox, Thomas J.; Bussmann, R. Shane; Brodwin, Mark; Jonsson, Patrik; Hopkins, Philip F.; Groves, Brent; Younger, Joshua D.; Hernquist, Lars
2010-09-01
We present a physical model for the origin of z ~ 2 dust-obscured galaxies (DOGs), a class of high-redshift ultraluminous infrared galaxies (ULIRGs) selected at 24μm which are particularly optically faint (F24μm/FR > 1000). By combining N-body/smoothed particle hydrodynamic simulations of high-redshift galaxy evolution with 3D polychromatic dust radiative transfer models, we find that luminous DOGs (with F24 >~ 0.3mJy at z ~ 2) are well modelled as extreme gas-rich mergers in massive (~5 × 1012-1013Msolar) haloes, with elevated star formation rates (SFR; ~500-1000Msolaryr-1) and/or significant active galactic nuclei (AGN) growth , whereas less luminous DOGs are more diverse in nature. At final coalescence, merger-driven DOGs transition from being starburst dominated to AGN dominated, evolving from a `bump' to a power-law (PL) shaped mid-IR (Infrared Array Camera, IRAC) spectral energy distribution (SED). After the DOG phase, the galaxy settles back to exhibiting a `bump' SED with bluer colours and lower SFRs. While canonically PL galaxies are associated with being AGN dominated, we find that the PL mid-IR SED can owe both to direct AGN contribution and to a heavily dust obscured stellar bump at times that the galaxy is starburst dominated. Thus, PL galaxies can be either starburst or AGN dominated. Less luminous DOGs can be well-represented either by mergers or by massive (Mbaryon ~ 5 × 1011Msolar) secularly evolving gas-rich disc galaxies (with SFR >~ 50Msolaryr-1). By utilizing similar models as those employed in the submillimetre galaxy (SMG) formation study of Narayanan et al., we investigate the connection between DOGs and SMGs. We find that the most heavily star-forming merger-driven DOGs can be selected as submillimetre galaxies, while both merger-driven and secularly evolving DOGs typically satisfy the BzK selection criteria. The model SEDs from the simulated galaxies match observed data reasonably well, though Mrk 231 and Arp 220 templates provide
On the Reaction Path Hamiltonian
孙家钟; 李泽生
1994-01-01
A vector-fiber bundle structure of the reaction path Hamiltonian, which has been introduced by Miller, Handy and Adams, is explored with respect to molecular vibrations orthogonal to the reaction path. The symmetry of the fiber bundle is characterized by the real orthogonal group O(3N- 7) for the dynamical system with N atoms. Under the action of group O(3N- 7). the kinetic energy of the reaction path Hamiltonian is left invariant. Furthermore , the invariant behaviour of the Hamiltonian vector fields is investigated.
Gemini imaging of QSO host galaxies at z~2
Croom, S; Boyle, B; Shanks, T; Miller, L; Smith, R; Croom, Scott; Schade, David; Boyle, Brian; Shanks, Tom; Miller, Lance; Smith, Robert
2004-01-01
We present results of a Gemini adaptive optics (AO) imaging program to investigate the host galaxies of typical QSOs at z~2. Our aim is to study the host galaxies of typical, L*_qso QSOs at the epoch of peak QSO and star formation activity. The large database of faint QSOs provided by the 2dF QSO Redshift Survey allows us to select a sample of QSOs at z=1.75-2.5 which have nearby (<12 arcsecond separation) bright stars suitable for use as AO guide stars. We have observed a sample of 9 QSOs. The images of these sources have AO corrected full-width at half-maximum of between 0.11 and 0.25 arcseconds. We use multiple observations of point spread function (PSF) calibration star pairs in order to quantify any uncertainty in the PSF. We then factored these uncertainties into our modelling of the QSO plus host galaxy. In only one case did we convincingly detect a host (2QZ J133311.4+001949, at z=1.93). This host galaxy has K=18.5+-0.2 mag with a half-light radius, r_e=0.55+-0.1'', equivalent to ~3L*_gal assuming ...
Galaxies at Z=2 extensions around radio-quiet QSOs
Aretxaga, I; Terlevich, R J
1995-01-01
We have been conducting an imaging survey to detect host galaxies of radio-quiet QSOs at high redshift (z = 2), in order to compare them with those of radio-loud objects. Six QSOs were observed in the R passband with the auxiliary port of the 4.2m WHT of the {\\it Observatorio de Roque de los Muchachos} indir August 1994. The objects were selected to be bright (M(B) < -28~mag) and have bright stars in the field, which could enable us to define the point spread function (PSF) accurately. The excellent seeing of La Palma (<0.9 arcsec thoughout the run) allowed us to detect extensions to the nuclear PSFs around three (one radio-loud and two radio-quiet) QSOs, out of 4 suitable targets. The extensions are most likely due to the host galaxies of these QSOs, with luminosities of at least 3-7% of the QSO luminosity. The most likely values for the luminosity of the host galaxies lie in the range 6-18% of the QSO luminosity. Our observations show that, if the extensions we have detected are indeed galaxies, extra...
Galaxy Clustering at z ~ 2 and Halo Radii
Roukema, B F; Mobasher, B; Bajtlik, S; Roukema, Boudewijn F.; Valls-Gabaud, David; Mobasher, Bahram; Bajtlik, Stanislaw
1999-01-01
The amplitude of the angular two-point galaxy correlation function w(\\theta) for galaxies at z~2 is estimated for galaxies in the Hubble Deep Field by using a U < 27 complete sub-sample. (i) It is confirmed that the amplitude of the correlation can be corrected for the integral constraint without having to make assumptions about the shape of the correlation function and by avoiding the introduction of linear error terms. The estimate using this technique is w(5'') = 0.10 \\pm 0.09. (ii) If the biases introduced in faint galaxy selection due to obscuration by large objects are not corrected for by masking areas around them, then the estimate would be w(5'') =0.16\\pm 0.07. (iii) The effective (3-D) galaxy pair separation at 5'' and this redshift range is ~ 25-250 /h kpc, so the correction to the spatial correlation function considered. For clustering stable in proper units in an Ømega=1,\\lambda=0 universe, our w(5\\arcs) estimate (a) implies a present-day correlation length of r_0 ~ 2.6^{+1.1}_{-1.7}/h Mpc if...
Toda lattices with indefinite metric II: Topology of the iso-spectral manifolds
Kodama, Yuji; Ye, Jian
1998-10-01
We consider the iso-spectral real manifolds of tridiagonal Hessenberg matrices with distinct real eigenvalues. The manifolds are described by the iso-spectral flows of indefinite Toda lattice equations introduced by the authors [Physica D 91 (1996) 321-339]. These Toda lattices consist of 2 N-1 different systems with hamiltonians H = {1}/{2} Σ k=1N y k2 + Σ k=1N-1 s ks k+1exp(x k-x k+1) , where sk = ±1, which blow up in finite time except the case with all sksk+1 = 1. We compactify the manifolds by adding infinities according to the Toda flows. The resulting manifolds are shown to be nonorientable for N > 2, and the symmetry group is the semi-direct product of ( Z2) N-1 and the permutation group S n. These properties identify themselves with “small covers” introduced by Davis and Januszkiewicz [Duke Math. J. 62 (1991) 417-451]. As a corollary of our construction, we give a formula for the total number of zeros for a system of exponential polynomials generated as Hankel determinants.
Kuramoto dynamics in Hamiltonian systems.
Witthaut, Dirk; Timme, Marc
2014-09-01
The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony (phase locking). Here we present a classical Hamiltonian (and thus conservative) system with 2N state variables that in its action-angle representation exactly yields Kuramoto dynamics on N-dimensional invariant manifolds. We show that locking of the phase of one oscillator on a Kuramoto manifold to the average phase emerges where the transverse Hamiltonian action dynamics of that specific oscillator becomes unstable. Moreover, the inverse participation ratio of the Hamiltonian dynamics perturbed off the manifold indicates the global synchronization transition point for finite N more precisely than the standard Kuramoto order parameter. The uncovered Kuramoto dynamics in Hamiltonian systems thus distinctly links dissipative to conservative dynamics.
Continuum Hamiltonian Hopf Bifurcation II
Hagstrom, G I
2013-01-01
Building on the development of [MOR13], bifurcation of unstable modes that emerge from continuous spectra in a class of infinite-dimensional noncanonical Hamiltonian systems is investigated. Of main interest is a bifurcation termed the continuum Hamiltonian Hopf (CHH) bifurcation, which is an infinite-dimensional analog of the usual Hamiltonian Hopf (HH) bifurcation. Necessary notions pertaining to spectra, structural stability, signature of the continuous spectra, and normal forms are described. The theory developed is applicable to a wide class of 2+1 noncanonical Hamiltonian matter models, but the specific example of the Vlasov-Poisson system linearized about homogeneous (spatially independent) equilibria is treated in detail. For this example, structural (in)stability is established in an appropriate functional analytic setting, and two kinds of bifurcations are considered, one at infinite and one at finite wavenumber. After defining and describing the notion of dynamical accessibility, Kre\\u{i}n-like the...
Hamiltonian Structure of PI Hierarchy
Kanehisa Takasaki
2007-03-01
Full Text Available The string equation of type (2,2g+1 may be thought of as a higher order analogue of the first Painlevé equation that corresponds to the case of g = 1. For g > 1, this equation is accompanied with a finite set of commuting isomonodromic deformations, and they altogether form a hierarchy called the PI hierarchy. This hierarchy gives an isomonodromic analogue of the well known Mumford system. The Hamiltonian structure of the Lax equations can be formulated by the same Poisson structure as the Mumford system. A set of Darboux coordinates, which have been used for the Mumford system, can be introduced in this hierarchy as well. The equations of motion in these Darboux coordinates turn out to take a Hamiltonian form, but the Hamiltonians are different from the Hamiltonians of the Lax equations (except for the lowest one that corresponds to the string equation itself.
Alternative Hamiltonian representation for gravity
Rosas-RodrIguez, R [Instituto de Fisica, Universidad Autonoma de Puebla, Apdo. Postal J-48, 72570, Puebla, Pue. (Mexico)
2007-11-15
By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity.
Hamiltonian analysis of interacting fluids
Banerjee, Rabin; Mitra, Arpan Krishna [S. N. Bose National Centre for Basic Sciences, Kolkata (India); Ghosh, Subir [Indian Statistical Institute, Kolkata (India)
2015-05-15
Ideal fluid dynamics is studied as a relativistic field theory with particular stress on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary roles of the canonical (Noether) stress tensor and the symmetric one obtained by metric variation are discussed. (orig.)
When are vector fields hamiltonian?
Crehan, P
1994-01-01
Dynamical systems can be quantised only if they are Hamiltonian. This prompts the question from which our talk gets its title. We show how the simple predator-prey equation and the damped harmonic oscillator can be considered to be Hamiltonian with respect to an infinite number of non-standard Poisson brackets. This raises some interesting questions about the nature of quantisation. Questions which are valid even for flows which possess a canonical structure.
When a local Hamiltonian must be frustration-free.
Sattath, Or; Morampudi, Siddhardh C; Laumann, Chris R; Moessner, Roderich
2016-06-07
A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion-a sufficient condition-under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer's theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian's interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.
None
2013-10-10
The U.S. Department of Energy (DOE) Oak Ridge Office of Environmental Management selected Oak Ridge Associated Universities (ORAU), through the Oak Ridge Institute for Science and Education (ORISE) contract, to perform independent verification (IV) at Zone 2 of the East Tennessee Technology Park (ETTP) in Oak Ridge, Tennessee. ORAU has concluded IV surveys, per the project-specific plan (PSP) (ORAU 2013a) covering exposure units (EUs) Z2-24, -31, -32, and -36. The objective of this effort was to verify the following. • Target EUs comply with requirements in the Zone 2 Record of Decision (ROD) (DOE 2005), as implemented by using the dynamic verification strategy presented in the dynamic work plan (DWP) (BJC 2007) • Commitments in the DWP were adequately implemented, as verified via IV surveys and soil sampling The Zone 2 ROD establishes maximum remediation level (RLmax) values and average RL (RLavg) values for the primary contaminants of concern (COCs) U-234, U-235, U-238, Cs-137, Np-237, Ra-226, Th-232, arsenic, mercury, and polychlorinated biphenyls (PCBs). Table 1.1 lists Zone 2 COCs with associated RLs. Additional radiological and chemical contaminants were also identified during past characterization and monitoring actions, though the ROD does not present RLs for these potential contaminants. IV activities focused on the identification and quantification of ROD-specific COCs in surface soils, but also generated data for other analytes to support future decisions. ORAU personnel also reviewed EU-specific phased construction completion reports (PCCRs) to focus IV activities and identify potential judgmental sample locations, if any.
Interchange graphs and the Hamiltonian cycle polytope
Sierksma, G
1998-01-01
This paper answers the (non)adjacency question for the whole spectrum of Hamiltonian cycles on the Hamiltonian cycle polytope (HC-polytope), also called the symmetric traveling salesman polytope, namely from Hamiltonian cycles that differ in only two edges through Hamiltonian cycles that are edge di
Hamiltonian description of the ideal fluid
Morrison, P.J.
1994-01-01
Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems.
Z-2 Suit Support Stand and MKIII Suit Center of Gravity Test
Nguyen, Tuan Q.
2014-01-01
NASA's next generation spacesuits are the Z-Series suits, made for a range of possible exploration missions in the near future. The prototype Z-1 suit has been developed and assembled to incorporate new technologies that has never been utilized before in the Apollo suits and the Extravehicular Mobility Unit (EMU). NASA engineers tested the Z-1 suit extensively in order to developed design requirements for the new Z-2 suit. At the end of 2014, NASA will be receiving the new Z-2 suit to perform more testing and to further develop the new technologies of the suit. In order to do so, a suit support stand will be designed and fabricated to support the Z-2 suit during maintenance, sizing, and structural leakage testing. The Z-2 Suit Support Stand (Z2SSS) will be utilized for these purposes in the early testing stages of the Z-2 suit.
AGN Feedback in Overdense Environments at z=2.23
Lucy, Adrian B.; Lehmer, B.; Alexander, D. M.; Best, P.; Geach, J.; Harrison, C. M.; Hornschemeier, A. E.; Matsuda, Y.; Mullaney, J.; Smail, I.; Sobral, D.
2013-01-01
We present results from a ≈100 ks Chandra observation of the 2QZ Cluster 1004+00 galaxy overdensity at z=2.23. This 2QZ Clus structure was first identified as an overdensity of four optically-selected quasars; that sample was subsequently found to overlap with an overdensity of 22 Hα-emitting galaxies (HAEs) identified through narrow and broad band near-infrared imaging by Matsuda et al. (2011). In addition to the preselected quasars in 2QZ Clus, our Chandra observation reveals that a further three HAEs are X-ray sources, all characterized by X-ray luminosities and spectral slopes consistent with unobscured active galactic nuclei (AGN). In total, we find that ≈30% of HAEs in our observed region of 2QZ Clus are AGN. This AGN fraction is high compared to AGN fractions among HAEs in the Chandra-COSMOS field (C-COSMOS), and if this enhancement is purely a result of the quasar selection bias of our sample, we estimate that such activity is rare at this redshift. Hα is a tracer of star formation, so 2QZ Clus is well suited to the investigation of the coeval growth of supermassive black holes and their host galaxies in the precursors to rich local clusters. Moreover, we have an ideal control sample in C-COSMOS; this survey contains a large sample of HAEs classified identically using infrared imaging, but without any selection of quasars. We calculate AGN fraction as a function of galaxy overdensity in C-COSMOS, and perform stacking analyses of Chandra and 250μ Herschel SPIRE data to obtain mean black hole accretion rates dMBH/dt and star formation rates SFR. Preliminary results indicate that dMBH/dt and its ratio to SFR are significantly elevated in 2QZ Clus compared to similarly overdense regions of C-COSMOS. We discuss these relations in the context of theoretical models describing the emergence of the MBH/Mgal relation of the local Universe.
Equilibration via Gaussification in Fermionic Lattice Systems
Gluza, M.; Krumnow, C.; Friesdorf, M.; Gogolin, C.; Eisert, J.
2016-11-01
In this Letter, we present a result on the nonequilibrium dynamics causing equilibration and Gaussification of quadratic noninteracting fermionic Hamiltonians. Specifically, based on two basic assumptions—clustering of correlations in the initial state and the Hamiltonian exhibiting delocalizing transport—we prove that non-Gaussian initial states become locally indistinguishable from fermionic Gaussian states after a short and well controlled time. This relaxation dynamics is governed by a power-law independent of the system size. Our argument is general enough to allow for pure and mixed initial states, including thermal and ground states of interacting Hamiltonians on large classes of lattices as well as certain spin systems. The argument gives rise to rigorously proven instances of a convergence to a generalized Gibbs ensemble. Our results allow us to develop an intuition of equilibration that is expected to be more generally valid and relates to current experiments of cold atoms in optical lattices.
Magnetic translation symmetry on the lattice
Sekiguchi, Ken-ichi; Okamoto, Tomohiro; Fujiwara, Takanori
2008-01-01
Magnetic translation symmetry on a finite periodic square lattice is investigated for an arbitrary uniform magnetic field in arbitrary dimensions. It can be used to classify eigenvectors of the Hamiltonian. The system can be converted to another system of half or lower dimensions. A higher dimensional generalization of Harper equation is obtained for tight-binding systems.
FAN Hong-Yi; LIN Jing-Xian
2001-01-01
In dealing with the square lattice model,we replace the traditionally needed Born-Von Karmann periodic boundary condition with additional Hamiltonian terms to make up a ring lattice.In doing so,the lattice Green's function of an infinite square lattice in the second nearest-neighbour interaction approximation can be derived by means of the matrix Green's function method.It is shown that the density of states may change when the second nearest-neighbour interaction is turned on.``
Quantum spin liquid in a breathing kagome lattice
Schaffer, Robert; Huh, Yejin; Hwang, Kyusung; Kim, Yong Baek
2017-02-01
Motivated by recent experiments on the vanadium oxyfluoride material DQVOF, we examine possible spin liquid phases on a breathing kagome lattice of S =1 /2 spins. By performing a projective symmetry group analysis, we determine the possible phases for both fermionic and bosonic Z2 spin liquids on this lattice, and establish the correspondence between the two. The nature of the ground state of the Heisenberg model on the isotropic kagome lattice is a hotly debated topic, with both Z2 and U(1) spin liquids argued to be plausible ground states. Using variational Monte Carlo techniques, we show that a gapped Z2 spin liquid emerges as the clear ground state in the presence of this breathing anisotropy. Our results suggest that the breathing anisotropy helps to stabilize this spin liquid ground state, which may aid us in understanding the results of experiments and help to direct future numerical studies on these systems.
Hamiltonian Dynamics of Preferential Attachment
Zuev, Konstantin; Krioukov, Dmitri
2015-01-01
Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment, known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evolution of a dynamical system is described by Hamilton's equations. We derive the explicit form of the Hamiltonian that governs network growth in preferential attachment. This Hamiltonian turns out to be nearly identical to graph energy in the configuration model, which shows that the ensemble of random graphs generated by preferential attachment is nearly identical to the ensemble of random graphs with scale-free degree d...
The electronic Hamiltonian for cuprates
Annett, James F.; Mcmahan, A. K.; Martin, Richard M.
1991-01-01
A realistic many-body Hamiltonian for the cuprate superconductors should include both copper d and oxygen p states, hopping matrix elements between them, and Coulomb energies, both on-site and inter-site. We have developed a novel computational scheme for deriving the relevant parameters ab initio from a constrained occupation local density functional. The scheme includes numerical calculation of appropriate Wannier functions for the copper and oxygen states. Explicit parameter values are given for La2CuO4. These parameters are generally consistent with other estimates and with the observed superexchange energy. Secondly, we address whether this complicated multi-band Hamiltonian can be reduced to a simpler one with fewer basis states per unit cell. We propose a mapping onto a new two-band effective Hamiltonian with one copper d and one oxygen p derived state per unit cell. This mapping takes into account the large oxygen-oxygen hopping given by the ab initio calculations.
First principles of Hamiltonian medicine.
Crespi, Bernard; Foster, Kevin; Úbeda, Francisco
2014-05-19
We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease.
Unified Hamiltonian for conducting polymers
Leitão Botelho, André; Shin, Yongwoo; Li, Minghai; Jiang, Lili; Lin, Xi
2011-11-01
Two transferable physical parameters are incorporated into the Su-Schrieffer-Heeger Hamiltonian to model conducting polymers beyond polyacetylene: the parameter γ scales the electron-phonon coupling strength in aromatic rings and the other parameter ɛ specifies the heterogeneous core charges. This generic Hamiltonian predicts the fundamental band gaps of polythiophene, polypyrrole, polyfuran, poly-(p-phenylene), poly-(p-phenylene vinylene), and polyacenes, and their oligomers of all lengths, with an accuracy exceeding time-dependent density functional theory. Its computational costs for moderate-length polymer chains are more than eight orders of magnitude lower than first-principles approaches.
Hamiltonian systems as selfdual equations
2008-01-01
Hamiltonian systems with various time boundary conditions are formulated as absolute minima of newly devised non-negative action func-tionals obtained by a generalization of Bogomolnyi's trick of 'completing squares'. Reminiscent of the selfdual Yang-Mills equations, they are not derived from the fact that they are critical points (i.e., from the correspond- ing Euler-Lagrange equations) but from being zeroes of the corresponding non-negative Lagrangians. A general method for resolving such variational problems is also described and applied to the construction of periodic solutions for Hamiltonian systems, but also to study certain Lagrangian intersections.
Relativistic Many-Body Hamiltonian Approach to Mesons
Llanes-Estrada, F J; Llanes-Estrada, Felipe J.; Cotanch, Stephen R.
2002-01-01
We represent QCD at the hadronic scale by means of an effective Hamiltonian, $H$, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is explicity broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. This interaction generates an infrared integrable singularity and we detail the computationally intensive procedure necessary for numerical solution. We focus upon applications for the $u, d, s$ and $c$ quark flavors and compute the mass spectrum for the pseudoscalar, scalar and vector mesons. We also perform a comparative study of alternative many-body techniques for approximately diagonalizing $H$: BCS for the vacuum ground state; TDA and RPA for the excited hadron states. The Dirac structure of the field theoretical Hamiltonian naturally generates spin-dependent interactions, including tensor, spin-orbit and hyperfine, and we clarify the degree of level splitting due to both spin an...
Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems.
Custódio, M S; Manchein, C; Beims, M W
2012-06-01
The dynamics in weakly chaotic Hamiltonian systems strongly depends on initial conditions (ICs) and little can be affirmed about generic behaviors. Using two distinct Hamiltonian systems, namely one particle in an open rectangular billiard and four particles globally coupled on a discrete lattice, we show that in these models, the transition from integrable motion to weak chaos emerges via chaotic stripes as the nonlinear parameter is increased. The stripes represent intervals of initial conditions which generate chaotic trajectories and increase with the nonlinear parameter of the system. In the billiard case, the initial conditions are the injection angles. For higher-dimensional systems and small nonlinearities, the chaotic stripes are the initial condition inside which Arnold diffusion occurs.
Diagonalization of the XXZ Hamiltonian by Vertex Operators
Davies, B; Jimbo, M; Miwa, T; Nakayashiki, A; Davies, Brian; Foda, Omar; Jimbo, Michio; Miwa, Tetsuji; Nakayashiki, Atsushi
1993-01-01
We diagonalize the anti-ferroelectric XXZ-Hamiltonian directly in the thermodynamic limit, where the model becomes invariant under the action of affine U_q( sl(2) ). Our method is based on the representation theory of quantum affine algebras, the related vertex operators and KZ equation, and thereby bypasses the usual process of starting from a finite lattice, taking the thermodynamic limit and filling the Dirac sea. From recent results on the algebraic structure of the corner transfer matrix of the model, we obtain the vacuum vector of the Hamiltonian. The rest of the eigenvectors are obtained by applying the vertex operators, which act as particle creation operators in the space of eigenvectors. We check the agreement of our results with those obtained using the Bethe Ansatz in a number of cases, and with others obtained in the scaling limit --- the $su(2)$-invariant Thirring model.
Pseudogene CYP4Z2P 3′UTR promotes angiogenesis in breast cancer
Zheng, Lufeng; Li, Xiaoman; Gu, Yi; Ma, Yihua; Xi, Tao, E-mail: xitao18@hotmail.com
2014-10-24
Highlights: • A new critical role of pseudogene CYP4Z2P 3′UTR in breast cancer is proposed. • We examine the level of pseudogene CYP4Z2P 3′UTR in breast cancer tissues. • The functions of CYP4Z2P 3′UTR and mechanism were studied. • The mechanism provides new insights for the breast cancer progression. - Abstract: Pseudogenes have long been marked as “false” genes, which are similar with real genes but have no apparent function. The 3′UTR is well-known to regulate gene expression post-transcriptionally. Our recent evidence, however, indicates novel functional roles of pseudogene CYP4Z2P 3′UTR (Z2P-UTR). We found that ectopic expression of Z2P-UTR in breast cancer cells significantly increased the expression of VEGF-A without affecting cell proliferation in vitro. Meanwhile, conditioned medium (CM) from Z2P-UTR overexpression cells enhanced proliferation, migration and tube formation of HUVEC, and promoted angiogenesis in ex vivo models. Also, CM increased the expression of VEGFR2 in HUVEC. Our data suggest that Z2P-UTR can promote breast cancer angiogenesis partly via paracrine pathway of VEGF-A/VEGFR2.
Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
Wiese, U -J
2013-01-01
Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is non-perturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should al...
When a local Hamiltonian must be frustration-free
Sattath, Or; Morampudi, Siddhardh C.; Laumann, Chris R.; Moessner, Roderich
2016-06-01
A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion—a sufficient condition—under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer’s theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian’s interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.
Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter
Cong, Iris; Cheng, Meng; Wang, Zhenghan
2017-07-01
We present an exactly solvable lattice Hamiltonian to realize gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories. We classify the elementary excitations on the boundary, and systematically describe the bulk-to-boundary condensation procedure. We also present the parallel algebraic/categorical structure of gapped boundaries.
Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter
Cong, Iris; Cheng, Meng; Wang, Zhenghan
2017-10-01
We present an exactly solvable lattice Hamiltonian to realize gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories. We classify the elementary excitations on the boundary, and systematically describe the bulk-to-boundary condensation procedure. We also present the parallel algebraic/categorical structure of gapped boundaries.
Ajoy, Ashok; Cappellaro, Paola
2013-05-31
We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a dynamical construction of a weighting function combined with a Bragg grating. As an example, we demonstrate how to generate the ideal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings starting from a large spin network, such as one naturally occurring in crystals, while decoupling all unwanted interactions. For realistic experimental parameters, our method can be used to drive almost perfect quantum information transport at room temperature. The Hamiltonian engineering method can be made more robust under decoherence and coupling disorder by a novel apodization scheme. Thus, the method is quite general and can be used to engineer the Hamiltonian of many complex spin lattices with different topologies and interactions.
Skurnick, Ronald; Davi, Charles; Skurnick, Mia
2005-01-01
Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…
Maslov index for Hamiltonian systems
Alessandro Portaluri
2008-01-01
Full Text Available The aim of this article is to give an explicit formula for computing the Maslov index of the fundamental solutions of linear autonomous Hamiltonian systems in terms of the Conley-Zehnder index and the map time one flow.
Dynamical stability of Hamiltonian systems
无
2000-01-01
Dynamical stability has become the center of study on Hamiltonian system. In this article we intro-duce the recent development in some areas closely related to this topic, such as the KAM theory, Mather theory, Arnolddiffusion and non-singular collision of n-body problem.
Time-reversible Hamiltonian systems
Schaft, Arjan van der
1982-01-01
It is shown that transfer matrices satisfying G(-s) = G(s) = G^T(-s) have a minimal Hamiltonian realization with an energy which is the sum of potential and kinetic energy, yielding the time reversibility of the equations. Furthermore connections are made with an associated gradient system. The
Advances in Lattice Quantum Chromodynamics
McGlynn, Greg
In this thesis we make four contributions to the state of the art in numerical lattice simulations of quantum chromodynamics (QCD). First, we present the most detailed investigation yet of the autocorrelations of topological observations in hybrid Monte Carlo simulations of QCD and of the effects of the boundary conditions on these autocorrelations. This results in a numerical criterion for deciding when open boundary conditions are useful for reducing these autocorrelations, which are a major barrier to reliable calculations at fine lattice spacings. Second, we develop a dislocation-enhancing determinant, and demonstrate that it reduces the autocorrelation time of the topological charge. This alleviates problems with slow topological tunneling at fine lattice spacings, enabling simulations on fine lattices to be completed with much less computational effort. Third, we show how to apply the recently developed zMobius technique to hybrid Monte Carlo evolutions with domain wall fermions, achieving nearly a factor of two speedup in the light quark determinant, the single most expensive part of the calculation. The dislocation-enhancing determinant and the zMobius technique have enabled us to begin simulations of fine ensembles with four flavors of dynamical domain wall quarks. Finally, we show how to include the previously-neglected G1 operator in nonperturbative renormalization of the DeltaS = 1 effective weak Hamiltonian on the lattice. This removes an important systematic error in lattice calculations of weak matrix elements, in particular the important K → pipi decay.
On third order integrable vector Hamiltonian equations
Meshkov, A. G.; Sokolov, V. V.
2017-03-01
A complete list of third order vector Hamiltonian equations with the Hamiltonian operator Dx having an infinite series of higher conservation laws is presented. A new vector integrable equation on the sphere is found.
Hamiltonian realizations of nonlinear adjoint operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2002-01-01
This paper addresses the issue of state-space realizations for nonlinear adjoint operators. In particular, the relationships between nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are established. Then, characterizations of the adjoints of control
Hamiltonian Realizations of Nonlinear Adjoint Operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel ope
Quantum Jacobi fields in Hamiltonian mechanics
Giachetta, G; Sardanashvily, G
2000-01-01
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
Quantization of noncommutative completely integrable Hamiltonian systems
Giachetta, G. [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino (Italy); Mangiarotti, L. [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino (Italy); Sardanashvily, G. [Department of Theoretical Physics, Moscow State University, 117234 Moscow (Russian Federation)]. E-mail: gennadi.sardanashvily@unicam.it
2007-02-26
Integrals of motion of a Hamiltonian system need not commute. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as the Abelian one.
Scattering matrix of arbitrary tight-binding Hamiltonians
Ramírez, C.; Medina-Amayo, L. A.
2017-03-01
A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kinds of fundamental structures is given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.
Port-Hamiltonian systems: an introductory survey
Schaft, van der Arjan; Sanz-Sole, M.; Soria, J.; Varona, J.L.; Verdera, J.
2006-01-01
The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian
New sufficient conditions for Hamiltonian paths.
Rahman, M Sohel; Kaykobad, M; Firoz, Jesun Sahariar
2014-01-01
A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph.
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
Geometric Hamiltonian structures and perturbation theory
Omohundro, S.
1984-08-01
We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging.
Driving Hamiltonian in a Quantum Search Problem
Oshima, K
2001-01-01
We examine the driving Hamiltonian in the analog analogue of Grover's algorithm by Farhi and Gutmann. For a quantum system with a given Hamiltonian $E|w> $ from an initial state $|s>$, the driving Hamiltonian $E^{\\prime}|s> < s|(E^{\\prime} \
Wenqi Li
Full Text Available The hormone auxin plays an important role not only in the growth and development of rice, but also in its defense responses. We've previously shown that the P450 gene CYP71Z2 enhances disease resistance to pathogens through regulation of phytoalexin biosynthesis in rice, though it remains unclear if auxin is involved in this process or not.The expression of CYP71Z2 was induced by Xanthomonas oryzae pv. oryzae (Xoo inoculation was analyzed by qRT-PCR, with GUS histochemical staining showing that CYP71Z2 expression was limited to roots, blades and nodes. Overexpression of CYP71Z2 in rice durably and stably increased resistance to Xoo, though no significant difference in disease resistance was detected between CYP71Z2-RNA interference (RNAi rice and wild-type. Moreover, IAA concentration was determined using the HPLC/electrospray ionization/tandem mass spectrometry system. The accumulation of IAA was significantly reduced in CYP71Z2-overexpressing rice regardless of whether plants were inoculated or not, whereas it was unaffected in CYP71Z2-RNAi rice. Furthermore, the expression of genes related to IAA, expansin and SA/JA signaling pathways was suppressed in CYP71Z2-overexpressing rice with or without inoculation.These results suggest that CYP71Z2-mediated resistance to Xoo may be via suppression of IAA signaling in rice. Our studies also provide comprehensive insight into molecular mechanism of resistance to Xoo mediated by IAA in rice. Moreover, an available approach for understanding the P450 gene functions in interaction between rice and pathogens has been provided.
Lattice realization of the generalized chiral symmetry in two dimensions
Kawarabayashi, Tohru; Aoki, Hideo; Hatsugai, Yasuhiro
2016-12-01
While it has been pointed out that the chiral symmetry, which is important for the Dirac fermions in graphene, can be generalized to tilted Dirac fermions as in organic metals, such a generalized symmetry was so far defined only for a continuous low-energy Hamiltonian. Here we show that the generalized chiral symmetry can be rigorously defined for lattice fermions as well. A key concept is a continuous "algebraic deformation" of Hamiltonians, which generates lattice models with the generalized chiral symmetry from those with the conventional chiral symmetry. This enables us to explicitly express zero modes of the deformed Hamiltonian in terms of that of the original Hamiltonian. Another virtue is that the deformation can be extended to nonuniform systems, such as fermion-vortex systems and disordered systems. Application to fermion vortices in a deformed system shows how the zero modes for the conventional Dirac fermions with vortices can be extended to the tilted case.
Lattice gauge theories and spin models
Mathur, Manu; Sreeraj, T. P.
2016-10-01
The Wegner Z2 gauge theory-Z2 Ising spin model duality in (2 +1 ) dimensions is revisited and derived through a series of canonical transformations. The Kramers-Wannier duality is similarly obtained. The Wegner Z2 gauge-spin duality is directly generalized to SU(N) lattice gauge theory in (2 +1 ) dimensions to obtain the SU(N) spin model in terms of the SU(N) magnetic fields and their conjugate SU(N) electric scalar potentials. The exact and complete solutions of the Z2, U(1), SU(N) Gauss law constraints in terms of the corresponding spin or dual potential operators are given. The gauge-spin duality naturally leads to a new gauge invariant magnetic disorder operator for SU(N) lattice gauge theory which produces a magnetic vortex on the plaquette. A variational ground state of the SU(2) spin model with nearest neighbor interactions is constructed to analyze SU(2) gauge theory.
The $Z_2$ Index of Disordered Topological Insulators with Time Reversal Symmetry
Katsura, Hosho
2015-01-01
We study disordered topological insulators with time reversal symmetry. Relying on the noncommutative index theorem which relates the Chern number to the projection onto the Fermi sea and the magnetic flux operator, we give a precise definition of the $Z_2$ index which is a noncommutative analogue of the Atiyah-Singer $Z_2$ index. We prove that the noncommutative $Z_2$ index is robust against any time-reversal symmetric perturbation including disorder potentials as long as the spectral gap at the Fermi level does not close.
Two-dimensional spin liquids with Z2 topological order in an array of quantum wires
Patel, Aavishkar A.; Chowdhury, Debanjan
2016-11-01
Insulating Z2 spin liquids are a phase of matter with bulk anyonic quasiparticle excitations and ground-state degeneracies on manifolds with nontrivial topology. We construct a time-reversal symmetric Z2 spin liquid in two spatial dimensions using an array of quantum wires. We identify the anyons as kinks in the appropriate Luttinger-liquid description, compute their mutual statistics, and construct local operators that transport these quasiparticles. We also present a construction of a fractionalized Fermi liquid (FL*) by coupling the spin sector of the Z2 spin liquid to a Fermi liquid via a Kondo-like coupling.
Fring, Andreas
2016-01-01
We propose a procedure to obtain exact analytical solutions to the time-dependent Schr\\"{o}dinger equations involving explicit time-dependent Hermitian Hamitonians from solutions to time-independent non-Hermitian Hamiltonian systems and the time-dependent Dyson relation together with the time-dependent quasi-Hermiticity relation. We illustrate the working of this method for a simple Hermitian Rabi-type model by relating it to a non-Hermitian time-independent system corresponding to the one-site lattice Yang-Lee model.
Z2 Invariance of Germanene on MoS2 from First Principles
Amlaki, T.; Bokdam, M.; Kelly, P.J.
2016-01-01
We present a low energy Hamiltonian generalized to describe how the energy bands of germanene (Ge ¯ ¯ ¯ ¯ ) are modified by interaction with a substrate or a capping layer. The parameters that enter the Hamiltonian are determined from first-principles relativistic calculations for Ge ¯ ¯ ¯ ¯ |MoS
Lattice Embedding of Heronian Simplices
Lunnon, W Fred
2012-01-01
A rational triangle has rational edge-lengths and area; a rational tetrahedron has rational faces and volume; either is Heronian when its edge-lengths are integer, and proper when its content is nonzero. A variant proof is given, via complex number GCD, of the previously known result that any Heronian triangle may be embedded in the Cartesian lattice Z^2; it is then shown that, for a proper triangle, such an embedding is unique modulo lattice isometry; finally the method is extended via quaternion GCD to tetrahedra in Z^3, where uniqueness no longer obtains, and embeddings also exist which are unobtainable by this construction. The requisite complex and quaternionic number theoretic background is summarised beforehand. Subsequent sections engage with subsidiary implementation issues: initial rational embedding, canonical reduction, exhaustive search for embeddings additional to those yielded via GCD; and illustrative numerical examples are provided. A counter-example shows that this approach must fail in high...
Wang, Da-Wei; Zhu, Shi-Yao; Scully, Marlan O
2014-01-01
We show that the timed Dicke states of a collection of three-level atoms can form a tight-binding lattice in the momentum space. This lattice, coined the superradiance lattice (SL), can be constructed based on an electromagnetically induced transparency (EIT) system. For a one-dimensional SL, we need the coupling field of the EIT system to be a standing wave. The detuning between the two components of the standing wave introduces an effective electric field. The quantum behaviours of electrons in lattices, such as Bloch oscillations, Wannier-Stark ladders, Bloch band collapsing and dynamic localization can be observed in the SL. The SL can be extended to two, three and even higher dimensions where no analogous real space lattices exist and new physics are waiting to be explored.
Renormalized Effective QCD Hamiltonian Gluonic Sector
Robertson, D G; Szczepaniak, A P; Ji, C R; Cotanch, S R
1999-01-01
Extending previous QCD Hamiltonian studies, we present a new renormalization procedure which generates an effective Hamiltonian for the gluon sector. The formulation is in the Coulomb gauge where the QCD Hamiltonian is renormalizable and the Gribov problem can be resolved. We utilize elements of the Glazek and Wilson regularization method but now introduce a continuous cut-off procedure which eliminates non-local counterterms. The effective Hamiltonian is then derived to second order in the strong coupling constant. The resulting renormalized Hamiltonian provides a realistic starting point for approximate many-body calculations of hadronic properties for systems with explicit gluon degrees of freedom.
Hamiltonian dynamics of extended objects
Capovilla, R [Departamento de FIsica, Centro de Investigacion y de Estudios Avanzados del IPN, Apdo Postal 14-740, 07000 Mexico, DF (Mexico); Guven, J [School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4 (Ireland); Rojas, E [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo Postal 70-543, 04510 Mexico, DF (Mexico)
2004-12-07
We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations.
Lowest Eigenvalues of Random Hamiltonians
Shen, J J; Arima, A; Yoshinaga, N
2008-01-01
In this paper we present results of the lowest eigenvalues of random Hamiltonians for both fermion and boson systems. We show that an empirical formula of evaluating the lowest eigenvalues of random Hamiltonians in terms of energy centroids and widths of eigenvalues are applicable to many different systems (except for $d$ boson systems). We improve the accuracy of the formula by adding moments higher than two. We suggest another new formula to evaluate the lowest eigenvalues for random matrices with large dimensions (20-5000). These empirical formulas are shown to be applicable not only to the evaluation of the lowest energy but also to the evaluation of excited energies of systems under random two-body interactions.
Hamiltonian formulation of teleparallel gravity
Ferraro, Rafael; Guzmán, María José
2016-11-01
The Hamiltonian formulation of the teleparallel equivalent of general relativity is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudoinverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first-class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms and the (local) Lorentz transformations of the vielbein. In particular, the Arnowitt, Deser, and Misner algebra of general relativity is recovered as a subalgebra.
On Hamiltonian formulation of cosmologies
K D Krori; S Dutta
2000-03-01
Novello et al [1,2] have shown that it is possible to ﬁnd a pair of canonically conjugate variables (written in terms of gauge-invariant variables) so as to obtain a Hamiltonian that describes the dynamics of a cosmological system. This opens up the way to the usual technique of quantization. Elbaz et al [4] have applied this method to the Hamiltonian formulation of FRW cosmological equations. This note presents a generalization of this approach to a variety of cosmologies. A general Schrödinger wave equation has been derived and exact solutions have been worked out for the stiff matter era for some cosmological models. It is argued that these solutions appear to hint at their possible relevance in the early phase of cosmological evolution.
A Hamiltonian approach to Thermodynamics
Baldiotti, M.C., E-mail: baldiotti@uel.br [Departamento de Física, Universidade Estadual de Londrina, 86051-990, Londrina-PR (Brazil); Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br [Universidade Federal do ABC, Av. dos Estados 5001, 09210-580, Santo André-SP (Brazil); Molina, C., E-mail: cmolina@usp.br [Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Bettio 1000, CEP 03828-000, São Paulo-SP (Brazil)
2016-10-15
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.
Hamiltonian formulation of teleparallel gravity
Ferraro, Rafael
2016-01-01
The Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudo-inverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms, and the (local) Lorentz transformations of the vielbein. In particular, the ADM algebra of general relativity is recovered as a sub-algebra.
Gauge-Higgs Unification on the Lattice
Irges, Nikos; Yoneyama, Kyoko
2012-01-01
The simplest Gauge-Higgs Unification model is a five-dimensional SU(2) gauge theory compactified on the S^1/Z_2 orbifold, such that on the four-dimensional boundaries of space-time there is an unbroken U(1) symmetry and a complex scalar, the latter identified with the Higgs boson. Perturbatively the U(1) remains spontaneously unbroken. Earlier lattice Monte Carlo simulations revealed however that the spontaneous breaking of the U(1) does occur at the non-perturbative level. Here, we verify the Monte Carlo result via an analytical lattice Mean-Field expansion.
Hamiltonian mechanics of stochastic acceleration.
Burby, J W; Zhmoginov, A I; Qin, H
2013-11-08
We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.
Hamiltonian chaos and fractional dynamics
Zaslavsky, George M
2008-01-01
The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image ...
The {\\mathbb{Z}_2}-Orbifold of the {\\mathcal{W}_3}-Algebra
Al-Ali, Masoumah; Linshaw, Andrew R.
2017-08-01
The Zamolodchikov {\\mathcal{W}_3}-algebra {\\mathcal{W}^c_3} with central charge c has full automorphism group {\\mathbb{Z}_2}. It was conjectured in the physics literature over 20 years ago that the orbifold {(\\mathcal{W}^c_3)^{\\mathbb{Z}_2}} is of type {\\mathcal{W}(2,6,8,10,12)} for generic values of c. We prove this conjecture for all {c \
A nonlinear lattice model for Heisenberg helimagnet and spin wave instabilities
Ludvin Felcy, A.; Latha, M. M.; Christal Vasanthi, C.
2016-10-01
We study the dynamics of a Heisenberg helimagnet by presenting a square lattice model and proposing the Hamiltonian associated with it. The corresponding equation of motion is constructed after averaging the Hamiltonian using a suitable wavefunction. The stability of the spin wave is discussed by means of Modulational Instability (MI) analysis. The influence of various types of inhomogeneities in the lattice is also investigated by improving the model.
Topological Insulators on the Ruby Lattice with Rashba Spin-Orbit Coupling
HOU Jing-Min; WANG Guo-Xiang
2013-01-01
We investigate a tight-binding model of the ruby lattice with Rashba spin-orbit coupling.We calculate the band structure of the lattice and evaluate the Z2 topological indices.According to the Z2 topological indices and the band structure,we present the phase diagrams of the lattice with different filling fractions.We find.that topological insulators occur in some range of parameters at 1/6,1/3,1/2,2/3 and 5/6 filling fractions.We analyze and discuss the characteristics of these topological insulators and their edge states.
Realizing the classical XY Hamiltonian in polariton simulators.
Berloff, Natalia G; Silva, Matteo; Kalinin, Kirill; Askitopoulos, Alexis; Töpfer, Julian D; Cilibrizzi, Pasquale; Langbein, Wolfgang; Lagoudakis, Pavlos G
2017-09-25
The vast majority of real-life optimization problems with a large number of degrees of freedom are intractable by classical computers, since their complexity grows exponentially fast with the number of variables. Many of these problems can be mapped into classical spin models, such as the Ising, the XY or the Heisenberg models, so that optimization problems are reduced to finding the global minimum of spin models. Here, we propose and investigate the potential of polariton graphs as an efficient analogue simulator for finding the global minimum of the XY model. By imprinting polariton condensate lattices of bespoke geometries we show that we can engineer various coupling strengths between the lattice sites and read out the result of the global minimization through the relative phases. Besides solving optimization problems, polariton graphs can simulate a large variety of systems undergoing the U(1) symmetry-breaking transition. We realize various magnetic phases, such as ferromagnetic, anti-ferromagnetic, and frustrated spin configurations on a linear chain, the unit cells of square and triangular lattices, a disordered graph, and demonstrate the potential for size scalability on an extended square lattice of 45 coherently coupled polariton condensates. Our results provide a route to study unconventional superfluids, spin liquids, Berezinskii-Kosterlitz-Thouless phase transition, and classical magnetism, among the many systems that are described by the XY Hamiltonian.
Zhang, N.G.; Henley, C.L.; Rischel, C.;
2002-01-01
We study the low-lying eigenenergy clustering patterns of quantum antiferromagnets with p sublattices (in particular p = 4). We treat each sublattice as a large spin, and using second-order degenerate perturbation theory, we derive the effective (biquadratic) Hamiltonian coupling the p large spins....... In order to compare with exact diagonalizations, the Hamiltonian is explicitly written for a finite-size lattice, and it contains information on energies of excited states as well as the ground state. The result is applied to the face-centered-cubic Type-I antiferromagnet of spin 1/2, including second...
XING Guan; WU Guo-Zhen
2001-01-01
A classical coset Hamiltonian is introduced for the system of one electron in multi-sites. By this Hamiltonian, thedynamical behaviour of the electronic motion can be readily simulated. The simulation reproduces the retardation of the electron density decay in a lattice with site energies randomly distributed － an analogy with Anderson localization. This algorithm is also applied to reproduce the Hammett equation which relates the reaction rate with the property of the substitutions in the organic chemical reactions. The advantages and shortcomings ofthis algorithm, as contrasted with traditional quantum methods such as the molecular orbital theory, are also discussed.
De Lyra, J L; Foong, S K; Gallivan, T E; Harrington, R; Kapulkin, A; Myers, E; Polchinski, Joseph; Lyra, Jorge de; Witt, Bryce De; Foong, See Kit; Gallivan, Timothy; Harrington, Rob; Kapulkin, Arie; Myers, Eric; Polchinski, Joseph
1992-01-01
The nonlinear sigma model for which the field takes its values in the coset space $O(1,2)/O(2)\\times Z_2$ is similar to quantum gravity in being perturbatively nonrenormalizable and having a noncompact curved configuration space. It is therefore a good model for testing nonperturbative methods that may be useful in quantum gravity, especially methods based on lattice field theory. In this paper we develop the theoretical framework necessary for recognizing and studying a consistent nonperturbative quantum field theory of the $O(1,2)/O(2)\\times Z_2$ model. We describe the action, the geometry of the configuration space, the conserved Noether currents, and the current algebra, and we construct a version of the Ward-Slavnov identity that makes it easy to switch from a given field to a nonlinearly related one. Renormalization of the model is defined via the effective action and via current algebra. The two definitions are shown to be equivalent. In a companion paper we develop a lattice formulation of the theory ...
Tamogami, Shigeru; Noge, Koji; Agrawal, Ganesh K; Rakwal, Randeep
2015-01-30
The medicinal herbal plant Achyranthes bidentata (A. bidentata) produces the sweet-odor ester - methyl (E)-2-hexenoate (1) as the major volatile in response to methyl jasmonate (MeJA). Here, we investigated the biosynthetic pathway of methyl (E)-2-hexenoate (1). The common plant precursor (Z)-3-hexenal was only slightly metabolized into methyl (E)-2-hexenoate (1), and its application scarcely enhanced the production of this ester. By contrast, a structurally related alcohol, (Z)-2-hexenol, as well as a deuteride derivative thereof could be efficiently metabolized into methyl (E)-2-hexenoate (1). Thus, we hypothesize that A. bidentata possess a specific pathway for the production of methyl (E)-2-hexenoate (1) from (Z)-2-hexenol in response to MeJA. Copyright © 2015 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.
Different models of gravitating Dirac fermions in optical lattices
Celi, Alessio
2017-07-01
In this paper I construct the naive lattice Dirac Hamiltonian describing the propagation of fermions in a generic 2D optical metric for different lattice and flux-lattice geometries. First, I apply a top-down constructive approach that we first proposed in [Boada et al., New J. Phys. 13, 035002 (2011)] to the honeycomb and to the brickwall lattices. I carefully discuss how gauge transformations that generalize momentum (and Dirac cone) shifts in the Brillouin zone in the Minkowski homogeneous case can be used in order to change the phases of the hopping. In particular, I show that lattice Dirac Hamiltonian for Rindler spacetime in the honeycomb and brickwall lattices can be realized by considering real and isotropic (but properly position dependent) tunneling terms. For completeness, I also discuss a suitable formulation of Rindler Dirac Hamiltonian in semi-synthetic brickwall and π-flux square lattices (where one of the dimension is implemented by using internal spin states of atoms as we originally proposed in [Boada et al., Phys. Rev. Lett. 108, 133001 (2012)] and [Celi et al., Phys. Rev. Lett. 112, 043001 (2014)]).
The Galaxy Counterparts of the two high-metallicity DLAs at z=2.412 and z=2.583 towards Q0918+1636
Fynbo, J P U; Christensen, L; Gallazzi, A; Krogager, J -K; Krühler, T; Ledoux, C; Maund, J; Møller, P; Noterdaeme, P; Rivera-Thorsen, T; Vestergaard, M
2013-01-01
The quasar Q0918+1636 (z=3.07) has two intervening high-metallicity Damped Lyman-alpha Absorbers (DLAs) along the line of sight, at redshifts of z=2.412 and 2.583. The z=2.583 DLA is located at a large impact parameter of 16.2 kpc, and despite this large impact parameter it has a very high metallicity (consistent with solar), a substantial fraction of H_2 molecules, and it is dusty as inferred from the reddened spectrum of the background QSO. The z=2.412 DLA has a metallicity of [M/H]=-0.6 (based on ZnII and SiII). In this paper we present new observations of this interesting sightline. HST/WFC3 imaging was obtained in the F606W, F105W and F160W bands. This is complemented by ground-based imaging in the u-, g-bands as well as K_s observations in the near-infrared (NIR). In addition, we present further spectroscopy with the ESO/VLT X-Shooter spectrograph. Based on these observations we obtain the following results: By fitting stellar population synthesis models to the photometric SED we constrain the physical ...
Monte Carlo Hamiltonian: Linear Potentials
LUO Xiang-Qian; LIU Jin-Jiang; HUANG Chun-Qing; JIANG Jun-Qin; Helmut KROGER
2002-01-01
We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. Weconsider two quantum mechanical models: a symmetric one V(x) = |x|/2; and an asymmetric one V(x) = ∞, forx ＜ 0 and V(x) = x, for x ≥ 0. The results for the spectrum, wave functions and thermodynamical observables are inagreement with the analytical or Runge-Kutta calculations.
LOCALIZATION THEOREM ON HAMILTONIAN GRAPHS
无
2000-01-01
Let G be a 2-connected graph of order n( 3).If I(u,v) S(u,v) or max {d(u),d(v)} n/2 for any two vertices u,v at distance two in an induced subgraph K1,3 or P3 of G,then G is hamiltonian.Here I(u,v) = ｜N(u)∩ N(v)｜,S(u,v) denotes thenumber of edges of maximum star containing u,v as an induced subgraph in G.
Discrete Hamiltonian for General Relativity
Ziprick, Jonathan
2015-01-01
Beginning from canonical general relativity written in terms of Ashtekar variables, we derive a discrete phase space with a physical Hamiltonian for gravity. The key idea is to define the gravitational fields within a complex of three-dimensional cells such that the dynamics is completely described by discrete boundary variables, and the full theory is recovered in the continuum limit. Canonical quantization is attainable within the loop quantum gravity framework, and we believe this will lead to a promising candidate for quantum gravity.
Chasing Hamiltonian structure in gyrokinetic theory
Burby, J W
2015-01-01
Hamiltonian structure is pursued and uncovered in collisional and collisionless gyrokinetic theory. A new Hamiltonian formulation of collisionless electromagnetic theory is presented that is ideally suited to implementation on modern supercomputers. The method used to uncover this structure is described in detail and applied to a number of examples, where several well-known plasma models are endowed with a Hamiltonian structure for the first time. The first energy- and momentum-conserving formulation of full-F collisional gyrokinetics is presented. In an effort to understand the theoretical underpinnings of this result at a deeper level, a \\emph{stochastic} Hamiltonian modeling approach is presented and applied to pitch angle scattering. Interestingly, the collision operator produced by the Hamiltonian approach is equal to the Lorentz operator plus higher-order terms, but does not exactly conserve energy. Conversely, the classical Lorentz collision operator is provably not Hamiltonian in the stochastic sense.
Topological spin models in Rydberg lattices
Kiffner, Martin; Jaksch, Dieter
2016-01-01
We show that resonant dipole-dipole interactions between Rydberg atoms in a triangular lattice can give rise to artificial magnetic fields for spin excitations. We consider the coherent dipole-dipole coupling between $np$ and $ns$ Rydberg states and derive an effective spin-1/2 Hamiltonian for the $np$ excitations. By breaking time-reversal symmetry via external fields we engineer complex hopping amplitudes for transitions between two rectangular sub-lattices. The phase of these hopping amplitudes depends on the direction of the hop. This gives rise to a staggered, artificial magnetic field which induces non-trivial topological effects. We calculate the single-particle band structure and investigate its Chern numbers as a function of the lattice parameters and the detuning between the two sub-lattices. We identify extended parameter regimes where the Chern number of the lowest band is $C=1$ or $C=2$.
Fractional Bloch oscillations in photonic lattices
Corrielli, Giacomo; Della Valle, Giuseppe; Longhi, Stefano; Osellame, Roberto; 10.1038/ncomms2578
2013-01-01
Bloch oscillations, the oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport. Originally studied in the context of electrons in crystals, Bloch oscillations manifest the wave nature of matter and are found in a wide variety of different physical systems. Here we report on the first experimental observation of fractional Bloch oscillations, using a photonic lattice as a model system of a two-particle extended Bose-Hubbard Hamiltonian. In our photonic simulator, the dynamics of two correlated particles hopping on a one-dimensional lattice is mapped into the motion of a single particle in a two-dimensional lattice with engineered defects and mimicked by light transport in a square waveguide lattice with a bent axis.
Fractional Bloch oscillations in photonic lattices.
Corrielli, Giacomo; Crespi, Andrea; Della Valle, Giuseppe; Longhi, Stefano; Osellame, Roberto
2013-01-01
Bloch oscillations, the oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport. Originally studied in the context of electrons in crystals, Bloch oscillations manifest the wave nature of matter and are found in a wide variety of different physical systems. Here we report on the first experimental observation of fractional Bloch oscillations, using a photonic lattice as a model system of a two-particle extended Bose-Hubbard Hamiltonian. In our photonic simulator, the dynamics of two correlated particles hopping on a one-dimensional lattice is mapped into the motion of a single particle in a two-dimensional lattice with engineered defects and mimicked by light transport in a square waveguide lattice with a bent axis.
The Fundamental Plane of massive quiescent galaxies out to z~2
van de Sande, Jesse; Franx, Marijn; Bezanson, Rachel; van Dokkum, Pieter G
2014-01-01
The Fundamental Plane (FP) of early-type galaxies, relating the effective radius, velocity dispersion, and surface brightness, has long been recognized as a unique tool for analyzing galaxy structure and evolution. With the discovery of distant quiescent galaxies and the introduction of high sensitivity near-infrared spectrographs, it is now possible to explore the FP out to z~2. In this Letter we study the evolution of the FP out to z~2 using kinematic measurements of massive quiescent galaxies ($M_{*}>10^{11} M_{\\odot}$). We find preliminary evidence for the existence of an FP out to z~2. The scatter of the FP, however, increases from z~0 to z~2, even when taking into account the larger measurement uncertainties at higher redshifts. We find a strong evolution of the zero point from z~2 to z~0: $\\Delta\\log_{10}M/L_g\\propto(-0.49\\pm0.03)~z$. In order to assess whether our spectroscopic sample is representative of the early-type galaxy population at all redshifts, we compare their rest-frame g-z colors with th...
Magnetic translation group on Abrikosov lattice
Goto, Akira
1996-02-01
We investigate the magnetic translational symmetry of the Bogoliubov-de Gennes equation describing quasiparticles in the vortex lattice state. Magnetic translation group is formulated for the quasiparticles and the generalized Bloch theorem is established. Projection operators are obtained and used to construct the symmetry adopted basis functions. Careful treatment of the phase of the pair potential and its quasiperiodicity enable us to get the magnetic Wannier functions, which are utilized to justify a part of Canel's assertion about the effective Hamiltonian theory.
Stochastic averaging of quasi-Hamiltonian systems
朱位秋
1996-01-01
A stochastic averaging method is proposed for quasi-Hamiltonian systems (Hamiltonian systems with light dampings subject to weakly stochastic excitations). Various versions of the method, depending on whether the associated Hamiltonian systems are integrable or nonintegrable, resonant or nonresonant, are discussed. It is pointed out that the standard stochastic averaging method and the stochastic averaging method of energy envelope are special cases of the stochastic averaging method of quasi-Hamiltonian systems and that the results obtained by this method for several examples prove its effectiveness.
Hamiltonian cosmology in bigravity and massive gravity
Soloviev, Vladimir O
2015-01-01
In the Hamiltonian language we provide a study of flat-space cosmology in bigravity and massive gravity constructed mostly with de Rham, Gabadadze, Tolley (dRGT) potential. It is demonstrated that the Hamiltonian methods are powerful not only in proving the absence of the Boulware-Deser ghost, but also in solving other problems. The purpose of this work is to give an introduction both to the Hamiltonian formalism and to the cosmology of bigravity. We sketch three roads to the Hamiltonian of bigravity with the dRGT potential: the metric, the tetrad and the minisuperspace approaches.
Asymptocic Freedom of Gluons in Hamiltonian Dynamics
Gómez-Rocha, María; Głazek, Stanisław D.
2016-07-01
We derive asymptotic freedom of gluons in terms of the renormalized SU(3) Yang-Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles to calculate the three-gluon interaction term in the front-form Yang-Mills Hamiltonian using a perturbative expansion in powers of g up to third order. The resulting three-gluon vertex is a function of the scale parameter s that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian {β} -function coincides with the one obtained in an earlier calculation using a different generator.
Borges, J; Fernandez-Cordoba, C
2009-01-01
Self-dual codes over $\\Z_2\\times\\Z_4$ are subgroups of $\\Z_2^\\alpha \\times\\Z_4^\\beta$ that are equal to their orthogonal under an inner-product that relates to the binary Hamming scheme. Three types of self-dual codes are defined. For each type, the possible values $\\alpha,\\beta$ such that there exist a code $\\C\\subseteq \\Z_2^\\alpha \\times\\Z_4^\\beta$ are established. Moreover, the construction of a $\\add$-linear code for each type and possible pair $(\\alpha,\\beta)$ is given. Finally, the standard techniques of invariant theory are applied to describe the weight enumerators for each type.
Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.
Gosset, David; Terhal, Barbara M; Vershynina, Anna
2015-04-10
We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.
Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions.
Changlani, Hitesh J; Zheng, Huihuo; Wagner, Lucas K
2015-09-14
We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U(∗)/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.
Donnellan, Thomas; Maxwell, E A; Plumpton, C
1968-01-01
Lattice Theory presents an elementary account of a significant branch of contemporary mathematics concerning lattice theory. This book discusses the unusual features, which include the presentation and exploitation of partitions of a finite set. Organized into six chapters, this book begins with an overview of the concept of several topics, including sets in general, the relations and operations, the relation of equivalence, and the relation of congruence. This text then defines the relation of partial order and then partially ordered sets, including chains. Other chapters examine the properti
Evidence for widespread active galactic nucleus activity among massive quiescent galaxies at z ~ 2
Olsen, K.P.; Rasmussen, J.; Toft, S.;
2013-01-01
We quantify the presence of active galactic nuclei (AGNs) in a mass-complete (M > 5 × 10 M ) sample of 123 star-forming and quiescent galaxies at 1.5 = z = 2.5, using X-ray data from the 4 Ms Chandra Deep Field-South (CDF-S) survey. 41% ± 7% of the galaxies are detected directly in X-rays, 22% ± ......%-65%). Our discovery of the ubiquity of AGNs in massive, quiescent z ~ 2 galaxies provides observational support for the importance of AGNs in impeding star formation during galaxy evolution. © 2013. The American Astronomical Society. All rights reserved.....
Ohno, T; Ichinose, I; Matsui, T; Ohno, Takuya; Arakawa, Gaku; Ichinose, Ikuo; Matsui, Tetsuo
2004-01-01
We study the phase structure of the random-plaquette Z_2 lattice gauge model in three dimensions. In this model, the "gauge coupling" for each plaquette is a quenched random variable that takes the value \\beta with the probability 1-p and -\\beta with the probability p. This model is relevant for the recently proposed quantum memory of toric code. The parameter p is the concentration of the plaquettes with "wrong-sign" couplings -\\beta, and interpreted as the error probability per qubit in quantum code. In the gauge system with p=0, i.e., with the uniform gauge couplings \\beta, it is known that there exists a second-order phase transition at a certain critical "temperature", T(\\equiv \\beta^{-1}) = T_c =1.31, which separates an ordered(Higgs) phase at TT_c. As p increases, the critical temperature T_c(p) decreases. In the p-T plane, the curve T_c(p) intersects with the Nishimori line T_{N}(p) at the certain point (p_c, T_{N}(p_c)). The value p_c is just the accuracy threshold for a fault-tolerant quantum memory...
Reorganization of Damaged Chromatin by the Exchange of Histone Variant H2A.Z-2
Nishibuchi, Ikuno [Department of Cellular Biology, Research Institute for Radiation Biology and Medicine, Hiroshima University, Hiroshima (Japan); Department of Radiation Oncology, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima (Japan); Department of Radiation Oncology, Hiroshima Prefectural Hospital, Hiroshima (Japan); Suzuki, Hidekazu; Kinomura, Aiko; Sun, Jiying; Liu, Ning-Ang [Department of Cellular Biology, Research Institute for Radiation Biology and Medicine, Hiroshima University, Hiroshima (Japan); Horikoshi, Yasunori [Department of Cellular Biology, Research Institute for Radiation Biology and Medicine, Hiroshima University, Hiroshima (Japan); Research Center for Mathematics of Chromatin Live Dynamics, Hiroshima University, Hiroshima (Japan); Shima, Hiroki [Department of Biochemistry, Graduate School of Medical Sciences, Tohoku University, Sendai (Japan); Kusakabe, Masayuki; Harata, Masahiko [Laboratory of Molecular Biology, Graduate School of Agricultural Science, Tohoku University, Sendai (Japan); Fukagawa, Tatsuo [Department of Molecular Genetics, National Institute of Genetics and The Graduate University for Advanced Studies, Mishima (Japan); Ikura, Tsuyoshi [Laboratory of Chromatin Regulatory Network, Department of Mutagenesis, Radiation Biology Center, Kyoto University, Kyoto (Japan); Ishida, Takafumi [Department of Cardiovascular Medicine, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima (Japan); Nagata, Yasushi [Department of Radiation Oncology, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima (Japan); Tashiro, Satoshi, E-mail: ktashiro@hiroshima-u.ac.jp [Department of Cellular Biology, Research Institute for Radiation Biology and Medicine, Hiroshima University, Hiroshima (Japan); Research Center for Mathematics of Chromatin Live Dynamics, Hiroshima University, Hiroshima (Japan)
2014-07-15
Purpose: The reorganization of damaged chromatin plays an important role in the regulation of the DNA damage response. A recent study revealed the presence of 2 vertebrate H2A.Z isoforms, H2A.Z-1 and H2A.Z-2. However, the roles of the vertebrate H2A.Z isoforms are still unclear. Thus, in this study we examined the roles of the vertebrate H2A.Z isoforms in chromatin reorganization after the induction of DNA double-strand breaks (DSBs). Methods and Materials: To examine the dynamics of H2A.Z isoforms at damaged sites, we constructed GM0637 cells stably expressing each of the green fluorescent protein (GFP)-labeled H2A.Z isoforms, and performed fluorescence recovery after photobleaching (FRAP) analysis and inverted FRAP analysis in combination with microirradiation. Immunofluorescence staining using an anti-RAD51 antibody was performed to study the kinetics of RAD51 foci formation after 2-Gy irradiation of wild-type (WT), H2A.Z-1- and H2A.Z-2-deficient DT40 cells. Colony-forming assays were also performed to compare the survival rates of WT, H2A.Z-1-, and H2A.Z-2-deficient DT40 cells with control, and H2A.Z-1- and H2A.Z-2-depleted U2OS cells after irradiation. Results: FRAP analysis revealed that H2A.Z-2 was incorporated into damaged chromatin just after the induction of DSBs, whereas H2A.Z-1 remained essentially unchanged. Inverted FRAP analysis showed that H2A.Z-2 was released from damaged chromatin. These findings indicated that H2A.Z-2 was exchanged at DSB sites immediately after the induction of DSBs. RAD51 focus formation after ionizing irradiation was disturbed in H2A.Z-2-deficient DT40 cells but not in H2A.Z-1-deficient cells. The survival rate of H2A.Z-2-deficient cells after irradiation was lower than those of WT and H2A.Z-1- DT40 cells. Similar to DT40 cells, H2A.Z-2-depleted U2OS cells were also radiation-sensitive compared to control and H2A.Z-1-depleted cells. Conclusions: We found that vertebrate H2A.Z-2 is involved in the regulation of the DNA
Cold atoms in a rotating optical lattice
Foot, Christopher J.
2009-05-01
We have demonstrated a novel experimental arrangement which can rotate a two-dimensional optical lattice at frequencies up to several kilohertz. Our arrangement also allows the periodicity of the optical lattice to be varied dynamically, producing a 2D ``accordion lattice'' [1]. The angles of the laser beams are controlled by acousto-optic deflectors and this allows smooth changes with little heating of the trapped cold (rubidium) atoms. We have loaded a BEC into lattices with periodicities ranging from 1.8μm to 18μm, observing the collapse and revival of the diffraction orders of the condensate over a large range of lattice parameters as recently reported by a group in NIST [2]. We have also imaged atoms in situ in a 2D lattice over a range of lattice periodicities. Ultracold atoms in a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields, i.e. the Hamiltonian of the atoms in the rotating frame resembles that of a charged particle in a strong magnetic field. In the future, we plan to use this to investigate a range of phenomena such as the analogue of the fractional quantum Hall effect. [4pt] [1] R. A. Williams, J. D. Pillet, S. Al-Assam, B. Fletcher, M. Shotter, and C. J. Foot, ``Dynamic optical lattices: two-dimensional rotating and accordion lattices for ultracold atoms,'' Opt. Express 16, 16977-16983 (2008) [0pt] [2] J. H. Huckans, I. B. Spielman, B. Laburthe Tolra, W. D. Phillips, and J. V. Porto, Quantum and Classical Dynamics of a BEC in a Large-Period Optical Lattice, arXiv:0901.1386v1
Implicit variational principle for contact Hamiltonian systems
Wang, Kaizhi; Wang, Lin; Yan, Jun
2017-02-01
We establish an implicit variational principle for the contact Hamiltonian systems generated by the Hamiltonian H(x, u, p) with respect to the contact 1-form α =\\text{d}u-p\\text{d}x under Tonelli and Lipschitz continuity conditions.
Some Graphs Containing Unique Hamiltonian Cycles
Lynch, Mark A. M.
2002-01-01
In this paper, two classes of graphs of arbitrary order are described which contain unique Hamiltonian cycles. All the graphs have mean vertex degree greater than one quarter the order of the graph. The Hamiltonian cycles are detailed, their uniqueness proved and simple rules for the construction of the adjacency matrix of the graphs are given.…
A parcel formulation for Hamiltonian layer models
Bokhove, O.; Oliver, M.
2009-01-01
Starting from the three-dimensional hydrostatic primitive equations, we derive Hamiltonian N-layer models with isentropic tropospheric and isentropic or isothermal stratospheric layers. Our construction employs a new parcel Hamiltonian formulation which describes the fluid as a continuum of Hamilton
Equivalence of Conformal Superalgebras to Hamiltonian Superoperators
Xiaoping Xu
2001-01-01
In this paper, we present a formal variational calculus of super functions in one real variable and find the conditions for a "matrix differential operator'' to be a Hamiltonian superoperator. Moreover, we prove that conformal superalgebras are equivalent to certain Hamiltonian superoperators.
ON THE STABILITY BOUNDARY OF HAMILTONIAN SYSTEMS
QI Zhao-hui(齐朝晖); Alexander P. Seyranian
2002-01-01
The criterion for the points in the parameter space being on the stability boundary of linear Hamiltonian system depending on arbitrary numbers of parameters was given, through the sensitivity analysis of eigenvalues and eigenvectors. The results show that multiple eigenvalues with Jordan chain take a very important role in the stability of Hamiltonian systems.
Hamiltonian for a restricted isoenergetic thermostat
Dettmann, C. P.
1999-01-01
Nonequilibrium molecular dynamics simulations often use mechanisms called thermostats to regulate the temperature. A Hamiltonian is presented for the case of the isoenergetic (constant internal energy) thermostat corresponding to a tunable isokinetic (constant kinetic energy) thermostat, for which a Hamiltonian has recently been given.
Normal Form for Families of Hamiltonian Systems
Zhi Guo WANG
2007-01-01
We consider perturbations of integrable Hamiltonian systems in the neighborhood of normally parabolic invariant tori. Using the techniques of KAM-theory we prove that there exists a canonical transformation that puts the Hamiltonian in normal form up to a remainder of weighted order 2d+1. And some dynamical consequences are obtained.
Bohr Hamiltonian with time-dependent potential
Naderi, L.; Hassanabadi, H.; Sobhani, H.
2016-04-01
In this paper, Bohr Hamiltonian has been studied with the time-dependent potential. Using the Lewis-Riesenfeld dynamical invariant method appropriate dynamical invariant for this Hamiltonian has been constructed and the exact time-dependent wave functions of such a system have been derived due to this dynamical invariant.
Infinite-dimensional Hamiltonian Lie superalgebras
无
2010-01-01
The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent elements.We are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra.
Momentum and hamiltonian in complex action theory
Nagao, Keiichi; Nielsen, Holger Frits Bech
2012-01-01
$-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator $\\hat{p}$, in FPI with a starting Lagrangian. Solving the eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led...
Square conservation systems and Hamiltonian systems
王斌; 曾庆存; 季仲贞
1995-01-01
The internal and external relationships between the square conservation scheme and the symplectic scheme are revealed by a careful study on the interrelation between the square conservation system and the Hamiltonian system in the linear situation, thus laying a theoretical basis for the application and extension of symplectic schemes to square conservations systems, and of those schemes with quadratic conservation properties to Hamiltonian systems.
Brugnano, Luigi; Trigiante, Donato
2009-01-01
One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself. For example, it is well known that standard (even symplectic) methods can only exactly preserve quadratic Hamiltonians. In this paper, a new family of methods, called Hamiltonian Boundary Value Methods (HBVMs), is introduced and analyzed. HBVMs are able to exactly preserve, in the discrete solution, Hamiltonian functions of polynomial type of arbitrarily high degree. These methods turn out to be symmetric, perfectly $A$-stable, and can have arbitrarily high order. A few numerical tests confirm the theoretical results.
XU Xi-Xiang; ZHANG Yu-Feng
2004-01-01
A discrete matrix spectral problem and the associated hierarchy of Lax integrable lattice equations are presented, and it is shown that the resulting Lax integrable lattice equations are all Liouville integrable discrete Hamiltonian systems. A new integrable symplectic map is given by binary Bargmann .constraint of the resulting hierarchy.Finally, an infinite set of conservation laws is given for the resulting hierarchy.
Sublattice signatures of transitions in a $\\mathcal{PT}$-symmetric dimer lattice
Harter, Andrew K
2016-01-01
Lattice models with non-hermitian, parity and time-reversal ($\\mathcal{PT}$) symmetric Hamiltonians, realized most readily in coupled optical systems, have been intensely studied in the past few years. A $\\mathcal{PT}$-symmetric dimer lattice consists of dimers with intra-dimer coupling $\
A Hamiltonian approach to Thermodynamics
Baldiotti, M C; Molina, C
2016-01-01
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed ontop of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac's theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases.
Effective Hamiltonians for Complexes of Unstable Particles
Urbanowski, K
2014-01-01
Effective Hamiltonians governing the time evolution in a subspace of unstable states can be found using more or less accurate approximations. A convenient tool for deriving them is the evolution equation for a subspace of state space sometime called the Krolikowski-Rzewuski (KR) equation. KR equation results from the Schr\\"{o}dinger equation for the total system under considerations. We will discuss properties of approximate effective Hamiltonians derived using KR equation for $n$--particle, two particle and for one particle subspaces. In a general case these affective Hamiltonians depend on time $t$. We show that at times much longer than times at which the exponential decay take place the real part of the exact effective Hamiltonian for the one particle subsystem (that is the instantaneous energy) tends to the minimal energy of the total system when $t \\rightarrow \\infty$ whereas the imaginary part of this effective Hamiltonian tends to the zero as $t\\rightarrow \\infty$.
Simulating sparse Hamiltonians with star decompositions
Childs, Andrew M
2010-01-01
We present an efficient algorithm for simulating the time evolution due to a sparse Hamiltonian. In terms of the maximum degree d and dimension N of the space on which the Hamiltonian H acts, this algorithm uses (d^2(d+log* N)||H||)^{1+o(1)} queries. This improves the complexity of the sparse Hamiltonian simulation algorithm of Berry, Ahokas, Cleve, and Sanders, which scales like (d^4(log* N)||H||)^{1+o(1)}. To achieve this, we decompose a general sparse Hamiltonian into a small sum of Hamiltonians whose graphs of non-zero entries have the property that every connected component is a star, and efficiently simulate each of these pieces.
Mozena, Mark; Faber, S. M.; Primack, J. R.; Dekel, A.; Ceverino, D.; Koo, D. C.; Fumagalli, M.; Wuyts, S.; Rosario, D. J.; Lai, K.; Kocevski, D. D.; McGrath, E. J.; Trump, J. R.; CANDELS
2011-01-01
The first data from the HST Multi-Cycle Treasury CANDELS (Cosmic Assembly Near Infra-red Deep Extragalactic Legacy Survey - candels.ucolick.org) are producing images of thousands of z 2 galaxies in observed optical (ACS) and NIR (WFC3) bands. We have developed a new visual classification scheme for z 2 galaxies which is motivated by the significant population of galaxies that are dominated by giant clumps in the HST images, and by the theoretical predictions for clumpy galaxies based on analytic studies and zoom-in hydrodynamical cosmological simulations. This classification method was developed using about a thousand z 2 galaxies in the GOODS-S Early Release Survey (ERS) region imaged with ACS and WFC3. The ERS data have been observed in a way similar to the CANDELS observations. I will also discuss the latest cosmologically motivated ART hydrodynamical simulations by Ceverino, Dekel, and Primack. We render these simulated z 2 galaxies to mimic our HST ACS and WFC3 images and visually classify their stellar structure to compare them with the galaxies observed in ERS. We have compared the effects of dust extinction due to the complex clumpy distribution of gas within these simulations. Comparing the visual classification of the HST observations with the simulations provides new clues to galaxy assembly.
宋贤梅; 熊蕾
2016-01-01
考虑环 R ＝Z2a ＋uZ2a上的线性码，其中 u2＝u。研究了环 R 上线性码的完全 Gray 权估计的 MacWilliams 恒等式。给出了环 R 上的自对偶码的生成矩阵及环 Z23＋uZ23上长为偶数 n 的自对偶码的数量公式。讨论了环 R上的挠码，得到挠码的生成矩阵及挠码与剩余码的关系。%The linear codes over R =Z2a +uZ2a with u2 =u are discussed.MacWilliams identity for the complete Gray weight enumerator is investigated firstly.Then,the generator matrices of self-dual codes over R and the number of dis-tinct self-dual codes of even length n over Z23 +uZ23 are given.The torsion codes over R are discussed and the genera-tor matrices of torsion codes and the relationship between the torsion codes and the residue codes are also obtained.
Narrowband Lyman-Continuum Imaging of Galaxies at z ~ 2.85
Mostardi, Robin E; Nestor, Daniel B; Steidel, Charles C; Reddy, Naveen A
2013-01-01
We present results from a survey for z~2.85 Lyman-Continuum (LyC) emission in the HS1549+1933 field and place constraints on the amount of ionizing radiation escaping from star-forming galaxies. Using a custom narrowband filter (NB3420) tuned to wavelengths just below the Lyman limit at z>=2.82$, we probe the LyC spectral region of 49 Lyman break galaxies (LBGs) and 70 Lya-emitters (LAEs) spectroscopically confirmed at z>=2.82, as well as 58 z~2.85 LAE photometric candidates. Four LBGs and 19 LAEs are detected in NB3420. Using V-band data probing the rest-frame non-ionizing UV, we observe that many NB3420-detected galaxies exhibit spatial offsets between their LyC and non-ionizing UV emission and are characterized by extremely blue NB3420-V colors, corresponding to low ratios of non-ionizing to ionizing radiation (F_UV/F_LyC) that are in tension with current stellar population synthesis models. We measure average values of (F_UV/F_LyC) for our spectroscopically confirmed LBG and LAE samples, correcting for fo...
Decline of the space density of quasars between z=2 and z=4
Vigotti, M; Benn, C R; De Zotti, G; Fanti, R; Serrano, J I G; Mack, K H; Holt, J
2003-01-01
We define a new complete sample of 13 optically-luminous radio quasars M_AB(1450 Angstrom) 25.7 with redshift 3.8 < z < 4.5, obtained by cross-correlating the FIRST radio survey and the APM catalogue of POSS-I. We measure the space density to be 1.0 +/- 0.3 /Gpc^3, a factor 1.9 +/- 0.7 smaller than the space density of similar quasars at z=2. Using a new measurement of the radio-loud fraction of quasars we find that at z=4 the total space density of quasars with M_AB(1450 Angstrom) < -26.9 is 7.4 +/- 2.6/Gpc^3. This is a factor 1.8 +/- 0.8 less than the space density at z=2, found by the 2dF quasar survey. This (z=2)/(z=4) ratio, consistent with that of the radio-loud quasars, is significantly different from the ratio of about 10 found for samples including lower-luminosity quasars. This suggests that the decline of the space density beyond z=2 is slower for optically-luminous quasars than for less-luminous ones.
Simulating 3D $Z_2$ Topological Nodes in Nonsymmorphic Photonic Crystals
Wang, Hai-Xiao; Hang, Zhi Hong; Chen, Huanyang; Kee, Hae-Young; Jiang, Jian-Hua
2016-01-01
We propose an all-dielectric, space-time reversal symmetric photonics-crystal architecture that possess 3D Dirac points and line-nodes with nontrivial $Z_2$ topological charge, which can be realized at infrared and microwave frequencies. The protected degeneracy of bands is achieved via nonsymmorphic symmetries despite the lack of Kramers degeneracy in photonic crystal systems. Two orthogonal screw axes lead to 3D $Z_2$ Dirac points on high symmetry Brillouin zone (BZ) boundary line. On the other hand, twofold $Z_2$ line-nodes appear around the $\\Gamma$-point due to a combination of nonsymmorphic and point-group symmetries. The lowest line-node is deterministic because of degeneracy partner switching between Bloch states with opposite parities. A pair of Fermi arcs associated with $Z_2$ topological charge is emerged below light-line and protected by total internal reflection on certain photonic-crystal-air interfaces. These robust surface states offer an unique opportunity to realize "open cavity" with strong...
Logarithmic two-Point Correlation Functions from a z = 2 Lifshitz Model
Zingg, T.
2013-01-01
The Einstein-Proca action is known to have asymptotically locally Lifshitz spacetimes as classical solutions. For dynamical exponent z=2, two-point correlation functions for fluctuations around such a geometry are derived analytically. It is found that the retarded correlators are stable in the sens
Quantum computing and polynomial equations over the finite field Z_2
Dawson, C M; Hines, A P; Mortimer, D; Nielsen, M A; Osborne, T J; Dawson, Christopher M.; Haselgrove, Henry L.; Hines, Andrew P.; Mortimer, Duncan; Nielsen, Michael A.; Osborne, Tobias J.
2004-01-01
What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z_2. This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes.
VIMOS-VLT and Spitzer observations of a radio galaxy at z=2.5
Villar-Martin, M; Sanchez, SF; De Breuck, C; Peletier, R; Vernet, J; Rettura, A; Seymour, N; Humphrey, A; Stern, D; Alighieri, SD; Fosbury, R
2006-01-01
We present: (i) a kinematic and morphological study of the giant Ly alpha nebula associated with the radio galaxy MRC 2104-242 (z = 2.49) based on integral field spectroscopic Visible Multiobject Spectrograph (VIMOS) data from the Very Large Telescope (VLT), and (ii) a photometric study of the host
$\\mathbb{Z}_2$ invariance of Germanene on MoS$_2$ from first principles
Amlaki, Taher; Bokdam, Menno; Paul J. Kelly
2016-01-01
We present a low energy Hamiltonian generalized to describe how the energy bands of germanene ($\\rm \\overline{Ge}$) are modified by interaction with a substrate or a capping layer. The parameters that enter the Hamiltonian are determined from first-principles relativistic calculations for $\\rm \\overline{Ge}|$MoS$_2$ bilayers and MoS$_2|\\rm \\overline{Ge} |$MoS$_2$ trilayers and are used to determine the topological nature of the system. For the lowest energy, buckled germanene structure, the g...
Dynamics for QCD on an infinite lattice
Grundling, Hendrik
2015-01-01
We prove the existence of the dynamics automorphism group for Hamiltonian QCD on an infinite lattice in R^3, and this is done in a C*-algebraic context. The existence of ground states is also obtained. Starting with the finite lattice model for Hamiltonian QCD developed by Kijowski and Rudolph, we state its field algebra and a natural representation. We then generalize this representation to the infinite lattice, and construct a Hilbert space which has represented on it all the local algebras (i.e. algebras associated with finite connected sublattices) equipped with the correct graded commutation relations. On a suitably large C*-algebra acting on this Hilbert space, and containing all the local algebras, we prove that there is a one parameter automorphism group, which is the pointwise norm limit of the local time evolutions along a sequence of finite sublattices, increasing to the full lattice. This is our global time evolution. We then take as our field algebra the C*-algebra generated by all the orbits of ...
Lattice Models of Quantum Gravity
Bittner, E R; Holm, C; Janke, W; Markum, H; Riedler, J
1998-01-01
Standard Regge Calculus provides an interesting method to explore quantum gravity in a non-perturbative fashion but turns out to be a CPU-time demanding enterprise. One therefore seeks for suitable approximations which retain most of its universal features. The $Z_2$-Regge model could be such a desired simplification. Here the quadratic edge lengths $q$ of the simplicial complexes are restricted to only two possible values $q=1+\\epsilon\\sigma$, with Ising model. To test whether this simpler model still contains the essential qualities of the standard Regge Calculus, we study both models in two dimensions and determine several observables on the same lattice size. In order to compare expectation values, e.g. of the average curvature or the Liouville field susceptibility, we employ in both models the same functional integration measure. The phase structure is under current investigation using mean field theory and numerical simulation.
Non-vanishing $U_{e3}$ and $\\cos{2 \\theta_{23}}$ from a broken $Z_2$ symmetry
Grimus, Walter; Kaneko, S; Lavoura, L; Sawanaka, H; Tanimoto, M; Grimus, Walter; Joshipura, Anjan S.; Kaneko, Satoru; Lavoura, Lu\\'{i}s; Sawanaka, Hideyuki; Tanimoto, Morimitsu
2004-01-01
It is shown that the neutrino mass matrices in the flavour basis yielding a vanishing $U_{e3}$ are characterized by invariance under a class of effective $Z_2$ symmetries. A specific $Z_2$ in this class also leads to a maximal atmospheric mixing angle $\\theta_{23}$. The breaking of that $Z_2$ can be parameterized by two dimensionless quantities, $\\e$ and $\\e'$; the effects of $\\e, \\e' \
Nonperturbative embedding for highly nonlocal Hamiltonians
Subaşı, Yiǧit; Jarzynski, Christopher
2016-07-01
The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with at most two-body interactions. Although valid for arbitrary k -body interactions, their use is limited to small k because the strength of interaction is k th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective k -body interactions using Hamiltonians consisting of at most l -body interactions with l effect of this procedure is shown to be equivalent to evolving the system with the original nonlocal Hamiltonian. This technique does not suffer from the aforementioned shortcoming of perturbative methods and requires only one ancilla qubit for each k -body interaction irrespective of the value of k . It works best for Hamiltonians with a few many-body interactions involving a large number of qubits and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme.
Hamiltonian truncation approach to quenches in the Ising field theory
Rakovszky, Tibor; Collura, Mario; Kormos, Márton; Takács, Gábor
2016-01-01
In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while...
Lectures on Hamiltonian Dynamics : Theory and Applications
Benettin, Giancarlo; Kuksin, Sergei
2005-01-01
This volume collects three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim is to describe the state of the art for some interesting problems, such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants and the phenomena related to stability over exponentially long times of Nekhoroshev's theory. The books may serve as an excellent basis for young researchers, who will find here a complete and accurate exposition of recent original results and many hints for further investigation.
Extended Hamiltonian approach to continuous tempering.
Gobbo, Gianpaolo; Leimkuhler, Benedict J
2015-06-01
We introduce an enhanced sampling simulation technique based on continuous tempering, i.e., on continuously varying the temperature of the system under investigation. Our approach is mathematically straightforward, being based on an extended Hamiltonian formulation in which an auxiliary degree of freedom, determining the effective temperature, is coupled to the physical system. The physical system and its temperature evolve continuously in time according to the equations of motion derived from the extended Hamiltonian. Due to the Hamiltonian structure, it is easy to show that a particular subset of the configurations of the extended system is distributed according to the canonical ensemble for the physical system at the correct physical temperature.
EXISTENCE OF HAMILTONIAN κ-FACTOR
CAI Maocheng; FANG Qizhi; LI Yanjun
2004-01-01
A Hamiltonian k-factor is a k-factor containing a Hamiltonian cycle. An n/2-critical graph G is a simple graph of order n which satisfies δ(G) ≥ n/2 and δ(G - e) ＜ n/2for any edge e ∈ E(G). Let κ≥ 2 be an integer and G be an n/2-critical graph of even order n ≥ 8κ - 14. It is shown in this paper that for any given Hamiltonian cycle Cexcept that G - C consists of two components of odd orders when κ is odd, G has a k-factor containing C.
Orthogonal separable Hamiltonian systems on T2
无
2007-01-01
In this paper we characterize the Liouvillian integrable orthogonal separable Hamiltonian systems on T2 for a given metric, and prove that the Hamiltonian flow on any compact level hypersurface has zero topological entropy. Furthermore, by examples we show that the integrable Hamiltonian systems on T2 can have complicated dynamical phenomena. For instance they can have several families of invariant tori, each family is bounded by the homoclinic-loop-like cylinders and heteroclinic-loop-like cylinders. As we know, it is the first concrete example to present the families of invariant tori at the same time appearing in such a complicated way.
EXTENDED CASIMIR APPROACH TO CONTROLLED HAMILTONIAN SYSTEMS
Yuqian GUO; Daizhan CHENG
2006-01-01
In this paper, we first propose an extended Casimir method for energy-shaping. Then it is used to solve some control problems of Hamiltonian systems. To solve the H∞ control problem, the energy function of a Hamiltonian system is shaped to such a form that could be a candidate solution of HJI inequality. Next, the energy function is shaped as a candidate of control ISS-Lyapunov function, and then the input-to-state stabilization of port-controlled Hamiltonian systems is achieved. Some easily verifiable sufficient conditions are presented.
Minimal Realizations of Supersymmetry for Matrix Hamiltonians
Andrianov, Alexandr A
2014-01-01
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant symmetry matrix for a matrix Hamiltonian are presented. A method of constructing of a matrix Hamiltonian with a given constant symmetry matrix in terms of a set of arbitrary scalar functions and eigen- and associated vectors of this matrix is offered. Examples of constructing of $2\\times2$ matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated.
Algebraic Hamiltonian for Vibrational Spectra of Stibine
HOU Xi-Wen
2004-01-01
@@ An algebraic Hamiltonian, which in a limit can be reduced to an extended local mode model by Law and Duncan,is proposed to describe both stretching and bending vibrational energy levels of polyatomic molecules, where Fermi resonances between the stretches and the bends are considered. The Hamiltonian is used to study the vibrational spectra of stibine (SbH3). A comparison with the extended local mode model is made. Results of fitting the experimental data show that the algebraic Hamiltonian reproduces the observed values better than the extended local mode model.
Hamiltonian and Lagrangian theory of viscoelasticity
Hanyga, A.; Seredyńska, M.
2008-03-01
The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity.
Dicycle Cover of Hamiltonian Oriented Graphs
Khalid A. Alsatami
2016-01-01
Full Text Available A dicycle cover of a digraph D is a family F of dicycles of D such that each arc of D lies in at least one dicycle in F. We investigate the problem of determining the upper bounds for the minimum number of dicycles which cover all arcs in a strong digraph. Best possible upper bounds of dicycle covers are obtained in a number of classes of digraphs including strong tournaments, Hamiltonian oriented graphs, Hamiltonian oriented complete bipartite graphs, and families of possibly non-Hamiltonian digraphs obtained from these digraphs via a sequence of 2-sum operations.
Improved Sufficient Conditions for Hamiltonian Properties
Bode Jens-P.
2015-05-01
Full Text Available In 1980 Bondy [2] proved that a (k+s-connected graph of order n ≥ 3 is traceable (s = −1 or Hamiltonian (s = 0 or Hamiltonian-connected (s = 1 if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1(n+s−1+1/2. It is shown in [1] that one can allow exceptional (k+ 1-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity condition.
Featureless quantum insulator on the honeycomb lattice
Kim, Panjin; Lee, Hyunyong; Jiang, Shenghan; Ware, Brayden; Jian, Chao-Ming; Zaletel, Michael; Han, Jung Hoon; Ran, Ying
2016-08-01
We show how to construct fully symmetric states without topological order on a honeycomb lattice for S =1/2 spins using the language of projected entangled pair states. An explicit example is given for the virtual bond dimension D =4 . Four distinct classes differing by lattice quantum numbers are found by applying the systematic classification scheme introduced by two of the authors [S. Jiang and Y. Ran, Phys. Rev. B 92, 104414 (2015), 10.1103/PhysRevB.92.104414]. Lack of topological degeneracy or other conventional forms of symmetry breaking in the proposed wave functions are checked by numerical calculations of the entanglement entropy and various correlation functions. Exponential decay of all correlation functions measured are strongly indicative of the energy gap for the putative parent Hamiltonian of the state. Our work provides the first explicit realization of a featureless quantum state for spin-1/2 particles on a honeycomb lattice.
Schaefer, Stefan [DESY (Germany). Neumann Inst. for Computing
2016-11-01
These configurations are currently in use in many on-going projects carried out by researchers throughout Europe. In particular this data will serve as an essential input into the computation of the coupling constant of QCD, where some of the simulations are still on-going. But also projects computing the masses of hadrons and investigating their structure are underway as well as activities in the physics of heavy quarks. As this initial project of gauge field generation has been successful, it is worthwhile to extend the currently available ensembles with further points in parameter space. These will allow to further study and control systematic effects like the ones introduced by the finite volume, the non-physical quark masses and the finite lattice spacing. In particular certain compromises have still been made in the region where pion masses and lattice spacing are both small. This is because physical pion masses require larger lattices to keep the effects of the finite volume under control. At light pion masses, a precise control of the continuum extrapolation is therefore difficult, but certainly a main goal of future simulations. To reach this goal, algorithmic developments as well as faster hardware will be needed.
Vlasov equation for long-range interactions on a lattice.
Bachelard, R; Dauxois, T; De Ninno, G; Ruffo, S; Staniscia, F
2011-06-01
We show that, in the continuum limit, the dynamics of Hamiltonian systems defined on a lattice with long-range couplings is well described by the Vlasov equation. This equation can be linearized around the homogeneous state, and a dispersion relation, which depends explicitly on the Fourier modes of the lattice, can be derived. This allows one to compute the stability thresholds of the homogeneous state, which turns out to depend on the mode number. When this state is unstable, the growth rates are also functions of the mode number. Explicit calculations are performed for the α-Hamiltonian mean field model with 0≤α<1, for which the mean-field mode is always found to dominate the exponential growth. The theoretical predictions are successfully compared with numerical simulations performed on a finite lattice.
From lattice gauge theories to hydrogen atoms
Manu Mathur
2015-10-01
Full Text Available We construct canonical transformations to obtain a complete and most economical realization of the physical Hilbert space Hp of pure SU(22+1 lattice gauge theory in terms of Wigner coupled Hilbert spaces of hydrogen atoms. One hydrogen atom is assigned to every plaquette of the lattice. A complete orthonormal description of the Wilson loop basis in Hp is obtained by all possible angular momentum Wigner couplings of hydrogen atom energy eigenstates |n l m〉 describing electric fluxes on the loops. The SU(2 gauge invariance implies that the total angular momenta of all hydrogen atoms vanish. The canonical transformations also enable us to rewrite the Kogut–Susskind Hamiltonian in terms of fundamental Wilson loop operators and their conjugate electric fields. The resulting loop Hamiltonian has a global SU(2 invariance and a simple weak coupling (g2→0 continuum limit. The canonical transformations leading to the loop Hamiltonian are valid for any SU(N. The ideas and techniques can also be extended to higher dimension.
Two viable large scalar multiplet models with an accidental Z2 symmetry
Earl, Kevin; Logan, Heather E; Pilkington, Terry
2013-01-01
Models in which the Higgs sector is extended by a single scalar electroweak multiplet Z will possess an accidental global Z2 symmetry if Z has isospin T=5/2 (sextet) or 7/2 (octet) and carries the same hypercharge as the Standard Model Higgs doublet. This Z2 symmetry keeps the lightest (neutral) member of Z stable and has interesting implications for phenomenology. We determine the constraints on these models from precision electroweak measurements and Higgs boson decays to two photons. We compute the thermal relic density of the stable member of Z and show that, for masses below 1 TeV, it can make up at most 1% of the dark matter in the universe. We also show that current dark matter direct detection experiments do not constrain the models, but future ton-scale experiments will probe their parameter space.
Some new operations on Zt x Z2,2-cocyclic Hadamard matrices
Alvarez, Victor; Guemes, Maria Belen
2011-01-01
Following the ideas of [AGG11] about Zt x Z2,2-cocyclic Hadamard matrices, we introduce the notion of diagram, which visually represents any set of coboundaries. Diagrams are a very useful tool for the description and the study of paths and intersections, as described in [AGG11]. Then, we will study four different operations on Zt x Z2,2-cocyclic matrices. These operations will be defined on the set of coboundaries defining the matrix, preserve the Hadamard character of the cocyclic matrices, and allow us to obtain new Hadamard matrices from old ones. We split the set of Hadamard matrices into disjoint orbits, define representatives for them and take advantage of this fact to compute them in an easier way than the usual purely exhaustive way.
Cold-Mode Accretion: Driving the Fundamental Mass-Metallicity Relation at z~2
Kacprzak, Glenn G; Glazebrook, Karl; Tran, Kim-Vy H; Yuan, Tiantian; Nanayakkara, Themiya; Allen, Rebecca J; Alcorn, Leo; Cowley, Michael; Labbe, Ivo; Spitler, Lee; Straatman, Caroline; Tomczak, Adam
2016-01-01
We investigate the star formation rate (SFR) dependence on the stellar mass and gas-phase metallicity relation at z=2 with MOSFIRE/Keck as part of the ZFIRE survey. We have identified 117 galaxies (1.98 10$~M$_{\\odot}$yr$^{-1}$) SFRs. At fixed mass, low star-forming galaxies tend to have higher metallicity than high star-forming galaxies. Using a few basic assumptions, we further show that the gas masses and metallicities required to produce the fundamental mass--metallicity relation, and its intrinsic scatter, are consistent with cold-mode accretion predictions obtained from the OWLS hydrodynamical simulations. Our results from both simulations and observations are suggestive that cold-mode accretion is responsible for the fundamental mass-metallicity relation at $z=2$ and demonstrates the direct relationship between cosmological accretion and the fundamental properties of galaxies.
Deep Ly alpha imaging of two z=2.04 GRB host galaxy fields
Fynbo, J.P.U.; Møller, Per; Thomsen, Bente
2002-01-01
We report on the results of deep narrow-band Lyalpha and broad-band U and I imaging of the fields of two Gamma-Ray bursts at redshift z = 2.04 (GRB 000301C and GRB 000926). We find that the host galaxy of GRB 000926 is an extended (more than 2 arcsec), strong Lyalpha emitter with a rest-frame equ......We report on the results of deep narrow-band Lyalpha and broad-band U and I imaging of the fields of two Gamma-Ray bursts at redshift z = 2.04 (GRB 000301C and GRB 000926). We find that the host galaxy of GRB 000926 is an extended (more than 2 arcsec), strong Lyalpha emitter with a rest...
Deep Ly alpha imaging of two z=2.04 GRB host galaxy fields
Fynbo, J.P.U.; Møller, Per; Thomsen, Bente
2002-01-01
We report on the results of deep narrow-band Lyalpha and broad-band U and I imaging of the fields of two Gamma-Ray bursts at redshift z = 2.04 (GRB 000301C and GRB 000926). We find that the host galaxy of GRB 000926 is an extended (more than 2 arcsec), strong Lyalpha emitter with a rest-frame equ......We report on the results of deep narrow-band Lyalpha and broad-band U and I imaging of the fields of two Gamma-Ray bursts at redshift z = 2.04 (GRB 000301C and GRB 000926). We find that the host galaxy of GRB 000926 is an extended (more than 2 arcsec), strong Lyalpha emitter with a rest...
4D gravity localized in non Z_2-symmetric thick branes
Barbosa-Cendejas, Nandinini; Barbosa-Cendejas, Nandinii; Herrera-Aguilar, Alfredo
2005-01-01
We present a comparative analysis of localization of 4D gravity on a non Z_2-symmetric scalar thick brane in both a 5-dimensional Riemannian space time and a pure geometric Weyl integrable manifold. This work was mainly motivated by the hypothesis which claims that Weyl geometries mimic quantum behaviour classically. We start by obtaining a classical 4-dimensional Poincare invariant thick brane solution which does not respect Z_2-symmetry along the (non-)compact extra dimension. The scalar energy density of our field configuration represents several series of thick branes with positive and negative energy densities centered at y_0. The only qualitative difference we have encountered when comparing both frames is that the scalar curvature of the Riemannian manifold turns out to be singular for the found solution, whereas its Weylian counterpart presents a regular behaviour. By studying the transverse traceless modes of the fluctuations of the classical backgrounds, we recast their equations into a Schroedinger...
Effective stability for generalized Hamiltonian systems
CONG; Fuzhong; LI; Yong
2004-01-01
An effective stability result for generalized Hamiltonian systems is obtained by applying the simultaneous approximation technique due to Lochak. Among these systems,dimensions of action variables and angle variables might be distinct.
Spinor-Like Hamiltonian for Maxwellian Optics
Kulyabov D.S.
2016-01-01
Conclusions. For Maxwell equations in the Dirac-like form we can expand research methods by means of quantum field theory. In this form, the connection between the Hamiltonians of geometric, beam and Maxwellian optics is clearly visible.
Integrable Hamiltonian systems and spectral theory
Moser, J
1981-01-01
Classical integrable Hamiltonian systems and isospectral deformations ; geodesics on an ellipsoid and the mechanical system of C. Neumann ; the Schrödinger equation for almost periodic potentials ; finite band potentials ; limit cases, Bargmann potentials.
Compressed quantum metrology for the Ising Hamiltonian
Boyajian, W. L.; Skotiniotis, M.; Dür, W.; Kraus, B.
2016-12-01
We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian that exhibits a quantum phase transition can be efficiently simulated on an exponentially smaller quantum computer. Specifically, by exploiting the fact that the ground state of such a Hamiltonian changes drastically around its phase-transition point, we construct a suitable observable from which one can estimate the relevant parameters of the Hamiltonian with Heisenberg scaling precision. We then show how, for the one-dimensional Ising Hamiltonian with transverse magnetic field acting on N spins, such a metrology protocol can be efficiently simulated on an exponentially smaller quantum computer while maintaining the same Heisenberg scaling for the squared error, i.e., O (N-2) precision, and derive the explicit circuit that accomplishes the simulation.
Momentum and Hamiltonian in Complex Action Theory
Nagao, Keiichi; Nielsen, Holger Bech
In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view based on the complex coordinate formalism of our foregoing paper. After reviewing the formalism briefly, we describe in FPI with a Lagrangian the time development of a ξ-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator. Solving this eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum relation again via the saddle point for p. This study confirms that the momentum and Hamiltonian in the CAT have the same forms as those in the real action theory. We also show the third derivation of the momentum relation via the saddle point for q.
A Student's Guide to Lagrangians and Hamiltonians
Hamill, Patrick
2013-11-01
Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.
Classical mechanics Hamiltonian and Lagrangian formalism
Deriglazov, Alexei
2016-01-01
This account of the fundamentals of Hamiltonian mechanics also covers related topics such as integral invariants and the Noether theorem. With just the elementary mathematical methods used for exposition, the book is suitable for novices as well as graduates.
Jacobi fields of completely integrable Hamiltonian systems
Giachetta, G.; Mangiarotti, L.; Sardanashvily, G
2003-03-31
We show that Jacobi fields of a completely integrable Hamiltonian system of m degrees of freedom make up an extended completely integrable system of 2m degrees of freedom, where m additional first integrals characterize a relative motion.
Polysymplectic Hamiltonian formalism and some quantum outcomes
Giachetta, G; Sardanashvily, G
2004-01-01
Covariant (polysymplectic) Hamiltonian field theory is formulated as a particular Lagrangian theory on a polysymplectic phase space that enables one to quantize it in the framework of familiar quantum field theory.
Asymptocic Freedom of Gluons in Hamiltonian Dynamics
Gómez-Rocha, María
2016-01-01
We derive asymptotic freedom of gluons in terms of the renormalized $SU(3)$ Yang-Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles (RGPEP) to calculate the three-gluon interaction term in the front-form Yang-Mills Hamiltonian using a perturbative expansion in powers of $g$ up to third order. The resulting three-gluon vertex is a function of the scale parameter $s$ that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian $\\beta$-function coincides with the one obtained in an earlier calculation using a different generator.
Hamiltonian cycle problem and Markov chains
Borkar, Vivek S; Filar, Jerzy A; Nguyen, Giang T
2014-01-01
This book summarizes a line of research that maps certain classical problems of discrete mathematics and operations research - such as the Hamiltonian cycle and the Travelling Salesman problems - into convex domains where continuum analysis can be carried out.
Many-body generalization of the Z2 topological invariant for the quantum spin Hall effect
Lee, Sung-Sik; Ryu, Shinsei
2007-01-01
We propose a many-body generalization of the Z2 topological invariant for the quantum spin Hall insulator, which does not rely on single-particle band structures. The invariant is derived as a topological obstruction that distinguishes topologically distinct many-body ground states on a torus. It is also expressed as a Wilson-loop of the SU(2) Berry gauge field, which is quantized due to the time-reversal symmetry.
Many-Body Generalization of the Z2 Topological Invariant for the Quantum Spin Hall Effect
Lee, Sung-Sik; Ryu, Shinsei
2008-05-01
We propose a many-body generalization of the Z2 topological invariant for the quantum spin Hall insulator, which does not rely on single-particle band structures. The invariant is derived as a topological obstruction that distinguishes topologically distinct many-body ground states on a torus. It is also expressed as a Wilson loop of the SU(2) Berry gauge field, which is quantized due to time-reversal symmetry.
Scotogenic $Z_2$ or $U(1)_D$ Model of Neutrino Mass with $\\Delta(27)$ Symmetry
Ma, Ernest
2014-01-01
The scotogenic model of radiative neutrino mass with $Z_2$ or $U(1)_D$ dark matter is shown to accommodate $\\Delta(27)$ symmetry naturally. The resulting neutrino mass matrix is identical to either of two forms, one proposed in 2006, the other in 2008. These two structures are studied in the context of present neutrino data, with predictions of $CP$ violation and neutrinoless double beta decay.
Flat Currents and Solutions of Sigma Model on Supercoset Targets with Z2m Grading
KE san-Min; SHI Kang-Jie; WANG Chun; WU Sheng
2007-01-01
We find one parameter flat currents of the sigma model on supercoset targets with Z2m grading given by Young satisfaction equations of motion and the Virasoro constraint.This meads that one can generate a series of classical solutions from the original one.For these new solutions one can also construct flat currents and conserved charges,which form the same set with the original one.
Hamiltonian formulation of guiding center motion
Stern, D. P.
1971-01-01
The nonrelativistic guiding center motion of a charged particle in a static magnetic field is derived using the Hamiltonian formalism. By repeated application of first-order canonical perturbation theory, the first two adiabatic invariants and their averaged Hamiltonians are obtained, including the first-order correction terms. Other features of guiding center theory are also given, including lowest order drifts and the flux invariant.
Continuous finite element methods for Hamiltonian systems
无
2007-01-01
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudosymplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory.
On Hamiltonians Generating Optimal-Speed Evolutions
2008-01-01
We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and provide an explicit expression for the most general optimal-speed quasi-Hermitian Hamiltonian. Our approach allows for an explicit description of the metric- (inner product-) dependence of the lower bound on the travel time and the universality ...
Hamiltonian Quantum Cellular Automata in 1D
Nagaj, Daniel; Wocjan, Pawel
2008-01-01
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process. We only require the ability to prepare an initial computational basis state which encodes both the quantum circuit and its input. The computational process is then carried out by the autonomous Hamiltonian time evolution. After a time polynomially long in th...
Regulation of Polycomb group genes Psc and Su(z)2 in Drosophila melanogaster.
Park, Sung Yeon; Schwartz, Yuri B; Kahn, Tatyana G; Asker, Dalal; Pirrotta, Vincenzo
2012-01-01
Certain Polycomb group (PcG) genes are themselves targets of PcG complexes. Two of these constitute the Drosophila Psc-Su(z)2 locus, a region whose chromatin is enriched for H3K27me3 and contains several putative Polycomb response elements (PREs) that bind PcG proteins. To understand how PcG mechanisms regulate this region, the repressive function of the PcG protein binding sites was analyzed using reporter gene constructs. We find that at least two of these are functional PREs that can silence a reporter gene in a PcG-dependent manner. One of these two can also display anti-silencing activity, dependent on the context. A PcG protein binding site near the Psc promoter behaves not as a silencer but as a down-regulation module that is actually stimulated by the Pc gene product but not by other PcG products. Deletion of one of the PREs increases the expression level of Psc and Su(z)2 by twofold at late embryonic stages. We present evidence suggesting that the Psc-Su(z)2 locus is flanked by insulator elements that may protect neighboring genes from inappropriate silencing. Deletion of one of these regions results in extension of the domain of H3K27me3 into a region containing other genes, whose expression becomes silenced in the early embryo.
Fumagalli, Michele; Prochaska, J Xavier
2015-01-01
We study the physical properties of a homogeneous sample of 157 optically-thick absorption line systems at redshifts ~1.8-4.4, selected from a high-dispersion spectroscopic survey of Lyman limit systems (LLSs). By means of multiple ionisation models and Bayesian techniques, we derive the posterior probability distribution functions for the density, metallicity, temperature, and dust content of the absorbing gas. We find that z>2 LLSs are highly ionised with ionisation parameters between -32 are characterised by a broad unimodal distribution over >4 orders of magnitude, with a peak at log Z/Zsun~-2. LLSs are metal poor, significantly less enriched than DLAs, with ~70% of the metallicity PDF below log Z/Zsun19 rapidly evolves with redshift, with a ten-fold increase between z~2.1-3.6 (~1.5 Gyr). Based on this sample, we find that LLSs at z=2.5-3.5 account for ~15% of all the metals produced by UV-selected galaxies. The implications for theories of cold gas accretion and metal ejection from galaxies are also disc...
The Assembly of Milky Way-like Galaxies Since z~2.5
van Dokkum, Pieter G; Nelson, Erica June; Patel, Shannon; Skelton, Rosalind E; Momcheva, Ivelina; Brammer, Gabrial; Whitaker, Katherine E; Lundgren, Britt; Fumagalli, Mattia; Conroy, Charlie; Schreiber, Natascha Förster; Franx, Marijn; Kriek, Mariska; Labbé, Ivo; Marchesini, Danilo; Rix, Hans-Walter; van der Wel, Arjen; Wuyts, Stijn
2013-01-01
Galaxies with the mass of the Milky Way dominate the stellar mass density of the Universe but it is uncertain how and when they were assembled. Here we study progenitors of these galaxies out to z~2.5, using data from the 3D-HST and CANDELS Treasury surveys. We find that galaxies with present-day stellar masses of log(M)~10.7 M_sun built ~90% of their stellar mass since z~2.5, with most of the star formation occurring before z~1. In marked contrast to the assembly history of massive elliptical galaxies, the centers and outer parts of the galaxies built up at roughly the same rate between z~2.5 and z~1. We therefore conclude that a "standard" model for the formation of spiral galaxies, with the bulge assembling first and the disk building around it, is probably not correct. Instead, bulges (and black holes) likely formed in lockstep with disks, through bar instabilities, clump migration or other processes. We find that after z~1 the growth in the central regions gradually stopped and the disk continued to buil...
The Majority of Compact Massive Galaxies at z~2 are Disk Dominated
van der Wel, Arjen; Wuyts, Stijn; McGrath, Elizabeth J; Koekemoer, Anton M; Bell, Eric F; Holden, Bradford P; Robaina, Aday R; McIntosh, Daniel H
2011-01-01
We investigate the stellar structure of massive, quiescent galaxies at z~2, based on HST/WFC3 imaging from the Early Release Science program. Our sample of 14 galaxies has stellar masses of M* > 10^{10.8} Msol and photometric redshifts of 1.5 < z < 2.5. In agreement with previous work, their half-light radii are <2 kpc, much smaller than equally massive galaxies in the present-day universe. A significant subset of the sample appear highly flattened in projection, which implies, considering viewing angle statistics, that a significant fraction of the galaxies in our sample have pronounced disks. This is corroborated by two-dimensional surface brightness profile fits. We estimate that 65% +/- 15% of the population of massive, quiescent z~2 galaxies are disk-dominated. The median disk scale length is 1.5 kpc, substantially smaller than the disks of equally massive galaxies in the present-day universe. Our results provide strong observational evidence that the much-discussed ultra-dense high-redshift gal...
Low Gas Fractions Connect Compact Star-Forming Galaxies to their z ~ 2 Quiescent Descendants
Spilker, Justin S; Marrone, Daniel P; Weiner, Benjamin J; Whitaker, Katherine E; Williams, Christina C
2016-01-01
Early quiescent galaxies at z~2 are known to be remarkably compact compared to their nearby counterparts. Possible progenitors of these systems include galaxies that are structurally similar, but are still rapidly forming stars. Here, we present Karl G. Jansky Very Large Array (VLA) observations of the CO(1-0) line towards three such compact, star-forming galaxies at z~2.3, significantly detecting one. The VLA observations indicate baryonic gas fractions >~5 times lower and gas depletion times >~10 times shorter than normal, extended massive star-forming galaxies at these redshifts. At their current star formation rates, all three objects will deplete their gas reservoirs within 100Myr. These objects are among the most gas-poor objects observed at z>2, and are outliers from standard gas scaling relations, a result which remains true regardless of assumptions about the CO-H2 conversion factor. Our observations are consistent with the idea that compact, star-forming galaxies are in a rapid state of transition t...
Revealing an Energetic Galaxy-Wide Outflow in a z~2 Ultraluminous Infrared Galaxy
Alexander, D M; Smail, I; McDermid, R; Nesvadba, N P H
2009-01-01
Leading models of galaxy formation require large-scale energetic outflows to regulate the growth of distant galaxies and their central black holes. However, current observational support for this hypothesis at high redshift is mostly limited to rare z>2 radio galaxies. Here we present Gemini-North NIFS Intregral Field Unit (IFU) observations of the [O III]5007 emission from a z~2 ultraluminous infrared galaxy (ULIRG; L_IR>10^12 L_sol) with an optically identified Active Galactic Nucleus (AGN). The spatial extent (~4-8 kpc) of the high velocity and broad [O III] emission are consistent with that found in z>2 radio galaxies, indicating the presence of a large-scale energetic outflow in a galaxy population potentially orders of magnitude more common than distant radio galaxies. The low radio luminosity of this system indicates that radio-bright jets are unlikely to be responsible for driving the outflow. However, the estimated energy input required to produce the large-scale outflow signatures (of order ~10^59 e...
HST Emission Line Galaxies at z ~ 2: The Mystery of Neon
Zeimann, Gregory; Gebhardt, Henry; Gronwall, Caryl; Hagen, Alex; Trump, Jonathan; Bridge, Joanna; Luo, Bin; Schneider, Donald
2014-01-01
We use near-IR grism spectroscopy from the Hubble Space Telescope to examine the strength of [Ne~III] 3869 relative to H-beta, [O~II] 3727 and [O~III] 5007 in 236 low mass (7.5 < log (Mstar/Msolar) < 10.5) star-forming galaxies in the redshift range 1.90 < z < 2.35. By stacking the data by stellar mass, we show that the [Ne~III]/[O~II] ratios of the z ~ 2 universe are marginally higher than those seen in a comparable set of local SDSS galaxies, and that [Ne~III]/[O~III] is enhanced by ~0.2 dex. We consider the possible explanations for this ~4-sigma result, including higher oxygen depletion out of the gas-phase, denser H~II regions, higher production of Ne22 via Wolf-Rayet stars, and the existence of a larger population of X-ray obscured AGN at z ~ 2 compared to z ~ 0. None of these simple scenarios, alone, are favored to explain the observed line ratios. We conclude by suggesting several avenues of future observations to further explore the mystery of enhanced [Ne~III] emission.
The Mass-Metallicity Relation Of A Z~2 Protocluster With MOSFIRE
Kulas, Kristin R; Shapley, Alice E; Steidel, Charles C; Konidaris, Nicholas P; Matthews, Keith; Mace, Gregory N; Rudie, Gwen C; Trainor, Ryan F; Reddy, Naveen A
2013-01-01
We present Keck/MOSFIRE observations of the role of environment in the formation of galaxies at z~2. Using K-band spectroscopy of H-alpha and [N II] emission lines, we have analyzed the metallicities of galaxies within and around a z=2.3 protocluster discovered in the HS1700+643 field. Our main sample consists of 23 protocluster and 20 field galaxies with estimates of stellar masses and gas-phase metallicities based on the N2 strong-line metallicity indicator. With these data we have examined the mass-metallicity relation (MZR) with respect to environment at z~2. We find that field galaxies follow the well-established trend between stellar mass and metallicity, such that more massive galaxies have larger metallicities. The protocluster galaxies, however, do not exhibit a dependence of metallicity on mass, with the low-mass protocluster galaxies showing an enhancement in metallicity compared to field galaxies spanning the same mass range. A comparison with galaxy formation models suggests that the mass-depende...
Residual $Z_2$ symmetries and leptonic mixing patterns from finite discrete subgroups of $U(3)$
Joshipura, Anjan S
2016-01-01
We study embedding of non-commuting $Z_2$ and $Z_m$, $m\\geq 3$ symmetries in discrete subgroups (DSG) of $U(3)$ and analytically work out the mixing patterns implied by the assumption that $Z_2$ and $Z_m$ describe the residual symmetries of the neutrino and the charged lepton mass matrices respectively. Both $Z_2$ and $Z_m$ are assumed to be subgroups of a larger discrete symmetry group $G_f$ possessing three dimensional faithful irreducible representation. The residual symmetries predict the magnitude of a column of the leptonic mixing matrix $U_{\\rm PMNS}$ which are studied here assuming $G_f$ as the DSG of $SU(3)$ designated as type C and D and large number of DSG of $U(3)$ which are not in $SU(3)$. These include the known group series $\\Sigma(3n^3)$, $T_n(m)$, $\\Delta(3n^2,m)$, $\\Delta(6n^2,m)$ and $\\Delta'(6n^2,j,k)$. It is shown that the predictions for a column of $|U_{\\rm PMNS}|$ in these group series and the C and D types of groups are all contained in the predictions of the $\\Delta(6N^2)$ groups for...
The Absence of an Environmental Dependence in the Mass-Metallicity Relation at z=2
Kacprzak, Glenn G; Nanayakkara, Themiya; Kobayashi, Chiaki; Tran, Kim-Vy H; Kewley, Lisa J; Glazebrook, Karl; Spitler, Lee; Taylor, Philip; Cowley, Michael; Labbé, Ivo; Straatman, Caroline; Tomczak, Adam
2015-01-01
We investigate the environmental dependence of the mass-metallicity relation at z=2 with MOSFIRE/Keck as part of the ZFIRE survey. Here, we present the chemical abundance of a Virgo-like progenitor at z=2.095 that has an established red sequence. We identified 43 cluster ($=2.095\\pm0.004$) and 74 field galaxies ($=2.195\\pm0.083$) for which we can measure metallicities. For the first time, we show that there is no discernible difference between the mass-metallicity relation of field and cluster galaxies to within 0.02dex. Both our field and cluster galaxy mass-metallicity relations are consistent with recent field galaxy studies at z~2. We present hydrodynamical simulations for which we derive mass-metallicity relations for field and cluster galaxies. We find at most a 0.1dex offset towards more metal-rich simulated cluster galaxies. Our results from both simulations and observations are suggestive that environmental effects, if present, are small and are secondary to the ongoing inflow and outflow processes t...
Classification of the chiral Z2XZ2 fermionic models in the heterotic superstring
Faraggi, A E; Nooij, S E M; Rizos, J
2004-01-01
The first particle physics observable whose origin may be sought in string theory is the triple replication of the matter generations. The class of Z2XZ2 orbifolds of six dimensional compactified tori, that have been most widely studied in the free fermionic formulation, correlate the family triplication with the existence of three twisted sectors in this class. In this work we seek an improved understanding of the geometrical origin of the three generation free fermionic models. Using fermionic and orbifold techniques we classify the Z2XZ2 orbifold with symmetric shifts on six dimensional compactified internal manifolds. We show that perturbative three generation models are not obtained in the case of Z2XZ2 orbifolds with symmetric shifts on complex tori, and that the perturbative three generation models in this class necessarily employ an asymmetric shift. We present a class of three generation models in which the SO(10) gauge symmetry cannot be broken perturbatively, while preserving the Standard Model mat...
Lattice calculation of nonleptonic charm decays
Simone, J.N.
1991-11-01
The decays of charmed mesons into two body nonleptonic final states are investigated. Weak interaction amplitudes of interest in these decays are extracted from lattice four-point correlation functions using a effective weak Hamiltonian including effects to order G{sub f} in the weak interactions yet containing effects to all orders in the strong interactions. The lattice calculation allows a quantitative examination of non-spectator processes in charm decays helping to elucidate the role of effects such as color coherence, final state interactions and the importance of the so called weak annihilation process. For D {yields} K{pi}, we find that the non-spectator weak annihilation diagram is not small, and we interpret this as evidence for large final state interactions. Moreover, there is indications of a resonance in the isospin {1/2} channel to which the weak annihilation process contributes exclusively. Findings from the lattice calculation are compared to results from the continuum vacuum saturation approximation and amplitudes are examined within the framework of the 1/N expansion. Factorization and the vacuum saturation approximation are tested for lattice amplitudes by comparing amplitudes extracted from lattice four-point functions with the same amplitude extracted from products of two-point and three-point lattice correlation functions arising out of factorization and vacuum saturation.
Lattice calculation of nonleptonic charm decays
Simone, James Nicholas [Univ. of California, Los Angeles, CA (United States)
1991-11-01
The decays of charmed mesons into two body nonleptonic final states are investigated. Weak interaction amplitudes of interest in these decays are extracted from lattice four-point correlation functions using a effective weak Hamiltonian including effects to order G_{f } in the weak interactions yet containing effects to all orders in the strong interactions. The lattice calculation allows a quantitative examination of non-spectator processes in charm decays helping to elucidate the role of effects such as color coherence, final state interactions and the importance of the so called weak annihilation process. For D → Kπ, we find that the non-spectator weak annihilation diagram is not small, and we interpret this as evidence for large final state interactions. Moreover, there is indications of a resonance in the isospin 1/2 channel to which the weak annihilation process contributes exclusively. Findings from the lattice calculation are compared to results from the continuum vacuum saturation approximation and amplitudes are examined within the framework of the 1/N expansion. Factorization and the vacuum saturation approximation are tested for lattice amplitudes by comparing amplitudes extracted from lattice four-point functions with the same amplitude extracted from products of two-point and three-point lattice correlation functions arising out of factorization and vacuum saturation.
Minimal realizations of supersymmetry for matrix Hamiltonians
Andrianov, Alexander A., E-mail: andrianov@icc.ub.edu; Sokolov, Andrey V., E-mail: avs_avs@rambler.ru
2015-02-06
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant symmetry matrix for a matrix Hamiltonian are presented. A method of constructing of a matrix Hamiltonian with a given constant symmetry matrix in terms of a set of arbitrary scalar functions and eigen- and associated vectors of this matrix is offered. Examples of constructing of 2×2 matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated. - Highlights: • Weak and strong minimization of a matrix intertwining operator. • Criterion of strong minimizability from the right of a matrix intertwining operator. • Conditions of existence of a constant symmetry matrix for a matrix Hamiltonian. • Method of constructing of a matrix Hamiltonian with a given constant symmetry matrix. • Examples of constructing of 2×2 matrix Hamiltonians with a given symmetry matrix.
Input-output decoupling of Hamiltonian systems : The linear case
Nijmeijer, H.; Schaft, A.J. van der
1985-01-01
In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure. In a second paper we treat the same problem for nonlinear Hamiltonian systems.
Input-output decoupling of Hamiltonian systems: The linear case
Nijmeijer, H.
1985-01-01
In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure. In a second paper we treat the same problem for nonlinear Hamiltonian systems.
Hamiltonian Dynamics at Spatial Infinity.
Alexander, Matthew
We employ a projective construction of spatial infinity in four-dimensional spacetimes which are asymptotically flat. In this construction, points of the spatial boundary of the spacetime manifold are identified with congruences of asymptotically parallel spacelike curves that are asymptotically geodesic. It is shown that for this type of construction spatial infinity is represented by a three-dimensional timelike hyperboloid, and that this follows as a consequence of the vacuum Einstein equations. We then construct tensor fields which are defined at spatial infinity, and which embody the information carried by the gravitational field regarding the total mass, linear, and angular momentum of the spacetime. It is shown that these tensor fields must satisfy a set of second order partial differential field equations at spatial infinity. The asymptotic symmetry group implied by the projective construction is examined, and is identified with the Spi group. The field equations satisfied by the tensor fields at spatial infinity can be derived from an action principle, however this action does not appear to be related in any obvious way to the Hilbert-Einstein action of general relativity. Under mappings generated by the Spi group our Lagrangian is left form -invariant, and the corresponding Noether-conserved quantities are examined. It is found that for spacetimes which are stationary or axisymmetric, these conserved quantities are not the limits of the conserved quantities associated with the infinitesimal four-dimensional coordinate transformations. It is shown that using the tensor fields at spatial infinity one can define a set of canonical variables. Further, we show that the "time" derivatives of the configuration variables can be expressed in terms of some of the momentum densities; the remaining momentum densities are constrained. Finally, we construct the Hamiltonian, and examine the transformations generated by it.
Lajer, Mathilde; Tarnow, L; Fleckner, Jan
2004-01-01
AIMS: The Z-2 allele of the (AC)n polymorphism in the aldose reductase gene (ALR2) confers increased risk of microvascular diabetic complications, whereas the Z+2 allele has been proposed to be a marker of protection. However data are conflicting. Therefore, we investigated whether this polymorph......AIMS: The Z-2 allele of the (AC)n polymorphism in the aldose reductase gene (ALR2) confers increased risk of microvascular diabetic complications, whereas the Z+2 allele has been proposed to be a marker of protection. However data are conflicting. Therefore, we investigated whether...... normoalbuminuria were genotyped for the case-control study. In addition, 102 case trios and 98 control trios were genotyped for a family-based study. RESULTS: Thirteen different alleles were identified. In the case-control study, the Z+2 allele frequency was significantly higher in the normoalbuminuric diabetic...
Structure of the Λ (1405 ) from Hamiltonian effective field theory
Liu, Zhan-Wei; Hall, Jonathan M. M.; Leinweber, Derek B.; Thomas, Anthony W.; Wu, Jia-Jun
2017-01-01
The pole structure of the Λ (1405 ) is examined by fitting the couplings of an underlying Hamiltonian effective field theory to cross sections of K-p scattering in the infinite-volume limit. Finite-volume spectra are then obtained from the theory, and compared to lattice QCD results for the mass of the Λ (1405 ) . Momentum-dependent, nonseparable potentials motivated by the well-known Weinberg-Tomozawa terms are used, with SU(3) flavor symmetry broken in the couplings and masses. In addition, we examine the effect on the behavior of the spectra from the inclusion of a bare triquarklike isospin-zero basis state. It is found that the cross sections are consistent with the experimental data with two complex poles for the Λ (1405 ) , regardless of whether a bare-baryon basis state is introduced or not. However, it is apparent that the bare baryon is important for describing the results of lattice QCD at high pion masses.
Resonant superfluidity in an optical lattice
Titvinidze, Irakli; Hofstetter, Walter [Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, 60438 Frankfurt am Main (Germany); Snoek, Michiel [Institute for Theoretical Physics, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)
2010-07-01
We study a system of ultracold fermionic Potassium ({sup 40}K) atoms in a three-dimensional optical lattice in the neighborhood of an s-wave Feshbach resonance. Close to resonance, the system is described by a multi-band Bose-Fermi Hubbard Hamiltonian. We derive an effective lowest-band Hamiltonian in which the effect of the higher band is incorporated by a self-consistent mean-field approximation. The resulting model is solved by means of Generalized Dynamical Mean-Field Theory. In addition to the BEC/BCS crossover we find on the BCS side of the resonance a phase transition to a fermionic Mott insulator at half filling, induced by the repulsive fermionic background scattering length. We also calculate the critical temperature of the BEC/BCS-state across the resonance and find it to be minimal at resonance.
Tanamoto, Tetsufumi; Ono, Keiji; Liu, Yu-xi; Nori, Franco
2015-06-17
Hamiltonian engineering is an important approach for quantum information processing, when appropriate materials do not exist in nature or are unstable. So far there is no stable material for the Kitaev spin Hamiltonian with anisotropic interactions on a honeycomb lattice, which plays a crucial role in the realization of both Abelian and non-Abelian anyons. Here, we show two methods to dynamically realize the Kitaev spin Hamiltonian from the conventional Heisenberg spin Hamiltonian using pulse-control techniques based on the Baker-Campbell-Hausdorff (BCH) formula. In the first method, the Heisenberg interaction is changed into Ising interactions in the first process of the pulse sequence. In the next process of the first method, we transform them to a desirable anisotropic Kitaev spin Hamiltonian. In the second more efficient method, we show that if we carefully design two-dimensional pulses that vary depending on the qubit location, we can obtain the desired Hamiltonian in only one step of applying the BCH formula. As an example, we apply our methods to spin qubits based on quantum dots, in which the effects of both the spin-orbit interaction and the hyperfine interaction are estimated.
Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems
Wang Xing-Zhong; Fu Hao; Fu Jing-Li
2012-01-01
This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems.Firstly,the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action.Secondly,the determining equations and structure equation of Lie symmetry of the system are obtained.Thirdly,the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems.Finally,an example is discussed to illustrate the application of the results.
Incorporation of New Information in an Approximate Hamiltonian
Viazminsky, C. P.; Baza, S
2002-01-01
Additional information about the eigenvalues and eigenvectors of a physical system demands extension of the effective Hamiltonian in use. In this work we extend the effective Hamiltonian that describes partially a physical system so that the new Hamiltonian comprises, in addition to the information in the old Hamiltonian, new information, available by means of experiment or theory. A simple expression of the enlarged Hamiltonian, which does not involve matrix inversion, is obtained. It is als...
Z2 Invariance of Germanene on MoS2 from First Principles
Amlaki, Taher; Bokdam, Menno; Kelly, Paul J.
2016-06-01
We present a low energy Hamiltonian generalized to describe how the energy bands of germanene (Ge ¯ ) are modified by interaction with a substrate or a capping layer. The parameters that enter the Hamiltonian are determined from first-principles relativistic calculations for Ge ¯ |MoS2 bilayers and MoS2|Ge ¯ |MoS2 trilayers and are used to determine the topological nature of the system. For the lowest energy, buckled germanene structure, the gap depends strongly on how germanene is oriented with respect to the MoS2 layer(s). Topologically nontrivial gaps for bilayers and trilayers can be almost as large as for a freestanding germanene layer.
Dual Lattice of ℤ-module Lattice
Futa Yuichi
2017-07-01
Full Text Available In this article, we formalize in Mizar [5] the definition of dual lattice and their properties. We formally prove that a set of all dual vectors in a rational lattice has the construction of a lattice. We show that a dual basis can be calculated by elements of an inverse of the Gram Matrix. We also formalize a summation of inner products and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász base reduction algorithm and cryptographic systems with lattice [20], [10] and [19].
Thick vortices in SU(2) lattice gauge theory
Cheluvaraja, Srinath
2004-01-01
Three dimensional SU(2) lattice gauge theory is studied after eliminating thin monopoles and the smallest thick monopoles. Kinematically this constraint allows the formation of thick vortex loops which produce Z(2) fluctuations at longer length scales. The thick vortex loops are identified in a three dimensional simulation. A condensate of thick vortices persists even after the thin vortices have all disappeared. The thick vortices decouple at a slightly lower temperature (higher beta) than t...
Radial Quantization for Conformal Field Theories on the Lattice
Brower, Richard C; Neuberger, Herbert
2012-01-01
We consider radial quantization for conformal quantum field theory with a lattice regulator. A Euclidean field theory on $\\mathbb R^D$ is mapped to a cylindrical manifold, $\\mathbb R\\times \\mathbb S^{D-1}$, whose length is logarithmic in scale separation. To test the approach, we apply this to the 3D Ising model and compute $\\eta$ for the first $Z_2$ odd primary operator.
Fumagalli, Michele; Prochaska, J Xavier; Rafelski, Marc; Kanekar, Nissim
2014-01-01
We present results from a survey designed to probe the star formation properties of 32 damped Ly-alpha systems (DLAs) at z~2.7. By using the "double-DLA" technique that eliminates the glare of the bright background quasars, we directly measure the rest-frame FUV flux from DLAs and their neighbouring galaxies. We place stringent constraints on the star formation rates (SFRs) of DLAs to 2-sigma limits of 2 M/yr at impact parameters b < SFR^(0.8)+6 kpc, in contrast with current samples of confirmed DLA galaxies, which appear to be biased. Our observations also disfavor a scenario in which the majority of DLAs arise from bright LBGs at distances 20 < b < 100 kpc. These new findings corroborate a picture in which DLAs do not originate from highly star forming systems that are coincident with the absorbers, and instead suggest that DLAs are associated with faint, possibly isolated, star-forming galaxies. Potential shortcomings of this scenario and future strategies for further investigation are discussed.
Hamiltonian Description of Multi-fluid Streaming
Valls, C.; de La Llave, R.; Morrison, P. J.
2001-10-01
The general noncanonical Hamiltonian description of interpenetrating fluids coupled by electrostatic, gravitational, or other forces is presented. This formalism is used to describe equilibrium and nonlinear stability using techniques of Hamiltonian dynamics theory. For example, we study the stability of two warm counter-streaming electron beams in a neutralizing ion background. The normal modes are obtained from an energy functional by computing the lowest-order expression for the perturbed energy about an equilibrium, and transforming the corresponding system into action-angle variables. Higher-order terms in the Hamiltonian provide coupling between normal modes and can lead to instability because of the presence of negative energy modes (NEM's). (The signature of the NEM's is determined by the signature of the Hamiltonian, Moser's bracket definition, or the conventional plasma definition in terms of the dielectric function, all of which are shown to be equivalent.) The possible nonlinear behavior is discovered by constructing the Birkhoff normal form. Accounting for resonances, we transform away terms in the Hamiltonian to address the question of long-time stability for such systems.
An intuitive Hamiltonian for quantum search
Fenner, S A
2000-01-01
We present new intuition behind Grover's quantum search algorithm by means of a Hamiltonian. Given a black-box Boolean function f mapping strings of length n into {0,1} such that f(w) = 1 for exactly one string w, L. K. Grover describes a quantum algorithm that finds w in O(2^{n/2}) time. Farhi & Gutmann show that w can also be found in the same amount time by letting the quantum system evolve according to a simple Hamiltonian depending only on f. Their system evolves along a path far from that taken by Grover's original algorithm, however. The current paper presents an equally simple Hamiltonian matching Grover's algorithm step for step. The new Hamiltonian is similar in appearance from that of Farhi & Gutmann, but has some important differences, and provides new intuition for Grover's algorithm itself. This intuition both contrasts with and supplements other explanations of Grover's algorithm as a rotation in two dimensions, and suggests that the Hamiltonian-based approach to quantum algorithms can ...
A Multi-Wavelength Census of Dust and Star Formation in Galaxies at z ~ 2
Shivaei, Irene; Reddy, Naveen; MOSDEF Collaboration
2017-01-01
Redshift of z ~ 2 is an important era in the history of the universe, as it contains the peak of star formation rate density and quasar activity. We study the galaxy properties during this era from two different, yet complementary, aspects: by studying formation of stars and mass assembly, and exploring the properties of galactic dust. We use a wealth of multi-wavelength data, from UV to far-IR, to obtain a complete census of obscured and unobscured star formation in galaxies. Our data consists of rest-frame optical spectra from the MOSDEF survey, rest-frame UV and optical photometric data from the 3D-HST survey, and mid- and far-IR data obtained by the Spitzer and Herschel telescopes. In the MOSDEF survey, we acquired rest-frame optical spectra of ~ 1500 galaxies with the MOSFIRE spectrograph on the Keck I telescope. MOSDEF is currently the largest survey of the rest-frame optical properties of galaxies at 1.37 ≤ z ≤ 3.80. Using the multi-wavelength data sets, we show that Hα SFRs, corrected for dust attenuation using the Hβ line, accurately trace SFRs up to ~ 300 M⊙ yr-1, when compared with panchromatic (UV-to-far-IR) SED models. Using Hα SFRs for a large sample of ~ 200 galaxies at z ~ 2, we explore the SFR-M* relation and show that the slope of this relation is shallower than previously measured. We conclude that the scatter in the SFR-M* relation is dominated by uncertainties in dust correction and cannot be used to measure the star formation stochasticity. Furthermore, we investigate the robustness of Spitzer/MIPS 24 micron flux as an SFR indicator and its variation with ISM physical parameters. We find that 24 micron flux, which at z ~ 2 traces the emission from the PAH grains, significantly depends on metallicity, such that there is a PAH deficiency in metal-poor galaxies. We demonstrate that commonly-used conversions of 24 micron flux to IR luminosity underestimate the IR luminosity of low-mass galaxies by more than a factor of 2. Our results
LOOKING FOR LYMAN ALPHA EMITTING GALAXIES AT Z - 2.1
Guaita, Lucia
2010-01-01
Este proyecto de tesis de doctorado tuvo su inicio en Diciembre de 2007. En esta fecha se tomaron imágenes de la región del cielo llamada Extended Chandra Deep Field-South (ECDF-S) a través del filtro de banda angosta NB3727 y con el instrumento MO-SAIC II del telescopio de 4 metros de Cerro Tololo. El filtro está caracterizado por una longitud de onda central que corresponde a la línea Lγα con un desplazamiento hacia el rojo (redshift). z - 2.1. En este campo hemos descubierto una muestra de...
Lyα Forest Tomography of the z > 2 Cosmic Web
Lee, Khee-Gan
2016-10-01
The hydrogen Lyα forest is an important probe of the z > 2 Universe that is otherwise challenging to observe with galaxy redshift surveys, but this technique has traditionally been limited to 1D studies in front of bright quasars. However, by pushing to faint magnitudes (g > 23) with 8-10m large telescopes it becomes possible to exploit the high area density of high-redshift star-forming galaxies to create 3D tomographic maps of large-scale structure in the foreground. I describe the first pilot observations using this technique, as well discuss future surveys and the resulting science possibilities for galaxy evolution and cosmology.
The first ultraviolet quasar stacked spectrum at z=2.4 from WFC3
Lusso, E; Hennawi, J F; Prochaska, J X; Vignali, C; Stern, J; O'Meara, J M
2015-01-01
The ionising continuum from active galactic nuclei (AGN) is fundamental for interpreting their broad emission lines and understanding their impact on the surrounding gas. Furthermore, it provides hints on how matter accretes onto supermassive black holes. Using HST's Wide Field Camera 3 we have constructed the first stacked ultraviolet (rest-frame wavelengths 600-2500\\AA) spectrum of 53 luminous quasars at z=2.4, with a state-of-the-art correction for the intervening Lyman forest and Lyman continuum absorption. The continuum slope ($f_\
The Evolution of M_*/M_BH Between z=2 and z=0
Trakhtenbrot, Benny; Netzer, Hagai
2010-01-01
We propose a novel method to estimate M_*/M_BH, the ratio of stellar mass (M_*) to black hole mass (M_BH), at various redshifts using two recent observational results: the correlation between the bolometric luminosity of active galactic nuclei (AGN) and the star formation rate (SFR) in their host galaxies, and the correlation between SFR and M_* in star-forming (SF) galaxies. Our analysis is based on M_BH and L_bol measurements in two large samples of type-I AGN at z~1 and z~2, and the measur...
Motion of particles on a $z=2$ Lifshitz black hole in 3+1 dimensions
Olivares, Marco; Villanueva, J R; Moncada, Felipe
2013-01-01
We study the geodesic structure of a $z=2$ Lifshitz black hole in 3+1 spacetime dimensions that is an exact solution to the Einstein-scalar-Maxwell theory. We investigate the motion of massless and massive particles in this background using the standard Lagrangian procedure. Analytical expressions are obtained for radial and angular motions of the test particles, where the polar trajectories are given in terms of the $\\wp$ - Weierstrass elliptic function. It is shown that confined orbits are not allowed on this spacetime, this result agrees with the obtained recently in the literature for other Lifshitz black holes.
SOUDAGE D'ACIER Z 2 CN 18-10 PAR LASER CO2
Petesch, B.; Sakout, A.; LAURENT M.; M. Robin
1987-01-01
Le soudage d'un acier Z 2 CN 18 par faisceau laser a été étudié. L'influence principaux paramètres vitesse, puissance, focalisation a été examinée. Les moyens classiques de caractérisation des soudures ont été utilisées : observations métallographiques forme de la zone fondue, quantité de porosités et énergie absorbée. Le maximum de pénétration correspond au maximum d'énergie absorbée.
Hirose, Yuhei; Oguchi, Akihide; Fukumoto, Yoshiyuki
2016-09-01
We study Heisenberg antiferromagnets on a diamond-like decorated square lattice perturbed by further neighbor couplings. The second-order effective Hamiltonian is calculated and the resultant Hamiltonian is found to be a square-lattice quantum-dimer model with a finite hopping amplitude and no repulsion, which suggests the stabilization of the plaquette phase. Our recipe for constructing quantum-dimer models can be adopted for other lattices and provides a route for the experimental realization of quantum-dimer models.
Exciton-polaritons in lattices: A non-linear photonic simulator
Amo, Alberto; Bloch, Jacqueline
2016-10-01
Microcavity polaritons are mixed light-matter quasiparticles with extraordinary nonlinear properties, which can be easily accessed in photoluminescence experiments. Thanks to the possibility of designing the potential landscape of polaritons, this system provides a versatile photonic platform to emulate 1D and 2D Hamiltonians. Polaritons allow transposing to the photonic world some of the properties of electrons in solid-state systems, and to engineer Hamiltonians for photons with novel transport properties. Here we review some experimental implementations of polariton Hamiltonians using lattice geometries. xml:lang="fr"
Nekhoroshev theorem for the periodic Toda lattice.
Henrici, Andreas; Kappeler, Thomas
2009-09-01
The periodic Toda lattice with N sites is globally symplectomorphic to a two parameter family of N-1 coupled harmonic oscillators. The action variables fill out the whole positive quadrant of R(N-1). We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's theorem applies on (almost) all parts of phase space (2000 Mathematics Subject Classification: 37J35, 37J40, 70H06).
Optimal control of Rydberg lattice gases
Cui, Jian; van Bijnen, Rick; Pohl, Thomas; Montangero, Simone; Calarco, Tommaso
2017-09-01
We present optimal control protocols to prepare different many-body quantum states of Rydberg atoms in optical lattices. Specifically, we show how to prepare highly ordered many-body ground states, GHZ states as well as some superposition of symmetric excitation number Fock states, that inherit the translational symmetry from the Hamiltonian, within sufficiently short excitation times minimising detrimental decoherence effects. For the GHZ states, we propose a two-step detection protocol to experimentally verify the optimised preparation of the target state based only on standard measurement techniques. Realistic experimental constraints and imperfections are taken into account by our optimisation procedure making it applicable to ongoing experiments.
Equivalent Hamiltonians with additional discrete states
Chinn, C.R. (Physics Department, Lawrence Livermore National Laboratory, Livermore, CA (USA)); Thaler, R.M. (Los Alamos National Laboratory, Los Alamos, NM (USA) Department of Physics, Case Western Reserve University, Cleveland, OH (USA))
1991-01-01
Given a particular Hamiltonian {ital H}, we present a method to generate a new Hamiltonian {ital {tilde H}}, which has the same discrete energy eigenvalues and the same continuum phase shifts as {ital H}, but which also has additional given discrete eigenstates. This method is used to generate a Hamiltonian {ital h}{sub 1}, which gives rise to a complete orthonormal set of basis states, which contain a given set of biorthonormal discrete states, the continuum states of which are asymptotic to plane waves (have zero phase shifts). Such a set of states may be helpful in representing the medium modification of the Green's function due to the Pauli principle, as well as including Pauli exclusion effects into scattering calculations.
Equivalent Hamiltonians with additional discrete states
Chinn, C. R.; Thaler, R. M.
1991-01-01
Given a particular Hamiltonian H, we present a method to generate a new Hamiltonian H~, which has the same discrete energy eigenvalues and the same continuum phase shifts as H, but which also has additional given discrete eigenstates. This method is used to generate a Hamiltonian h1, which gives rise to a complete orthonormal set of basis states, which contain a given set of biorthonormal discrete states, the continuum states of which are asymptotic to plane waves (have zero phase shifts). Such a set of states may be helpful in representing the medium modification of the Green's function due to the Pauli principle, as well as including Pauli exclusion effects into scattering calculations.
Hamiltonian Dynamics of Cosmological Quintessence Models
Ivanov, Rossen I
2016-01-01
The time-evolution dynamics of two nonlinear cosmological real gas models has been reexamined in detail with methods from the theory of Hamiltonian dynamical systems. These examples are FRWL cosmologies, one based on a gas, satisfying the van der Waals equation and another one based on the virial expansion gas equation. The cosmological variables used are the expansion rate, given by the Hubble parameter, and the energy density. The analysis is aided by the existence of global first integral as well as several special (second) integrals in each case. In addition, the global first integral can serve as a Hamiltonian for a canonical Hamiltonian formulation of the evolution equations. The conserved quantities lead to the existence of stable periodic solutions (closed orbits) which are models of a cyclic Universe. The second integrals allow for explicit solutions as functions of time on some special trajectories and thus for a deeper understanding of the underlying physics. In particular, it is shown that any pos...
Gravitational surface Hamiltonian and entropy quantization
Ashish Bakshi
2017-02-01
Full Text Available The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos–Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.
Gravitational surface Hamiltonian and entropy quantization
Bakshi, Ashish; Majhi, Bibhas Ranjan; Samanta, Saurav
2017-02-01
The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos-Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.
Manifest Covariant Hamiltonian Theory of General Relativity
Cremaschini, Claudio
2016-01-01
The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source fields is addressed, by extending the so-called "DeDonder-Weyl" formalism to the treatment of classical fields in curved space-time. The theory is based on a synchronous variational principle for the Einstein equation, formulated in terms of superabundant variables. The technique permits one to determine the continuum covariant Hamiltonian structure associated with the Einstein equation. The corresponding continuum Poisson bracket representation is also determined. The theory relies on first-principles, in the sense that the conclusions are reached in the framework of a non-perturbative covariant approach, which allows one to preserve both the 4-scalar nature of Lagrangian and Hamiltonian densities as well as the gauge invariance property of the theory.
Near integrability of kink lattice with higher order interactions
Jiang, Yunguo; He, Song
2016-01-01
In the paper, we make use of Manton's analytical method to investigate the force between kink and the anti-kink with large distance in $1+1$ dimensional field theory. The related potential has infinite order corrections of exponential pattern, and coefficients for each order are determined. These coefficients can also be obtained by solving the equation of the fluctuation around the vacuum. At the lowest order, the kink lattice represents the Toda lattice. With higher order correction terms, the kink lattice can represent one kind of the generic Toda lattice. With only two sites, the kink lattice is classically integrable. If the number of sites of the lattice is larger than two, the kink lattice is not integrable but a near integrable system. We take use of the Flaschka's variables to study the Lax pair of the kink lattice. These Flaschka's variables have interesting algebraic relations and the non-integrability can be manifested. We also discussed the higher Hamiltonians for the deformed open Toda lattice, ...
ZFIRE: A KECK/MOSFIRE Spectroscopic Survey of Galaxies in Rich Environments at z~2
Nanayakkara, Themiya; Kacprzak, Glenn G; Yuan, Tiantian; Tran, Kim-Vy; Spitler, Lee; Straatman, Lisa Kewley Caroline; Cowley, Michael; Fisher, David; Labbe, Ivo; Tomczak, Adam; Allen, Rebecca; Alcorn, Leo
2016-01-01
We present an overview and the first data release of ZFIRE, a spectroscopic redshift survey of star-forming galaxies that utilizes the MOSFIRE instrument on Keck-I to study galaxy properties in rich environments at $1.5<z<2.5$. ZFIRE measures accurate spectroscopic redshifts and basic galaxy properties derived from multiple emission lines. The galaxies are selected from a stellar mass limited sample based on deep near infra-red imaging ($\\mathrm{K_{AB}<25}$) and precise photometric redshifts from the ZFOURGE and UKIDSS surveys as well as grism redshifts from 3DHST. Between 2013--2015 ZFIRE has observed the COSMOS and UDS legacy fields over 13 nights and has obtained 211 galaxy redshifts over $1.57<z<2.66$ from a combination of nebular emission lines (such as \\Halpha, \\NII, \\Hbeta, \\OII, \\OIII, \\SII) observed at 1--2\\micron. Based on our medium-band NIR photometry, we are able to spectrophotometrically flux calibrate our spectra to \\around10\\% accuracy. ZFIRE reaches $5\\sigma$ emission line flux...
The nature of z ~ 2.3 Lyman-alpha emitters
Nilsson, Kim K; Møller, Palle; Möller-Nilsson, Ole; Tapken, Christian; Freudling, Wolfram; Fynbo, Johan P U
2010-01-01
We study the multi-wavelength properties of a set of 171 Ly-alpha emitting candidates at redshift z = 2.25 found in the COSMOS field. The candidates are shown to have different properties from those of Ly-alpha emitters found at higher redshift, by fitting the spectral energy distributions (SEDs) using a Monte-Carlo Markov-Chain technique and including nebular emission in the spectra. The dust contents and stellar masses are both higher, with A_V = 0.0 - 2.0 mag and stellar masses in the range log M_* = 9.0 - 11.0 M_sun. Young population ages are well constrained, but older population ages are typically unconstrained. In 40 % of the galaxies only a single, young population of stars is observed. We show that the ages and Ly-alpha fluxes of the best fit galaxies are correlated with their dust properties, with higher dust extinction in younger galaxies. We conclude that the stellar properties of Ly-alpha emitters at z = 2.25 are different from those at higher redshift and that they are very diverse. Ly-alpha sel...
Evolution in the properties of Lyman-alpha emitters from redshifts z ~ 3 to z ~ 2
Nilsson, Kim K; Moeller, Palle; Freudling, Wolfram; Fynbo, Johan P U; Meisenheimer, Klaus; Laursen, Peter; Oestlin, Goeran
2008-01-01
Context: Narrow-band surveys for Ly-alpha emitters (LAEs) is a powerful tool in detecting high, and very high, redshift galaxies. Even though samples are growing at redshifts z = 3 - 6, the nature of these galaxies is still poorly known. Aims: To study the properties of z = 2.25 LAEs and compare those with the properties of z > 3 LAEs. Methods: We present narrow-band imaging made with the MPG/ESO 2.2m telescope with the WFI detector. We have made a selection for emission-line objects and find 170 candidate typical LAEs and 17 candidates which we regard as high UV-transmission LAEs. We have derived the magnitudes of these objects in 8 bands from u* to Ks, and studied if they have X-ray and/or radio counterparts. Results: We show that there has been significant evolution in the properties of LAEs between redshift z ~ 3 and z = 2.25. The spread in spectral energy distributions (SEDs) at the lower redshift is larger and we detect a significant AGN contribution in the sample. The distribution of the equivalent wid...
Submillimeter observations of the J2142-4423 Lya protocluster at z = 2.38
Beelen, A; Kovács, A; Lagache, G; De Breuck, C; Weiss, A; Menten, K M; Colbert, J W; Dole, H; Siringo, G; Kreysa, E
2008-01-01
We present observations aimed at exploring both the nature of Lya emitting nebulae (Lya blobs) at z=2.38 and the way they trace large scale structure (LSS), by exploring their proximity to maximum starbursts through submillimeter emission. Our most important objectives are to make a census of associated submillimeter galaxies (SMGs), check their properties, and look for a possible overdensity in the protocluster J2142-4426 at z=2.38. We used the newly commissioned Large APEX Bolometer Camera (LABoCa) on the Atacama Pathfinder EXperiment (APEX) telescope, in its Science Verification phase, to carry out a deep 10'x10' map at 870 micron, and we performed multiple checks of the quality of data processing and source extraction. Our map, the first published deep image, confirms the capabilities of APEX/LABoCa as the most efficient current equipment for wide and deep submm mapping. Twenty-two sources were securely extracted with 870 micron flux densities in the range 3-21 mJy, rms noise 0.8-2.4 mJy, and far-IR lumin...
Bulge-forming galaxies with an extended rotating disk at z~2
Tadaki, Ken-ichi; Kodama, Tadayuki; Wuyts, Stijn; Wisnioski, Emily; Schreiber, Natascha M Förster; Burkert, Andreas; Lang, Philipp; Tacconi, Linda J; Lutz, Dieter; Belli, Sirio; Davies, Richard I; Hatsukade, Bunyo; Hayashi, Masao; Herrera-Camus, Rodrigo; Ikarashi, Soh; Inoue, Shigeki; Kohno, Kotaro; Koyama, Yusei; Mendel, J Trevor; Nakanishi, Kouichiro; Shimakawa, Rhythm; Suzuki, Tomoko L; Tamura, Yoichi; Tanaka, Ichi; Übler, Hannah; Wilman, Dave J
2016-01-01
We present 0".2-resolution Atacama Large Millimeter/submillimeter Array observations at 870 um for 25 Halpha-seleced star-forming galaxies (SFGs) around the main-sequence at z=2.2-2.5. We detect significant 870 um continuum emission in 16 (64%) of these SFGs. The high-resolution maps reveal that the dust emission is mostly radiated from a single region close to the galaxy center. Exploiting the visibility data taken over a wide $uv$ distance range, we measure the half-light radii of the rest-frame far-infrared emission for the best sample of 12 SFGs. We find nine galaxies to be associated with extremely compact dust emission with R_{1/2,870um}1e10 Msol/kpc^2 in several hundred Myr, i.e. by z~2. Moreover, ionized gas kinematics reveal that they are rotation-supported with an angular momentum as large as that of typical SFGs at z=1-3. Our results suggest bulges are commonly formed in extended rotating disks by internal processes, not involving major mergers.
Galactic Outflows in Absorption and Emission: Near-UV Spectroscopy of Galaxies at 1<z<2
Erb, Dawn K; Henry, Alaina L; Martin, Crystal L
2012-01-01
We study large-scale outflows in a sample of 96 star-forming galaxies at 1<z<2, using near-UV spectroscopy of FeII and MgII absorption and emission. The average blueshift of the FeII interstellar absorption lines with respect to the systemic velocity is -85+/-10 km/s at z~1.5, with standard deviation 87 km/s; this is a decrease of a factor of two from the average blueshift measured for far-UV interstellar absorption lines in similarly selected galaxies at z~2. The profiles of the MgII 2796, 2803 lines show much more variety than the FeII profiles, which are always seen in absorption; MgII ranges from strong emission to pure absorption, with emission more common in galaxies with blue UV slopes and at lower stellar masses. Outflow velocities, as traced by the centroids and maximum extent of the absorption lines, increase with increasing stellar mass with 2-3sigma significance, in agreement with previous results. We study fine structure emission from FeII*, finding several lines of evidence in support of t...
The Curious Case of Lyman Alpha Emitters: Growing Younger from z ~ 3 to z ~ 2?
Acquaviva, Viviana; Gawiser, Eric; Guaita, Lucia
2011-01-01
Lyman Alpha Emitting (LAE) galaxies are thought to be progenitors of present-day L* galaxies. Clustering analyses have suggested that LAEs at z ~ 3 might evolve into LAEs at z ~ 2, but it is unclear whether the physical nature of these galaxies is compatible with this hypothesis. Several groups have investigated the properties of LAEs using spectral energy distribution (SED) fitting, but direct comparison of their results is complicated by inconsistencies in the treatment of the data and in the assumptions made in modeling the stellar populations, which are degenerate with the effects of galaxy evolution. By using the same data analysis pipeline and SED fitting software on two stacked samples of LAEs at z = 3.1 and z = 2.1, and by eliminating several systematic uncertainties that might cause a discrepancy, we determine that the physical properties of these two samples of galaxies are dramatically different. LAEs at z = 3.1 are found to be old (age ~ 1 Gyr) and metal-poor (Z Z_Sun). The difference in the obse...
The declining importance of major mergers for galaxy assembly at 1<z<2
Williams, Rik J; Franx, Marijn
2011-01-01
Using mass-selected galaxy samples from deep multiwavelength data we investigate the incidence of close galaxy pairs between z=0.4-2. Many such close pairs will eventually merge, and the pair fraction is therefore connected to the merger rate. In this analysis we distinguish between likely progenitors of "dry mergers" (two quiescent red galaxies) and those that include star-forming constituents. Over this redshift range 4-7% of log M/Msun>10.5 quiescent galaxies have a similar-mass quiescent galaxy within 30h^-1 kpc; when minor companions (1:10 mass ratio or greater) are included, the "dry" pair fraction increases to 5-15%. The mean total pair fraction, including both star-forming and quiescent companions to massive "dead" galaxies, is essentially constant (within ~10%) to z=2 for both major and minor merger candidates. If the constant pair fraction to z=2 implies a roughly constant merger rate per unit time, then most mergers in fact occur at z<1. Thus, even though other studies find major mergers to be r...
The Properties of H{\\alpha} Emission-Line Galaxies at $z$ = 2.24
An, F X; Wang, W -H; Huang, J -S; Kong, X; Wang, J -X; Fang, G W; Zhu, F; Gu, Q -S; Wu, H; Hao, L; Xia, X -Y
2014-01-01
Using deep narrow-band $H_2S1$ and $K_{s}$-band imaging data obtained with CFHT/WIRCam, we identify a sample of 56 H$\\alpha$ emission-line galaxies (ELGs) at $z=2.24$ with the 5$\\sigma$ depths of $H_2S1=22.8$ and $K_{s}=24.8$ (AB) over 383 arcmin$^{2}$ area in the ECDFS. A detailed analysis is carried out with existing multi-wavelength data in this field. Three of the 56 H$\\alpha$ ELGs are detected in Chandra 4 Ms X-ray observation and two of them are classified as AGNs. The rest-frame UV and optical morphologies revealed by HST/ACS and WFC3 deep images show that nearly half of the H$\\alpha$ ELGs are either merging systems or with a close companion, indicating that the merging/interacting processes play a key role in regulating star formation at cosmic epoch z=2-3; About 14% are too faint to be resolved in the rest-frame UV morphology due to high dust extinction. We estimate dust extinction form SEDs. We find that dust extinction is generally correlated with H$\\alpha$ luminosity and stellar mass (SM). Our res...
Identification of z~>2 Herschel 500 micron sources using color-deconfusion
Shu, X W; Bourne, N; Schreiber, C; Wang, T; Dunlop, J S; Fontana, A; Leiton, R; Pannella, M; Okumura, K; Michalowski, M J; Santini, P; Merlin, E; Buitrago, F; Bruce, V A; Amorin, R; Castellano, M; Derriere, S; Comastri, A; Cappelluti, N; Wang, J X; Ferguson, H C
2015-01-01
We present a new method to search for candidate z~>2 Herschel 500{\\mu}m sources in the GOODS-North field, using a S500{\\mu}m/S24{\\mu}m "color deconfusion" technique. Potential high-z sources are selected against low-redshift ones from their large 500{\\mu}m to 24{\\mu}m flux density ratios. By effectively reducing the contribution from low-redshift populations to the observed 500{\\mu}m emission, we are able to identify counterparts to high-z 500{\\mu}m sources whose 24{\\mu}m fluxes are relatively faint. The recovery of known z~4 starbursts confirms the efficiency of this approach in selecting high-z Herschel sources. The resulting sample consists of 34 dusty star-forming galaxies at z~>2. The inferred infrared luminosities are in the range 1.5x10^12-1.8x10^13 Lsun, corresponding to dust-obscured star formation rates (SFRs) of ~260-3100 Msun/yr for a Salpeter IMF. Comparison with previous SCUBA 850{\\mu}m-selected galaxy samples shows that our method is more efficient at selecting high-z dusty galaxies with a medi...
Quasars Probing Quasars VI. Excess HI Absorption Within One Proper Mpc of z~2 Quasars
Prochaska, J Xavier; Lee, Khee-Gan; Cantalupo, Sebastiano; Bovy, Jo; Djorgovski, S G; Ellison, Sara L; Lau, Marie Wingyee; Martin, Crystal L; Myers, Adam; Rubin, Kate H R; Simcoe, Robert A
2013-01-01
With close pairs of quasars at different redshifts, a background quasar sightline can be used to study a foreground quasar's environment in absorption. We use a sample of 650 projected quasar pairs to study the HI Lya absorption transverse to luminous, z~2 quasars at proper separations of 30kpc 17.3) at separations R<200kpc, which decreases to ~20% at R~1Mpc, but still represents a significant excess over the cosmic average. This excess of optically thick absorption can be described by a quasar-absorber cross-correlation function xi_QA(r) = (r/r_0)^gamma with a large correlation length r_0 = 12.5+2.7-1.4 Mpc/h (comoving) and gamma = 1.68+0.14-0.30. The HI absorption measured around quasars exceeds that of any previously studied population, consistent with quasars being hosted by massive dark matter halos Mhalo~10^12.5 Msun at z~2.5. The environments of these massive halos are highly biased towards producing optically thick gas, and may even dominate the cosmic abundance of Lyman limit systems and hence th...
CANDELS: Constraining the AGN-Merger Connection with Host Morphologies at z~2
Kocevski, Dale D; Mozena, Mark; Koekemoer, Anton M; Nandra, Kirpal; Rangel, Cyprian; Laird, Elise S; Brusa, Marcella; Wuyts, Stijn; Trump, Jonathan R; Koo, David C; Somerville, Rachel S; Bell, Eric F; Lotz, Jennifer M; Alexander, David M; Bournaud, Frederic; Conselice, Christopher J; Dahlen, Tomas; Dekel, Avashi; Donley, Jennifer L; Dunlop, James S; Finoguenov, Alexis; Georgakakis, Antonis; Giavalisco, Mauro; Guo, Yicheng; Grogin, Norman A; Hathi, Nimish P; Juneau, Stephanie; Kartaltepe, Jeyhan S; Lucas, Ray A; McGrath, Elizabeth J; McIntosh, Daniel H; Mobasher, Bahram; Robaina, Aday R; Rosario, David; Straughn, Amber N; van der Wel, Arjen; Villforth, Carolin
2011-01-01
Using HST/WFC3 imaging taken as part of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS), we examine the role that major galaxy mergers play in triggering active galactic nuclei (AGN) activity at z~2. Our sample consists of 72 moderate-luminosity (Lx ~ 1E42-1E44 erg/s) AGN at 1.5<z<2.5 that are selected using the 4 Msec Chandra observations in the Chandra Deep Field South, the deepest X-ray observations to date. Employing visual classifications, we have analyzed the rest-frame optical morphologies of the AGN host galaxies and compared them to a mass-matched control sample of 216 non-active galaxies at the same redshift. We find that most of the AGN reside in disk galaxies (51.4%), while a smaller percentage are found in spheroids (27.8%). Roughly 16.7% of the AGN hosts have highly disturbed morphologies and appear to be involved in a major merger or interaction, while most of the hosts (55.6%) appear relatively relaxed and undisturbed. These fractions are statistically consis...
The interstellar medium and feedback in the progenitors of the compact passive galaxies at z~2
Williams, Christina C; Lee, Bomee; Tundo, Elena; Mobasher, Bahram; Nayyeri, Hooshang; Ferguson, Henry C; Koekemoer, Anton; Trump, Jonathan R; Cassata, Paolo; Dekel, Avishai; Guo, Yicheng; Lee, Kyoung-Soo; Pentericci, Laura; Bell, Eric F; Castellano, Marco; Finkelstein, Steven L; Fontana, Adriano; Grazian, Andrea; Grogin, Norman; Kocevski, Dale; Koo, David C; Lucas, Ray A; Ravindranath, Swara; Santini, Paola; Vanzella, Eros; Weiner, Benjamin J
2014-01-01
The first quenched galaxies (z>2) are both the most massive, and most compact, suggesting a physical connection between high stellar density and efficient, rapid cessation of star-formation. We present rest-frame UV spectra of Lyman-break galaxies (LBGs) at z~3 selected to be candidate progenitors of the quenched galaxies at z~2, compared to other LBGs of similar mass and star-formation rate (non-candidates). We find that candidate progenitors have faster outflow velocities and higher equivalent widths of interstellar absorption lines, implying larger velocity spread among absorbing clouds. Candidates deviate from the relationship between equivalent widths of Lyman-alpha and interstellar absorption lines in that their Lyman-alpha emission remains strong despite high interstellar absorption, possibly indicating that the neutral HI fraction is patchy, such that Lyman-alpha photons can escape. We detect stronger CIV P-Cygni features (emission and absorption) and HeII emission in candidates, indicative of larger ...
Collet, C; De Breuck, C; Lehnert, M D; Best, P; Bryant, J J; Hunstead, R; Dicken, D; Johnston, H
2015-01-01
Most successful galaxy formation scenarios now postulate that the intense star formation in massive, high-redshift galaxies during their major growth period was truncated when powerful AGNs launched galaxy-wide outflows of gas that removed large parts of the interstellar medium. The most powerful radio galaxies at z~2 show clear signatures of such winds, but are too rare to be good representatives of a generic phase in the evolution of all massive galaxies at high redshift. Here we present SINFONI imaging spectroscopy of 12 radio galaxies at z~2 that are intermediate between the most powerful radio and vigorous starburst galaxies in radio power, and common enough to represent a generic phase in the early evolution of massive galaxies. The kinematic properties are diverse, with regular velocity gradients with amplitudes of Delta v=200-400 km s^-1 as in rotating disks as well as irregular kinematics with multiple velocity jumps of a few 100 km s^-1. Line widths are generally high, typically around FWHM=800 km s...
The chemical enrichment of long gamma-ray bursts nurseries up to z = 2
Vergani, S. D.; Palmerio, J.; Salvaterra, R.; Japelj, J.; Mannucci, F.; Perley, D. A.; D'Avanzo, P.; Krühler, T.; Puech, M.; Boissier, S.; Campana, S.; Covino, S.; Hunt, L. K.; Petitjean, P.; Tagliaferri, G.
2017-03-01
Aims: We investigate the existence of a metallicity threshold for the production of long gamma-ray bursts (LGRBs). Methods: We used the host galaxies of the Swift/BAT6 sample of LGRBs. We considered the stellar mass, star formation rate (SFR), and metallicity determined from the host galaxy photometry and spectroscopy up to z = 2 and used them to compare the distribution of host galaxies to that of field galaxies in the mass-metallicity and fundamental metallicity relation plane. Results: We find that although LGRBs also form in galaxies with relatively large stellar masses, the large majority of host galaxies have metallicities below log (O/H) 8.6. The extension to z = 2 results in a good sampling of stellar masses also above Log(M∗/M⊙) 9.5 and provides evidence that LGRB host galaxies do not follow the fundamental metallicity relation. As shown by the comparison with dedicated numerical simulations of LGRB host galaxy population, these results are naturally explained by the existence of a mild ( 0.7 Z⊙) threshold for the LGRB formation. The present statistics does not allow us to discriminate between different shapes of the metallicity cutoff, but the relatively high metallicity threshold found in this work is somewhat in disagreement to most of the standard single-star models for LGRB progenitors.
From z>6 to z~2: Unearthing Galaxies at the Edge of the Dark Ages
Illingworth, G D; Illingworth, Garth D.; Bouwens, Rychard J.
2004-01-01
Galaxies undergoing formation and evolution can now be observed over a time baseline of some 12 Gyr. An inherent difficulty with high-redshift observations is that the objects are very faint and the best resolution (HST) is only ~0.5 kpc. Such studies thereby combine in a highly synergistic way with the great detail that can be obtained for nearby galaxies. 3 new developments are highlighted. First is the derivation of stellar masses for galaxies from SEDs using HST and now Spitzer data, and dynamical masses from both sub-mm observations of CO lines and near-IR observations of optical lines like Halpha. A major step has been taken with evidence that points to the z~2-3 LBGs having masses that are a few x 10^10 Msolar. Second is the discovery of a population of evolved red galaxies at z~2-3 which appear to be the progenitors of the more massive early-type galaxies of today, with dynamical masses around a few x 10^11 Msolar. Third are the remarkable advances that have occurred in characterizing dropout galaxies...
Evaluation of $\\alpha(M_{Z}^{2})$ and $(g-2)_{\\mu}$
Davier, M
1998-01-01
This talk summarizes the recent developments in the evaluation of the leading order hadronic contributions to the running of the QED f\\/ine structure constant \\aqed, at $s=M_{\\rm Z}^2$, and to the anomalous magnetic moment of the muon $(g-2)_\\mu$. The accuracy of the theoretical prediction of these observables is limited by the uncertainties on the hadronic contributions. Signif\\/icant improvement has been achieved in a series of new analyses which is presented historically in three steps: (I), use of $\\tau$ spectral functions in addition to \\eee\\ cross sections, (II), extended use of perturbative QCD and (III), application of QCD sum rule techniques. The most precise values obtained are: \\daqedhZ\\,$=(276.3\\pm1.6)\\times10^{-4}$, yielding $\\alpha^{-1}(M_{\\rm Z}^2)=128.933\\pm0.021$, and $a_\\mu^{\\rm had}=(692.4\\pm6.2)\\times 10^{-10}$ with which one f\\/inds for the complete Standard Model prediction $a_\\mu^{\\rm SM}=(11\\,659\\,159.6\\pm6.7)\\times10^{-10}$. For the electron $(g-2)_e$, the hadronic contribution is $a_...
Z2Pack: Numerical implementation of hybrid Wannier centers for identifying topological materials
Gresch, Dominik; Autès, Gabriel; Yazyev, Oleg V.; Troyer, Matthias; Vanderbilt, David; Bernevig, B. Andrei; Soluyanov, Alexey A.
2017-02-01
The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but often challenging, problem, with no exhaustive solution at the present time. In this work we compile a series of techniques, some previously known, that allow for a solution to this problem for a large set of the possible band topologies. The method is based on tracking hybrid Wannier charge centers computed for relevant Bloch states, and it works at all levels of materials modeling: continuous k .p models, tight-binding models, and ab initio calculations. We apply the method to compute and identify Chern, Z2, and crystalline topological insulators, as well as topological semimetal phases, using real material examples. Moreover, we provide a numerical implementation of this technique (the Z2Pack software package) that is ideally suited for high-throughput screening of materials databases for compounds with nontrivial topologies. We expect that our work will allow researchers to (a) identify topological materials optimal for experimental probes, (b) classify existing compounds, and (c) reveal materials that host novel, not yet described, topological states.
GMASS Ultradeep Spectroscopy of Galaxies at redshift z~2. I. The stellar metallicity
Halliday, C; Cimatti, A; Kurk, J; Renzini, A; Mignoli, M; Bolzonella, M; Pozzetti, L; Dickinson, M; Zamorani, G; Berta, S; Franceschini, A; Cassata, P; Rodighiero, G; Rosati, P
2008-01-01
Context: Galaxy metallicities have been measured to redshift z~2 by gas-phase oxygen abundances of the interstellar medium using the R23 and N2 methods. Galaxy stellar metallicities provide crucial data for chemical evolution models but have not been assessed reliably much outside the local Universe. Aims: We determine the iron-abundance, stellar metallicity of star-forming galaxies (SFGs) at redshift z~2, observed as part of the Galaxy Mass Assembly ultra-deep Spectroscopic Survey (GMASS). Methods: We compute the equivalent width of a rest-frame mid-ultraviolet, photospheric absorption-line index, the 1978 index found to vary monotonically with stellar metallicity by Rix and collaborators. We normalise and combine 75 SFG spectra from the GMASS survey to produce a spectrum corresponding to a total integration time 1652.5 hours (and a signal-to-noise ratio ~100 for our 1.5 angstrom binning) of FORS2 spectroscopic observations at the Very Large Telescope. Results: We measure an iron-abundance, stellar metallici...
Gas reservoir of a hyper-luminous QSO at z=2.6
Feruglio, C; Fiore, F; Krips, M; Brusa, M; Daddi, E; Gavignaud, I; Maiolino, R; Piconcelli, E; Sargent, M; Vignali, C; Zappacosta, L
2014-01-01
Understanding the relationship between the formation and evolution of galaxies and their central super massive black holes (SMBH) is one of the main topics in extragalactic astrophysics. Links and feedback may reciprocally affect both black hole and galaxy growth. Observations of the CO line at redshifts of 2-4 are crucial to investigate the gas mass, star formation activity and accretion onto SMBHs, as well as the effect of AGN feedback. Potential correlations between AGN and host galaxy properties can be highlighted by observing extreme objects. Despite their luminosity, hyper-luminous QSOs at z=2-4 are still little studied at mm wavelengths. We targeted CO(3-2) in ULAS J1539+0557, an hyper-luminos QSO (Lbol> 10^48 erg/s) at z=2.658, selected through its unusual red colors in the UKIDSS Large Area Survey (ULAS). We find a molecular gas mass of 4.1+-0.8 10^10 Msun, and a gas fraction of 0.4-0.1, depending mostly on the assumed source inclination. We also find a robust lower limit to the star-formation rate (...
The HDUV Survey: Six Lyman Continuum Emitter Candidates at z~2 Revealed by HST UV Imaging
Naidu, R P; Reddy, N; Holden, B; Steidel, C C; Montes, M; Atek, H; Bouwens, R J; Carollo, C M; Cibinel, A; Illingworth, G D; Labbe, I; Magee, D; Morselli, L; Nelson, E J; van Dokkum, P G; Wilkins, S
2016-01-01
We present six galaxies at z~2 that show evidence of Lyman continuum (LyC) emission based on the newly acquired UV imaging of the Hubble Deep UV legacy survey (HDUV) conducted with the WFC3/UVIS camera on the Hubble Space Telescope (HST). At the redshift of these sources, the HDUV F275W images partially probe the ionizing continuum. By exploiting the HST multi-wavelength data available in the HDUV/GOODS fields, models of the UV spectral energy distributions, and detailed Monte Carlo simulations of the intergalactic medium absorption, we estimate the absolute ionizing photon escape fractions of these galaxies to be very high -- typically >60% (>13% for all sources at 90% likelihood). Our findings are in broad agreement with previous studies that found only a small fraction of galaxies to show high escape fraction. These six galaxies comprise the largest sample yet of LyC leaking candidates at z~2 whose inferred LyC flux has been cleanly observed at HST resolution. While three of our six candidates show evidenc...
Limits on Lyman Continuum escape from z=2.2 H-alpha emitting galaxies
Sandberg, A; Melinder, J; Bik, A; Guaita, L
2015-01-01
The leakage of Lyman continuum photons from star forming galaxies is an elusive parameter. When observed, it provides a wealth of information on star formation in galaxies and the geometry of the interstellar medium, and puts constraints on the role of star forming galaxies in the reionization of the universe. H-alpha-selected galaxies at z~2 trace the highest star formation population at the peak of cosmic star formation history, providing a base for directly measuring Lyman continuum escape. Here we present this method, and highlight its benefits as well as caveats. We also use the method on 10 H-alpha emitters in the Chandra Deep Field South at z=2.2, also imaged with the Hubble Space Telescope in the ultraviolet. We find no individual Lyman continuum detections, and our stack puts a 5 sigma upper limit on the average absolute escape fraction of <24%, consistent with similar studies. With future planned observations, the sample sizes would rapidly increase and the method presented here would provide ver...
The canonical form of the Rabi hamiltonian
Szopa, M; Ceulemans, A; Szopa, Marek; Mys, Geert; Ceulemans, Arnout
1996-01-01
The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.
Effective Hamiltonians for phosphorene and silicene
Voon, L. C. Lew Yan; Lopez-Bezanilla, A.; Wang, J.;
2015-01-01
We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field andmagnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (NewJ. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene.......Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expressionfor band warping is obtained analytically and found to be of different order than for graphene. Weprove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature...
Hamiltonian Dynamics of Protein Filament Formation.
Michaels, Thomas C T; Cohen, Samuel I A; Vendruscolo, Michele; Dobson, Christopher M; Knowles, Tuomas P J
2016-01-22
We establish the Hamiltonian structure of the rate equations describing the formation of protein filaments. We then show that this formalism provides a unified view of the behavior of a range of biological self-assembling systems as diverse as actin, prions, and amyloidogenic polypeptides. We further demonstrate that the time-translation symmetry of the resulting Hamiltonian leads to previously unsuggested conservation laws that connect the number and mass concentrations of fibrils and allow linear growth phenomena to be equated with autocatalytic growth processes. We finally show how these results reveal simple rate laws that provide the basis for interpreting experimental data in terms of specific mechanisms controlling the proliferation of fibrils.
Hamiltonian dynamics for complex food webs.
Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno
2016-03-01
We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.
Hamiltonian adaptive resolution simulation for molecular liquids.
Potestio, Raffaello; Fritsch, Sebastian; Español, Pep; Delgado-Buscalioni, Rafael; Kremer, Kurt; Everaers, Ralf; Donadio, Davide
2013-03-08
Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global Hamiltonian. Within this approach equilibrium states corresponding to well-defined statistical ensembles can be generated making use of all standard molecular dynamics or Monte Carlo methods. Models at different resolutions can thus be coupled, and thermodynamic equilibrium can be modulated keeping each region at desired pressure or density without disrupting the Hamiltonian framework.
Stability of Frustration-Free Hamiltonians
Michalakis, Spyridon
2011-01-01
We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call "Local Topological Quantum Order" and show that this condition implies an area law for the entanglement entropy of the groundstate subspace. This result extends previous work by Bravyi et al., on the stability of topological quantum order for Hamiltonians composed of commuting projections with a common zero-energy subspace. We conclude with a list of open problems relevant to spectral gaps and topological quantum order.
Hamiltonian theory of guiding-center motion
Cary, John R.; Brizard, Alain J. [Center for Integrated Plasma Studies and Department of Physics, University of Colorado, Boulder, Colorado 80309-0390 (United States) and Tech-X Corporation, Boulder, Colorado 80303 (United States); Department of Chemistry and Physics, Saint Michael' s College, Colchester, Vermont 05439 (United States)
2009-04-15
Guiding-center theory provides the reduced dynamical equations for the motion of charged particles in slowly varying electromagnetic fields, when the fields have weak variations over a gyration radius (or gyroradius) in space and a gyration period (or gyroperiod) in time. Canonical and noncanonical Hamiltonian formulations of guiding-center motion offer improvements over non-Hamiltonian formulations: Hamiltonian formulations possess Noether's theorem (hence invariants follow from symmetries), and they preserve the Poincare invariants (so that spurious attractors are prevented from appearing in simulations of guiding-center dynamics). Hamiltonian guiding-center theory is guaranteed to have an energy conservation law for time-independent fields--something that is not true of non-Hamiltonian guiding-center theories. The use of the phase-space Lagrangian approach facilitates this development, as there is no need to transform a priori to canonical coordinates, such as flux coordinates, which have less physical meaning. The theory of Hamiltonian dynamics is reviewed, and is used to derive the noncanonical Hamiltonian theory of guiding-center motion. This theory is further explored within the context of magnetic flux coordinates, including the generic form along with those applicable to systems in which the magnetic fields lie on nested tori. It is shown how to return to canonical coordinates to arbitrary accuracy by the Hazeltine-Meiss method and by a perturbation theory applied to the phase-space Lagrangian. This noncanonical Hamiltonian theory is used to derive the higher-order corrections to the magnetic moment adiabatic invariant and to compute the longitudinal adiabatic invariant. Noncanonical guiding-center theory is also developed for relativistic dynamics, where covariant and noncovariant results are presented. The latter is important for computations in which it is convenient to use the ordinary time as the independent variable rather than the proper time
Hamiltonian dynamics of the parametrized electromagnetic field
G., J Fernando Barbero; Villaseñor, Eduardo J S
2015-01-01
We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.
Hamiltonian dynamics of the parametrized electromagnetic field
Barbero G, J. Fernando; Margalef-Bentabol, Juan; Villaseñor, Eduardo J. S.
2016-06-01
We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.
Convergence to equilibrium under a random Hamiltonian.
Brandão, Fernando G S L; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K; Mozrzymas, Marek
2012-09-01
We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.
Classical R-matrix theory for bi-Hamiltonian field systems
Blaszak, Maciej [Department of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznan (Poland); Szablikowski, Blazej M [Department of Mathematics, University of Glasgow, Glasgow G12 8QW (United Kingdom)], E-mail: blaszakm@amu.edu.pl, E-mail: b.szablikowski@maths.gla.ac.uk
2009-10-09
This is a survey of the application of the classical R-matrix formalism to the construction of infinite-dimensional integrable Hamiltonian field systems. The main point is the study of bi-Hamiltonian structures. Appropriate constructions on Poisson, noncommutative and loop algebras as well as the central extension procedure are presented. The theory is developed for (1 + 1)- and (2 + 1)-dimensional field and lattice soliton systems as well as hydrodynamic systems. The formalism presented contains sufficiently many proofs and important details to make it self-contained and complete. The general theory is applied to several infinite-dimensional Lie algebras in order to construct both dispersionless and dispersive (soliton) integrable field systems.
Incorporation of New Information in an Approximate Hamiltonian
Viazminsky, C P
2002-01-01
Additional information about the eigenvalues and eigenvectors of a physical system demands extension of the effective Hamiltonian in use. In this work we extend the effective Hamiltonian that describes partially a physical system so that the new Hamiltonian comprises, in addition to the information in the old Hamiltonian, new information, available by means of experiment or theory. A simple expression of the enlarged Hamiltonian, which does not involve matrix inversion, is obtained. It is also shown that the Lee-Suzuki transformation effectively put the initial Hamiltonian in a diagonal block form.
Competing bosonic condensates in optical lattice with a mixture of single and pair hoppings
Travin, V. M.; Kopeć, T. K.
2017-01-01
A system of ultra-cold atoms with single boson and pair tunneling of bosonic atoms is considered in an optical lattice at arbitrary temperature. A mean-field theory was applied to the extended Bose-Hubbard Hamiltonian describing the system in order to investigate the competition between superfluid and pair superfluid as a function of the chemical potential and the temperature. To this end we have applied a method based on the Laplace transform method for the efficient calculation of the statistical sum for the quantum Hamiltonian. These results may be of interest for experiments on cold atom systems in optical lattices.
Cloning and functional analysis of chloroplast division gene NtFtsZ2-1 in Nicotiana tabacum
无
2003-01-01
FtsZ protein plays an important role in the division of chloroplasts. With the finding and functional analysis of higher plant FtsZ proteins, people have deepened the understanding in the molecular mechanism of chloroplast division. Multiple ftsZ genes are diversified into two families in higher plants, ftsZ1 and ftsZ2. On the basis of the research on ftsZ1 family, we analyzed the function of NtFtsZ2-1 gene in Nicotiana tabacum. Microscopic analysis of the sense and antisense NtFtsZ2-1 transgenic tobacco plants revealed that the chloroplasts were abnormal in size and also in number when compared with wild-type tobacco chloroplasts. Our investigations confirmed that the NtFtsZ2-1 gene is involved in plant chloroplast division.
${\\cal N}=4$ Supersymmetric Yang-Mills Theory on Orbifold-$T^4\\/{\\bf Z}_$2 Higher Rank Case
Jinzenji, M; Jinzenji, Masao; Sasaki, Toru
2001-01-01
We derive the partition function of ${\\cal N}=4$ supersymmetric Yang-Mills theory on orbifold-$T^4/{\\bf Z}_2$ for SU(N). We generalize our previous work for SU(2) to the SU(N) case. These partition functions can be factorized into product of bulk contribution of quotient space $T^4/{\\bf Z}_2$ and of blow-up formula including $A_{N-1}$ theta functions with level N.
Szalay, Viktor
2015-05-07
A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic energy term, Tˆ, is presented. It is in the Eckart frame and it is of the same form as Watson's normal coordinate Hamiltonian. However, the vibrational coordinates employed are not normal coordinates. The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact Tˆ given in terms of any desired set of vibrational coordinates. A general expression of the Eckart frame ro-vibrational Hamiltonian operator is given and some of its properties are discussed.
Dybeck, Eric C; Schieber, Natalie P; Shirts, Michael R
2016-08-09
We examine the free energies of three benzene polymorphs as a function of temperature in the point-charge OPLS-AA and GROMOS54A7 potentials as well as the polarizable AMOEBA09 potential. For this system, using a polarizable Hamiltonian instead of the cheaper point-charge potentials is shown to have a significantly smaller effect on the stability at 250 K than on the lattice energy at 0 K. The benzene I polymorph is found to be the most stable crystal structure in all three potentials examined and at all temperatures examined. For each potential, we report the free energies over a range of temperatures and discuss the added value of using full free energy methods over the minimized lattice energy to determine the relative crystal stability at finite temperatures. The free energies in the polarizable Hamiltonian are efficiently calculated using samples collected in a cheaper point-charge potential. The polarizable free energies are estimated from the point-charge trajectories using Boltzmann reweighting with MBAR. The high configuration-space overlap necessary for efficient Boltzmann reweighting is achieved by designing point-charge potentials with intramolecular parameters matching those in the expensive polarizable Hamiltonian. Finally, we compare the computational cost of this indirect reweighted free energy estimate to the cost of simulating directly in the expensive polarizable Hamiltonian.
Santocanale, Luigi
2002-01-01
A μ-lattice is a lattice with the property that every unary polynomial has both a least and a greatest fix-point. In this paper we define the quasivariety of μ-lattices and, for a given partially ordered set P, we construct a μ-lattice JP whose elements are equivalence classes of games in a preor...
Implicit Hamiltonian formulation of bond graphs
Golo, G.; Schaft, A.J. van der; Breedveld, P.C.; Maschke, B.M.
2003-01-01
This paper deals with mathematical formulation of bond graphs. It is proven that the power continuous part of bond graphs, the junction structure, can be associated with a Dirac structure and that equations describing a bond graph model correspond to an implicit port-controlled Hamiltonian system wi
Hamiltonian Approach to the Gribov Problem
Heinzl, T
1996-01-01
We study the Gribov problem within a Hamiltonian formulation of pure Yang-Mills theory. For a particular gauge fixing, a finite volume modification of the axial gauge, we find an exact characterization of the space of gauge-inequivalent gauge configurations.
Edge-disjoint Hamiltonian cycles in hypertournaments
Thomassen, Carsten
2006-01-01
We introduce a method for reducing k-tournament problems, for k >= 3, to ordinary tournaments, that is, 2-tournaments. It is applied to show that a k-tournament on n >= k + 1 + 24d vertices (when k >= 4) or on n >= 30d + 2 vertices (when k = 3) has d edge-disjoint Hamiltonian cycles if and only...
Lagrangian tetragons and instabilities in Hamiltonian dynamics
Entov, Michael; Polterovich, Leonid
2017-01-01
We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium.
Linear Hamiltonian Behaviors and Bilinear Differential Forms
Rapisarda, P.; Trentelman, H.L.
2004-01-01
We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows us to use the same concepts and techniques to deal with systems isolated from their environment and with systems subject to external influences and allows us to study
Discrete variable representation for singular Hamiltonians
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...
An underlying geometrical manifold for Hamiltonian mechanics
Horwitz, L. P.; Yahalom, A.; Levitan, J.; Lewkowicz, M.
2017-02-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture), that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamiltonian-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical picture and establish a correspondence which provides a basis for understanding how the instability in the geometrical picture is manifested in the instability of the the original Hamiltonian motion.
Bifurcations and safe regions in open Hamiltonians
Barrio, R; Serrano, S [GME, Dpto Matematica Aplicada and IUMA, Universidad de Zaragoza, E-50009 Zaragoza (Spain); Blesa, F [GME, Dpto Fisica Aplicada, Universidad de Zaragoza, E-50009 Zaragoza (Spain)], E-mail: rbarrio@unizar.es, E-mail: fblesa@unizar.es, E-mail: sserrano@unizar.es
2009-05-15
By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Henon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.
Bifurcations and safe regions in open Hamiltonians
Barrio, R.; Blesa, F.; Serrano, S.
2009-05-01
By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Hénon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.
Basis Optimization Renormalization Group for Quantum Hamiltonian
Sugihara, Takanori
2001-01-01
We find an algorithm of numerical renormalization group for spin chain models. The essence of this algorithm is orthogonal transformation of basis states, which is useful for reducing the number of relevant basis states to create effective Hamiltonian. We define two types of rotations and combine them to create appropriate orthogonal transformation.
Hamiltonian analysis of BHT massive gravity
Blagojević, M
2010-01-01
We study the Hamiltonian structure of the Bergshoeff-Hohm-Townsend (BHT) massive gravity with a cosmological constant. In the space of coupling constants $(\\Lambda_0,m^2)$, our canonical analysis reveals the special role of the condition $\\Lambda_0/m^2\
Hamiltonian and self-adjoint control systems
Schaft, A. van der; Crouch, P.E.
1987-01-01
This paper outlines results recently obtained in the problem of determining when an input-output map has a Hamiltonian realization. The results are obtained in terms of variations of the system trajectories, as in the solution of the Inverse Problem in Classical Mechanics. The variational and adjoin
Hamiltonian constants for several new entire solutions
2008-01-01
Using the Hamiltonian identities and the corresponding Hamilto- nian constants for entire solutions of elliptic partial differential equations, we investigate several new entire solutions whose existence were shown recently, and show interesting properties of the solutions such as formulas for contact angles at infinity of concentration curves.
Transparency in Port-Hamiltonian-Based Telemanipulation
Secchi, Cristian; Stramigioli, Stefano; Fantuzzi, Cesare
2008-01-01
After stability, transparency is the major issue in the design of a telemanipulation system. In this paper, we exploit the behavioral approach in order to provide an index for the evaluation of transparency in port-Hamiltonian-based teleoperators. Furthermore, we provide a transparency analysis of p
Relativistic Stern-Gerlach Deflection: Hamiltonian Formulation
Mane, S R
2016-01-01
A Hamiltonian formalism is employed to elucidate the effects of the Stern-Gerlach force on beams of relativistic spin-polarized particles, for passage through a localized region with a static magnetic or electric field gradient. The problem of the spin-orbit coupling for nonrelativistic bounded motion in a central potential (hydrogen-like atoms, in particular) is also briefly studied.
Momentum and Hamiltonian in Complex Action Theory
Nagao, Keiichi
2011-01-01
In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view. In arXiv:1104.3381[quant-ph], introducing a philosophy to keep the analyticity in parameter variables of FPI and defining a modified set of complex conjugate, hermitian conjugates and bras, we have extended $| q >$ and $| p >$ to complex $q$ and $p$ so that we can deal with a complex coordinate $q$ and a complex momentum $p$. After reviewing them briefly, we describe in terms of the newly introduced devices the time development of a $\\xi$-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator $\\hat{p}$, in FPI with a starting Lagrangian. Solving the eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum again via the saddle point for $p$. This study confirms that the momentum and Hamiltonian in the CAT have t...
Notch filters for port-Hamiltonian systems
Dirksz, Daniel; Scherpen, Jacquelien M.A.; van der Schaft, Abraham; Steinbuch, M.
2012-01-01
Network modeling of lumped-parameter physical systems naturally leads to a geometrically defined class of systems, i.e., port-Hamiltonian (PH) systems [4, 6]. The PH modeling framework describes a large class of (nonlinear) systems including passive mechanical systems, electrical systems, electromec
The Maslov indices of Hamiltonian periodic orbits
Gosson, Maurice de [Blekinge Institute of Technology, SE 371 79 Karlskrona (Sweden); Gosson, Serge de [Vaexjoe University (MSI), SE 351 95 Vaexjoe (Sweden)
2003-12-05
We use the properties of the Leray index to give precise formulae in arbitrary dimensions for the Maslov index of the monodromy matrix arising in periodic Hamiltonian systems. We compare our index with other indices appearing in the literature. (letter to the editor)
Global Properties of Integrable Hamiltonian Systems
Lukina, O.V.; Takens, F.; Broer, H.W.
2008-01-01
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our
Global Properties of Integrable Hamiltonian Systems
Lukina, O.V.; Takens, F.; Broer, H.W.
2008-01-01
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our approa
Scattering for Infinite Dimensional Port Hamiltonian Systems
Macchelli, Alessandro; Stramigioli, Stefano; Schaft, Arjan van der; Melchiorri, Claudio
2002-01-01
In this paper, an introduction to scattering for infinite dimensional systems within the framework of port Hamiltonian system is presented. The classical results on wave propagation can be extended to generic power propagation phenomena, for example to fluid dynamics or flexible structures. The key-
0,1 distribution in the highest level sequences of primitive sequences over Z2e
FAN; Shuqin(
2003-01-01
［1］Ward, M., The arithmetical theory of linear recurring sequences, Trans. Amer. Math. Soc, 1933, 35(6):600-628.［2］Dai Zongduo, Binary sequences derived from ML-sequences over rings I: Periods and minimal polynomials,Journal of Cryptology, 1992, 5: 193-207.［3］Dai, Z. D., Beth, T., Gollman, D., Lower bounds for the linear complexity of sequences over residue rings, Advances in Cryptology-Eurocrypt's 90, Spring-Verlag LNCS 19991, 473: 189-195.［4］Zeng Kencheng, Dai Zongduo, Huang Minqiang, Injectiveness of mappings from ring sequences to their sequences of the significant bits, Symposium on Theoretical Problems of Cryptology, State Key Laboratory of Information Security, Beijing, China, June 1995, 132-141.［5］Boztas, S., Hammons, A. R., Kumar, P. V., 4-phase sequences with near-optimum correlation properties, IEEE. Trans. Inform. Theory, 1992, 38: 1101-1113.［6］Kuzmin, A. S., Nechaev, A. A., A construction of noise stable codes using linear recurrents over Galois rings,Russian Math. Surveys, 1992, 47: 189-190.［7］Qi Wenfeng, Zhou Jinjun, Distribution of 0 and 1 in highest level of primitive sequences over Z2e, Science in China, Ser. A, 1997, 40(6): 606-611.［8］Qi Wenfeng, Zhou Jinjun, Distribution of 0 and 1 in highest level of primitive sequences over Z2e (Ц),Chinese Science Bulletin, 1998, 43(8): 633-635.［9］Zhu Fengxiang, Qi Wenfeng, Distribution of 0 and 1 in the highest level of primitive sequences over Z2e,Advances in Cryptology-CHINACRYPT' 2000, Beijing: Science Press, 2000, 1-5.［10］Kamlovski, O. V., Kuzmin, A. S., Distribution of elements on cycles of linear recurrents sequences over Galois rings, Russian Math. Surveys, 1998, 53(2): 392-393.［11］Kumar, P. V., Helleseth, T., Calderbank, A. R., An upper bound for Weil exponential sums over Galois rings and applications, IEEE. Trans. Infor. Theory, 1995, 41:456-468.
Dynamics for QCD on an Infinite Lattice
Grundling, Hendrik; Rudolph, Gerd
2017-02-01
We prove the existence of the dynamics automorphism group for Hamiltonian QCD on an infinite lattice in R^3, and this is done in a C*-algebraic context. The existence of ground states is also obtained. Starting with the finite lattice model for Hamiltonian QCD developed by Kijowski, Rudolph (cf. J Math Phys 43:1796-1808 [15], J Math Phys 46:032303 [16]), we state its field algebra and a natural representation. We then generalize this representation to the infinite lattice, and construct a Hilbert space which has represented on it all the local algebras (i.e., kinematics algebras associated with finite connected sublattices) equipped with the correct graded commutation relations. On a suitably large C*-algebra acting on this Hilbert space, and containing all the local algebras, we prove that there is a one parameter automorphism group, which is the pointwise norm limit of the local time evolutions along a sequence of finite sublattices, increasing to the full lattice. This is our global time evolution. We then take as our field algebra the C*-algebra generated by all the orbits of the local algebras w.r.t. the global time evolution. Thus the time evolution creates the field algebra. The time evolution is strongly continuous on this choice of field algebra, though not on the original larger C*-algebra. We define the gauge transformations, explain how to enforce the Gauss law constraint, show that the dynamics automorphism group descends to the algebra of physical observables and prove that gauge invariant ground states exist.
Effective Hamiltonian approach to periodically perturbed quantum optical systems
Sainz, I. [Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Diaz de Leon, 47460 Lagos de Moreno, Jal. (Mexico)]. E-mail: isa@culagos.udg.mx; Klimov, A.B. [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44410 Guadalajara, Jal. (Mexico)]. E-mail: klimov@cencar.udg.mx; Saavedra, C. [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)]. E-mail: csaaved@udec.cl
2006-02-20
We apply the method of Lie-type transformations to Floquet Hamiltonians for periodically perturbed quantum systems. Some typical examples of driven quantum systems are considered in the framework of this approach and corresponding effective time dependent Hamiltonians are found.
Integrable Coupling of KN Hierarchy and Its Hamiltonian Structure
GUO Fu-Kui; ZHANG Yu-Feng
2006-01-01
The Hamiltonian structure of the integrable couplings obtained by our method has not been solved. In this paper, the Hamiltonian structure of the KN hierarchy is obtained by making use of the quadratic-form identity.
Supersymmetric quantum mechanics approach to a nonlinear lattice
Ricotta, Regina Maria [Faculdade de Tecnologia de Sao Paulo (FATEC), SP (Brazil); Drigo Filho, Elso [Universidade Estadual Paulista Julio de Mesquita Filho (UNESP), SP (Brazil)
2011-07-01
Full text: DNA is one of the most important macromolecules of all biological system. New discoveries about it have open a vast new field of research, the physics of nonlinear DNA. A particular feature that has attracted a lot of attention is the thermal denaturation, i.e., the spontaneous separation of the two strands upon heating. In 1989 a simple lattice model for the denaturation of the DNA was proposed, the Peyrard-Bishop model, PB. The bio molecule is described by two chains of particles coupled by nonlinear springs, simulating the hydrogen bonds that connect the two basis in a pair. The potential for the hydrogen bonds is usually approximated by a Morse potential. The Hamiltonian system generates a partition function which allows the evaluation of the thermodynamical quantities such as mean strength of the basis pairs. As a byproduct the Hamiltonian system was shown to be a NLSE (nonlinear Schroedinger equation) having soliton solutions. On the other hand, a reflectionless potential with one bound state, constructed using supersymmetric quantum mechanics, SQM, can be shown to be identical to a soliton solution of the KdV equation. Thus, motivated by this Hamiltonian problem and inspired by the PB model, we consider the Hamiltonian of a reflectionless potential through SQM, in order to evaluate thermodynamical quantities of a unidimensional lattice with possible biological applications. (author)
Designing lattice structures with maximal nearest-neighbor entanglement
Navarro-Munoz, J C; Lopez-Sandoval, R [Instituto Potosino de Investigacion CientIfica y Tecnologica, Camino a la presa San Jose 2055, 78216 San Luis Potosi (Mexico); Garcia, M E [Theoretische Physik, FB 18, Universitaet Kassel and Center for Interdisciplinary Nanostructure Science and Technology (CINSaT), Heinrich-Plett-Str.40, 34132 Kassel (Germany)
2009-08-07
In this paper, we study the numerical optimization of nearest-neighbor concurrence of bipartite one- and two-dimensional lattices, as well as non-bipartite two-dimensional lattices. These systems are described in the framework of a tight-binding Hamiltonian while the optimization of concurrence was performed using genetic algorithms. Our results show that the concurrence of the optimized lattice structures is considerably higher than that of non-optimized systems. In the case of one-dimensional chains, the concurrence increases dramatically when the system begins to dimerize, i.e., it undergoes a structural phase transition (Peierls distortion). This result is consistent with the idea that entanglement is maximal or shows a singularity near quantum phase transitions. Moreover, the optimization of concurrence in two-dimensional bipartite and non-bipartite lattices is achieved when the structures break into smaller subsystems, which are arranged in geometrically distinguishable configurations.
Logarithmic two-point correlation functions from a z=2 Lifshitz model
Zingg, T. [Institute for Theoretical Physics and Spinoza Institute, Universiteit Utrecht,Leuvenlaan 4, 3584 CE Utrecht (Netherlands)
2014-01-21
The Einstein-Proca action is known to have asymptotically locally Lifshitz spacetimes as classical solutions. For dynamical exponent z=2, two-point correlation functions for fluctuations around such a geometry are derived analytically. It is found that the retarded correlators are stable in the sense that all quasinormal modes are situated in the lower half-plane of complex frequencies. Correlators in the longitudinal channel exhibit features that are reminiscent of a structure usually obtained in field theories that are logarithmic, i.e. contain an indecomposable but non-diagonalizable highest weight representation. This provides further evidence for conjecturing the model at hand as a candidate for a gravity dual of a logarithmic field theory with anisotropic scaling symmetry.
Top-quark loop corrections in Z+jet and Z + 2 jet production
Campbell, John M.; Keith Ellis, R.
2017-01-01
The sophistication of current predictions for $Z+$jet production at hadron colliders necessitates a re-evaluation of any approximations inherent in the theoretical calculations. In this paper we address one such issue, the inclusion of mass effects in top-quark loops. We ameliorate an existing calculation of $Z+1$~jet and $Z+2$~jet production by presenting exact analytic formulae for amplitudes containing top-quark loops that enter at next-to-leading order in QCD. Although approximations based on an expansion in powers of $1/m_t^2$ can lead to poor high-energy behavior, an exact treatment of top-quark loops demonstrates that their effect is small and has limited phenomenological interest.
Path-integral Monte Carlo method for the local Z2 Berry phase.
Motoyama, Yuichi; Todo, Synge
2013-02-01
We present a loop cluster algorithm Monte Carlo method for calculating the local Z(2) Berry phase of the quantum spin models. The Berry connection, which is given as the inner product of two ground states with different local twist angles, is expressed as a Monte Carlo average on the worldlines with fixed spin configurations at the imaginary-time boundaries. The "complex weight problem" caused by the local twist is solved by adopting the meron cluster algorithm. We present the results of simulation on the antiferromagnetic Heisenberg model on an out-of-phase bond-alternating ladder to demonstrate that our method successfully detects the change in the valence bond pattern at the quantum phase transition point. We also propose that the gauge-fixed local Berry connection can be an effective tool to estimate precisely the quantum critical point.
Herschel reveals a molecular outflow in a z = 2.3 ULIRG
George, Richard; Smail, Ian; Swinbank, Mark; Hopwood, Rosalind; Stanley, Fiona; Swinyard, Bruce; Valtchanov, Ivan; van der Werf, Paul
2014-01-01
We report the results from a 19-hr integration with the SPIRE Fourier Transform Spectrometer aboard the Herschel Space Observatory which has revealed the presence of a molecular outflow from the Cosmic Eyelash (SMM J2135-0102, hereafter SMMJ2135) via the detection of blueshifted OH absorption. Detections of several fine-structure emission lines indicate low-excitation HII regions contribute strongly to the [CII] luminosity in this z = 2.3 ULIRG. The OH feature suggests a maximum wind velocity of 700 km/s and outflow rate of ~60 Msun/yr. This is lower than the expected escape velocity of the host dark matter halo, ~1000 km/s. A large fraction of the available molecular gas could thus be converted into stars via a burst protracted by the resulting gas fountain, until an AGN-driven outflow can eject the remaining gas.
Top-quark loop corrections in Z+jet and Z+2 jet production
Campbell, John M
2016-01-01
The sophistication of current predictions for $Z+$jet production at hadron colliders necessitates a re-evaluation of any approximations inherent in the theoretical calculations. In this paper we address one such issue, the inclusion of mass effects in top-quark loops. We ameliorate an existing calculation of $Z+1$~jet and $Z+2$~jet production by presenting exact analytic formulae for amplitudes containing top-quark loops that enter at next-to-leading order in QCD. Although approximations based on an expansion in powers of $1/m_t^2$ can lead to poor high-energy behavior, an exact treatment of top-quark loops demonstrates that their effect is small and has limited phenomenological interest.
Clustering of galaxies near damped Lyman-alpha systems with (z) = 2.6
Wolfe, A. M
1993-01-01
The galaxy two-point correlation function, xi, at (z) = 2.6 is determined by comparing the number of Ly-alpha-emitting galaxies in narrowband CCD fields selected for the presence of damped L-alpha absorption to their number in randomly selected control fields. Comparisons between the presented determination of (xi), a density-weighted volume average of xi, and model predictions for (xi) at large redshifts show that models in which the clustering pattern is fixed in proper coordinates are highly unlikely, while better agreement is obtained if the clustering pattern is fixed in comoving coordinates. Therefore, clustering of Ly-alpha-emitting galaxies around damped Ly-alpha systems at large redshifts is strong. It is concluded that the faint blue galaxies are drawn from a parent population different from normal galaxies, the presumed offspring of damped Ly-alpha systems.
An Asymptotic Faber-Krahn Inequality for the Combinatorial Laplacian on Z^2
Shlapentokh-Rothman, Yakov
2010-01-01
The Faber-Krahn inequality states that among all open domains with a fixed volume in R^n, the ball minimizes the first Dirichlet eigenvalue of the Laplacian. We study an asymptotic discrete analogue of this for the combinatorial Dirichlet Laplacian acting on induced subgraphs of Z^2. Namely, an induced subgraph G with n vertices is called a minimizing subgraph if it minimizes the first eigenvalue of the combinatorial Dirichlet Laplacian among all induced subgraphs with n vertices. Consider an induced subgraph G and take the interior of the union of closed squares of area 1 about each point of G. Let G* denote this domain scaled down to have area 1. Our main theorem states that if {G_n} is a sequence of minimizing subgraphs where each G_n has n vertices, then after translation the measure of the symmetric difference of G_n* and the unit disk converges to 0.
Star-formation in active galaxies to z~2: a perspective from Herschel studies
Rosario, D J
2013-01-01
In the era of deep, large-area far-infrared (FIR) surveys from the Herschel Space Telescope, the bulk of the star-formation in distant galaxies, once hidden by dust, is now being revealed. The FIR provides probably the cleanest view of SF in the host galaxies of Active Galactic Nuclei (AGNs) over cosmic time. We report results from studies of the relationships between SF, AGN activity and AGN obscuration out to z=2.5, which employ some of the deepest Herschel and X-ray datasets currently available, while spanning orders of magnitude in the dynamic range of AGN properties. We highlight the role of gaseous supply in modulating both SF and AGN activity without necessarily implying a direct causal connection between these phenomenon. The role of starburst- or major merger-fueled AGN activity at low and high redshifts is discussed in the context of our results.
Two Component Dark Matters in S_4 x Z_2 Flavor Symmetric Extra U(1) Model
Daikoku, Yasuhiro; Toma, Takashi
2011-01-01
We study cosmic-ray anomaly observed by PAMELA based on E_6 inspired extra U(1) model with S_4 x Z_2 flavor symmetry. In our model, the lightest flavon has very long lifetime of O(10^{18)) second which is longer than the age of the universe, but not long enough to explain the PAMELA result ~ O(10^{26}) sec. Such a situation could be avoidable by considering that the flavon is not the dominant component of dark matters and the dominant one is the lightest neutralino. With appropriate parameter set, density parameter of dark matter and over-abundance of positron flux in cosmic-ray are realized at the same time. There is interesting correlation between spectrum of positron flux and V_{MNS}. No excess of anti-proton in cosmic-ray suggests that sfermions are heavier than 4 TeV and the masses of the light Higgs bosons are degenerated.
The evolution of post-starburst galaxies from z=2 to z= 0.5
Wild, Vivienne; Dunlop, Jim; Simpson, Chris; Rowlands, Kate; Bowler, Rebecca; Maltby, David; McLure, Ross
2016-01-01
We present the evolution in the number density and stellar mass functions of photometrically selected post-starburst galaxies in the UKIDSS Deep Survey (UDS), with redshifts of 0.510. We find that this transitionary species of galaxy is rare at all redshifts, contributing ~5% of the total population at z~2, to 2 they are exclusively massive galaxies that have formed the bulk of their stars during a rapid assembly period, followed by complete quenching of further star formation, (2) at z<1 they are caused by the rapid quenching of gas-rich star-forming galaxies, independent of stellar mass, possibly due to environment and/or gas-rich major mergers.
Compact z = 2 electrodynamics in 2 + 1 dimensions: confinement with gapless modes.
Das, Sumit R; Murthy, Ganpathy
2010-05-01
We consider 2+1-dimensional compact U(1) gauge theory at the Lifshitz point with a dynamical critical exponent z=2. As in the usual z=1 theory, monopoles proliferate the vacuum for any value of the coupling, generating a mass scale. The theory of the dilute monopole gas is written in terms of a nonrelativistic sine-Gordon model with two real fields. While monopoles remove some of the massless poles of the perturbative field strength propagator, a gapless mode representing the incomplete screening of monopoles remains, and is protected by a shift invariance of the original theory. Timelike Wilson loops still obey area laws, implying that minimal charges are confined, but the action of spacelike Wilson loops of linear size L goes instead as L(3).
Measures of Galaxy Environment - III. Difficulties in identifying proto-clusters at z ~ 2
Shattow, Genevieve M; Skibba, Ramin A; Muldrew, Stuart I; Pearce, Frazer R; Abbas, Ummi
2013-01-01
Galaxy environment is frequently discussed, but inconsistently defined. It is especially difficult to measure at high redshift where only photometric redshifts are available. With a focus on early forming proto-clusters, we use a semi-analytical model of galaxy formation to show how the environment measurement around high redshift galaxies is sensitive to both scale and metric, as well as to cluster viewing angle, evolutionary state, and the availability of either spectroscopic or photometric data. We use two types of environment metrics (nearest neighbour and fixed aperture) at a range of scales on simulated high-z clusters to see how "observed" overdensities compare to "real" overdensities. We also "observationally" identify z = 2 proto-cluster candidates in our model and track the growth histories of their parent halos through time, considering in particular their final state at z = 0. Although the measured environment of early forming clusters is critically dependent on all of the above effects (and in pa...
Exploring Low Luminosity Quasar Diversity at z ~ 2.5 with the Gran Telescopio Canarias
Sulentic, J W; Marziani, P
2013-01-01
We present preliminary results from a pencil-beam spectroscopic survey of low-luminosity quasars at z ~ 2.2-2.5. Our goal is to compare these sources with low redshift analogues of similar luminosity. High s/n and moderate resolution spectra were obtained for 15 sources using the faint object spectrograph Osiris on the 10m Gran Telescopio Canarias. The new data make possible an almost unprecedented comparison between sources with the same (moderate) luminosity at widely different cosmic epochs. Preliminary analysis of our spectra confirms the presence of a relatively evolved population of quasars radiating at modest Eddington ratios. A notable difference between the low and high z quasars may involve the presence of lower metallicity quasars at high redshift.
Flat edge modes of graphene and of Z 2 topological insulator
Mao Shijun
2011-01-01
Full Text Available Abstract A graphene nano-ribbon in the zigzag edge geometry exhibits a specific type of gapless edge modes with a partly flat band dispersion. We argue that the appearance of such edge modes are naturally understood by regarding graphene as the gapless limit of a Z 2 topological insulator. To illustrate this idea, we consider both Kane-Mele (graphene-based and Bernevig-Hughes-Zhang models: the latter is proposed for HgTe/CdTe 2D quantum well. Much focus is on the role of valley degrees of freedom, especially, on how they are projected onto and determine the 1D edge spectrum in different edge geometries.
Hamiltonian Structures for the Generalized Dispersionless KdV Hierarchy
Brunelli, J. C.
1996-01-01
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and third Hamiltonian structures are calculated directly from the r-matrix approach. Since the third structure is not related recursively with the first two ones the generalized dispersionless KdV hierarchy can be characterized as a truly tri-Hamiltonian system.
Correlated hopping of bosonic atoms induced by optical lattices
Eckholt, Maria [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, Garching, D-85478 (Germany); Garcia-Ripoll, Juan Jose [Instituto de Fisica Fundamental, CSIC, c/Serrano 113b, Madrid E-28006 (Spain)], E-mail: maria.eckholt@mpq.mpg.de
2009-09-15
In this work, we analyze a particular setup with ultracold atoms trapped in state-dependent lattices. We show that any asymmetry in the contact interaction translates into one of two classes of correlated hopping. After deriving the effective lattice Hamiltonian for the atoms, we obtain analytically and numerically the different phases and quantum phase transitions. We find for weak correlated hopping both Mott insulators and charge density waves, while for stronger correlated hopping the system transitions into a pair superfluid. We demonstrate that this phase exists for a wide range of interaction asymmetries and has interesting correlation properties that differentiate it from an ordinary atomic Bose-Einstein condensate.
Spin Waves in 2D ferromagnetic square lattice stripe
Ahmed, Maher Z.
2011-01-01
In this work, the area and edges spin wave calculations were carried out using the Heisenberg Hamiltonian and the tridiagonal method for the 2D ferromagnetic square lattice stripe, where the SW modes are characterized by a 1D in-plane wave vector $q_x$. The results show a general and an unexpected feature that the area and edge spin waves only exist as optic modes. This behavior is also seen in 2D Heisenberg antiferromagnetic square lattice. This absence of the acoustic modes in the 2D square...
Anderson localization in optical lattices with speckle disorder
Sucu, Serpil; Aktas, Saban; Okan, S. Erol [Department of Physics, Trakya University, 22030 Edirne (Turkey); Akdeniz, Zehra [Piri Reis University, 34940 Tuzla-Istanbul (Turkey); Vignolo, Patrizia [Universite de Nice-Sophia Antipolis, Institut non Lineaire de Nice, CNRS, 1361 route des Lucioles, F-06560 Valbonne (France)
2011-12-15
We study the localization properties of noninteracting waves propagating in a speckle-like potential superposed on a one-dimensional lattice. Using a combined decimation-renormalization procedure, we estimate the localization length for a tight-binding Hamiltonian where site energies are square-sinc-correlated random variables. By decreasing the width of the correlation function, the disorder patterns approach a {delta}-correlated disorder, and the localization length becomes almost energy independent in the strong disorder limit. We show that this regime can be reached for a size of the speckle grains on the order of (lower than) four lattice steps.
METAL DEFICIENCY IN CLUSTER STAR-FORMING GALAXIES AT Z = 2
Valentino, F.; Daddi, E.; Strazzullo, V.; Gobat, R.; Bournaud, F.; Juneau, S.; Zanella, A. [Laboratoire AIM-Paris-Saclay, CEA/DSM-CNRS-Université Paris Diderot, Irfu/Service d’Astrophysique, CEA Saclay, Orme des Merisiers, F-91191 Gif sur Yvette (France); Onodera, M.; Carollo, M. [Institute for Astronomy, ETH Zürich Wolfgang-Pauli-strasse 27, 8093 Zürich (Switzerland); Renzini, A. [INAF-Osservatorio Astronomico di Padova Vicolo dell’Osservatorio 5, I-35122 Padova (Italy); Arimoto, N., E-mail: francesco.valentino@cea.fr [Subaru Telescope, National Astronomical Observatory of Japan 650 North A’ohoku Place, Hilo, HI 96720 (United States)
2015-03-10
We investigate the environmental effect on the metal enrichment of star-forming galaxies (SFGs) in the farthest spectroscopically confirmed and X-ray-detected cluster, CL J1449+0856 at z = 1.99. We combined Hubble Space Telescope/WFC3 G141 slitless spectroscopic data, our thirteen-band photometry, and a recent Subaru/Multi-object InfraRed Camera and Spectrograph (MOIRCS) near-infrared spectroscopic follow-up to constrain the physical properties of SFGs in CL J1449+0856 and in a mass-matched field sample. After a conservative removal of active galactic nuclei, stacking individual MOIRCS spectra of 6 (31) sources in the cluster (field) in the mass range 10 ≤ log(M/M{sub ⊙}) ≤ 11, we find a ∼4σ lower [N ii]/Hα ratio in the cluster than in the field. Stacking a subsample of 16 field galaxies with Hβ and [O iii] in the observed range, we measure an [O iii]/Hβ ratio fully compatible with the cluster value. Converting these ratios into metallicities, we find that the cluster SFGs are up to 0.25 dex poorer in metals than their field counterparts, depending on the adopted calibration. The low metallicity in cluster sources is confirmed using alternative indicators. Furthermore, we observe a significantly higher Hα luminosity and equivalent width in the average cluster spectrum than in the field. This is likely due to the enhanced specific star formation rate; even if lower dust reddening and/or an uncertain environmental dependence on the continuum-to-nebular emission differential reddening may play a role. Our findings might be explained by the accretion of pristine gas around galaxies at z = 2 and from cluster-scale reservoirs, possibly connected with a phase of rapid halo mass assembly at z > 2 and of a high galaxy merging rate.
Evaluating and improving the redshifts of z > 2.2 quasars
Mason, Michelle; Brotherton, Michael S.; Myers, Adam
2017-08-01
Quasar redshifts require the best possible precision and accuracy for a number of applications, such as setting the velocity scale for outflows as well as measuring small-scale quasar-quasar clustering. The most reliable redshift standard in luminous quasars is arguably the narrow [O iii] λλ4959, 5007 emission line doublet in the rest-frame optical. We use previously published [O iii] redshifts obtained using near-infrared spectra in a sample of 45 high-redshift (z > 2.2) quasars to evaluate redshift measurement techniques based on rest-frame ultraviolet spectra. At redshifts above z = 2.2, the Mg ii λ2798 emission line is not available in observed-frame optical spectra and the most prominent unblended and unabsorbed spectral feature available is usually C iv λ1549. Peak and centroid measurements of the C iv profile are often blueshifted relative to the rest-frame of the quasar, which can significantly bias redshift determinations. We show that redshift determinations for these high-redshift quasars are significantly correlated with the emission-line properties of C iv (i.e. the equivalent width, or EW, and the full width at half-maximum, or FWHM) as well as the luminosity, which we take from the Sloan Digital Sky Survey Data Release 7. We demonstrate that empirical corrections based on multiple regression analyses yield significant improvements in both the precision and accuracy of the redshifts of the most distant quasars and are required to establish consistency with redshifts determined in more local quasars.
Computing the real-time Green's Functions of large Hamiltonian matrices
Iitaka, T
1996-01-01
A numerical method is developed for calculating the real time Green's functions of very large sparse Hamiltonian matrices, which exploits the numerical solution of the inhomogeneous time-dependent Schroedinger equation. The method has a clear-cut structure reflecting the most naive definition of the Green's functions, and is very suitable to parallel and vector supercomputers. The effectiveness of the method is illustrated by applying it to simple lattice models. An application of this method to condensed matter physics will be found in H. Tanaka, Phys. PRB 57, 2168 (1998).
Topological Hamiltonian as an exact tool for topological invariants.
Wang, Zhong; Yan, Binghai
2013-04-17
We propose the concept of 'topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of the topological Hamiltonian are significantly different from the physical energy spectra, but we show that the topological Hamiltonian contains the information of gapless surface states, therefore it is an exact tool for topological invariants.
THE HAMILTONIAN EQUATIONS IN SOME MATHEMATICS AND PHYSICS PROBLEMS
陈勇; 郑宇; 张鸿庆
2003-01-01
Some new Hamiltonian canonical system are discussed for a series of partialdifferential equations in Mathematics and Physics. It includes the Hamiltonian formalism forthe symmetry second-order equation with the variable coefficients, the new nonhomogeneousHamiltonian representation for fourth-order symmetry equation with constant coefficients,the one of MKdV equation and KP equation.
HAMILTONIAN MECHANICS ON K(A)HLER MANIFOLDS
无
2006-01-01
Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was established. Then the complex mathematical aspect of Hamiltonian vector field and Hamilton's equations was obtained, and so on.
Introduction to thermodynamics of spin models in the Hamiltonian limit
Berche, B; Berche, Bertrand; Lopez, Alexander
2006-01-01
A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian, and the calculation of thermal averages is explicitly done in the case of small systems described, in Hamiltonian field theory, by small matrices.
Weyl points in three-dimensional optical lattices: synthetic magnetic monopoles in momentum space
Buljan, Hrvoje; Dubcek, Tena; Kennedy, Colin; Lu, Ling; Ketterle, Wolfgang; Soljacic, Marin
2015-05-01
We show that Hamiltonians with Weyl points can be realized for ultracold atoms using laser-assisted tunneling in three-dimensional (3D) optical lattices. Weyl points are synthetic magnetic monopoles that exhibit a robust, 3D linear dispersion (e.g., see). They are associated with many interesting topological states of matter, such as Weyl semimetals and chiral Weyl fermions. However, Weyl points have yet to be experimentally observed in any system. We show that this elusive goal is well-within experimental reach with an extension of the techniques recently used to obtain the Harper Hamiltonian. We propose using laser assisted tunneling to create a 3D optical lattice, with specifically designed hopping between lattice sites that breaks inversion symmetry. The design leads to creation of four Weyl points in the Brillouin zone of the lattice, which are verified to be monopoles of the synthetic magnetic field. Supported by the Unity through Knowledge Fund (Grant 5/13).
A Hierarchy of Integrable Lattice Soliton Equations and New Integrable Symplectic Map
无
2006-01-01
Starting from a discrete spectral problem, a hierarchy of integrable lattice soliton equations is derived. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses discrete bi-Hamiltonian structure.A new integrable symplectic map and finite-dimensional integrable systems are given by nonlinearization method. The binary Bargmann constraint gives rise to a B(a)cklund transformation for the resulting integrable lattice equations. At last, conservation laws of the hierarchy are presented.
Bott periodicity for Z2 symmetric ground states of gapped free-fermion systems
Kennedy, Ricardo
2014-01-01
Building on the symmetry classification of disordered fermions, we give a proof of the proposal by Kitaev, and others, for a "Bott clock" topological classification of free-fermion ground states of gapped systems with symmetries. Our approach differs from previous ones in that (i) we work in the standard framework of Hermitian quantum mechanics over the complex numbers, (ii) we directly formulate a mathematical model for ground states rather than spectrally flattened Hamiltonians, and (iii) we use homotopy-theoretic tools rather than K-theory. Key to our proof is a natural transformation that squares to the standard Bott map and relates the ground state of a d-dimensional system in symmetry class s to the ground state of a (d+1)-dimensional system in symmetry class s+1. This relation gives a new vantage point on topological insulators and superconductors.
Hamiltonian truncation approach to quenches in the Ising field theory
T. Rakovszky
2016-10-01
Full Text Available In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.
Hamiltonian truncation approach to quenches in the Ising field theory
Rakovszky, T.; Mestyán, M.; Collura, M.; Kormos, M.; Takács, G.
2016-10-01
In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1 + 1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.
Singularity-conquering ZG controllers of z2g1 type for tracking control of the IPC system
Zhang, Yunong; Yu, Xiaotian; Yin, Yonghua; Peng, Chen; Fan, Zhengping
2014-09-01
With wider investigations and applications of autonomous robotics and intelligent vehicles, the inverted pendulum on a cart (IPC) system has become more attractive for numerous researchers due to its concise and representative structure. In this article, the tracking-control problem of the IPC system is considered and investigated. Based on Zhang dynamics (ZD) and gradient dynamics (GD), a novel kind of ZG controllers are developed and investigated for achieving the tracking-control purpose, which contains controllers of z2g0 and z2g1 types according to the number of times of using the ZD and GD methods. Besides, theoretical analyses are presented to guarantee the global and exponential convergence performance of both z2g0 and z2g1 controllers. Computer simulations are further performed to substantiate the feasibility and effectiveness of ZG controllers. More importantly, comparative simulation results demonstrate that controllers of z2g1 type can conquer the singularity problem (i.e. the division-by-zero problem).
Hamiltonian[k,k+1]-因子%Hamiltonian [k, k + 1]-Factor
蔡茂诚; 方奇志; 李延军
2003-01-01
A Hamiltonian [k, k + 1]-factor is a [k, k + 1]-factor containing a Hamiltonian cycle. A simple graph G of order n is n/2-critical if δ(G) ≥ n/2 but δ(G - e) ＜ n/2 for any edge e ∈ E(G). Let k ≥ 2 be an integer and G be an n/2-critical graph with n ≥ 4k - 6 and n ≥ 7. In this paper it is proved that for any given Hamiltonian cycle C of G, G has a [k, k + 1]-factor containing C. This result is an improvement on some recent results about the existence of Hamiltonian [k, k + 1]-factor.%本文考虑n/2-临界图中Hamiltonian[k,k+1]-因子的存在性.Hamiltonian[k,k+1]-因子是指包含Hamiltonian圈的[k,k+1]-因子;给定阶数为n的简单图G,若δ(G)≥n/2而δ(G\\e)＜n/2(对任意的e∈E(G)),则称G为n/2-临界图.设k为大于等于2的整数,G为n/2-临界图(其中n≥4k-6且n≥7),我们证明了对于G的任何Hamiltonian圈C,G中必存在包含C的[k,k+1]-因子.该结果改进了现有的一些有关Hamiltonian[k,k+1]-因子存在性的结果.
Lax operator algebras and Hamiltonian integrable hierarchies
Sheinman, Oleg K
2009-01-01
We consider the theory of Lax equations in complex simple and reductive classical Lie algebras with the spectral parameter on a Riemann surface of finite genus. Our approach is based on the new objects -- the Lax operator algebras, and develops the approach of I.Krichever treating the $\\gl(n)$ case. For every Lax operator considered as the mapping sending a point of the cotangent bundle on the space of extended Tyrin data to an element of the corresponding Lax operator algebra we construct the hierarchy of mutually commuting flows given by Lax equations and prove that those are Hamiltonian with respect to the Krichever-Phong symplectic structure. The corresponding Hamiltonians give integrable finite-dimensional Hitchin-type systems. For example we derive elliptic $A_n$, $C_n$, $D_n$ Calogero-Moser systems in frame of our approach.
Lax operator algebras and Hamiltonian integrable hierarchies
Sheinman, Oleg K [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2011-02-28
This paper considers the theory of Lax equations with a spectral parameter on a Riemann surface, proposed by Krichever in 2001. The approach here is based on new objects, the Lax operator algebras, taking into consideration an arbitrary complex simple or reductive classical Lie algebra. For every Lax operator, regarded as a map sending a point of the cotangent bundle on the space of extended Tyurin data to an element of the corresponding Lax operator algebra, a hierarchy of mutually commuting flows given by the Lax equations is constructed, and it is proved that they are Hamiltonian with respect to the Krichever-Phong symplectic structure. The corresponding Hamiltonians give integrable finite-dimensional Hitchin-type systems. For example, elliptic A{sub n}, C{sub n}, and D{sub n} Calogero-Moser systems are derived in the framework of our approach. Bibliography: 13 titles.
An Underlying Geometrical Manifold for Hamiltonian Mechanics
Horwitz, L P; Levitan, J; Lewkowicz, M
2015-01-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamilton-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical pictu...
Hamiltonian Approach To Dp-Brane Noncommutativity
Nikolic, B.; Sazdovic, B.
2010-07-01
In this article we investigate Dp-brane noncommutativity using Hamiltonian approach. We consider separately open bosonic string and type IIB superstring which endpoints are attached to the Dp-brane. From requirement that Hamiltonian, as the time translation generator, has well defined derivatives in the coordinates and momenta, we obtain boundary conditions directly in the canonical form. Boundary conditions are treated as canonical constraints. Solving them we obtain initial coordinates in terms of the effective ones as well as effective momenta. Presence of momenta implies noncommutativity of the initial coordinates. Effective theory, defined as initial one on the solution of boundary conditions, is its Ω even projection, where Ω is world-sheet parity transformation Ω:σ→-σ. The effective background fields are expressed in terms of Ω even and squares of the Ω odd initial background fields.
Hamiltonian approach to hybrid plasma models
Tronci, Cesare
2010-01-01
The Hamiltonian structures of several hybrid kinetic-fluid models are identified explicitly, upon considering collisionless Vlasov dynamics for the hot particles interacting with a bulk fluid. After presenting different pressure-coupling schemes for an ordinary fluid interacting with a hot gas, the paper extends the treatment to account for a fluid plasma interacting with an energetic ion species. Both current-coupling and pressure-coupling MHD schemes are treated extensively. In particular, pressure-coupling schemes are shown to require a transport-like term in the Vlasov kinetic equation, in order for the Hamiltonian structure to be preserved. The last part of the paper is devoted to studying the more general case of an energetic ion species interacting with a neutralizing electron background (hybrid Hall-MHD). Circulation laws and Casimir functionals are presented explicitly in each case.
ON THE ELUSIVENESS OF HAMILTONIAN PROPERTY
高随祥
2001-01-01
Decision tree complexity is an important measure of computational complexity. A graph property is a set of graphs such that if some graph G is in the set then each isomorphic graph to G is also in the set. Let P be a graph property on n vertices, if every decision tree algorithm recognizing P must examine at least k pairs of vertices in the worst case, then it is said that the decision tree complexity of P is k. If every decision tree algorithm recognizing P must examine all n(n-1)/2 pairs of vertices in the worst case, then P is said to be elusive. Karp conjectured that every nontrivial monotone graph property is elusive. This paper concerns the elusiveness of Hamiltonian property. It is proved that if n=p+1, pq or pq+1, (where p,q are distinct primes),then Hamiltonian property on n vertices is elusive.
Quantum Hamiltonian complexity and the detectability lemma
Aharonov, Dorit; Landau, Zeph; Vazirani, Umesh
2010-01-01
Quantum Hamiltonian complexity studies computational complexity aspects of local Hamiltonians and ground states; these questions can be viewed as generalizations of classical computational complexity problems related to local constraint satisfaction (such as SAT), with the additional ingredient of multi-particle entanglement. This additional ingredient of course makes generalizations of celebrated theorems such as the PCP theorem from classical to the quantum domain highly non-trivial; it also raises entirely new questions such as bounds on entanglement and correlations in ground states, and in particular area laws. We propose a simple combinatorial tool that helps to handle such questions: it is a simplified, yet more general version of the detectability lemma introduced by us in the more restricted context on quantum gap amplification a year ago. Here, we argue that this lemma is applicable in much more general contexts. We use it to provide a simplified and more combinatorial proof of Hastings' 1D area law...
General formalism for singly thermostated Hamiltonian dynamics.
Ramshaw, John D
2015-11-01
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems are ergodic, canonical ensemble averages can be computed as dynamical time averages over a single trajectory. Systems of this type were unknown until their recent discovery by Hoover and colleagues. The present formalism should facilitate the discovery, construction, and classification of other such systems by encompassing a wide class of them within a single unified framework. This formalism includes both canonical and generalized Hamiltonian systems in a state space of arbitrary dimensionality (either even or odd) and therefore encompasses both few- and many-particle systems. Particular attention is devoted to the physical motivation and interpretation of the formalism, which largely determine its structure. An analogy to stochastic thermostats and fluctuation-dissipation theorems is briefly discussed.
Hamiltonian partial differential equations and applications
Nicholls, David; Sulem, Catherine
2015-01-01
This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.
Hamiltonian hierarchy and the Hulthen potential
Gönül, B
2000-01-01
We deal with the Hamiltonian hierarchy problem of the Hulth\\'{e}n potential within the frame of the supersymmetric quantum mechanics and find that the associated superymmetric partner potentials simulate the effect of the centrifugal barrier. Incorporating the supersymmetric solutions and using the first-order perturbation theory we obtain an expression for the energy levels of theHulth\\'{e}n potential which gives satisfactory values for the non-zero angular momentum states.
Hamiltonian theory of guiding-center motion
Littlejohn, R.G.
1980-05-01
A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion.
Analytical Special Solutions of the Bohr Hamiltonian
Bonatsos, D; Petrellis, D; Terziev, P A; Yigitoglu, I
2005-01-01
The following special solutions of the Bohr Hamiltonian are briefly described: 1) Z(5) (approximately separable solution in five dimensions with gamma close to 30 degrees), 2) Z(4) (exactly separable gamma-rigid solution in four dimensions with gamma = 30 degrees), 3) X(3) (exactly separable gamma-rigid solution in three dimensions with gamma =0). The analytical solutions obtained using Davidson potentials in the E(5), X(5), Z(5), and Z(4) frameworks are also mentioned.
Information, disturbance and Hamiltonian quantum feedback control
Doherty, A C; Jungman, G; Doherty, Andrew C.; Jacobs, Kurt; Jungman, Gerard
2001-01-01
We consider separating the problem of designing Hamiltonian quantum feedback control algorithms into a measurement (estimation) strategy and a feedback (control) strategy, and consider optimizing desirable properties of each under the minimal constraint that the available strength of both is limited. This motivates concepts of information extraction and disturbance which are distinct from those usually considered in quantum information theory. Using these concepts we identify an information trade-off in quantum feedback control.
Some Oscillation Results for Linear Hamiltonian Systems
Nan Wang; Fanwei Meng
2012-01-01
The purpose of this paper is to develop a generalized matrix Riccati technique for the selfadjoint matrix Hamiltonian system ${U}^{\\prime }=A(t)U+B(t)V$ , ${V}^{\\prime }=C(t)U-{A}^{\\ast }(t)V$ . By using the standard integral averaging technique and positive functionals, new oscillation and interval oscillation criteria are established for the system. These criteria extend and improve some results that have been required before. An interesting example is included to illustrate the...
Monte Carlo Hamiltonian:Inverse Potential
LUO Xiang-Qian; CHENG Xiao-Ni; Helmut KR(O)GER
2004-01-01
The Monte Carlo Hamiltonian method developed recently allows to investigate the ground state and low-lying excited states of a quantum system,using Monte Carlo(MC)algorithm with importance sampling.However,conventional MC algorithm has some difficulties when applied to inverse potentials.We propose to use effective potential and extrapolation method to solve the problem.We present examples from the hydrogen system.
Gauge symmetry enhancement in Hamiltonian formalism
Hong, S T; Lee, T H; Oh, P; Oh, Phillial
2003-01-01
We study the Hamiltonian structure of the gauge symmetry enhancement in the enlarged CP(N) model coupled with U(2) chern-Simons term, which contains a free parameter governing explicit symmetry breaking and symmetry enhancement. After giving a general discussion of the geometry of constrained phase space suitable for the symmetry enhancement, we explicitly perform the Dirac analysis of out model and compute the Dirac brackets for the symmetry enhanced and broken cases. We also discuss some related issues.
The Effective Hamiltonian in the Scalar Electrodynamics
Dineykhan, M D; Zhaugasheva, S A; Sakhyev, S K
2002-01-01
On the basis of an investigation of the asymptotic behaviour of the polarization loop for the scalar particles in the external electromagnetic field the relativistic corrections to the Hamiltonian are determined. The constituent mass of the particles in the bound state is analytically derived. It is shown that the constituent mass of the particles differs from the mass of the particles in the free state. The corrections connected with the Thomas precession have been calculated.
Hamiltonian methods in the theory of solitons
Fadeev, Ludwig
1987-01-01
The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrodinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.
Optimal Hamiltonian Simulation by Quantum Signal Processing
Low, Guang Hao; Chuang, Isaac L.
2017-01-01
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a d -sparse Hamiltonian H ^ for time-interval t with error ɛ is O [t d ∥H ^ ∥max+log (1 /ɛ ) /log log (1 /ɛ ) ] , which matches lower bounds in all parameters. This connection is made through general three-step "quantum signal processing" methodology, comprised of (i) transducing eigenvalues of H ^ into a single ancilla qubit, (ii) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (iii) projecting this ancilla with near unity success probability.
Redesign of the DFT/MRCI Hamiltonian.
Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M
2016-01-21
The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.
Reinforcement learning for port-hamiltonian systems.
Sprangers, Olivier; Babuška, Robert; Nageshrao, Subramanya P; Lopes, Gabriel A D
2015-05-01
Passivity-based control (PBC) for port-Hamiltonian systems provides an intuitive way of achieving stabilization by rendering a system passive with respect to a desired storage function. However, in most instances the control law is obtained without any performance considerations and it has to be calculated by solving a complex partial differential equation (PDE). In order to address these issues we introduce a reinforcement learning (RL) approach into the energy-balancing passivity-based control (EB-PBC) method, which is a form of PBC in which the closed-loop energy is equal to the difference between the stored and supplied energies. We propose a technique to parameterize EB-PBC that preserves the systems's PDE matching conditions, does not require the specification of a global desired Hamiltonian, includes performance criteria, and is robust. The parameters of the control law are found by using actor-critic (AC) RL, enabling the search for near-optimal control policies satisfying a desired closed-loop energy landscape. The advantage is that the solutions learned can be interpreted in terms of energy shaping and damping injection, which makes it possible to numerically assess stability using passivity theory. From the RL perspective, our proposal allows for the class of port-Hamiltonian systems to be incorporated in the AC framework, speeding up the learning thanks to the resulting parameterization of the policy. The method has been successfully applied to the pendulum swing-up problem in simulations and real-life experiments.
Dynamics of Hamiltonian Systems and Memristor Circuits
Itoh, Makoto; Chua, Leon
In this paper, we show that any n-dimensional autonomous systems can be regarded as subsystems of 2n-dimensional Hamiltonian systems. One of the two subsystems is identical to the n-dimensional autonomous system, which is called the driving system. Another subsystem, called the response system, can exhibit interesting behaviors in the neighborhood of infinity. That is, the trajectories approach infinity with complicated nonperiodic (chaotic-like) behaviors, or periodic-like behavior. In order to show the above results, we project the trajectories of the Hamiltonian systems onto n-dimensional spheres, or n-dimensional balls by using the well-known central projection transformation. Another interesting behavior is that the transient regime of the subsystems can exhibit Chua corsage knots. We next show that generic memristors can be used to realize the above Hamiltonian systems. Finally, we show that the internal state of two-element memristor circuits can have the same dynamics as n-dimensional autonomous systems.
Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions
Changlani, Hitesh J.; Zheng, Huihuo; Wagner, Lucas K. [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green St., Urbana, Illinois 61801 (United States)
2015-09-14
We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U{sup ∗}/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.