Topological color codes and two-body quantum lattice Hamiltonians
Kargarian, M.; Bombin, H.; Martin-Delgado, M. A.
2010-02-01
Topological color codes are among the stabilizer codes with remarkable properties from the quantum information perspective. In this paper, we construct a lattice, the so-called ruby lattice, with coordination number 4 governed by a two-body Hamiltonian. In a particular regime of coupling constants, in a strong coupling limit, degenerate perturbation theory implies that the low-energy spectrum of the model can be described by a many-body effective Hamiltonian, which encodes the color code as its ground state subspace. Ground state subspace corresponds to a vortex-free sector. The gauge symmetry Z2×Z2 of the color code could already be realized by identifying three distinct plaquette operators on the ruby lattice. All plaquette operators commute with each other and with the Hamiltonian being integrals of motion. Plaquettes are extended to closed strings or string-net structures. Non-contractible closed strings winding the space commute with Hamiltonian but not always with each other. This gives rise to exact topological degeneracy of the model. A connection to 2-colexes can be established via the coloring of the strings. We discuss it at the non-perturbative level. The particular structure of the two-body Hamiltonian provides a fruitful interpretation in terms of mapping onto bosons coupled to effective spins. We show that high-energy excitations of the model have fermionic statistics. They form three families of high-energy excitations each of one color. Furthermore, we show that they belong to a particular family of topological charges. The emergence of invisible charges is related to the string-net structure of the model. The emerging fermions are coupled to nontrivial gauge fields. We show that for particular 2-colexes, the fermions can see the background fluxes in the ground state. Also, we use the Jordan-Wigner transformation in order to test the integrability of the model via introducing Majorana fermions. The four-valent structure of the lattice prevents the
Analytic approximations to hamiltonian lattice field theories. Pt. 2
International Nuclear Information System (INIS)
Surany, P.
1983-01-01
It is shown that at weak coupling physical quantities in hamiltonian U(1) lattice gauge (or global symmetric) theories of arbitrary dimension are provided as expectation values in a d - 1 dimensional lagrangian Z(2) gauge (or spin) theory with calculable long-range interactions. Confinement and the existence of a magnetic mass gap are equivalent to the existence of infinite-range plaquette-plaquette (or link-link) correlations in the spin field. The existence of infinite range correlations is simply related to the dimension of the lattice and the transformation property of the order parameter. As expected, only the d = 2 + 1 U(1) gauge theory confines electric charges at all non-vanishing coupling. (orig.)
Z2 monopoles in the standard SU(2) lattice gauge theory model
International Nuclear Information System (INIS)
Mack, G.; Petkova, V.B.
1979-04-01
The standard SU(2) lattice gauge theory model without fermions may be considered as a Z 2 model with monopoles and fluctuating coupling constants. At low temperatures β -1 (= small bare coupling constant) the monopoles are confined. (orig.) [de
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.
On confinement potentials in gauge theory: the Z2 case on a lattice
International Nuclear Information System (INIS)
Messager, A.; Ruiz, J.
1981-02-01
We show that a sufficient decrease of the Wilson loop implies automatically an area decrease; i.e. the energy to separate quarks at distance L is either at most Log L or L in the Z 2 case. We believe that it is a general fact on a lattice
Residual gauge invariance of Hamiltonian lattice gauge theories
International Nuclear Information System (INIS)
Ryang, S.; Saito, T.; Shigemoto, K.
1984-01-01
The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegengauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically. (orig.)
Digital Quantum Simulation of Z_{2} Lattice Gauge Theories with Dynamical Fermionic Matter.
Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J Ignacio
2017-02-17
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 Z_{2} model in (2+1) dimensions.
Fermion Bag Approach to Lattice Hamiltonian Field Theories
Huffman, Emilie
2018-03-01
Using a model in the Gross-Neveu Ising universality class, we show how the fermion bag idea can be applied to develop algorithms to Hamiltonian lattice field theories. We argue that fermion world lines suggest an alternative method to the traditional techniques for calculating ratios of determinants in a stable manner. We show the power behind these ideas by extracting the physics of the model on large lattices.
Hamiltonian Cycles on a Random Three-coordinate Lattice
DEFF Research Database (Denmark)
Eynard, B.; Guitter, E.; Kristjansen, C.
1998-01-01
Consider a random three-coordinate lattice of spherical topology having 2v vertices and being densely covered by a single closed, self-avoiding walk, i.e. being equipped with a Hamiltonian cycle. We determine the number of such objects as a function of v. Furthermore we express the partition...
Hamiltonian approach to the lattice massive Schwinger model
International Nuclear Information System (INIS)
Sidorov, A.V.; Zastavenko, L.G.
1996-01-01
The authors consider the limit e 2 /m 2 much-lt 1 of the lattice massive Schwinger model, i.e., the lattice massive QED in two space-time dimensions, up to lowest order in the effective coupling constant e 2 /m 2 . Here, m is the fermion mass parameter and e is the electron charge. They compare their lattice QED model with the analogous continuous space and lattice space models, (CSM and LSM), which do not take account of the zero momentum mode, z.m.m., of the vector potential. The difference is that (due to extra z.m.m. degree of freedom) to every eigenstate of the CSM and LSM there corresponds a family of eigenstates of the authors lattice QED with the parameter λ. They restrict their consideration to small values of the parameter λ. Then, the energies of the particle states of their lattice QED and LSM do coincide (in their approximation). In the infinite periodicity length limit the Hamiltonian of the authors lattice QED (as well as the Hamiltonian of the LSM) possesses two different Hilbert spaces of eigenfunctions. Thus, in this limit the authors lattice QED model (as well as LSM) describes something like two connected, but different, worlds
Hamiltonian lattice studies of chiral meson field theories
International Nuclear Information System (INIS)
Chin, S.A.
1998-01-01
The latticization of the non-linear sigma model reduces a chiral meson field theory to an O(4) spin lattice system with quantum fluctuations. The result is an interesting marriage between quantum many-body theory and classical spin systems. By solving the resulting lattice Hamiltonian by Monte Carlo methods, the dynamics and thermodynamics of pions can be determined non-perturbatively. In a variational 16 3 lattice study, the ground state chiral phase transition is shown to be first order. Moreover, as the chiral phase transition is approached, the mass gap of pionic collective modes with quantum number of the ω vector meson drops toward zero. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)
Green function simulation of Hamiltonian lattice models with stochastic reconfiguration
International Nuclear Information System (INIS)
Beccaria, M.
2000-01-01
We apply a recently proposed Green function Monte Carlo procedure to the study of Hamiltonian lattice gauge theories. This class of algorithms computes quantum vacuum expectation values by averaging over a set of suitable weighted random walkers. By means of a procedure called stochastic reconfiguration the long standing problem of keeping fixed the walker population without a priori knowledge of the ground state is completely solved. In the U(1) 2 model, which we choose as our theoretical laboratory, we evaluate the mean plaquette and the vacuum energy per plaquette. We find good agreement with previous works using model-dependent guiding functions for the random walkers. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Xu Xixiang, E-mail: xu_xixiang@hotmail.co [College of Science, Shandong University of Science and Technology, Qingdao, 266510 (China)
2010-01-04
An integrable coupling family of Merola-Ragnisco-Tu lattice systems is derived from a four-by-four matrix spectral problem. The Hamiltonian structure of the resulting integrable coupling family is established by the discrete variational identity. Each lattice system in the resulting integrable coupling family is proved to be integrable discrete Hamiltonian system in Liouville sense. Ultimately, a nonisospectral integrable lattice family associated with the resulting integrable lattice family is constructed through discrete zero curvature representation.
International Nuclear Information System (INIS)
Xu Xixiang
2010-01-01
An integrable coupling family of Merola-Ragnisco-Tu lattice systems is derived from a four-by-four matrix spectral problem. The Hamiltonian structure of the resulting integrable coupling family is established by the discrete variational identity. Each lattice system in the resulting integrable coupling family is proved to be integrable discrete Hamiltonian system in Liouville sense. Ultimately, a nonisospectral integrable lattice family associated with the resulting integrable lattice family is constructed through discrete zero curvature representation.
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...
Quantum Monte Carlo studies in Hamiltonian lattice gauge theory
International Nuclear Information System (INIS)
Hamer, C.J.; Samaras, M.; Bursill, R.J.
2000-01-01
Full text: The application of Monte Carlo methods to the 'Hamiltonian' formulation of lattice gauge theory has been somewhat neglected, and lags at least ten years behind the classical Monte Carlo simulations of Euclidean lattice gauge theory. We have applied a Green's Function Monte Carlo algorithm to lattice Yang-Mills theories in the Hamiltonian formulation, combined with a 'forward-walking' technique to estimate expectation values and correlation functions. In this approach, one represents the wave function in configuration space by a discrete ensemble of random walkers, and application of the time development operator is simulated by a diffusion and branching process. The approach has been used to estimate the ground-state energy and Wilson loop values in the U(1) theory in (2+1)D, and the SU(3) Yang-Mills theory in (3+1)D. The finite-size scaling behaviour has been explored, and agrees with the predictions of effective Lagrangian theory, and weak-coupling expansions. Crude estimates of the string tension are derived, which agree with previous results at intermediate couplings; but more accurate results for larger loops will be required to establish scaling behaviour at weak couplings. A drawback to this method is that it is necessary to introduce a 'trial' or 'guiding wave function' to guide the walkers towards the most probable regions of configuration space, in order to achieve convergence and accuracy. The 'forward-walking' estimates should be independent of this guidance, but in fact for the SU(3) case they turn out to be sensitive to the choice of trial wave function. It would be preferable to use some sort of Metropolis algorithm instead to produce a correct distribution of walkers: this may point in the direction of a Path Integral Monte Carlo approach
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.
Random walks and a simple chirally invariant lattice Hamiltonian without fermion doubling
International Nuclear Information System (INIS)
Belyea, C.I.
1992-01-01
It is shown that there is a simple chirally-invariant lattice Hamiltonian for fermions which is doubling-free but non-Hermitian and which may be valuable in lattice Hamiltonian studies of quantum chromodynamics. A connection is established between the existence of random walk representations of spinor propagators and this doubling-free formulation, in analogy with Wilson fermions. 15 refs
Hamiltonian Monte Carlo study of the N=1 Wess-Zumino model on the lattice in 1+1 dimensions
International Nuclear Information System (INIS)
Schiller, A.
1984-01-01
1+1 dimensional models with restricted supersymmetry are studied. The problems of formulating supersymmetric models on the lattice are overcome by working in the Hamiltonian lattice formulation and using restricted supersymmetry algebra involving only the Hamiltonian. For the two-dimensional Wess-Zumino model a lattice Hamiltonian suitable for the local Hamiltonian method is obtained. Using this method field theoretical models with fermions and scalar Higgs fields are investigated. Emphasis is laid on supersymmetry breaking and soliton formation
The lattice spinor QED Hamiltonian critique of the continuous space approach
International Nuclear Information System (INIS)
Sidorov, A.V.; Zastavenko, L.G.
1993-01-01
We give the irreproachable, from the point of view of gauge invariance, derivation of the lattice spinor QED Hamiltonian. Our QED Hamiltonian is manifestly gauge invariant. We point out important defects of the continuous space formulation of the QED that make, in our opinion, the lattice QED obviously preferable to the continuous space QED. We state that it is impossible to give a continuous space QED formulation which is compatible with the condition of gauge invariance. 17 refs
Gauge-invariant variational methods for Hamiltonian lattice gauge theories
International Nuclear Information System (INIS)
Horn, D.; Weinstein, M.
1982-01-01
This paper develops variational methods for calculating the ground-state and excited-state spectrum of Hamiltonian lattice gauge theories defined in the A 0 = 0 gauge. The scheme introduced in this paper has the advantage of allowing one to convert more familiar tools such as mean-field, Hartree-Fock, and real-space renormalization-group approximation, which are by their very nature gauge-noninvariant methods, into fully gauge-invariant techniques. We show that these methods apply in the same way to both Abelian and non-Abelian theories, and that they are at least powerful enough to describe correctly the physics of periodic quantum electrodynamics (PQED) in (2+1) and (3+1) space-time dimensions. This paper formulates the problem for both Abelian and non-Abelian theories and shows how to reduce the Rayleigh-Ritz problem to that of computing the partition function of a classical spin system. We discuss the evaluation of the effective spin problem which one derives the PQED and then discuss ways of carrying out the evaluation of the partition function for the system equivalent to a non-Abelian theory. The explicit form of the effective partition function for the non-Abelian theory is derived, but because the evaluation of this function is considerably more complicated than the one derived in the Abelian theory no explicit evaluation of this function is presented. However, by comparing the gauge-projected Hartree-Fock wave function for PQED with that of the pure SU(2) gauge theory, we are able to show that extremely interesting differences emerge between these theories even at this simple level. We close with a discussion of fermions and a discussion of how one can extend these ideas to allow the computation of the glueball and hadron spectrum
Comparison of lattice gauge theories with gauge groups Z2 and SU(2)
International Nuclear Information System (INIS)
Mack, G.; Petkova, B.
1978-11-01
We study a model of a pure Yang Mills theory with gauge group SU(2) on a lattice in Euclidean space. We compare it with the model obtained by restricting varibales to 2 . An inequality relating expectation values of the Wilson loop integral in the two theories is established. It shows that confinement of static quarks is true in our SU(2) model whenever it holds for the corresponding 2 -model. The SU(2) model is shown to have high and low temperature phases that are distinguished by a qualitatively different behavior of the t'Hooft disorder parameter. (orig.) [de
International Nuclear Information System (INIS)
Ranft, J.; Schiller, A.
1984-01-01
Lattice versions with restricted suppersymmetry of simple (1+1)-dimensional supersymmetric models are numerically studied using a local hamiltonian Monte Carlo method. The pattern of supersymmetry breaking closely follows the expectations of Bartels and Bronzan obtain in an alternative lattice formulation. (orig.)
A Discrete Spectral Problem and Related Hierarchy of Discrete Hamiltonian Lattice Equations
International Nuclear Information System (INIS)
Xu Xixiang; Cao Weili
2007-01-01
Staring from a discrete matrix spectral problem, a hierarchy of lattice soliton equations is presented though discrete zero curvature representation. The resulting lattice soliton equations possess non-local Lax pairs. The Hamiltonian structures are established for the resulting hierarchy by the discrete trace identity. Liouville integrability of resulting hierarchy is demonstrated.
International Nuclear Information System (INIS)
Decker, K.; Hamburg Univ.
1985-12-01
An efficient description of all clusters contributing to the strong coupling expansion of the mass gap in three-dimensional pure Z 2 lattice gauge theory is presented. This description is correct to all orders in the strong coupling expansion and is chosen in such a way that it remains valid in four dimensions for gauge group Z 2 . Relying on this description an algorithm has been constructed which generates and processes all the contributing graphs to the exact strong coupling expansion of the mass gap in the three-dimensional model in a fully automatic fashion. A major component of this algorithm can also be used to generate exact strong coupling expansions for the free energy logZ. The algorithm is correct to any order; thus the order of these expansions is only limited by the available computing power. The presentation of the algorithm is such that it can serve as a guide-line for the construction of a generalized one which would also generate exact strong coupling expansions for the masses of low-lying excited states of four-dimensional pure Yang-Mills theories. (orig.)
Analytic calculations of masses in Hamiltonian lattice theories
International Nuclear Information System (INIS)
Horn, D.
1985-01-01
The t-expansion of the vacuum energy function is discussed and several relations involving the connected matrix elements of powers of the hamiltonian are established. On the basis of these relations we show that the masses of the lowest lying O ++ states can be expressed as ratios of derivatives of the energy function. Other sectors of Hilbert space are discussed and a recent result for the SU(2) glueball mass, derived by using such relations as described here, is briefly reviewed. (author)
Hamiltonian lattice field theory: Computer calculations using variational methods
International Nuclear Information System (INIS)
Zako, R.L.
1991-01-01
I develop a variational method for systematic numerical computation of physical quantities -- bound state energies and scattering amplitudes -- in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. I present an algorithm for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. I also show how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. I show how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. I discuss the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, I do not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. I apply the method to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. I describe a computer implementation of the method and present numerical results for simple quantum mechanical systems
Hamiltonian lattice field theory: Computer calculations using variational methods
International Nuclear Information System (INIS)
Zako, R.L.
1991-01-01
A variational method is developed for systematic numerical computation of physical quantities-bound state energies and scattering amplitudes-in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. An algorithm is presented for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. It is shown how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. It is shown how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. The author discusses the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, the author does not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. The method is applied to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. The author describes a computer implementation of the method and present numerical results for simple quantum mechanical systems
A modified Toda spectral problem and its hierarchy of bi-Hamiltonian lattice equations
International Nuclear Information System (INIS)
Ma Wenxiu; Xu Xixiang
2004-01-01
Starting from a modified Toda spectral problem, a hierarchy of generalized Toda lattice equations with two arbitrary constants is constructed through discrete zero curvature equations. It is shown that the hierarchy possesses a bi-Hamiltonian structure and a hereditary recursion operator, which implies that there exist infinitely many common commuting symmetries and infinitely many common commuting conserved functionals. Two cases of the involved constants present two specific integrable sub-hierarchies, one of which is exactly the Toda lattice hierarchy
Optical-lattice Hamiltonians for relativistic quantum electrodynamics
International Nuclear Information System (INIS)
Kapit, Eliot; Mueller, Erich
2011-01-01
We show how interpenetrating optical lattices containing Bose-Fermi mixtures can be constructed to emulate the thermodynamics of quantum electrodynamics (QED). We present models of neutral atoms on lattices in 1+1, 2+1, and 3+1 dimensions whose low-energy effective action reduces to that of photons coupled to Dirac fermions of the corresponding dimensionality. We give special attention to (2+1)-dimensional quantum electrodynamics (QED3) and discuss how two of its most interesting features, chiral symmetry breaking and Chern-Simons physics, could be observed experimentally.
Extending the reach of strong-coupling: an iterative technique for Hamiltonian lattice models
International Nuclear Information System (INIS)
Alberty, J.; Greensite, J.; Patkos, A.
1983-12-01
The authors propose an iterative method for doing lattice strong-coupling-like calculations in a range of medium to weak couplings. The method is a modified Lanczos scheme, with greatly improved convergence properties. The technique is tested on the Mathieu equation and on a Hamiltonian finite-chain XY model, with excellent results. (Auth.)
Optical Lattice Design Assisted by Non-Hermitian Hamiltonians
International Nuclear Information System (INIS)
Rodríguez-Lara, B M
2016-01-01
A brief introduction to non-Hermitian arrays of coupled waveguides is presented. The PT-symmetric dimer is revisited for the sake of clarity. It belongs to the class of photonic lattices with underlying SO(2,1) symmetry that have been shown to provide all-optical conversion from phase to amplitude. (paper)
International Nuclear Information System (INIS)
Tian Shoufu; Zhang Hongqing
2010-01-01
In this paper, we start from the discrete spectral problem and construct a lattice hierarchy by properly choosing an auxiliary spectral problem V-tilde n (m) , which can reduce to the Volterra hierarchy, the Ablowitz-Ladik hierarchy, positive and negative lattice hierarchies and a new hierarchy. The new hierarchy is integrable in involutory Lax's sense and possesses multi-Hamiltonian structure. In addition, the Darboux transformation of the lattice hierarchy is obtained when the freely adjustable function εn (1) =0 and m=1. Then some soliton solutions are obtained by using Darboux transformation. This method is also suitable for other more general spectral problems in mathematics and physics.
Fermion bag approach to Hamiltonian lattice field theories in continuous time
Huffman, Emilie; Chandrasekharan, Shailesh
2017-12-01
We extend the idea of fermion bags to Hamiltonian lattice field theories in the continuous time formulation. Using a class of models we argue that the temperature is a parameter that splits the fermion dynamics into small spatial regions that can be used to identify fermion bags. Using this idea we construct a continuous time quantum Monte Carlo algorithm and compute critical exponents in the 3 d Ising Gross-Neveu universality class using a single flavor of massless Hamiltonian staggered fermions. We find η =0.54 (6 ) and ν =0.88 (2 ) using lattices up to N =2304 sites. We argue that even sizes up to N =10 ,000 sites should be accessible with supercomputers available today.
First-principles lattice-gas Hamiltonian revisited: O-Pd(100)
Kappus, Wolfgang
2016-01-01
The methodology of deriving an adatom lattice-gas Hamiltonian (LGH) from first principles (FP) calculations is revisited. Such LGH cluster expansions compute a large set of lateral pair-, trio-, quarto interactions by solving a set of linear equations modelling regular adatom configurations and their FP energies. The basic assumption of truncating interaction terms beyond fifth nearest neighbors does not hold when adatoms show longer range interactions, e.g. substrate mediated elastic interac...
Hamiltonian and potentials in derivative pricing models: exact results and lattice simulations
Baaquie, Belal E.; Corianò, Claudio; Srikant, Marakani
2004-03-01
The pricing of options, warrants and other derivative securities is one of the great success of financial economics. These financial products can be modeled and simulated using quantum mechanical instruments based on a Hamiltonian formulation. We show here some applications of these methods for various potentials, which we have simulated via lattice Langevin and Monte Carlo algorithms, to the pricing of options. We focus on barrier or path dependent options, showing in some detail the computational strategies involved.
The hidden fermions in Z(2) theories
International Nuclear Information System (INIS)
Srednicki, M.
1983-01-01
Low dimensional Z(2) gauge theories have been rewritten in terms of locally coupled fermionic degrees of freedom by means of the Jordan-Wigner transformation. In this paper it is shown that higher dimensional Z(2) gauge theories are also fermionic theories in disguise. The SML solution to the 1+1 dimension Ising model is reviewed. Psi operators are represented pictorially as arrows, psi 1 points to the left, psi 2 to the right, each site of H a multiple of two operators. The 2+1 dimension Ising model is then considered. A fermion plaquette operator is introduced as the generator of a gauge symmetry for the fermionic H. Findings in 1+1 and 2+1 are then applied to 3+1 dimensional Z(2) gauge theory. A construction of this lattice is undertaken. Psi formalism replaces sigma formalism, as it permits extremely simple duality transformations to be made on any Z(2) Hamiltonian. It is shown that the fermionic formalism will lead to new ideas in Z(2) theories
Hamiltonian study of improved U(1) lattice gauge theory in three dimensions
International Nuclear Information System (INIS)
Loan, Mushtaq; Hamer, Chris
2004-01-01
A comprehensive analysis of the Symanzik improved anisotropic three-dimensional U(1) lattice gauge theory in the Hamiltonian limit is made. Monte Carlo techniques are used to obtain numerical results for the static potential, ratio of the renormalized and bare anisotropies, the string tension, lowest glueball masses and the mass ratio. Evidence that rotational symmetry is established more accurately for the Symanzik improved anisotropic action is presented. The discretization errors in the static potential and the renormalization of the bare anisotropy are found to be only a few percent compared to errors of about 20-25 % for the unimproved gauge action. Evidence of scaling in the string tension, antisymmetric mass gap and the mass ratio is observed in the weak coupling region and the behavior is tested against analytic and numerical results obtained in various other Hamiltonian studies of the theory. We find that more accurate determination of the scaling coefficients of the string tension and the antisymmetric mass gap has been achieved, and the agreement with various other Hamiltonian studies of the theory is excellent. The improved action is found to give faster convergence to the continuum limit. Very clear evidence is obtained that in the continuum limit the glueball ratio M S /M A approaches exactly 2, as expected in a theory of free, massive bosons
International Nuclear Information System (INIS)
Dahmen, Bernd
1994-01-01
A systematic method to obtain strong coupling expansions for scattering quantities in hamiltonian lattice field theories is presented. I develop the conceptual ideas for the case of the hamiltonian field theory analogue of the Ising model, in d space and one time dimension. The main result is a convergent series representation for the scattering states and the transition matrix. To be explicit, the special cases of d=1 and d=3 spatial dimensions are discussed in detail. I compute the next-to-leading order approximation for the phase shifts. The application of the method to investigate low-energy scattering phenomena in lattice gauge theory and QCD is proposed. ((orig.))
Energy Technology Data Exchange (ETDEWEB)
Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn
2009-10-02
Integrable couplings of relativistic Toda lattice systems in polynomial form and rational form, and their hierarchies, are derived from a four-by-four discrete matrix eigenvalue problem. The bi-Hamiltonian structure for every integrable coupling in the two hierarchies obtained is established by means of the discrete variational identity. Ultimately, Liouvolle integrability of the obtained integrable couplings is demonstrated.
International Nuclear Information System (INIS)
Ranft, J.
1984-01-01
Hamiltonian lattice models with fermions, gauge bosons and scalar fields are studied in 1+1 dimensions using the local Hamiltonian Monte-Carlo method. Results are presented for the massive Schwinger model with one and two flavors, for a model with interacting Higgs fields, fermions and gauge bosons, where fractionally charged solitons are found as free states of the lattice model, and for Wess-Zumino type models with restricted lattice supersymmetry, where examples for spontaneous breaking of supersymmetry are found
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.
Lattice Hamiltonian approach to the massless Schwinger model. Precise extraction of the mass gap
International Nuclear Information System (INIS)
Cichy, Krzysztof; Poznan Univ.; Kujawa-Cichy, Agnieszka; Szyniszewski, Marcin; Manchester Univ.
2012-12-01
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 -6 %.
Lattice Hamiltonian approach to the massless Schwinger model. Precise extraction of the mass gap
Energy Technology Data Exchange (ETDEWEB)
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} %.
LeMesurier, Brenton
2012-01-01
A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.
Mapping between Hamiltonians with attractive and repulsive potentials on a lattice
International Nuclear Information System (INIS)
Joglekar, Yogesh N.
2010-01-01
Through a simple and exact analytical derivation, we show that for a particle on a lattice there is a one-to-one correspondence between the spectrum in the presence of an attractive potential V and its repulsive counterpart -V. For a Hermitian potential, this result implies that the number of localized states is the same in both attractive and repulsive cases although these states occur above (below) the band continuum for the repulsive (attractive) case. For a PT-symmetric potential that is odd under parity, our result implies that, in the PT-unbroken phase, the energy eigenvalues are symmetric around zero and that the corresponding eigenfunctions are closely related to each other.
International Nuclear Information System (INIS)
Dahmen, B.
1994-12-01
A recently proposed method for a strong coupling analysis of scattering phenomena in hamiltonian lattice field theories is applied to the SU(2) Yang-Mills model in (2 + 1) dimensions. The calculation is performed up to second order in the hopping parameter. All relevant quantities that characterize the collision between the lightest glueballs in the elastic region - cross section, phase shifts, resonance parameters - are determined. (orig.)
International Nuclear Information System (INIS)
Peggs, S.; Talman, R.
1987-01-01
As proton accelerators get larger, and include more magnets, the conventional tracking programs which simulate them run slower. The purpose of this paper is to describe a method, still under development, in which element-by-element tracking around one turn is replaced by a single man, which can be processed far faster. It is assumed for this method that a conventional program exists which can perform faithful tracking in the lattice under study for some hundreds of turns, with all lattice parameters held constant. An empirical map is then generated by comparison with the tracking program. A procedure has been outlined for determining an empirical Hamiltonian, which can represent motion through many nonlinear kicks, by taking data from a conventional tracking program. Though derived by an approximate method this Hamiltonian is analytic in form and can be subjected to further analysis of varying degrees of mathematical rigor. Even though the empirical procedure has only been described in one transverse dimension, there is good reason to hope that it can be extended to include two transverse dimensions, so that it can become a more practical tool in realistic cases
Martins, Ricardo Spagnuolo; Konstantinova, Elena; Belich, Humberto; Helayël-Neto, José Abdalla
2017-11-01
Magnetic and thermodynamical properties of a system of spins in a honeycomb lattice, such as magnetization, magnetic susceptibility and specific heat, in a low-temperature regime are investigated by considering the effects of a Kekulé scalar exchange and QED vacuum polarization corrections to the interparticle potential. The spin lattice calculations are carried out by means of Monte Carlo simulations. We present a number of comparative plots of all the physical quantities we have considered and a detailed analysis is presented to illustrate the main features and the variation profiles of the properties with the applied external magnetic field and temperature.
Invariant metrics for Hamiltonian systems
International Nuclear Information System (INIS)
Rangarajan, G.; Dragt, A.J.; Neri, F.
1991-05-01
In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs
International Nuclear Information System (INIS)
Bernal, Nicolás; Chu, Xiaoyong
2016-01-01
Dark matter with strong self-interactions provides a compelling solution to several small-scale structure puzzles. Under the assumption that the coupling between dark matter and the Standard Model particles is suppressed, such strongly interacting massive particles (SIMPs) allow for a successful thermal freeze-out through N-to-N' processes, where N dark matter particles annihilate to N' of them. In the most common scenarios, where dark matter stability is guaranteed by a Z 2 symmetry, the seemingly leading annihilating channel, i.e. 3-to-2 process, is forbidden, so the 4-to-2 one dominate the production of the dark matter relic density. Moreover, cosmological observations require that the dark matter sector is colder than the thermal bath of Standard Model particles, a condition that can be dynamically generated via a small portal between dark matter and Standard Model particles, à la freeze-in. This scenario is exemplified in the context of the Singlet Scalar dark matter model
Quantum Hamiltonian reduction in superspace formalism
International Nuclear Information System (INIS)
Madsen, J.O.; Ragoucy, E.
1994-02-01
Recently the quantum Hamiltonian reduction was done in the case of general sl(2) embeddings into Lie algebras and superalgebras. The results are extended to the quantum Hamiltonian reduction of N=1 affine Lie superalgebras in the superspace formalism. It is shown that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum Hamiltonian reduction reduces to quantum Hamiltonian reduction of non-supersymmetric Lie superalgebras. The super energy-momentum tensor is constructed explicitly as well as all generators of spin 1 (and 1/2); thus all generators in the superconformal, quasi-superconformal and Z 2 *Z 2 superconformal algebras are constructed. (authors). 21 refs
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...
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
Variational identities and Hamiltonian structures
International Nuclear Information System (INIS)
Ma Wenxiu
2010-01-01
This report is concerned with Hamiltonian structures of classical and super soliton hierarchies. In the classical case, basic tools are variational identities associated with continuous and discrete matrix spectral problems, targeted to soliton equations derived from zero curvature equations over general Lie algebras, both semisimple and non-semisimple. In the super case, a supertrace identity is presented for constructing Hamiltonian structures of super soliton equations associated with Lie superalgebras. We illustrate the general theories by the KdV hierarchy, the Volterra lattice hierarchy, the super AKNS hierarchy, and two hierarchies of dark KdV equations and dark Volterra lattices. The resulting Hamiltonian structures show the commutativity of each hierarchy discussed and thus the existence of infinitely many commuting symmetries and conservation laws.
Generalized Hubbard Hamiltonian: renormalization group approach
International Nuclear Information System (INIS)
Cannas, S.A.; Tamarit, F.A.; Tsallis, C.
1991-01-01
We study a generalized Hubbard Hamiltonian which is closed within the framework of a Quantum Real Space Renormalization Group, which replaces the d-dimensional hypercubic lattice by a diamond-like lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled band case in d = 2 and d = 3. Some evidence for superconductivity is presented. (author). 44 refs., 12 figs., 2 tabs
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
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.
Z(2) vortices and the SU(2) string tension
International Nuclear Information System (INIS)
Goepfert, M.
1981-01-01
Topologically determined Z(2) variables in pure SU(2) lattice gauge theory are discussed. They count the number of 'vortex souls'. The high temperature expansion for the corresponding Z(2) loops is examined. They obey an area law. The coefficient of the area is shown to be equal to the string tension to all orders of the high temperature expansion. This shows that the string tension is determined by the probability distribution of the vortex souls, at least in the high temperature region. The dependence of the string tension α(β,h) on an external field h that is coupled to the Z(2) field strength is calculated to lowest order of the high temperature expansion. In this approximation, α(β,h) is determined by the free energy of a 2-dimensional Ising model in an external magnetic field 1/2log(β/4tanhh) at an inverse temperature 1/2log3/4π = 0.429. (orig.)
International Nuclear Information System (INIS)
Barnes, T.; Daniell, G.J.
1982-09-01
A finite lattice technique is introduced for calculating the spectrum of fluctuating Bose theories in the continuum limit. The method gives the continuum spectrum to an estimated approximately 1% accuracy in (1+1) dimensions using available computer memory. The spectrum of lambda phi 4 theory in (1+1) dimensions is studied as a trial application; results are found consistent with a free theory spectrum. (author)
Energy Technology Data Exchange (ETDEWEB)
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.
A hierarchy of Liouville integrable discrete Hamiltonian equations
Energy Technology Data Exchange (ETDEWEB)
Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn
2008-05-12
Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.
On the structure of the commutative Z2 graded algebra valued integrable equations
International Nuclear Information System (INIS)
Konopelchenko, B.G.
1980-01-01
Partial differential equations integrable by the linear matrix spectral problem of arbitrary order are considered for the case that the 'potentials' take their values in the commutative infinte-dimensional Z 2 graded algebra (superalgebra). The general form of the integrable equations and their Baecklund transformations are found. The infinite sets of the integrals of the motion are constructed. The hamiltonian character of the integrable equations is proved. (orig.)
Indirect quantum tomography of quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
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.
z~2: An Epoch of Disk Assembly
Simons, Raymond C.; Kassin, Susan A.; Weiner, Benjamin; Heckman, Timothy M.; Trump, Jonathan; SIGMA, DEEP2
2018-01-01
At z = 0, the majority of massive star-forming galaxies contain thin, rotationally supported gas disks. It was once accepted that galaxies form thin disks early: collisional gas with high velocity dispersion should dissipate energy, conserve angular momentum, and develop strong rotational support in only a few galaxy crossing times (~few hundred Myr). However, this picture is complicated at high redshift, where the processes governing galaxy assembly tend to be violent and inhospitable to disk formation. We present results from our SIGMA survey of star-forming galaxy kinematics at z = 2. These results challenge the simple picture described above: galaxies at z = 2 are unlike local well-ordered disks. Their kinematics tend to be much more disordered, as quantified by their low ratios of rotational velocity to gas velocity dispersion (Vrot/σg): less than 35% of galaxies have Vrot/σg > 3. For comparison, nearly 100% of local star-forming galaxies meet this same threshold. We combine our high redshift sample with a similar low redshift sample from the DEEP2 survey. This combined sample covers a continuous redshift baseline over 0.1 < z < 2.5, spanning 10 Gyrs of cosmic time. Over this period, galaxies exhibit remarkably smooth kinematic evolution on average. All galaxies tend towards rotational support with time, and it is reached earlier in higher mass systems. This is due to both a significant decline in gas velocity dispersion and a mild rise in ordered rotational motions. These results indicate that z = 2 is a period of disk assembly, during which the strong rotational support present in today’s massive disk galaxies is only just beginning to emerge.
International Nuclear Information System (INIS)
Peggs, S.; Talman, R.
1986-08-01
As proton accelerators get larger, and include more magnets, the conventional tracking programs which simulate them run slower. At the same time, in order to more carefully optimize the higher cost of the accelerators, they must return more accurate results, even in the presence of a longer list of realistic effects, such as magnet errors and misalignments. For these reasons conventional tracking programs continue to be computationally bound, despite the continually increasing computing power available. This limitation is especially severe for a class of problems in which some lattice parameter is slowly varying, when a faithful description is only obtained by tracking for an exceedingly large number of turns. Examples are synchrotron oscillations in which the energy varies slowly with a period of, say, hundreds of turns, or magnet ripple or noise on a comparably slow time scale. In these cases one may with to track for hundreds of periods of the slowly varying parameter. The purpose of this paper is to describe a method, still under development, in which element-by-element tracking around one turn is replaced by a single map, which can be processed far faster. Similar programs have already been written in which successive elements are ''concatenated'' with truncation to linear, sextupole, or octupole order, et cetera, using Lie algebraic techniques to preserve symplecticity. The method described here is rather more empirical than this but, in principle, contains information to all orders and is able to handle resonances in a more straightforward fashion
Derivation of Hamiltonians for accelerators
Energy Technology Data Exchange (ETDEWEB)
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.
Face centered cubic SnSe as a Z2 trivial Dirac nodal line material
Tateishi, Ikuma; Matsuura, Hiroyasu
2018-01-01
The presence of Dirac nodal line in the time-reversal and inversion symmetric system is dictated by Z2 index when spin-orbit interaction is absent. With the first principles calculation, we show that the Dirac nodal line can emerge in Z2 trivial material by calculating the band structure of SnSe of face centered cubic lattice as an example and it becomes a topological crystalline insulator when spin-orbit interaction is taken into account. We clarify the origin of the Dirac nodal line by obta...
Z2×Z2 generalizations of 𝒩 =2 super Schrödinger algebras and their representations
Aizawa, N.; Segar, J.
2017-11-01
We generalize the real and chiral N =2 super Schrödinger algebras to Z2×Z2-graded Lie superalgebras. This is done by D-module presentation, and as a consequence, the D-module presentations of Z2×Z2-graded superalgebras are identical to the ones of super Schrödinger algebras. We then generalize the calculus over the Grassmann number to Z2×Z2 setting. Using it and the standard technique of Lie theory, we obtain a vector field realization of Z2×Z2-graded superalgebras. A vector field realization of the Z2×Z2 generalization of N =1 super Schrödinger algebra is also presented.
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.
Energy Technology Data Exchange (ETDEWEB)
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.
New integrable lattice hierarchies
International Nuclear Information System (INIS)
Pickering, Andrew; Zhu Zuonong
2006-01-01
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
Generic Local Hamiltonians are Gapless
Movassagh, Ramis
2017-12-01
We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded maximum vertex degree. The type of interactions allowed for include translational invariance in a disorder (i.e., probabilistic) sense with some assumptions on the local distributions. Examples include many-body localization and random spin models. We calculate the scaling of the gap with the system's size when the local terms are distributed according to a Gaussian β orthogonal random matrix ensemble. As a corollary, there exist finite size partitions with respect to which the ground state is arbitrarily close to a product state. When the local eigenvalue distribution is discrete, in addition to the lack of an energy gap in the limit, we prove that the ground state has finite size degeneracies. The proofs are simple and constructive. This work excludes the important class of truly translationally invariant Hamiltonians where the local terms are all equal.
Global constraints on Z2 fluxes in two different anisotropic limits of a hypernonagon Kitaev model
Kato, Yasuyuki; Kamiya, Yoshitomo; Nasu, Joji; Motome, Yukitoshi
2018-05-01
The Kitaev model is an exactly-soluble quantum spin model, whose ground state provides a canonical example of a quantum spin liquid. Spin excitations from the ground state are fractionalized into emergent matter fermions and Z2 fluxes. The Z2 flux excitation is pointlike in two dimensions, while it comprises a closed loop in three dimensions because of the local constraint for each closed volume. In addition, the fluxes obey global constraints involving (semi)macroscopic number of fluxes. We here investigate such global constraints in the Kitaev model on a three-dimensional lattice composed of nine-site elementary loops, dubbed the hypernonagon lattice, whose ground state is a chiral spin liquid. We consider two different anisotropic limits of the hypernonagon Kitaev model where the low-energy effective models are described solely by the Z2 fluxes. We show that there are two kinds of global constraints in the model defined on a three-dimensional torus, namely, surface and volume constraints: the surface constraint is imposed on the even-odd parity of the total number of fluxes threading a two-dimensional slice of the system, while the volume constraint is for the even-odd parity of the number of the fluxes through specific plaquettes whose total number is proportional to the system volume. In the two anisotropic limits, therefore, the elementary excitation of Z2 fluxes occurs in a pair of closed loops so as to satisfy both two global constraints as well as the local constraints.
Z-2 Threaded Insert Design and Testing
Ross, Amy; Rhodes, Richard; Jones, Robert J.; Graziosi, David; Ferl, Jinny; Sweeny, Mitch; Scarborough, Stephen
2016-01-01
NASA's Z-2 prototype space suit contains several components fabricated from an advanced hybrid composite laminate consisting of IM10 carbon fiber and fiber glass. One requirement was to have removable, replaceable helicoil inserts to which other suit components would be fastened. An approach utilizing bonded in inserts with helicoils inside of them was implemented. During initial assembly, cracking sounds were heard followed by the lifting of one of the blind inserts out of its hole when the screws were torqued. A failure investigation was initiated to understand the mechanism of the failure. Ultimately, it was determined that the pre-tension caused by torqueing the fasteners is a much larger force than induced from the pressure loads of the suit which was not considered in the insert design. Bolt tension is determined by dividing the torque on the screw by a k value multiplied by the thread diameter of the bolt. The k value is a factor that accounts for friction in the system. A common value used for k for a non-lubricated screw is 0.2. The k value can go down by as much as 0.1 if the screw is lubricated which means for the same torque, a much larger tension could be placed on the bolt and insert. This paper summarizes the failure investigation that was performed to identify the root cause of the suit failure and details how the insert design was modified to resist a higher pull out tension.
Bäcklund transformations and Hamiltonian flows
International Nuclear Information System (INIS)
Zullo, Federico
2013-01-01
In this work we show that, under certain conditions, parametric Bäcklund transformations for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous Hamiltonian. The two systems share the same constants of motion. This observation leads to the identification of the Hamiltonian interpolating the iteration of the discrete map defined by the transformations, which indeed in numerical applications can be considered a linear combination of the integrals appearing in the spectral curve of the Lax matrix. An example with the periodic Toda lattice is given. (paper)
Excitation Potentials and Shell Corrections for the Elements Z2=20 to Z2=30
DEFF Research Database (Denmark)
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...
Effective Hamiltonian for travelling discrete breathers
MacKay, Robert S.; Sepulchre, Jacques-Alexandre
2002-05-01
Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.
Renormalization of Hamiltonian QCD
International Nuclear Information System (INIS)
Andrasi, A.; Taylor, John C.
2009-01-01
We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.
Magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1984-03-01
The magnetic field line Hamiltonian and the associated canonical form for the magnetic field are important concepts both for understanding toroidal plasma physics and for practical calculations. A number of important properties of the canonical or Hamiltonian representation are derived and their importance is explained
DEFF Research Database (Denmark)
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 ...
Magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1985-02-01
The basic properties of the Hamiltonian representation of magnetic fields in canonical form are reviewed. The theory of canonical magnetic perturbation theory is then developed and applied to the time evolution of a magnetic field embedded in a toroidal plasma. Finally, the extension of the energy principle to tearing modes, utilizing the magnetic field line Hamiltonian, is outlined
Diagonalization of Hamiltonian; Diagonalization of Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
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.
Bifurcation in Z2-symmetry quadratic polynomial systems with delay
International Nuclear Information System (INIS)
Zhang Chunrui; Zheng Baodong
2009-01-01
Z 2 -symmetry systems are considered. Firstly the general forms of Z 2 -symmetry quadratic polynomial system are given, and then a three-dimensional Z 2 equivariant system is considered, which describes the relations of two predator species for a single prey species. Finally, the explicit formulas for determining the Fold and Hopf bifurcations are obtained by using the normal form theory and center manifold argument.
Boundary Hamiltonian Theory for Gapped Topological Orders
Hu, Yuting; Wan, Yidun; Wu, Yong-Shi
2017-06-01
We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.
Hamiltonian evolutions of twisted polygons in RPn
International Nuclear Information System (INIS)
Beffa, Gloria Marì; Wang, Jing Ping
2013-01-01
In this paper we find a discrete moving frame and their associated invariants along projective polygons in RP n , and we use them to describe invariant evolutions of projective N-gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N-gon invariant evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that any Hamiltonian evolution is induced on invariants by an invariant evolution of N-gons—what we call a projective realization—and both evolutions are connected explicitly in a very simple way. Finally, we provide a completely integrable evolution (the Boussinesq lattice related to the lattice W 3 -algebra), its projective realization in RP 2 and its Hamiltonian pencil. We generalize both structures to n-dimensions and we prove that they are Poisson, defining explicitly the n-dimensional generalization of the planar evolution (a discretization of the W n -algebra). We prove that the generalization is completely integrable, and we also give its projective realization, which turns out to be very simple. (paper)
The vortex free energy in the screening phase of the Z(2) Higgs model
International Nuclear Information System (INIS)
Meyer, H.
1983-06-01
The vortex free energy was proposed to distinguish between the confinement - and the Higgs phase (in the sense of 't Hooft) in lattice gauge theory, when matter fields are present that transform according to an arbitrary representation of the gauge group. In this paper I consider the Z(2) Higgs model and calculate the vortex free energy in the screening part of the confining/screening phase of Fradkin and Shenker. The result does not agree with the expected behavior that corresponds to the structure of the phase diagram. Therefore the vortex free energy is no longer a good indicator for confinement when matter fields transform nontrivially under the center of the gauge group (such as Z(2) Higgs scalars). (orig.)
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.
Spatiotemporal complexity in coupled map lattices
International Nuclear Information System (INIS)
Kaneko, Kunihiko
1986-01-01
Some spatiotemporal patterns of couple map lattices are presented. The chaotic kink-like motions are shown for the phase motion of the coupled circle lattices. An extension of the couple map lattice approach to Hamiltonian dynamics is briefly reported. An attempt to characterize the high-dimensional attractor by the extension of the correlation dimension is discussed. (author)
Schrödinger holography for z < 2
International Nuclear Information System (INIS)
Andrade, Tomás; Peach, Alex; Ross, Simon F; Keeler, Cynthia
2015-01-01
We investigate holography for asymptotically Schrödinger spacetimes, using a frame formalism. Our dictionary is based on the anisotropic scaling symmetry. We consider z < 2, where the holographic dictionary is cleaner; we make some comments on z = 2. We propose a definition of asymptotically locally Schrödinger spacetime where the leading components of the frame fields provide suitable geometric boundary data. We show that an asymptotic expansion exists for generic boundary data satisfying our boundary conditions for z < 2. (paper)
Renormalization of Hamiltonians
International Nuclear Information System (INIS)
Glazek, S.D.; Wilson, K.G.
1993-01-01
This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method
Theory of collective Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Zhang Qingying
1982-02-01
Starting from the cranking model, we derive the nuclear collective Hamiltonian. We expand the total energy of the collective motion of the ground state of even--even nuclei in powers of the deformation parameter ..beta... In the first approximation, we only take the lowest-order non-vanished terms in the expansion. The collective Hamiltonian thus obtained rather differs from the A. Bohr's Hamiltonian obtained by the irrotational incompressible liquid drop model. If we neglect the coupling term between ..beta..-and ..gamma..-vibration, our Hamiltonian then has the same form as that of A. Bohr. But there is a difference between these collective parameters. Our collective parameters are determined by the state of motion of the nucleous in the nuclei. They are the microscopic expressions. On the contrary, A. Bohr's collective parameters are only the simple functions of the microscopic physical quantities (such as nuclear radius and surface tension, etc.), and independent of the state of motion of the nucleons in the nuclei. Furthermore, there exist the coupling term between ..beta..-and ..gamma..-vibration and the higher-order terms in our expansion. They can be treated as the perturbations. There are no such terms in A. Bohr's Hamiltonian. These perturbation terms will influence the rotational, vibrational spectra and the ..gamma..-transition process, etc.
Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices
Energy Technology Data Exchange (ETDEWEB)
Habib, K. M. Masum, E-mail: masum.habib@virginia.edu; Ghosh, Avik W. [Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, Virginia 22904 (United States); Sajjad, Redwan N. [Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2016-03-14
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.
Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices
International Nuclear Information System (INIS)
Habib, K. M. Masum; Ghosh, Avik W.; Sajjad, Redwan N.
2016-01-01
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.
Time dependent drift Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1982-04-01
The motion of individual charged particles in a given magnetic and an electric fields is discussed. An idea of a guiding center distribution function f is introduced. The guiding center distribution function is connected to the asymptotic Hamiltonian through the drift kinetic equation. The general non-stochastic magnetic field can be written in a contravariant and a covariant forms. The drift Hamiltonian is proposed, and the canonical gyroradius is presented. The proposed drift Hamiltonian agrees with Alfven's drift velocity to lowest non-vanishing order in the gyroradius. The relation between the exact, time dependent equations of motion and the guiding center equation is clarified by a Lagrangian analysis. The deduced Lagrangian represents the drift motion. (Kato, T.)
Lagrangian and Hamiltonian dynamics
Mann, Peter
2018-01-01
An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Mo...
Classical Exchange Algebra of the Nonlinear Sigma Model on a Supercoset Target with Z2n Grading
International Nuclear Information System (INIS)
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 Z 2n 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 AdS 5 × S 5 string theory (when the ghost terms are omitted). (the physics of elementary particles and fields)
Multi-Hamiltonian structure of Lotka-Volterra and quantum Volterra models
International Nuclear Information System (INIS)
Cronstroem, C.; Noga, M.
1995-01-01
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 a classical and as a quantum system. (orig.)
A Monte Carlo procedure for Hamiltonians with small nonlocal correction terms
International Nuclear Information System (INIS)
Mack, G.; Pinn, K.
1986-03-01
We consider lattice field theories whose Hamiltonians contain small nonlocal correction terms. We propose to do simulations for an auxiliarly polymer system with field dependent activities. If a nonlocal correction term to the Hamiltonian is small, it need to be evaluated only rarely. (orig.)
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
Effective magnetic Hamiltonians
Czech Academy of Sciences Publication Activity Database
Drchal, Václav; Kudrnovský, Josef; Turek, I.
2013-01-01
Roč. 26, č. 5 (2013), s. 1997-2000 ISSN 1557-1939 R&D Projects: GA ČR GA202/09/0775 Institutional support: RVO:68378271 Keywords : effective magnetic Hamiltonian * ab initio * magnetic structure Subject RIV: BE - Theoretical Physics Impact factor: 0.930, year: 2013
Dissipative systems and Bateman's Hamiltonian
International Nuclear Information System (INIS)
Pedrosa, I.A.; Baseia, B.
1983-01-01
It is shown, by using canonical transformations, that one can construct Bateman's Hamiltonian from a Hamiltonian for a conservative system and obtain a clear physical interpretation which explains the ambiguities emerging from its application to describe dissipative systems. (Author) [pt
Infinite-dimensional Z2sup(k)-supermanifolds
International Nuclear Information System (INIS)
Molotkov, V.
1984-10-01
In this paper the theory of finite-dimensional supermanifolds of Berezin, Leites and Kostant is generalized in two directions. First, we introduce infinite-dimensional supermanifolds ''locally isomorphic'' to arbitrary Banach (or, more generally, locally convex) superspaces. This is achieved by considering supermanifolds as functors (equipped with some additional structure) from the category of finite-dimensional Grassman superalgebras into the category of the corresponding smooth manifolds (Banach or locally convex). As examples, flag supermanifolds of Banach superspaces as well as unitary supergroups of Hilbert superspaces are constructed. Second, we define ''generalized'' supermanifolds, graded by Abelian groups Z 2 sup(k), instead of the group Z 2 (Z 2 sup(k)-supermanifolds). The corresponding superfields, describing, potentially, particles with more general statistics than Bose + Fermi, generally speaking, turn out to have an infinite number of components. (author)
DEFF Research Database (Denmark)
Jørgensen, Michael Finn
1995-01-01
It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...... particular configurations of the Discrete Self-Trapping (DST) system are shown to be completely solvable. One of these systems includes the Toda lattice in a certain limit. An explicit integration is carried through for this Near-Toda lattice. The Near-Toda lattice is then generalized to include singular...
Noncanonical Hamiltonian mechanics
International Nuclear Information System (INIS)
Litteljohn, R.G.
1986-01-01
Noncanonical variables in Hamiltonian mechanics were first used by Lagrange in 1808. In spite of this, most work in Hamiltonian mechanics has been carried out in canonical variables, up to this day. One reason for this is that noncanonical coordinates are seldom needed for mechanical problems based on Lagrangians of the form L = T - V, where T is the kinetic energy and V is the potential energy. Of course, such Lagrangians arise naturally in celestial mechanics, and as a result they form the paradigms of nineteenth-century mechanics and have become enshrined in all the mechanics textbooks. Certain features of modern problems, however, lead to the use of noncanonical coordinates. Among these are issues of gauge invariance and singular Lagrange a Poisson structures. In addition, certain problems, like the flow of magnetic-field lines in physical space, are naturally formulated in terms of noncanonical coordinates. None of these features is present in the nineteenth-century paradigms of mechanics, but they do arise in problems involving particle motion in the presence of magnetic fields. For example, the motion of a particle in an electromagnetic wave is an important one in plasma physics, but the usual Hamiltonian formulation is gauge dependent. For this problem, noncanonical approaches based on Lagrangians in phase space lead to powerful computational techniques which are gauge invariant. In the limit of strong magnetic fields, particle motion becomes 'guiding-center motion'. Guiding-center motion is also best understood in terms of noncanonical coordinates. Finally the flow of magnetic-field lines through physical space is a Hamiltonian system which is best understood with noncanonical coordinates. No doubt many more systems will arise in the future for which these noncanonical techniques can be applied. (author)
Instability in Hamiltonian systems
Directory of Open Access Journals (Sweden)
A. Pumarino
2005-11-01
Besides proving the existence of Arnold diffusion for a new family of three degrees of freedom Hamiltonian systems, another goal of this book is not only to show how Arnold-like results can be extended to substantially larger sets of parameters, but also how to obtain effective estimates on the splitting of separatrices size when the frequency of the perturbation belongs to open real sets.
Discrete variational Hamiltonian mechanics
International Nuclear Information System (INIS)
Lall, S; West, M
2006-01-01
The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms
Approximate symmetries of Hamiltonians
Chubb, Christopher T.; Flammia, Steven T.
2017-08-01
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.
Membrane models and generalized Z2 gauge theories
International Nuclear Information System (INIS)
Lowe, M.J.; Wallace, D.J.
1980-01-01
We consider models of (d-n)-dimensional membranes fluctuating in a d-dimensional space under the action of surface tension. We investigate the renormalization properties of these models perturbatively and in 1/n expansion. The potential relationships of these models to generalized Z 2 gauge theories are indicated. (orig.)
Functional integral and effective Hamiltonian t-J-V model of strongly correlated electron system
International Nuclear Information System (INIS)
Belinicher, V.I.; Chertkov, M.V.
1990-09-01
The functional integral representation for the generating functional of t-J-V model is obtained. In the case close to half filling this functional integral representation reduces the conventional Hamiltonian of t-J-V model to the Hamiltonian of the system containing holes and spins 1/2 at each lattice size. This effective Hamiltonian coincides with that one obtained one of the authors by different method. This Hamiltonian and its dynamical variables can be used for description of different magnetic phases of t-J-V model. (author). 16 refs
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
Hamiltonian formulation of QCD in the Schwinger gauge
International Nuclear Information System (INIS)
Schutte, D.
1989-01-01
The structure of the Hamiltonian related to a regularized non-Abelian gauge field theory is discussed in the light of different choices for gauge-invariant wave functionals (loop space, Coulomb, axial, Schwinger gauge). Arguments are given for the suggestion that the Schwinger gauge offers a specially suited framework for the computation of bound-state (hadron) properties. The most important reasons are the manifest rotation invariance, the lack of a Gribov horizon (giving standard many-body techniques a better chance), and the fact that a regularization analogous to the lattice regularization is easily implementable. Some details of the Schwinger-gauge Hamiltonian theory are discussed
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Problems related to consideration of operator nonpermutability in Hamiltonian path integral (HPI) are considered in the review. Integrals are investigated using trajectories in configuration space (nonrelativistic quantum mechanics). Problems related to trajectory integrals in HPI phase space are discussed: the problem of operator nonpermutability consideration (extra terms problem) and corresponding equivalence rules; ambiguity of HPI usual recording; transition to curvilinear coordinates. Problem of quantization of dynamical systems with couplings has been studied. As in the case of canonical transformations, quantization of the systems with couplings of the first kind requires the consideration of extra terms
Hamiltonian quantum simulation with bounded-strength controls
International Nuclear Information System (INIS)
Bookatz, Adam D; Wocjan, Pawel; Viola, Lorenza
2014-01-01
We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an ‘Eulerian decoupling cycle,’ that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation. We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls. In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed. (papers)
Symmetry fractionalization of visons in Z2 spin liquids
Qi, Yang; Cheng, Meng; Fang, Chen
In this work we study symmetry fractionalization of vison excitations in topological Z2 spin liquids. We show that in the presence of the full SO (3) spin-rotational symmetry and if there is an odd number of spin-1/2 per unit cell, the symmetry fractionalization of visons is completely fixed. On the other hand, visons can have different classes of symmetry fractionalization if the spin-rotational symmetry is reduced. As a concrete example, we show that visons in the Balents-Fisher-Girvin Z2 spin liquid have crystal symmetry fractionalization classes which are not allowed in SO (3) symmetric spin liquids, due to the reduced spin-rotational symmetry.
Protected Pseudohelical Edge States in Z2-Trivial Proximitized Graphene
Frank, Tobias; Högl, Petra; Gmitra, Martin; Kochan, Denis; Fabian, Jaroslav
2018-04-01
We investigate topological properties of models that describe graphene on realistic substrates which induce proximity spin-orbit coupling in graphene. A Z2 phase diagram is calculated for the parameter space of (generally different) intrinsic spin-orbit coupling on the two graphene sublattices, in the presence of Rashba coupling. The most fascinating case is that of staggered intrinsic spin-orbit coupling which, despite being topologically trivial, Z2=0 , does exhibit edge states protected by time-reversal symmetry for zigzag ribbons as wide as micrometers. We call these states pseudohelical as their helicity is locked to the sublattice. The spin character and robustness of the pseudohelical modes is best exhibited on a finite flake, which shows that the edge states have zero g factor, carry a pure spin current in the cross section of the flake, and exhibit spin-flip reflectionless tunneling at the armchair edges.
Thermal transport in a two-dimensional Z2 spin liquid
Metavitsiadis, Alexandros; Pidatella, Angelo; Brenig, Wolfram
2017-11-01
We study the dynamical thermal conductivity of the two-dimensional Kitaev spin model on the honeycomb lattice. We find a strongly temperature dependent low-frequency spectral intensity as a direct consequence of fractionalization of spins into mobile Majorana matter and a static Z2 gauge field. The latter acts as an emergent thermally activated disorder, leading to the appearance of a pseudogap which closes in the thermodynamic limit, indicating a dissipative heat conductor. Our analysis is based on complementary calculations of the current correlation function, comprising exact diagonalization by means of a complete summation over all gauge sectors, as well as a phenomenological mean-field treatment of thermal gauge fluctuations, valid at intermediate and high temperatures. The results will also be contrasted against the conductivity discarding gauge fluctuations.
Z2 vortex strings in grand unified theories
International Nuclear Information System (INIS)
Olive, D.; Turok, N.
1982-01-01
Spontaneously broken gauge theories may display distinct vortex string solutions for the disconnected components of the exact gauge symmetry group. A type of Higgs mechanism thought to apply in grand unified theories as being responsible for fermion masses yields Z 2 vortex lines, irrespectively of the group. These could seed galaxy formation if the corresponding fermion masses are superheavy. More generally a Higgs mechanism producing Zsub(n) vortex strings is presented. (orig.)
Robust online Hamiltonian learning
International Nuclear Information System (INIS)
Granade, Christopher E; Ferrie, Christopher; Wiebe, Nathan; Cory, D G
2012-01-01
In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer–Rao lower bound, certifying its own performance. (paper)
Chromatic roots and hamiltonian paths
DEFF Research Database (Denmark)
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...
Dimensional versus lattice regularization within Luescher's Yang Mills theory
International Nuclear Information System (INIS)
Diekmann, B.; Langer, M.; Schuette, D.
1993-01-01
It is pointed out that the coefficients of Luescher's effective model space Hamiltonian, which is based upon dimensional regularization techniques, can be reproduced by applying folded diagram perturbation theory to the Kogut Susskind Hamiltonian and by performing a lattice continuum limit (keeping the volume fixed). Alternative cutoff regularizations of the Hamiltonian are in general inconsistent, the critical point beeing the correct prediction for Luescher's tadpole coefficient which is formally quadratically divergent and which has to become a well defined (negative) number. (orig.)
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.
Relativistic Many-Body Hamiltonian Approach to Mesons
Llanes-Estrada, Felipe J.; Cotanch, Stephen R.
2001-01-01
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 app...
Towards a nonperturbative calculation of weak Hamiltonian Wilson coefficients
Bruno, Mattia; Lehner, Christoph; Soni, Amarjit; Rbc; Ukqcd Collaborations
2018-04-01
We propose a method to compute the Wilson coefficients of the weak effective Hamiltonian to all orders in the strong coupling constant using Lattice QCD simulations. We perform our calculations adopting an unphysically light weak boson mass of around 2 GeV. We demonstrate that systematic errors for the Wilson coefficients C1 and C2 , related to the current-current four-quark operators, can be controlled and present a path towards precise determinations in subsequent works.
A partial Hamiltonian approach for current value Hamiltonian systems
Naz, R.; Mahomed, F. M.; Chaudhry, Azam
2014-10-01
We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.
Elevating the Free-Fermion $Z_{2} \\times Z_{2}$ Orbifold Model to a Compactification of $F$-Theory
Berglund, P; Faraggi, A E; Nanopoulos, Dimitri V; Qiu, Z; Berglund, Per; Ellis, John; Faraggi, Alon E.; Qiu, Zongan
2000-01-01
We study the elliptic fibrations of some Calabi-Yau three-folds, including the $Z_2\\times Z_2$ orbifold with $(h_{1,1},h_{2,1})=(27,3)$, which is equivalent to the common framework of realistic free-fermion models, as well as related models with $(h_{1,1},h_{2,1})=(51,3)$ and $(31,7)$. Two related puzzles arise when one considers the $(h_{1,1},h_{2,1})=(27,3)$ model as an F-theory compactification to six dimensions. One is that the condition for the vanishing of the gravitational anomaly is not satisfied. This suggests that either a new feature must appear in the F-theory limit of the corresponding four-dimensional type-IIA vacuum, or that the F-theory compactification does not make sense. However, the elliptic fibration is well defined everywhere except at four singular points in the base. We speculate on the possible existence of N=1 tensor and hypermultiplets at these points which would cancel the gravitational anomaly.
Alternative Hamiltonian representation for gravity
Energy Technology Data Exchange (ETDEWEB)
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.
Alternative Hamiltonian representation for gravity
International Nuclear Information System (INIS)
Rosas-RodrIguez, R
2007-01-01
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
Energy Technology Data Exchange (ETDEWEB)
King, David A. [Oak Ridge Inst. for Science and Education (ORISE), Oak Ridge, TN (United States)
2013-10-01
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 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); and confirm commitments in the DWP were adequately implemented, as verified via IV surveys and soil sampling.
On the marginally relevant operator in z=2 Lifshitz holography
International Nuclear Information System (INIS)
Holsheimer, Kristian
2014-01-01
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
Scattering theory for Stark Hamiltonians
International Nuclear Information System (INIS)
Jensen, Arne
1994-01-01
An introduction to the spectral and scattering theory for Schroedinger operators is given. An abstract short range scattering theory is developed. It is applied to perturbations of the Laplacian. Particular attention is paid to the study of Stark Hamiltonians. The main result is an explanation of the discrepancy between the classical and the quantum scattering theory for one-dimensional Stark Hamiltonians. (author). 47 refs
International Nuclear Information System (INIS)
Hasenfratz, P.
1983-01-01
The author presents a general introduction to lattice gauge theories and discusses non-perturbative methods in the gauge sector. He then shows how the lattice works in obtaining the string tension in SU(2). Lattice QCD at finite physical temperature is discussed. Universality tests in SU(2) lattice QCD are presented. SU(3) pure gauge theory is briefly dealt with. Finally, fermions on the lattice are considered. (Auth.)
Hamiltonian description of the ideal fluid
International Nuclear Information System (INIS)
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
Kondo length in bosonic lattices
Giuliano, Domenico; Sodano, Pasquale; Trombettoni, Andrea
2017-09-01
Motivated by the fact that the low-energy properties of the Kondo model can be effectively simulated in spin chains, we study the realization of the effect with bond impurities in ultracold bosonic lattices at half filling. After presenting a discussion of the effective theory and of the mapping of the bosonic chain onto a lattice spin Hamiltonian, we provide estimates for the Kondo length as a function of the parameters of the bosonic model. We point out that the Kondo length can be extracted from the integrated real-space correlation functions, which are experimentally accessible quantities in experiments with cold atoms.
A lattice hierarchy and its continuous limits
International Nuclear Information System (INIS)
Fan Engui
2008-01-01
By introducing a discrete spectral problem, we derive a lattice hierarchy which is integrable in Liouville's sense and possesses a multi-Hamiltonian structure. It is show that the discrete spectral problem converges to the well-known AKNS spectral problem under a certain continuous limit. In particular, we construct a sequence of equations in the lattice hierarchy which approximates the AKNS hierarchy as a continuous limit
Identifying Two-Dimensional Z 2 Antiferromagnetic Topological Insulators
Bègue, F.; Pujol, P.; Ramazashvili, R.
2018-01-01
We revisit the question of whether a two-dimensional topological insulator may arise in a commensurate Néel antiferromagnet, where staggered magnetization breaks the symmetry with respect to both elementary translation and time reversal, but retains their product as a symmetry. In contrast to the so-called Z 2 topological insulators, an exhaustive characterization of antiferromagnetic topological phases with the help of topological invariants has been missing. We analyze a simple model of an antiferromagnetic topological insulator and chart its phase diagram, using a recently proposed criterion for centrosymmetric systems [13]. We then adapt two methods, originally designed for paramagnetic systems, and make antiferromagnetic topological phases manifest. The proposed methods apply far beyond the particular examples treated in this work, and admit straightforward generalization. We illustrate this by two examples of non-centrosymmetric systems, where no simple criteria have been known to identify topological phases. We also present, for some cases, an explicit construction of edge states in an antiferromagnetic topological insulator.
Matrix quantum mechanics on S1/Z2
Directory of Open Access Journals (Sweden)
P. Betzios
2018-03-01
Full Text Available We study Matrix Quantum Mechanics on the Euclidean time orbifold S1/Z2. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two dimensional non-critical string theory where the orbifold fixed points become cosmological singularities. We derive the MQM partition function both in the canonical and grand canonical ensemble in two different formulations and demonstrate agreement between them. We pinpoint the contribution of twisted states in both of these formulations either in terms of bi-local operators acting at the end-points of time or branch-cuts on the complex plane. We calculate, in the matrix model, the contribution of the twisted states to the torus level partition function explicitly and show that it precisely matches the world-sheet result, providing a non-trivial test of the proposed duality. Finally we discuss some interesting features of the partition function and the possibility of realising it as a τ-function of an integrable hierarchy.
Matrix quantum mechanics on S1 /Z2
Betzios, P.; Gürsoy, U.; Papadoulaki, O.
2018-03-01
We study Matrix Quantum Mechanics on the Euclidean time orbifold S1 /Z2. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two dimensional non-critical string theory where the orbifold fixed points become cosmological singularities. We derive the MQM partition function both in the canonical and grand canonical ensemble in two different formulations and demonstrate agreement between them. We pinpoint the contribution of twisted states in both of these formulations either in terms of bi-local operators acting at the end-points of time or branch-cuts on the complex plane. We calculate, in the matrix model, the contribution of the twisted states to the torus level partition function explicitly and show that it precisely matches the world-sheet result, providing a non-trivial test of the proposed duality. Finally we discuss some interesting features of the partition function and the possibility of realising it as a τ-function of an integrable hierarchy.
Machine learning Z2 quantum spin liquids with quasiparticle statistics
Zhang, Yi; Melko, Roger G.; Kim, Eun-Ah
2017-12-01
After decades of progress and effort, obtaining a phase diagram for a strongly correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and long-range entanglement, evaluating these nonlocal observables at many points in phase space can be prohibitively costly. With growing excitement over topological quantum computation comes the need for an efficient approach for obtaining topological phase diagrams. Here we turn to machine learning using quantum loop topography (QLT), a notion we have recently introduced. Specifically, we propose a construction of QLT that is sensitive to quasiparticle statistics. We then use mutual statistics between the spinons and visons to detect a Z2 quantum spin liquid in a multiparameter phase space. We successfully obtain the quantum phase boundary between the topological and trivial phases using a simple feed-forward neural network. Furthermore, we demonstrate advantages of our approach for the evaluation of phase diagrams relating to speed and storage. Such statistics-based machine learning of topological phases opens new efficient routes to studying topological phase diagrams in strongly correlated systems.
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.
Dynamical decoupling of unbounded Hamiltonians
Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin
2018-03-01
We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.
Fermions in light front transverse lattice quantum chromodynamics
Indian Academy of Sciences (India)
Ur(x-aˆr)]}. (3). After eliminating the constraint fields we arrive at the transverse lattice Hamiltonian. P. =P. 1 +P. 2 ,. (4) where P. 1 arises from the elimination of ψ (hence sensitive to how fermions are put on the transverse lattice) and P. 2 contains Wilson plaquette term and the terms arising from the elimination of A . Explicitly.
International Nuclear Information System (INIS)
Schulz, P.A.B.; Silva, C.E.T.G. da
1984-01-01
We introduce a model for the lattice dynamics of SI 3 N 4 in its amorphous phase. This model is based on a Born hamiltonian, solved in the Bethe lattice approximation. We included the local vicinity until third nearest neighbours, building up the central cluster. (M.W.O.) [pt
Quasars Probing Quasars: the Circumgalactic Medium Surrounding z ~ 2 Quasars
Lau, Marie; Quasars Probing Quasars survey
2018-01-01
Understanding the circumgalactic medium--the gaseous halo surrounding a galaxy, is an integral part to understanding galaxy evolution. The z ~ 2-3 universe is interesting as this is when the star formation rate and AGN activity peak. My thesis concludes the decade-long Quasars Probing Quasars survey designed for studying massive galaxy formation and quasar feedback. I use background quasar sightlines that pass close to foreground quasars to study the circumgalactic medium of quasar-host galaxies in absorption. My sample of 149 quasar pairs involve spectra taken with 17 different optical and near IR instruments. I present results on the statistical and physical properties of the circumgalactic medium. The circumgalactic medium is enriched even beyond the virial radius. The alpha/Fe abundance ratio is enhanced, suggesting enrichment from core-collapse supernovae. The cool gas mass within the virial radius is enough to fuel star formation for another Gyr, and may account for 1/3 of the baryonic budget of the galaxy halo. The ionization state increases with projected distance from the quasar, which implies the quasar does not dominate the ionizing radiation flux. However, detection of fluorescent Lyman-alpha emission and NV absorption imply these transverse absorbers are partially illuminated by the quasar. In one peculiar case, the absorbing clump has density >100 cm^-3 and sub-parsec size. The average absorption in the circumgalactic medium exhibits large velocity widths, and is asymmetric about the systemic redshift of the galaxies. The widths are consistent with gravitational motions and Hubble flow, and outflows are not required to explain them. The asymmetry can be explained if the ionizing radiation from the quasar is anisotropic or intermittent and the gas is not in inflow. My results pose challenges for cosmological hydrodynamic simulations to produce a substantial cool gas reservoir surrounding quasars, that is also enriched and shows extreme kinematics.
Hamiltonian cycles in polyhedral maps
Indian Academy of Sciences (India)
We present a necessary and sufficient condition for existence of a contractible, non-separating and non-contractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces.We also present algorithms to construct such cycles whenever it exists where one of them is linear time and another is ...
Maslov index for Hamiltonian systems
Directory of Open Access Journals (Sweden)
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.
Hamiltonian formulation of the supermembrane
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; Tanii, Y.
1987-06-01
The Hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed. Gauge conditions are imposed in such a way that the reparametrizations of the membrane with divergence free 2-vectors are unfixed. (author). 10 refs
Relativistic non-Hamiltonian mechanics
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2010-01-01
Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ + c 2 = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.
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.
Mathematical Modeling of Constrained Hamiltonian Systems
Schaft, A.J. van der; Maschke, B.M.
1995-01-01
Network modelling of unconstrained energy conserving physical systems leads to an intrinsic generalized Hamiltonian formulation of the dynamics. Constrained energy conserving physical systems are directly modelled as implicit Hamiltonian systems with regard to a generalized Dirac structure on the
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.
Geometric Hamiltonian structures and perturbation theory
International Nuclear Information System (INIS)
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
Notch filters for port-Hamiltonian systems
Dirksz, D.A.; Scherpen, J.M.A.; van der Schaft, A.J.; Steinbuch, M.
2012-01-01
In this paper a standard notch filter is modeled in the port-Hamiltonian framework. By having such a port-Hamiltonian description it is proven that the notch filter is a passive system. The notch filter can then be interconnected with another (nonlinear) port-Hamiltonian system, while preserving the
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…
The Hamiltonian of QED. Zero mode
International Nuclear Information System (INIS)
Zastavenko, L.G.
1990-01-01
We start with the standard QED Lagrangian. New derivation of the spinor QED Hamiltonian is given. We have taken into account the zero mode. Our derivation is faultless from the point of view of gauge invariance. It gives important corrections to the standard QED Hamiltonian. Our derivation of the Hamiltonian can be generalized to the case of QCD. 5 refs
Symmetry and fermion degeneracy on a lattice
International Nuclear Information System (INIS)
Raszillier, H.
1982-03-01
In this paper we consider the general form of finite difference approximation to the Dirac (Weyl) Hamiltonian on a lattice and investigate systematically the dependence on symmetry of the number of particles described by it. Our result is, that to a symmetry - expressed by a crystallographic space group - there corresponds a minimal number of particles, which are associated to prescribed points of momentum space (the unit cell of the reciprocal lattice). For convenience of the reader we show, using the existing detailed descriptions of space groups, how these results look for all the relevant (symmorphic) symmetry groups. Only for lattice Hamiltonians with a momentum dependent mass term can this degeneracy be reduced and even eliminated without reducing the symmetry. (orig./HSI)
Hamiltonian PDEs and Frobenius manifolds
International Nuclear Information System (INIS)
Dubrovin, Boris A
2008-01-01
In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
Hamiltonian PDEs and Frobenius manifolds
Energy Technology Data Exchange (ETDEWEB)
Dubrovin, Boris A [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2008-12-31
In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
Weak KAM for commuting Hamiltonians
International Nuclear Information System (INIS)
Zavidovique, M
2010-01-01
For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax–Oleinik semi-groups, a result of Barles and Tourin (2001 Indiana Univ. Math. J. 50 1523–44), using a direct geometrical method (Stoke's theorem). We also obtain a 'generalization' of a theorem of Maderna (2002 Bull. Soc. Math. France 130 493–506). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton–Jacobi equation) for G and for H are the same. As a corollary we obtain the equality of the Aubry sets and of the Peierls barrier. This is also related to works of Sorrentino (2009 On the Integrability of Tonelli Hamiltonians Preprint) and Bernard (2007 Duke Math. J. 136 401–20)
Hamiltonian dynamics of extended objects
Capovilla, R.; Guven, J.; Rojas, E.
2004-12-01
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.
A Hamiltonian approach to Thermodynamics
Energy Technology Data Exchange (ETDEWEB)
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 description of bubble dynamics
International Nuclear Information System (INIS)
Maksimov, A. O.
2008-01-01
The dynamics of a nonspherical bubble in a liquid is described within the Hamiltonian formalism. Primary attention is focused on the introduction of the canonical variables into the computational algorithm. The expansion of the Dirichlet-Neumann operator in powers of the displacement of a bubble wall from an equilibrium position is obtained in the explicit form. The first three terms (more specifically, the second-, third-, and fourth-order terms) in the expansion of the Hamiltonian in powers of the canonical variables are determined. These terms describe the spectrum and interaction of three essentially different modes, i.e., monopole oscillations (pulsations), dipole oscillations (translational motions), and surface oscillations. The cubic nonlinearity is analyzed for the problem associated with the generation of Faraday ripples on the wall of a bubble in an acoustic field. The possibility of decay processes occurring in the course of interaction of surface oscillations for the first fifteen (experimentally observed) modes is investigated.
Hamiltonian dynamics of extended objects
International Nuclear Information System (INIS)
Capovilla, R; Guven, J; Rojas, E
2004-01-01
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
Hamiltonian dynamics of extended objects
Energy Technology Data Exchange (ETDEWEB)
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.
A Hamiltonian approach to Thermodynamics
International Nuclear Information System (INIS)
Baldiotti, M.C.; Fresneda, R.; 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 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.
On the domain of the Nelson Hamiltonian
Griesemer, M.; Wünsch, A.
2018-04-01
The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper, we study the mapping properties of the Gross-transform in order to characterize the regularity properties of vectors in the form domain of the Nelson Hamiltonian. Since the operator domain is a subset of the form domain, our results apply to vectors in the domain of the Hamiltonian as well. This work is a continuation of our previous work on the Fröhlich Hamiltonian.
Hamiltonian systems in accelerator physics
International Nuclear Information System (INIS)
Laslett, L.J.
1985-06-01
General features of the design of annular particle accelerators or storage rings are outlined and the Hamiltonian character of individual-ion motion is indicated. Examples of phase plots are presented, for the motion in one spatial degree of freedom, of an ion subject to a periodic nonlinear focusing force. A canonical transformation describing coupled nonlinear motion also is given, and alternative types of graphical display are suggested for the investigation of long-term stability in such cases. 7 figs
Contact symmetries and Hamiltonian thermodynamics
International Nuclear Information System (INIS)
Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.
2015-01-01
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production
Hamiltonian dynamics of preferential attachment
International Nuclear Information System (INIS)
Zuev, Konstantin; Papadopoulos, Fragkiskos; Krioukov, Dmitri
2016-01-01
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 (PA), 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 PA. 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 PA is nearly identical to the ensemble of random graphs with scale-free degree distributions. In other words, PA generates nothing but random graphs with power-law degree distribution. The extension of the developed canonical formalism for network analysis to richer geometric network models with non-degenerate groups of symmetries may eventually lead to a system of equations describing network dynamics at small scales. (paper)
Anomalous Z2 antiferromagnetic topological phase in pressurized SmB6
Chang, Kai-Wei; Chen, Peng-Jen
2018-05-01
Antiferromagnetic materials, whose time-reversal symmetry is broken, can be classified into the Z2 topology if they respect some specific symmetry. Since the theoretical proposal, however, no materials have been found to host such Z2 antiferromagnetic topological (Z2-AFT ) phase to date. Here we demonstrate that the topological Kondo insulator SmB6 can be a Z2-AFT system when pressurized to undergo an antiferromagnetic phase transition. In addition to proposing the possible candidate for a Z2-AFT material, in this work we also illustrate the anomalous topological surface states of the Z2-AFT phase which have not been discussed before. Originating from the interplay between the topological properties and the antiferromagnetic surface magnetization, the topological surface states of the Z2-AFT phase behave differently as compared with those of a topological insulator. Besides, the Z2-AFT insulators are also found promising in the generation of tunable spin currents, which is an important application in spintronics.
International Nuclear Information System (INIS)
Chadderton, L.T.; Johnson, E.; Wohlenberg, T.
1976-01-01
Void lattices in metals apparently owe their stability to elastically anisotropic interactions. An ordered array of voids on the anion sublattice in fluorite does not fit so neatly into this scheme of things. Crowdions may play a part in the formation of the void lattice, and stability may derive from other sources. (Auth.)
International Nuclear Information System (INIS)
Randjbar-Daemi, S.
1995-12-01
The so-called doubling problem in the lattice description of fermions led to a proof that under certain circumstances chiral gauge theories cannot be defined on the lattice. This is called the no-go theorem. It implies that if Γ/sub/A is defined on a lattice then its infrared limit, which should correspond to the quantum description of the classical action for the slowly varying fields on lattice scale, is inevitably a vector like theory. In particular, if not circumvented, the no-go theorem implies that there is no lattice formulation of the Standard Weinberg-Salam theory or SU(5) GUT, even though the fermions belong to anomaly-free representations of the gauge group. This talk aims to explain one possible attempt at bypassing the no-go theorem. 20 refs
Energy Technology Data Exchange (ETDEWEB)
Randjbar-Daemi, S
1995-12-01
The so-called doubling problem in the lattice description of fermions led to a proof that under certain circumstances chiral gauge theories cannot be defined on the lattice. This is called the no-go theorem. It implies that if {Gamma}/sub/A is defined on a lattice then its infrared limit, which should correspond to the quantum description of the classical action for the slowly varying fields on lattice scale, is inevitably a vector like theory. In particular, if not circumvented, the no-go theorem implies that there is no lattice formulation of the Standard Weinberg-Salam theory or SU(5) GUT, even though the fermions belong to anomaly-free representations of the gauge group. This talk aims to explain one possible attempt at bypassing the no-go theorem. 20 refs.
Bernabé Ferreira, Miguel Jorge; Ibieta Jimenez, Juan Pablo; Padmanabhan, Pramod; Teôtonio Sobrinho, Paulo
2015-12-01
State sum constructions, such as Kuperberg’s algorithm, give partition functions of physical systems, like lattice gauge theories, in various dimensions by associating local tensors or weights with different parts of a closed triangulated manifold. Here we extend this construction by including matter fields to build partition functions in both two and three space-time dimensions. The matter fields introduce new weights to the vertices and they correspond to Potts spin configurations described by an {A}-module with an inner product. Performing this construction on a triangulated manifold with a boundary we obtain transfer matrices which are decomposed into a product of local operators acting on vertices, links and plaquettes. The vertex and plaquette operators are similar to the ones appearing in the quantum double models (QDMs) of Kitaev. The link operator couples the gauge and the matter fields, and it reduces to the usual interaction terms in known models such as {{{Z}}}2 gauge theory with matter fields. The transfer matrices lead to Hamiltonians that are frustration-free and are exactly solvable. According to the choice of the initial input, that of the gauge group and a matter module, we obtain interesting models which have a new kind of ground state degeneracy that depends on the number of equivalence classes in the matter module under gauge action. Some of the models have confined flux excitations in the bulk which become deconfined at the surface. These edge modes are protected by an energy gap provided by the link operator. These properties also appear in ‘confined Walker-Wang’ models which are 3D models having interesting surface states. Apart from the gauge excitations there are also excitations in the matter sector which are immobile and can be thought of as defects like in the Ising model. We only consider bosonic matter fields in this paper.
International Nuclear Information System (INIS)
Thorn, C.B.
1988-01-01
The possibility of studying non-perturbative effects in string theory using a world sheet lattice is discussed. The light-cone lattice string model of Giles and Thorn is studied numerically to assess the accuracy of ''coarse lattice'' approximations. For free strings a 5 by 15 lattice seems sufficient to obtain better than 10% accuracy for the bosonic string tachyon mass squared. In addition a crude lattice model simulating string like interactions is studied to find out how easily a coarse lattice calculation can pick out effects such as bound states which would qualitatively alter the spectrum of the free theory. The role of the critical dimension in obtaining a finite continuum limit is discussed. Instead of the ''gaussian'' lattice model one could use one of the vertex models, whose continuum limit is the same as a gaussian model on a torus of any radius. Indeed, any critical 2 dimensional statistical system will have a stringy continuum limit in the absence of string interactions. 8 refs., 1 fig. , 9 tabs
Hamiltonian Chaos and Fractional Dynamics
International Nuclear Information System (INIS)
Combescure, M
2005-01-01
This book provides an introduction and discussion of the main issues in the current understanding of classical Hamiltonian chaos, and of its fractional space-time structure. It also develops the most complex and open problems in this context, and provides a set of possible applications of these notions to some fundamental questions of dynamics: complexity and entropy of systems, foundation of classical statistical physics on the basis of chaos theory, and so on. Starting with an introduction of the basic principles of the Hamiltonian theory of chaos, the book covers many topics that can be found elsewhere in the literature, but which are collected here for the readers' convenience. In the last three parts, the author develops topics which are not typically included in the standard textbooks; among them are: - the failure of the traditional description of chaotic dynamics in terms of diffusion equations; - he fractional kinematics, its foundation and renormalization group analysis; - 'pseudo-chaos', i.e. kinetics of systems with weak mixing and zero Lyapunov exponents; - directional complexity and entropy. The purpose of this book is to provide researchers and students in physics, mathematics and engineering with an overview of many aspects of chaos and fractality in Hamiltonian dynamical systems. In my opinion it achieves this aim, at least provided researchers and students (mainly those involved in mathematical physics) can complement this reading with comprehensive material from more specialized sources which are provided as references and 'further reading'. Each section contains introductory pedagogical material, often illustrated by figures coming from several numerical simulations which give the feeling of what's going on, and thus is very useful to the reader who is not very familiar with the topics presented. Some problems are included at the end of most sections to help the reader to go deeper into the subject. My one regret is that the book does not
International Nuclear Information System (INIS)
Yu Fajun
2008-01-01
In [W.X. Ma, J. Phys. A: Math. Theor. 40 (2007) 15055], Prof. Ma gave a beautiful result (a discrete variational identity). In this Letter, based on a discrete block matrix spectral problem, a new hierarchy of Lax integrable lattice equations with four potentials is derived. By using of the discrete variational identity, we obtain Hamiltonian structure of the discrete soliton equation hierarchy. Finally, an integrable coupling system of the soliton equation hierarchy and its Hamiltonian structure are obtained through the discrete variational identity
Hamiltonian approach to QCD in Coulomb gauge: From the vacuum to finite temperatures
Directory of Open Access Journals (Sweden)
Reinhardt H.
2016-01-01
Full Text Available The variational Hamiltonian approach to QCD in Coulomb gauge is reviewedand the essential results obtained in recent years are summarized. First the results for thevacuum sector are discussed, with a special emphasis on the mechansim of confinementand chiral symmetry breaking. Then the deconfinement phase transition is described byintroducing temperature in the Hamiltonian approach via compactification of one spatialdimension. The effective action for the Polyakov loop is calculated and the order of thephase transition as well as the critical temperatures are obtained for the color group SU(2 and SU(3. In both cases, our predictions are in good agreement with lattice calculations.
Energy Technology Data Exchange (ETDEWEB)
Yu Fajun [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)], E-mail: yufajun888@163.com
2008-06-09
In [W.X. Ma, J. Phys. A: Math. Theor. 40 (2007) 15055], Prof. Ma gave a beautiful result (a discrete variational identity). In this Letter, based on a discrete block matrix spectral problem, a new hierarchy of Lax integrable lattice equations with four potentials is derived. By using of the discrete variational identity, we obtain Hamiltonian structure of the discrete soliton equation hierarchy. Finally, an integrable coupling system of the soliton equation hierarchy and its Hamiltonian structure are obtained through the discrete variational identity.
Divide and conquer method for proving gaps of frustration free Hamiltonians
DEFF Research Database (Denmark)
Kastoryano, Michael J.; Lucia, Angelo
2018-01-01
Providing system-size independent lower bounds on the spectral gap of local Hamiltonian is in general a hard problem. For the case of finite-range, frustration free Hamiltonians on a spin lattice of arbitrary dimension, we show that a property of the ground state space is sufficient to obtain...... such a bound. We furthermore show that such a condition is necessary and equivalent to a constant spectral gap. Thanks to this equivalence, we can prove that for gapless models in any dimension, the spectral gap on regions of diameter $n$ is at most $o\\left(\\frac{\\log(n)^{2+\\epsilon}}{n}\\right)$ for any...... positive $\\epsilon$....
DEFF Research Database (Denmark)
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...
Lattice dynamics of ionic crystals
International Nuclear Information System (INIS)
Mahan, G.D.
1990-01-01
The theory of lattice dynamics for ionic and rare-gas crystals is derived in the harmonic approximation. We start from a Hamiltonian and average over electron coordinates in order to obtain an effective interaction between ion displacements. We assume that electronic excitations are localized on a single ion, which limits the theory to ionic crystals. The deformation-dipole model and the indirect-ionic-interaction model are derived. These two contributions are closely linked, and together provide an accurate description of short-range forces
Coherent states for quadratic Hamiltonians
International Nuclear Information System (INIS)
Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes
2011-01-01
The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.
Perturbation theory of effective Hamiltonians
International Nuclear Information System (INIS)
Brandow, B.H.
1975-01-01
This paper constitutes a review of the many papers which have used perturbation theory to derive ''effective'' or ''model'' Hamiltonians. It begins with a brief review of nondegenerate and non-many-body perturbation theory, and then considers the degenerate but non-many-body problem in some detail. It turns out that the degenerate perturbation problem is not uniquely defined, but there are some practical criteria for choosing among the various possibilities. Finally, the literature dealing with the linked-cluster aspects of open-shell many-body systems is reviewed. (U.S.)
Integrable and nonintegrable Hamiltonian systems
International Nuclear Information System (INIS)
Percival, I.
1986-01-01
Traditionally Hamiltonian systems with a finite number of degrees of freedom have been divided into those with few degrees of freedom which were supposed to exhibit some kind of regular ordered motions and those with large numbers of degrees of freedom for which the methods of statistical mechanics should be used. The last few decades have seen a complete change of view. The change of view affects almost all the practical applications, particularly in mathematical physics, which has been dominated for many decades by linear mathematics, coming from quantum theory. The authors consider how this change of view affects some specific applications of dynamics and also the relation between dynamical theory and applications
Absence of coherent peaks in a Z2 fractionalized BCS superconducting state
Zhong, Yin; Lu, Han-Tao; Luo, Hong-Gang
2015-01-01
We explore a Z2 fractionalized Bardeen-Cooper-Schrieffer (BCS) superconducting state, which is a minimal extension of usual BCS framework. It is found that this state has similar thermal and transport properties, but its single-particle feature strongly deviates from the coherent quasiparticle behavior of the classic/conventional BCS superconducting state. The fingerprint of such Z2 BCS state is the absence of the BCS coherent peaks and instead a kink in the local density of state occurs, which in principle could be probed by scanning tunneling microscopy or point-contact spectroscopy experiments. The corresponding exactly soluble models that realize the desirable Z2 fractionalized BCS state are presented. In addition, we also study the extended t-U-J model by using Z2 slave-spin representation and find that the Z2 BCS state may exist when the paring structure is fully gapped or has nodes. The prototypical wave-function of such a Z2 BCS state is also proposed, which could be taken as trial wave-function in current numerical techniques. Furthermore, the pairing mechanism of Z2 BCS state is argued from both weak and strong coupling perspective. The present work may be helpful to further study the unconventional superconductivity and its relation to non-Fermi liquids.
Perspective: Quantum Hamiltonians for optical interactions
Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy
2018-01-01
The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.
Directory of Open Access Journals (Sweden)
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.
Generalized oscillator representations for Calogero Hamiltonians
International Nuclear Information System (INIS)
Tyutin, I V; Voronov, B L
2013-01-01
This paper is a natural continuation of the previous paper (Gitman et al 2011 J. Phys. A: Math. Theor. 44 425204), where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant α ⩾ − 1/4 were constructed. In this paper, we present generalized oscillator representations for all Calogero Hamiltonians with α ⩾ − 1/4. These representations are generally highly nonunique, but there exists an optimum representation for each Hamiltonian. (comment)
Hamiltonian formulation of reduced magnetohydrodynamics
International Nuclear Information System (INIS)
Morrison, P.J.; Hazeltine, R.D.
1983-07-01
Reduced magnetohydrodynamics (RMHD) has become a principal tool for understanding nonlinear processes, including disruptions, in tokamak plasmas. Although analytical studies of RMHD turbulence have been useful, the model's impressive ability to simulate tokamak fluid behavior has been revealed primarily by numerical solution. The present work describes a new analytical approach, not restricted to turbulent regimes, based on Hamiltonian field theory. It is shown that the nonlinear (ideal) RMHD system, in both its high-beta and low-beta versions, can be expressed in Hanmiltonian form. Thus a Poisson bracket, [ , ], is constructed such that each RMHD field quantitity, xi/sub i/, evolves according to xi/sub i/ = [xi/sub i/,H], where H is the total field energy. The new formulation makes RMHD accessible to the methodology of Hamiltonian mechanics; it has lead, in particular, to the recognition of new RMHD invariants and even exact, nonlinear RMHD solutions. A canonical version of the Poisson bracket, which requires the introduction of additional fields, leads to a nonlinear variational principle for time-dependent RMHD
General technique to produce isochronous Hamiltonians
International Nuclear Information System (INIS)
Calogero, F; Leyvraz, F
2007-01-01
We introduce a new technique-characterized by an arbitrary positive constant Ω, with which we associate the period T = 2π/Ω-to 'Ω-modify' a Hamiltonian so that the new Hamiltonian thereby obtained is entirely isochronous, namely it yields motions all of which (except possibly for a lower dimensional set of singular motions) are periodic with the same fixed period T in all their degrees of freedom. This technique transforms real autonomous Hamiltonians into Ω-modified Hamiltonians which are also real and autonomous, and it is widely applicable, for instance, to the most general many-body problem characterized by Newtonian equations of motion ('acceleration equal force') provided it is translation invariant. The Ω-modified Hamiltonians are of course not translation invariant, but for Ω = 0 they reduce (up to marginal changes) to the unmodified Hamiltonians they were obtained from. Hence, when this technique is applied to translation-invariant Hamiltonians yielding, in their center-of-mass systems, chaotic motions with a natural time scale much smaller than T, the corresponding Ω-modified Hamiltonians shall display a chaotic behavior for quite some time before the isochronous character of the motions takes over. We moreover show that the quantized versions of these Ω-modified Hamiltonians feature equispaced spectra
Collective Hamiltonians for dipole giant resonances
International Nuclear Information System (INIS)
Weiss, L.I.
1991-07-01
The collective hamiltonian for the Giant Dipole resonance (GDR), in the Goldhaber-Teller-Model, is analytically constructed using the semiclassical and generator coordinates method. Initially a conveniently parametrized set of many body wave functions and a microscopic hamiltonian, the Skyrme hamiltonian - are used. These collective Hamiltonians are applied to the investigation of the GDR, in He 4 , O 16 and Ca 40 nuclei. Also the energies and spectra of the GDR are obtained in these nuclei. The two sets of results are compared, and the zero point energy effects analysed. (author)
Canonical transformations and hamiltonian path integrals
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Behaviour of the Hamiltonian path integrals under canonical transformations produced by a generator, is investigated. An exact form is determined for the kernel of the unitary operator realizing the corresponding quantum transformation. Equivalence rules are found (the Hamiltonian formalism, one-dimensional case) enabling one to exclude non-standard terms from the action. It is shown that the Hamiltonian path integral changes its form under cononical transformations: in the transformed expression besides the classical Hamiltonian function there appear some non-classical terms
Noncanonical Hamiltonian methods in plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1981-11-01
A Hamiltonian approach to plasma dynamics has numerous advantages over equivalent formulations which ignore the underlying Hamiltonian structure. In addition to achieving a deeper understanding of processes, Hamiltonian methods yield concise expressions (such as the Kubo form for linear susceptibility), greatly shorten the length of calculations, expose relationships (such as between the ponderomotive Hamiltonian and the linear susceptibility), determine invariants in terms of symmetry operations, and cover situations of great generality. In addition, they yield the Poincare invariants, in particular Liouville volume and adiabatic actions
International Nuclear Information System (INIS)
Smith, L.
1975-01-01
An analysis is given of a number of variants of the basic lattice of the planned ISABELLE storage rings. The variants were formed by removing cells from the normal part of the lattice and juggling the lengths of magnets, cells, and insertions in order to maintain a rational relation of circumference to that of the AGS and approximately the same dispersion. Special insertions, correction windings, and the working line with nonlinear resonances are discussed
Identity of the SU(3) model phenomenological hamiltonian and the hamiltonian of nonaxial rotator
International Nuclear Information System (INIS)
Filippov, G.F.; Avramenko, V.I.; Sokolov, A.M.
1984-01-01
Interpretation of nonspheric atomic nuclei spectra on the basis of phenomenological hamiltonians of SU(3) model showed satisfactory agreement of simulation calculations with experimental data. Meanwhile physical sense of phenomenological hamiltonians was not yet discussed. It is shown that phenomenological hamiltonians of SU(3) model are reduced to hamiltonian of nonaxial rotator but with additional items of the third and fourth powers angular momentum operator of rotator
Vortex structure in abelian-projected lattice gauge theory
International Nuclear Information System (INIS)
Ambjoern, J.; Giedt, J.; Greensite, J.
2000-01-01
We report on a breakdown of both monopole dominance and positivity in abelian-projected lattice Yang-Mills theory. The breakdown is associated with observables involving two units of the abelian charge. We find that the projected lattice has at most a global Z 2 symmetry in the confined phase, rather than the global U(1) symmetry that might be expected in a dual superconductor or monopole Coulomb gas picture. Implications for monopole and center vortex theories of confinement are discussed
Hamiltonian closures in fluid models for plasmas
Tassi, Emanuele
2017-11-01
This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and
A thermoluminescence study of Z2-centres in terbium-doped NaCl crystals
International Nuclear Information System (INIS)
Reddy, K.N.; Ahmed, I.M.; Pandaraiah, N.; Rao, U.V.S.; Babu, V.H.
1983-01-01
Thermoluminescence (TL), optical absorption are used to correlate thermal annealing of Z 2 -centres with TL peak occurring around 110 0 C in terbium-doped NaCl crystals. The TL glow peak occurring around 190 0 C is attributed to the thermal annealing of F-centres. The thermal activation parameters are calculated for both Z 2 - and F-centre peaks. (author)
Analytic progress on exact lattice chiral symmetry
International Nuclear Information System (INIS)
Kikukawa, Y.
2002-01-01
Theoretical issues of exact chiral symmetry on the lattice are discussed and related recent works are reviewed. For chiral theories, the construction with exact gauge invariance is reconsidered from the point of view of domain wall fermion. The issue in the construction of electroweak theory is also discussed. For vector-like theories, we discuss unitarity (positivity), Hamiltonian approach, and several generalizations of the Ginsparg-Wilson relation (algebraic and odd-dimensional)
International Nuclear Information System (INIS)
Fort, H.
1994-01-01
We present a survey on the state of the art in the formulation of lattice compact QED in the space of loops. In a first part we review our most recent Hamiltonian results which signal a second order transition for (3+1) compact QED. We devote the second part to the Lagrangian loop formalism, showing the equivalence of the recently proposed loop action with the Villain form. (orig.)
Hamiltonian analysis of Plebanski theory
International Nuclear Information System (INIS)
Buffenoir, E; Henneaux, M; Noui, K; Roche, Ph
2004-01-01
We study the Hamiltonian formulation of Plebanski theory in both the Euclidean and Lorentzian cases. A careful analysis of the constraints shows that the system is non-regular, i.e., the rank of the Dirac matrix is non-constant on the non-reduced phase space. We identify the gravitational and topological sectors which are regular subspaces of the non-reduced phase space. The theory can be restricted to the regular subspace which contains the gravitational sector. We explicitly identify first- and second-class constraints in this case. We compute the determinant of the Dirac matrix and the natural measure for the path integral of the Plebanski theory (restricted to the gravitational sector). This measure is the analogue of the Leutwyler-Fradkin-Vilkovisky measure of quantum gravity
Quantum Statistical Operator and Classically Chaotic Hamiltonian ...
African Journals Online (AJOL)
Quantum Statistical Operator and Classically Chaotic Hamiltonian System. ... Journal of the Nigerian Association of Mathematical Physics ... In a Hamiltonian system von Neumann Statistical Operator is used to tease out the quantum consequence of (classical) chaos engendered by the nonlinear coupling of system to its ...
A Direct Method of Hamiltonian Structure
International Nuclear Information System (INIS)
Li Qi; Chen Dengyuan; Su Shuhua
2011-01-01
A direct method of constructing the Hamiltonian structure of the soliton hierarchy with self-consistent sources is proposed through computing the functional derivative under some constraints. The Hamiltonian functional is related with the conservation densities of the corresponding hierarchy. Three examples and their two reductions are given. (general)
Port Hamiltonian modeling of Power Networks
van Schaik, F.; van der Schaft, Abraham; Scherpen, Jacquelien M.A.; Zonetti, Daniele; Ortega, R
2012-01-01
In this talk a full nonlinear model for the power network in port–Hamiltonian framework is derived to study its stability properties. For this we use the modularity approach i.e., we first derive the models of individual components in power network as port-Hamiltonian systems and then we combine all
Hamiltonian representation of divergence-free fields
International Nuclear Information System (INIS)
Boozer, A.H.
1984-11-01
Globally divergence-free fields, such as the magnetic field and the vorticity, can be described by a two degree of freedom Hamiltonian. The Hamiltonian function provides a complete topological description of the field lines. The formulation also separates the dissipative and inertial time scale evolution of the magnetic and the vorticity fields
Hamiltonian structure of linearly extended Virasoro algebra
International Nuclear Information System (INIS)
Arakelyan, T.A.; Savvidi, G.K.
1991-01-01
The Hamiltonian structure of linearly extended Virasoro algebra which admits free bosonic field representation is described. An example of a non-trivial extension is found. The hierarchy of integrable non-linear equations corresponding to this Hamiltonian structure is constructed. This hierarchy admits the Lax representation by matrix Lax operator of second order
Momentum and hamiltonian in complex action theory
DEFF Research Database (Denmark)
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...
A parcel formulation for Hamiltonian layer models
Bokhove, Onno; Oliver, M.
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
On Distributed Port-Hamiltonian Process Systems
Lopezlena, Ricardo; Scherpen, Jacquelien M.A.
2004-01-01
In this paper we use the term distributed port-Hamiltonian Process Systems (DPHPS) to refer to the result of merging the theory of distributed Port-Hamiltonian systems (DPHS) with the theory of process systems (PS). Such concept is useful for combining the systematic interconnection of PHS with the
Relativistic magnetohydrodynamics as a Hamiltonian system
International Nuclear Information System (INIS)
Holm, D.D.; Kupershmidt, A.
1985-01-01
The equations of ideal relativistic magnetohydrodynamics in the laboratory frame form a noncanonical Hamiltonian system with the same Poisson bracket as for the nonrelativistic system, but with dynamical variables and Hamiltonian obtained via a regular deformation of their nonrelativistic counterparts [fr
Hamiltonian Cycles on Random Eulerian Triangulations
DEFF Research Database (Denmark)
Guitter, E.; Kristjansen, C.; Nielsen, Jakob Langgaard
1998-01-01
. Considering the case n -> 0, this implies that the system of random Eulerian triangulations equipped with Hamiltonian cycles describes a c=-1 matter field coupled to 2D quantum gravity as opposed to the system of usual random triangulations equipped with Hamiltonian cycles which has c=-2. Hence, in this case...
Almost periodic Hamiltonians: an algebraic approach
International Nuclear Information System (INIS)
Bellissard, J.
1981-07-01
We develop, by analogy with the study of periodic potential, an algebraic theory for almost periodic hamiltonians, leading to a generalized Bloch theorem. This gives rise to results concerning the spectral measures of these operators in terms of those of the corresponding Bloch hamiltonians
Nested Sampling with Constrained Hamiltonian Monte Carlo
Betancourt, M. J.
2010-01-01
Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian Monte Carlo is readily adapted to efficiently sample from any smooth, constrained distribution. Utilizing this constrained Hamiltonian Monte Carlo, I introduce a general implementation of the nested sampling algorithm.
Electron-lattice Interaction and Nonlinear Excitations in Cuprate Structures
International Nuclear Information System (INIS)
Paulsen, J.; Eschrig, H.; Drechsler, S.L.; Malek, J.
1995-01-01
A low temperature lattice modulation of the chains of the YBa 2 Cu 3 O 7 is considered by deriving a Hamiltonian of electron-lattice interaction from density-functional calculations for deformed lattice and solving it for the groundstate. Hubbard-type Coulomb interaction is included. The obtained groundstate is a charge-density-wave state with a pereodicity of four lattice constants and a gap for one-electron excitations of about 1eV, sensitively depending on parameters of the Hamiltonian. There are lots of polaronic and solitonic excitations with formation energies deep in the gap, which can pin the Fermi level and thus produce again metallicity of the chain. They might also contribute to pairing of holes in adjacent CuO 2 -planes. (author)
International Nuclear Information System (INIS)
Catterall, Simon
2013-01-01
Discretization of supersymmetric theories is an old problem in lattice field theory. It has resisted solution until quite recently when new ideas drawn from orbifold constructions and topological field theory have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theory in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local and free of doublers and in the case of Yang-Mills theories also possess exact gauge invariance. In principle they form the basis for a truly non-perturbative definition of the continuum supersymmetric field theory. In this talk these ideas are reviewed with particular emphasis being placed on N = 4 super Yang-Mills theory.
Weak mixing angle and the SU(3)CxSU(3) model on M4xS1/(Z2xZ'2)
International Nuclear Information System (INIS)
Li Tianjun; Wei Liao
2002-05-01
We show that the desirable weak mixing angle sin 2 θ W =0.2312 at m Z scale can be generated naturally in the SU(3) C xSU(3) model on M 4 xS 1 /(Z 2 x Z 2 ') where the gauge symmetry SU(3) is broken down to SU(2) L xU(1) Y by orbifold projection. For a supersymmetric model with a TeV scale extra dimension, the SU(3) unification scale is about hundreds of TeVs at which the gauge couplings for SU(3) C and SU(3) can also be equal in the mean time. For the non-supersymmetric model, SU(2) L xU(1) Y are unified at order of 10 TeV. These models may serve as good candidates for physics beyond the SM or MSSM. (author)
Finite-size scaling theory and quantum hamiltonian Field theory: the transverse Ising model
International Nuclear Information System (INIS)
Hamer, C.J.; Barber, M.N.
1979-01-01
Exact results for the mass gap, specific heat and susceptibility of the one-dimensional transverse Ising model on a finite lattice are generated by constructing a finite matrix representation of the Hamiltonian using strong-coupling eigenstates. The critical behaviour of the limiting infinite chain is analysed using finite-size scaling theory. In this way, excellent estimates (to within 1/2% accuracy) are found for the critical coupling and the exponents α, ν and γ
Computing the real-time Green's Functions of large Hamiltonian matrices
Iitaka, Toshiaki
1998-01-01
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...
International Nuclear Information System (INIS)
Creutz, M.
1984-01-01
After reviewing some recent developments in supercomputer access, the author discusses a few areas where perturbation theory and lattice gauge simulations make contact. The author concludes with a brief discussion of a deterministic dynamics for the Ising model. This may be useful for numerical studies of nonequilibrium phenomena. 13 references
Discrete breathers in classical ferromagnetic lattices with easy-plane anisotropy
DEFF Research Database (Denmark)
Khalack, J. M.; Zolotaryuk, Yaroslav; Christiansen, Peter Leth
2003-01-01
Discrete breathers (nonlinear localized modes) have been shown to exist in various nonlinear Hamiltonian lattice systems. This paper is devoted to the investigation of a classical d-dimensional ferromagnetic lattice with easy plane anisotropy. Its dynamics is described via the Heisenberg model...
Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy
International Nuclear Information System (INIS)
Bogdanov, L V
2010-01-01
We consider two-component integrable generalizations of the dispersionless two-dimensional Toda lattice (2DTL) hierarchy connected with non-Hamiltonian vector fields, similar to the Manakov-Santini hierarchy generalizing the dKP hierarchy. They form a one-parametric family connected by hodograph-type transformations. Generating equations and Lax-Sato equations are introduced, and a dressing scheme based on the vector nonlinear Riemann problem is formulated. The simplest two-component generalization of the dispersionless 2DTL equation is derived, and its differential reduction analogous to the Dunajski interpolating system is presented. A symmetric two-component generalization of the dispersionless elliptic 2DTL equation is also constructed.
Superconducting tunneling with the tunneling Hamiltonian. II. Subgap harmonic structure
International Nuclear Information System (INIS)
Arnold, G.B.
1987-01-01
The theory of superconducting tunneling without the tunneling Hamiltonian is extended to treat superconductor/insulator/superconductor junctions in which the transmission coefficient of the insulating barrier approaches unity. The solution for the current in such junctions is obtained by solving the problem of a particle hopping in a one-dimensional lattice of sites, with forward and reverse transfer integrals that depend on the site. The results are applied to the problem of subgap harmonic structure in superconducting tunneling. The time-dependent current at finite voltage through a junction exhibiting subgap structure is found to have terms that oscillate at all integer multiples of the Josephson frequency, n(2eV/h). The amplitudes of these new, and as yet unmeasured, ac current contributions as a function of voltage are predicted
Lattice quantum phase space and Yang-Baxter equation
International Nuclear Information System (INIS)
Djemai, A.E.F.
1995-04-01
In this work, we show that it is possible to construct the quantum group which preserves the quantum symplectic structure introduced in the context of the matrix Hamiltonian formalism. We also study the braiding existing behind the lattice quantum phase space, and present another type of non-trivial solution to the resulting Yang-Baxter equation. (author). 20 refs, 1 fig
Excitation spectrum and staggering transformations in lattice quantum models.
Faria da Veiga, Paulo A; O'Carroll, Michael; Schor, Ricardo
2002-08-01
We consider the energy-momentum excitation spectrum of diverse lattice Hamiltonian operators: the generator of the Markov semigroup of Ginzburg-Landau models with Langevin stochastic dynamics, the Hamiltonian of a scalar quantum field theory, and the Hamiltonian associated with the transfer matrix of a classical ferromagnetic spin system at high temperature. The low-lying spectrum consists of a one-particle state and a two-particle band. The two-particle spectrum is determined using a lattice version of the Bethe-Salpeter equation. In addition to the two-particle band, depending on the lattice dimension and on the attractive or repulsive character of the interaction between the particles of the system, there is, respectively, a bound state below or above the two-particle band. We show how the existence or nonexistence of these bound states can be understood in terms of a nonrelativistic single-particle lattice Schrödinger Hamiltonian with a delta potential. A staggering transformation relates the spectra of the attractive and the repulsive cases.
Effective low-energy Hamiltonians for interacting nanostructures
Kinza, Michael; Ortloff, Jutta; Honerkamp, Carsten
2010-10-01
We present a functional renormalization group (fRG) treatment of trigonal graphene nanodisks and composites thereof, modeled by finite-size Hubbard-like Hamiltonians with honeycomb lattice structure. At half filling, the noninteracting spectrum of these structures contains a certain number of half-filled states at the Fermi level. For the case of trigonal nanodisks, including interactions between these degenerate states was argued to lead to a large ground state spin with potential spintronics applications [M. Ezawa, Eur. Phys. J. B 67, 543 (2009)10.1140/epjb/e2009-00041-7]. Here we perform a systematic fRG flow where the excited single-particle states are integrated out with a decreasing energy cutoff, yielding a renormalized low-energy Hamiltonian for the zero-energy states that includes effects of the excited levels. The numerical implementation corroborates the results obtained with a simpler Hartree-Fock treatment of the interaction effects within the zero-energy states only. In particular, for trigonal nanodisks the degeneracy of the one-particle-states with zero energy turns out to be protected against influences of the higher levels. As an explanation, we give a general argument that within this fRG scheme the zero-energy degeneracy remains unsplit under quite general conditions and for any size of the trigonal nanodisk. We also discuss a second class of nanostructures, bow-tie-shaped systems, where the zero-energy states are not protected.
Single-particle dynamics - Hamiltonian formulation
International Nuclear Information System (INIS)
Montague, B.W.
1977-01-01
In this paper the Hamiltonian formalism is applied to the linear theory of accelerator dynamics. The reasons for the introduction of this method rather than the more straightforward use of second order differential equations of motion are briefly discussed. An outline of Lagrangian and Hamiltonian formalism is given, some properties of the Hamiltonian are discussed and canonical transformations are illustrated. The methods are demonstrated using elementary examples such as the simple pendulum and the procedures adopted to handle specific problems in accelerator theory are indicated. (B.D.)
Incomplete Dirac reduction of constrained Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Chandre, C., E-mail: chandre@cpt.univ-mrs.fr
2015-10-15
First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.
Quantum entangling power of adiabatically connected Hamiltonians
International Nuclear Information System (INIS)
Hamma, Alioscia; Zanardi, Paolo
2004-01-01
The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bipartite quantum state space. When the different Hamiltonians in the family fall in the same adiabatic class, one can manipulate entanglement by moving through energy eigenstates corresponding to different values of the control parameters. We introduce an associated notion of adiabatic entangling power. This novel measure is analyzed for general dxd quantum systems, and specific two-qubit examples are studied
Quantum Hamiltonian Physics with Supercomputers
International Nuclear Information System (INIS)
Vary, James P.
2014-01-01
The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed
Quantum Hamiltonian Physics with Supercomputers
Energy Technology Data Exchange (ETDEWEB)
Vary, James P.
2014-06-15
The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed.
A New Numerical Method for Z2 Topological Insulators with Strong Disorder
Akagi, Yutaka; Katsura, Hosho; Koma, Tohru
2017-12-01
We propose a new method to numerically compute the Z2 indices for disordered topological insulators in Kitaev's periodic table. All of the Z2 indices are derived from the index formulae which are expressed in terms of a pair of projections introduced by Avron, Seiler, and Simon. For a given pair of projections, the corresponding index is determined by the spectrum of the difference between the two projections. This difference exhibits remarkable and useful properties, as it is compact and has a supersymmetric structure in the spectrum. These properties enable highly efficient numerical calculation of the indices of disordered topological insulators. The method, which we propose, is demonstrated for the Bernevig-Hughes-Zhang and Wilson-Dirac models whose topological phases are characterized by a Z2 index in two and three dimensions, respectively.
Application to supersymmetric models of Dirac-kaehler formalism on the lattice
International Nuclear Information System (INIS)
Zimerman, A.H.
1987-01-01
Using Dirac-Kaehler techniques we formulate some supersymmetric models on the lattice. Specifically we consider the Wess-Zumino model with N=2 in two dimensions which is formulated on a space lattice in its Hamiltonian version (continuous time) as well as on the space-time lattice in its Lagrangean version (euclidean space). On the space lattice (Hamiltonian formulation) we study also the supersymmetric Yanh-Mills model with N=4 in four dimensions. After the introduction of lattice covariant derivatives for fields in the adjoint representation of a compact group we write down some new relations which we have obtained and which constitute generalizations on the lattice of those which are known in the continuous case. (author) [pt
Jacobi fields of completely integrable Hamiltonian systems
International Nuclear Information System (INIS)
Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.
2003-01-01
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
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.
Spectral properties of almost-periodic Hamiltonians
International Nuclear Information System (INIS)
Lima, R.
1983-12-01
We give a description of some spectral properties of almost-periodic hamiltonians. We put the stress on some particular points of the proofs of the existence of absolutely continuous or pure point spectrum [fr
Air parcels and air particles: Hamiltonian dynamics
Bokhove, Onno; Lynch, Peter
We present a simple Hamiltonian formulation of the Euler equations for fluid flow in the Lagrangian framework. In contrast to the conventional formulation, which involves coupled partial differential equations, our "innovative'' mathematical formulation involves only ordinary differential equations
Discrete Hamiltonian evolution and quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Winkler, Oliver
2004-01-01
We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization
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.
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.
Variable Delay in port-Hamiltonian Telemanipulation
Secchi, C; Stramigioli, Stefano; Fantuzzi, C.
2006-01-01
In several applications involving bilateral telemanipulation, master and slave act at different power scales. In this paper a strategy for passively dealing with variable communication delay in scaled port-Hamiltonian based telemanipulation over packet switched networks is proposed.
Reorganization of Damaged Chromatin by the Exchange of Histone Variant H2A.Z-2
Energy Technology Data Exchange (ETDEWEB)
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
Reorganization of Damaged Chromatin by the Exchange of Histone Variant H2A.Z-2
International Nuclear Information System (INIS)
Nishibuchi, Ikuno; Suzuki, Hidekazu; Kinomura, Aiko; Sun, Jiying; Liu, Ning-Ang; Horikoshi, Yasunori; Shima, Hiroki; Kusakabe, Masayuki; Harata, Masahiko; Fukagawa, Tatsuo; Ikura, Tsuyoshi; Ishida, Takafumi; Nagata, Yasushi; Tashiro, Satoshi
2014-01-01
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
On local Hamiltonians and dissipative systems
Energy Technology Data Exchange (ETDEWEB)
Castagnino, M. [CONICET-Institutos de Fisica Rosario y de Astronomia y Fisica del Espacio Casilla de Correos 67, Sucursal 28, 1428, Buenos Aires (Argentina); Gadella, M. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina) and Departamento de Fisica Teorica, Facultad de Ciencias c. Real de Burgos, s.n., 47011 Valladolid (Spain)]. E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina)
2006-11-15
We study a type of one-dimensional dynamical systems on the corresponding two-dimensional phase space. By using arguments related to the existence of integrating factors for Pfaff equations, we show that some one-dimensional non-Hamiltonian systems like dissipative systems, admit a Hamiltonian description by sectors on the phase plane. This picture is not uniquely defined and is coordinate dependent. A simple example is exhaustively discussed. The method, is not always applicable to systems with higher dimensions.
Higher derivative operators from Scherk-Schwarz supersymmetry breaking on Τ2/Z2
International Nuclear Information System (INIS)
Ghilencea, D.M.
2005-09-01
In orbifold compactifications on Τ 2 /Z 2 with Scherk-Schwarz supersymmetry breaking, it is shown that (brane-localised) superpotential interactions and (bulk) gauge interactions generate at one-loop higher derivative counterterms to the mass of the brane (or zero-mode of the bulk) scalar field. These brane-localised operators are generated by integrating out the bulk modes of the initial theory which, although supersymmetric, is nevertheless non-renormalisable. It is argued that such operators, of non-perturbative origin and not protected by non-renormalisation theorems, are generic in orbifold compactifications and play a crucial role in the UV behaviour of the two-point Green function of the scalar field self-energy. Their presence in the action with unknown coefficients prevents one from making predictions about physics at (momentum) scales close to/above the compactification scale(s). Our results extend to the case of two dimensional orbifolds, previous findings for S 1 /Z 2 and S 1 /(Z 2 x Z 2 ') compactifications where brane-localised higher derivative operators are also dynamically generated at loop level, regardless of the details of the supersymmetry breaking mechanism. We stress the importance of these operators for the hierarchy and the cosmological constant problems in compactified theories. (orig.)
Energy Technology Data Exchange (ETDEWEB)
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.
The topology of Lagrangian foliations of integrable systems with hyperelliptic Hamiltonian
International Nuclear Information System (INIS)
Kudryavtseva, Elena A; Lepskii, Timur A
2011-01-01
We study the integrable Hamiltonian systems (C 2 ,Re(dz and dw),H=Ref(z,w)) with the additional first integral F=Imf which correspond to the complex Hamiltonian systems (C 2 ,dz and dw,f(z,w)) with a hyperelliptic Hamiltonian f(z,w)=z 2 +P n (w), n element of N. For n≥3 the system has incomplete flows on any Lagrangian leaf f -1 (a). The topology of the Lagrangian foliation of such systems in a small neighbourhood of any leaf f -1 (a) is described in terms of the number n and the combinatorial type of the leaf--the set of multiplicities of the critical points of the function f that belong to the leaf. For odd n, a complex analogue of Liouville's theorem is obtained for those systems corresponding to polynomials P n (w) with simple real roots. In particular, a set of complex canonical variables analogous to action-angle variables is constructed in a small neighbourhood of the leaf f -1 (0). Bibliography: 12 titles.
Low-energy scattering on the lattice
International Nuclear Information System (INIS)
Bour Bour, Shahin
2014-01-01
In this thesis we present precision benchmark calculations for two-component fermions in the unitarity limit using an ab initio method, namely Hamiltonian lattice formalism. We calculate the ground state energy for unpolarized four particles (Fermi gas) in a periodic cube as a fraction of the ground state energy of the non-interacting system for two independent representations of the lattice Hamiltonians. We obtain the values 0.211(2) and 0.210(2). These results are in full agreement with the Euclidean lattice and fixed-node diffusion Monte Carlo calculations. We also give an expression for the energy corrections to the binding energy of a bound state in a moving frame. These corrections contain information about the mass and number of the constituents and are topological in origin and will have a broad applications to the lattice calculations of nucleons, nuclei, hadronic molecules and cold atoms. As one of its applications we use this expression and determine the low-energy parameters for the fermion dimer elastic scattering in shallow binding limit. For our lattice calculations we use Luescher's finite volume method. From the lattice calculations we find κa fd =1.174(9) and κr fd =-0.029(13), where κ represents the binding momentum of dimer and a fd (r fd ) denotes the scattering length (effective-range). These results are confirmed by the continuum calculations using the Skorniakov-Ter-Martirosian integral equation which gives 1.17907(1) and -0.0383(3) for the scattering length and effective range, respectively.
Surface representations of Wilson loop expectations in lattice gauge theory
International Nuclear Information System (INIS)
Brydges, D.C.; Giffen, C.; Durhuus, B.; Froehlich, J.
1986-01-01
Expectations of Wilson loops in lattice gauge theory with gauge group G=Z 2 , U(1) or SU(2) are expressed as weighted sums over surfaces with boundary equal to the loops labelling the observables. For G=Z 2 and U(1), the weights are all positive. For G=SU(2), the weights can have either sign depending on the Euler characteristic of the surface. Our surface (or flux sheet-) representations are partial resummations of the strong coupling expansion and provide some qualitative understanding of confinement. The significance of flux sheets with nontrivial topology for permanent confinement in the SU(2)-theory is elucidated. (orig.)
Hot B violation, the lattice, and hard thermal loops
International Nuclear Information System (INIS)
Arnold, P.
1997-01-01
It has recently been argued that the rate per unit volume of baryon number violation (topological transitions) in the hot, symmetric phase of electroweak theory is of the form ηα w 5 T 4 in the weak-coupling limit, where η is a nonperturbative numerical coefficient. Over the past several years, there have been attempts to extract the rate of baryon number violation from real-time simulations of classical thermal field theory on a spatial lattice. Unfortunately, the coefficient η will not be the same for classical lattice theories and the real quantum theory. However, by analyzing the appropriate effective theory on the lattice using the method of hard thermal loops, I show that the only obstruction to precisely relating the rates in the real and lattice theories is the fact that the long-distance physics on the lattice is not rotationally invariant. (This is unlike Euclidean-time measurements, where rotational invariance is always recovered in the continuum limit.) I then propose how this violation of rotational invariance can be eliminated emdash and the real B violation rate measured emdash by choosing an appropriate lattice Hamiltonian. I also propose a rough measure of the systematic error to be expected from using simpler, unimproved Hamiltonians. As a byproduct of my investigation, the plasma frequency and Debye mass are computed for classical thermal field theory on the lattice. copyright 1997 The American Physical Society
Lattice calculation of nonleptonic charm decays
International Nuclear Information System (INIS)
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 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
Scott, Paul
2006-01-01
A lattice is a (rectangular) grid of points, usually pictured as occurring at the intersections of two orthogonal sets of parallel, equally spaced lines. Polygons that have lattice points as vertices are called lattice polygons. It is clear that lattice polygons come in various shapes and sizes. A very small lattice triangle may cover just 3…
Gravitational surface Hamiltonian and entropy quantization
Directory of Open Access Journals (Sweden)
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.
Noncanonical Hamiltonian methods in plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-01-01
A Hamiltonian approach to plasma dynamics is described. The Poisson bracket of two observables g 1 and g 2 is given by using an antisymmetric tensor J, and must satisfy the Jacobi condition. The J can be obtained by elementary tensor analysis. The evolution in time of an observable g is given in terms of the Poisson bracket and a Hamiltonian H(Z). The guiding-center description of particle motion was presented by Littlejohn. The ponderomotive drift and force, the wave-induced oscillation-center velocity, and the gyrofrequency shift are obtained. The Lie transform yields the wave-induced increment to the gyromomentum. In the coulomb model for a Vlasov system, the dynamical variable is the Vlasov distribution f(z). The Hamiltonian functional and the Poisson bracket are obtained. The coupling of f(z) to the Maxwell field appears in the Poisson bracket. The evolution equation yields the Vlasov-Maxwell system. (Kato, T.)
Hamiltonian boundary term and quasilocal energy flux
International Nuclear Information System (INIS)
Chen, C.-M.; Nester, James M.; Tung, R.-S.
2005-01-01
The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasilocal values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found four particular quasilocal energy-momentum boundary term expressions; each corresponds to a physically distinct and geometrically clear boundary condition. Here, from a consideration of the asymptotics, we show how a fundamental Hamiltonian identity naturally leads to the associated quasilocal energy flux expressions. For electromagnetism one of the four is distinguished: the only one which is gauge invariant; it gives the familiar energy density and Poynting flux. For Einstein's general relativity two different boundary condition choices correspond to quasilocal expressions which asymptotically give the ADM energy, the Trautman-Bondi energy and, moreover, an associated energy flux (both outgoing and incoming). Again there is a distinguished expression: the one which is covariant
Direct measurement of α_Q_E_D(m_Z"2) at the FCC-ee
International Nuclear Information System (INIS)
Janot, Patrick
2016-01-01
When the measurements from the FCC-ee become available, an improved determination of the standard-model “input' parameters will be needed to fully exploit the new precision data towards either constraining or fitting the parameters of beyond-the-standard-model theories. Among these input parameters is the electromagnetic coupling constant estimated at the Z mass scale, α_Q_E_D(m_Z"2). The measurement of the muon forward-backward asymmetry at the FCC-ee, just below and just above the Z pole, can be used to make a direct determination of α_Q_E_D(m_Z"2) with an accuracy deemed adequate for an optimal use of the FCC-ee precision data.
Prats, J. M.; Lopez-Aguilar, F.
1996-01-01
Using unitary transformations, we express the Kondo lattice Hamiltonian in terms of fermionic operators that annihilate the ground state of the interacting system and that represent the best possible approximations to the actual charged excitations. In this way, we obtain an effective Hamiltonian which, for small couplings, consists in a kinetic term for conduction electrons and holes, an RKKY-like term, and a renormalized Kondo interaction. The physical picture of the system implied by this ...
Dissecting the intensely star-forming clumps in a z ~ 2 Einstein Ring
Rujopakarn, Wiphu
2013-10-01
Clumps of star formation spreading widely in galactic disks are common features of star-forming galaxies at 1 test cases to study the mechanism that drives intense star formation at z ~ 2. We propose WFC3 near-IR imaging and spatially-resolved spectroscopy of a gravitationally lensed, kinematically ordered, vigorously star-forming galaxy at z = 1.885 with physical resolutions up to 40 pc. This galaxy contains two luminous clumps that are forming stars at the rates of 100 solar mass/yr/clump. Spatially-resolved map of star formation from HST provides the most critical missing piece to interpret our existing observations of this galaxy in far-IR, CO emission lines, and radio continuum. We will probe the frontier research areas in z ~ 2 star formation, particularly the spatially-resolved star formation laws and dynamics of cold and ionized gases, which have never been probed at this spatial resolution. Our proposed observations will provide a benchmark against which to interpret the structures of vigorous star-forming clumps in general. This object can therefore have a unique impact on our understanding of the star-forming modes that dominate at z ~ 2.
Weinberg-Salam theory based on a Z2-graded algebra
International Nuclear Information System (INIS)
Iizuka, Jugoro; Morita, Katsusada; Kase, Hiromi; Okumura, Yositaka; Tanaka-Yamawaki, Mieko.
1994-01-01
Generalized differential calculus on discrete space M 4 xZ 2 which is an underlying space-time in the non-commutative geometry for the standard model is reformulated in terms of a Z 2 -graded algebra, even and odd elements of which being pairs of complex matrices defined over Minkowski space-time with different properties of product and involution. It is shown that the Z 2 -grading is equivalent to that of Coquereaux et al. if the pair is represented by 2x2 matrices, although our formalism has closer contact with the differential calculus on the discrete space. A graded differential algebra is then defined, in which the exterior derivative with respect to the pair is assumed to determine the pattern of symmetry breaking of the theory. On the basis of it the Weinberg-Salam theory in both bosonic and fermionic sectors is constructed. It is pointed out that, in contrast to usual assertion in non-commutative geometry, the Weinberg angle and the Higgs mass in the tree level are not fixed separately but related through m H = 2√2εm W sinθ W . Connes' prescription of constructing gauge-invariant Lagrangian, which is based on the assumption that there arise only logarithmic divergences from one-loop diagrams, corresponds to the case ε = 1. In principle, however, the parameter ε is arbitrary due to possible presence of Sitarz' linear term so that noncommutative geometry alone says nothing about the Higgs mass. (author)
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.
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.
Ostrogradski Hamiltonian approach for geodetic brane gravity
International Nuclear Information System (INIS)
Cordero, Ruben; Molgado, Alberto; Rojas, Efrain
2010-01-01
We present an alternative Hamiltonian description of a branelike universe immersed in a flat background spacetime. This model is named geodetic brane gravity. We set up the Regge-Teitelboim model to describe our Universe where such field theory is originally thought as a second order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. This approach comprize the manage of both first- and second-class constraints and the counting of degrees of freedom follows accordingly.
A Dirac-Kaehler approach to the two dimensional Wess-Zumino N=2 model on the lattice
International Nuclear Information System (INIS)
Zimerman, A.H.; Aratyn, H.
1983-08-01
We introduce a Dirac-Kaehler model for the two dimensional Wess-Zumino N=2 Lagrangean. We can show that in the model, when we go to the euclidean space-time lattive, we have no energy doubling, the action has no lattice surface terms (contrary to other authors), while the Hamiltonians (when time is continuous) present lattice surface terms. (orig.)
Does a Single Eigenstate Encode the Full Hamiltonian?
Garrison, James R.; Grover, Tarun
2018-04-01
The eigenstate thermalization hypothesis (ETH) posits that the reduced density matrix for a subsystem corresponding to an excited eigenstate is "thermal." Here we expound on this hypothesis by asking: For which class of operators, local or nonlocal, is ETH satisfied? We show that this question is directly related to a seemingly unrelated question: Is the Hamiltonian of a system encoded within a single eigenstate? We formulate a strong form of ETH where, in the thermodynamic limit, the reduced density matrix of a subsystem corresponding to a pure, finite energy density eigenstate asymptotically becomes equal to the thermal reduced density matrix, as long as the subsystem size is much less than the total system size, irrespective of how large the subsystem is compared to any intrinsic length scale of the system. This allows one to access the properties of the underlying Hamiltonian at arbitrary energy densities (or temperatures) using just a single eigenstate. We provide support for our conjecture by performing an exact diagonalization study of a nonintegrable 1D quantum lattice model with only energy conservation. In addition, we examine the case in which the subsystem size is a finite fraction of the total system size, and we find that, even in this case, many operators continue to match their canonical expectation values, at least approximately. In particular, the von Neumann entanglement entropy equals the thermal entropy as long as the subsystem is less than half the total system. Our results are consistent with the possibility that a single eigenstate correctly predicts the expectation values of all operators with support on less than half the total system, as long as one uses a microcanonical ensemble with vanishing energy width for comparison. We also study, both analytically and numerically, a particle-number conserving model at infinite temperature that substantiates our conjectures.
LATTICE: an interactive lattice computer code
International Nuclear Information System (INIS)
Staples, J.
1976-10-01
LATTICE is a computer code which enables an interactive user to calculate the functions of a synchrotron lattice. This program satisfies the requirements at LBL for a simple interactive lattice program by borrowing ideas from both TRANSPORT and SYNCH. A fitting routine is included
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.
Optimal control of Rydberg lattice gases
DEFF Research Database (Denmark)
Cui, Jian; Bijnen, Rick van; Pohl, Thomas
2017-01-01
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.......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...
Adaptive control of port-Hamiltonian systems
Dirksz, D.A.; Scherpen, J.M.A.; Edelmayer, András
2010-01-01
In this paper an adaptive control scheme is presented for general port-Hamiltonian systems. Adaptive control is used to compensate for control errors that are caused by unknown or uncertain parameter values of a system. The adaptive control is also combined with canonical transformation theory for
Iterated Hamiltonian type systems and applications
Tiba, Dan
2018-04-01
We discuss, in arbitrary dimension, certain Hamiltonian type systems and prove existence, uniqueness and regularity properties, under the independence condition. We also investigate the critical case, define a class of generalized solutions and prove existence and basic properties. Relevant examples and counterexamples are also indicated. The applications concern representations of implicitly defined manifolds and their perturbations, motivated by differential systems involving unknown geometries.
Symmetry and resonance in Hamiltonian systems
Tuwankotta, J.M.; Verhulst, F.
2000-01-01
In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After giving a sharp estimate of the resonance domain, we
Symmetry and resonance in Hamiltonian systems
Tuwankotta, J.M.; Verhulst, F.
1999-01-01
In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After determining the size of the resonance domain, we
Discrete variable representation for singular Hamiltonians
DEFF Research Database (Denmark)
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...
The hamiltonian structures of the KP hierarchy
International Nuclear Information System (INIS)
Das, A.; Panda, S.; Huang Wenjui
1991-01-01
We obtain the two hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra. (orig.)
Hamiltonian structure for rescaled integrable Lorenz systems
International Nuclear Information System (INIS)
Haas, F.; Goedert, J.
1993-01-01
It is shown that three among the known invariants for the Lorenz system recast the original equations into a Hamiltonian form. This is made possible by an appropriate time-dependent rescaling and the use of a generalized formalism with non-trivial structure functions. (author)
Singularities of Poisson structures and Hamiltonian bifurcations
Meer, van der J.C.
2010-01-01
Consider a Poisson structure on C8(R3,R) with bracket {, } and suppose that C is a Casimir function. Then {f, g} =<¿C, (¿g x ¿f) > is a possible Poisson structure. This confirms earlier observations concerning the Poisson structure for Hamiltonian systems that are reduced to a one degree of freedom
Transparency in port-Hamiltonian based telemanipulation
Secchi, C; Stramigioli, Stefano; Fantuzzi, C.
2005-01-01
After stability, transparency is the major issue in the design of a telemanipulation system. In this paper we exploit a 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
Transparency in Port-Hamiltonian-Based Telemanipulation
Secchi, Cristian; Stramigioli, Stefano; Fantuzzi, Cesare
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
Equivalence of Lagrangian and Hamiltonian BRST quantizations
International Nuclear Information System (INIS)
Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.
1992-01-01
Two approaches to the quantization of gauge theories using BRST symmetry are widely used nowadays: the Lagrangian quantization, developed in (BV-quantization) and Hamiltonian quantization, formulated in (BFV-quantization). For all known examples of field theory (Yang-Mills theory, gravitation etc.) both schemes give equivalent results. However the equivalence of these approaches in general wasn't proved. The main obstacle in comparing of these formulations consists in the fact, that in Hamiltonian approach the number of ghost fields is equal to the number of all first-class constraints, while in the Lagrangian approach the number of ghosts is equal to the number of independent gauge symmetries, which is equal to the number of primary first-class constraints only. This paper is devoted to the proof of the equivalence of Lagrangian and Hamiltonian quantizations for the systems with first-class constraints only. This is achieved by a choice of special gauge in the Hamiltonian approach. It's shown, that after integration over redundant variables on the functional integral we come to effective action which is constructed according to rules for construction of the effective action in Lagrangian quantization scheme
Hamiltonian formulation of anomaly free chiral bosons
International Nuclear Information System (INIS)
Abdalla, E.; Abdalla, M.C.B.; Devecchi, F.P.; Zadra, A.
1988-01-01
Starting out of an anomaly free Lagrangian formulation for chiral scalars, which a Wess-Zumino Term (to cancel the anomaly), we formulate the corresponding hamiltonian problem. Ther we use the (quantum) Siegel invariance to choose a particular, which turns out coincide with the obtained by Floreanini and Jackiw. (author) [pt
Hamiltonian structure of gravitational field theory
International Nuclear Information System (INIS)
Rayski, J.
1992-01-01
Hamiltonian generalizations of Einstein's theory of gravitation introducing a laminar structure of spacetime are discussed. The concepts of general relativity and of quasi-inertial coordinate systems are extended beyond their traditional scope. Not only the metric, but also the coordinate system, if quantized, undergoes quantum fluctuations
Port-Hamiltonian Systems on Open Graphs
Schaft, A.J. van der; Maschke, B.M.
2010-01-01
In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac
Gauge theories of infinite dimensional Hamiltonian superalgebras
International Nuclear Information System (INIS)
Sezgin, E.
1989-05-01
Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs
The Hamiltonian structures of the KP hierarchy
International Nuclear Information System (INIS)
Das, A.; Panda, S.; Huang Wenjui
1991-08-01
We obtain the two Hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra. (author). 18 refs
Quasi exact solution of the Rabi Hamiltonian
Koç, R; Tuetuencueler, H
2002-01-01
A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.
Edge-disjoint Hamiltonian cycles in hypertournaments
DEFF Research Database (Denmark)
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...
Near integrability of kink lattice with higher order interactions
Jiang, Yun-Guo; Liu, Jia-Zhen; He, Song
2017-11-01
We make use of Manton’s analytical method to investigate the force between kinks and anti-kinks at large distances in 1+1 dimensional field theory. The related potential has infinite order corrections of exponential pattern, and the coefficients for each order are determined. These coefficients can also be obtained by solving the equation of the fluctuations 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 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 is a near integrable system. We make use of Flaschka’s variables to study the Lax pair of the kink lattice. These Flaschka’s variables have interesting algebraic relations and non-integrability can be manifested. We also discuss the higher Hamiltonians for the deformed open Toda lattice, which has a similar result to the ordinary deformed Toda. Supported by Shandong Provincial Natural Science Foundation (ZR2014AQ007), National Natural Science Foundation of China (11403015, U1531105), S. He is supported by Max-Planck fellowship in Germany and National Natural Science Foundation of China (11305235)
Hamiltonian constraint in polymer parametrized field theory
International Nuclear Information System (INIS)
Laddha, Alok; Varadarajan, Madhavan
2011-01-01
Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.
The group of Hamiltonian automorphisms of a star product
La Fuente-Gravy, Laurent
2015-01-01
We deform the group of Hamiltonian diffeomorphisms into the group of Hamiltonian automorphisms of a formal star product on a symplectic manifold. We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
QCD string with quarks. 2. Light cone Hamiltonian
International Nuclear Information System (INIS)
Dubin, A.Yu.; Kaidalov, A.B.; Simonov, Yu.A.
1994-01-01
The light-cone Hamiltonian is derived from the general gauge - and Lorentz - invariant expression for the qq-bar Green function. The resulting Hamiltonian contains in a non-additive way contributions from quark and string degrees of freedom
Competing bosonic condensates in optical lattice with a mixture of single and pair hoppings
Energy Technology Data Exchange (ETDEWEB)
Travin, V.M., E-mail: v.travin@int.pan.wroc.pl; Kopeć, T.K., E-mail: t.kopec@int.pan.wroc.pl
2017-01-15
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.
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...
Hamiltonian analysis of transverse dynamics in axisymmetric rf photoinjectors
International Nuclear Information System (INIS)
Wang, C.-x.
2006-01-01
A general Hamiltonian that governs the beam dynamics in an rf photoinjector is derived from first principles. With proper choice of coordinates, the resulting Hamiltonian has a simple and familiar form, while taking into account the rapid acceleration, rf focusing, magnetic focusing, and space-charge forces. From the linear Hamiltonian, beam-envelope evolution is readily obtained, which better illuminates the theory of emittance compensation. Preliminary results on the third-order nonlinear Hamiltonian will be given as well.
On integrable Hamiltonians for higher spin XXZ chain
International Nuclear Information System (INIS)
Bytsko, Andrei G.
2003-01-01
Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to (3/2) are given. Relations between Hamiltonians for some U q (sl 2 )-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable U q (sl 2 )-symmetric Hamiltonian for an open chain
Finite-lattice form factors in free-fermion models
International Nuclear Information System (INIS)
Iorgov, N; Lisovyy, O
2011-01-01
We consider the general Z 2 -symmetric free-fermion model on the finite periodic lattice, which includes as special cases the Ising model on the square and triangular lattices and the Z n -symmetric BBS τ (2) -model with n = 2. Translating Kaufman's fermionic approach to diagonalization of Ising-like transfer matrices into the language of Grassmann integrals, we determine the transfer matrix eigenvectors and observe that they coincide with the eigenvectors of a square lattice Ising transfer matrix. This allows us to find exact finite-lattice form factors of spin operators for the statistical model and the associated finite-length quantum chains, of which the most general is equivalent to the XY chain in a transverse field
Quantum thetas on noncommutative T4 from embeddings into lattice
International Nuclear Information System (INIS)
Chang-Young, Ee; Kim, Hoil
2007-01-01
In this paper, we investigate the theta vector and quantum theta function over noncommutative T 4 from the embedding of RxZ 2 . Manin has constructed the quantum theta functions from the lattice embedding into vector space (x finite group). We extend Manin's construction of the quantum theta function to the embedding of vector space x lattice case. We find that the holomorphic theta vector exists only over the vector space part of the embedding, and over the lattice part we can only impose the condition for the Schwartz function. The quantum theta function built on this partial theta vector satisfies the requirement of the quantum theta function. However, two subsequent quantum translations from the embedding into the lattice part are nonadditive, contrary to the additivity of those from the vector space part
Flavor S4xZ2 symmetry and neutrino mixing
International Nuclear Information System (INIS)
Zhang He
2007-01-01
We present a model of the lepton masses and flavor mixing based on the discrete group S 4 xZ 2 . In this model, all the charged leptons and neutrinos are assigned to the 3 - b arα representation of S 4 in the Yamanouchi bases. The charged lepton and neutrino masses are mainly determined by the vacuum expectation value structures of the Higgs fields. A nearly tri-bimaximal lepton flavor mixing pattern, which is in agreement with the current experimental results, can be accommodated in our model. The neutrino mass spectrum takes the nearly degenerate pattern, and thus can be well tested in the future precise experiments
International Nuclear Information System (INIS)
Sanpera, A.; Lewenstein, M.; Kantian, A.; Sanchez-Palencia, L.; Zakrzewski, J.
2004-01-01
We investigate strongly interacting atomic Fermi-Bose mixtures in inhomogeneous and random optical lattices. We derive an effective Hamiltonian for the system and discuss its low temperature physics. We demonstrate the possibility of controlling the interactions at local level in inhomogeneous but regular lattices. Such a control leads to the achievement of Fermi glass, quantum Fermi spin-glass, and quantum percolation regimes involving bare and/or composite fermions in random lattices
Numerical determination of the magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Kuo-Petravic, G.; Boozer, A.H.
1986-03-01
The structure of a magnetic field is determined by a one-degree of freedom, time-dependent Hamiltonian. This Hamiltonian is evaluated for a given field in a perturbed action-angle form. The location and the size of magnetic islands in the given field are determined from Hamiltonian perturbation theory and from an ordinary Poincare plot of the field line trajectories
Effective Hamiltonians in quantum physics: resonances and geometric phase
International Nuclear Information System (INIS)
Rau, A R P; Uskov, D
2006-01-01
Effective Hamiltonians are often used in quantum physics, both in time-dependent and time-independent contexts. Analogies are drawn between the two usages, the discussion framed particularly for the geometric phase of a time-dependent Hamiltonian and for resonances as stationary states of a time-independent Hamiltonian
International Nuclear Information System (INIS)
Mack, G.
1982-01-01
After a description of a pure Yang-Mills theory on a lattice, the author considers a three-dimensional pure U(1) lattice gauge theory. Thereafter he discusses the exact relation between lattice gauge theories with the gauge groups SU(2) and SO(3). Finally he presents Monte Carlo data on phase transitions in SU(2) and SO(3) lattice gauge models. (HSI)
Hamiltonian quantization of self-dual tensor fields and a bosonic Nielsen-Ninomiya theorem
International Nuclear Information System (INIS)
Tang Waikeung
1989-01-01
The quantization of self-dual tensor fields is carried out following the procedure of Batalin and Fradkin. The (anti) self-duality constraints (either fermionic or bosonic) in the action leads to the gravitational anomaly. In the process of gauge fixing, the impossibility of the co-existence of a positive hamiltonian and covariant action is shown. A version of the Nielsen-Ninomiya theorem applies to self-dual tensor fields viz. the lattice version of the theory shows species doubling with zero net chirality. (orig.)
Dynamical Aperture Control in Accelerator Lattices With Multipole Potentials
Morozov, I
2017-01-01
We develop tools for symbolic representation of a non-linear accelerator model and analytical methods for description of non-linear dynamics. Information relevant to the dynamic aperture (DA) is then obtained from this model and can be used for indirect DA control or as a complement to direct numerical optimization. We apply two analytical methods and use multipole magnets to satisfy derived analytical constraints. The accelerator model is represented as a product of unperturbed and perturbed exponential operators with the exponent of the perturbed operator given as a power series in the perturbation parameter. Normal forms can be applied to this representation and the lattice parameters are used to control the normal form Hamiltonian and normal form transformation. Hamiltonian control is used to compute a control term or controlled operator. Lattice parameters are then fitted to satisfy the imposed control constraints. Theoretical results, as well as illustrative examples, are presented.
Supersymmetric quantum mechanics approach to a nonlinear lattice
International Nuclear Information System (INIS)
Ricotta, Regina Maria; Drigo Filho, Elso
2011-01-01
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)
Lattices with unique complements
Saliĭ, V N
1988-01-01
The class of uniquely complemented lattices properly contains all Boolean lattices. However, no explicit example of a non-Boolean lattice of this class has been found. In addition, the question of whether this class contains any complete non-Boolean lattices remains unanswered. This book focuses on these classical problems of lattice theory and the various attempts to solve them. Requiring no specialized knowledge, the book is directed at researchers and students interested in general algebra and mathematical logic.
Seifert, Richard; Hung, Chao-Ling; Casey, Caitlin M.; Chiang, Yi-Kuan
2018-01-01
A galaxy’s evolution is affected by its environment. Today, we see quiescent elliptical galaxies preferentially in the high-density environments of galaxy clusters, while star-forming galaxies are found only in lower density environments. However, this trend is less clear at z > 2, with some works arguing for a possible reversal of star formation with environmental density. While star formation is quenched in the cores of today's galaxy clusters, their progenitors likely had ongoing star formation in line with cosmic downsizing. In order to better understand when and how the cores of galaxy protoclusters formed their stars, We search for a dependence between environment and gas content in galaxy protoclusters at z > 2. To do this, we utilize the 2deg^2 COSMOS survey and SCUBA2 850 micron maps of the COSMOS field to trace galaxy gas content and environment. We conduct a stacking analysis with the code SIMSTACK to aide in our search for a relationship between environment and gas content.
Deep Ly alpha imaging of two z=2.04 GRB host galaxy fields
DEFF Research Database (Denmark)
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...... - I colour than the eastern component, suggesting the presence of at least some dust. We do not detect the host galaxy of GRB 000301C in neither Lyalpha emission nor in U and I broad-band images. The strongest limit comes from combining the narrow and U-band imaging where we infer a limit of U...
Mixtures of bosonic and fermionic atoms in optical lattices
International Nuclear Information System (INIS)
Albus, Alexander; Illuminati, Fabrizio; Eisert, Jens
2003-01-01
We discuss the theory of mixtures of bosonic and fermionic atoms in periodic potentials at zero temperature. We derive a general Bose-Fermi Hubbard Hamiltonian in a one-dimensional optical lattice with a superimposed harmonic trapping potential. We study the conditions for linear stability of the mixture and derive a mean-field criterion for the onset of a bosonic superfluid transition. We investigate the ground-state properties of the mixture in the Gutzwiller formulation of mean-field theory, and present numerical studies of finite systems. The bosonic and fermionic density distributions and the onset of quantum phase transitions to demixing and to a bosonic Mott-insulator are studied as a function of the lattice potential strength. The existence is predicted of a disordered phase for mixtures loaded in very deep lattices. Such a disordered phase possessing many degenerate or quasidegenerate ground states is related to a breaking of the mirror symmetry in the lattice
Designing lattice structures with maximal nearest-neighbor entanglement
Energy Technology Data Exchange (ETDEWEB)
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.
Rest-Frame Optical Spectra of Three Strongly Lensed Galaxies at z ~ 2
Hainline, Kevin N.; Shapley, Alice E.; Kornei, Katherine A.; Pettini, Max; Buckley-Geer, Elizabeth; Allam, Sahar S.; Tucker, Douglas L.
2009-08-01
We present Keck II NIRSPEC rest-frame optical spectra for three recently discovered lensed galaxies: the Cosmic Horseshoe (z = 2.38), the Clone (z = 2.00), and SDSS J090122.37+181432.3 (z = 2.26). The boost in signal-to-noise ratio (S/N) from gravitational lensing provides an unusually detailed view of the physical conditions in these objects. A full complement of high S/N rest-frame optical emission lines is measured, spanning from rest frame 3600 to 6800 Å, including robust detections of fainter lines such as Hγ, [S II]λ6717,6732, and in one instance [Ne III]λ3869. SDSS J090122.37+181432.3 shows evidence for active galactic nucleus activity, and therefore we focus our analysis on star-forming regions in the Cosmic Horseshoe and the Clone. For these two objects, we estimate a wide range of physical properties. Current lensing models for the Cosmic Horseshoe and the Clone allow us to correct the measured Hα luminosity and calculated star formation rate. Metallicities have been estimated with a variety of indicators, which span a range of values of 12+ log(O/H) = 8.3-8.8, between ~0.4 and ~1.5 of the solar oxygen abundance. Dynamical masses were computed from the Hα velocity dispersions and measured half-light radii of the reconstructed sources. A comparison of the Balmer lines enabled measurement of dust reddening coefficients. Variations in the line ratios between the different lensed images are also observed, indicating that the spectra are probing different regions of the lensed galaxies. In all respects, the lensed objects appear fairly typical of ultraviolet-selected star-forming galaxies at z ~ 2. The Clone occupies a position on the emission-line diagnostic diagram of [O III]/Hβ versus [N II]/Hα that is offset from the locations of z ~ 0 galaxies. Our new NIRSPEC measurements may provide quantitative insights into why high-redshift objects display such properties. From the [S II] line ratio, high electron densities (~1000 cm-3) are inferred compared
Analytic operator approach to fermionic lattice field theories
International Nuclear Information System (INIS)
Duncan, A.
1985-01-01
An analytic Lanczos algorithm previously used to extract the spectrum of bosonic lattice field theories in the continuum region is extended to theories with fermions. The method is illustrated in detail for the (1+1)-dimensional Gross-Neveu model. All parameters in the model (coupling, lattice size N, number of fermion flavors Nsub(F), etc.) appear explicitly in analytic formulas for matrix elements of the hamiltonian. The method is applied to the calculation of the collective field vacuum expectation value and the mass gap, and excellent agreement obtained with explicit results available from the large Nsub(F) solution of the model. (orig.)
Hamiltonian truncation approach to quenches in the Ising field theory
Directory of Open Access Journals (Sweden)
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.
Combinatorial quantization of the Hamiltonian Chern-Simons theory
International Nuclear Information System (INIS)
Alekseev, A.Yu.; Grosse, H.; Schomerus, V.
1996-01-01
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observables A CS of the Chern Simons model. It is a *-algebra of ''functions on the quantum moduli space of flat connections'' and comes equipped with a positive functional ω (''integration''). We prove that this data does not depend on the particular choices which have been made in the construction. The algebra A CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group. (orig.). With 1 fig
Coherent states of systems with quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica
2015-06-15
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)
Coherent states of systems with quadratic Hamiltonians
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.
2015-01-01
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)
Effective Hamiltonian for high Tc Cu oxides
International Nuclear Information System (INIS)
Fukuyama, H.; Matsukawa, H.
1989-01-01
Effective Hamiltonian has been derived for CuO 2 layers in the presence of extra holes doped mainly into O-sites by taking both on-site and intersite Coulomb interaction into account. A special case with a single hole has been examined in detail. It is found that there exist various types of bound states, singlet and triplet with different spatial symmetry, below the hole bank continuum. The spatial extent of the Zhang-Rice singlet state, which is most stabilized, and the effective transfer integral between these singlet states are seen to be very sensitive to the relative magnitude of the direct and the indirect transfer integrals between O-sites. Effective Hamiltonian for the case of electron doping has also been derived
Partial quantization of Lagrangian-Hamiltonian systems
International Nuclear Information System (INIS)
Amaral, C.M. do; Soares Filho, P.C.
1979-05-01
A classical variational principle is constructed in the Weiss form, for dynamical systems with support spaces of the configuration-phase kind. This extended principle rules the dynamics of classical systems, partially Hamiltonian, in interaction with Lagrangean parameterized subsidiary dynamics. The variational family of equations obtained, consists of an equation of the Hamilton-Jacobi type, coupled to a family of differential equations of the Euler-Lagrange form. The basic dynamical function appearing in the equations is a function of the Routh kind. By means of an ansatz induced by the variationally obtained family, a generalized set of equation, is proposed constituted by a wave equation of Schroedinger type, coupled to a family of equations formaly analog to those Euler-Lagrange equations. A basic operator of Routh type appears in our generalized set of equations. This operator describes the interaction between a quantized Hamiltonian dynamics, with a parameterized classical Lagrangean dynamics in semi-classical closed models. (author) [pt
Quadratic hamiltonians and relativistic quantum mechanics
International Nuclear Information System (INIS)
Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.
1981-01-01
For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru
Hamiltonian mechanics and divergence-free fields
International Nuclear Information System (INIS)
Boozer, A.H.
1986-08-01
The field lines, or integral curves, of a divergence-free field in three dimensions are shown to be topologically equivalent to the trajectories of a Hamiltonian with two degrees of freedom. The consideration of fields that depend on a parameter allow the construction of a canonical perturbation theory which is valid even if the perturbation is large. If the parametric dependence of the magnetic, or the vorticity field is interpreted as time dependence, evolution equations are obtained which give Kelvin's theorem or the flux conservation theorem for ideal fluids and plasmas. The Hamiltonian methods prove especially useful for study of fields in which the field lines must be known throughout a volume of space
Quantum mechanical Hamiltonian models of discrete processes
International Nuclear Information System (INIS)
Benioff, P.
1981-01-01
Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement
Hamiltonian reduction of Kac-Moody algebras
International Nuclear Information System (INIS)
Kimura, Kazuhiro
1991-01-01
Feigin-Fucks construction provides us methods to treat rational conformal theories in terms of free fields. This formulation enables us to describe partition functions and correlation functions in the Fock space of free fields. There are several attempt extending to supersymmetric theories. In this report authors present an explicit calculation of the Hamiltonian reduction based on the free field realization. In spite of the results being well-known, the relations can be clearly understood in the language of bosons. Authors perform the hamiltonian reduction by imposing a constraint with appropriate gauge transformations which preserve the constraint. This approaches enables us to gives the geometric interpretation of super Virasoro algebras and relations of the super gravity. In addition, author discuss the properties of quantum groups by using the explicit form of the group element. It is also interesting to extend to super Kac-Moody algebras. (M.N.)
Phase transitions in the Hubbard Hamiltonian
International Nuclear Information System (INIS)
Chaves, C.M.; Lederer, P.; Gomes, A.A.
1977-05-01
Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques is studied, using the epsilon = 4 - d expansion to first order in epsilon. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. This coupling is pure imaginary, which has interesting consequences on the critical properties of this coupled field system. The effect of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also 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.
Bogoliubov transformations and fermion condensates in lattice field theories
International Nuclear Information System (INIS)
Caracciolo, Sergio; Palumbo, Fabrizio; Viola, Giovanni
2009-01-01
We apply generalized Bogoliubov transformations to the transfer matrix of relativistic field theories regularized on a lattice. We derive the conditions these transformations must satisfy to factorize the transfer matrix into two terms which propagate fermions and antifermions separately, and we solve the relative equations under some conditions. We relate these equations to the saddle point approximation of a recent bosonization method and to the Foldy-Wouthuysen transformations which separate positive from negative energy states in the Dirac Hamiltonian
Hadron mass spectrum in a lattice gauge theory
International Nuclear Information System (INIS)
Seo, Koichi
1978-01-01
We perform the strong coupling expansion in a lattice gauge theory and obtain the hadron mass spectrum. We develop a theory in the Hamiltonian formalism following Kogut and Susskind, but our treatment of quark fields is quite different from theirs. Thus our results largely differ from theirs. In our model and approximation, the pseudoscalar mesons have the same mass as the vectors. The baryon decuplet and the octet are also degenerate. The excited meson states are studied in detail. (auth.)
A diagrammatic construction of formal E-independent model hamiltonian
International Nuclear Information System (INIS)
Kvasnicka, V.
1977-01-01
A diagrammatic construction of formal E-independent model interaction (i.e., without second-quantization formalism) is suggested. The construction starts from the quasi-degenerate Brillouin-Wigner perturbation theory, in the framework of which an E-dependent model Hamiltonian is simply constructed. Applying the ''E-removing'' procedure to this E-dependent model Hamiltonian, the E-independent formal model Hamiltonian either Hermitian or non-Hermitian can diagrammatically be easily derived. For the formal E-independent model Hamiltonian the separability theorem is proved, which can be profitably used for a rather ''formalistic ''construction of a many-body E-independent model Hamiltonian
Boson mapping and the microscopic collective nuclear Hamiltonian
International Nuclear Information System (INIS)
Dobes, J.; Ivanova, S.P.; Dzholos, R.V.; Pedrosa, R.
1990-01-01
Starting with the mapping of the quadrupole collective states in the fermion space onto the boson space, the fermion nuclear problem is transformed into the boson one. The boson images of the bifermion operators and of the fermion Hamiltonian are found. Recurrence relations are used to obtain approximately the norm matrix which appears in the boson-fermion mapping. The resulting boson Hamiltonian contains terms which go beyond the ordinary SU(6) symmetry Hamiltonian of the interacting boson model. Calculations, however, suggest that on the phenomenological level the differences between the mapped Hamiltonian and the SU(6) Hamiltonian are not too important. 18 refs.; 2 figs
Recursive tridiagonalization of infinite dimensional Hamiltonians
International Nuclear Information System (INIS)
Haydock, R.; Oregon Univ., Eugene, OR
1989-01-01
Infinite dimensional, computable, sparse Hamiltonians can be numerically tridiagonalized to finite precision using a three term recursion. Only the finite number of components whose relative magnitude is greater than the desired precision are stored at any stage in the computation. Thus the particular components stored change as the calculation progresses. This technique avoids errors due to truncation of the orbital set, and makes terminators unnecessary in the recursion method. (orig.)
Hamiltonian theory of guiding-center motion
International Nuclear Information System (INIS)
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
Hamiltonian kinetic theory of plasma ponderomotive processes
International Nuclear Information System (INIS)
McDonald, S.W.; Kaufman, A.N.
1982-01-01
The nonlinear nonresonant interaction of plasma waves and particles is formulated in Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility
Symplectic Geometric Algorithms for Hamiltonian Systems
Feng, Kang
2010-01-01
"Symplectic Geometry Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development
Dynamical invariants for variable quadratic Hamiltonians
International Nuclear Information System (INIS)
Suslov, Sergei K
2010-01-01
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.
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.
Quantization of non-Hamiltonian physical systems
International Nuclear Information System (INIS)
Bolivar, A.O.
1998-09-01
We propose a general method of quantization of non-Hamiltonian physical systems. Applying it, for example, to a dissipative system coupled to a thermal reservoir described by the Fokker-Planck equation, we are able to obtain the Caldeira-Leggett master equation, the non-linear Schroedinger-Langevin equation and Caldirola-Kanai equation (with an additional term), as particular cases. (author)
Hamiltonian kinetic theory of plasma ponderomotive processes
International Nuclear Information System (INIS)
McDonald, S.W.; Kaufman, A.N.
1981-12-01
The nonlinear nonresonant interaction of plasma waves and particles is formulated in a Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility
Symplectic topology of integrable Hamiltonian systems
International Nuclear Information System (INIS)
Nguyen Tien Zung.
1993-08-01
We study the topology of integrable Hamiltonian systems, giving the main attention to the affine structure of their orbit spaces. In particular, we develop some aspects of Fomenko's theory about topological classification of integrable non-degenerate systems, and consider some relations between such systems and ''pure'' contact and symplectic geometry. We give a notion of integrable surgery and use it to obtain some interesting symplectic structures. (author). Refs, 10 figs
Hamiltonian description and quantization of dissipative systems
Enz, Charles P.
1994-09-01
Dissipative systems are described by a Hamiltonian, combined with a “dynamical matrix” which generalizes the simplectic form of the equations of motion. Criteria for dissipation are given and the examples of a particle with friction and of the Lotka-Volterra model are presented. Quantization is first introduced by translating generalized Poisson brackets into commutators and anticommutators. Then a generalized Schrödinger equation expressed by a dynamical matrix is constructed and discussed.
Hamiltonian theory of guiding-center motion
Energy Technology Data Exchange (ETDEWEB)
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.
Hamiltonian description of the ideal fluid
International Nuclear Information System (INIS)
Morrison, P.J.
1998-01-01
The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom Hamiltonian dynamics are reviewed, in the context of the passive advection of a scalar or tracer field by a fluid. The notions of integrability, invariant-tori, chaos, overlap criteria, and invariant-tori breakup are described in this context. Preparatory to the introduction of field theories, systems with an infinite number of degrees of freedom, elements of functional calculus and action principles of mechanics are reviewed. The action principle for the ideal compressible fluid is described in terms of Lagrangian or material variables. Hamiltonian systems in terms of noncanonical variables are presented, including several examples of Eulerian or inviscid fluid dynamics. Lie group theory sufficient for the treatment of reduction is reviewed. The reduction from Lagrangian to Eulerian variables is treated along with Clebsch variable decompositions. Stability in the canonical and noncanonical Hamiltonian contexts is described. Sufficient conditions for stability, such as Rayleigh-like criteria, are seen to be only sufficient in the general case because of the existence of negative-energy modes, which are possessed by interesting fluid equilibria. Linearly stable equilibria with negative energy modes are argued to be unstable when nonlinearity or dissipation is added. The energy-Casimir method is discussed and a variant of it that depends upon the notion of dynamical accessibility is described. The energy content of a perturbation about a general fluid equilibrium is calculated using three methods. copyright 1998 The American Physical Society
Large-scale stochasticity in Hamiltonian systems
International Nuclear Information System (INIS)
Escande, D.F.
1982-01-01
Large scale stochasticity (L.S.S.) in Hamiltonian systems is defined on the paradigm Hamiltonian H(v,x,t) =v 2 /2-M cos x-P cos k(x-t) which describes the motion of one particle in two electrostatic waves. A renormalization transformation Tsub(r) is described which acts as a microscope that focusses on a given KAM (Kolmogorov-Arnold-Moser) torus in phase space. Though approximate, Tsub(r) yields the threshold of L.S.S. in H with an error of 5-10%. The universal behaviour of KAM tori is predicted: for instance the scale invariance of KAM tori and the critical exponent of the Lyapunov exponent of Cantori. The Fourier expansion of KAM tori is computed and several conjectures by L. Kadanoff and S. Shenker are proved. Chirikov's standard mapping for stochastic layers is derived in a simpler way and the width of the layers is computed. A simpler renormalization scheme for these layers is defined. A Mathieu equation for describing the stability of a discrete family of cycles is derived. When combined with Tsub(r), it allows to prove the link between KAM tori and nearby cycles, conjectured by J. Greene and, in particular, to compute the mean residue of a torus. The fractal diagrams defined by G. Schmidt are computed. A sketch of a methodology for computing the L.S.S. threshold in any two-degree-of-freedom Hamiltonian system is given. (Auth.)
NLO renormalization in the Hamiltonian truncation
Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.
2017-09-01
Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.
Redesign of the DFT/MRCI Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M., E-mail: Christel.Marian@hhu.de [Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf (Germany)
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.
The properties of Hα emission-line galaxies at z = 2.24
International Nuclear Information System (INIS)
An, Fang Xia; Zheng, Xian Zhong; Wang, Wei-Hao; Huang, Jia-Sheng; Kong, Xu; Wang, Jun-Xian; Zhu, Feifan; Fang, Guan Wen; Gu, Qiu-Sheng; Wu, Hong; Hao, Lei; Xia, Xiao-Yang
2014-01-01
Using deep narrowband H 2 S1 and K s -band imaging data obtained with CFHT/WIRCam, we identify a sample of 56 Hα emission-line galaxies (ELGs) at z = 2.24 with the 5σ depths of H 2 S1 = 22.8 and K s = 24.8 (AB) over a 383 arcmin 2 area in the Extended Chandra Deep Field South. A detailed analysis is carried out with existing multi-wavelength data in this field. Three of the 56 Hα ELGs are detected in Chandra 4 Ms X-ray observations and two of them are classified as active galactic nuclei. The rest-frame UV and optical morphologies revealed by HST/ACS and WFC3 deep images show that nearly half of the Hα ELGs are either merging systems or have 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 from spectral energy distributions. We find that dust extinction is generally correlated with Hα luminosity and stellar mass. Our results suggest that Hα ELGs are representative of star-forming galaxies. Applying extinction corrections to individual objects, we examine the intrinsic Hα luminosity function (LF) at z = 2.24, obtaining a best-fit Schechter function characterized by a faint-end slope of α = – 1.3. This is shallower than the typical slope of α ≅ –1.6 in previous works based on constant extinction correction. We demonstrate that this difference is mainly due to the different extinction corrections. The proper extinction correction is thus the key to recovering the intrinsic LF as the extinction globally increases with Hα luminosity. Moreover, we find that our Hα LF mirrors the stellar mass function of star-forming galaxies at the same cosmic epoch. This finding indeed reflects the tight correlation between star formation rate and stellar mass for star-forming galaxies, i.e., the so-called main sequence.
Cluster-Bethe-Lattice study of a planar antiferromagnet: Rb2NiF4
International Nuclear Information System (INIS)
Cruz, G.A.C. de la; Silva, C.E.T.G. da
1979-01-01
A discussion of the Cluster-Bethe-Lattice method is presented for a planar antiferromagnet for which the hamiltonian parameters are known and the one-magnon density of states may be computed exactly. All the square clusters of 1 to 121 atoms are studied both connected to and isolated from the Bethe lattices. It is shown that, even for the largest cluster treated, the approximation is still far from the exact result. It is discussed the limitations of the method [pt
International Nuclear Information System (INIS)
Gerdt, Vladimir P.; Severyanov, Vasily M.
2006-01-01
A C package is presented that allows a user for an input quantum circuit to generate a set of multivariate polynomials over the finite field Z 2 whose total number of solutions in Z 2 determines the output of the quantum computation defined by the circuit. The generated polynomial system can further be converted to the canonical Grobner basis form which provides a universal algorithmic tool for counting the number of common roots of the polynomials
The Chloroplast Division Protein ARC6 Acts to Inhibit Disassembly of GDP-bound FtsZ2.
Sung, Min Woo; Shaik, Rahamthulla; TerBush, Allan D; Osteryoung, Katherine W; Vitha, Stanislav; Holzenburg, Andreas
2018-05-16
Chloroplasts host photosynthesis and fulfill other metabolic functions that are essential to plant life. They have to divide by binary fission to maintain their numbers throughout cycles of cell division. Chloroplast division is achieved by a complex ring-shaped division machinery located on both the inner (stromal) and the outer (cytosolic) side of the chloroplast envelope. The inner division ring (termed the Z ring) is formed by the assembly of tubulin-like FtsZ1 and FtsZ2 proteins. ARC6 is a key chloroplast division protein that interacts with the Z ring. ARC6 spans the inner envelope membrane, is known to stabilize or maintain the Z ring, and anchors the Z ring to the inner membrane through interaction with FtsZ2. The underlying mechanism of Z-ring stabilization is not well understood. Here, biochemical and structural characterization of ARC6 was conducted using light scattering, sedimentation, and light and transmission electron microscopy. The recombinant protein was purified as a dimer. The results indicated that a truncated form of ARC6 (tARC6), representing the stromal portion of ARC6, affects FtsZ2 assembly without forming higher-order structures, and exerts its effect via FtsZ2 dynamics. tARC6 prevented GDP-induced FtsZ2 disassembly and caused a significant net increase in FtsZ2 assembly when GDP was present. Single particle analysis and 3D reconstruction were performed to elucidate the structural basis of ARC6 activity. Together, the data reveal that a dimeric form of tARC6 binds to FtsZ2 filaments and does not increase FtsZ polymerization rates but rather inhibits GDP-associated FtsZ2 disassembly. Published under license by The American Society for Biochemistry and Molecular Biology, Inc.
Lattice gauge theory approach to quantum chromodynamics
International Nuclear Information System (INIS)
Kogut, J.B.
1983-01-01
The author reviews in a pedagogical fashion some of the recent developments in lattice quantum chromodynamics. This review emphasizes explicit examples and illustrations rather than general proofs and analyses. It begins with a discussion of the heavy-quark potential in continuum quantum chromodynamics. Asymptotic freedom and renormalization-group improved perturbation theory are discussed. A simple dielectric model of confinement is considered as an intuitive guide to the vacuum of non-Abelian gauge theories. Next, the Euclidean form of lattice gauge theory is introduced, and an assortment of calculational methods are reviewed. These include high-temperature expansions, duality, Monte Carlo computer simulations, and weak coupling expansions. A #betta#-parameter calculation for asymptotically free-spin models is presented. The Hamiltonian formulation of lattice gauge theory is presented and is illustrated in the context of flux tube dynamics. Roughening transitions, Casimir forces, and the restoration of rotational symmetry are discussed. Mechanisms of confinement in lattice theories are illustrated in the two-dimensional electrodynamics of the planar model and the U(1) gauge theory in four dimensions. Generalized actions for SU(2) gauge theories and the relevance of monopoles and strings to crossover phenomena are considered. A brief discussion of the continuity of fields and topologial charge in asymptotically free lattice models is presented. The final major topic of this review concerns lattice fermions. The species doubling problem and its relation to chiral symmetry are illustrated. Staggered Euclidean fermion methods are discussed in detail, with an emphasis on species counting, remnants of chiral symmetry, Block spin variables, and the axial anomaly. Numerical methods for including fermions in computer simulations are considered. Jacobi and Gauss-Siedel inversion methods to obtain the fermion propagator in a background gauge field are reviewed
Deep absorption line studies of quiescent galaxies at z similar z ~ 2
DEFF Research Database (Denmark)
Toft, Sune; Gallazzi, Anna Rita; Zirm, Andrew Wasmuth
2012-01-01
the majority of its stars at z > 3 and currently has little or no ongoing star formation. We compile a sample of three other z similar to 2 quiescent galaxies with measured velocity dispersions, two of which are also post-starburst like. Their dynamical-mass-size relation is offset significantly less than...... the stellar-mass-size relation from the local early-type relations, which we attribute to a lower central dark matter fraction. Recent cosmological merger simulations agree qualitatively with the data, but cannot fully account for the evolution in the dark matter fraction. The z similar to 2 FP requires......We present dynamical and structural scaling relations of quiescent galaxies at z = 2, including the dynamical-mass-size relation and the first constraints on the fundamental plane (FP). The backbone of the analysis is a new, very deep Very Large Telescope/X-shooter spectrum of a massive, compact...
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.
Top-quark loop corrections in Z+jet and Z + 2 jet production
Energy Technology Data Exchange (ETDEWEB)
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.
Logarithmic two-point correlation functions from a z=2 Lifshitz model
International Nuclear Information System (INIS)
Zingg, T.
2014-01-01
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 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
The soft supersymmetry breaking in D=5 supergravity compactified on S_1/Z_2 orbifolds
Diamandis, G A; Kouroumalou, P; Lahanas, A B
2010-01-01
We study the origin of the supersymmetry breaking induced by the mediation of gravity and the radion multiplet from the hidden to the visible brane in the context of the N=2, D=5 supergravity compactified on S_1/Z_2 orbifolds. The soft supersymmetry breaking terms for scalar masses, trilinear scalar couplings and gaugino masses are calculated to leading order in the five dimensional Newton's constant k_5^2 and the gravitino mass m_{3/2}. These are finite and non-vanishing, with the scalar soft masses be non-tachyonic, and are all expressed in terms of the gravitino mass and the length scale R of the fifth dimension. The soft supersymmetry breaking parameters are thus correlated and the phenomenological implications are discussed.
VizieR Online Data Catalog: CANDELS z~2 galaxy properties (Trump+, 2014)
Trump, J. R.; Barro, G.; Juneau, S.; Weiner, B. J.; Luo, B.; Brammer, G. B.; Bell, E. F.; Brandt, W. N.; Dekel, A.; Guo, Y.; Hopkins, P. F.; Koo, D. C.; Kocevski, D. D.; McIntosh, D. H.; Momcheva, I.; Faber, S. M.; Ferguson, H. C.; Grogin, N. A.; Kartaltepe, J.; Koekemoer, A. M.; Lotz, J.; Maseda, M.; Mozena, M.; Nandra, K.; Rosario, D. J.; Zeimann, G. R.
2017-04-01
We select a sample of 44 clumpy galaxies from the Great Observatories Origins Deep Survey South (GOODS-S; Giavalisco et al. 2004ApJ...600L..93G) region of CANDELS. For comparison, we also construct mass-matched samples of 41 smooth (non-clumpy) and 35 intermediate galaxies. All galaxies have H<24 (to ensure reliable classification of clumpiness) and have [O III] detected at the 3σ level (for reliable AGN line ratio diagnostics) in the redshift range 1.3<z<2.4. Each morphology category has a median redshift of z=1.85. Redshifts and emission line measurements come from HST/WFC3 grism spectroscopy taken by the 3D-HST survey (Brammer et al. 2012ApJS..200...13B). (1 data file).
METAL DEFICIENCY IN CLUSTER STAR-FORMING GALAXIES AT Z = 2
Energy Technology Data Exchange (ETDEWEB)
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.
Adhesive pad differentiation in Drosophila melanogaster depends on the Polycomb group gene Su(z)2.
Hüsken, Mirko; Hufnagel, Kim; Mende, Katharina; Appel, Esther; Meyer, Heiko; Peisker, Henrik; Tögel, Markus; Wang, Shuoshuo; Wolff, Jonas; Gorb, Stanislav N; Paululat, Achim
2015-04-15
The ability of many insects to walk on vertical smooth surfaces such as glass or even on the ceiling has fascinated biologists for a long time, and has led to the discovery of highly specialized adhesive organs located at the distal end of the animals' legs. So far, research has primarily focused on structural and ultrastructural investigations leading to a deeper understanding of adhesive organ functionality and to the development of new bioinspired materials. Genetic approaches, e.g. the analysis of mutants, to achieve a better understanding of adhesive organ differentiation have not been used so far. Here, we describe the first Drosophila melanogaster mutant that develops malformed adhesive organs, resulting in a complete loss of climbing ability on vertical smooth surfaces. Interestingly, these mutants fail to make close contact between the setal tips and the smooth surface, a crucial condition for wet adhesion mediated by capillary forces. Instead, these flies walk solely on their claws. Moreover, we were able to show that the mutation is caused by a P-element insertion into the Su(z)2 gene locus. Remobilization of the P-element restores climbing ability. Furthermore, we provide evidence that the P-element insertion results in an artificial Su(z)2 transcript, which most likely causes a gain-of-function mutation. We presume that this transcript causes deregulation of yet unknown target genes involved in pulvilli differentiation. Our results nicely demonstrate that the genetically treatable model organism Drosophila is highly suitable for future investigations on adhesive organ differentiation. © 2015. Published by The Company of Biologists Ltd.
International Nuclear Information System (INIS)
Shen, Z.; Allen, J.W.; Yeh, J.J.
1987-01-01
We describe valence-band and core-level photoemission data for copper oxide superconductors using the Anderson Hamiltonian applied to an impurity-cluster configuration-interaction model. We obtain experimental values of the parameters of the model the copper X oxygen charge transfer energy Δ∼0.4 eV, the d-d Coulomb interaction U∼6 eV, and the ligand-d hybridization T∼2.4 eV. Using these parameters, we evaluate the linear Cu-O-Cu superexchange interaction J and find it is dominated by the charge-transfer fluctuations. The magnitude obtained for J is much larger than typical Neel temperatures of these materials, and is somewhat larger than that estimated from applying the resonating-valence-bond picture to La 2 CuO 4 . We point out that for Δ >Δ, the charge-transfer degrees of freedom, and the lattice aspects of the Anderson lattice Hamiltonian, should not be neglected in constructing models for the high-T/sub c/ superconductivity. We also emphasize our resonant-photoemission result that the very small density of states at or near the Fermi level in all these materials has a substantial contribution from Cu 3d states, suggesting their importance for the superconductivity. We report other details of the resonant-photoemission data involving La and Ba states in the materials containing these elements
Solitary heat waves in nonlinear lattices with squared on-site potential
Indian Academy of Sciences (India)
A model Hamiltonian is proposed for heat conduction in a nonlinear lattice with squared on-site potential using the second quantized operators and averaging the same using a suitable wave function, equations are derived in discrete form for the field amplitude and the properties of heat transfer are examined theoretically.
Solitary heat waves in nonlinear lattices with squared on-site potential
Indian Academy of Sciences (India)
Abstract. A model Hamiltonian is proposed for heat conduction in a nonlinear lattice with squared on-site potential using the second quantized operators and averaging the same using a suitable wave function, equations are derived in discrete form for the field amplitude and the prop- erties of heat transfer are examined ...
Towards a coupled-cluster treatment of SU(N) lattice gauge field theory
Bishop, Raymond F.; Ligterink, N.E.; Walet, Niels R.
2006-01-01
A consistent approach to Hamiltonian SU(N) lattice gauge field theory is developed using the maximal-tree gauge and an appropriately chosen set of angular variables. The various constraints are carefully discussed, as is a practical means for their implementation. A complete set of variables for the
Quantum Hamiltonian reduction and conformal field theories
International Nuclear Information System (INIS)
Bershadsky, M.
1991-01-01
It is proved that irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of the SL (2, R) current algebra by putting a constraint on the latter using the BRST formalism. Thus there is a SL(2, R) symmetry in the Virasoro algebra which is gauged and hidden. This construction of the Virasoro algebra is the quantum analog of the Hamiltonian reduction. The author then naturally leads to consider an SL(2, R) Wess-Zumino-Witten model. This system is related to the quantum field theory of the coadjoint orbit of the Virasoro group. Based on this result he presents the canonical derivation of the SL(2, R) current algebra in Polyakov's theory of two dimensional gravity; it is manifestation of the SL(2, R) symmetry in the conformal field theory hidden by the quantum Hamiltonian reduction. He discusses the quantum Hamiltonian reduction of the SL(n, R) current algebra for the general type of constraints labeled by index 1 ≤ l ≤ (n - 1) and claim that it leads to the new extended conformal algebras W n l . For l = 1 he recovers the well known W n algebra introduced by A. Zamolodchikov. For SL(3, R) Wess-Zumino-Witten model there are two different possibilities of constraining it. The first possibility gives the W 3 algebra, while the second leads to the new chiral algebra W 3 2 generated by the stress-energy tensor, two bosonic supercurrents with spins 3/2 and the U(1) current. He conjectures a Kac formula that describes the highly reducible representation for this algebra. He also makes some speculations concerning the structure of W gravity
Lagrangian and Hamiltonian structures in an integrable hierarchy and space–time duality
International Nuclear Information System (INIS)
Avan, Jean; Caudrelier, Vincent; Doikou, Anastasia; Kundu, Anjan
2016-01-01
We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonlinear Schrödinger (NLS) hierarchy. For each integrable nonlinear evolution equation (NLEE) in the hierarchy, dual integrable structures are characterized by the fact that the zero-curvature representation of the NLEE can be realized by two Hamiltonian formulations stemming from two distinct choices of the configuration space, yielding two inequivalent Poisson structures on the corresponding phase space and two distinct Hamiltonians. This is fundamentally different from the standard bi-Hamiltonian or generally multitime structure. The first formulation chooses purely space-dependent fields as configuration space; it yields the standard Poisson structure for NLS. The other one is new: it chooses purely time-dependent fields as configuration space and yields a different Poisson structure at each level of the hierarchy. The corresponding NLEE becomes a space evolution equation. We emphasize the role of the Lagrangian formulation as a unifying framework for deriving both Poisson structures, using ideas from covariant field theory. One of our main results is to show that the two matrices of the Lax pair satisfy the same form of ultralocal Poisson algebra (up to a sign) characterized by an r-matrix structure, whereas traditionally only one of them is involved in the classical r-matrix method. We construct explicit dual hierarchies of Hamiltonians, and Lax representations of the triggered dynamics, from the monodromy matrices of either Lax matrix. An appealing procedure to build a multi-dimensional lattice of Lax pair, through successive uses of the dual Poisson structures, is briefly introduced.
Lagrangian and Hamiltonian structures in an integrable hierarchy and space–time duality
Energy Technology Data Exchange (ETDEWEB)
Avan, Jean, E-mail: Jean.Avan@u-cergy.fr [Laboratoire de Physique Théorique et Modélisation (CNRS UMR 8089), Université de Cergy-Pontoise, F-95302 Cergy-Pontoise (France); Caudrelier, Vincent, E-mail: v.caudrelier@city.ac.uk [Department of Mathematics, City University London, Northampton Square, EC1V 0HB London (United Kingdom); Doikou, Anastasia, E-mail: A.Doikou@hw.ac.uk [Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh (United Kingdom); Kundu, Anjan, E-mail: Anjan.Kundu@saha.ac.in [Saha Institute of Nuclear Physics, Theory Division, Kolkata (India)
2016-01-15
We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonlinear Schrödinger (NLS) hierarchy. For each integrable nonlinear evolution equation (NLEE) in the hierarchy, dual integrable structures are characterized by the fact that the zero-curvature representation of the NLEE can be realized by two Hamiltonian formulations stemming from two distinct choices of the configuration space, yielding two inequivalent Poisson structures on the corresponding phase space and two distinct Hamiltonians. This is fundamentally different from the standard bi-Hamiltonian or generally multitime structure. The first formulation chooses purely space-dependent fields as configuration space; it yields the standard Poisson structure for NLS. The other one is new: it chooses purely time-dependent fields as configuration space and yields a different Poisson structure at each level of the hierarchy. The corresponding NLEE becomes a space evolution equation. We emphasize the role of the Lagrangian formulation as a unifying framework for deriving both Poisson structures, using ideas from covariant field theory. One of our main results is to show that the two matrices of the Lax pair satisfy the same form of ultralocal Poisson algebra (up to a sign) characterized by an r-matrix structure, whereas traditionally only one of them is involved in the classical r-matrix method. We construct explicit dual hierarchies of Hamiltonians, and Lax representations of the triggered dynamics, from the monodromy matrices of either Lax matrix. An appealing procedure to build a multi-dimensional lattice of Lax pair, through successive uses of the dual Poisson structures, is briefly introduced.
Integrable Time-Dependent Quantum Hamiltonians
Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen
2018-05-01
We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.
Discrete variable representation for singular Hamiltonians
DEFF Research Database (Denmark)
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...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...
Resonant driving of a nonlinear Hamiltonian system
International Nuclear Information System (INIS)
Palmisano, Carlo; Gervino, Gianpiero; Balma, Massimo; Devona, Dorina; Wimberger, Sandro
2013-01-01
As a proof of principle, we show how a classical nonlinear Hamiltonian system can be driven resonantly over reasonably long times by appropriately shaped pulses. To keep the parameter space reasonably small, we limit ourselves to a driving force which consists of periodic pulses additionally modulated by a sinusoidal function. The main observables are the average increase of kinetic energy and of the action variable (of the non-driven system) with time. Applications of our scheme aim for driving high frequencies of a nonlinear system with a fixed modulation signal.
Nonabelian N=2 superstrings: Hamiltonian structure
International Nuclear Information System (INIS)
Isaev, A.P.; Ivanov, E.A.
1991-04-01
We examine the Hamiltonian structure of nonabelian N=2 superstring models which are the supergroup manifold extensions of N=2 Green-Schwarz superstring. We find the Kac-Moody and Virasoro type superalgebras of the relevant constraints and present elements of the corresponding quantum theory. A comparison with the type IIA Green-Schwarz superstring moving in a general curved 10-d supergravity background is also given. We find that nonabelian superstrings (for d=10) present a particular case of this general system corresponding to a special choice of the background. (author). 22 refs
Effective Hamiltonians for phosphorene and silicene
DEFF Research Database (Denmark)
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.......For phosphorene, it is shown that the bands near the Brillouin zone center only have terms ineven powers of the wave vector. We predict that the energies change quadratically in the presence of aperpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to thosefor silicene...
Hamiltonian Description of Convective-cell Generation
International Nuclear Information System (INIS)
Krommes, J.A.; Kolesnikov, R.A.
2004-01-01
The nonlinear statistical growth rate eq for convective cells driven by drift-wave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates eq to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic ion-temperature-gradient-driven modes at small ion temperature, and (ii) weakly electromagnetic collisional DW's are noted
Eigenfunctions of quadratic hamiltonians in Wigner representation
International Nuclear Information System (INIS)
Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.
1984-01-01
Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail
Action-minimizing methods in Hamiltonian dynamics
Sorrentino, Alfonso
2015-01-01
John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach-known as Aubry-Mather theory-singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as a
A new perturbative treatment of pentadiagonal Hamiltonians
International Nuclear Information System (INIS)
Znojil, M.
1987-01-01
A new formulation of the Rayleich - Schroedinger perturbation theory is proposed. It is inspired by a recurent construction of propagators, and its main idea lies in a replacement of the auxiliary matrix elements (generalized continued fractions) by their non-numerical approximants. In a test of convergence (the anharmonic oscillator), the asymptotic fixed-point approximation scheme is used. The results indicate a good applicability of this fixed-point version of our formalism to systems with a band-matrix structure of the Hamiltonian
The coupled cluster theory of quantum lattice systems
International Nuclear Information System (INIS)
Bishop, R.; Xian, Yang
1994-01-01
The coupled cluster method is widely recognized nowadays as providing an ab initio method of great versatility, power, and accuracy for handling in a fully microscopic and systematic way the correlations between particles in quantum many-body systems. The number of successful applications made to date within both chemistry and physics is impressive. In this article, the authors review recent extensions of the method which now provide a unifying framework for also dealing with strongly interacting infinite quantum lattice systems described by a Hamiltonian. Such systems include both spin-lattice models (such as the anisotropic Heisenberg or XXZ model) exhibiting interesting magnetic properties, and electron lattice models (such as the tJ and Hubbard models), where the spins or fermions are localized on the sites of a regular lattice; as well as lattice gauge theories [such as the Abelian U(1) model of quantum electrodynamics and non-Abelian SU(n) models]. Illustrative results are given for both the XXZ spin lattice model and U(1) lattice gauge theory
Effective hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Avramenko, V.I.; Blokhin, A.L.
1989-01-01
Within the microscopic version of the unitary collective model with the horizontal mixing the effective Hamiltonian for 18 O and 18 Ne nuclei is constructed. The algebraic structure of the Hamiltonian is compared to the familiar phenomenological ones with the SU(3)-mixing terms which describe the coupled rotational and vibrational spectra. The Hamiltonian, including central nuclear and Coulomb interaction, is diagonalized on the basis of three SU(3) irreducible representations with two orbital symmetries. 32 refs.; 2 figs.; 4 tabs
A Hamiltonian functional for the linearized Einstein vacuum field equations
International Nuclear Information System (INIS)
Rosas-RodrIguez, R
2005-01-01
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained
Introduction to thermodynamics of spin models in the Hamiltonian limit
Energy Technology Data Exchange (ETDEWEB)
Berche, Bertrand [Groupe M, Laboratoire de Physique des Materiaux, UMR CNRS No 7556, Universite Henri Poincare, Nancy 1, BP 239, F-54506 Vandoeuvre les Nancy, (France); Lopez, Alexander [Instituto Venezolano de Investigaciones CientIficas, Centro de Fisica, Carr. Panamericana, km 11, Altos de Pipe, Aptdo 21827, 1020-A Caracas, (Venezuela)
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. The targeted students are those of a graduate statistical physics course.
Hamiltonian structure of the Lotka-Volterra equations
Nutku, Y.
1990-03-01
The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.
Hamiltonian structures of some non-linear evolution equations
International Nuclear Information System (INIS)
Tu, G.Z.
1983-06-01
The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)
Anderson localization in bipartite lattices
International Nuclear Information System (INIS)
Fabrizio, Michele; Castellani, Claudio
2000-01-01
We study the localization properties of a disordered tight-binding Hamiltonian on a generic bipartite lattice close to the band center. By means of a fermionic replica trick method, we derive the effective non-linear σ-model describing the diffusive modes, which we analyse by using the Wilson-Polyakov renormalization group. In addition to the standard parameters which define the non-linear σ-model, namely, the conductance and the external frequency, a new parameter enters, which may be related to the fluctuations of the staggered density of states. We find that, when both the regular hopping and the disorder only couple one sublattice to the other, the quantum corrections to the Kubo conductivity vanish at the band center, thus implying the existence of delocalized states. In two dimensions, the RG equations predict that the conductance flows to a finite value, while both the density of states and the staggered density of states fluctuations diverge. In three dimensions, we find that, sufficiently close to the band center, all states are extended, independently of the disorder strength. We also discuss the role of various symmetry breaking terms, as a regular hopping between same sublattices, or an on-site disorder
Anderson localization in bipartite lattices
International Nuclear Information System (INIS)
Fabrizio, M.; Castellani, C.
2000-04-01
We study the localization properties of a disordered tight-binding Hamiltonian on a generic bipartite lattice close to the band center. By means of a fermionic replica trick method, we derive the effective non-linear σ-model describing the diffusive modes, which we analyse by using the Wilson-Polyakov renormalization group. In addition to the standard parameters which define the non-linear σ-model, namely the conductance and the external frequency, a new parameter enters, which may be related to the fluctuations of the staggered density of states. We find that, when both the regular hopping and the disorder only couple one sublattice to the other, the quantum corrections to the Kubo conductivity vanish at the band center, thus implying the existence of delocalized states. In two dimensions, the RG equations predict that the conductance flows to a finite value, while both the density of states and the staggered density of states fluctuations diverge. In three dimensions, we find that, sufficiently close to the band center, all states are extended, independently of the disorder strength. We also discuss the role of various symmetry breaking terms, as a regular hopping between same sublattices, or an on-site disorder. (author)
Geometry and Hamiltonian mechanics on discrete spaces
International Nuclear Information System (INIS)
Talasila, V; Clemente-Gallardo, J; Schaft, A J van der
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed
Thermalization Time Bounds for Pauli Stabilizer Hamiltonians
Temme, Kristan
2017-03-01
We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of N-qubits, serve as one of the most frequently considered candidates for a self-correcting quantum memory. A spectral gap bound on the Davies generator establishes an upper limit on the life time of such a quantum memory and can be used to estimate the time until the system relaxes to thermal equilibrium when brought into contact with a thermal heat bath. The bound can be shown to behave as {λ ≥ O(N^{-1} exp(-2β overline{ɛ}))}, where {overline{ɛ}} is a generalization of the well known energy barrier for logical operators. Particularly in the low temperature regime we expect this bound to provide the correct asymptotic scaling of the gap with the system size up to a factor of N -1. Furthermore, we discuss conditions and provide scenarios where this factor can be removed and a constant lower bound can be proven.
Normal form for mirror machine Hamiltonians
International Nuclear Information System (INIS)
Dragt, A.J.; Finn, J.M.
1979-01-01
A systematic algorithm is developed for performing canonical transformations on Hamiltonians which govern particle motion in magnetic mirror machines. These transformations are performed in such a way that the new Hamiltonian has a particularly simple normal form. From this form it is possible to compute analytic expressions for gyro and bounce frequencies. In addition, it is possible to obtain arbitrarily high order terms in the adiabatic magnetic moment expansion. The algorithm makes use of Lie series, is an extension of Birkhoff's normal form method, and has been explicitly implemented by a digital computer programmed to perform the required algebraic manipulations. Application is made to particle motion in a magnetic dipole field and to a simple mirror system. Bounce frequencies and locations of periodic orbits are obtained and compared with numerical computations. Both mirror systems are shown to be insoluble, i.e., trajectories are not confined to analytic hypersurfaces, there is no analytic third integral of motion, and the adiabatic magnetic moment expansion is divergent. It is expected also that the normal form procedure will prove useful in the study of island structure and separatrices associated with periodic orbits, and should facilitate studies of breakdown of adiabaticity and the onset of ''stochastic'' behavior
Nonextensive formalism and continuous Hamiltonian systems
International Nuclear Information System (INIS)
Boon, Jean Pierre; Lutsko, James F.
2011-01-01
A recurring question in nonequilibrium statistical mechanics is what deviation from standard statistical mechanics gives rise to non-Boltzmann behavior and to nonlinear response, which amounts to identifying the emergence of 'statistics from dynamics' in systems out of equilibrium. Among several possible analytical developments which have been proposed, the idea of nonextensive statistics introduced by Tsallis about 20 years ago was to develop a statistical mechanical theory for systems out of equilibrium where the Boltzmann distribution no longer holds, and to generalize the Boltzmann entropy by a more general function S q while maintaining the formalism of thermodynamics. From a phenomenological viewpoint, nonextensive statistics appeared to be of interest because maximization of the generalized entropy S q yields the q-exponential distribution which has been successfully used to describe distributions observed in a large class of phenomena, in particular power law distributions for q>1. Here we re-examine the validity of the nonextensive formalism for continuous Hamiltonian systems. In particular we consider the q-ideal gas, a model system of quasi-particles where the effect of the interactions are included in the particle properties. On the basis of exact results for the q-ideal gas, we find that the theory is restricted to the range q<1, which raises the question of its formal validity range for continuous Hamiltonian systems.
Hamiltonian Anomalies from Extended Field Theories
Monnier, Samuel
2015-09-01
We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.
Effective Hamiltonians for phosphorene and silicene
International Nuclear Information System (INIS)
Lew Yan Voon, L C; Lopez-Bezanilla, A; Wang, J; Zhang, Y; Willatzen, M
2015-01-01
We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (New J. 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 expression for band warping is obtained analytically and found to be of different order than for graphene. We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, it is shown that the bands near the Brillouin zone center only have terms in even powers of the wave vector. We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k⋅p parameters. (paper)
Phase space eigenfunctions of multidimensional quadratic Hamiltonians
International Nuclear Information System (INIS)
Dodonov, V.V.; Man'ko, V.I.
1986-01-01
We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)
Diffeomorphism invariance in the Hamiltonian formulation of General Relativity
International Nuclear Information System (INIS)
Kiriushcheva, N.; Kuzmin, S.V.; Racknor, C.; Valluri, S.R.
2008-01-01
It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The first-class constraints of such a Hamiltonian formulation, with the metric tensor taken as a canonical variable, allow one to derive the generator of gauge transformations, which directly leads to diffeomorphism invariance. The given Hamiltonian formulation preserves general covariance of the transformations derivable from it. This characteristic should be used as the crucial consistency requirement that must be met by any Hamiltonian formulation of General Relativity
Matchings Extend to Hamiltonian Cycles in 5-Cube
Directory of Open Access Journals (Sweden)
Wang Fan
2018-02-01
Full Text Available Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Qn for n ∈ {2, 3, 4}. In this paper, we prove that every matching in Q5 can be extended to a Hamiltonian cycle of Q5.
Squeezed states from a quantum deformed oscillator Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Ramírez, R. [IFLP, CONICET–Department of Mathematics, University of La Plata c.c. 67 1900, La Plata (Argentina); Reboiro, M., E-mail: marta.reboiro@gmail.com [IFLP, CONICET–Department of Physics, University of La Plata c.c. 67 1900, La Plata (Argentina)
2016-03-11
The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions. - Highlights: • A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra. • It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian. • It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state. • The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.
Spectral and resonance properties of the Smilansky Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Exner, Pavel [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Břehová 7, 11519 Prague (Czech Republic); Lotoreichik, Vladimir [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Tater, Miloš, E-mail: tater@ujf.cas.cz [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic)
2017-02-26
We analyze the Hamiltonian proposed by Smilansky to describe irreversible dynamics in quantum graphs and studied further by Solomyak and others. We derive a weak-coupling asymptotics of the ground state and add new insights by finding the discrete spectrum numerically in the subcritical case. Furthermore, we show that the model then has a rich resonance structure. - Highlights: • We derive conditions on bound states and on resonances of the Smilansky Hamiltonian. • Using these conditions we find numerically discrete spectrum and resonances of this Hamiltonian. • Our numerical tests confirm known properties of the Hamiltonian and allow us to conjecture new ones.
A Hamiltonian approach to model and analyse networks of ...
Indian Academy of Sciences (India)
2015-09-24
Sep 24, 2015 ... Gyroscopes; energy harvesters; synchronization; Hamiltonian mechanics. ... ideas and methods from nonlinear dynamics system theory, in particular, ... deploy highly sensitive, lowpower, magnetic and electric field sensors.
Generalized isothermic lattices
International Nuclear Information System (INIS)
Doliwa, Adam
2007-01-01
We study multi-dimensional quadrilateral lattices satisfying simultaneously two integrable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Moebius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constraint imposed on the (complex) cross-ratio of the circular lattice. We derive the analogous condition for our generalized isothermic lattices using Steiner's projective structure of conics, and we present basic geometric constructions which encode integrability of the lattice. In particular, we introduce the Darboux transformation of the generalized isothermic lattice and we derive the corresponding Bianchi permutability principle. Finally, we study two-dimensional generalized isothermic lattices, in particular geometry of their initial boundary value problem
A CONSISTENT STUDY OF METALLICITY EVOLUTION AT 0.8 < z < 2.6
Energy Technology Data Exchange (ETDEWEB)
Wuyts, Eva; Kurk, Jaron; Förster Schreiber, Natascha M.; Genzel, Reinhard; Wisnioski, Emily; Bandara, Kaushala; Wuyts, Stijn; Beifiori, Alessandra; Bender, Ralf; Buschkamp, Peter; Chan, Jeffrey; Davies, Ric; Eisenhauer, Frank; Fossati, Matteo; Kulkarni, Sandesh K.; Lang, Philipp [Max-Planck-Institut für extraterrestrische Physik, Giessenbachstr. 1, D-85741 Garching (Germany); Brammer, Gabriel B. [Space Telescope Science Institute, Baltimore, MD 21218 (United States); Burkert, Andreas [Universitäts-Sternwarte München, Scheinerstr. 1, D-81679 München (Germany); Carollo, C. Marcella; Lilly, Simon J., E-mail: evawuyts@mpe.mpg.de [Institute of Astronomy, Department of Physics, Eidgensösische Technische Hochschule, ETH Zürich, CH-8093 (Switzerland); and others
2014-07-10
We present the correlations between stellar mass, star formation rate (SFR), and the [N II]/Hα flux ratio as an indicator of gas-phase metallicity for a sample of 222 galaxies at 0.8 < z < 2.6 and log (M {sub *}/M {sub ☉}) = 9.0-11.5 from the LUCI, SINS/zC-SINF, and KMOS{sup 3D} surveys. This sample provides a unique analysis of the mass-metallicity relation (MZR) over an extended redshift range using consistent data analysis techniques and a uniform strong-line metallicity indicator. We find a constant slope at the low-mass end of the relation and can fully describe its redshift evolution through the evolution of the characteristic turnover mass where the relation begins to flatten at the asymptotic metallicity. At a fixed mass and redshift, our data do not show a correlation between the [N II]/Hα ratio and SFR, which disagrees with the 0.2-0.3 dex offset in [N II]/Hα predicted by the ''fundamental relation'' between stellar mass, SFR, and metallicity discussed in recent literature. However, the overall evolution toward lower [N II]/Hα at earlier times does broadly agree with these predictions.
What kind of galaxies dominate the cosmic SFR density at z~2?
Perez-Gonzalez, P. G.; Rieke, George; Gonzalez, Anthony; Gallego, Jesus; Guzman, Rafael; Pello, Roser; Egami, Eiichi; Marcillac, D.; Pascual, S.
2006-08-01
We propose to obtain near-infrared (JHK-bands) spectroscopy with GEM-S+GNIRS for a sample of 12 galaxies representative of the 3 types of spitzer/MIPS 24 micron detections at 2.0≲z≲2.6: power-law galaxies, star-forming galaxies with prominent 1.6 micron bumps, and Distant Red Galaxies. These sources are located in the Chandra Deep Field South, a unique field for the study of galaxy evolution, given the top quality data available at all wavelengths. Our main goal is to characterize the mid-IR selected galaxy population at this epoch by measuring H(alpha), H(beta), [NII], and [OIII] fluxes and profiles, and combining these observations with the already merged x-ray, ultraviolet, optical, near- and mid-infrared imaging data, to obtain the most reliable estimations of the SFRs, metallicities, stellar and dynamical masses, AGN activity, and extinction properties of the luminous infrared galaxies detected by MIPS, which dominate the SFR density of the Universe at z≳2. Our targets are complementary to others selected in the rest-frame UV/optical at high-z, and they extend the H(alpha) observations of galaxies selected with ISO from z~1 to z~2.6. The work proposed here will help to interpret the results obtained by the spitzer surveys at z≳2, thus substantially improving our understanding of the formation of massive galaxies and their connection to AGN.
POLARIZED EXTENDED Ly{alpha} EMISSION FROM A z = 2.3 RADIO GALAXY
Energy Technology Data Exchange (ETDEWEB)
Humphrey, A. [Centro de Astrofisica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto (Portugal); Vernet, J.; Fosbury, R. A. E. [European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching (Germany); Villar-Martin, M. [Centro de Astrobiologia (INTA-CSIC), Carretera de Ajalvir, km 4, E-28850 Torrejon de Ardoz, Madrid (Spain); Di Serego Alighieri, S. [INAF-Osservatorio Astrofisico di Arcetri, L.go E. Fermi 5, I-50125 Firenze (Italy); Cimatti, A., E-mail: andrew.humphrey@astro.up.pt [Dipartimento di Astronomia, Universita di Bologna, Via Ranzani 1, I-40127 Bologna (Italy)
2013-05-01
We present spatially resolved spectropolarimetric measurements of the 100 kpc scale gaseous environment of the z = 2.34 radio galaxy TXS 0211-122. The polarization level of the narrow Ly{alpha} emission is low centrally (P < 5%), but rises to P = 16.4% {+-} 4.6% in the eastern part of the nebula, indicating that the nebula is at least partly powered by the scattering of Ly{alpha} photons by H I. Not only is this the first detection of polarized Ly{alpha} around a radio-loud active galaxy, it is also the second detection to date for any kind of Ly{alpha} nebula. We also detect a pair of diametrically opposed UV continuum sources along the slit, at the outer edges of the Ly{alpha} nebula, which we suggest may be the limb of a dusty shell, related to the large-scale H I absorbers often associated with high-z radio galaxies.
A CONSISTENT STUDY OF METALLICITY EVOLUTION AT 0.8 < z < 2.6
International Nuclear Information System (INIS)
Wuyts, Eva; Kurk, Jaron; Förster Schreiber, Natascha M.; Genzel, Reinhard; Wisnioski, Emily; Bandara, Kaushala; Wuyts, Stijn; Beifiori, Alessandra; Bender, Ralf; Buschkamp, Peter; Chan, Jeffrey; Davies, Ric; Eisenhauer, Frank; Fossati, Matteo; Kulkarni, Sandesh K.; Lang, Philipp; Brammer, Gabriel B.; Burkert, Andreas; Carollo, C. Marcella; Lilly, Simon J.
2014-01-01
We present the correlations between stellar mass, star formation rate (SFR), and the [N II]/Hα flux ratio as an indicator of gas-phase metallicity for a sample of 222 galaxies at 0.8 < z < 2.6 and log (M * /M ☉ ) = 9.0-11.5 from the LUCI, SINS/zC-SINF, and KMOS 3D surveys. This sample provides a unique analysis of the mass-metallicity relation (MZR) over an extended redshift range using consistent data analysis techniques and a uniform strong-line metallicity indicator. We find a constant slope at the low-mass end of the relation and can fully describe its redshift evolution through the evolution of the characteristic turnover mass where the relation begins to flatten at the asymptotic metallicity. At a fixed mass and redshift, our data do not show a correlation between the [N II]/Hα ratio and SFR, which disagrees with the 0.2-0.3 dex offset in [N II]/Hα predicted by the ''fundamental relation'' between stellar mass, SFR, and metallicity discussed in recent literature. However, the overall evolution toward lower [N II]/Hα at earlier times does broadly agree with these predictions
Z-2 Space Suit: A Case Study in Human Spaceflight Public Outreach
McFarland, Shane M.
2016-01-01
NASA Johnson Space Center's Z-series of planetary space suit prototypes is an iterative development platform with a Mars-forward design philosophy, targeting a Mars surface mission in the mid-2030s. The first space suit assembly, called the Z-1, was delivered in 2012. While meeting the project's stated requirements and objectives, the general public's reception primarily focused on the color scheme, which vaguely invoked similarity to a certain animated cartoon character. The public at large has and continues to be exposed to varying space suit design aesthetics from popular culture and low TRL technology maturation efforts such as mechanical counterpressure. The lesson learned was that while the design aesthetic is not important from an engineering perspective, the perception of the public is important for NASA and human spaceflight in general. For the Z-2 space suit, an integrated public outreach strategy was employed to engage, excite and educate the public on the current technology of space suits and NASA's plans moving forward. The keystone of this strategy was a public vote on three different suit cover layer aesthetics, the winner of which would be used as inspiration in fabrication. Other components included social media, university collaboration, and select media appearances, the cumulative result of which, while intangible in its benefit, was ultimately a positive effect in terms of the image of NASA as well as the dissemination of information vital to dispelling public misconceptions.
Evolution of optically selected quasars with z<2.2 and B<20
International Nuclear Information System (INIS)
Marshall, H.L.
1985-01-01
Several complete samples of optically selected quasars are combined to give details of the quasar luminosity function and its evolution for redshifts less than 2.2. Sufficient coverage of the Hubble diagram is obtained that luminosity-dependent density evolution models can be tested and compared against pure luminosity evolution models. Although luminosity-dependent evolution is indicated if the evolution function has an exponential form, the data are consistent with a power-law evolution model that is independent of luminosity. When the sample is split into halves by redshift, a better fit is obtained with a power-law evolution model than with an exponential model. Furthermore, the luminosity function is consistent with a power-law shape whose slope is independent of redshift. Pure luminosity evolution models wherein luminosities evolve as (1+z)/sup 3.5/ and the luminosity functioin is given by dN/dLproportionalL/sup -3.6/ are consistent with these results and fit the data very well. These results suggest that the same mass supply and energy generation mechanisms apply over several decades of optical luminosity and for z<2.2
Naturalness of three generations in free fermionic Z2n direct-product Z4 string models
International Nuclear Information System (INIS)
Faraggi, A.E.; Nanopoulos, D.V.
1993-01-01
We study the construction of free fermionic spin structure models with Z 2 n direct-product Z 4 boundary-condition vectors. We argue that requiring chiral space-time fermions in the massless spectrum and the existence of a well-defined hidden gauge group severely constrain the allowed boundary-condition vectors. We show that the minimal way to obtain these requirements is given by a unique set of Z 2 5 boundary-condition vectors. We classify the possible extensions to this basic set. We argue that a result of this fundamental set is that obtaining three generations in this construction is correlated with projecting out all the enhanced gauge symmetries which arise from nonzero vacuum expectation values of background fields. We propose that this correlation and the properties of the fundamental Z 2 5 subset suggest that three generations is natural in this construction
Pressure induced valence transitions in the Anderson lattice model
International Nuclear Information System (INIS)
Bernhard, B.H.; Coqblin, B.
2009-01-01
We apply the equation of motion method to the Anderson lattice model, which describes the physical properties of heavy fermion compounds. In particular, we focus here on the variation of the number of f electrons with pressure, associated to the crossover from the Kondo regime to the intermediate valence regime. We treat here the non-magnetic case and introduce an improved approximation, which consists of an alloy analogy based decoupling for the Anderson lattice model. It is implemented by partial incorporation of the spatial correlations contained in higher-order Green's functions involved in the problem that have been formerly neglected. As it has been verified in the framework of the Hubbard model, the alloy analogy avoids the breakdown of sum rules and is more appropriate to explore the asymmetric case of the periodic Anderson Hamiltonian. The densities of states for a simple cubic lattice are calculated for various values of the model parameters V, t, E f , and U.
Anomalous dimensions from boson lattice models
de Carvalho, Shaun; de Mello Koch, Robert; Larweh Mahu, Augustine
2018-06-01
Operators dual to strings attached to giant graviton branes in AdS5×S5 can be described rather explicitly in the dual N =4 super-Yang-Mills theory. They have a bare dimension of order N so that for these operators the large N limit and the planar limit are distinct; summing only the planar diagrams will not capture the large N dynamics. Focusing on the one-loop S U (3 ) sector of the theory, we consider operators that are a small deformation of a 1/2 -Bogomol'nyi-Prasad-Sommerfield (BPS) multigiant graviton state. The diagonalization of the dilatation operator at one loop has been carried out in previous studies, but explicit formulas for the operators of a good scaling dimension are only known when certain terms which were argued to be small are neglected. In this article, we include the terms which were neglected. The diagonalization is achieved by a novel mapping which replaces the problem of diagonalizing the dilatation operator with a system of bosons hopping on a lattice. The giant gravitons define the sites of this lattice, and the open strings stretching between distinct giant gravitons define the hopping terms of the Hamiltonian. Using the lattice boson model, we argue that the lowest energy giant graviton states are obtained by distributing the momenta carried by the X and Y fields evenly between the giants with the condition that any particular giant carries only X or Y momenta, but not both.
A review of the Z2-FET 1T-DRAM memory: Operation mechanisms and key parameters
Cristoloveanu, S.; Lee, K. H.; Parihar, M. S.; El Dirani, H.; Lacord, J.; Martinie, S.; Le Royer, C.; Barbe, J.-Ch.; Mescot, X.; Fonteneau, P.; Galy, Ph.; Gamiz, F.; Navarro, C.; Cheng, B.; Duan, M.; Adamu-Lema, F.; Asenov, A.; Taur, Y.; Xu, Y.; Kim, Y.-T.; Wan, J.; Bawedin, M.
2018-05-01
The band-modulation and sharp-switching mechanisms in Z2-FET device operated as a capacitorless 1T-DRAM memory are reviewed. The main parameters that govern the memory performance are discussed based on detailed experiments and simulations. This 1T-DRAM memory does not suffer from super-coupling effect and can be integrated in sub-10 nm thick SOI films. It offers low leakage current, high current margin, long retention, low operating voltage especially for programming, and high speed. The Z2-FET is suitable for embedded memory applications.
Quantum phases of dipolar rotors on two-dimensional lattices.
Abolins, B P; Zillich, R E; Whaley, K B
2018-03-14
The quantum phase transitions of dipoles confined to the vertices of two-dimensional lattices of square and triangular geometry is studied using path integral ground state quantum Monte Carlo. We analyze the phase diagram as a function of the strength of both the dipolar interaction and a transverse electric field. The study reveals the existence of a class of orientational phases of quantum dipolar rotors whose properties are determined by the ratios between the strength of the anisotropic dipole-dipole interaction, the strength of the applied transverse field, and the rotational constant. For the triangular lattice, the generic orientationally disordered phase found at zero and weak values of both dipolar interaction strength and applied field is found to show a transition to a phase characterized by net polarization in the lattice plane as the strength of the dipole-dipole interaction is increased, independent of the strength of the applied transverse field, in addition to the expected transition to a transverse polarized phase as the electric field strength increases. The square lattice is also found to exhibit a transition from a disordered phase to an ordered phase as the dipole-dipole interaction strength is increased, as well as the expected transition to a transverse polarized phase as the electric field strength increases. In contrast to the situation with a triangular lattice, on square lattices, the ordered phase at high dipole-dipole interaction strength possesses a striped ordering. The properties of these quantum dipolar rotor phases are dominated by the anisotropy of the interaction and provide useful models for developing quantum phases beyond the well-known paradigms of spin Hamiltonian models, implementing in particular a novel physical realization of a quantum rotor-like Hamiltonian that possesses an anisotropic long range interaction.
Quantum phases of dipolar rotors on two-dimensional lattices
Abolins, B. P.; Zillich, R. E.; Whaley, K. B.
2018-03-01
The quantum phase transitions of dipoles confined to the vertices of two-dimensional lattices of square and triangular geometry is studied using path integral ground state quantum Monte Carlo. We analyze the phase diagram as a function of the strength of both the dipolar interaction and a transverse electric field. The study reveals the existence of a class of orientational phases of quantum dipolar rotors whose properties are determined by the ratios between the strength of the anisotropic dipole-dipole interaction, the strength of the applied transverse field, and the rotational constant. For the triangular lattice, the generic orientationally disordered phase found at zero and weak values of both dipolar interaction strength and applied field is found to show a transition to a phase characterized by net polarization in the lattice plane as the strength of the dipole-dipole interaction is increased, independent of the strength of the applied transverse field, in addition to the expected transition to a transverse polarized phase as the electric field strength increases. The square lattice is also found to exhibit a transition from a disordered phase to an ordered phase as the dipole-dipole interaction strength is increased, as well as the expected transition to a transverse polarized phase as the electric field strength increases. In contrast to the situation with a triangular lattice, on square lattices, the ordered phase at high dipole-dipole interaction strength possesses a striped ordering. The properties of these quantum dipolar rotor phases are dominated by the anisotropy of the interaction and provide useful models for developing quantum phases beyond the well-known paradigms of spin Hamiltonian models, implementing in particular a novel physical realization of a quantum rotor-like Hamiltonian that possesses an anisotropic long range interaction.
DEFF Research Database (Denmark)
Patrick, Christopher; Thygesen, Kristian Sommer
2016-01-01
In non-self-consistent calculations of the total energy within the random-phase approximation (RPA) for electronic correlation, it is necessary to choose a single-particle Hamiltonian whose solutions are used to construct the electronic density and noninteracting response function. Here we...... investigate the effect of including a Hubbard-U term in this single-particle Hamiltonian, to better describe the on-site correlation of 3d electrons in the transitionmetal compounds ZnS, TiO2, and NiO.We find that the RPA lattice constants are essentially independent of U, despite large changes...... in the underlying electronic structure. We further demonstrate that the non-selfconsistent RPA total energies of these materials have minima at nonzero U. Our RPA calculations find the rutile phase of TiO2 to be more stable than anatase independent of U, a result which is consistent with experiments...
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
Hamiltonian indices and rational spectral densities
Byrnes, C. I.; Duncan, T. E.
1980-01-01
Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.
Betatron coupling: Merging Hamiltonian and matrix approaches
Directory of Open Access Journals (Sweden)
R. Calaga
2005-03-01
Full Text Available Betatron coupling is usually analyzed using either matrix formalism or Hamiltonian perturbation theory. The latter is less exact but provides a better physical insight. In this paper direct relations are derived between the two formalisms. This makes it possible to interpret the matrix approach in terms of resonances, as well as use results of both formalisms indistinctly. An approach to measure the complete coupling matrix and its determinant from turn-by-turn data is presented. Simulations using methodical accelerator design MAD-X, an accelerator design and tracking program, were performed to validate the relations and understand the scope of their application to real accelerators such as the Relativistic Heavy Ion Collider.
A Hamiltonian five-field gyrofluid model
Energy Technology Data Exchange (ETDEWEB)
Keramidas Charidakos, I.; Waelbroeck, F. L.; Morrison, P. J. [Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, TX 78712 (United States)
2015-11-15
A Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of the electron and ion gyro-center densities, the parallel component of the ion and electron velocities, and the ion temperature. The quasineutrality property and Ampère's law determine, respectively, the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated with five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models.
Hamiltonian circuited simulations in reactor physics
International Nuclear Information System (INIS)
Rio Hirowati Shariffudin
2002-01-01
In the assessment of suitability of reactor designs and in the investigations into reactor safety, the steady state of a nuclear reactor has to be studied carefully. The analysis can be done through mockup designs but this approach costs a lot of money and consumes a lot of time. A less expensive approach is via simulations where the reactor and its neutron interactions are modelled mathematically. Finite difference discretization of the diffusion operator has been used to approximate the steady state multigroup neutron diffusion equations. The steps include the outer scheme which estimates the resulting right hand side of the matrix equation, the group scheme which calculates the upscatter problem and the inner scheme which solves for the flux for a particular group. The Hamiltonian circuited simulations for the inner iterations of the said neutron diffusion equation enable the effective use of parallel computing, especially where the solutions of multigroup neutron diffusion equations involving two or more space dimensions are required. (Author)
Hamiltonian inclusive fitness: a fitter fitness concept.
Costa, James T
2013-01-01
In 1963-1964 W. D. Hamilton introduced the concept of inclusive fitness, the only significant elaboration of Darwinian fitness since the nineteenth century. I discuss the origin of the modern fitness concept, providing context for Hamilton's discovery of inclusive fitness in relation to the puzzle of altruism. While fitness conceptually originates with Darwin, the term itself stems from Spencer and crystallized quantitatively in the early twentieth century. Hamiltonian inclusive fitness, with Price's reformulation, provided the solution to Darwin's 'special difficulty'-the evolution of caste polymorphism and sterility in social insects. Hamilton further explored the roles of inclusive fitness and reciprocation to tackle Darwin's other difficulty, the evolution of human altruism. The heuristically powerful inclusive fitness concept ramified over the past 50 years: the number and diversity of 'offspring ideas' that it has engendered render it a fitter fitness concept, one that Darwin would have appreciated.
Renormalized semiclassical quantization for rescalable Hamiltonians
International Nuclear Information System (INIS)
Takahashi, Satoshi; Takatsuka, Kazuo
2004-01-01
A renormalized semiclassical quantization method for rescalable Hamiltonians is proposed. A classical Hamilton system having a potential function that consists of homogeneous polynomials like the Coulombic potential can have a scale invariance in its extended phase space (phase space plus time). Consequently, infinitely many copies of a single trajectory constitute a one-parameter family that is characterized in terms of a scaling factor. This scaling invariance in classical dynamics is lost in quantum mechanics due to the presence of the Planck constant. It is shown that in a system whose classical motions have a self-similarity in the above sense, classical trajectories adopted in the semiclassical scheme interact with infinitely many copies of their own that are reproduced by the relevant scaling procedure, thereby undergoing quantum interference among themselves to produce a quantized spectrum
Effective hamiltonian calculations using incomplete model spaces
International Nuclear Information System (INIS)
Koch, S.; Mukherjee, D.
1987-01-01
It appears that the danger of encountering ''intruder states'' is substantially reduced if an effective hamiltonian formalism is developed for incomplete model spaces (IMS). In a Fock-space approach, the proof a ''connected diagram theorem'' is fairly straightforward with exponential-type of ansatze for the wave-operator W, provided the normalization chosen for W is separable. Operationally, one just needs a suitable categorization of the Fock-space operators into ''diagonal'' and ''non-diagonal'' parts that is generalization of the corresponding procedure for the complete model space. The formalism is applied to prototypical 2-electron systems. The calculations have been performed on the Cyber 205 super-computer. The authors paid special attention to an efficient vectorization for the construction and solution of the resulting coupled non-linear equations
Non-self-adjoint hamiltonians defined by Riesz bases
Energy Technology Data Exchange (ETDEWEB)
Bagarello, F., E-mail: fabio.bagarello@unipa.it [Dipartimento di Energia, Ingegneria dell' Informazione e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, I-90128 Palermo, Italy and INFN, Università di Torino, Torino (Italy); Inoue, A., E-mail: a-inoue@fukuoka-u.ac.jp [Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180 (Japan); Trapani, C., E-mail: camillo.trapani@unipa.it [Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo (Italy)
2014-03-15
We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators.
The Group of Hamiltonian Automorphisms of a Star Product
Energy Technology Data Exchange (ETDEWEB)
La Fuente-Gravy, Laurent, E-mail: lfuente@ulg.ac.be [Université de Liège, Département de Mathématique (Belgium)
2016-09-15
We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
Hamiltonian formulation for the Martin-Taylor model
International Nuclear Information System (INIS)
Vasconcelos, D.B.; Viana, R.L.
1993-01-01
Locally stochastic layer and its optimization are studied. In order to accomplish this task, it is employed a Hamiltonian formulation of magnetic field line flow with a subsequent application of Escande-Doveil renormalization method which have been extensively used to obtain accurate estimates of stochasticity thresholds in systems exhibiting Hamiltonian chaos. (author)
Formulation of Hamiltonian mechanics with even and odd Poisson brackets
International Nuclear Information System (INIS)
Khudaverdyan, O.M.; Nersesyan, A.P.
1987-01-01
A possibility is studied as to constrict the odd Poisson bracket and odd Hamiltonian by the given dynamics in phase superspace - the even Poisson bracket and even Hamiltonian so the transition to the new structure does not change the equations of motion. 9 refs
Effective Hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Filippov, G.F.; Blokhin, A.L.
1989-01-01
A technique of projecting the microscopic nuclear Hamiltonian on the SU(3)-group enveloping algebra is developed. The approach proposed is based on the effective Hamiltonian restored from the matrix elements between the coherent states of the SU(3) irreducible representations. The technique is displayed for almost magic nuclei within the mixed representation basis, and for arbitrary nuclei within the single representation. 40 refs
Classical and quantum mechanics of complex Hamiltonian systems ...
Indian Academy of Sciences (India)
Vol. 73, No. 2. — journal of. August 2009 physics pp. 287–297. Classical and quantum mechanics of complex. Hamiltonian systems: An extended complex phase space ... 1Department of Physics, Ramjas College (University Enclave), University of Delhi,. Delhi 110 ... 1.1 Motivation behind the study of complex Hamiltonians.
Local Hamiltonians for maximally multipartite-entangled states
Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.
2010-10-01
We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.
Local Hamiltonians for maximally multipartite-entangled states
International Nuclear Information System (INIS)
Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.
2010-01-01
We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.
Modelling chaotic Hamiltonian systems as a Markov Chain ...
African Journals Online (AJOL)
The behaviour of chaotic Hamiltonian system has been characterised qualitatively in recent times by its appearance on the Poincaré section and quantitatively by the Lyapunov exponent. Studying the dynamics of the two chaotic Hamiltonian systems: the Henon-Heiles system and non-linearly coupled oscillators as their ...
On the physical applications of hyper-Hamiltonian dynamics
International Nuclear Information System (INIS)
Gaeta, Giuseppe; Rodriguez, Miguel A
2008-01-01
An extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds ('hyper-Hamiltonian dynamics') and sharing many of the attractive features of standard Hamiltonian dynamics, was introduced in previous work. In this paper, we discuss applications of the theory to physically interesting cases, dealing with the dynamics of particles with spin 1/2 in a magnetic field, i.e. the Pauli and the Dirac equations. While the free Pauli equation corresponds to a hyper-Hamiltonian flow, it turns out that the hyper-Hamiltonian description of the Dirac equation, and of the full Pauli one, is in terms of two commuting hyper-Hamiltonian flows. In this framework one can use a factorization principle discussed here (which is a special case of a general phenomenon studied by Walcher) and provide an explicit description of the resulting flow. On the other hand, by applying the familiar Foldy-Wouthuysen and Cini-Tousheck transformations (and the one recently introduced by Mulligan) which separate-in suitable limits-the Dirac equation into two equations, each of these turn out to be described by a single hyper-Hamiltonian flow. Thus the hyper-Hamiltonian construction is able to describe the fundamental dynamics for particles with spin
The Group of Hamiltonian Automorphisms of a Star Product
International Nuclear Information System (INIS)
La Fuente-Gravy, Laurent
2016-01-01
We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
Hamiltonian reduction of SU(2) Yang-Mills field theory
International Nuclear Information System (INIS)
Khvedelidze, A.M.; Pavel, H.-P.
1998-01-01
The unconstrained system equivalent to SU (2) Yang-Mills field theory is obtained in the framework of the generalized Hamiltonian formalism using the method of Hamiltonian reduction. The reduced system is expressed in terms of fields with 'nonrelativistic' spin-0 and spin-2
An effective Hamiltonian approach to quantum random walk
Indian Academy of Sciences (India)
2017-02-09
Feb 9, 2017 ... Abstract. 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 Hamil- tonians are generators of time translations. Then an attempt has been made to ...
Model reduction of port-Hamiltonian systems as structured systems
Polyuga, R.V.; Schaft, van der A.J.
2010-01-01
The goal of this work is to demonstrate that a specific projection-based model reduction method, which provides an H2 error bound, turns out to be applicable to port-Hamiltonian systems, preserving the port-Hamiltonian structure for the reduced order model, and, as a consequence, passivity.
Port Hamiltonian Formulation of Infinite Dimensional Systems I. Modeling
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-variable case.
Port-Hamiltonian approaches to motion generation for mechanical systems
Sakai, Satoru; Stramigioli, Stefano
This paper gives new motion generation methods for mechanical port-Hamiltonian systems. First, we propose a generation method based on an asymptotic stabilization method without damping assignment. This asymptotic stabilization method preserves the Hamiltonian structure in the closed-loop system
Structure preserving port-Hamiltonian model reduction of electrical circuits
Polyuga, R.; Schaft, van der A.J.; Benner, P.; Hinze, M.; Maten, ter E.J.W.
2011-01-01
This paper discusses model reduction of electrical circuits based on a port-Hamiltonian representation. It is shown that by the use of the Kalman decomposition an uncontrollable and/or unobservable port-Hamiltonian system is reduced to a controllable/observable system that inherits the
Discovery of a Lensed Ultrabright Submillimeter Galaxy at z = 2.0439
Díaz-Sánchez, A.; Iglesias-Groth, S.; Rebolo, R.; Dannerbauer, H.
2017-07-01
We report an ultrabright lensed submillimeter galaxy (SMG) at z = 2.0439, WISE J132934.18+224327.3, identified as a result of a full-sky cross-correlation of the AllWISE and Planck compact source catalogs aimed to search for bright analogs of the SMG SMM J2135, the Cosmic Eyelash. Inspection of archival SCUBA-2 observations of the candidates revealed a source with fluxes ({S}850μ {{m}}=130 mJy) consistent with the Planck measurements. The centroid of the SCUBA-2 source coincides within 1 arcsec with the position of the AllWISE mid-IR source, and, remarkably, with an arc-shaped lensed galaxy in HST images at visible wavelengths. Low-resolution rest-frame UV-optical spectroscopy of this lensed galaxy obtained with 10.4 m GTC reveals the typical absorption lines of a starburst galaxy. Gemini-N near-IR spectroscopy provided a clear detection of {{{H}}}α emission. The lensed source appears to be gravitationally magnified by a massive foreground galaxy cluster lens at z = 0.44 modeling with Lenstool indicates a lensing amplification factor of 11 ± 2. We determine an intrinsic rest-frame 8-1000 μm luminosity, {L}{IR}, of (1.3+/- 0.1)× {10}13 {L}⊙ , and a likely star formation rate (SFR) of ˜ 500{--}2000 {M}⊙ {{yr}}-1. The SED shows a remarkable similarity with the Cosmic Eyelash from optical-mid/IR to submillimeter/radio, albeit at higher fluxes.
The Curious Molecular Gas Conditions in a z=2.6 Radio-loud Quasar
Sharon, Chelsea; Riechers, Dominik A.; Kuk Leung, Tsz; Weiss, Axel; Walter, Fabian; Carilli, Chris; Kraiburg Knudsen, Kirsten; Hodge, Jacqueline
2018-01-01
Theoretical work suggests that AGN play an important role in quenching star formation in massive galaxies. In addition to molecular outflows observed in the local universe, emission from very high-J CO rotational transitions has been one of the key pieces of evidence for AGN directly affecting the molecular gas reservoirs that fuel star formation. However, very few observations of Jupper>9 transitions exist for galaxies in the early universe. Here we will present the peculiar molecular gas conditions in MG 0414+0534 (MG 0414 hereafter), one of the few high-z galaxies with very high-J CO detections. MG 0414 is a strongly lensed IR-bright radio-loud quasar with broad Hα emission at z=2.6390. We recently confirmed the CO(3–2) detection from Barvainis et al. (1998), but were unable to detect the CO(1–0) line. The 3σ lower limit on the 3–2/1–0 line ratio (in units of brightness temperature) is r3,1>5.72, which is significantly higher than the r3,1≤1 typical for thermalized optically thick emission in other z˜2–3 AGN host galaxies. In addition, the CO(11–10) line was detected to high significance using the Atacama Large Millimeter/submillimeter Array, and the CO(11–10) line FWHM is nearly double that of the CO(3–2) line. We will discuss possible explanations for the peculiar line ratios in MG 0414 (such as optically thin emission, molecular outflows, and differential lensing) and what the origin of these ratios imply for molecular gas observations of other high-z AGN host galaxies.
Bulge growth and quenching since z = 2.5 in CANDELS/3D-HST
International Nuclear Information System (INIS)
Lang, Philipp; Wuyts, Stijn; Schreiber, Natascha M. Förster; Genzel, Reinhard; Lutz, Dieter; Rosario, David J.; Somerville, Rachel S.; Bell, Eric F.; Brammer, Gabe; Dekel, Avishai; Faber, Sandra M.; Momcheva, Ivelina; Ferguson, Henry C.; Grogin, Norman A.; Koekemoer, Anton M.; Kocevski, Dale D.; McGrath, Elizabeth J.; Nelson, Erica J.; Primack, Joel R.; Skelton, Rosalind E.
2014-01-01
Exploiting the deep high-resolution imaging of all five CANDELS fields, and accurate redshift information provided by 3D-HST, we investigate the relation between structure and stellar populations for a mass-selected sample of 6764 galaxies above 10 10 M ☉ , spanning the redshift range 0.5 < z < 2.5. For the first time, we fit two-dimensional models comprising a single Sérsic fit and two-component (i.e., bulge + disk) decompositions not only to the H-band light distributions, but also to the stellar mass maps reconstructed from resolved stellar population modeling. We confirm that the increased bulge prominence among quiescent galaxies, as reported previously based on rest-optical observations, remains in place when considering the distributions of stellar mass. Moreover, we observe an increase of the typical Sérsic index and bulge-to-total ratio (with median B/T reaching 40%-50%) among star-forming galaxies above 10 11 M ☉ . Given that quenching for these most massive systems is likely to be imminent, our findings suggest that significant bulge growth precedes a departure from the star-forming main sequence. We demonstrate that the bulge mass (and ideally knowledge of the bulge and total mass) is a more reliable predictor of the star-forming versus quiescent state of a galaxy than the total stellar mass. The same trends are predicted by the state-of-the-art, semi-analytic model by Somerville et al. In this model, bulges and black holes grow hand in hand through merging and/or disk instabilities, and feedback from active galactic nuclei shuts off star formation. Further observations will be required to pin down star formation quenching mechanisms, but our results imply that they must be internal to the galaxies and closely associated with bulge growth.
Bulge Growth and Quenching since z = 2.5 in CANDELS/3D-HST
Lang, Philipp; Wuyts, Stijn; Somerville, Rachel S.; Förster Schreiber, Natascha M.; Genzel, Reinhard; Bell, Eric F.; Brammer, Gabe; Dekel, Avishai; Faber, Sandra M.; Ferguson, Henry C.; Grogin, Norman A.; Kocevski, Dale D.; Koekemoer, Anton M.; Lutz, Dieter; McGrath, Elizabeth J.; Momcheva, Ivelina; Nelson, Erica J.; Primack, Joel R.; Rosario, David J.; Skelton, Rosalind E.; Tacconi, Linda J.; van Dokkum, Pieter G.; Whitaker, Katherine E.
2014-06-01
Exploiting the deep high-resolution imaging of all five CANDELS fields, and accurate redshift information provided by 3D-HST, we investigate the relation between structure and stellar populations for a mass-selected sample of 6764 galaxies above 1010 M ⊙, spanning the redshift range 0.5 < z < 2.5. For the first time, we fit two-dimensional models comprising a single Sérsic fit and two-component (i.e., bulge + disk) decompositions not only to the H-band light distributions, but also to the stellar mass maps reconstructed from resolved stellar population modeling. We confirm that the increased bulge prominence among quiescent galaxies, as reported previously based on rest-optical observations, remains in place when considering the distributions of stellar mass. Moreover, we observe an increase of the typical Sérsic index and bulge-to-total ratio (with median B/T reaching 40%-50%) among star-forming galaxies above 1011 M ⊙. Given that quenching for these most massive systems is likely to be imminent, our findings suggest that significant bulge growth precedes a departure from the star-forming main sequence. We demonstrate that the bulge mass (and ideally knowledge of the bulge and total mass) is a more reliable predictor of the star-forming versus quiescent state of a galaxy than the total stellar mass. The same trends are predicted by the state-of-the-art, semi-analytic model by Somerville et al. In this model, bulges and black holes grow hand in hand through merging and/or disk instabilities, and feedback from active galactic nuclei shuts off star formation. Further observations will be required to pin down star formation quenching mechanisms, but our results imply that they must be internal to the galaxies and closely associated with bulge growth.
The star formation history of redshift z ~ 2 galaxies: the role of the infrared prior
Fan, Lu-Lu; Lapi, Andrea; Bressan, Alessandro; Nonino, Mario; De Zotti, Gianfranco; Danese, Luigi
2014-01-01
We build a sample of 298 spectroscopically-confirmed galaxies at redshift z ~ 2, selected in the z850-band from the GOODS-MUSIC catalog. By utilizing the rest frame 8 μm luminosity as a proxy of the star formation rate (SFR), we check the accuracy of the standard SED-fitting technique, finding it is not accurate enough to provide reliable estimates of the physical parameters of galaxies. We then develop a new SED-fitting method that includes the IR luminosity as a prior and a generalized Calzetti law with a variable RV. Then we exploit the new method to re-analyze our galaxy sample, and to robustly determine SFRs, stellar masses and ages. We find that there is a general trend of increasing attenuation with the SFR. Moreover, we find that the SFRs range between a few to 103 Msolar yr-1, the masses from 109 to 4 × 1011 Msolar, and the ages from a few tens of Myr to more than 1 Gyr. We discuss how individual age measurements of highly attenuated objects indicate that dust must have formed within a few tens of Myr and already been copious at <=100 Myr. In addition, we find that low luminosity galaxies harbor, on average, significantly older stellar populations and are also less massive than brighter ones; we discuss how these findings and the well known ‘downsizing’ scenario are consistent in a framework where less massive galaxies form first, but their star formation lasts longer. Finally, we find that the near-IR attenuation is not scarce for luminous objects, contrary to what is customarily assumed; we discuss how this affects the interpretation of the observed M*/L ratios.
Spitzer Imaging of Planck-Herschel Dusty Proto-Clusters at z=2-3
Cooray, Asantha; Ma, Jingzhe; Greenslade, Joshua; Kubo, Mariko; Nayyeri, Hooshang; Clements, David; Cheng, Tai-An
2018-05-01
We have recently introduced a new proto-cluster selection technique by combing Herschel/SPIRE imaging data and Planck/HFIk all-sky survey point source catalog. These sources are identified as Planck point sources with clumps of Herschel source over-densities with far-IR colors comparable to z=0 ULIRGS redshifted to z=2 to 3. The selection is sensitive to dusty starbursts and obscured QSOs and we have recovered couple of the known proto-clusters and close to 30 new proto-clusters. The candidate proto-clusters selected from this technique have far-IR flux densities several times higher than those that are optically selected, such as using LBG selection, implying that the member galaxies are in a special phase of heightened dusty starburst and dusty QSO activity. This far-IR luminous phase may be short but likely to be necessary piece to understand the whole stellar mass assembly history of clusters. Moreover, our photo-clusters are missed in optical selections, suggesting that optically selected proto-clusters alone do not provide adequate statistics and a comparison of the far-IR and optical selected clusters may reveal the importance of the dusty stellar mass assembly. Here, we propose IRAC observations of six of the highest priority new proto-clusters, to establish the validity of the technique and to determine the total stellar mass through SED models. For a modest observing time the science program will have a substantial impact on an upcoming science topic in cosmology with implications for observations with JWST and WFIRST to understand the mass assembly in the universe.
A comprehensive model on field-effect pnpn devices (Z2-FET)
Taur, Yuan; Lacord, Joris; Parihar, Mukta Singh; Wan, Jing; Martinie, Sebastien; Lee, Kyunghwa; Bawedin, Maryline; Barbe, Jean-Charles; Cristoloveanu, Sorin
2017-08-01
A comprehensive model for field-effect pnpn devices (Z2-FET) is presented. It is based on three current continuity equations coupled to two MOS equations. The model reproduces the characteristic S-shaped I-V curve when the device is driven by a current source. The negative resistance region at intermediate currents occurs as the center junction undergoes a steep transition from reverse to forward bias. Also playing a vital role are the mix and match of the minority carrier diffusion current and the generation recombination current. Physical insights to the key mechanisms at work are gained by regional approximations of the model, from which analytical expressions for the maximum and minimum voltages at the switching points are derived. From 1981 to 2001, he was with the Silicon Technology Department of IBM Thomas J. Watson Research Center, Yorktown Heights, New York, where he was Manager of Exploratory Devices and Processes. Areas in which he has worked and published include latchup-free 1-um CMOS, self-aligned TiSi2, 0.5-um CMOS and BiCMOS, shallow trench isolation, 0.25-um CMOS with n+/p + poly gates, SOI, low-temperature CMOS, and 0.1-um CMOS. Since October 2001, he has been a professor in the Department of Electrical and Computer Engineering, University of California, San Diego. Dr. Yuan Taur was elected a Fellow of the IEEE in 1998. He has served as Editor-in-Chief of the IEEE Electron Device Letters from 1999 to 2011. He authored or co-authored over 200 technical papers and holds 14 U.S. patents. He co-authored a book, ;Fundamentals of Modern VLSI Devices,; published by Cambridge University Press in 1998. The 2nd edition was published in 2009. Dr. Yuan Taur received IEEE Electron Devices Society's J. J. Ebers Award in 2012 ;for contributions to the advancement of several generations of CMOS process technologies.;
Lattice theory for nonspecialists
International Nuclear Information System (INIS)
Hari Dass, N.D.
1984-01-01
These lectures were delivered as part of the academic training programme at the NIKHEF-H. These lectures were intended primarily for experimentalists, and theorists not specializing in lattice methods. The goal was to present the essential spirit behind the lattice approach and consequently the author has concentrated mostly on issues of principle rather than on presenting a large amount of detail. In particular, the author emphasizes the deep theoretical infra-structure that has made lattice studies meaningful. At the same time, he has avoided the use of heavy formalisms as they tend to obscure the basic issues for people trying to approach this subject for the first time. The essential ideas are illustrated with elementary soluble examples not involving complicated mathematics. The following subjects are discussed: three ways of solving the harmonic oscillator problem; latticization; gauge fields on a lattice; QCD observables; how to solve lattice theories. (Auth.)
International Nuclear Information System (INIS)
Creutz, M.
1983-04-01
In the last few years lattice gauge theory has become the primary tool for the study of nonperturbative phenomena in gauge theories. The lattice serves as an ultraviolet cutoff, rendering the theory well defined and amenable to numerical and analytical work. Of course, as with any cutoff, at the end of a calculation one must consider the limit of vanishing lattice spacing in order to draw conclusions on the physical continuum limit theory. The lattice has the advantage over other regulators that it is not tied to the Feynman expansion. This opens the possibility of other approximation schemes than conventional perturbation theory. Thus Wilson used a high temperature expansion to demonstrate confinement in the strong coupling limit. Monte Carlo simulations have dominated the research in lattice gauge theory for the last four years, giving first principle calculations of nonperturbative parameters characterizing the continuum limit. Some of the recent results with lattice calculations are reviewed
PREFACE: 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics
Fring, Andreas; Jones, Hugh; Znojil, Miloslav
2008-06-01
Attempts to understand the quantum mechanics of non-Hermitian Hamiltonian systems can be traced back to the early days, one example being Heisenberg's endeavour to formulate a consistent model involving an indefinite metric. Over the years non-Hermitian Hamiltonians whose spectra were believed to be real have appeared from time to time in the literature, for instance in the study of strong interactions at high energies via Regge models, in condensed matter physics in the context of the XXZ-spin chain, in interacting boson models in nuclear physics, in integrable quantum field theories as Toda field theories with complex coupling constants, and also very recently in a field theoretical scenario in the quantization procedure of strings on an AdS5 x S5 background. Concrete experimental realizations of these types of systems in the form of optical lattices have been proposed in 2007. In the area of mathematical physics similar non-systematic results appeared sporadically over the years. However, intensive and more systematic investigation of these types of non- Hermitian Hamiltonians with real eigenvalue spectra only began about ten years ago, when the surprising discovery was made that a large class of one-particle systems perturbed by a simple non-Hermitian potential term possesses a real energy spectrum. Since then regular international workshops devoted to this theme have taken place. This special issue is centred around the 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics held in July 2007 at City University London. All the contributions contain significant new results or alternatively provide a survey of the state of the art of the subject or a critical assessment of the present understanding of the topic and a discussion of open problems. Original contributions from non-participants were also invited. Meanwhile many interesting results have been obtained and consensus has been reached on various central conceptual issues in the
A generalized AKNS hierarchy and its bi-Hamiltonian structures
International Nuclear Information System (INIS)
Xia Tiecheng; You Fucai; Chen Dengyuan
2005-01-01
First we construct a new isospectral problem with 8 potentials in the present paper. And then a new Lax pair is presented. By making use of Tu scheme, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses bi-Hamiltonian structures. After making some reductions, the well-known AKNS hierarchy and other hierarchies of evolution equations are obtained. Finally, in order to illustrate that soliton hierarchy obtained in the paper possesses bi-Hamiltonian structures exactly, we prove that the linear combination of two-Hamiltonian operators admitted are also a Hamiltonian operator constantly. We point out that two Hamiltonian operators obtained of the system are directly derived from a recurrence relations, not from a recurrence operator
Local modular Hamiltonians from the quantum null energy condition
Koeller, Jason; Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin
2018-03-01
The vacuum modular Hamiltonian K of the Rindler wedge in any relativistic quantum field theory is given by the boost generator. Here we investigate the modular Hamiltonian for more general half-spaces which are bounded by an arbitrary smooth cut of a null plane. We derive a formula for the second derivative of the modular Hamiltonian with respect to the coordinates of the cut which schematically reads K''=Tv v . This formula can be integrated twice to obtain a simple expression for the modular Hamiltonian. The result naturally generalizes the standard expression for the Rindler modular Hamiltonian to this larger class of regions. Our primary assumptions are the quantum null energy condition—an inequality between the second derivative of the von Neumann entropy of a region and the stress tensor—and its saturation in the vacuum for these regions. We discuss the validity of these assumptions in free theories and holographic theories to all orders in 1 /N .
Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions
Energy Technology Data Exchange (ETDEWEB)
Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)
2010-05-15
In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)
Sdg interacting boson hamiltonian in the seniority scheme
Energy Technology Data Exchange (ETDEWEB)
Yoshinaga, N.
1989-03-06
The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagnoalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.
sdg Interacting boson hamiltonian in the seniority scheme
Yoshinaga, N.
1989-03-01
The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagonalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.
Frustration-free Hamiltonians supporting Majorana zero edge modes
International Nuclear Information System (INIS)
Jevtic, Sania; Barnett, Ryan
2017-01-01
A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs. (paper)
Frustration-free Hamiltonians supporting Majorana zero edge modes
Jevtic, Sania; Barnett, Ryan
2017-10-01
A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs.
On Traveling Waves in Lattices: The Case of Riccati Lattices
Dimitrova, Zlatinka
2012-09-01
The method of simplest equation is applied for analysis of a class of lattices described by differential-difference equations that admit traveling-wave solutions constructed on the basis of the solution of the Riccati equation. We denote such lattices as Riccati lattices. We search for Riccati lattices within two classes of lattices: generalized Lotka-Volterra lattices and generalized Holling lattices. We show that from the class of generalized Lotka-Volterra lattices only the Wadati lattice belongs to the class of Riccati lattices. Opposite to this many lattices from the Holling class are Riccati lattices. We construct exact traveling wave solutions on the basis of the solution of Riccati equation for three members of the class of generalized Holling lattices.
Lattice degeneracies of fermions
International Nuclear Information System (INIS)
Raszillier, H.
1983-10-01
We present a detailed description of the minimal degeneracies of geometric (Kaehler) fermions on all the lattices of maximal symmetries in n = 1, ..., 4 dimensions. We also determine the isolated orbits of the maximal symmetry groups, which are related to the minimal numbers of ''naive'' fermions on the reciprocals of these lattices. It turns out that on the self-reciprocal lattices the minimal numbers of naive fermions are equal to the minimal numbers of degrees of freedom of geometric fermions. The description we give relies on the close connection of the maximal lattice symmetry groups with (affine) Weyl groups of root systems of (semi-) simple Lie algebras. (orig.)
International Nuclear Information System (INIS)
Shindler, A.
2007-07-01
I review the theoretical foundations, properties as well as the simulation results obtained so far of a variant of the Wilson lattice QCD formulation: Wilson twisted mass lattice QCD. Emphasis is put on the discretization errors and on the effects of these discretization errors on the phase structure for Wilson-like fermions in the chiral limit. The possibility to use in lattice simulations different lattice actions for sea and valence quarks to ease the renormalization patterns of phenomenologically relevant local operators, is also discussed. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Shindler, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2007-07-15
I review the theoretical foundations, properties as well as the simulation results obtained so far of a variant of the Wilson lattice QCD formulation: Wilson twisted mass lattice QCD. Emphasis is put on the discretization errors and on the effects of these discretization errors on the phase structure for Wilson-like fermions in the chiral limit. The possibility to use in lattice simulations different lattice actions for sea and valence quarks to ease the renormalization patterns of phenomenologically relevant local operators, is also discussed. (orig.)
Conformal field theories, representations and lattice constructions
International Nuclear Information System (INIS)
Dolan, L.; Montague, P.
1996-01-01
An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and Z 2 -twisted theories, H(Λ) and H(Λ) respectively, which may be constructed from a suitable even Euclidean lattice Λ. Similarly, one may construct lattices Λ C and Lambda C by analogous constructions from a doubly-even binary code C. In the case when C is self-dual, the corresponding lattices are also. Similarly, H(Λ) and H(Λ) are self-dual if and only if Λ is. We show that H(Λ C ) has a natural triality structure, which induces an isomorphism H(Λ C )≡H(Λ C ) and also a triality structure on H(Λ C ). For C the Golay code, Λ C is the Leech lattice, and the triality on H(Λ C ) is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories H(Λ) and H(Λ) with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code. (orig.). With 8 figs., 2 tabs
Quantum nonlinear lattices and coherent state vectors
DEFF Research Database (Denmark)
Ellinas, Demosthenes; Johansson, M.; Christiansen, Peter Leth
1999-01-01
for the state vectors invokes the study of the Riemannian and symplectic geometry of the CSV manifolds as generalized phase spaces. Next, we investigate analytically and numerically the behavior of mean values and uncertainties of some physically interesting observables as well as the modifications...... (FP) model. Based on the respective dynamical symmetries of the models, a method is put forward which by use of the associated boson and spin coherent state vectors (CSV) and a factorization ansatz for the solution of the Schrodinger equation, leads to quasiclassical Hamiltonian equations of motion...... state vectors, and accounts for the quantum correlations of the lattice sites that develop during the time evolution of the systems. (C) 1999 Elsevier Science B.V. All rights reserved....
DEFF Research Database (Denmark)
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...... this polymorphism is associated with diabetic nephropathy and retinopathy in Type 1 diabetes mellitus in a large case-control study and a family-based analysis. METHODS: A total of 431 Type 1 diabetic patients with diabetic nephropathy and 468 patients with longstanding Type 1 diabetes and persistent...... of the ALR2 promoter polymorphism is associated with a reduced susceptibility to diabetic nephropathy in Danish Type 1 diabetic patients, suggesting a minor role for the polyol pathway in the pathogenesis of diabetic kidney disease. No association of the ALR2 polymorphism with diabetic retinopathy was found....
An end-to-end coupled model ROMS-N 2 P 2 Z 2 D 2 -OSMOSE of ...
African Journals Online (AJOL)
An end-to-end coupled model ROMS-N 2 P 2 Z 2 D 2 -OSMOSE of the southern Benguela foodweb: parameterisation, calibration and pattern-oriented validation. ... We also highlight the capacity of this model for tracking indicators at various hierarchical levels. Keywords: individual-based model, model validation, ...
International Nuclear Information System (INIS)
Szyniszewski, Marcin; Manchester Univ.; Cichy, Krzysztof; Poznan Univ.; Kujawa-Cichy, Agnieszka
2014-10-01
We employ exact diagonalization with strong coupling expansion to the massless and massive Schwinger model. New results are presented for the ground state energy and scalar mass gap in the massless model, which improve the precision to nearly 10 -9 %. We also investigate the chiral condensate and compare our calculations to previous results available in the literature. Oscillations of the chiral condensate which are present while increasing the expansion order are also studied and are shown to be directly linked to the presence of flux loops in the system.
Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.
Risser, Steven Michael
This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb
Atomic interferometers in an optical lattice
International Nuclear Information System (INIS)
Pelle, Bruno
2013-01-01
The aim of the ForCa-G project, for Casimir force and short range Gravitation, lies into the measurement of short range forces between atoms and a mirror using atomic interferometry techniques. Particularly, the Casimir-Polder force and the pursuit of short range gravitational tests in the frame of potential deviations of Newton's law are aimed. This experiment is based on the trapping of neutral atoms in a 1D vertical optical lattice, where the energy eigenvalues of the Hamiltonian describing this system is the so-called Wannier-Stark ladder of discrete energy states localized in each lattice well. This work constitutes a demonstration of principle of this project with atoms set far from the mirror. Each energy state is thus separated from the one of the adjacent well by the potential energy increment between those two wells, called the Bloch frequency ν B . Then, atomic interferometers are realized in the lattice using Raman or microwave pulses where the trapped atomic wave functions are placed, and then recombined, in a superposition of states between different energy states localized either in the same well, either in adjacent wells. This work presents the study of different kinds of atomic interferometers in this optical lattice, characterized in terms of sensibility and systematic effects on the Bloch frequency measurement. One of the studied interferometers accessed to a sensitivity on the Bloch frequency of σ δ ν B /ν B =9.0x10 -6 at 1∼s in relative, which integrates until σ δ ν B /ν B =1. 10 -7 in 2800∼s. This corresponds to a state-of-the-art measurement of the gravity acceleration g for a trapped atomic gravimeter. (author)
A Compact Group of Galaxies at z = 2.48 Hosting an AGN-driven Outflow
Shih, Hsin-Yi; Stockton, Alan
2015-12-01
We present observations of a remarkable compact group of galaxies at z = 2.48. Four galaxies, all within 40 kpc of each other, surround a powerful high-redshift radio source. This group comprises two compact red passive galaxies and a pair of merging galaxies. One of the red galaxies, with an apparent stellar mass of 3.6 × 1011M⊙ and an effective radius of 470 pc, is one of the most extreme examples of a massive quiescent compact galaxy found so far. One of the pair of merging galaxies hosts the active galactic nucleus (AGN) producing the large powerful radio structure. The merger is massive and enriched, consistent with the mass-metallicity relation expected at this redshift. Close to the merging nuclei, the emission lines exhibit broad and asymmetric profiles that suggest outflows powered either by a very young expanding radio jet or by AGN radiation. At ≳50 kpc from the system, we found a fainter extended-emission region that may be a part of a radio-jet-driven outflow. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The work is also based, in part, on data collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan, and on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência, Tecnologia e Inovação (Brazil), and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina).
The matrix realization of affine Jacobi varieties and the extended Lotka-Volterra lattice
International Nuclear Information System (INIS)
Inoue, Rei
2004-01-01
We study completely integrable Hamiltonian systems whose monodromy matrices are related to the representatives for the set of gauge equivalence classes M F of polynomial matrices. Let X be the algebraic curve given by the common characteristic equation for M F . We construct the isomorphism from the set of representatives to an affine part of the Jacobi variety of X. This variety corresponds to the invariant manifold of the system, where the Hamiltonian flow is linearized. As an application, we discuss the algebraic complete integrability of the extended Lotka-Volterra lattice with a periodic boundary condition
Spin-lattice relaxation of individual solid-state spins
Norambuena, A.; Muñoz, E.; Dinani, H. T.; Jarmola, A.; Maletinsky, P.; Budker, D.; Maze, J. R.
2018-03-01
Understanding the effect of vibrations on the relaxation process of individual spins is crucial for implementing nanosystems for quantum information and quantum metrology applications. In this work, we present a theoretical microscopic model to describe the spin-lattice relaxation of individual electronic spins associated to negatively charged nitrogen-vacancy centers in diamond, although our results can be extended to other spin-boson systems. Starting from a general spin-lattice interaction Hamiltonian, we provide a detailed description and solution of the quantum master equation of an electronic spin-one system coupled to a phononic bath in thermal equilibrium. Special attention is given to the dynamics of one-phonon processes below 1 K where our results agree with recent experimental findings and analytically describe the temperature and magnetic-field scaling. At higher temperatures, linear and second-order terms in the interaction Hamiltonian are considered and the temperature scaling is discussed for acoustic and quasilocalized phonons when appropriate. Our results, in addition to confirming a T5 temperature dependence of the longitudinal relaxation rate at higher temperatures, in agreement with experimental observations, provide a theoretical background for modeling the spin-lattice relaxation at a wide range of temperatures where different temperature scalings might be expected.
Directory of Open Access Journals (Sweden)
Epelbaum E.
2010-04-01
Full Text Available We review recent progress on nuclear lattice simulations using chiral eﬀective ﬁeld theory. We discuss lattice results for dilute neutron matter at next-to-leading order, three-body forces at next-to-next-toleading order, isospin-breaking and Coulomb eﬀects, and the binding energy of light nuclei.
International Nuclear Information System (INIS)
Jersak, J.
1986-01-01
This year has brought a sudden interest in lattice Higgs models. After five years of only modest activity we now have many new results obtained both by analytic and Monte Carlo methods. This talk is a review of the present state of lattice Higgs models with particular emphasis on the recent development
Mean field with corrections in lattice gauge theory
International Nuclear Information System (INIS)
Flyvbjerg, H.; Zuber, J.B.; Lautrup, B.
1981-12-01
A systematic expansion of the path integral for lattice gauge theory is performed around the mean field solution. In this letter the authors present the results for the pure gauge groups Z(2), SU(2) and SO(3). The agreement with Monte Carlo calculations is excellent. For the discrete group the calculation is performed with and without gauge fixing, whereas for the continuous groups gauge fixing is mandatory. In the case of SU(2) the absence of a phase transition is correctly signalled by mean field theory. (Auth.)
Phase-averaged transport for quasiperiodic Hamiltonians
Bellissard, J; Schulz-Baldes, H
2002-01-01
For a class of discrete quasi-periodic Schroedinger operators defined by covariant re- presentations of the rotation algebra, a lower bound on phase-averaged transport in terms of the multifractal dimensions of the density of states is proven. This result is established under a Diophantine condition on the incommensuration parameter. The relevant class of operators is distinguished by invariance with respect to symmetry automorphisms of the rotation algebra. It includes the critical Harper (almost-Mathieu) operator. As a by-product, a new solution of the frame problem associated with Weyl-Heisenberg-Gabor lattices of coherent states is given.
Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge
International Nuclear Information System (INIS)
Reinhardt, H.; Schleifenbaum, W.
2009-01-01
We study the Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss' law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev-Popov kernel in the pure Coulomb gauge. By Gauss' law the zero modes of the Faddeev-Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schroedinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson-Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the Gribov region chosen. In this sense, the Dyson-Schwinger equations alone do not provide the full non-abelian quantum gauge theory, but subsidiary conditions must be required. Implications of Gribov copy effects for lattice calculations of the infrared behaviour of gauge-fixed propagators are discussed. We compute the ghost-gluon vertex and provide a sensible truncation of Dyson-Schwinger equations. Approximations of the variational approach to the 3 + 1 dimensional theory are checked by comparison to the 1 + 1 dimensional case
New Hamiltonian constraint operator for loop quantum gravity
Directory of Open Access Journals (Sweden)
Jinsong Yang
2015-12-01
Full Text Available A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
Greenberger-Horne-Zeilinger States and Few-Body Hamiltonians
Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V.
2011-12-01
The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.
Homotopical Dynamics IV: Hopf invariants and hamiltonian flows
Cornea, Octavian
2001-01-01
In a non-compact context the first natural step in the search for periodic orbits of a hamiltonian flow is to detect bounded ones. In this paper we show that, in a non-compact setting, certain algebraic topological constraints imposed to a gradient flow of the hamiltonian function $f$ imply the existence of bounded orbits for the hamiltonian flow of $f$. Once the existence of bounded orbits is established, under favorable circumstances, application of the $C^{1}$-closing lemma leads to period...
New Hamiltonian constraint operator for loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Yang, Jinsong, E-mail: yangksong@gmail.com [Department of Physics, Guizhou university, Guiyang 550025 (China); Institute of Physics, Academia Sinica, Taiwan (China); Ma, Yongge, E-mail: mayg@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)
2015-12-17
A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
Remarks on Hamiltonian structures in G2-geometry
International Nuclear Information System (INIS)
Cho, Hyunjoo; Salur, Sema; Todd, A. J.
2013-01-01
In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry
Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen
2006-01-01
We apply the technique of Hamiltonian reduction for the construction of three-dimensional N=4 supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional N=4 supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparision with previous work is also carried out
The Hamiltonian structure of general relativistic perfect fluids
International Nuclear Information System (INIS)
Bao, D.; Houston Univ., TX; Marsden, J.; Walton, R.
1985-01-01
We show that the evolution equations for a perfect fluid coupled to general relativity in a general lapse and shift, are Hamiltonian relative to a certain Poisson structure. For the fluid variables, a Lie-Poisson structure associated to the dual of a semi-direct product Lie algebra is used, while the bracket for the gravitational variables has the usual canonical symplectic structure. The evolution is governed by a Hamiltonian which is equivalent to that obtained from a canonical analysis. The relationship of our Hamiltonian structure with other approaches in the literature, such as Clebsch potentials, Lagrangian to Eulerian transformations, and its use in clarifying linearization stability, are discussed. (orig.)
Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces
Jacob, Birgit
2012-01-01
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir
Toric codes and quantum doubles from two-body Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Brell, Courtney G; Bartlett, Stephen D; Doherty, Andrew C [Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney (Australia); Flammia, Steven T, E-mail: cbrell@physics.usyd.edu.au [Perimeter Institute for Theoretical Physics, Waterloo (Canada)
2011-05-15
We present here a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a projected entangled pair states (PEPS) description of the target models, and reproduces the target models' behavior using only couplings that are natural in terms of the original Hamiltonians. This allows our construction to capture the symmetries of the target models.
Greenberger-Horne-Zeilinger states and few-body Hamiltonians.
Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V
2011-12-23
The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.
Quantum bootstrapping via compressed quantum Hamiltonian learning
International Nuclear Information System (INIS)
Wiebe, Nathan; Granade, Christopher; Cory, D G
2015-01-01
A major problem facing the development of quantum computers or large scale quantum simulators is that general methods for characterizing and controlling are intractable. We provide a new approach to this problem that uses small quantum simulators to efficiently characterize and learn control models for larger devices. Our protocol achieves this by using Bayesian inference in concert with Lieb–Robinson bounds and interactive quantum learning methods to achieve compressed simulations for characterization. We also show that the Lieb–Robinson velocity is epistemic for our protocol, meaning that information propagates at a rate that depends on the uncertainty in the system Hamiltonian. We illustrate the efficiency of our bootstrapping protocol by showing numerically that an 8 qubit Ising model simulator can be used to calibrate and control a 50 qubit Ising simulator while using only about 750 kilobits of experimental data. Finally, we provide upper bounds for the Fisher information that show that the number of experiments needed to characterize a system rapidly diverges as the duration of the experiments used in the characterization shrinks, which motivates the use of methods such as ours that do not require short evolution times. (fast track communication)
Relativistic and separable classical hamiltonian particle dynamics
International Nuclear Information System (INIS)
Sazdjian, H.
1981-01-01
We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincare invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincare invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light
On singularities of lattice varieties
Mukherjee, Himadri
2013-01-01
Toric varieties associated with distributive lattices arise as a fibre of a flat degeneration of a Schubert variety in a minuscule. The singular locus of these varieties has been studied by various authors. In this article we prove that the number of diamonds incident on a lattice point $\\a$ in a product of chain lattices is more than or equal to the codimension of the lattice. Using this we also show that the lattice varieties associated with product of chain lattices is smooth.
STRUCTURAL EVOLUTION OF EARLY-TYPE GALAXIES TO z = 2.5 IN CANDELS
Energy Technology Data Exchange (ETDEWEB)
Chang, Yu-Yen; Van der Wel, Arjen; Rix, Hans-Walter [Max-Planck Institut fuer Astronomie, Koenigstuhl 17, D-69117 Heidelberg (Germany); Holden, Bradford; Faber, S. M.; Mozena, Mark; Guo Yicheng; Kocevski, Dale D. [UCO/Lick Observatory, Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064 (United States); Bell, Eric F. [Department of Astronomy, University of Michigan, 500 Church Street, Ann Arbor, MI 48109 (United States); McGrath, Elizabeth J. [Department of Physics and Astronomy, Colby College, Waterville, ME 04901 (United States); Wuyts, Stijn [Max-Planck-Institut fuer Extraterrestrische Physik, Postfach 1312, Giessenbachstr., D-85741 Garching (Germany); Haeussler, Boris [Schools of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom); Barden, Marco [Institute of Astro- and Particle Physics, University of Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria); Ferguson, Henry C.; Grogin, Norman A.; Koekemoer, Anton M.; Huang, Kuang-Han [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States); Galametz, Audrey [INAF-Osservatorio di Roma, Via Frascati 33, I-00040 Monteporzio (Italy); Dekel, Avishai [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel); Hathi, Nimish P., E-mail: chang@mpia.de [Observatories of the Carnegie Institution for Science, Pasadena, CA (United States); and others
2013-08-20
Projected axis ratio measurements of 880 early-type galaxies at redshifts 1 < z < 2.5 selected from CANDELS are used to reconstruct and model their intrinsic shapes. The sample is selected on the basis of multiple rest-frame colors to reflect low star-formation activity. We demonstrate that these galaxies as an ensemble are dust-poor and transparent and therefore likely have smooth light profiles, similar to visually classified early-type galaxies. Similar to their present-day counterparts, the z > 1 early-type galaxies show a variety of intrinsic shapes; even at a fixed mass, the projected axis ratio distributions cannot be explained by the random projection of a set of galaxies with very similar intrinsic shapes. However, a two-population model for the intrinsic shapes, consisting of a triaxial, fairly round population, combined with a flat (c/a {approx} 0.3) oblate population, adequately describes the projected axis ratio distributions of both present-day and z > 1 early-type galaxies. We find that the proportion of oblate versus triaxial galaxies depends both on the galaxies' stellar mass, and-at a given mass-on redshift. For present-day and z < 1 early-type galaxies the oblate fraction strongly depends on galaxy mass. At z > 1, this trend is much weaker over the mass range explored here (10{sup 10} < M{sub *}/M{sub Sun} < 10{sup 11}), because the oblate fraction among massive (M{sub *} {approx} 10{sup 11} M{sub Sun }) was much higher in the past: 0.59 {+-} 0.10 at z > 1, compared to 0.20 {+-} 0.02 at z {approx} 0.1. When combined with previous findings that the number density and sizes of early-type galaxies substantially increase over the same redshift range, this can be explained by the gradual emergence of merger-produced elliptical galaxies, at the expense of the destruction of pre-existing disks that were common among their high-redshift progenitors. In contrast, the oblate fraction among low-mass early-type galaxies (log (M{sub *}/M{sub Sun }) < 10
Search for the non-canonical Ising spin glass on rewired square lattices
Surungan, Tasrief
2018-03-01
A spin glass (SG) of non-canonical type is a purely antiferromagnetic (AF) system, exemplified by the AF Ising model on a scale free network (SFN), studied by Bartolozzi et al. [ Phys. Rev. B73, 224419 (2006)]. Frustration in this new type of SG is rendered by topological factor and its randomness is caused by random connectivity. As an SFN corresponds to a large dimensional lattice, finding non-canonical SG in lattice with physical dimension is desireable. However, a regular lattice can not have random connectivity. In order to obtain lattices with random connection and preserving the notion of finite dimension, we costructed rewired lattices. We added some extra bonds randomly connecting each site of a regular lattice to its next-nearest neighbors. Very recently, Surungan et al., studied AF Heisenberg system on rewired square lattice and found no SG behavior [AIP Conf. Proc. 1719, 030006 (2016)]. Due to the importance of discrete symmetry for phase transition, here we study similar structure for the Ising model (Z 2 symmetry). We used Monte Carlo simulation with Replica Exchange algorithm. Two types of structures were studied, firstly, the rewired square lattices with one extra bonds added to each site, and secondly, two bonds added to each site. We calculated the Edwards-Anderson paremeter, the commonly used parameter in searching for SG phase. The non-canonical SG is clearly observed in the rewired square lattice with two extra bonds added.
Gauge-Higgs Unification Models in Six Dimensions with S2/Z2 Extra Space and GUT Gauge Symmetry
Directory of Open Access Journals (Sweden)
Cheng-Wei Chiang
2012-01-01
Full Text Available We review gauge-Higgs unification models based on gauge theories defined on six-dimensional spacetime with S2/Z2 topology in the extra spatial dimensions. Nontrivial boundary conditions are imposed on the extra S2/Z2 space. This review considers two scenarios for constructing a four-dimensional theory from the six-dimensional model. One scheme utilizes the SO(12 gauge symmetry with a special symmetry condition imposed on the gauge field, whereas the other employs the E6 gauge symmetry without requiring the additional symmetry condition. Both models lead to a standard model-like gauge theory with the SU(3×SU(2L×U(1Y(×U(12 symmetry and SM fermions in four dimensions. The Higgs sector of the model is also analyzed. The electroweak symmetry breaking can be realized, and the weak gauge boson and Higgs boson masses are obtained.
A quadruple quasar coincident with a giant Ly-alpha nebula and a protocluster at z=2
Vignali, Cristian
2016-09-01
We propose to observe the only known quadruple AGN system in the Universe, embedded in a giant Ly-alpha nebula at z 2. These active nuclei and the large number of Ly-alpha emitting galaxies at the same redshift are clear indications that this is one of the most overdense protoclusters known z 2. We request a 140 ks Chandra exposure to (a) define the basic X-ray properties of all the AGN and then their bolometric luminosities and Eddington ratios, and compare these with those of "isolated" quasars at similar redshifts/luminosities; (b) detect the hot gas emission in the protocluster. Chandra is unique for this investigation: the close (few arcsec) distance of some of the AGN needs high spatial resolution, and the extended emission requires low background contribution.
Cavity assisted measurements of heat and work in optical lattices
Directory of Open Access Journals (Sweden)
Louis Villa
2018-01-01
Full Text Available We propose a method to experimentally measure the internal energy of a system of ultracold atoms trapped in optical lattices by coupling them to the fields of two optical cavities. We show that the tunnelling and self-interaction terms of the one-dimensional Bose-Hubbard Hamiltonian can be mapped to the field and photon number of each cavity, respectively. We compare the energy estimated using this method with numerical results obtained using the density matrix renormalisation group algorithm. Our method can be employed for the assessment of power and efficiency of thermal machines whose working substance is a strongly correlated many-body system.
Strongly correlated Fermi-Bose mixtures in disordered optical lattices
International Nuclear Information System (INIS)
Sanchez-Palencia, L; Ahufinger, V; Kantian, A; Zakrzewski, J; Sanpera, A; Lewenstein, M
2006-01-01
We investigate theoretically the low-temperature physics of a two-component ultracold mixture of bosons and fermions in disordered optical lattices. We focus on the strongly correlated regime. We show that, under specific conditions, composite fermions, made of one fermion plus one bosonic hole, form. The composite picture is used to derive an effective Hamiltonian whose parameters can be controlled via the boson-boson and the boson-fermion interactions, the tunnelling terms and the inhomogeneities. We finally investigate the quantum phase diagram of the composite fermions and show that it corresponds to the formation of Fermi glasses, spin glasses and quantum percolation regimes
Lattice field theories: non-perturbative methods of analysis
International Nuclear Information System (INIS)
Weinstein, M.
1978-01-01
A lecture is given on the possible extraction of interesting physical information from quantum field theories by studying their semiclassical versions. From the beginning the problem of solving for the spectrum states of any given continuum quantum field theory is considered as a giant Schroedinger problem, and then some nonperturbative methods for diagonalizing the Hamiltonian of the theory are explained without recourse to semiclassical approximations. The notion of a lattice appears as an artifice to handle the problems associated with the familiar infrared and ultraviolet divergences of continuum quantum field theory and in fact for all but gauge theories. 18 references
Strongly correlated Fermi-Bose mixtures in disordered optical lattices
Energy Technology Data Exchange (ETDEWEB)
Sanchez-Palencia, L [Laboratoire Charles Fabry de l' Institut d' Optique, CNRS and Universite Paris-Sud XI, Bat 503, Centre scientifique, F-91403 Orsay Cedex (France); Ahufinger, V [ICREA and Grup d' optica, Departament de FIsica, Universitat Autonoma de Barcelona, E-08193 Belaterra (Barcelona) (Spain); Kantian, A [Institut fuer Theoretische Physik, Universitaet Innsbruck, A-6020 Innsbruck (Austria); Zakrzewski, J [Instytut Fizyki imienia Mariana Smoluchowskiego i Centrum Badan Ukladow Zlozonych imienia Marka Kaca, Uniwersytet Jagiellonski, ulica Reymonta 4, PL-30-059 Krakow (Poland); Sanpera, A [ICREA and Grup de FIsica Teorica, Departament de FIsica, Universitat Autonoma de Barcelona, E-08193 Belaterra (Barcelona) (Spain); Lewenstein, M [ICREA and ICFO-Institut de Ciencies Fotoniques, Parc Mediterrani de la TecnologIa, E-08860 Castelldefels (Barcelona) (Spain); Institut fuer Theoretische Physik, Universitaet Hannover, D-30167 Hannover (Germany)
2006-05-28
We investigate theoretically the low-temperature physics of a two-component ultracold mixture of bosons and fermions in disordered optical lattices. We focus on the strongly correlated regime. We show that, under specific conditions, composite fermions, made of one fermion plus one bosonic hole, form. The composite picture is used to derive an effective Hamiltonian whose parameters can be controlled via the boson-boson and the boson-fermion interactions, the tunnelling terms and the inhomogeneities. We finally investigate the quantum phase diagram of the composite fermions and show that it corresponds to the formation of Fermi glasses, spin glasses and quantum percolation regimes.
International Nuclear Information System (INIS)
Nauchi, Yasushi; Kameyama, Takanori
2003-01-01
Criticality analysis has been performed for dozens of tank type cores in which fuel lattices are loaded vertically and partially immersed in light water. The reactivity effect of dry part of lattices stuck above the critical water level has been calculated using the continuous energy Monte Carlo method. The reactivity effect exceeds 0.8% both for MOX and UOX fuel lattices of large buckling (B z 2 > 0.0025 cm -2 ). It is evaluated that at least 20 cm length of fuel rods above the critical water level has significant reactivity effect. (author)
g Algebra and two-dimensional quasiexactly solvable Hamiltonian ...
Indian Academy of Sciences (India)
Keywords. g2 algebra; quasiexactly solvable Hamiltonian; hidden algebra; Poschl–Teller potential. ... space of the polynomials, restricting to a linear transformation on this space, the associ- .... The operators L6 and L7 are the positive root.
Integrable Hamiltonian systems and interactions through quadratic constraints
International Nuclear Information System (INIS)
Pohlmeyer, K.
1975-08-01
Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de
Towards practical characterization of quantum systems with quantum Hamiltonian learning
Santagati, R.; Wang, J.; Paesani, S.; Knauer, S.; Gentile, A. A.; Wiebe, N.; Petruzzella, M.; O'Brien, J. L.; Rarity, J. G.; Laing, A.; Thompson, M. G.
2017-01-01
Here we show the first experimental implementation of quantum Hamiltonian Learning, where a silicon-on-insulator quantum photonic simulator is used to learn the dynamics of an electron-spin in an NV center in diamond.
On the quantization of sectorially Hamiltonian dissipative systems
Energy Technology Data Exchange (ETDEWEB)
Castagnino, M. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Instituto de Astronomia y Fisica del Espacio, Casilla de Correos 67, Sucursal 28, 1428 Buenos Aires (Argentina); Gadella, M. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Departamento de Fisica Teorica, Atomica y Optica, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid (Spain)], E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Instituto de Fisica de Rosario, 2000 Rosario (Argentina); Facultad Regional Rosario, UTN, 2000 Rosario (Argentina)
2009-10-15
We present a theoretical discussion showing that, although some dissipative systems may have a sectorial Hamiltonian description, this description does not allow for canonical quantization. However, a quantum Liouville counterpart of these systems is possible, although it is not unique.
On the quantization of sectorially Hamiltonian dissipative systems
International Nuclear Information System (INIS)
Castagnino, M.; Gadella, M.; Lara, L.P.
2009-01-01
We present a theoretical discussion showing that, although some dissipative systems may have a sectorial Hamiltonian description, this description does not allow for canonical quantization. However, a quantum Liouville counterpart of these systems is possible, although it is not unique.
Hamiltonian formalisms and symmetries of the Pais–Uhlenbeck oscillator
Directory of Open Access Journals (Sweden)
Krzysztof Andrzejewski
2014-12-01
Full Text Available The study of the symmetry of Pais–Uhlenbeck oscillator initiated in Andrzejewski et al. (2014 [24] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck Hamiltonian approach as well as the canonical transformation to the Ostrogradski Hamiltonian framework are derived. The resulting algebra of generators appears to be the central extension of the one obtained on the Lagrangian level; in particular, in the case of odd frequencies one obtains the centrally extended l-conformal Newton–Hooke algebra. In this important case the canonical transformation to an alternative Hamiltonian formalism (related to the free higher derivatives theory is constructed. It is shown that all generators can be expressed in terms of the ones for the free theory and the result agrees with that obtained by the orbit method.
Experimental Hamiltonian identification for controlled two-level systems
International Nuclear Information System (INIS)
Schirmer, S.G.; Kolli, A.; Oi, D.K.L.
2004-01-01
We present a strategy to empirically determine the internal and control Hamiltonians for an unknown two-level system (black box) subject to various (piecewise constant) control fields when direct readout by measurement is limited to a single, fixed observable
A local inverse spectral theorem for Hamiltonian systems
International Nuclear Information System (INIS)
Langer, Matthias; Woracek, Harald
2011-01-01
We consider (2 × 2)-Hamiltonian systems of the form y'(x) = zJH(x)y(x), x in [s − , s + ). If a system of this form is in the limit point case, an analytic function is associated with it, namely its Titchmarsh–Weyl coefficient q H . The (global) uniqueness theorem due to de Branges says that the Hamiltonian H is (up to reparameterization) uniquely determined by the function q H . In this paper we give a local uniqueness theorem; if the Titchmarsh–Weyl coefficients q H 1 and q H 2 corresponding to two Hamiltonian systems are exponentially close, then the Hamiltonians H 1 and H 2 coincide (up to reparameterization) up to a certain point of their domain, which depends on the quantitative degree of exponential closeness of the Titchmarsh–Weyl coefficients
Hamiltonian Approach to 2+1 Dimensional Gravity
Cantini, L.; Menotti, P.; Seminara, D.
2002-12-01
It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge has hamiltonian form. We give the exact diffeomorphism which transforms the spinning cone metric in the Deser, Jackiw, 't Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the hamiltonian for the reduced particle dynamics. The quantum mechanical translation of the two particle hamiltonian gives rise to the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit is given by the total energy of the system irrespective of the masses of the particles thus proving at the quantum level a conjecture by 't Hooft on the two particle dynamics.
Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians
Bringewatt, Jacob; Dorland, William; Jordan, Stephen P.; Mink, Alan
2018-02-01
Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k -SAT problems, use k -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.
Matrix product states for lattice field theories
Energy Technology Data Exchange (ETDEWEB)
Banuls, M.C.; Cirac, J.I. [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Saito, H. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Tsukuba Univ., Ibaraki (Japan). Graduate School of Pure and Applied Sciences
2013-10-15
The term Tensor Network States (TNS) refers to a number of families of states that represent different ansaetze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case of TNS, and have become the most precise tool for the numerical study of one dimensional quantum many-body systems, as the basis of the Density Matrix Renormalization Group method. Lattice Gauge Theories (LGT), in their Hamiltonian version, offer a challenging scenario for these techniques. While the dimensions and sizes of the systems amenable to TNS studies are still far from those achievable by 4-dimensional LGT tools, Tensor Networks can be readily used for problems which more standard techniques, such as Markov chain Monte Carlo simulations, cannot easily tackle. Examples of such problems are the presence of a chemical potential or out-of-equilibrium dynamics. We have explored the performance of Matrix Product States in the case of the Schwinger model, as a widely used testbench for lattice techniques. Using finite-size, open boundary MPS, we are able to determine the low energy states of the model in a fully non-perturbativemanner. The precision achieved by the method allows for accurate finite size and continuum limit extrapolations of the ground state energy, but also of the chiral condensate and the mass gaps, thus showing the feasibility of these techniques for gauge theory problems.
Squeezed Dirac and Topological Magnons in a Bosonic Honeycomb Optical Lattice.
Owerre, Solomon; Nsofini, Joachim
2017-09-20
Quantum information storage using charge-neutral quasiparticles are expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-$1/2$ XYZ Heisenberg model on the honeycomb lattice with discrete Z$_2$ symmetry and a Dzyaloshinskii-Moriya interaction. We show that the squeezed magnons can be controlled by the Z$_2$ anisotropy and demonstrate how the noise in the system is periodically modified in the ferromagnetic and antiferromagnetic phases of the model. Our results also apply to solid-state honeycomb (anti)ferromagnetic insulators. . © 2017 IOP Publishing Ltd.
Squeezed Dirac and topological magnons in a bosonic honeycomb optical lattice
Owerre, S. A.; Nsofini, J.
2017-11-01
Quantum information storage using charge-neutral quasiparticles is expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-1/2 XYZ Heisenberg model on the honeycomb lattice with discrete Z2 symmetry and a Dzyaloshinskii-Moriya interaction. We show that the squeezed magnons can be controlled by the Z2 anisotropy and demonstrate how the noise in the system is periodically modified in the ferromagnetic and antiferromagnetic phases of the model. Our results also apply to solid-state honeycomb (anti)ferromagnetic insulators.