Matrix elements of Lorentzian Hamiltonian constraint in loop quantum gravity
Alesci, Emanuele; Liegener, Klaus; Zipfel, Antonia
2013-10-01
The Hamiltonian constraint is the key element of the canonical formulation of loop quantum gravity (LQG) coding its dynamics. In Ashtekar-Barbero variables it naturally splits into the so-called Euclidean and Lorentzian parts. However, due to the high complexity of this operator, only the matrix elements of the Euclidean part have been considered so far. Here we evaluate the action of the full constraint, including the Lorentzian part. The computation requires heavy use of SU(2) recoupling theory and several tricky identities among n-j symbols are used to find the final result: these identities, together with the graphical calculus used to derive them, also simplify the Euclidean constraint and are of general interest in LQG computations.
How random are matrix elements of the nuclear shell model Hamiltonian?
无
2009-01-01
In this paper we study the general behavior of matrix elements of the nuclear shell model Hamiltonian.We find that nonzero off-diagonal elements exhibit a regular pattern,if one sorts the diagonal matrix elements from smaller to larger values.The correlation between eigenvalues and diagonal matrix elements for the shell model Hamiltonian is more remarkable than that for random matrices with the same distribution unless the dimension is small.
How random are matrix elements of the nuclear shell model Hamiltonian?
SHEN JiaJie; ZHAO YuMing
2009-01-01
In this paper we study the general behavior of matrix elements of the nuclear shell model Hamiltonlan.We find that nonzero off-diagonal elements exhibit a regular pattern,if one sorts the diagonal matrix elements from smaller to larger values.The correlation between eigenvalues and diagonal matrix elements for the shell model Hamiltonian is more remarkable than that for random matrices with the same distribution unless the dimension is small.
Efficient computation of Hamiltonian matrix elements between non-orthogonal Slater determinants
Utsuno, Yutaka; Otsuka, Takaharu; Abe, Takashi
2012-01-01
We present an efficient numerical method for computing Hamiltonian matrix elements between non-orthogonal Slater determinants, focusing on the most time-consuming component of the calculation that involves a sparse array. In the usual case where many matrix elements should be calculated, this computation can be transformed into a multiplication of dense matrices. It is demonstrated that the present method based on the matrix-matrix multiplication attains $\\sim$80\\% of the theoretical peak performance measured on systems equipped with modern microprocessors, a factor of 5-10 better than the normal method using indirectly indexed arrays to treat a sparse array. The reason for such different performances is discussed from the viewpoint of memory access.
Jankiewicz, Justyna
2004-01-01
We study the properties of time evolution of the $K^{0}-\\bar{K}^{0} $ system in spectral formulation. Within the one--pole model we find the exact form of the diagonal matrix elements of the effective Hamiltonian for this system. It appears that, contrary to the Lee--Oehme--Yang (LOY) result, these exact diagonal matrix elements are different if the total system is CPT--invariant but CP--noninvariant.
Minimal Realizations of Supersymmetry for Matrix Hamiltonians
Andrianov, Alexandr A
2014-01-01
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant symmetry matrix for a matrix Hamiltonian are presented. A method of constructing of a matrix Hamiltonian with a given constant symmetry matrix in terms of a set of arbitrary scalar functions and eigen- and associated vectors of this matrix is offered. Examples of constructing of $2\\times2$ matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated.
Minimal realizations of supersymmetry for matrix Hamiltonians
Andrianov, Alexander A., E-mail: andrianov@icc.ub.edu; Sokolov, Andrey V., E-mail: avs_avs@rambler.ru
2015-02-06
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant symmetry matrix for a matrix Hamiltonian are presented. A method of constructing of a matrix Hamiltonian with a given constant symmetry matrix in terms of a set of arbitrary scalar functions and eigen- and associated vectors of this matrix is offered. Examples of constructing of 2×2 matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated. - Highlights: • Weak and strong minimization of a matrix intertwining operator. • Criterion of strong minimizability from the right of a matrix intertwining operator. • Conditions of existence of a constant symmetry matrix for a matrix Hamiltonian. • Method of constructing of a matrix Hamiltonian with a given constant symmetry matrix. • Examples of constructing of 2×2 matrix Hamiltonians with a given symmetry matrix.
PLANE INFINITE ANALYTICAL ELEMENT AND HAMILTONIAN SYSTEM
孙雁; 周钢; 刘正兴
2003-01-01
It is not convenient to solve those engineering problems defined in an infinitefield by using FEM. An infinite area can be divided into a regular infinite external area anda finite internal area. The finite internal area was dealt with by the FEM and the regularinfinite external area was settled in a polar coordinate. All governing equations weretransformed into the Hamiltonian system. The methods of variable separation andeigenfunction expansion were used to derive the stiffness matrix of a new infinite analyticalelement. This new element, like a super finite element, can be combined with commonlyused finite elements. The proposed method was verified by numerical case studies. Theresults show that the preparation work is very simple, the infinite analytical element has ahigh precision, and it can be used conveniently. The method can also be easily extended to a three-dimensional problem.
Effective Hamiltonian and unitarity of the S matrix.
Rotter, I
2003-07-01
The properties of open quantum systems are described well by an effective Hamiltonian H that consists of two parts: the Hamiltonian H of the closed system with discrete eigenstates and the coupling matrix W between discrete states and continuum. The eigenvalues of H determine the poles of the S matrix. The coupling matrix elements W(cc')(k) between the eigenstates k of H and the continuum may be very different from the coupling matrix elements W(cc')(k) between the eigenstates of H and the continuum. Due to the unitarity of the S matrix, the W(cc')(k) depend on energy in a nontrivial manner. This conflicts with the assumptions of some approaches to reactions in the overlapping regime. Explicit expressions for the wave functions of the resonance states and for their phases in the neighborhood of, respectively, avoided level crossings in the complex plane and double poles of the S matrix are given.
Continuous finite element methods for Hamiltonian systems
无
2007-01-01
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudosymplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory.
Perturbation Theory for Parent Hamiltonians of Matrix Product States
Szehr, Oleg; Wolf, Michael M.
2015-05-01
This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by Yarotsky that develops a perturbation theory for relatively bounded quantum perturbations of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltonian of a Matrix product state into a classical Hamiltonian plus some perturbation. We can thus extend Yarotsky's results to provide a perturbation theory for parent Hamiltonians of Matrix product states and recover some of the findings of the independent contributions (Cirac et al in Phys Rev B 8(11):115108, 2013) and (Michalakis and Pytel in Comm Math Phys 322(2):277-302, 2013).
Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar
2016-06-15
We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators are useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.
Matrix factorization method for the Hamiltonian structure of integrable systems
S Ghosh; B Talukdar; S Chakraborti
2003-07-01
We demonstrate that the process of matrix factorization provides a systematic mathematical method to investigate the Hamiltonian structure of non-linear evolution equations characterized by hereditary operators with Nijenhuis property.
Spectrum of an Elliptic Free Fermionic Corner Transfer Matrix Hamiltonian
Cuerno, R
1993-01-01
The eigenvalues of the Corner Transfer Matrix Hamiltonian associated to the elliptic $R$ matrix of the eight vertex free fermion model are computed in the anisotropic case for magnetic field smaller than the critical value. An argument based on generating functions is given, and the results are checked numerically. The spectrum consists of equally spaced levels.
Diagonal representation for a generic matrix valued quantum Hamiltonian
Gosselin, Pierre [Universite Grenoble I, Institut Fourier, UMR 5582 CNRS-UJF UFR de Mathematiques, BP74, Saint Martin d' Heres Cedex (France); Mohrbach, Herve [Universite Paul Verlaine-Metz, Laboratoire de Physique Moleculaire et des Collisions, ICPMB-FR CNRS 2843, Metz Cedex 3 (France)
2009-12-15
A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a running variable are introduced. This method leads to a formal compact expression for the diagonal Hamiltonian which can be expanded in a power series of the Planck constant. In particular, we provide an explicit expression for the diagonal representation of a generic Hamiltonian to the second order in the Planck constant. This result is applied, as a physical illustration, to Dirac electrons and neutrinos in external fields. (orig.)
Distribution of matrix elements of random operators
Hussein, M S
1999-01-01
It is shown that an operator can be defined in the abstract space of random matrices ensembles whose matrix elements statistical distribution simulates the behavior of the distribution found in real physical systems. It is found that the key quantity that determines these distribution is the commutator of the operator with the Hamiltonian. Application to symmetry breaking in quantum many-body systems is discussed.
Hamiltonian and Lagrangian Dynamical Matrix Approaches Applied to Magnetic Nanostructures
Roberto Zivieri
2012-01-01
Full Text Available Two micromagnetic tools to study the spin dynamics are reviewed. Both approaches are based upon the so-called dynamical matrix method, a hybrid micromagnetic framework used to investigate the spin-wave normal modes of confined magnetic systems. The approach which was formulated first is the Hamiltonian-based dynamical matrix method. This method, used to investigate dynamic magnetic properties of conservative systems, was originally developed for studying spin excitations in isolated magnetic nanoparticles and it has been recently generalized to study the dynamics of periodic magnetic nanoparticles. The other one, the Lagrangian-based dynamical matrix method, was formulated as an extension of the previous one in order to include also dissipative effects. Such dissipative phenomena are associated not only to intrinsic but also to extrinsic damping caused by injection of a spin current in the form of spin-transfer torque. This method is very accurate in identifying spin modes that become unstable under the action of a spin current. The analytical development of the system of the linearized equations of motion leads to a complex generalized Hermitian eigenvalue problem in the Hamiltonian dynamical matrix method and to a non-Hermitian one in the Lagrangian approach. In both cases, such systems have to be solved numerically.
Scattering matrix of arbitrary tight-binding Hamiltonians
Ramírez, C.; Medina-Amayo, L. A.
2017-03-01
A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kinds of fundamental structures is given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.
Matrix product states for Hamiltonian lattice gauge theories
Buyens, Boye; Haegeman, Jutho; Verstraete, Frank
2014-01-01
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional systems. In [1] we considered the MPS formalism for the simulation of the Hamiltonian lattice gauge formulation of 1+1 dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model. We deduced the ground state and lowest lying excitations. Furthermore, we performed a full quantum real-time simulation for a quench with a uniform background electric field. In this proceeding we continue our work on the Schwinger model. We demonstrate the advantage of working with gauge invariant MPS by comparing with MPS simulations on the full Hilbert space, that includes numerous non-physical gauge variant states. Furthermore, we compute the chiral condensate and recover the predicted UV-divergent behavior.
Matrix elements of unstable states
Bernard, V; Meißner, U -G; Rusetsky, A
2012-01-01
Using the language of non-relativistic effective Lagrangians, we formulate a systematic framework for the calculation of resonance matrix elements in lattice QCD. The generalization of the L\\"uscher-Lellouch formula for these matrix elements is derived. We further discuss in detail the procedure of the analytic continuation of the resonance matrix elements into the complex energy plane and investigate the infinite-volume limit.
Matrix Elements for Hylleraas CI
Harris, Frank E.
The limitation to at most a single interelectron distance in individual configurations of a Hylleraas-type multiconfiguration wave function restricts significantly the types of integrals occurring in matrix elements for energy calculations, but even then if the formulation is not handled efficiently the angular parts of these integrals escalate to create expressions of great complexity. This presentation reviews ways in which the angular-momentum calculus can be employed to systematize and simplify the matrix element formulas, particularly those for the kinetic-energy matrix elements.
A weak Hamiltonian finite element method for optimal control problems
Hodges, Dewey H.; Bless, Robert R.
1990-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Weak Hamiltonian finite element method for optimal control problems
Hodges, Dewey H.; Bless, Robert R.
1991-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
(Anti-Hermitian Generalized (Anti-Hamiltonian Solution to a System of Matrix Equations
Juan Yu
2014-01-01
Full Text Available We mainly solve three problems. Firstly, by the decomposition of the (anti-Hermitian generalized (anti-Hamiltonian matrices, the necessary and sufficient conditions for the existence of and the expression for the (anti-Hermitian generalized (anti-Hamiltonian solutions to the system of matrix equations AX=B,XC=D are derived, respectively. Secondly, the optimal approximation solution minX∈K∥X^-X∥ is obtained, where K is the (anti-Hermitian generalized (anti-Hamiltonian solution set of the above system and X^ is the given matrix. Thirdly, the least squares (anti-Hermitian generalized (anti-Hamiltonian solutions are considered. In addition, algorithms about computing the least squares (anti-Hermitian generalized (anti-Hamiltonian solution and the corresponding numerical examples are presented.
(Anti-)Hermitian Generalized (Anti-)Hamiltonian Solution to a System of Matrix Equations
Juan Yu; Qing-Wen Wang; Chang-Zhou Dong
2014-01-01
We mainly solve three problems. Firstly, by the decomposition of the (anti-)Hermitian generalized (anti-)Hamiltonian matrices, the necessary and sufficient conditions for the existence of and the expression for the (anti-)Hermitian generalized (anti-)Hamiltonian solutions to the system of matrix equations AX=B,XC=D are derived, respectively. Secondly, the optimal approximation solution minX∈K∥X^-X∥ is obtained, where K is the (anti-)Hermitian generalized (anti-)Hamiltonian solution set of t...
The matrix Hamiltonian for hadrons and the role of negative-energy components
Simonov, Yu. A.
2004-01-01
The world-line (Fock-Feynman-Schwinger) representation is used for quarks in arbitrary (vacuum and valence gluon) field to construct the relativistic Hamiltonian. After averaging the Green's function of the white $q\\bar q$ system over gluon fields one obtains the relativistic Hamiltonian, which is matrix in spin indices and contains both positive and negative quark energies. The role of the latter is studied in the example of the heavy-light meson and the standard einbein technic is extended ...
Strong Linear Correlation Between Eigenvalues and Diagonal Matrix Elements
Shen, J J; Zhao, Y M; Yoshinaga, N
2008-01-01
We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. We find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the smaller values to larger ones. By using this linear correlation we are able to predict reasonably all eigenvalues of given shell model Hamiltonian without complicated iterations.
Compression of Hamiltonian matrix: Application to spin-1/2 Heisenberg square lattice
Seongsoo Choi
2016-09-01
Full Text Available We introduce a simple algorithm providing a compressed representation (∈ℝNorbits×Norbits×ℕNorbits of an irreducible Hamiltonian matrix (number of magnons M constrained, dimension: Nspins!M!(Nspins−M!>Norbits of the spin-1/2 Heisenberg antiferromagnet on the L×L non-periodic lattice, not looking for a good basis. As L increases, the ratio of the matrix dimension to Norbits converges to 8 (order of the symmetry group of square for the exact ground state computation. The sparsity of the Hamiltonian is retained in the compressed representation. Thus, the computational time and memory consumptions are reduced in proportion to the ratio.
Collective potential for large N hamiltonian matrix models and free Fisher information
Agarwal, A; Krishnaswami, G S; Rajeev, S G
2003-01-01
We formulate the planar `large N limit' of matrix models with a continuously infinite number of matrices directly in terms of U(N) invariant variables.good language to describe this formulation. The change of variables frommatrix elements to invariants induces an extra term in the hamiltonian,which is crucual in determining the ground state. We find that this collective potential has a natural meaning in terms of non-commutative probability theory:it is the `free Fisher information' discovered by Voiculescu. This formulation allows us to find a variational principle for the classical theory described by such large N limits. We then use the variational principle to study models more complex than the one describing the quantum mechanics of a single hermitian matrix (i.e., go beyond the so called D=1 barrier). We carry out approximate variational calculations for a few models and find excellent agreement with known results where such comparisons are possible. We also discover a lower bound for the ground state b...
Derivation of R-matrix from local Hamiltonian density
Bibikov, P N
2000-01-01
A computer algebra algoritm for solving the quantum Yang-Baxter equation is presented. It is based on the Taylor expansion of R-matrix which is developed up to the order \\lambda^6. As an example the classification of 4x4 R-matrices is given.
Analytic matrix elements with shifted correlated Gaussians
Fedorov, D. V.
2017-01-01
Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.......Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics....
Localization in band random matrix models with and without increasing diagonal elements.
Wang, Wen-ge
2002-06-01
It is shown that localization of eigenfunctions in the Wigner band random matrix model with increasing diagonal elements can be related to localization in a band random matrix model with random diagonal elements. The relation is obtained by making use of a result of a generalization of Brillouin-Wigner perturbation theory, which shows that reduced Hamiltonian matrices with relatively small dimensions can be introduced for nonperturbative parts of eigenfunctions, and by employing intermediate basis states, which can improve the method of the reduced Hamiltonian matrix. The latter model deviates from the standard band random matrix model mainly in two aspects: (i) the root mean square of diagonal elements is larger than that of off-diagonal elements within the band, and (ii) statistical distributions of the matrix elements are close to the Lévy distribution in their central parts, except in the high top regions.
Hamiltonian Systems and Darboux Transformation Associated with a 3 × 3 Matrix Spectral Problem
无
2007-01-01
Starting from a 3 × 3 matrix spectral problem, we derive a hierarchy of nonlinear equations. It is shown that the hierarchy possesses bi-Hamiltonian structure. Under the symmetry constraints between the potentials and the eigenfunctions, Lax pair and adjoint Lax pairs including partial part and temporal part are nonlinearied into two finitedimensional Hamiltonian systems (FDHS) in Liouville sense. Moreover, an explicit N-fold Darboux transformation for CDNS equation is constructed with the help of a gauge transformation of the spectral problem.
Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions.
Changlani, Hitesh J; Zheng, Huihuo; Wagner, Lucas K
2015-09-14
We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U(∗)/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.
An efficient matrix product operator representation of the quantum chemical Hamiltonian
Keller, Sebastian, E-mail: sebastian.keller@phys.chem.ethz.ch; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch [ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich (Switzerland); Dolfi, Michele, E-mail: dolfim@phys.ethz.ch; Troyer, Matthias, E-mail: troyer@phys.ethz.ch [ETH Zürich, Institute of Theoretical Physics, Wolfgang-Pauli-Strasse 27, 8093 Zürich (Switzerland)
2015-12-28
We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from the point of view of Hilbert space decimation and attained higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states, where operators are correspondingly represented as matrix product operators (MPOs). The MPO construction scheme presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach, for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries — abelian and non-abelian — and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.
Yu, Xiongjie; Pekker, David; Clark, Bryan K.
2017-01-01
A key property of many-body localized Hamiltonians is the area law entanglement of even highly excited eigenstates. Matrix product states (MPS) can be used to efficiently represent low entanglement (area law) wave functions in one dimension. An important application of MPS is the widely used density matrix renormalization group (DMRG) algorithm for finding ground states of one-dimensional Hamiltonians. Here, we develop two algorithms, the shift-and-invert MPS (SIMPS) and excited state DMRG which find highly excited eigenstates of many-body localized Hamiltonians. Excited state DMRG uses a modified sweeping procedure to identify eigenstates, whereas SIMPS applies the inverse of the shifted Hamiltonian to a MPS multiple times to project out the targeted eigenstate. To demonstrate the power of these methods, we verify the breakdown of the eigenstate thermalization hypothesis in the many-body localized phase of the random field Heisenberg model, show the saturation of entanglement in the many-body localized phase, and generate local excitations.
Compression of Hamiltonian matrix: Application to spin-1/2 Heisenberg square lattice
Choi, Seongsoo; Kim, Woohyun; Kim, Jongho
2016-09-01
We introduce a simple algorithm providing a compressed representation (∈ℝNorbits×Norbits×ℕNorbits ) of an irreducible Hamiltonian matrix (number of magnons M constrained, dimension: N/spins!M ! (N spins-M ) ! >Norbits ) of the spin-1/2 Heisenberg antiferromagnet on the L ×L non-periodic lattice, not looking for a good basis. As L increases, the ratio of the matrix dimension to Norbits converges to 8 (order of the symmetry group of square) for the exact ground state computation. The sparsity of the Hamiltonian is retained in the compressed representation. Thus, the computational time and memory consumptions are reduced in proportion to the ratio.
Varga, K
1997-01-01
We present a computer code that analytically evaluates the matrix elements of the microscopic nuclear Hamiltonian and unity operator between Slater determinants of displaced gaussian single particle orbits. Such matrix elements appear in the generator coordinate model and the resonating group model versions of the microscopic multicluster calculations.
Gilles Regniers
2009-11-01
Full Text Available In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian describing such a system has been done in the canonical case. In this paper, we take a more general approach and look at the system as a Wigner quantum system. Hereby, one does not assume the canonical commutation relations, but instead one just requires the compatibility between the Hamilton and Heisenberg equations. Solutions of this problem are related to the Lie superalgebras gl(1|n and osp(1|2n. We determine the spectrum of the considered Hamiltonian in specific representations of these Lie superalgebras and discuss the results in detail. We also make the connection with the well-known canonical case.
Classical R-matrix theory for bi-Hamiltonian field systems
Blaszak, Maciej [Department of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznan (Poland); Szablikowski, Blazej M [Department of Mathematics, University of Glasgow, Glasgow G12 8QW (United Kingdom)], E-mail: blaszakm@amu.edu.pl, E-mail: b.szablikowski@maths.gla.ac.uk
2009-10-09
This is a survey of the application of the classical R-matrix formalism to the construction of infinite-dimensional integrable Hamiltonian field systems. The main point is the study of bi-Hamiltonian structures. Appropriate constructions on Poisson, noncommutative and loop algebras as well as the central extension procedure are presented. The theory is developed for (1 + 1)- and (2 + 1)-dimensional field and lattice soliton systems as well as hydrodynamic systems. The formalism presented contains sufficiently many proofs and important details to make it self-contained and complete. The general theory is applied to several infinite-dimensional Lie algebras in order to construct both dispersionless and dispersive (soliton) integrable field systems.
Structure of Hamiltonian Matrix and the Shape of Eigenfunctions: Nuclear Octupole Deformation Model
XING Yong-Zhong; LI Jun-Qing; LIU Fang; ZUO Wei
2002-01-01
The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformationmodel, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstates ofa quantum integrable system is studied with the help ofgeneralized Brillouin-Wigner pcrturbation theory. The resultsshow that a significant randomness in this distribution can be observed when its classical counterpart is under the strongchaotic condition. The averaged shape of the eigenfunctions fits with the Gaussian distribution only when the effects ofthe symmetry have been removed.
Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions
Changlani, Hitesh J.; Zheng, Huihuo; Wagner, Lucas K. [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green St., Urbana, Illinois 61801 (United States)
2015-09-14
We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U{sup ∗}/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.
Vogl, M.; Pankratov, O.; Shallcross, S.
2017-07-01
We present a tractable and physically transparent semiclassical theory of matrix-valued Hamiltonians, i.e., those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a n ×n dimensional Hamiltonian H (p ̂,q ̂) . The classical dynamics is governed by n Hamilton-Jacobi (HJ) equations that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of H (p ,q ) ; these vectors describe the internal structure of the semiclassical particles. At the O (ℏ1) level and for nondegenerate HJ systems, this curvature results in an additional semiclassical phase composed of (i) a Berry phase and (ii) a dynamical phase resulting from the classical particles "moving through the Berry curvature". We show that the dynamical part of this semiclassical phase will, generally, be zero only for the case in which the Berry phase is topological (i.e., depends only on the winding number). We illustrate the method by calculating the Landau spectrum for monolayer graphene, the four-band model of AB bilayer graphene, and for a more complicated matrix Hamiltonian describing the silicene band structure. Finally, we apply our method to an inhomogeneous system consisting of a strain engineered one-dimensional moiré in bilayer graphene, finding localized states near the Dirac point that arise from electron trapping in a semiclassical moiré potential. The semiclassical density of states of these localized states we show to be in perfect agreement with an exact quantum mechanical calculation of the density of states.
Khemani, Vedika; Pollmann, Frank; Sondhi, S L
2016-06-17
The eigenstates of many-body localized (MBL) Hamiltonians exhibit low entanglement. We adapt the highly successful density-matrix renormalization group method, which is usually used to find modestly entangled ground states of local Hamiltonians, to find individual highly excited eigenstates of MBL Hamiltonians. The adaptation builds on the distinctive spatial structure of such eigenstates. We benchmark our method against the well-studied random field Heisenberg model in one dimension. At moderate to large disorder, the method successfully obtains excited eigenstates with high accuracy, thereby enabling a study of MBL systems at much larger system sizes than those accessible to exact-diagonalization methods.
The addition of the lower level to spectrums of matrix and scalar components of d=2 SUSY Hamiltonian
Leble, S B
1998-01-01
Supersymmetrical quantum--mechanical system is consider in the case of d=2. The problem of addition of the lower level to spectrums of matrix and scalar components of d=2 SUSY Hamiltonian is investigated. It is shown that in the case, the level E=0 may be degenerate. The multi--dimensional scalar Hamiltonians with energy spectra coinciding up to finite number of discrete levels are constructed.
Comix, a New Matrix Element Generator
Gleisberg, Tanju; /SLAC; Hoche, Stefan; /Durham U., IPPP
2008-09-03
We present a new tree-level matrix element generator, based on the color dressed Berends-Giele recursive relations. We discuss two new algorithms for phase space integration, dedicated to be used with large multiplicities and color sampling.
Siminovitch, David; Untidt, Thomas; Nielsen, Niels Chr
2004-01-01
Our recent exact effective Hamiltonian theory (EEHT) for exact analysis of nuclear magnetic resonance (NMR) experiments relied on a novel entanglement of unitary exponential operators via finite expansion of the logarithmic mapping function. In the present study, we introduce simple alternant quotient expressions for the coefficients of the polynomial matrix expansion of these entangled operators. These expressions facilitate an extension of our previous closed solution to the Baker-Campbell-Hausdorff problem for SU(N) systems from Nfunction. The general applicability of these expressions is demonstrated by several examples with relevance for NMR spectroscopy. The specific form of the alternant quotients is also used to demonstrate the fundamentally important equivalence of Sylvester's theorem (also known as the spectral theorem) and the EEHT expansion.
Cohen, D; Kottos, T
2001-03-01
We study a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) are the canonical coordinates of a particle in a two-dimensional well, and x is a parameter. By changing x we can deform the "shape" of the well. The quantum eigenstates of the system are /n(x)>. We analyze numerically how the parametric kernel P(n/m)=//(2) evolves as a function of delta(x)[triple bond](x-x(0)). This kernel, regarded as a function of n-m, characterizes the shape of the wave functions, and it also can be interpreted as the local density of states. The kernel P(n/m) has a well-defined classical limit, and the study addresses the issue of quantum-classical correspondence. Both the perturbative and the nonperturbative regimes are explored. The limitations of the random matrix theory approach are demonstrated.
闫庆友; 熊西文
2002-01-01
An efficient and stable structure preserving algorithm, which is a variant of the QR like (SR) algorithm due to Bunse-Gerstner and Mehrmann, is presented for computing the eigenvalues and stable invariant subspaces of a Hamiltonian matrix. In the algorithm two strategies are employed, one of which is called dis- unstabilization technique and the other is preprocessing technique. Together with them, a so-called ratio-reduction equation and a backtrack technique are introduced to avoid the instability and breakdown in the original algorithm. It is shown that the new algorithm can overcome the instability and breakdown at low cost. Numerical results have demonstrated that the algorithm is stable and can compute the eigenvalues to very high accuracy.
Rolling Element Bearing Stiffness Matrix Determination (Presentation)
Guo, Y.; Parker, R.
2014-01-01
Current theoretical bearing models differ in their stiffness estimates because of different model assumptions. In this study, a finite element/contact mechanics model is developed for rolling element bearings with the focus of obtaining accurate bearing stiffness for a wide range of bearing types and parameters. A combined surface integral and finite element method is used to solve for the contact mechanics between the rolling elements and races. This model captures the time-dependent characteristics of the bearing contact due to the orbital motion of the rolling elements. A numerical method is developed to determine the full bearing stiffness matrix corresponding to two radial, one axial, and two angular coordinates; the rotation about the shaft axis is free by design. This proposed stiffness determination method is validated against experiments in the literature and compared to existing analytical models and widely used advanced computational methods. The fully-populated stiffness matrix demonstrates the coupling between bearing radial, axial, and tilting bearing deflections.
Matrix elements from moments of correlation functions
Bouchard, Chris; Orginos, Kostas; Richards, David
2016-01-01
Momentum-space derivatives of matrix elements can be related to their coordinate-space moments through the Fourier transform. We derive these expressions as a function of momentum transfer $Q^2$ for asymptotic in/out states consisting of a single hadron. We calculate corrections to the finite volume moments by studying the spatial dependence of the lattice correlation functions. This method permits the computation of not only the values of matrix elements at momenta accessible on the lattice, but also the momentum-space derivatives, providing {\\it a priori} information about the $Q^2$ dependence of form factors. As a specific application we use the method, at a single lattice spacing and with unphysically heavy quarks, to directly obtain the slope of the isovector form factor at various $Q^2$, whence the isovector charge radius. The method has potential application in the calculation of any hadronic matrix element with momentum transfer, including those relevant to hadronic weak decays.
Accelerated Matrix Element Method with Parallel Computing
Schouten, Doug; Stelzer, Bernd
2014-01-01
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current collider experiments. However, the computational complexity of this method for final states with many particles and degrees of freedom sets it at a disadvantage compared to supervised classification methods such as decision trees, k nearest-neighbour, or neural networks. This note presents a concrete implementation of the matrix element technique using graphics processing units. Due to the intrinsic parallelizability of multidimensional integration, dramatic speedups can be readily achieved, which makes the matrix element technique viable for general usage at collider experiments.
Matrix elements from moments of correlation functions
Chang, Chia Cheng [SLAC National Accelerator Lab., Menlo Park, CA (United States); Bouchard, Chris [College of William and Mary, Williamsburg, VA (United States); Orginos, Konstantinos [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States); Richards, David G. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2016-10-01
Momentum-space derivatives of matrix elements can be related to their coordinate-space moments through the Fourier transform. We derive these expressions as a function of momentum transfer Q2 for asymptotic in/out states consisting of a single hadron. We calculate corrections to the finite volume moments by studying the spatial dependence of the lattice correlation functions. This method permits the computation of not only the values of matrix elements at momenta accessible on the lattice, but also the momentum-space derivatives, providing {\\it a priori} information about the Q2 dependence of form factors. As a specific application we use the method, at a single lattice spacing and with unphysically heavy quarks, to directly obtain the slope of the isovector form factor at various Q2, whence the isovector charge radius. The method has potential application in the calculation of any hadronic matrix element with momentum transfer, including those relevant to hadronic weak decays.
CDENPROP: Transition matrix elements involving continuum states
Harvey, Alex G; Morales, Felipe; Smirnova, Olga
2014-01-01
Transition matrix elements between electronic states where one electron can be in the continuum are required for a wide range of applications of the molecular R-matrix method. These include photoionization, photorecombination and photodetachment; electron-molecule scattering and photon-induced processes in the presence of an external D.C. field, and time-dependent R-matrix approaches to study the effect of the exposure of molecules to strong laser fields. We present a new algorithm, implemented as a module (CDENPROP) in the UKRmol electron-molecule scattering code suite.
The Density Matrix Renormalization Group Method applied to Interaction Round a Face Hamiltonians
1996-01-01
Given a Hamiltonian with a continuous symmetry one can generally factorize that symmetry and consider the dynamics on invariant Hilbert spaces. In statistical mechanics this procedure is known as the vertex-IRF map, and in certain cases, like rotational invariant Hamiltonians, it can be implemented via group theoretical techniques. Using this map we translate the DMRG method, which applies to 1D vertex Hamiltonians, into a formulation adequate to study IRF Hamiltonians. The advantage of the I...
Komninos, Yannis; Nicolaides, Cleanthes A
2014-01-01
In a variety of problems concerning the coupling of atomic and molecular states to strong and or short electromagnetic pulses, it is necessary to solve the time-dependent Schroedinger equation nonperturbatively. To this purpose, we have proposed and applied to various problems the state-specific expansion approach. Its implementation requires the computation of bound-bound, bound-free and free-free N-electron matrix elements of the operator that describes the coupling of the electrons to the external electromagnetic field. The present study penetrates into the mathematical properties of the free-free matrix elements of the full electric field operator of the multipolar Hamiltonian. kk is the photon wavenumber, and the field is assumed linearly polarized, propagating along the z axis. Special methods are developed and applied for the computation of such matrix elements using energy-normalized, numerical scattering wavefunctions. It is found that, on the momentum (energy) axis, the free-free matrix elements hav...
Zeroes in continuum - continuum dipole matrix elements
Obolensky, Oleg I.; Pratt, R. H.; Korol, Andrei
2003-05-01
It is well known that Cooper minima in photoeffect cross sections are due to zeroes in corresponding bound-free dipole matrix elements. As was discussed before(C. D. Shaffer, R. H. Pratt, and S. D. Oh, Phys. Rev. A. 57), 227 (1998)., free-free dipole matrix elements in screened (atomic or ionic) potentials can also have zeroes. Such zeroes (existing at energies of the order of 1-100 eV) result in structures in the energy dependence of bremsstrahlung cross sections and angular distributions(A. Florescu, O. I. Obolensky, C. D. Shaffer, and R. H. Pratt, AIP Conference Proceedings, 576), 60 (2001).. In the soft photon limit, zeroes of radiative free-free matrix elements are related to Ramsauer-Townsend minima in elastic scattering of electrons by atoms. Here we study properties of the trajectories of dipole matrix element zeroes in the plane of initial and final electron energies. We show how the trajectories in this plane evolve with ionicity for several low ℓ dipole transitions ℓ → ℓ ± 1.
A simple representation of energy matrix elements in terms of symmetry-invariant bases.
Cui, Peng; Wu, Jian; Zhang, Guiqing; Boyd, Russell J
2010-02-01
When a system under consideration has some symmetry, usually its Hamiltonian space can be parallel partitioned into a set of subspaces, which is invariant under symmetry operations. The bases that span these invariant subspaces are also invariant under the symmetry operations, and they are the symmetry-invariant bases. A standard methodology is available to construct a series of generator functions (GFs) and corresponding symmetry-adapted basis (SAB) functions from these symmetry-invariant bases. Elements of the factorized Hamiltonian and overlap matrix can be expressed in terms of these SAB functions, and their simple representations can be deduced in terms of GFs. The application of this method to the Heisenberg spin Hamiltonian is demonstrated.
Recurrence relation for relativistic atomic matrix elements
Martínez y Romero, R P; Salas-Brito, A L
2000-01-01
Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired on the relativistic extension of the second hypervirial method that has been succesfully employed to deduce an analogous relationship in non relativistic quantum mechanics. We obtain first the relativistic extension of the second hypervirial and then the relativistic recurrence relation. Furthermore, we use such relation to deduce relativistic versions of the Pasternack-Sternheimer rule and of the virial theorem.
A weak Hamiltonian finite element method for optimal guidance of an advanced launch vehicle
Hodges, Dewey H.; Calise, Anthony J.; Bless, Robert R.; Leung, Martin
1989-01-01
A temporal finite-element method based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables, which are expanded in terms of nodal values and simple shape functions. Time derivatives of the states and costates do not appear in the governing variational equation; the only quantities whose time derivatives appear therein are virtual states and virtual costates. Numerical results are presented for an elementary trajectory optimization problem; they show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The feasibility of this approach for real-time guidance applications is evaluated. A simplified model for an advanced launch vehicle application that is suitable for finite-element solution is presented.
Relativistic recursion relations for transition matrix elements
Martínez y Romero, R P; Salas-Brito, A L
2004-01-01
We review some recent results on recursion relations which help evaluating arbitrary non-diagonal, radial hydrogenic matrix elements of $r^\\lambda$ and of $\\beta r^\\lambda$ ($\\beta$ a Dirac matrix) derived in the context of Dirac relativistic quantum mechanics. Similar recursion relations were derived some years ago by Blanchard in the non relativistic limit. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schr\\"odinger case. An extension of the relations to the case of two potentials in the so-called unshifted case, but using an arbitrary radial function instead of a power one, is also given. Several important results are obtained as special instances of our recurrence relations, such as a generalization to the relativistic case of the Pasternack-Sternheimer rule. Our results are useful in any atomic or molecular calculation which take into account relativistic corrections.
The Matrix Element Method and Vector-Like Quark Searches
Morrison, Benjamin
2016-01-01
In my time at the CERN summer student program, I worked on applying the matrix element method to vector-like quark identification. I worked in the ATLAS University of Geneva group under Dr. Olaf Nackenhorst. I developed automated plotting tools with ROOT, a script for implementing and optimizing generated matrix element calculation code, and kinematic transforms for the matrix element method.
Radial Matrix Elements of Hydrogen Atom and the Correspondence Principle
T. N. Chakrabarty
2004-03-01
Radial dipole matrix elements having astrophysical importance have been computed for highly excited states of hydrogen atom. Computation is based on Heisenberg’s form of correspondence principle for Coulomb potential. Particular attention has been paid to the choice of classical analogue (c) of principal quantum number (). The computed radial matrix elements are in good agreement with quantum mechanical results. Further, radial matrix elements for few transitions involving high neighboring states of hydrogen atom are presented.
The Calculation of Matrix Elements in Relativistic Quantum Mechanics
Ilarraza-Lomelí, A. C.; Valdés-Martínez, M. N.; Salas-Brito, A. L.; Martínez-y-Romero, R. P.; Núñez-Yépez, H. N
2001-01-01
Employing a relativistic version of a hypervirial result, recurrence relations for arbitrary non-diagonal radial hydrogenic matrix elements have recently been obtained in Dirac relativistic quantum mechanics. In this contribution honoring Professor L\\"owdin, we report on a new relation we have recently discovered between the matrix elements $$ and $$---where $\\beta$ is a Dirac matrix and the numbers distiguish between different radial eigenstates--- that allow for a simplification and hence f...
Tunnelling matrix elements with Gutzwiller wave functions
Di Ciolo, Andrea; Tocchio, Luca F.; Gros, Claudius [Institut fuer Theoretische Physik, Goethe Universitaet Frankfurt, Frankfurt Am Main (Germany)
2011-07-01
We use a generalized Gutzwiller approach, in order to study projected particle (hole) excitations for superconducting systems and systems with antiferromagnetic (AFM) order. As in the standard Gutzwiller scheme the effects of the strong electronic correlations are given via the suppression of the site double occupancy; for our computations it is helpful to consider a lattice with a reservoir site unaffected by this suppression of the double occupancy. In this approach we obtain the probabilities for the tunnelling of a particle (hole) into the projected state. Our results are due only to the physical properties of the trial state and not to the choice of a specifical Hamiltonian: in this sense, they are model-independent but not universal, because they rely on the features of the chosen Gutzwiller wave function (projected Fermi Sea, BCS superconductor, AFM..) The accuracy and the reliability of our analytical approximation is tested using the Variational Monte Carlo. Possible comparisons with tunnelling experiments are discussed.
Rotordynamic Analysis with Shell Elements for the Transfer Matrix Method
1989-08-01
jACCESSION NO. 11. TITLE (Include Security Classification) (UNCLASSIFIED) ROTORDYNAMIC ANALYSIS WITH SHELL ELEMENTS FOR THE TRANSFER MATRIX METHOD 12...SECURITY CLASSIFICATION OF THIS PAGE AFIT/CI "OVERPRINT" iii ABSTRACT Rotordynamic Analysis with Shell Elements for the Transfer Matrix Method. (August...analysts in indus- try . ’ . ," Accesiu:, For NTIS CR,4i Fi FilC TA,: [3 0. fi A-1 B I ., ,.................. ,., ROTORDYNAMIC ANALYSIS WITH SHELL ELEMENTS
Elements of matrix modeling and computing with Matlab
White, Robert E
2006-01-01
As discrete models and computing have become more common, there is a need to study matrix computation and numerical linear algebra. Encompassing a diverse mathematical core, Elements of Matrix Modeling and Computing with MATLAB examines a variety of applications and their modeling processes, showing you how to develop matrix models and solve algebraic systems. Emphasizing practical skills, it creates a bridge from problems with two and three variables to more realistic problems that have additional variables. Elements of Matrix Modeling and Computing with MATLAB focuses on seven basic applicat
The electronic Hamiltonian for cuprates
Annett, James F.; Mcmahan, A. K.; Martin, Richard M.
1991-01-01
A realistic many-body Hamiltonian for the cuprate superconductors should include both copper d and oxygen p states, hopping matrix elements between them, and Coulomb energies, both on-site and inter-site. We have developed a novel computational scheme for deriving the relevant parameters ab initio from a constrained occupation local density functional. The scheme includes numerical calculation of appropriate Wannier functions for the copper and oxygen states. Explicit parameter values are given for La2CuO4. These parameters are generally consistent with other estimates and with the observed superexchange energy. Secondly, we address whether this complicated multi-band Hamiltonian can be reduced to a simpler one with fewer basis states per unit cell. We propose a mapping onto a new two-band effective Hamiltonian with one copper d and one oxygen p derived state per unit cell. This mapping takes into account the large oxygen-oxygen hopping given by the ab initio calculations.
W+jets Matrix Elements and the Dipole Cascade
Lavesson, N; Lavesson, Nils; Lonnblad, Leif
2005-01-01
We extend the algorithm for matching fixed-order tree-level matrix element generators with the Dipole Cascade Model in Ariadne to apply to processes with incoming hadrons. We test the algoritm on for the process W+n jets at the Tevatron, and find that the results are fairly insensitive to the cutoff used to regularize the soft and collinear divergencies in the tree-level matrix elements. We also investigate a few observables to check the sensitivity to the matrix element correction.
W+jets matrix elements and the dipole cascade
Lavesson, Nils; Lönnblad, Leif
2005-07-01
We extend the algorithm for matching fixed-order tree-level matrix element generators with the Dipole Cascade Model in Ariadne to apply to processes with incoming hadrons. We test the algoritm on for the process W+n jets at the Tevatron, and find that the results are fairly insensitive to the cutoff used to regularize the soft and collinear divergencies in the tree-level matrix elements. We also investigate a few observables to check the sensitivity to the matrix element correction.
Hamiltonian Truncation Study of Supersymmetric Quantum Mechanics: S-Matrix and Metastable States
Balthazar, Bruno; Yin, Xi
2016-01-01
We implement the Rayleigh-Ritz method in supersymmetric quantum mechanics with flat directions, and extract the S-matrix and metastable resonances. The effectiveness of the method is demonstrated in two strongly coupled systems: an N=1 toy supermembrane model, and an N=4 model with a U(1) gauge multiplet and a charged chiral multiplet.
Automatic generation of matrix element derivatives for tight binding models
Elena, Alin M.; Meister, Matthias
2005-10-01
Tight binding (TB) models are one approach to the quantum mechanical many-particle problem. An important role in TB models is played by hopping and overlap matrix elements between the orbitals on two atoms, which of course depend on the relative positions of the atoms involved. This dependence can be expressed with the help of Slater-Koster parameters, which are usually taken from tables. Recently, a way to generate these tables automatically was published. If TB approaches are applied to simulations of the dynamics of a system, also derivatives of matrix elements can appear. In this work we give general expressions for first and second derivatives of such matrix elements. Implemented in a tight binding computer program, like, for instance, DINAMO, they obviate the need to type all the required derivatives of all occurring matrix elements by hand.
Vanishing of dipole matrix elements at level crossings.
Kocher, C. A.
1972-01-01
Demonstration that the vanishing of certain coupling matrix elements at level crossings follow from angular momentum commutation relations. A magnetic dipole transition having delta M = plus or minus 1, induced near a crossing of the levels in a nonzero magnetic field, is found to have a dipole matrix element comparable to or smaller than the quotient of the level separation and the field. This result also applies in the analogous electric field electric dipole case.
Oscillation Criteria Based on a New Weighted Function for Linear Matrix Hamiltonian Systems
Yingxin Guo
2011-01-01
Full Text Available By employing a generalized Riccati technique and an integral averaging technique, some new oscillation criteria are established for the second-order matrix differential system U′=A(xU+B(tV, V′=C(xU−A∗(tV, where A(t, B(t, and C(t are (n×n-matrices, and B, C are Hermitian. These results are sharper than some previous results.
Casimir, J. B.; Kevorkian, S.; Vinh, T.
2005-10-01
This paper describes a procedure for building the dynamic stiffness matrix of two-dimensional elements with free edge boundary conditions. The dynamic stiffness matrix is the basis of the continuous element method. Then, the formulation is used to build a Kirchhoff rectangular plate element. Gorman's method of boundary condition decomposition and Levy's series are used to obtain the strong solution of the elementary problem. A symbolic computation software partially performs the construction of the dynamic stiffness matrix from this solution. The performances of the element are evaluated from comparisons with harmonic responses of plates obtained by the finite element method.
Simplified formula for isoparametric quadrilateral element stiffness matrix
Changlian, X.
1987-02-01
Homogeneous parallelogram and quasi-parallelogram elements are usually used in finite element seismic modeling. Theoretically, the coordinates of element nodes may be arbitrary values on condition that elements are successive and not superposed. Isoparametric quadrilateral elements, whose nodes are presumed to be in laterally uniform distribution, are used so that not only unit stiffness matrix formula is essentially simplified to cut computing time but also finite element method remains flexible enough to be used in complex modeling. Simplified formulae for computing the stiffness matrices in four cases are derived, which, compared with corresponding Gauss integration algorithm, can cut 94-98% computing time.
Correlations of the elements of the neutrino mass matrix
Grimus, Walter
2012-01-01
Assuming Majorana nature of neutrinos, we re-investigate, in the light of the recent measurement of the reactor mixing angle, the allowed ranges for the absolute values of the elements of the neutrino mass matrix in the basis where the charged-lepton mass matrix is diagonal. Apart from the derivation of upper and lower bounds on the values of the matrix elements, we also study their correlations. Moreover, we analyse the sensitivity of bounds and correlations to the global fit results of the neutrino oscillation parameters which are available in the literature.
Generalized hypervirial and Blanchard's recurrence relations for radial matrix elements
Dong Shihai [Programa de IngenierIa Molecular, Instituto Mexicano del Petroleo, Lazaro Cardenas 152, 07730 Mexico, DF (Mexico); Chen Changyuan [Department of Physics, Yancheng Teachers College, Yancheng 224002 (China); Lozada-Cassou, M [Programa de Ingenieria Molecular, Instituto Mexicano del Petroleo, Lazaro Cardenas 152, 07730 Mexico, DF (Mexico)
2005-07-14
Based on the Hamiltonian identity, we propose a generalized expression of the second hypervirial for an arbitrary central potential wavefunction in arbitrary dimensions D. We demonstrate that the new proposed second hypervirial formula is very powerful in deriving the general Blanchard's and Kramers' recurrence relations among the radial matrix elements. As their useful and important applications, we derive all general Blanchard's and Kramers' recurrence relations and some identities for the Coulomb-like potential, harmonic oscillator and Kratzer oscillator. The recurrence relation and identity between the exponential functions and the powers of the radial function are established for the Morse potential. The corresponding general Blanchard's and Kramers' recurrence relations in 2D are also briefly studied.
Acceleration of matrix element computations for precision measurements
Brandt, Oleg; Wang, Michael H L S; Ye, Zhenyu
2014-01-01
The matrix element technique provides a superior statistical sensitivity for precision measurements of important parameters at hadron colliders, such as the mass of the top quark or the cross section for the production of Higgs bosons. The main practical limitation of the technique is its high computational demand. Using the concrete example of the top quark mass, we present two approaches to reduce the computation time of the technique by two orders of magnitude. First, we utilize low-discrepancy sequences for numerical Monte Carlo integration in conjunction with a dedicated estimator of numerical uncertainty, a novelty in the context of the matrix element technique. Second, we utilize a new approach that factorizes the overall jet energy scale from the matrix element computation, a novelty in the context of top quark mass measurements. The utilization of low-discrepancy sequences is of particular general interest, as it is universally applicable to Monte Carlo integration, and independent of the computing e...
The matrix element method at next-to-leading order
Campbell, John M.; Giele, Walter T.; Williams, Ciaran
2012-11-01
This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory, for electro-weak final states. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of unweighted next-to-leading order events. As examples of the application of our next-to-leading order matrix element method we consider the measurement of the mass of the Z boson and also the search for the Higgs boson in the four lepton channel.
Excited state effects in nucleon matrix element calculations
Alexandrou, Constantia [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; The Cyprus Institute, Nicosia (Cyprus). Computation-based Science and Technology Research Center; Constantinou, Martha [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Dinter, Simon; Drach, Vincent; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Leontiou, Theodoros [Frederick Univ., Nicosia (Cyprus). General Dept.; Renner, Dru B. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
2011-12-15
We perform a high-statistics precision calculation of nucleon matrix elements using an open sink method allowing us to explore a wide range of sink-source time separations. In this way the influence of excited states of nucleon matrix elements can be studied. As particular examples we present results for the nucleon axial charge g{sub A} and for the first moment of the isovector unpolarized parton distribution left angle x right angle {sub u-d}. In addition, we report on preliminary results using the generalized eigenvalue method for nucleon matrix elements. All calculations are performed using N{sub f}=2+1+1 maximally twisted mass Wilson fermions. (orig.)
A Matrix Element for Chaotic Tunnelling Rates and Scarring Intensities
Creagh, S C; Creagh, Stephen C.; Whelan, Niall D.
1998-01-01
It is shown that tunnelling splittings in ergodic double wells and resonant widths in ergodic metastable wells can be approximated as easily-calculated matrix elements involving the wavefunction in the neighbourhood of a certain real orbit. This orbit is a continuation of the complex orbit which crosses the barrier with minimum imaginary action. The matrix element is computed by integrating across the orbit in a surface of section representation, and uses only the wavefunction in the allowed region and the stability properties of the orbit. When the real orbit is periodic, the matrix element is a natural measure of the degree of scarring of the wavefunction. This scarring measure is canonically invariant and independent of the choice of surface of section, within semiclassical error. The result can alternatively be interpretated as the autocorrelation function of the state with respect to a transfer operator which quantises a certain complex surface of section mapping. The formula provides an efficient numeri...
The Matrix Element Method at Next-to-Leading Order
Campbell, John M.; Giele, Walter T.; Williams, Ciaran
2012-01-01
This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of...
The effects of flavour symmetry breaking on hadron matrix elements
Cooke, A.N.; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Kobe (Japan); Pleiter, D. [Juelich Research Centre (Germany); Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Division; Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Zanotti, J.M. [Adelaide Univ. (Australia). School of Chemistry and Physics
2012-12-15
By considering a flavour expansion about the SU(3)-flavour symmetric point, we investigate how flavour-blindness constrains octet baryon matrix elements after SU(3) is broken by the mass difference between the strange and light quarks. We find the expansions to be highly constrained along a mass trajectory where the singlet quark mass is held constant, which proves beneficial for extrapolations of 2+1 flavour lattice data to the physical point. We investigate these effects numerically via a lattice calculation of the flavour-conserving and flavour-changing matrix elements of the vector and axial operators between octet baryon states.
Nucleon matrix elements using the variational method in lattice QCD
Dragos, Jack; Kamleh, Waseem; Leinweber, Derek B; Nakamura, Yoshifumi; Rakow, Paul E L; Schierholz, Gerrit; Young, Ross D; Zanotti, James M
2016-01-01
The extraction of hadron matrix elements in lattice QCD using the standard two- and three-point correlator functions demands careful attention to systematic uncertainties. One of the most commonly studied sources of systematic error is contamination from excited states. We apply the variational method to calculate the axial vector current $g_{A}$, the scalar current $g_{S}$ and the quark momentum fraction $\\left$ of the nucleon and we compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.
On nuclear matrix element uncertainties in short range $0\
Klapdor-Kleingrothaus, H V
2000-01-01
The evaluation of short range contributions to neutrinoless double beta decay has been challenged due to critics of the ansatz of the nuclear matrix element calculations. We comment on the critics and uncertainties of these calculations and the effect on the derived limits.
Relativistically extended Blanchard recurrence relation for hydrogenic matrix elements
Martínez y Romero, R P; Salas-Brito, A L
2001-01-01
General recurrence relations for arbitrary non-diagonal, radial hydrogenic matrix elements are derived in Dirac relativistic quantum mechanics. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schr\\"odinger case. A relativistic version of the Pasternack-Sternheimer relation is thence obtained in the diagonal (i.e. total angular momentum and parity the same) case, from such relation an expression for the relativistic virial theorem is deduced. To contribute to the utility of the relations, explicit expressions for the radial matrix elements of functions of the form $r^\\lambda$ and $\\beta r^\\lambda$ ---where $\\beta$ is a Dirac matrix--- are presented.
Komninos, Yannis; Mercouris, Theodoros; Nicolaides, Cleanthes A.
2017-01-01
The present study examines the mathematical properties of the free-free ( f - f) matrix elements of the full electric field operator, O E (κ, r̅), of the multipolar Hamiltonian. κ is the photon wavenumber. Special methods are developed and applied for their computation, for the general case where the scattering wavefunctions are calculated numerically in the potential of the term-dependent ( N - 1) electron core, and are energy-normalized. It is found that, on the energy axis, the f - f matrix elements of O E (κ, r̅) have singularities of first order, i.e., as ɛ' → ɛ, they behave as ( ɛ - ɛ')-1. The numerical applications are for f - f transitions in hydrogen and neon, obeying electric dipole and quadrupole selection rules. In the limit κ = 0, O E (κ, r̅) reduces to the length form of the electric dipole approximation (EDA). It is found that the results for the EDA agree with those of O E (κ, r̅), with the exception of a wave-number region k' = k ± κ about the point k' = k.
Multipole Matrix Elements for Dh-Systems and Their Asymptotics
Tarasov, V. F.
A “DH-system” is defined as a multidimensional hydrogen atom (or its one-particle analogue), D≥1. Investigating many Coulomb problems in ℝD it is necessary to know exact analytical expressions of multipole matrix elements D for DH-systems, where q=(N, µ) is a set of parameters, N —"principal” and µ — "orbital” quantum numbers. The paper deals with the new method for the evaluation of similar matrix elements using new properties of Appell’s function F2(x, y) to the vicinity of the singular point (1, 1). Such approach allows: 1) to get exact analytical expressions of these matrix elements (considering the selection rules) by means of Appell’s F2 (or Clausen’s 3F2) functions; 2) to reveal “latent” symmetry of diagonal matrix elements with respect to the point k0=-3/2, the above symmetry is connected with the property of Appell’s function F2 (1,1) mirror-like symmetry; 3) to find (exact) asymptotics of the off-diagonal matrix elements in terms of Horn’s function ψ1 (x, y); 4) to prove that the orthogonality of radial functions fNµ (D, r) over N and μ for DH-systems is connected with the properties of Appell’s F2 function to the vicinity of the singular point (1, 1), it generalizes the known result for 3H-atom by Pasternack and Sternheimer, J. Math. Phys. 3, 1280 (1962).
Nucleon matrix elements using the variational method in lattice QCD
Dragos, J.; Horsley, R.; Kamleh, W.; Leinweber, D. B.; Nakamura, Y.; Rakow, P. E. L.; Schierholz, G.; Young, R. D.; Zanotti, J. M.
2016-10-01
The extraction of hadron matrix elements in lattice QCD using the standard two- and three-point correlator functions demands careful attention to systematic uncertainties. One of the most commonly studied sources of systematic error is contamination from excited states. We apply the variational method to calculate the axial vector current gA, the scalar current gS, the scalar current gT and the quark momentum fraction ⟨x ⟩ of the nucleon and we compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.
Glueball Spectrum and Matrix Elements on Anisotropic Lattices
Y. Chen; A. Alexandru; S.J. Dong; T. Draper; I. Horvath; F.X. Lee; K.F. Liu; N. Mathur; C. Morningstar; M. Peardon; S. Tamhankar; B.L. Young; J.B. Zhang
2006-01-01
The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing ranging from 0.1fm - 0.2fm. These matrix elements are needed to predict the glueball branching ratios in J/{psi} radiative decays which will help identify the glueball states in experiments. Two types of improved local gluonic operators are constructed for a self-consistent check and the finite volume effects are studied. We find that lattice spacing dependence of our results is very weak and the continuum limits are reliably extrapolated, as a result of improvement of the lattice gauge action and local operators. We also give updated glueball masses with various quantum numbers.
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Emir Gülümser
2014-01-01
Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.
Reweighting QCD matrix-element and parton-shower calculations
Bothmann, Enrico; Schönherr, Marek; Schumann, Steffen
2016-11-01
We present the implementation and validation of the techniques used to efficiently evaluate parametric and perturbative theoretical uncertainties in matrix-element plus parton-shower simulations within the Sherpa event-generator framework. By tracing the full α _s and PDF dependences, including the parton-shower component, as well as the fixed-order scale uncertainties, we compute variational event weights on-the-fly, thereby greatly reducing the computational costs to obtain theoretical-uncertainty estimates.
Reweighting QCD matrix-element and parton-shower calculations
Bothmann, Enrico; Schumann, Steffen
2016-01-01
We present the implementation and validation of the techniques used to efficiently evaluate parametric and perturbative theoretical uncertainties in matrix-element plus parton-shower simulations within the Sherpa event-generator framework. By tracing the full $\\alpha_s$ and PDF dependences, including the parton-shower component, as well as the fixed-order scale uncertainties, we compute variational event weights on-the-fly, thereby greatly reducing the computational costs to obtain theoretical-uncertainty estimates.
[Electron transfer between globular proteins. Evaluation of a matrix element].
Lakhno, V D; Chuev, G N; Ustinin, M N
1998-01-01
The dependence of the matrix element of the probability of interprotein electron transfer on the mutual orientation of the donor and acceptor centers and the distance between them was calculated. The calculations were made under the assumption that electron transfer proceeds mainly by a collective excitation of polaron nature, like a solvated electron state. The results obtained are consistent with experimental data and indicate the nonexponential behavior of this dependence in the case when the distance transfer is less than 20 A.
Reweighting QCD matrix-element and parton-shower calculations
Bothmann, Enrico; Schumann, Steffen [Universitaet Goettingen, II. Physikalisches Institut, Goettingen (Germany); Schoenherr, Marek [Universitaet Zuerich, Physik-Institut, Zuerich (Switzerland)
2016-11-15
We present the implementation and validation of the techniques used to efficiently evaluate parametric and perturbative theoretical uncertainties in matrix-element plus parton-shower simulations within the Sherpa event-generator framework. By tracing the full α{sub s} and PDF dependences, including the parton-shower component, as well as the fixed-order scale uncertainties, we compute variational event weights on-the-fly, thereby greatly reducing the computational costs to obtain theoretical-uncertainty estimates. (orig.)
A stochastic method for computing hadronic matrix elements
Alexandrou, Constantia [University of Cyprus, Department of Physics, P.O. Box 20537, Nicosia (Cyprus); The Cyprus Institute, Computation-based Science and Technology Research Center, Nicosia (Cyprus); Constantinou, Martha; Hadjiyiannakou, Kyriakos [University of Cyprus, Department of Physics, P.O. Box 20537, Nicosia (Cyprus); Dinter, Simon; Drach, Vincent; Jansen, Karl [NIC, DESY Zeuthen, Zeuthen (Germany); Renner, Dru B. [NIC, DESY Zeuthen, Zeuthen (Germany); Jefferson Lab., Newport News (United States); Collaboration: ETM Collaboration
2014-01-15
We present a stochastic method for the calculation of baryon three-point functions that is more versatile than the typically used sequential method. We analyze the scaling of the error of the stochastically evaluated three-point function with the lattice volume, and we found a favorable signal-to-noise ratio suggesting that our stochastic method can be used efficiently at large volumes to compute hadronic matrix elements. (orig.)
CP violation and Kaon weak matrix elements from Lattice QCD
Garron, Nicolas
2015-01-01
In this short review, I present the recent lattice computations of kaon weak matrix elements relevant to $K \\to \\pi\\pi$ decays and neutral kaon mixing. These matrix elements are key to the theoretical determination of the CP violation parameters $\\epsilon$ and $\\epsilon'$ . Impressive progress have been achieved recently, in particular the first realistic computation of $\\epsilon'/\\epsilon$ with physical kinematics has been reported in [1]. The novelty is the $\\Delta I = 1/2$ channel, whereas the $\\Delta I = 3/2$ contribution is now computed at several values of the lattice spacing and extrapolated to the continuum limit. I will also present the status of $B_K$ and discuss its error budget, with a particular emphasis on the perturbative error. Finally I will review the matrix elements of neutral kaon mixing beyond the standard model and will argue that the discrepancy observed by different collaborations could be explained by the renormalisation procedure of the relevant four-quark operators.
Algebraic evaluation of matrix elements in the Laguerre function basis
McCoy, A. E.; Caprio, M. A.
2016-02-01
The Laguerre functions constitute one of the fundamental basis sets for calculations in atomic and molecular electron-structure theory, with applications in hadronic and nuclear theory as well. While similar in form to the Coulomb bound-state eigenfunctions (from the Schrödinger eigenproblem) or the Coulomb-Sturmian functions (from a related Sturm-Liouville problem), the Laguerre functions, unlike these former functions, constitute a complete, discrete, orthonormal set for square-integrable functions in three dimensions. We construct the SU(1, 1) × SO(3) dynamical algebra for the Laguerre functions and apply the ideas of factorization (or supersymmetric quantum mechanics) to derive shift operators for these functions. We use the resulting algebraic framework to derive analytic expressions for matrix elements of several basic radial operators (involving powers of the radial coordinate and radial derivative) in the Laguerre function basis. We illustrate how matrix elements for more general spherical tensor operators in three dimensional space, such as the gradient, may then be constructed from these radial matrix elements.
Ryan, M.
1972-01-01
The study of cosmological models by means of equations of motion in Hamiltonian form is considered. Hamiltonian methods applied to gravity seem to go back to Rosenfeld (1930), who constructed a quantum-mechanical Hamiltonian for linearized general relativity theory. The first to notice that cosmologies provided a simple model in which to demonstrate features of Hamiltonian formulation was DeWitt (1967). Applications of the ADM formalism to homogeneous cosmologies are discussed together with applications of the Hamiltonian formulation, giving attention also to Bianchi-type universes. Problems involving the concept of superspace and techniques of quantization are investigated.
Kaon matrix elements and CP violation from quenched lattice QCD
Cristian, Calin-Radu
We report the results of a calculation of the K → pipi matrix elements relevant for the DeltaI = 1/2 rule and epsilon '/epsilon in quenched lattice QCD using domain wall fermions at a fixed lattice spacing of a-1 ˜ 2 GeV. Working in the three-quark effective theory, where only the u, d and s quarks enter and which is known perturbatively to next-to-leading order; we calculate the lattice K → pi and K → |0> matrix elements of dimension six, four-fermion operators. Through lowest order chiral perturbation theory these yield K → pipi matrix elements, which we then normalize to continuum values through a non-perturbative renormalization technique. For the Delta I = 1/2 rule we find a value of 25.3 +/- 1.8 (statistical error only) compared to the experimental value of 22.2, with individual isospin amplitudes 10--20% below the experimental values. For epsilon '/epsilon; using known central values for standard model parameters, we calculate (-4.0 +/- 2.3) x 10-4 (statistical error only) compared to the current experimental average of (17.2 +/- 1.8) x 10-4. Because we find a large cancellation between the I = 0 and I = 2 contributions to epsilon'/epsilon, the result may be very sensitive to the approximations employed. Among these are the use of: quenched QCD, lowest order chiral perturbation theory and continuum perturbation theory below 1.3 GeV. We have also calculated the kaon B parameter, BK and find BK(2 GeV) = 0.532(11). Although currently unable to give a reliable systematic error; we have control over statistical errors and more simulations will yield information about the effects of the approximations on this first-principles determination of these important quantities.
A modified beam stiffness matrix for superconductor elements
Gori, R.; Schrefler, B.A. (Padua Univ. (Italy). Ist. di Scienza e Tecnica delle Costruzioni)
1989-10-01
The components of the stiffness matrix of superconductor elements are derived taking into account the effects of the wrapping of superconductor strands around the internal insulating strip and of possible stabilizing profiles around conductor core. It is already known that the inclination of the strands referred to the longitudinal axis of the superconductor produces a reduction of the axial stiffness and a considerable increase in torsional stiffness. Here also the effects of bending are taken into account, completing hence the previous investigation. Examples relating to superconductors proposed for the Toroidal Field Coil of the Next European Torus are shown. In that instance the strand transposition is carried out by roebling. (orig.).
Controlling inclusive cross sections in parton shower + matrix element merging
Plaetzer, Simon
2012-11-15
We propose an extension of matrix element plus parton shower merging at tree level to preserve inclusive cross sections obtained from the merged and showered sample. Implementing this constraint generates approximate next-to-leading order (NLO) contributions similar to the LoopSim approach. We then show how full NLO, or in principle even higher order, corrections can be added consistently, including constraints on inclusive cross sections to account for yet missing parton shower accuracy at higher logarithmic order. We also show how NLO accuracy below the merging scale can be obtained.
The Matrix Element Method in the LHC era
Wertz, Sébastien
2017-03-01
The Matrix Element Method (MEM) is a powerful multivariate method allowing to maximally exploit the experimental and theoretical information available to an analysis. The method is reviewed in depth, and several recent applications of the MEM at LHC experiments are discussed, such as searches for rare processes and measurements of Standard Model observables in Higgs and Top physics. Finally, a new implementation of the MEM is presented. This project builds on established phase-space parametrisations known to greatly improve the speed of the calculations, and aims at a much improved modularity and maintainability compared to previous software, easing the use of the MEM for high-statistics data analyses.
Hamiltonian tomography of photonic lattices
Ma, Ruichao; Owens, Clai; LaChapelle, Aman; Schuster, David I.; Simon, Jonathan
2017-06-01
In this paper we introduce an approach to Hamiltonian tomography of noninteracting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites α and β may be obtained directly from Sα β(ω ) , the (suitably normalized) two-port measurement between sites α and β at frequency ω . This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band projectors in finite, disordered systems with good band flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in between.
Axial Vector Current Matrix Elements and QCD Sum Rules
Pasupathy, J; Singh, Ritesh K.
2003-01-01
The matrix element of the isoscalar axial vector current, $\\bar{u}\\gamma_\\mu\\gamma_5u + \\bar{d}\\gamma_\\mu\\gamma_5d $, between nucleon states is computed using the external field QCD sum rule method. The external field induced correlator, $$, is calculated from the spectrum of the isoscalar axial vector meson states. Since it is difficult to ascertain, from QCD sum rule for hyperons, the accuracy of validity of flavour SU(3) symmetry in hyperon decays when strange quark mass is taken into account, we rely on the empirical validity of Cabbibo theory to dertermine the matrix element $\\bar{u}\\gamma_{\\mu}\\gamma_5 u + \\bar{d}\\gamma_{\\mu}\\gamma_5 d - 2 \\bar{s}\\gamma_{\\mu}\\gamma_5 s$ between nucleon states. Combining with our calculation of $\\bar{u}\\gamma_{\\mu}\\gamma_5 u + \\bar{d}\\gamma_{\\mu}\\gamma_5 d$ and the well known nucleon $\\beta$-decay constant allows us to determine $$ occuring in the Bjorken sum rule. The result is in reasonable agreement with experiment. We also discuss the role of the anomaly in maintaini...
NRQCD Factorization and Universality of NRQCD matrix elements
Ma, J P
2005-01-01
The approach of nonrelativistic QCD(NRQCD) factorization was proposed to study inclusive production of a quarkonium. It is widely used and successful. The NRQCD factorization is based an expansion in the small velocity v, with which a heavy quark moves inside a quarkonium. However, a recent study of gluon fragmentation into a quarkonium at two-loop level shows that the factorization is broken and some infrared singularities remain at order of v^2. It is suggested that the relevant NRQCD matrix elements should be modified by adding a gauge link to restore the factorization. The modified matrix elements will have then extra soft-divergences at one-loop level which the unmodified can not have and this can affect the NRQCD factorization in other cases at one-loop level beside the gluon fragmentation. In this letter, we examine in detail the NRQCD factorization for inclusive quarkonium production in e^+ e^- annihilation at one-loop level. Our results show that the factorization can be made at order of $v^2$ withou...
Measurement of the CKM matrix element |V_ts|²
Unverdorben, Christopher Gerhard
This is the first direct measurement of the CKM matrix element |V_ts|, using data collected by the ATLAS detector in 2012 at √s=8 TeV pp-collisions with a total integrated luminosity of 20.3 fb⁻¹. The analysis is based on 112171 reconstructed tt̅ candidate events in the lepton+jets channel, having a purity of 90.0 %. 183 tt̅→WWbs̅ decays are expected (charge conjugation implied), which are available for the extraction of the CKM matrix element |V_ts|². To identify these rare decays, several observables are examined, such as the properties of jets, tracks and of b-quark identification algorithms. Furthermore, the s-quark hadrons K0s are considered, reconstructed by a kinematic fit. The best observables are combined in a multivariate analysis, called "boosted decision trees". The responses from Monte Carlo simulations are used as templates for a fit to data events yielding a significance value of 0.7σ for t→s+W decays. An upper limit of |V_ts|² < 1.74 % at 95 % confidence level is set, includi...
Closed String S-matrix Elements in Open String Field Theory
Garousi, Mohammad R.; Maktabdaran, G. R.
2005-03-01
We study the S-matrix elements of the gauge invariant operators corresponding to on-shell closed strings, in open string field theory. In particular, we calculate the tree level S-matrix element of two arbitrary closed strings, and the S-matrix element of one closed string and two open strings. By mapping the world-sheet of these amplitudes to the upper half z-plane, and by evaluating explicitly the correlators in the ghost part, we show that these S-matrix elements are exactly identical to the corresponding disk level S-matrix elements in perturbative string theory.
Running Couplings in Hamiltonians
Glazek, S D
2000-01-01
We describe key elements of the perturbative similarity renormalization group procedure for Hamiltonians using two, third-order examples: phi^3 interaction term in the Hamiltonian of scalar field theory in 6 dimensions and triple-gluon vertex counterterm in the Hamiltonian of QCD in 4 dimensions. These examples provide insight into asymptotic freedom in Hamiltonian approach to quantum field theory. The renormalization group procedure also suggests how one may obtain ultraviolet-finite effective Schrödinger equations that correspond to the asymptotically free theories, including transition from quark and gluon to hadronic degrees of freedom in case of strong interactions. The dynamics is invariant under boosts and allows simultaneous analysis of bound state structure in the rest and infinite momentum frames.
Diagonal multi-soliton matrix elements in finite volume
Pálmai, T
2012-01-01
We consider diagonal matrix elements of local operators between multi-soliton states in finite volume in the sine-Gordon model, and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential in the volume. This conjecture extends the results of Pozsgay and Tak\\'acs which were only valid for diagonal scattering. In order to test the conjecture we implement a numerical renormalization group improved truncated conformal space approach. The numerical comparisons confirm the conjecture, which is expected to be valid for general integrable field theories. The conjectured formula can be used to evaluate finite temperature one-point and two-point functions using recently developed methods.
Application of FIRE for the calculation of photon matrix elements
Norihisa Watanabe
2009-10-01
The next-to-next-to-leading order (the order $ _{s}^{2}$ ) corrections to the first moment of the polarized virtual photon structure function $g_{1}^{} (x, Q^{2}, P^{2})$ are studied in perturbative QCD for the kinematical region $^{2} \\ll P^{2} Q^{2}$, where $−Q^{2} (−P^{2})$ is the mass square of the probe (target) photon and is the QCD scale parameter. In order to evaluate the two-loop Feynman diagrams for the photon matrix element of the gluon operator, I apply the recently developed algorithm FIRE which reduces a complicated sum of scalar Feynman integrals to a linear combination of a few master integrals. The details of the calculation are presented.
Precision study of excited state effects in nucleon matrix elements
Dinter, Simon; Drach, Vincent; Jansen, Karl; Renner, Dru B. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Alexandrou, Constantia [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; The Cyprus Insitute, Nicosia (Cyprus). Computation-Based Science and Technology Research Center; Constantinou, Martha [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics
2011-08-15
We present a dedicated analysis of the influence of excited states on the calculation of nucleon matrix elements. This calculation is performed at a fixed value of the lattice spacing, volume and pion mass that are typical of contemporary lattice computations. We focus on the nucleon axial charge, g{sub A}, for which we use about 7,500 measurements, and on the average momentum of the unpolarized isovector parton distribution, left angle x right angle {sub u-d}, for which we use about 23,000 measurements. All computations are done employing N{sub f}=2+1+1 maximally-twisted-mass Wilson fermions and using nonperturbatively calculated renormalization factors. Excited state e ects are shown to be negligible for g{sub A}, whereas they lead to an O(10%) downward shift for left angle x right angle {sub u-d}. (orig.)
Structure of nuclear transition matrix elements for neutrinoless double- decay
P K Rath
2010-08-01
The structure of nuclear transition matrix elements (NTMEs) required for the study of neutrinoless double- decay within light Majorana neutrino mass mechanism is disassembled in the PHFB model. The NTMEs are calculated using a set of HFB intrinsic wave functions, the reliability of which has been previously established by obtaining an overall agreement between the theoretically calculated spectroscopic properties and the available experimental data. Presently, we study the role of short-range correlations, radial evolution of NTMEs and deformation effects due to quadrupolar correlations. In addition, limits on effective light neutrino mass $\\langle m_{} \\rangle$ are extracted from the observed limits on half-lives $T_{1/2}^{0}$ of neutrinoless double- decay.
Quantum control by means of hamiltonian structure manipulation.
Donovan, A; Beltrani, V; Rabitz, H
2011-04-28
A traditional quantum optimal control experiment begins with a specific physical system and seeks an optimal time-dependent field to steer the evolution towards a target observable value. In a more general framework, the Hamiltonian structure may also be manipulated when the material or molecular 'stockroom' is accessible as a part of the controls. The current work takes a step in this direction by considering the converse of the normal perspective to now start with a specific fixed field and employ the system's time-independent Hamiltonian structure as the control to identify an optimal form. The Hamiltonian structure control variables are taken as the system energies and transition dipole matrix elements. An analysis is presented of the Hamiltonian structure control landscape, defined by the observable as a function of the Hamiltonian structure. A proof of system controllability is provided, showing the existence of a Hamiltonian structure that yields an arbitrary unitary transformation when working with virtually any field. The landscape analysis shows that there are no suboptimal traps (i.e., local extrema) for controllable quantum systems when unconstrained structural controls are utilized to optimize a state-to-state transition probability. This analysis is corroborated by numerical simulations on model multilevel systems. The search effort to reach the top of the Hamiltonian structure landscape is found to be nearly invariant to system dimension. A control mechanism analysis is performed, showing a wide variety of behavior for different systems at the top of the Hamiltonian structure landscape. It is also shown that reducing the number of available Hamiltonian structure controls, thus constraining the system, does not always prevent reaching the landscape top. The results from this work lay a foundation for considering the laboratory implementation of optimal Hamiltonian structure manipulation for seeking the best control performance, especially with limited
Angeli, C.; Cimiraglia, R.
2013-02-01
A symbolic program performing the Formal Reduction of Density Operators (FRODO), formerly developed in the MuPAD computer algebra system with the purpose of evaluating the matrix elements of the electronic Hamiltonian between internally contracted functions in a complete active space (CAS) scheme, has been rewritten in Mathematica. New version : A program summaryProgram title: FRODO Catalogue identifier: ADV Y _v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVY_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3878 No. of bytes in distributed program, including test data, etc.: 170729 Distribution format: tar.gz Programming language: Mathematica Computer: Any computer on which the Mathematica computer algebra system can be installed Operating system: Linux Classification: 5 Catalogue identifier of previous version: ADV Y _v1_0 Journal reference of previous version: Comput. Phys. Comm. 171(2005)63 Does the new version supersede the previous version?: No Nature of problem. In order to improve on the CAS-SCF wavefunction one can resort to multireference perturbation theory or configuration interaction based on internally contracted functions (ICFs) which are obtained by application of the excitation operators to the reference CAS-SCF wavefunction. The previous formulation of such matrix elements in the MuPAD computer algebra system, has been rewritten using Mathematica. Solution method: The method adopted consists in successively eliminating all occurrences of inactive orbital indices (core and virtual) from the products of excitation operators which appear in the definition of the ICFs and in the electronic Hamiltonian expressed in the second quantization formalism. Reasons for new version: Some years ago we published in this journal a couple of papers [1, 2
Redesign of the DFT/MRCI Hamiltonian.
Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M
2016-01-21
The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.
What do we know about neutrinoless double-beta decay nuclear matrix elements?
Menéndez, J
2016-01-01
The detection of neutrinoless double-beta decay will establish the Majorana nature of neutrinos. In addition, if the nuclear matrix elements of this process are reliably known, the experimental lifetime will provide precious information about the absolute neutrino masses and hierarchy. I review the status of nuclear structure calculations for neutrinoless double-beta decay matrix elements, and discuss some key issues to be addressed in order to meet the demand for accurate nuclear matrix elements.
Neutrinoless Double Beta Nuclear Matrix Elements Around Mass 80 in the Nuclear Shell Model
Yoshinaga, Naotaka; Higashiyama, Koji; Taguchi, Daisuke; Teruya, Eri
The observation of the neutrinoless double-beta decay can determine whether the neutrino is a Majorana particle or not. In its theoretical nuclear side it is particularly important to estimate three types of nuclear matrix elements, namely, Fermi (F), Gamow-Teller (GT), and tensor (T) types matrix elements. The shell model calculations and also the pair-truncated shell model calculations are carried out to check the model dependence on nuclear matrix elements. In this work the neutrinoless double-beta decay for mass A = 82 nuclei is studied. It is found that the matrix elements are quite sensitive to the ground state wavefunctions.
Closed String S-matrix Elements in Open String Field Theory
Garousi, M R; Garousi, Mohammad R
2005-01-01
Using the gauge invariant operators corresponding to on-shell closed string states in open string field theory, we study the tree level S-matrix element of two arbitrary closed string states, and the S-matrix element of one closed string and two open string states. By mapping the world-sheet of the amplitudes to the upper half z-plane, and by evaluating the correlators in the ghost parts, we show that the S-matrix elements are exactly identical to the corresponding disk level S-matrix elements in bosonic string theory.
Controlling Excited-State Contamination in Nucleon Matrix Elements
Yoon, Boram; Bhattacharya, Tanmoy; Engelhardt, Michael; Green, Jeremy; Joó, Bálint; Lin, Huey-Wen; Negele, John; Orginos, Kostas; Pochinsky, Andrew; Richards, David; Syritsyn, Sergey; Winter, Frank
2016-01-01
We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2+1 flavor ensemble with lattices of size $32^3 \\times 64$ generated using the rational hybrid Monte Carlo algorithm at $a=0.081$~fm and with $M_\\pi=312$~MeV. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a two-state fit to data at multiple values of the source-sink separation $t_{\\rm sep}$. We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost-effectiveness. A detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of $t_{\\rm sep}$ needed to demonstrate convergence of the isovector charges of the nucleon to the $t_...
Matrix element method for high performance computing platforms
Grasseau, G.; Chamont, D.; Beaudette, F.; Bianchini, L.; Davignon, O.; Mastrolorenzo, L.; Ochando, C.; Paganini, P.; Strebler, T.
2015-12-01
Lot of efforts have been devoted by ATLAS and CMS teams to improve the quality of LHC events analysis with the Matrix Element Method (MEM). Up to now, very few implementations try to face up the huge computing resources required by this method. We propose here a highly parallel version, combining MPI and OpenCL, which makes the MEM exploitation reachable for the whole CMS datasets with a moderate cost. In the article, we describe the status of two software projects under development, one focused on physics and one focused on computing. We also showcase their preliminary performance obtained with classical multi-core processors, CUDA accelerators and MIC co-processors. This let us extrapolate that with the help of 6 high-end accelerators, we should be able to reprocess the whole LHC run 1 within 10 days, and that we have a satisfying metric for the upcoming run 2. The future work will consist in finalizing a single merged system including all the physics and all the parallelism infrastructure, thus optimizing implementation for best hardware platforms.
Controlling excited-state contamination in nucleon matrix elements
Yoon, Boram; Gupta, Rajan; Bhattacharya, Tanmoy; Engelhardt, Michael; Green, Jeremy; Joó, Bálint; Lin, Huey-Wen; Negele, John; Orginos, Kostas; Pochinsky, Andrew; Richards, David; Syritsyn, Sergey; Winter, Frank
2016-06-01
We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2+1 flavor ensemble with lattices of size $32^3 \\times 64$ generated using the rational hybrid Monte Carlo algorithm at $a=0.081$~fm and with $M_\\pi=312$~MeV. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a two-state fit to data at multiple values of the source-sink separation $t_{\\rm sep}$. We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost-effectiveness. A detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of $t_{\\rm sep}$ needed to demonstrate convergence of the isovector charges of the nucleon to the $t_{\\rm sep} \\to \\infty $ estimates is presented.
A top quark mass measurement using a matrix element method
Linacre, Jacob Thomas [St. John' s College, Annapolis, MD (United States)
2009-01-01
A measurement of the mass of the top quark is presented, using top-antitop pair (t$\\bar{t}$) candidate events for the lepton+jets decay channel. The measurement makes use of Tevatron p$\\bar{p}$ collision data at centre-of-mass energy √s = 1.96 TeV, collected at the CDF detector. The top quark mass is measured by employing an unbinned maximum likelihood method where the event probability density functions are calculated using signal (t$\\bar{t}$) and background (W+jets) matrix elements, as well as a set of parameterised jet-to-parton mapping functions. The likelihood function is maximised with respect to the top quark mass, the fraction of signal events, and a correction to the jet energy scale (JES) of the calorimeter jets. The simultaneous measurement of the JES correction (Δ_{JES}) provides an in situ jet energy calibration based on the known mass of the hadronically decaying W boson. Using 578 lepton+jets candidate events corresponding to 3.2 fb ^{-1} of integrated luminosity, the top quark mass is measured to be m_{t} = 172.4± 1.4 (stat+Δ_{JES}) ±1.3 (syst) GeV=c^{2}, one of the most precise single measurements to date.
A top quark mass measurement using a matrix element method
Linacre, Jacob Thomas [St. John' s College, Annapolis, MD (United States)
2009-01-01
A measurement of the mass of the top quark is presented, using top-antitop pair (t$\\bar{t}$) candidate events for the lepton+jets decay channel. The measurement makes use of Tevatron p$\\bar{p}$ collision data at centre-of-mass energy √s = 1.96 TeV, collected at the CDF detector. The top quark mass is measured by employing an unbinned maximum likelihood method where the event probability density functions are calculated using signal (t$\\bar{t}$) and background (W+jets) matrix elements, as well as a set of parameterised jet-to-parton mapping functions. The likelihood function is maximised with respect to the top quark mass, the fraction of signal events, and a correction to the jet energy scale (JES) of the calorimeter jets. The simultaneous measurement of the JES correction (Δ_{JES}) provides an in situ jet energy calibration based on the known mass of the hadronically decaying W boson. Using 578 lepton+jets candidate events corresponding to 3.2 fb ^{-1} of integrated luminosity, the top quark mass is measured to be m_{t} = 172.4± 1.4 (stat+Δ_{JES}) ±1.3 (syst) GeV=c^{2}, one of the most precise single measurements to date.
BAMPS with the improved Gunion–Bertsch matrix element
Senzel, Florian; Fochler, Oliver; Uphoff, Jan [Institut für Theoretische Physik, Goethe-Universität Frankfurt, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main (Germany); Xu, Zhe [Department of Physics, Tsinghua University, Beijing 100084 (China); Greiner, Carsten [Institut für Theoretische Physik, Goethe-Universität Frankfurt, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main (Germany)
2014-12-15
Focusing on the simultaneous investigation of the hard and the soft regime of ultra-relativistic heavy-ion collisions at the Relativistic Heavy-Ion Collider (RHIC) at the Brookhaven National Laboratory (BNL) and the Large Hadron Collider (LHC) at CERN, we present our recent results on the nuclear modification factor R{sub AA} and the elliptic flow v{sub 2} within the partonic transport model BAMPS (Boltzmann Approach to Multi-Parton Scatterings). While using interactions provided by perturbative QCD, BAMPS allows the full 3+1D simulation of the quark–gluon plasma (QGP) at the microscopic level by solving the relativistic Boltzmann equation for quarks and gluons. The microscopic interactions include both elastic 2→2 collisions, calculated by screened leading order pQCD matrix elements, and inelastic 2↔3 processes, calculated within an improved Gunion–Bertsch approximation. Furthermore, for all partonic processes a microscopic, running coupling is explicitly taken into account. We show that when fixing the parameter X{sub LPM} resulting from the effective modeling of the Landau–Pomeranchuk–Migdal effect, we find not only a good description of R{sub AA} at both RHIC and LHC, but also a sizable elliptic flow is built up within the partonic phase.
Controlling excited-state contamination in nucleon matrix elements
Yoon, Boram; Gupta, Rajan; Bhattacharya, Tanmoy; Engelhardt, Michael; Green, Jeremy; Joó, Bálint; Lin, Huey-Wen; Negele, John; Orginos, Kostas; Pochinsky, Andrew; Richards, David; Syritsyn, Sergey; Winter, Frank; Nucleon Matrix Elements NME Collaboration
2016-06-01
We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2 +1 -flavor ensemble with lattices of size 323×64 generated using the rational hybrid Monte Carlo algorithm at a =0.081 fm and with Mπ=312 MeV . The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a 2-state fit to data at multiple values of the source-sink separation tsep. We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost effectiveness. A detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of tsep needed to demonstrate convergence of the isovector charges of the nucleon to the tsep→∞ estimates is presented.
Orsucci, Davide [Scuola Normale Superiore, I-56126 Pisa (Italy); Burgarth, Daniel [Department of Mathematics, Aberystwyth University, Aberystwyth SY23 3BZ (United Kingdom); Facchi, Paolo; Pascazio, Saverio [Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Nakazato, Hiromichi; Yuasa, Kazuya [Department of Physics, Waseda University, Tokyo 169-8555 (Japan); Giovannetti, Vittorio [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy)
2015-12-15
The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.
Dirac matrices as elements of a superalgebraic matrix algebra
Monakhov, V. V.
2016-08-01
The paper considers a Clifford extension of the Grassmann algebra, in which operators are built from Grassmann variables and by the derivatives with respect to them. It is shown that a subalgebra which is isomorphic to the usual matrix algebra exists in this algebra, the Clifford exten-sion of the Grassmann algebra is a generalization of the matrix algebra and contains superalgebraic operators expanding matrix algebra and produces supersymmetric transformations.
Meeds, E.; Leenders, R.; Welling, M.; Meila, M.; Heskes, T.
2015-01-01
Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively lowdimensional problems. We introduce Hamiltonian ABC (HABC), a set of lik
Ender, I. A.; Bakaleinikov, L. A.; Flegontova, E. Yu.; Gerasimenko, A. B.
2017-08-01
We have proposed an algorithm for the sequential construction of nonisotropic matrix elements of the collision integral, which are required to solve the nonlinear Boltzmann equation using the moments method. The starting elements of the matrix are isotropic and assumed to be known. The algorithm can be used for an arbitrary law of interactions for any ratio of the masses of colliding particles.
Computation of Two-Body Matrix Elements From the Argonne $v_{18}$ Potential
Mihaila, B; Mihaila, Bogdan; Heisenberg, Jochen H.
1998-01-01
We discuss the computation of two-body matrix elements from the Argonne $v_{18}$ interaction. The matrix elements calculation is presented both in particle-particle and in particle-hole angular momentum coupling. The procedures developed here can be applied to the case of other NN potentials, provided that they have a similar operator format.
The rovibrational Hamiltonian for ammonia-like molecules.
Makarewicz, Jan; Skalozub, Alexander
2002-03-01
A new exact quantum mechanical rovibrational Hamiltonian operator for ammonia-like molecules is derived. The Hamiltonian is constructed in a molecular system of axes, such that its z' axis makes a trisection of the pyramidal angle formed by three bond vectors with the vertex on the central atom. The introduced set of the internal rovibrational coordinates is adapted to facilitate a convenient description of the inversion motion. These internal coordinates and the molecular axis system have a remarkable property, namely, the internal vibrational angular momentum of the molecule equals zero. This property significantly reduces the Coriolis coupling and simplifies the form of the Hamiltonian. The correctness of this Hamiltonian is proved by a numerical procedure. The orthogonal Radau vectors allowing us to define a similar molecular axis system and the internal coordinates are considered. The Hamiltonian for the Radau parameterization takes a form simple enough to carry out effectively variational calculations of the molecular rovibrational states. Under the appropriate choice of the variational basis functions, the Hamiltonian matrix elements are fully factorizable and do not have any singularities. A convenient method of symmetrization of the basis functions is proposed.
SU(3) Breaking in Neutral Current Axial Matrix Elements and the Spin Content of the Nucleon
Savage, M J; Savage, Martin J.; Walden, James
1997-01-01
We examine the effects of SU(3) breaking in the matrix elements of the flavour-diagonal axial currents between octet baryon states and find that SU(3) breaking may be substantial for some matrix elements. We estimate the strange axial matrix element in the proton to be between -0.35 and 0 and the matrix element of the flavour-singlet current in the proton to be between -0.1 and +0.3 from the E-143 measurement g_1(x) . The up-quark content of the $\\Xi^-$ is discussed and its implications for nonleptonic weak processes discussed. We also estimate the matrix element of the axial current coupling to the $Z^0$ between all octet baryon states. This may be important for neutrino interactions in dense nuclear environments, where hyperons may play an important role.
Mukherjee, Saikat; Bandyopadhyay, Sudip; Paul, Amit Kumar; Adhikari, Satrajit
2013-04-25
We present the molecular symmetry (MS) adapted treatment of nonadiabatic coupling terms (NACTs) for the excited electronic states (2(2)E' and 1(2)A1') of Na3 cluster, where the adiabatic potential energy surfaces (PESs) and the NACTs are calculated at the MRCI level by using an ab initio quantum chemistry package (MOLPRO). The signs of the NACTs at each point of the configuration space (CS) are determined by employing appropriate irreducible representations (IREPs) arising due to MS group, and such terms are incorporated into the adiabatic to diabatic transformation (ADT) equations to obtain the ADT angles. Since those sign corrected NACTs and the corresponding ADT angles demonstrate the validity of curl condition for the existence of three-state (2(2)E' and 1(2)A1') sub-Hilbert space, it becomes possible to construct the continuous, single-valued, symmetric, and smooth 3 × 3 diabatic Hamiltonian matrix. Finally, nuclear dynamics has been carried out on such diabatic surfaces to explore whether our MS-based treatment of diabatization can reproduce the pattern of the experimental spectrum for system B of Na3 cluster.
Mochon, C
2006-01-01
Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In this limit, the problem of finding the optimal query algorithm can be mapped into the problem of finding shortest paths on a manifold. The study of these shortest paths leads to lower bounds of the original unitary oracle problem. A number of example Hamiltonian oracles are studied in this paper, including oracle interrogation and the problem of computing the XOR of the hidden bits. Both of these problems are related to the study of geodesics on spheres with non-round metrics. For the case of two hidden bits a complete description of the geodesics is given. For n hidden bits a simple lower bound is proven that shows the problems require a query time proportional to n, even in the continuum limit. Finally, the problem of continuous Grover search is reexamined leading to a modest improvement to the protocol of Farhi and Gutmann.
Incorporation of New Information in an Approximate Hamiltonian
Viazminsky, C. P.; Baza, S
2002-01-01
Additional information about the eigenvalues and eigenvectors of a physical system demands extension of the effective Hamiltonian in use. In this work we extend the effective Hamiltonian that describes partially a physical system so that the new Hamiltonian comprises, in addition to the information in the old Hamiltonian, new information, available by means of experiment or theory. A simple expression of the enlarged Hamiltonian, which does not involve matrix inversion, is obtained. It is als...
A METHOD FOR STIFFNESS MATRIX OF TRIANGULAR TORUS ELEMENT
Durmuş GÜNAY
1996-01-01
Full Text Available The matrices of constants for the stiffness matrices of triangular torus elements family are generated on computer by using the expression given in literature. After the matrices are generated once, it is easy to obtain the stiffness matrices for all member of family of triangular torus elements without need for numerical integration.
Lü, Ling; Liu, Shuo; Li, Gang; Zhao, Guannan; Gu, Jiajia; Tian, Jing; Wang, Zhouyang
2016-11-01
In this paper, we research the outer synchronization among discrete networks with different topologies. Based on Lyapunov theorem, a novel synchronization technique is designed. Further, the control inputs of the networks and the adaptive laws of configuration matrix element are obtained. In the end, a numerical example is given to illustrate the effectiveness of the synchronization technique. It is found that the designed control input of the networks ensures the convergence of the errors among the networks to zero. And the designed adaptive law of configuration matrix element can replace effectively configuration matrix element in networks.
Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
Engel, Jonathan
2016-01-01
The nuclear matrix elements that govern the rate of neutrinoless double beta decay must be accurately calculated if experiments are to reach their full potential. Theorists have been working on the problem for a long time but have recently stepped up their efforts as ton-scale experiments have begun to look feasible. Here we review past and recent work on the matrix elements in a wide variety of nuclear models and discuss work that will be done in the near future. Ab initio nuclear-structure theory, which is developing rapidly, holds out hope of more accurate matrix elements with quantifiable error bars.
QCD event generators with next-to-leading order matrix-elements and parton showers
Kurihara, Y; Ishikawa, T; Kato, K; Kawabata, S; Munehisa, T; Tanaka, H
2003-01-01
A new method to construct event-generators based on next-to-leading order QCD matrix-elements and leading-logarithmic parton showers is proposed. Matrix elements of loop diagram as well as those of a tree level can be generated using an automatic system. A soft/collinear singularity is treated using a leading-log subtraction method. Higher order re-summation of the soft/collinear correction by the parton shower method is combined with the NLO matrix-element without any double-counting in this method. An example of the event generator for Drell-Yan process is given for demonstrating a validity of this method.
Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review
Engel, Jonathan; Menéndez, Javier
2017-04-01
The nuclear matrix elements that govern the rate of neutrinoless double beta decay must be accurately calculated if experiments are to reach their full potential. Theorists have been working on the problem for a long time but have recently stepped up their efforts as ton-scale experiments have begun to look feasible. Here we review past and recent work on the matrix elements in a wide variety of nuclear models and discuss work that will be done in the near future. Ab initio nuclear-structure theory, which is developing rapidly, holds out hope of more accurate matrix elements with quantifiable error bars.
EH3 matrix mineralogy with major and trace element composition compared to chondrules
Lehner, S. W.; McDonough, W. F.; NéMeth, P.
2014-12-01
We investigated the matrix mineralogy in primitive EH3 chondrites Sahara 97072, ALH 84170, and LAR 06252 with transmission electron microscopy; measured the trace and major element compositions of Sahara 97072 matrix and ferromagnesian chondrules with laser-ablation, inductively coupled, plasma mass spectrometry (LA-ICPMS); and analyzed the bulk composition of Sahara 97072 with LA-ICPMS, solution ICPMS, and inductively coupled plasma atomic emission spectroscopy. The fine-grained matrix of EH3 chondrites is unlike that in other chondrite groups, consisting primarily of enstatite, cristobalite, troilite, and kamacite with a notable absence of olivine. Matrix and pyroxene-rich chondrule compositions differ from one another and are distinct from the bulk meteorite. Refractory lithophile elements are enriched by a factor of 1.5-3 in chondrules relative to matrix, whereas the matrix is enriched in moderately volatile elements. The compositional relation between the chondrules and matrix is reminiscent of the difference between EH3 pyroxene-rich chondrules and EH3 Si-rich, highly sulfidized chondrules. Similar refractory element ratios between the matrix and the pyroxene-rich chondrules suggest the fine-grained material primarily consists of the shattered, sulfidized remains of the formerly pyroxene-rich chondrules with the minor addition of metal clasts. The matrix, chondrule, and metal-sulfide nodule compositions are probably complementary, suggesting all the components of the EH3 chondrites came from the same nebular reservoir.
Design of a shielded coil element of a matrix gradient coil
Jia, Feng; Littin, Sebastian; Layton, Kelvin J.; Kroboth, Stefan; Yu, Huijun; Zaitsev, Maxim
2017-08-01
The increasing interest in spatial encoding with non-linear magnetic fields has intensified the need for coils that generates such fields. Matrix coils consisting of multiple coil elements appear to offer a high flexibility in generating customized encoding fields and are particularly promising for localized high resolution imaging applications. However, coil elements of existing matrix coils were primarily designed and constructed for better shimming and therefore are not expected to achieve an optimal performance for local spatial encoding. Moreover, eddy current properties of such coil elements were not fully explored. In this work, an optimization problem is formulated based on the requirement of local non-linear encoding and eddy current reduction that results in novel designs of coil elements for an actively-shielded matrix gradient coil. Two metrics are proposed to assess the performance of different coil element designs. The results are analyzed to reveal new insights into coil element design.
Renormalized Effective QCD Hamiltonian Gluonic Sector
Robertson, D G; Szczepaniak, A P; Ji, C R; Cotanch, S R
1999-01-01
Extending previous QCD Hamiltonian studies, we present a new renormalization procedure which generates an effective Hamiltonian for the gluon sector. The formulation is in the Coulomb gauge where the QCD Hamiltonian is renormalizable and the Gribov problem can be resolved. We utilize elements of the Glazek and Wilson regularization method but now introduce a continuous cut-off procedure which eliminates non-local counterterms. The effective Hamiltonian is then derived to second order in the strong coupling constant. The resulting renormalized Hamiltonian provides a realistic starting point for approximate many-body calculations of hadronic properties for systems with explicit gluon degrees of freedom.
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
Toward Universality in Similarity Renormalization Group Evolved Few-body Potential Matrix Elements
Dainton, Brian
2015-01-01
We first examine how T-matrix equivalence drives the flow of similarity renormalization group (SRG) evolved potential matrix elements to a universal form, with the ultimate goal of gaining insight into universality for three-nucleon forces. In agreement with observations made previously for Lee-Suzuki transformations, regions of universal potential matrix elements are restricted to where half-on-shell T-matrix equivalence holds, but the potentials must also reproduce binding energies. We find universality in local energy regions, reflecting a local decoupling by the SRG. To continue the study in the 3-body sector, we create a simple 1-D spinless boson "theoretical laboratory" for a dramatic improvement in computational efficiency. We introduce a basis-transformation, harmonic oscillator (HO) basis, which is used for current many-body calculations and discuss the imposed truncations. When SRG evolving in a HO-basis, we show that the evolved matrix elements, once transformed back into momentum-representation, d...
Symmetric Matrix Fields in the Finite Element Method
Gerard Awanou
2010-07-01
Full Text Available The theory of elasticity is used to predict the response of a material body subject to applied forces. In the linear theory, where the displacement is small, the stress tensor which measures the internal forces is the variable of primal importance. However the symmetry of the stress tensor which expresses the conservation of angular momentum had been a challenge for finite element computations. We review in this paper approaches based on mixed finite element methods.
Matrix Elements of a Hyperbolic Vector Operator under SO(2,1)
Zettili, Nouredine; Boukahil, Abdelkrim
We deal here with the use of Wigner-Eckart type arguments to calculate the matrix elements of a hyperbolic vector operator /rightarrow{V} by expressing them in terms of reduced matrix elements. In particular, we focus on calculating the matrix elements of this vector operator within the basis of the hyperbolic angular momentum /rightarrow{T} whose components ̂ {T}1, ̂ {T}2, ̂ {T}3 satisfy an SO(2,1) Lie algebra. We show that the commutation rules between the components of /rightarrow{V} and /rightarrow{T} can be inferred from the algebra of ordinary angular momentum. We then show that, by analogy to the Wigner-Eckart theorem, we can calculate the matrix elements of /rightarrow{V} within a representation where /rightarrow {T}2 and ̂ {T}3 are jointly diagonal.
Nuclear matrix element for two neutrino double beta decay from 136Xe
Ejiri, Hiroyasu
2012-01-01
The nuclear matrix element for the two neutrino double beta decay (DBD) of 136Xe was evaluated by FSQP (Fermi Surface Quasi Particle model), where experimental GT strengths measured by the charge exchange reaction and those by the beta decay rates were used. The 2 neutrino DBD matrix element is given by the sum of products of the single beta matrix elements via low-lying (Fermi Surface) quasi-particle states in the intermediate nucleus. 136Xe is the semi-magic nucleus with the closed neutron-shell, and the beta + transitions are almost blocked. Thus the 2 neutrino DBD is much suppressed. The evaluated 2 neutrino DBD matrix element is consistent with the observed value.
Hadronic matrix elements of neutral-meson mixing through lattice QCD
Chang, C C
2015-01-01
Neutral-meson mixing is loop suppressed in the Standard Model, leading to the possibility of enhanced sensitivity to new physics. The uncertainty in Standard Model predictions for $B$-meson oscillation frequencies is dominated by theoretical uncertainties within the short-distance $B$-meson hadronic matrix elements, motivating the need for improved precision. In $D$-meson mixing, the Standard Model short-distance contributions are further suppressed by the GIM mechanism allowing for the possibility of large new physics enhancements. A first-principle determination of the $D$-meson short-distance hadronic matrix elements will allow for model-discrimination between the new physics theories. I review recently published and ongoing lattice calculations of hadronic matrix elements in $B$ and $D$-meson mixing with emphasis on the Fermilab lattice and MILC collaboration effort on the determination of the $B$ and $D$-meson mixing hadronic matrix elements using the methods of lattice QCD.
The calculating formula for radial matrix elements of a relativistic harmonic oscillator
强稳朝
2003-01-01
A universal practical formula is given for calculating an integral which includes two confluent hypergeometric functions, power and exponential functions; then by means of this formula, the expressions of the radial matrix elements for a relativistic harmonic oscillator are given.
Matrix Elements of One- and Two-Body Operators in the Unitary Group Approach (II) - Application
DAI Lian-Rong; PAN Feng
2001-01-01
Simple analytical expressions for one- and two-body matrix elements in the unitary group approach to the configuration interaction problems of many-electron systems are obtained based on the previous results for general Un irreps.
无
2002-01-01
Effects of rare earth element La on the microstructure of Cu matrix diamond tools were researched under the conditions of various materials componentsand the process parameters in order to improve materials properties. SEM, XPS and X-ray were used to investigate the fracture section, microstructure and the element valence in materials. The results shown that the combination of rare earth element La and transition element Ti is advantageous to the bonding state between diamond particles and matrix, so it can improve the materials properties. Suitable sintering temperature is 790℃.
Second level semi-degenerate fields in W3 Toda theory: matrix element and differential equation
Belavin, Vladimir; Estienne, Benoit; Santachiara, Raoul
2016-01-01
In a recent study we considered W3 Toda 4-point functions that involve matrix elements of a primary field with the highest-weight in the adjoint representation of sl3. We generalize this result by considering a semi-degenerate primary field, which has one null vector at level two. We obtain a sixth-order Fuchsian differential equation for the conformal blocks. We discuss the presence of multiplicities, the matrix elements and the fusion rules.
Neutrinoless double beta nuclear matrix elements around mass 80 in the nuclear shell-model
Yoshinaga, N.; Higashiyama, K.; Taguchi, D.; Teruya, E.
2015-05-01
The observation of the neutrinoless double-beta decay can determine whether the neutrino is a Majorana particle or not. For theoretical nuclear physics it is particularly important to estimate three types of matrix elements, namely Fermi (F), Gamow-Teller (GT), and tensor (T) matrix elements. In this paper, we carry out shell-model calculations and also pair-truncated shell-model calculations to check the model dependence in the case of mass A=82 nuclei.
Neutrinoless double beta nuclear matrix elements around mass 80 in the nuclear shell-model
Yoshinaga N.
2015-01-01
Full Text Available The observation of the neutrinoless double-beta decay can determine whether the neutrino is a Majorana particle or not. For theoretical nuclear physics it is particularly important to estimate three types of matrix elements, namely Fermi (F, Gamow-Teller (GT, and tensor (T matrix elements. In this paper, we carry out shell-model calculations and also pair-truncated shell-model calculations to check the model dependence in the case of mass A=82 nuclei.
XU Xiu-Wei; REN Ting-Qi; LIU Shu-Yan; MA Qiu-Ming; LIU Sheng-Dian
2007-01-01
Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators (BEQPO's), we present the analytic expression of arbitrary matrix elements for BEQPO's. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO's.
Calculation of Radiative Corrections to E1 matrix elements in the Neutral Alkalis
Sapirstein, J; Cheng, K T
2004-09-28
Radiative corrections to E1 matrix elements for ns-np transitions in the alkali metal atoms lithium through francium are evaluated. They are found to be small for the lighter alkalis but significantly larger for the heavier alkalis, and in the case of cesium much larger than the experimental accuracy. The relation of the matrix element calculation to a recent decay rate calculation for hydrogenic ions is discussed, and application of the method to parity nonconservation in cesium is described.
A nodal spectral stiffness matrix for the finite-element method
Bittencourt, Marco L.; Vazquez, Thais G.
2008-12-01
In this paper, shape functions are proposed for the spectral finite-element method aiming to finding a nodal spectral stiffness matrix. The proposed shape functions obtain a nearly diagonal 1D stiffness matrix with better conditioning than using the Lagrange and Jacobi bases.
Bethe ansatz matrix elements as non-relativistic limits of form factors of quantum field theory
Kormos, M.; Mussardo, G.; Pozsgay, B.
2010-01-01
We show that the matrix elements of integrable models computed by the algebraic Bethe ansatz (BA) can be put in direct correspondence with the form factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe ansatz model can be regarded as a suitable non-relativistic
Some recurrence relations among the radial matrix elements for the relativistic hydrogenic atoms
Dong Shihai [Programa de Ingenieria Molecular, Instituto Mexicano del Petroleo, Lazaro Cardenas 152, 07730 Mexico, D.F. (Mexico)]. E-mail: dongsh2@yahoo.com; Chen Changyuan [Department of Physics, Yancheng Teachers College, Yancheng 224002 (China)]. E-mail: yctcccy@tom.com; Lozada-Cassou, M. [Programa de Ingenieria Molecular, Instituto Mexicano del Petroleo, Lazaro Cardenas 152, 07730 Mexico, D.F. (Mexico)]. E-mail: marcelo@www.imp.mx
2004-12-06
The general calculation formula for the matrix elements
THE STRESS SUBSPACE OF HYBRID STRESS ELEMENT AND THE DIAGONALIZATION METHOD FOR FLEXIBILITY MATRIX H
张灿辉; 冯伟; 黄黔
2002-01-01
The following is proved: 1 ) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular fiexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt 's method. Because of the resulting diagonal fiexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency is improved greatly. The numerical examples show that the method is effective.
Some Graphs Containing Unique Hamiltonian Cycles
Lynch, Mark A. M.
2002-01-01
In this paper, two classes of graphs of arbitrary order are described which contain unique Hamiltonian cycles. All the graphs have mean vertex degree greater than one quarter the order of the graph. The Hamiltonian cycles are detailed, their uniqueness proved and simple rules for the construction of the adjacency matrix of the graphs are given.…
Equivalence of Conformal Superalgebras to Hamiltonian Superoperators
Xiaoping Xu
2001-01-01
In this paper, we present a formal variational calculus of super functions in one real variable and find the conditions for a "matrix differential operator'' to be a Hamiltonian superoperator. Moreover, we prove that conformal superalgebras are equivalent to certain Hamiltonian superoperators.
Romanas Karkauskas
2011-04-01
Full Text Available The expressions of the finite element method tangent stiffness matrix of geometrically nonlinear constructions are not fully presented in publications. The matrixes of small displacements stiffness are usually presented only. To solve various problems of construction analysis or design and to specify the mode of the real deflection of construction, it is necessary to have a fully described tangent matrix analytical expression. This paper presents a technique of tangent stiffness matrix generation using discrete body total potential energy stationary conditions considering geometrically nonlinear 2D frame element taking account of interelement interaction forces only. The obtained vector-function derivative of internal forces considering nodal displacements is the tangent stiffness matrix. The analytical expressions having nodal displacements of matrixes forming the content of the 2D frame construction element tangent stiffness matrix are presented in the article. The suggested methodology has been checked making symbolical calculations in the medium of MatLAB calculation complex. The analytical expression of the stiffness matrix has been obtained.Article in Lithuanian
Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)
Werry, Jason L.; Gould, Mark D.; Isaac, Phillip S. [School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072 (Australia)
2015-12-15
The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible gl(m|n) modules. In particular, we give matrix element formulae for all gl(m|n) generators, including the non-elementary generators, together with their phases on finite dimensional type 2 unitary irreducible representations which include the contravariant tensor representations and an additional class of essentially typical representations. Remarkably, we find that the type 2 unitary matrix element equations coincide with the type 1 unitary matrix element equations for non-vanishing matrix elements up to a phase.
On the generalized eigenvalue method for energies and matrix elements in lattice field theory
Blossier, Benoit; von Hippel, Georg; Mendes, Tereza; Sommer, Rainer
2009-01-01
We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as $\\exp(-(E_{N+1}-E_n) t)$. The gap $E_{N+1}-E_n$ can be made large by increasing the number $N$ of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order $1/m_b$ in HQET.
Generalized ray-transfer matrix for an optical element having an arbitrary wavefront aberration.
Jeong, Tae Moon; Ko, Do-Kyeong; Lee, Jongmin
2005-11-15
A generalized ray-transfer matrix for describing the action of an optical element having an arbitrary wavefront aberration is obtained. In this generalized ray-transfer matrix, the action of the aberrated optical element is represented by the product of radial ray-transfer matrices and tangential ray-transfer matrices. The refraction angle of an incident ray is calculated from the gradient of the wavefront aberration at the point of incidence, and the radial and tangential ray-transfer matrices directly use the gradient as a matrix component. To show the validity of the generalized ray-transfer matrix, intercept heights from a spot diagram are calculated with the generalized ray-transfer matrix and compared with those calculated with commercial ray-tracing software.
Dynamic Stiffness Matrix for a Beam Element with Shear Deformation
Walter D. Pilkey
1995-01-01
Full Text Available A method for calculating the dynamic transfer and stiffness matrices for a straight Timoshenko shear beam is presented. The method is applicable to beams with arbitrarily shaped cross sections and places no restrictions on the orientation of the element coordinate system axes in the plane of the cross section. These new matrices are needed because, for a Timoshenko beam with an arbitrarily shaped cross section, deflections due to shear in the two perpendicular planes are coupled even when the coordinate axes are chosen to be parallel to the principal axes of inertia.
Matrix exponentials, SU(N) group elements, and real polynomial roots
Van Kortryk, T S
2015-01-01
The exponential of an NxN matrix can always be expressed as a matrix polynomial of order N-1. In particular, a general group element for the fundamental representation of SU(N) can be expressed as a matrix polynomial of order N-1 in a traceless NxN hermitian generating matrix, with polynomial coefficients consisting of elementary trigonometric functions dependent on N-2 invariants in addition to the group parameter. These invariants are just angles determined by the direction of a real N-vector whose components are the eigenvalues of the hermitian matrix. Equivalently, the eigenvalues are given by projecting the vertices of an (N-1)-simplex onto a particular axis passing through the center of the simplex. The orientation of the simplex relative to this axis determines the angular invariants and hence the real eigenvalues of the matrix.
Iemini, Fernando; da Silva Souza, Leonardo; Debarba, Tiago; Cesário, André T.; Maciel, Thiago O.; Vianna, Reinaldo O.
2017-05-01
We obtain the analytical expression for the Kraus decomposition of the quantum map of an environment modeled by an arbitrary quadratic fermionic Hamiltonian acting on one or two qubits, and derive simple functions to check the non-positivity of the intermediate map. These functions correspond to two different sufficient criteria for non-Markovianity. In the particular case of an environment represented by the Ising Hamiltonian, we discuss the two sources of non-Markovianity in the model, one due to the finite size of the lattice, and another due to the kind of interactions.
Incorporation of New Information in an Approximate Hamiltonian
Viazminsky, C P
2002-01-01
Additional information about the eigenvalues and eigenvectors of a physical system demands extension of the effective Hamiltonian in use. In this work we extend the effective Hamiltonian that describes partially a physical system so that the new Hamiltonian comprises, in addition to the information in the old Hamiltonian, new information, available by means of experiment or theory. A simple expression of the enlarged Hamiltonian, which does not involve matrix inversion, is obtained. It is also shown that the Lee-Suzuki transformation effectively put the initial Hamiltonian in a diagonal block form.
Determining matrix elements and resonance widths from finite volume: the dangerous mu-terms
Takacs, G
2011-01-01
The standard numerical approach to determining matrix elements of local operators and width of resonances uses the finite volume dependence of energy levels and matrix elements. Finite size corrections that decay exponentially in the volume are usually neglected or taken into account using perturbation expansion in effective field theory. Using two-dimensional sine-Gordon field theory as "toy model" it is shown that some exponential finite size effects could be much larger than previously thought, potentially spoiling the determination of matrix elements in frameworks such as lattice QCD. The particular class of finite size corrections considered here are mu-terms arising from bound state poles in the scattering amplitudes. In sine-Gordon model, these can be explicitly evaluated and shown to explain the observed discrepancies to high precision. It is argued that the effects observed are not special to the two-dimensional setting, but rather depend on general field theoretic features that are common with model...
The 0nbb-decay nuclear matrix elements with self-consistent short-range correlations
Simkovic, Fedor; Muther, Herbert; Rodin, Vadim; Stauf, Markus
2009-01-01
A self-consistent calculation of nuclear matrix elements of the neutrinoless double beta decays (0nbb) of 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128Te, 130Te and 130Xe is presented in the framework of the renormalized quasiparticle random phase approximation (RQRPA) and the standard QRPA. The pairing and residual interactions as well as the two-nucleon short-range correlations are for the first time derived from the same modern realistic nucleon-nucleon potentials, namely from charge-dependent Bonn potential (CD-Bonn) and the Argonne V18 potential. In a comparison with the traditional approach of using the Miller-Spencer Jastrow correlations matrix elements for the 0nbb-decay are obtained, which are larger in magnitude. We analyze the differences among various two-nucleon correlations including those of the unitary correlation operator method (UCOM) and quantify the uncertainties in the calculated 0nbb-decay matrix elements.
Quasi-exact evaluation of time domain MFIE MOT matrix elements
Shi, Yifei
2013-07-01
A previously proposed quasi-exact scheme for evaluating matrix elements resulting from the marching-on-in-time (MOT) discretization of the time domain electric field integral equation (EFIE) is extended to matrix entries resulting from the discretization of its magnetic field integral equation (MFIE) counterpart. Numerical results demonstrate the accuracy of the scheme as well as the late-time stability of the resulting MOT-MFIE solver. © 2013 IEEE.
Measurement of Rotatory Optics Element in Tensor Dielectric Matrix for Rotatory Optical Fiber
LIU Jinghao; ZHANG Xiaofan; LI Huazhou; BAO Zhenwu
2005-01-01
The rotatory optics element in the tensor dielectric coefficient matrix is an important parameter for analyzing and calculating a rotatory optical fiber by electromagnetic theory. But the mea-surement of rotatory optics element is difficult for the rotatory optical fiber. A simple principle and method for measuring rotatory optics element are put forward in this paper. Firstly by using electromagnetic theory it was demonstrated that the rotatory optics element has a simple linear relation with the rotatory angle, and then the rotatory optics element has a simple linear relation with the magnetic field strength (or bias current in the helix coil) . Secondly a measurement system for the rotatory optics element in the rotatory optical fiber was designed. Using the measurement system the rotatory element can be obtained by measuring the bias current simply.
Correlation functions of scattering matrix elements in microwave cavities with strong absorption
Schaefer, R [Fachbereich Physik, Philipps-Universitaet Marburg, Renthof 5, D-35032 Marburg (Germany); Gorin, T [Theoretische Quantendynamik, Fakultaet fuer Physik, Universitaet Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg (Germany); Seligman, T H [Centro de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico, Campus Morelos, CP 62251, Cuernavaca, Morelos (Mexico); Stoeckmann, H-J [Fachbereich Physik, Philipps-Universitaet Marburg, Renthof 5, D-35032 Marburg (Germany)
2003-03-28
The scattering matrix was measured for microwave cavities with two antennae. It was analysed in the regime of overlapping resonances. The theoretical description in terms of a statistical scattering matrix and the rescaled Breit-Wigner approximation has been applied to this regime. The experimental results for the auto-correlation function show that the absorption in the cavity walls yields an exponential decay. This behaviour can only be modelled using a large number of weakly coupled channels. In comparison to the auto-correlation functions, the cross-correlation functions of the diagonal S-matrix elements display a more pronounced difference between regular and chaotic systems.
Correlation functions of scattering matrix elements in microwave cavities with strong absorption
Schäfer, R.; Gorin, T.; Seligman, T. H.; Stöckmann, H.-J.
2003-03-01
The scattering matrix was measured for microwave cavities with two antennae. It was analysed in the regime of overlapping resonances. The theoretical description in terms of a statistical scattering matrix and the rescaled Breit-Wigner approximation has been applied to this regime. The experimental results for the auto-correlation function show that the absorption in the cavity walls yields an exponential decay. This behaviour can only be modelled using a large number of weakly coupled channels. In comparison to the auto-correlation functions, the cross-correlation functions of the diagonal S-matrix elements display a more pronounced difference between regular and chaotic systems.
Short-range correlation effects on the nuclear matrix element of neutrinoless double-$\\beta$ decay
Benhar, Omar; Speranza, Enrico
2014-01-01
We report the results of a calculation of the nuclear matrix element of neutrinoless double-$\\beta$ decay of $^{48}$Ca, carried out taking into account nucleon-nucleon correlations in both coordinate- and spin-space. Our numerical results, obtained using nuclear matter correlation functions, suggest that inclusion of correlations leads to a $\\sim$ $20\\%$ decrease of the matrix element, with respect to the shell model prediction. This conclusion is supported by the results of an independent calculation, in which correlation effects are taken into account using the spectroscopic factors of $^{48}$Ca obtained from an {\\em ab intitio} many body approach.
Cave, Robert J.; Newton, Marshall D.
1996-01-01
A new method for the calculation of the electronic coupling matrix element for electron transfer processes is introduced and results for several systems are presented. The method can be applied to ground and excited state systems and can be used in cases where several states interact strongly. Within the set of states chosen it is a non-perturbative treatment, and can be implemented using quantities obtained solely in terms of the adiabatic states. Several applications based on quantum chemical calculations are briefly presented. Finally, since quantities for adiabatic states are the only input to the method, it can also be used with purely experimental data to estimate electron transfer matrix elements.
Axial-Current Matrix Elements in Light Nuclei from Lattice QCD
Savage, Martin [Univ. of Washington, Seattle, WA (United States); Shanahan, Phiala E. [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Tiburzi, Brian C. [Univ. of Maryland, College Park, MD (United States); Wagman, Michael L. [Univ. of Washington, Seattle, WA (United States); Winter, Frank T. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Beane, Silas [Univ. of New Hampshire, Durham, NH (United States); Chang, Emmanuel [Univ. of Washington, Seattle, WA (United States); Davoudi, Zohreh; Detmold, William [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Orginos, Konstantinos [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States)
2016-12-01
I present results from the first lattice QCD calculations of axial-current matrix elements in light nuclei, performed by the NPLQCD collaboration. Precision calculations of these matrix elements, and the subsequent extraction of multi-nucleon axial-current operators, are essential in refining theoretical predictions of the proton-proton fusion cross section, neutrino-nucleus cross sections and $\\beta\\beta$-decay rates of nuclei. In addition, they are expected to shed light on the phenomenological quenching of $g_A$ that is required in nuclear many-body calculations.
Axial-Current Matrix Elements in Light Nuclei from Lattice QCD
Savage, Martin J; Tiburzi, Brian C; Wagman, Michael L; Winter, Frank; Beane, Silas R; Chang, Emmanuel; Davoudi, Zohreh; Detmold, William; Orginos, Kostas
2016-01-01
I present results from the first lattice QCD calculations of axial-current matrix elements in light nuclei, performed by the NPLQCD collaboration. Precision calculations of these matrix elements, and the subsequent extraction of multi-nucleon axial-current operators, are essential in refining theoretical predictions of the proton-proton fusion cross section, neutrino-nucleus cross sections and $\\beta\\beta$-decay rates of nuclei. In addition, they are expected to shed light on the phenomenological quenching of $g_A$ that is required in nuclear many-body calculations.
Two-loop QED operator matrix elements with massive external fermion lines
Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Freitas, Abilio de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Universidad Simon Bolivar, Caracas (Venezuela). Dept. de Fisica; Neerven, Wilhelmus van [Leiden Univ. (Netherlands). Institut-Lorentz
2011-07-15
The two-loop massive operator matrix elements for the fermionic local twist-2 operators with external massive fermion lines in Quantum Electrodynamics (QED) are calculated up to the constant terms in the dimensional parameter {epsilon}=D-4. We investigate the hypothesis of F. A. Berends et al. (1988) that the 2-loop QED initial state corrections to e{sup +}e{sup -} annihilation into a virtual neutral gauge boson, except power corrections of O((m{sup 2}{sub f}/s){sup k}), k {>=} 1, can be represented in terms of these matrix elements and the massless 2-loop Wilson coefficients of the Drell-Yan process. (orig.)
Hamiltonian Structures for the Generalized Dispersionless KdV Hierarchy
Brunelli, J. C.
1996-01-01
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and third Hamiltonian structures are calculated directly from the r-matrix approach. Since the third structure is not related recursively with the first two ones the generalized dispersionless KdV hierarchy can be characterized as a truly tri-Hamiltonian system.
Infinite-dimensional Hamiltonian Lie superalgebras
无
2010-01-01
The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent elements.We are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra.
陈金兵; 史大
2005-01-01
给出了一Bargmann型有限维哈密顿系统的Lax表示及其在Poisson括号下的动态r-矩阵关系,从而利用一般r-矩阵理论证明了此Bargmann型有限维哈密顿系统在Liouville意义下的完全可积性.%The integrability for a finite-dimensional Hamiltonian system (FDHS) is studied. For this purpose the explicit Lax representation of the FDHS is calculated. It is remarkable to see that the Lax representation admits a dynamical r-matrix formula instead of a classical one in the Poisson bracket. Consequently the integrability of the FDHS is completed in the framework of r-matrix theory.
Lee, Young-Woo; Yeo, Seunghwan; Cho, Moon Sung [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2015-05-15
The fuel elements for the HTGRs (i.e., spherical fuel element in pebble-bed type core design and fuel compact in prismatic core design) consists of coated fuel particles dispersed and bonded in a closely packed array within a carbonaceous matrix. This matrix is generally made by mixing fully graphitized natural and needle- or pitchcoke originated powders admixed with a binder material (pitch or phenolic resin), The resulting resinated graphite powder mixture, when compacted, may influence a number of material properties as well as its behavior under neutron irradiation during reactor operation. In the fabrication routes of these two different fuel element forms, different consolidation methods are employed; a quasi-isostatic pressing method is generally adopted to make pebbles while fuel compacts are fabricated by uni-axial pressing mode. The result showed that the hardness values obtained from the two directions showed an anisotropic behavior: The values obtained from the perpendicular section showed much higher micro hardness (176.6±10.5MPa in average) than from the parallel section ((125.6±MPa in average). This anisotropic behavior was concluded to be related to the microstructure of the matrix graphite. This may imply that the uni-axial pressing method to make compacts influence the microstructure of the matrix and hence the material properties of the matrix graphite.
Unified description of hydrogen bonding by a two-state effective Hamiltonian
McKenzie, Ross H
2011-01-01
An effective Hamiltonian is considered for hydrogen bonding between two molecules due to the quantum mechanical interaction between the orbitals of the H-atom and the donor and acceptor atoms in the molecules. The Hamiltonian acts on two diabatic states and has a simple chemically motivated form for its matrix elements. The model gives insight into the "H-bond puzzle", describes different classes of bonds, and empirical correlations between the donor-acceptor distance $R$ and binding energies, bond lengths, and the softening of vibrational frequencies. A key prediction is the UV photo-dissociation of H-bonded complexes via an excited electronic state with an exalted vibrational frequency.
On Hamiltonian realization of time-varying nonlinear systems
无
2007-01-01
This paper Investigates Hamiltonian realization of time-varying nonlinear (TVN) systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacooian matrix of a TVN system is nonsingu-lar, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is singular, this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a nonsingular main diagonal block. Furthermore, some sufficient (necessary and sufficient) conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper.
CHEN CHANG-YUAN
2000-01-01
In this paper, the general formulas and the recurrence formulas for radial matrix elements of N-dimensional isotropic harmonic oscillator are obtained. The relevant results of 2- dimensional and 3- dimensiona] isotropic harmonic oscillators reported in the reference papers are contained in a more general equations derived in this paper as special cases.
Nuclear Matrix Elements for the $\\beta\\beta$ Decay of the $^{76}$Ge
Brown, B A; Horoi, M
2015-01-01
The nuclear matrix elements for two-neutrino double-beta (2 n$\\beta\\beta$ ) and zero-neutrino double-beta (0 n$\\beta\\beta$) decay of 76 Ge are evaluated in terms of the configuration interaction (CI), quasiparticle random phase approximation (QRPA) and interacting boson model (IBM) methods. We show that the decomposition of the matrix elements in terms of interemediate states in 74 Ge is dominated by ground state of this nucleus. We consider corrections to the CI results that arise from configurations admixtures involving orbitals out-side of the CI configuration space by using results from QRPA, many-body-perturbation theory, and the connections to related observables. The CI two-neutrino matrix element is reduced due to the inclusion of spin-orbit partners, and to many-body correlations connected with Gamow-Teller beta decay. The CI zero-neutrino matrix element for the heavy neutrino is enhanced due to particle-particle correlations that are connected with the odd-even oscillations in the nuclear masse...
On the Feynman-Hellmann theorem in quantum field theory and the calculation of matrix elements
Bouchard, Chris; Chang, Chia Cheng; Kurth, Thorsten; Orginos, Kostas; Walker-Loud, André
2017-07-01
The Feynman-Hellmann theorem can be derived from the long Euclidean-time limit of correlation functions determined with functional derivatives of the partition function. Using this insight, we fully develop an improved method for computing matrix elements of external currents utilizing only two-point correlation functions. Our method applies to matrix elements of any external bilinear current, including nonzero momentum transfer, flavor-changing, and two or more current insertion matrix elements. The ability to identify and control all the systematic uncertainties in the analysis of the correlation functions stems from the unique time dependence of the ground-state matrix elements and the fact that all excited states and contact terms are Euclidean-time dependent. We demonstrate the utility of our method with a calculation of the nucleon axial charge using gradient-flowed domain-wall valence quarks on the Nf=2 +1 +1 MILC highly improved staggered quark ensemble with lattice spacing and pion mass of approximately 0.15 fm and 310 MeV respectively. We show full control over excited-state systematics with the new method and obtain a value of gA=1.213 (26 ) with a quark-mass-dependent renormalization coefficient.
Effects of quenching and partial quenching on QCD penguin matrix elements
Golterman, Maarten; Pallante, Elisabetta
2002-01-01
We point out that chiral transformation properties of penguin operators change in the transition from unquenched to (partially) quenched QCD. The way in which this affects the lattice determination of weak matrix elements can be understood in the framework of (partially) quenched chiral perturbation
$B^0_{(s)}$-mixing matrix elements from lattice QCD for the Standard Model and beyond
Bazavov, A; Bouchard, C M; Chang, C C; DeTar, C; Du, Daping; El-Khadra, A X; Freeland, E D; Gamiz, E; Gottlieb, Steven; Heller, U M; Kronfeld, A S; Laiho, J; Mackenzie, P B; Neil, E T; Simone, J; Sugar, R; Toussaint, D; Van de Water, R S; Zhou, Ran
2016-01-01
We calculate---for the first time in three-flavor lattice QCD---the hadronic matrix elements of all five local operators that contribute to neutral $B^0$- and $B_s$-meson mixing in and beyond the Standard Model. We present a complete error budget for each matrix element and also provide the full set of correlations among the matrix elements. We also present the corresponding bag parameters and their correlations, as well as specific combinations of the mixing matrix elements that enter the expression for the neutral $B$-meson width difference. We obtain the most precise determination to date of the SU(3)-breaking ratio $\\xi = 1.203(17)(6)$, where the second error stems from the omission of charm sea quarks, while the first encompasses all other uncertainties. The threefold reduction in total uncertainty tightens the constraint from $B$ mixing on the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle. Our calculation employs gauge-field ensembles generated by the MILC Collaboration with four lattice spacings a...
Effects of Cerium on Alloy Elements Distribution in Ferrous Matrix Material
刘英才; 刘俊友; 尹衍生; 刘国权
2001-01-01
The effect of the addition of rare earths in Fe-based high chromium alloy powders on elements distribution in matrix materials and mechanical properties were studied. The results show that the addition of cerium can increase the chromium amount in carbonides and increase the micro-hardness after carbonization and the wear-resistant property of materials.
Stoyanova, A.; Sousa, C.; De Graaf, C.; Broer, R.
2006-01-01
We recently developed a scheme for first-principles calculations of hopping matrix elements between localized states in extended systems. We apply the scheme to the determination of double exchange (DE) parameters in lightly hole-doped LaMnO(3) and electron-doped CaMnO(3). DE is one of the important
Shao, H; Guan, H; Li, C; Shi, T; Gao, K
2016-01-01
We report the first experimental determination of the $4s \\ ^{2}S_{1/2} $ $\\leftrightarrow $ $3d \\ ^{2}D_{5/2}$ quadrupole transition matrix element in $^{40}$Ca$^+$ by measuring the branching ratio of the $3d \\ ^{2}D_{5/2} $ state decaying into the ground state $4s \\ ^{2}S_{1/2} $ and the lifetime of the $3d \\ ^{2}D_{5/2} $ state, using a technique of highly synchronized measurement sequence for laser control and highly efficient quantum state detection for quantum jumps. The measured branching ratio and improved lifetime are, respectively, 0.9992(80) and 1.1652(46) s, which yield the value of the quadrupole transition matrix element (in absolute value) 9.737(43)~$ea_{0}^{2}$ with the uncertainty at the level of 0.44\\%. The measured quadrupole transition matrix element is in good agreement with the most precise many-body atomic structure calculations. Our method can be universally applied to measurements of transition matrix elements in single ions and atoms of similar structure.
Darboux transformations of the Jaynes-Cummings Hamiltonian
Samsonov, B F; Samsonov, Boris F; Negro, Javier
2004-01-01
A detailed analysis of matrix Darboux transformations under the condition that the derivative of the superpotential be self-adjoint is given. As a onsequence, a class of the symmetries associated to Schr\\"odinger matrix Hamiltonians is characterized. The applications are oriented towards the Jaynes-Cummings eigenvalue problem, so that exactly solvable $2\\times 2$ matrix Hamiltonians of the Jaynes-Cummings type are obtained. It is also established that the Jaynes-Cummings Hamiltonian is a quadratic function of a Dirac-type Hamiltonian.
Nuclear matrix element of neutrinoless double-β decay: Relativity and short-range correlations
Song, L. S.; Yao, J. M.; Ring, P.; Meng, J.
2017-02-01
Background:The discovery of neutrinoless double-β (0 ν β β ) decay would demonstrate the nature of neutrinos, have profound implications for our understanding of matter-antimatter mystery, and solve the mass hierarchy problem of neutrinos. The calculations for the nuclear matrix elements M0 ν of 0 ν β β decay are crucial for the interpretation of this process. Purpose: We study the effects of relativity and nucleon-nucleon short-range correlations on the nuclear matrix elements M0 ν by assuming the mechanism of exchanging light or heavy neutrinos for the 0 ν β β decay. Methods:The nuclear matrix elements M0 ν are calculated within the framework of covariant density functional theory, where the beyond-mean-field correlations are included in the nuclear wave functions by configuration mixing of both angular-momentum and particle-number projected quadrupole deformed mean-field states. Results: The nuclear matrix elements M0 ν are obtained for ten 0 ν β β -decay candidate nuclei. The impact of relativity is illustrated by adopting relativistic or nonrelativistic decay operators. The effects of short-range correlations are evaluated. Conclusions: The effects of relativity and short-range correlations play an important role in the mechanism of exchanging heavy neutrinos though the influences are marginal for light neutrinos. Combining the nuclear matrix elements M0 ν with the observed lower limits on the 0 ν β β -decay half-lives, the predicted strongest limits on the effective masses are || |-1>3.065 ×108GeV for heavy neutrinos.
Entanglement Concentration with Quantum Non Demolition Hamiltonians
Tatham, Richard
2011-01-01
We devise and examine two procrustean entanglement concentration schemes using Quantum Non- Demolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox to the use of a much more general, versatile and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian post-measurement, the second a non-Gaussian ancillary mode and a Gaussian post-measurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function based method in a numerically efficient manner. We then quantify the entanglement increase calculating the Logarithmic Negativity of the output state and discuss and compare the performance of the protocols.
Modelling of polypropylene fibre-matrix composites using finite element analysis
2009-01-01
Full Text Available Polypropylene (PP fibre-matrix composites previously prepared and studied experimentally were modelled using finite element analysis (FEA in this work. FEA confirmed that fibre content and composition controlled stress distribution in all-PP composites. The stress concentration at the fibre-matrix interface became greater with less fibre content. Variations in fibre composition were more significant in higher stress regions of the composites. When fibre modulus increased, the stress concentration at the fibres decreased and the shear stress at the fibre-matrix interface became more intense. The ratio between matrix modulus and fibre modulus was important, as was the interfacial stress in reducing premature interfacial failure and increasing mechanical properties. The model demonstrated that with low fibre concentration, there were insufficient fibres to distribute the applied stress. Under these conditions the matrix yielded when the applied stress reached the matrix yield stress, resulting in increased fibre axial stress. When the fibre content was high, there was matrix depletion and stress transfer was inefficient. The predictions of the FEA model were consistent with experimental and published data.
Hamiltonian formulation of teleparallel gravity
Ferraro, Rafael; Guzmán, María José
2016-11-01
The Hamiltonian formulation of the teleparallel equivalent of general relativity is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudoinverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first-class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms and the (local) Lorentz transformations of the vielbein. In particular, the Arnowitt, Deser, and Misner algebra of general relativity is recovered as a subalgebra.
Hamiltonian formulation of teleparallel gravity
Ferraro, Rafael
2016-01-01
The Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudo-inverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms, and the (local) Lorentz transformations of the vielbein. In particular, the ADM algebra of general relativity is recovered as a sub-algebra.
Alborzpour, Jonathan P.; Tew, David P.; Habershon, Scott
2016-11-01
Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations.
Three-body matrix elements for calculations of mean field and exp(S) ground state correlations
Mihaila, B; Mihaila, Bogdan; Heisenberg, Jochen H.
1999-01-01
In this document we present our approach to the computation of three-body matrix elements, based on the Urbana family of three-nucleon potentials. The calculations refer only to the necessary matrix elements needed to include the three-nucleon interaction in the manner presented in nucl-th/9912023.
Modular Hamiltonian for Excited States in Conformal Field Theory.
Lashkari, Nima
2016-07-22
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Z_{n} replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.
Modular Hamiltonian of Excited States in Conformal Field Theory
Lashkari, Nima
2015-01-01
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the replica Z_n symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.
Hamiltonian Algorithm Sound Synthesis
大矢, 健一
2013-01-01
Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.
Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510 (Mexico)
2017-01-15
In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.
Frederiksson, Per; Gudmundson, Peter; Mikkelsen, Lars Pilgaard
2009-01-01
A framework of finite element equations for strain gradient plasticity is presented. The theoretical framework requires plastic strain degrees of freedom in addition to displacements and a plane strain version is implemented into a commercial finite element code. A couple of different elements...... of quadrilateral type are examined and a few numerical issues are addressed related to these elements as well as to strain gradient plasticity theories in general. Numerical results are presented for an idealized cell model of a metal matrix composite under shear loading. It is shown that strengthening due...... to fiber size is captured but strengthening due to fiber shape is not. A few modelling aspects of this problem are discussed as well. An analytic solution is also presented which illustrates similarities to other theories....
Kinetic-energy matrix elements for atomic Hylleraas-CI wave functions.
Harris, Frank E
2016-05-28
Hylleraas-CI is a superposition-of-configurations method in which each configuration is constructed from a Slater-type orbital (STO) product to which is appended (linearly) at most one interelectron distance rij. Computations of the kinetic energy for atoms by this method have been difficult due to the lack of formulas expressing these matrix elements for general angular momentum in terms of overlap and potential-energy integrals. It is shown here that a strategic application of angular-momentum theory, including the use of vector spherical harmonics, enables the reduction of all atomic kinetic-energy integrals to overlap and potential-energy matrix elements. The new formulas are validated by showing that they yield correct results for a large number of integrals published by other investigators.
Banik, Subrata; Pal, Sourav; Prasad, M Durga
2010-10-12
An effective operator approach based on the coupled cluster method is described and applied to calculate vibrational expectation values and absolute transition matrix elements. Coupled cluster linear response theory (CCLRT) is used to calculate excited states. The convergence pattern of these properties with the rank of the excitation operator is studied. The method is applied to a water molecule. Arponen-type double similarity transformation in extended coupled cluster (ECCM) framework is also used to generate an effective operator, and the convergence pattern of these properties is compared to the normal coupled cluster (NCCM) approach. It is found that the coupled cluster method provides an accurate description of these quantities for low lying vibrational excited states. The ECCM provides a significant improvement for the calculation of the transition matrix elements.
Pire, B
2009-01-01
QCD is the theory of strong interactions and non-perturbative methods have been developed to address the confinement property of QCD. Many experimental measurements probe the confining dynamics, and it is well-known that hard scattering processes allow the extraction of non perturbative hadronic matrix elements. To study exclusive hard processes, such as electromagnetic form factors and reactions like gamma* N -> gamma N', gamma* N -> pi N', gamma* gamma -> pi pi, antiproton proton ->gamma* pi in particular kinematics (named as generalized Bjorken regime), one introduces specific non-perturbative objects, namely generalized parton distributions (GPDs), distribution amplitudes (DA) and transition distribution amplitudes (TDA), which are Fourier transformed non-diagonal matrix elements of non-local operators on the light-cone. We review here a selected sample of exclusive amplitudes in which the quark and gluon content of hadrons is probed, and emphasize that much remains to be done to successfully compute thei...
Nuclear matrix elements of the double beta decay for mass around 80
Yoshinaga, Naotaka; Higashiyama, Koji; Teruya, Eri
2014-09-01
In nature there are 30 kinds of nuclei which are expected to have double beta decays. Among them ten nuclei are actually observed for the neutrino double beta decays. Still no observation is made for the neutrinoless double beta decays (0 νββ) . The 0 νββ decay is expected to occur only when neutrinos have masses and they are Majorana particles. In that respect observation of 0 νββ is to determine whether neutrinos are Majorana particles or not. In theoretical side in order to estimate the half life of 0 νββ determination of the nuclear matrix elements are essential. They were calculated in many theoretical frameworks, but the results are not consistent in various models. In this study we carry out shell model calculations for 82Se and 82Kr nuclei. After obtaining the wavefunctions, we calculate the nuclear matrix elements. For comparison we make pair truncated shell model calculations.
A new formulation to calculate general HFB matrix elements through Pfaffian
Mizusaki, Takahiro
2012-01-01
A new formula is presented for the calculation of matrix elements between multi-quasiparticle Hartree-Fock-Bogoliubov (HFB) states. The formula is expressed in terms of the Pfaffian, and is derived by using the Fermion coherent states with Grassmann numbers. It turns out that the formula corresponds to an extension of generalized Wick's theorem and simplifies the combinatorial complexity resulting from practical applications of generalized Wick's theorem by unifying the transition density and the transition pairing tensor in the HFB theory. The resultant formula is simpler and more compact than the traditional description of matrix elements of general many-body operators. In addition, through the derivation of our new formula, we found that the Pfaffian version of the Lewis Carroll formula corresponds to the relation conjectrured by Balian and Brezin for the HFB theory in 1969.
Short-distance matrix elements for $D$-meson mixing for 2+1 lattice QCD
Chang, Chia Cheng [Univ. of Illinois, Champaign, IL (United States)
2015-01-01
We study the short-distance hadronic matrix elements for D-meson mixing with partially quenched N_{f} = 2+1 lattice QCD. We use a large set of the MIMD Lattice Computation Collaboration's gauge configurations with a^{2} tadpole-improved staggered sea quarks and tadpole-improved Lüscher-Weisz gluons. We use the a^{2} tadpole-improved action for valence light quarks and the Sheikoleslami-Wohlert action with the Fermilab interpretation for the valence charm quark. Our calculation covers the complete set of five operators needed to constrain new physics models for D-meson mixing. We match our matrix elements to the MS-NDR scheme evaluated at 3 GeV. We report values for the Beneke-Buchalla-Greub-Lenz-Nierste choice of evanescent operators.
Study of the Matrix Effect on the Plasma Characterization of Heavy Elements in Soil Sediments
Tawfik W.
2007-01-01
Full Text Available Laser-induced breakdown spectroscopy (LIBS has been applied to perform a study of the matrix effect on the plasma characterization of soil sediment targets. The plasma is generated by focusing a pulsed Nd: YAG laser on the target in air at atmospheric pressure. The plasma emission spectrum was detected using a portable Echelle spectrometer (Mechelle 7500 — Multichannel Instruments, Stockholm, Sweden with intensified CCD camera. Spectroscopic analysis of plasma evolution of laser produced plasmas has been characterized in terms of their spectra, and electron temperature. Four heavy elements V, Pb, Mn and Co were determined in the obtained spectra. The LTE and optically thin plasma conditions were verified for the produced plasma. The electron temperature and density were determined using the emission intensity and stark broadening, respectively, of the spectral lines of the heavy elements in the soil sediments. The electron temperature does not change with concentration. For environmental applications, the obtained results showed the capability of the proposed LIBS setup with the portable Mechelle 7500 spectrometer to be applied in-situ for real-time measurements of the variation of the matrix elemental composition of soil sediments by following up only a single element as a marker for the composition of the soil sediment without need of analysis of the other elements.
Ingredients of nuclear matrix element for two-neutrino double-beta decay of 48Ca
Iwata, Y; Utsuno, Y; Honma, M; Abe, T; Otsuka, T
2014-01-01
Large-scale shell model calculations including two major shells are carried out, and the ingredients of nuclear matrix element for two-neutrino double beta decay are investigated. Based on the comparison between the shell model calculations accounting only for one major shell ($pf$-shell) and those for two major shells ($sdpf$-shell), the effect due to the excitation across the two major shells is quantitatively evaluated.
Ablinger, J.; Blümlein, J.; De Freitas, A.; Hasselhuhn, A.; Schneider, C.; Wißbrock, F.
2017-08-01
Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η = mc2 / mb2 ∼ 1 / 10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived in [1]. We present the moments N = 2 , 4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element Agq(3). We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element Agg. As it turns out, the expansion in η is usually inapplicable for general values of N. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.
Sarkadi, L.
2017-03-01
The program MTRDCOUL [1] calculates the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ∫ ψf∗ (r) ∣ R - r∣-1ψi(r) d r. Bound-free transitions are considered, and relativistic hydrogenic wave functions are used. In this revised version a bug discovered in the F3Y CPC Program Library subprogram [2] is fixed.
Three-loop contributions to the gluonic massive operator matrix elements at general values of N
Ablinger, Jakob; Hasselhuhn, Alexander [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Bluemlein, Johannes; Raab, Clemens [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); De Freitas, Abilio; Round, Mark; Schneider, Carsten; Wissbrock, Fabian [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Klein, Sebastian [RWTH Aachen Univ. (Germany). Inst. fuer Theoretische Physik E
2012-12-15
Recent results on the calculation of 3-loop massive operator matrix elements in case of one and two heavy quark masses are reported. They concern the O(n{sub f}T{sup 2}{sub F}C{sub F,A}) and O(T{sup 2}{sub F}C{sub F,A}) gluonic corrections, two-mass quarkonic moments, and ladder- and Benz-topologies. We also discuss technical aspects of the calculations.
Some thoughts on how to match Leading Log Parton Showers with NLO Matrix Elements
Friberg, C; Friberg, Christer; Sjöstrand, Torbjörn
1999-01-01
We propose a scheme that could offer a convenient Monte Carlo sampling of next-to-leading-order matrix elements and, at the same time, allow the interfacing of such parton configurations with a parton-shower approach for the estimation of higher-order effects. No actual implementation exists so far, so this note should only be viewed as the outline of a possible road for the future, submitted for discussion.
Three-Loop Contributions to the Gluonic Massive Operator Matrix Elements at General Values of N
Ablinger, J; De Freitas, A; Hasselhuhn, A; Klein, S; Raab, C; Round, M; Schneider, C; Wi\\ssbrock, F
2013-01-01
Recent results on the calculation of 3-loop massive operator matrix elements in case of one and two heavy quark masses are reported. They concern the $O(n_f T_F^2 C_{F,A})$ and $O(T_F^2 C_{F,A})$ gluonic corrections, two-mass quarkonic moments, and ladder- and Benz-topologies. We also discuss technical aspects of the calculations.
Classical-Wigner Phase Space Approximation to Cumulative Matrix Elements in Coherent Control
McQuarrie, B. R.; Abrashkevich, Dmitri G.; Brumer, Paul
2003-01-01
The classical limit of the Wigner-Weyl representation is used to approximate products of bound-continuum matrix elements that are fundamental to many coherent control computations. The range of utility of the method is quantified through an examination of model problems, single-channel Na_2 dissociation and multi-arrangement channel photodissociation of CH_2IBr. Very good agreement with the exact quantum results is found for a wide range of system parameters.
Ablinger, J.; Hasselhuhn, A.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Wissbrock, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); IHES, Bures-sur-Yvette (France)
2017-05-15
Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η=m{sup 2}{sub c}/m{sup 2}{sub b}∝1/10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived earlier (I. Bierenbaum, J: Bluemlein, S. Klein, 2009). We present the moments N=2,4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element A{sup (3)}{sub gq}. We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element A{sub gg}. As it turns out, the expansion in η is usually inapplicable for general values of N. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.
LETTER TO THE EDITOR: Recurrence relations for relativistic atomic matrix elements
Martínez-y-Romero, R. P.; Núñez-Yépez, H. N.; Salas-Brito, A. L.
2000-05-01
Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired by the relativistic extension of the second hypervirial method that has been succesfully employed to deduce an analogous relationship in non-relativistic quantum mechanics. We first obtain the relativistic extension of the second hypervirial and then the relativistic recurrence relation. Furthermore, we use this relation to deduce relativistic versions of the Pasternack-Sternheimer rule and of the virial theorem.
Qi Song
2013-01-01
Full Text Available This paper proposes a partial refactorization for faster nonlinear analysis based on sparse matrix solution, which is nowadays the default solution choice in finite element analysis and can solve finite element models up to millions degrees of freedom. Among various fill-in’s reducing strategies for sparse matrix solution, the graph partition is in general the best in terms of resultant fill-ins and floating-point operations and furthermore produces a particular graph of sparse matrix that prevents local change of entries from wide spreading in factorization. Based on this feature, an explicit partial triangular refactorization with local change is efficiently constructed with limited additional storage requirement in row-sparse storage scheme. The partial refactorization of the changed stiffness matrix inherits a big percentage of the original factor and is carried out only on partial factor entries. The proposed method provides a new possibility for faster nonlinear analysis and is mainly suitable for material nonlinear problems and optimization problems. Compared to full factorization, it can significantly reduce the factorization time and can make nonlinear analysis more efficient.
Günay, E.
2017-02-01
This study defined as micromechanical finite element (FE) approach examining the stress transfer mechanism in single-walled carbon nanotube (SWCN) reinforced composites. In the modeling, 3D unit-cell method was evaluated. Carbon nanotube reinforced composites were modeled as three layers which comprises CNT, interface and matrix material. Firstly; matrix, fiber and interfacial materials all together considered as three layered cylindrical nanocomposite. Secondly, the cylindrical matrix material was assumed to be isotropic and also considered as a continuous medium. Then, fiber material was represented with zigzag type SWCNs. Finally, SWCN was combined with the elastic medium by using springs with different constants. In the FE modeling of SWCN reinforced composite model springs were modeled by using ANSYS spring damper element COMBIN14. The developed interfacial van der Waals interaction effects between the continuous matrix layer and the carbon nanotube fiber layer were simulated by applying these various spring stiffness values. In this study, the layered composite cylindrical FE model was presented as the equivalent mechanical properties of SWCN structures in terms of Young's modulus. The obtained results and literature values were presented and discussed. Figures, 16, 17, and 18 of the original article PDF file, as supplied to AIP Publishing, were affected by a PDF-processing error. Consequently, a solid diamond symbol appeared instead of a Greek tau on the y axis labels for these three figures. This article was updated on 17 March 2017 to correct the PDF-processing error, with the scientific content remaining unchanged.
Ma'zoozeh E. Abu-Amra
2008-04-01
Full Text Available In this paper we derive close form for the matrix elements for $hat H=-Delta +V$, where $V$ is a pure power-law potential. We use trial functions of the form $$ psi _n(r= sqrt{{frac{2eta ^{gamma/2}(gamma _n} {n!Gamma(gamma }}} r^{gamma - 1/2} e^{-frac{sqrt{eta }}{2}r^q} _pF_1 ( -n,a_2,ldots ,a_p;gamma;sqrt {eta } r^q, $$ for $eta, q,gamma >0$ to obtain the matrix elements for $hat H$. These formulas are then optimized with respect to variational parameters $eta ,q$ and $gamma $ to obtain accurate upper bounds for the given nonsolvable eigenvalue problem in quantum mechanics. Moreover, we write the matrix elements in terms of the generalized hypergeomtric functions. These results are generalization of those found earlier in [2], [8-16] for power-law potentials. Applications and comparisons with earlier work are presented.
Fukushima, Noboru, E-mail: noboru.fukushima@gmail.com [Motomachi 13-23, Sanjo, Niigata 955-0072 (Japan)
2011-02-18
Renormalization of non-magnetic and magnetic impurities due to electron double-occupancy prohibition is derived analytically by an improved Gutzwiller approximation. Non-magnetic impurities are effectively weakened by the same renormalization factor as that for the hopping amplitude, whereas magnetic impurities are strengthened by the square root of the spin-exchange renormalization factor, in contrast to results by the conventional Gutzwiller approximation. We demonstrate it by showing that transition matrix elements of number operators between assumed excited states and between an assumed ground state and excited states are renormalized differently than diagonal matrix elements. Deviation from such simple renormalization with a factor is also discussed. In addition, as a related calculation, we correct an error in treatment of the renormalization of charge interaction in the literature. Namely, terms from the second order of the transition matrix elements are strongly suppressed. Since all these results do not depend on the signs of impurity potential or the charge interaction parameter, they are valid both in attractive and repulsive cases.
Robinson, S J Q; Robinson, Shadow J.Q.; Zamick, Larry
2002-01-01
Calculations of the spectra of various even-even nuclei in the fp shell ($^{44}$Ti, $^{46}$Ti, $^{48}$Cr, and $^{50}$Cr) are performed with two sets of two-body interaction matrix elements. The first set consists of the matrix elements of the FPD6 interaction. The second set have the same T=1 two-body matrix elements as the FPD6 interaction, but all the T=0 two-body matrix elements are set equal to zero. Despite the drastic differences between the two interactions, the spectra they yield are very similar and indeed it is difficult to say which set gives a better fit to experiment. That the results for the yrast spectra are insensitive to the presence or absence of T=0 two-body matrix elements is surprising because the only bound two nucleon system has T=0, namely the deuteron. Also there is the general folklore that T=0 matrix elements are responsible for nuclear collectivity. Electric quadrupole transition rates are also examined. It is found that the reintroduction of T=0 matrix elements leads to an enhance...
A Data Matrix Method for Improving the Quantification of Element Percentages of SEM/EDX Analysis
Lane, John
2009-01-01
A simple 2D M N matrix involving sample preparation enables the microanalyst to peer below the noise floor of element percentages reported by the SEM/EDX (scanning electron microscopy/ energy dispersive x-ray) analysis, thus yielding more meaningful data. Using the example of a 2 3 sample set, there are M = 2 concentration levels of the original mix under test: 10 percent ilmenite (90 percent silica) and 20 percent ilmenite (80 percent silica). For each of these M samples, N = 3 separate SEM/EDX samples were drawn. In this test, ilmenite is the element of interest. By plotting the linear trend of the M sample s known concentration versus the average of the N samples, a much higher resolution of elemental analysis can be performed. The resulting trend also shows how the noise is affecting the data, and at what point (of smaller concentrations) is it impractical to try to extract any further useful data.
Evaluation of Solid Modeling Software for Finite Element Analysis of Woven Ceramic Matrix Composites
Nemeth, Noel N.; Mital, Subodh; Lang, Jerry
2010-01-01
Three computer programs, used for the purpose of generating 3-D finite element models of the Repeating Unit Cell (RUC) of a textile, were examined for suitability to model woven Ceramic Matrix Composites (CMCs). The programs evaluated were the open-source available TexGen, the commercially available WiseTex, and the proprietary Composite Material Evaluator (COMATE). A five-harness-satin (5HS) weave for a melt-infiltrated (MI) silicon carbide matrix and silicon carbide fiber was selected as an example problem and the programs were tested for their ability to generate a finite element model of the RUC. The programs were also evaluated for ease-of-use and capability, particularly for the capability to introduce various defect types such as porosity, ply shifting, and nesting of a laminate. Overall, it was found that TexGen and WiseTex were useful for generating solid models of the tow geometry; however, there was a lack of consistency in generating well-conditioned finite element meshes of the tows and matrix. TexGen and WiseTex were both capable of allowing collective and individual shifting of tows within a ply and WiseTex also had a ply nesting capability. TexGen and WiseTex were sufficiently userfriendly and both included a Graphical User Interface (GUI). COMATE was satisfactory in generating a 5HS finite element mesh of an idealized weave geometry but COMATE lacked a GUI and was limited to only 5HS and 8HS weaves compared to the larger amount of weave selections available with TexGen and WiseTex.
On a general Heisenberg exchange effective Hamiltonian
Blanco, J.A.; Prida Pidal, V.M. [Dept. de Fisica, Oviedo Univ. (Spain)
1995-07-01
A general Heisenberg exchange effective Hamiltonian is deduced in a straightforward way from the elemental quantum mechanical principles for the case of magnetic ions with non-orbital degeneracy in a crystalline lattice. Expressions for the high order direct exchange coupling constants or parameters are presented. The meaning of this effective Hamiltonian is important because extracting information from the Heisenberg Hamiltonian is a difficult task and is however taken as the starting point for many quite profound investigations of magnetism in solids and therefore could play an important role in an introductory course to solid state physics. (author)
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.
Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir;
2007-01-01
The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...... results in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We discuss some examples of unstable Hamiltonian systems in two dimensions....
Restricted Closed Shell Hartree Fock Roothaan Matrix Method Applied to Helium Atom Using Mathematica
Acosta, César R.; Tapia, J. Alejandro; Cab, César
2014-01-01
Slater type orbitals were used to construct the overlap and the Hamiltonian core matrices; we also found the values of the bi-electron repulsion integrals. The Hartree Fock Roothaan approximation process starts with setting an initial guess value for the elements of the density matrix; with these matrices we constructed the initial Fock matrix.…
Equivalence of two sets of deformed Calogero-Moser Hamiltonians
Gorbe, T F
2015-01-01
The equivalence of two complete sets of Poisson commuting Hamiltonians of the (super)integrable rational BC(n) Ruijsenaars-Schneider-van Diejen system is established. Specifically, the commuting Hamiltonians constructed by van Diejen are shown to be linear combinations of the Hamiltonians generated by the characteristic polynomial of the Lax matrix obtained recently by Pusztai, and the explicit formula of this invertible linear transformation is found.
IMPACT OF MATRIX INVERSION ON THE COMPLEXITY OF THE FINITE ELEMENT METHOD
M. Sybis
2016-04-01
Full Text Available Purpose. The development of a wide construction market and a desire to design innovative architectural building constructions has resulted in the need to create complex numerical models of objects having increasingly higher computational complexity. The purpose of this work is to show that choosing a proper method for solving the set of equations can improve the calculation time (reduce the complexity by a few levels of magnitude. Methodology. The article presents an analysis of the impact of matrix inversion algorithm on the deflection calculation in the beam, using the finite element method (FEM. Based on the literature analysis, common methods of calculating set of equations were determined. From the found solutions the Gaussian elimination, LU and Cholesky decomposition methods have been implemented to determine the effect of the matrix inversion algorithm used for solving the equations set on the number of computational operations performed. In addition, each of the implemented method has been further optimized thereby reducing the number of necessary arithmetic operations. Findings. These optimizations have been performed on the use of certain properties of the matrix, such as symmetry or significant number of zero elements in the matrix. The results of the analysis are presented for the division of the beam to 5, 50, 100 and 200 nodes, for which the deflection has been calculated. Originality. The main achievement of this work is that it shows the impact of the used methodology on the complexity of solving the problem (or equivalently, time needed to obtain results. Practical value. The difference between the best (the less complex and the worst (the most complex is in the row of few orders of magnitude. This result shows that choosing wrong methodology may enlarge time needed to perform calculation significantly.
The effects of strand transposition on the stiffness matrix of superconductor core elements
Schnefler, B.; Gori, R.
1988-03-01
The axial and torsional components of the stiffness matrix of superconductor core elements are derived taking into account the effects of the wrapping of superconductor strands around the internal insulating strip. It is shown that the inclination of the strands referred to the longitudinal axis of the superconductor produces a reduction of the axial stiffness and a considerable increase in torsional stiffness. Examples relating to superconductors proposed for the NET Toroidal Field Coil are shown. In that instance the strand transposition is carried out by roebling.
Spin dipole nuclear matrix elements for double beta decay nuclei by charge-exchange reactions
Ejiri, H
2016-01-01
Spin dipole (SD) strengths for double beta-decay (DBD) nuclei were studied experimentally for the first time by using measured cross sections of (3He,t) charge exchange reactions (CERs). Then SD nuclear matrix elements (NMEs) for low-lying 2- states were derived from the experimental SD strengths by referring to the experimental GT (Gamow-Teller) and F (Fermi) strengths. They are consistent with the empirical SD NMEs based on the quasi-particle model with the empirical effective SD coupling constant. The CERs are used to evaluate the SD NME, which is associated with one of the major components of the neutrino-less DBD NME.
Sarkadi, L.
2017-03-01
The program MTRXCOUL [1] calculates the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ∫ ψf∗ (r) | R - r | - 1ψi(r) d r. Bound-free transitions are considered, and non-relativistic hydrogenic wave functions are used. In this revised version a bug discovered in the F3Y CPC Program Library (PL) subprogram [2] is fixed. Furthermore, the COULCC CPC PL subprogram [3] applied for the calculations of the radial wave functions of the free states and the Bessel functions is replaced by the CPC PL subprogram DCOUL [4].
Stochastic sandwich method with low mode substitution for nucleon isovector matrix elements
Yang, Yi-Bo; Draper, Terrence; Gong, Ming; Liu, Keh-Fei
2015-01-01
We introduce a stochastic sandwich method with low-mode substitution to evaluate the connected three-point functions. The isovector matrix elements of the nucleon for the axial-vector coupling $g_A^3$, scalar couplings $g_S^3$ and the quark momentum fraction $\\langle x\\rangle_{u -d}$ are calculated with overlap fermion on 2+1 flavor domain-wall configurations on a $24^3 \\times 64$ lattice at $m_{\\pi} = 330$ MeV with lattice spacing $a = 0.114$ fm.
Goeckeler, M.; Schaefer, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Division, Dept. of Mathematical Sciences; Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC]|[Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2006-06-15
We consider the renormalisation of lattice QCD operators with one and two covariant derivatives related to the first and second moments of generalised parton distributions and meson distribution amplitudes. Employing the clover fermion action we calculate their non-forward quark matrix elements in one-loop lattice perturbation theory. For some representations of the hypercubic group commonly used in simulations we determine the sets of all possible mixing operators and compute the matrices of renormalisation factors in one-loop approximation. We describe how tadpole improvement is applied to the results. (Orig.)
The O(αs3TF2) contributions to the gluonic operator matrix element
Ablinger, J.; Blümlein, J.; De Freitas, A.; Hasselhuhn, A.; von Manteuffel, A.; Round, M.; Schneider, C.
2014-08-01
The O(αs3TF2CF(CA)) contributions to the transition matrix element Agg,Q relevant for the variable flavor number scheme at 3-loop order are calculated. The corresponding graphs contain two massive fermion lines of equal mass leading to terms given by inverse binomially weighted sums beyond the usual harmonic sums. In x-space two root-valued letters contribute in the iterated integrals in addition to those forming the harmonic polylogarithms. We outline technical details needed in the calculation of graphs of this type, which are as well of importance in the case of two different internal massive lines.
Equilibrium and equilibration in a gluon plasma with improved matrix elements
Zhang Bin
2014-03-01
Full Text Available The hot and dense matter created in the early stage of a relativistic heavy ion collision is composed mainly of gluons. Radiative processes can play an important role for the thermalization of such partonic systems. The simplest parton number changing processes are commonly described by the Gunion-Bertsch formula. We show that the cross section from the exact matrix element for the lowest order radiative process could be significantly smaller than that based on the Gunion-Bertsch formula. In light of this, we discuss the role of radiative processes on the equilibrium and equilibration of a gluon plasma.
Using the modified matrix element method to constrain Lμ-Lτ interactions
Elahi, Fatemeh; Martin, Adam
2017-07-01
In this paper, we explore the discriminatory power of the matrix element method (MEM) in constraining the Lμ-Lτ model at the LHC. The Z' boson associated with the spontaneously broken U (1 )Lμ-Lτ symmetry only interacts with the second and third generation of leptons at tree level, and is thus difficult to produce at the LHC. We argue that the best channels for discovering this Z' are in Z →4 μ and 2 μ + ET. Both these channels have a large number of kinematic observables, which strongly motivates the usage of a multivariate technique. The MEM is a multivariate analysis that uses the squared matrix element |M |2 to quantify the likelihood of the testing hypotheses. As the computation of the |M |2 requires knowing the initial and final state momenta and the model parameters, it is not commonly used in new physics searches. Conventionally, new parameters are estimated by maximizing the likelihood of the signal with respect to the background, and we outline scenarios in which this procedure is (in)effective. We illustrate that the new parameters can also be estimated by studying the |M |2 distributions, and, even if our parameter estimation is off, we can gain better sensitivity than cut-and-count methods. Additionally, unlike the conventional MEM, where one integrates over all unknown momenta in processes with ET, we show an example scenario where these momenta can be estimated using the process topology. This procedure, which we refer to as the "modified squared matrix element," is computationally much faster than the canonical matrix element method and maintains signal-background discrimination. Bringing the MEM and the aforementioned modifications to bear on the Lμ-Lτ model, we find that with 300 fb-1 of integrated luminosity, we are sensitive to the couplings of gZ'≳0.002 g1 and MZ'<20 GeV , and gZ'≳0.005 g1 and 20 GeV
Spin Density Matrix Elements in exclusive production of ω mesons at Hermes
Marianski B.
2014-03-01
Full Text Available Spin density matrix elements have been determined for exclusive ω meson production on hydrogen and deuterium targets, in the kinematic region of 1.0 < Q2 < 10.0 GeV2, 3.0 < W < 6.3 GeV and –t' < 0.2 GeV2. The data, from which SDMEs are determined, were accumulated with the HERMES forward spectrometer during the running period of 1996 to 2007 using the 27.6 GeV electron or positron beam of HERA. A sizable contribution of unnatural parity exchange amplitudes is found for exclusive ω meson production.
The Matrix Element Method at next-to-leading order accuracy
Martini, Till
2015-01-01
The Matrix Element Method (MEM) has proven beneficial to make maximal use of the information available in experimental data. However, so far it has mostly been used in Born approximation only. In this paper we discuss an extension to NLO accuracy. As a prerequisite we present an efficient method to calculate event weights for jet events at NLO accuracy. As illustration and proof of concept we apply the method to the extraction of the top-quark mass in e+e- annihilation. We observe significant differences when moving from LO to NLO which may be relevant for the interpretation of top-quark mass measurements at hadron colliders relying on the MEM.
3-loop Massive $O(T_F^2)$ Contributions to the DIS Operator Matrix Element $A_{gg}$
Ablinger, J; De Freitas, A; Hasselhuhn, A; von Manteuffel, A; Round, M; Schneider, C
2014-01-01
Contributions to heavy flavour transition matrix elements in the variable flavour number scheme are considered at 3-loop order. In particular a calculation of the diagrams with two equal masses that contribute to the massive operator matrix element $A_{gg,Q}^{(3)}$ is performed. In the Mellin space result one finds finite nested binomial sums. In $x$-space these sums correspond to iterated integrals over an alphabet containing also square-root valued letters.
Tokmachev, A. M.; Robb, M. A.
The spin-Hamiltonian valence bond theory relies upon covalent configurations formed by singly occupied orbitals differing by their spin counterparts. This theory has been proven to be successful in studying potential energy surfaces of the ground and lowest excited states in organic molecules when used as a part of the hybrid molecular mechanics - valence bond method. The method allows one to consider systems with large active spaces formed by n electrons in n orbitals and relies upon a specially proposed graphical unitary group approach. At the same time, the restriction of the equality of the numbers of electrons and orbitals in the active space is too severe: it excludes from the consideration a lot of interesting applications. We can mention here carbocations and systems with heteroatoms. Moreover, the structure of the method makes it difficult to study charge-transfer excited states because they are formed by ionic configurations. In the present work we tackle these problems by significant extension of the spin-Hamiltonian approach. We consider (i) more general active space formed by n ± m electrons in n orbitals and (ii) states with the charge transfer. The main problem addressed is the generation of Hamiltonian matrices for these general cases. We propose a scheme combining operators of electron exchange and hopping, generating all nonzero matrix elements step-by-step. This scheme provides a very efficient way to generate the Hamiltonians, thus extending the applicability of spin-Hamiltonian valence bond theory.
Massive 3-loop ladder diagrams for quarkonic local operator matrix elements
Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes; Hasselhuhn, Alexander; Wissbrock, Fabian [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Klein, Sebastian [Technische Hochschule Aachen (Germany). Inst. fuer Theoretische Physik
2012-06-15
3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable N using Appell-function representations and applying modern summation technologies provided by the package Sigma and the method of hyperlogarithms. In some of the diagrams generalized harmonic sums with {xi} element of {l_brace}1,1/2,2{r_brace} emerge beyond the usual nested harmonic sums. As the asymptotic representation of the corresponding integrals shows, the generalized sums conspire giving well behaved expressions for large values of N. These diagrams contribute to the 3-loop heavy flavor Wilson coefficients of the structure functions in deep-inelastic scattering in the region Q{sup 2} >> m{sup 2}.
殷婷; 王杰
2013-01-01
对于传统的电力系统广义Hamilton实现，判定Hamilton函数Hessian矩阵的正定性是保证系统Lyapunov意义下稳定的充分条件，而复杂电力系统中此Hessian矩阵通常为高维分块矩阵，其正定性判定较为困难。基于二次型和块对角占优的思想，推导出判断高阶分块矩阵正定性的一般方法，利用矩阵分块理论并结合矩阵块的行或列的性质来实现。计算过程简单，大大减小了计算量。运用电力系统暂态能量函数方法有助于控制的设计和研究，并使用上述方法判断系统在平衡点处Hessian 矩阵的正定性。在四机系统中进行 Simulink 仿真，证明了所推导判据的准确性和控制策略的有效性，简化了广义Hamilton系统实现的Hessian矩阵正定性的判断过程。%The positive definiteness judgment of Hessian matrix of Hamilton function is a sufficient condition to guarantee the system stability in the Lyapunov sense for the generalized Hamiltonian realization of the traditional power system.However,the Hessian matrices of complex power system are usually high-dimension blocked matrices and the judgments of positive definiteness are very difficult.The general method to judge the positive definiteness of high-order blocked matrix is derived based on the idea of quadratic form and block diagonal dominance,and it can be realized by using the characteristics of the blocked rows or columns of matrix and blocked matrix theory.The calculating process will be simpler,and it greatly reduces the amount of calculations.At the same time, it will be conducive to the research and design of the control by means of the transient energy function method of power system,and the positive definiteness of Hessian matrix at the equilibrium point is judged by the above methods.The simulation example is given for four-machine system to prove the accuracy of the criterion and the effectiveness of the control strategy,which simplifies the
Improving the Effective Hamiltonian%改进等效哈密顿量
成晓妮; KROEGER; Helmut; 等
2002-01-01
The effective Hamiltonian method is useful for describing the physics in the low energy regime.The basic idea is to construct the effective Hamiltonian from the quantum transition matrix elements.The transition matrix is calculated more precisely than before in order to improve the precision of the relative physics value.A simple 1-spatial dimension quantum mechanical system is considered as an example.%有效哈密顿方法适用于低能区物理,以简单的一维量子系统为例,从量子跃迁矩阵元素出发构造一个等效哈密顿量.通过提高矩阵元的精确度来提高相关物理量的精度,达到改善计算结果的目的.
Symbolic algorithms for the computation of Moshinsky brackets and nuclear matrix elements
Ursescu, D.; Tomaselli, M.; Kuehl, T.; Fritzsche, S.
2005-12-01
To facilitate the use of the extended nuclear shell model (NSM), a FERMI module for calculating some of its basic quantities in the framework of MAPLE is provided. The Moshinsky brackets, the matrix elements for several central and non-central interactions between nuclear two-particle states as well as their expansion in terms of Talmi integrals are easily given within a symbolic formulation. All of these quantities are available for interactive work. Program summaryTitle of program:Fermi Catalogue identifier:ADVO Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVO Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:None Computer for which the program is designed and others on which is has been tested:All computers with a licence for the computer algebra package MAPLE [Maple is a registered trademark of Waterloo Maple Inc., produced by MapleSoft division of Waterloo Maple Inc.] Instalations:GSI-Darmstadt; University of Kassel (Germany) Operating systems or monitors under which the program has beentested: WindowsXP, Linux 2.4 Programming language used:MAPLE 8 and 9.5 from MapleSoft division of Waterloo Maple Inc. Memory required to execute with typical data:30 MB No. of lines in distributed program including test data etc.:5742 No. of bytes in distributed program including test data etc.:288 939 Distribution program:tar.gz Nature of the physical problem:In order to perform calculations within the nuclear shell model (NSM), a quick and reliable access to the nuclear matrix elements is required. These matrix elements, which arise from various types of forces among the nucleons, can be calculated using Moshinsky's transformation brackets between relative and center-of-mass coordinates [T.A. Brody, M. Moshinsky, Tables of Transformation Brackets, Monografias del Instituto de Fisica, Universidad Nacional Autonoma de Mexico, 1960] and by the proper use of the nuclear states in different coupling notations
Top Quark Mass Measurement in the Lepton plus Jets Channel Using a Modified Matrix Element Method
Aaltonen, T.; /Helsinki Inst. of Phys.; Adelman, J.; /Chicago U., EFI; Akimoto, T.; /Tsukuba U.; Alvarez Gonzalez, B.; /CSIC, Catalunya; Amerio, S.; /INFN, Padua; Amidei, D.; /Michigan U.; Anastassov, A.; /Northwestern U.; Annovi, A.; /Frascati; Antos, J.; /Comenius U.; Apollinari, G.; /Fermilab; Apresyan, A.; /Purdue U. /Waseda U.
2008-12-01
The authors report a measurement of the top quark mass, m{sub t}, obtained from p{bar p} collisions at {radical}s = 1.96 TeV at the Fermilab Tevatron using the CDF II detector. They analyze a sample corresponding to an integrated luminosity of 1.9 rfb{sup -1}. They select events with an electron or muon, large missing transverse energy, and exactly four high-energy jets in the central region of the detector, at least one of which is tagged as coming from a b quark. They calculate a signal likelihood using a matrix element integration method, where the matrix element is modified by using effective propagators to take into account assumptions on event kinematics. The event likelihood is a function of m{sub t} and a parameter JES that determines in situ the calibration of the jet energies. They use a neural network discriminant to distinguish signal from background events. They also apply a cut on the peak value of each event likelihood curve to reduce the contribution of background and badly reconstructed events. Using the 318 events that pass all selection criteria, they find m{sub t} = 172.7 {+-} 1.8 (stat. + JES) {+-} 1.2(syst.) GeV/c{sup 2}.
Measurement of single top quark production at D0 using a matrix element method
Mitrevski, Jovan Pavle [Columbia Univ., New York, NY (United States)
2007-01-01
Until now, the top quark has only been observed produced in pairs, by the strong force. According to the standard model, it can also be produced singly, via an electroweak interaction. Top quarks produced this way provide powerful ways to test the charged-current electroweak interactions of the top quark, to measure |V_{tb}|, and to search for physics beyond the standard model. This thesis describes the application of the matrix element analysis technique to the search for single top quark production with the D0 detector using 0.9 fb^{-1} of Run II data. From a comparison of the matrix element discriminants between data and the background model, assuming a Standard Model s-channel to t-channel cross section ratio of σ_{s}/σ_{t} = 0.44, we measure the single top quark production cross section: σ(p$\\bar{p}$ → tb + X, tqb + X) = 4.8$-1.4\\atop{+1.6}$ pb. This result has a p-value of 0.08%, corresponding to a 3.2 standard deviation Gaussian equivalent significance.
Haxton, Wick
2007-01-01
Semi-leptonic electroweak interactions in nuclei - such as \\beta decay, \\mu capture, charged- and neutral-current neutrino reactions, and electron scattering - are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order |\\vec{p}|/M, where \\vec{p} and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q^2, where q is the magnitude of the three-momentum transfer. While results for such matrix elements a...
On the computation of hadron-to-hadron transition matrix elements in lattice QCD
Bulava, John; Donnellan, Michael; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2011-10-15
We discuss the accurate determination of matrix elements left angle f vertical stroke h{sub w} vertical stroke i right angle where neither vertical stroke i right angle nor vertical stroke f right angle is the vacuum state and h{sub w} is some operator. Using solutions of the Generalized Eigenvalue Problem (GEVP) we construct estimators for matrix elements which converge rapidly as a function of the Euclidean time separations involved. vertical stroke i right angle and vertical stroke f right angle may be either the ground state in a given hadron channel or an excited state. Apart from a model calculation, the estimators are demonstrated to work well for the computation of the B{sup *}B{pi}-coupling in the quenched approximation. They are also compared to a standard ratio as well as to a ''summed ratio method''. In the model, we also illustrate the ordinary use of the GEVP for energy levels. (orig.)
TAUOLA of tau lepton decays-- framework for hadronic currens, matrix elements and anomalous decays
Chrzaszcz, M; Was, Z; Zaremba, J
2016-01-01
We present an update of the Monte Carlo event generator TAUOLA for tau lepton decays, with substantially increased list of decay channels and new initialization options. The core of the program remains written in FORTRAN but necessary arrangements have been made to allow handling of the user-provided hadronic currents and matrix elements at the execution time. Such solution may simplify preparation of new hadronic currents and may be useful for fitting to the experimental data as well. We have implemented as default for TAUOLA a set of hadronic currents, which is compatible with the default initialization used by BaBar collaboration. Options for currents available in previous releases are still stored in the code, sometimes left defunct or activated by internal flags only. The new version of the program, includes also implementation of Lepton Flavour Violating tau decays. Finally, we present, as an example, a set of C++ methods for handling user-provided currents, matrix elements or complete new decay channel...
Precision Measurement of the Neutron Twist-3 Matrix Element dn2: Probing Color Forces
Posik, Matthew; Flay, David; Parno, Diana; Allada, Kalyan; Armstrong, Whitney; Averett, Todd; Benmokhtar, Fatiha; Bertozzi, William; Camsonne, Alexandre; Canan, Mustafa; Cates, Gordon; Chen, Chunhua; Chen, Jian-Ping; Choi, Seonho; Chudakov, Eugene; Cusanno, Francesco; Dalton, Mark; Deconinck, Wouter; De Jager, Cornelis; Deng, Xiaoyan; Deur, Alexandre; Dutta, Chiranjib; El Fassi, Lamiaa; Franklin, Gregg; Friend, Megan; Gao, Haiyan; Garibaldi, Franco; Gilad, Shalev; Gilman, Ronald; Glamazdin, Oleksandr; Golge, Serkan; Gomez, Javier; Guo, Lei; Hansen, Jens-Ole; Higinbotham, Douglas; Holmstrom, Timothy; Huang, J; Hyde, Charles; Ibrahim Abdalla, Hassan; Jiang, Xiaodong; Jin, Ge; Katich, Joseph; Kelleher, Aidan; Kolarkar, Ameya; Korsch, Wolfgang; Kumbartzki, Gerfried; LeRose, John; Lindgren, Richard; Liyanage, Nilanga; Long, Elena; Lukhanin, Oleksandr; Mamyan, Vahe; McNulty, Dustin; Meziani, Zein-Eddine; Michaels, Robert; Mihovilovic, Miha; Moffit, Bryan; Muangma, Navaphon; Nanda, Sirish; Narayan, Amrendra; Nelyubin, Vladimir; Norum, Blaine; Nuruzzaman, nfn; Oh, Yongseok; Peng, Jen-chieh; Qian, Xin; Qiang, Yi; Rakhman, Abdurahim; Riordan, Seamus; Saha, Arunava; Sawatzky, Bradley; Hashemi Shabestari, Mitra; Shahinyan, Albert; Sirca, Simon; Solvignon-Slifer, Patricia; Subedi, Ramesh; Sulkosky, Vincent; Tobias, William; Troth, Wolfgang; Wang, Diancheng; Wang, Y; Wojtsekhowski, Bogdan; Yan, X; Yao, Huan; Ye, Yunxiu; Ye, Zhihong; Yuan, Lulin; Zhan, X; Zhang, Y; Zhang, Y -W; Zhao, Bo; Zheng, Xiaochao
2014-07-01
Double-spin asymmetries and absolute cross sections were measured at large Bjorken x (0.25 lte x lte 0.90), in both the deep-inelastic and resonance regions, by scattering longitudinally polarized electrons at beam energies of 4.7 and 5.9 GeV from a transversely and longitudinally polarized 3He target. In this dedicated experiment, the spin structure function g2 on 3He was determined with precision at large x, and the neutron twist-three matrix element dn2 was measured at ?Q2? of 3.21 and 4.32 GeV2/c2, with an absolute precision of about 10?5. Our results are found to be in agreement with lattice QCD calculations and resolve the disagreement found with previous data at ?Q2?= 5 GeV2/c2. Combining dn2 and a newly extracted twist-four matrix element, fn2, the average neutron color electric and magnetic forces were extracted and found to be of opposite sign and about 60 MeV/fm in magnitude.
A Precision Measurement of the Neutron Twist-3 Matrix Element $d_2^n$: Probing Color Forces
Posik, M; Parno, D S; Allada, K; Armstrong, W; Averett, T; Benmokhtar, F; Bertozzi, W; Camsonne, A; Canan, M; Cates, G D; Chen, C; Chen, J -P; Choi, S; Chudakov, E; Cusanno, F; Dalton, M M; Deconinck, W; de Jager, C W; Deng, X; Deur, A; Dutta, C; Fassi, L El; Franklin, G B; Friend, M; Gao, H; Garibaldi, F; Gilad, S; Gilman, R; Glamazdin, O; Golge, S; Gomez, J; Guo, L; Hansen, O; Higinbotham, D W; Holmstrom, T; Huang, J; Hyde, C; Ibrahim, H F; Jiang, X; Jin, G; Katich, J; Kelleher, A; Kolarkar, A; Korsch, W; Kumbartzki, G; LeRose, J J; Lindgren, R; Liyanage, N; Long, E; Lukhanin, A; Mamyan, V; McNulty, D; Meziani, Z -E; Michaels, R; Mihovilovič, M; Moffit, B; Muangma, N; Nanda, S; Narayan, A; Nelyubin, V; Norum, B; Nuruzzaman,; Oh, Y; Peng, J C; Qian, X; Qiang, Y; Rakhman, A; Riordan, S; Saha, A; Sawatzky, B; Shabestari, M H; Shahinyan, A; Širca, S; Solvignon, P; Subedi, R; Sulkosky, V; Tobias, A; Troth, W; Wang, D; Wang, Y; Wojtsekhowski, B; Yan, X; Yao, H; Ye, Y; Ye, Z; Yuan, L; Zhan, X; Zhang, Y; Zhang, Y -W; Zhao, B; Zheng, X
2014-01-01
Double-spin asymmetries and absolute cross sections were measured at large Bjorken $x$ (0.25 $ \\le x \\le $ 0.90), in both the deep-inelastic and resonance regions, by scattering longitudinally polarized electrons at beam energies of 4.7 and 5.9 GeV from a transversely and longitudinally polarized $^3$He target. In this dedicated experiment, the spin structure function $g_2$ on $^3$He was determined with precision at large $x$, and the neutron twist-three matrix element $d_2^n$ was measured at $\\left$ of 3.21 and 4.32 GeV$^2$/$c^2$, with an absolute precision of about $10^{-5}$. Our results are found to be in agreement with lattice QCD calculations and resolve the disagreement found with previous data at $\\left =$ 5 GeV$^2$/$c^2$. Combining $d_2^n$ and a newly extracted twist-four matrix element, $f_2^n$, the average neutron color electric and magnetic forces were extracted and found to be of opposite sign and about 60 MeV/fm in magnitude.
Maxwell's Optics Symplectic Hamiltonian
Kulyabov, D S; Sevastyanov, L A
2015-01-01
The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and Hamiltonian in the case of hyperregular Lagrangian. It is impossible to do the same in gauge-invariant field theories. In the case of irregular Lagrangian the Dirac Hamiltonian formalism with constraints is usually used, and this leads to a number of certain difficulties. The paper proposes a reformulation of the problem to the case of a field without sources. This allows to use a symplectic Hamiltonian formalism. The proposed formalism will be used by the authors in the future to justify the methods of vector bundles (Hamiltonian bundles) in transformation optics.
Diagonalization of Hamiltonian; Diagonalization of Hamiltonian
Garrido, L. M.; Pascual, P.
1960-07-01
We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.
The Maslov indices of Hamiltonian periodic orbits
Gosson, Maurice de [Blekinge Institute of Technology, SE 371 79 Karlskrona (Sweden); Gosson, Serge de [Vaexjoe University (MSI), SE 351 95 Vaexjoe (Sweden)
2003-12-05
We use the properties of the Leray index to give precise formulae in arbitrary dimensions for the Maslov index of the monodromy matrix arising in periodic Hamiltonian systems. We compare our index with other indices appearing in the literature. (letter to the editor)
Cao, Zhanli; Li, Zhendong; Wang, Fan; Liu, Wenjian
2017-02-01
The spin-separated exact two-component (X2C) relativistic Hamiltonian [sf-X2C+so-DKHn, J. Chem. Phys., 2012, 137, 154114] is combined with the equation-of-motion coupled-cluster method with singles and doubles (EOM-CCSD) for the treatment of spin-orbit splittings of open-shell molecular systems. Scalar relativistic effects are treated to infinite order from the outset via the spin-free part of the X2C Hamiltonian (sf-X2C), whereas the spin-orbit couplings (SOC) are handled at the CC level via the first-order Douglas-Kroll-Hess (DKH) type of spin-orbit operator (so-DKH1). Since the exponential of single excitations, i.e., exp(T1), introduces sufficient spin orbital relaxations, the inclusion of SOC at the CC level is essentially the same in accuracy as the inclusion of SOC from the outset in terms of the two-component spinors determined variationally by the sf-X2C+so-DKH1 Hamiltonian, but is computationally more efficient. Therefore, such an approach (denoted as sf-X2C-EOM-CCSD(SOC)) can achieve uniform accuracy for the spin-orbit splittings of both light and heavy elements. For light elements, the treatment of SOC can even be postponed until the EOM step (denoted as sf-X2C-EOM(SOC)-CCSD), so as to further reduce the computational cost. To reveal the efficacy of sf-X2C-EOM-CCSD(SOC) and sf-X2C-EOM(SOC)-CCSD, the spin-orbit splittings of the (2)Π states of monohydrides up to the sixth row of the periodic table are investigated. The results show that sf-X2C-EOM-CCSD(SOC) predicts very accurate results (within 5%) for elements up to the fifth row, whereas sf-X2C-EOM(SOC)-CCSD is useful only for light elements (up to the third row but with some exceptions). For comparison, the sf-X2C-S-TD-DFT-SOC approach [spin-adapted open-shell time-dependent density functional theory, Mol. Phys., 2013, 111, 3741] is applied to the same systems. The overall accuracy (1-10%) is satisfactory.
A.N. Kulik
2009-01-01
Full Text Available The influence of sample matrix prepared on the basis of hydrofluoric acid on the measured content of trace elements in zirconium was studied. The accuracy of determination of the trace element content was verified by the “introduced-found” method. Based on verification results the temperature regime of electrothermal atomizer was optimized.
Arnold, Randy J.; Arndt, Brett; Blaser, Emilia; Blosser, Chris; Caulton, Dana; Chung, Won Sog; Fiorenza, Garrett; Heath, Wyatt; Jacobs, Alex; Kahng, Eunice; Koh, Eun; Le, Thao; Mandla, Kyle; McCory, Chelsey; Newman, Laura; Pithadia, Amit; Reckelhoff, Anna; Rheinhardt, Joseph; Skljarevski, Sonja; Stuart, Jordyn; Taylor, Cassie; Thomas, Scott; Tse, Kyle; Wall, Rachel; Warkentien, Chad
2011-01-01
A multivitamin tablet and liquid are analyzed for the elements calcium, magnesium, iron, zinc, copper, and manganese using atomic absorption spectrometry. Linear calibration and standard addition are used for all elements except calcium, allowing for an estimate of the matrix effects encountered for this complex sample. Sample preparation using…
A New Scheme of Integrability for (bi)Hamiltonian PDE
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
2016-10-01
We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.
Some Oscillation Results for Linear Hamiltonian Systems
Nan Wang; Fanwei Meng
2012-01-01
The purpose of this paper is to develop a generalized matrix Riccati technique for the selfadjoint matrix Hamiltonian system ${U}^{\\prime }=A(t)U+B(t)V$ , ${V}^{\\prime }=C(t)U-{A}^{\\ast }(t)V$ . By using the standard integral averaging technique and positive functionals, new oscillation and interval oscillation criteria are established for the system. These criteria extend and improve some results that have been required before. An interesting example is included to illustrate the...
Spin filtering on a ring with Rashba hamiltonian
Harmer, M.
2007-01-01
We consider a quantum graph consisting of a ring with Rashba hamiltonian and an arbitrary number of semi-infinite wires attached. We describe the scattering matrix for this system and investigate spin filtering for a three terminal device.
Spin filtering on a ring with Rashba hamiltonian
Harmer, M
2006-01-01
We consider a quantum graph consisting of a ring with Rashba hamiltonian and an arbitrary number of semi-infinite wires attached. We describe the scattering matrix for this system and investigate spin filtering for a three terminal device.
Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms
Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Reserach Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Raab, Clemens [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Wissbrock, Fabian [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Reserach Inst. for Symbolic Computation (RISC)
2014-02-15
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version to the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∝30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N element of C. Integrals with a power-like divergence in N-space∝a{sup N}, a element of R, a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions.
Path Integrals and Hamiltonians
Baaquie, Belal E.
2014-03-01
1. Synopsis; Part I. Fundamental Principles: 2. The mathematical structure of quantum mechanics; 3. Operators; 4. The Feynman path integral; 5. Hamiltonian mechanics; 6. Path integral quantization; Part II. Stochastic Processes: 7. Stochastic systems; Part III. Discrete Degrees of Freedom: 8. Ising model; 9. Ising model: magnetic field; 10. Fermions; Part IV. Quadratic Path Integrals: 11. Simple harmonic oscillators; 12. Gaussian path integrals; Part V. Action with Acceleration: 13. Acceleration Lagrangian; 14. Pseudo-Hermitian Euclidean Hamiltonian; 15. Non-Hermitian Hamiltonian: Jordan blocks; 16. The quartic potential: instantons; 17. Compact degrees of freedom; Index.
Cwik, T.; Jamnejad, V.; Zuffada, C. [California Institute of Technology, Pasadena, CA (United States)
1994-12-31
The usefulness of finite element modeling follows from the ability to accurately simulate the geometry and three-dimensional fields on the scale of a fraction of a wavelength. To make this modeling practical for engineering design, it is necessary to integrate the stages of geometry modeling and mesh generation, numerical solution of the fields-a stage heavily dependent on the efficient use of a sparse matrix equation solver, and display of field information. The stages of geometry modeling, mesh generation, and field display are commonly completed using commercially available software packages. Algorithms for the numerical solution of the fields need to be written for the specific class of problems considered. Interior problems, i.e. simulating fields in waveguides and cavities, have been successfully solved using finite element methods. Exterior problems, i.e. simulating fields scattered or radiated from structures, are more difficult to model because of the need to numerically truncate the finite element mesh. To practically compute a solution to exterior problems, the domain must be truncated at some finite surface where the Sommerfeld radiation condition is enforced, either approximately or exactly. Approximate methods attempt to truncate the mesh using only local field information at each grid point, whereas exact methods are global, needing information from the entire mesh boundary. In this work, a method that couples three-dimensional finite element (FE) solutions interior to the bounding surface, with an efficient integral equation (IE) solution that exactly enforces the Sommerfeld radiation condition is developed. The bounding surface is taken to be a surface of revolution (SOR) to greatly reduce computational expense in the IE portion of the modeling.
OMC studies for the matrix elements in ββ decay
Zinatulina, D.; Brudanin, V.; Egorov, V.; Shirchenko, M.; Vasiliev, R.; Yyutlandov, I. [Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Briançon, Ch. [Centre de Spectrometrie Nucleaire et de Spectrometrie de Masse, Universite Paris-Sud-CNRS-IN2P3, 91405 Orsay Campus (France); Petitjean, C. [Paul Scherrer Institute, 5232 Villigen PSI (Switzerland)
2013-12-30
Energy and time spectra of gamma-rays following μ-capture in natural Kr, Se, Cd and Sm, as well as isotopic enriched {sup 82}Kr, {sup 76}Se, {sup 106}Cd and {sup 150}Sm, have been measured. Total life-times of muons in different isotopes, as well as partial μ-capture rates to the excited states of {sup 48}Sc, {sup 76}As and {sup 106}Ag, were extracted. These results are discussed in the context of the double-beta decay matrix elements. The data are also compared with data from theoretical calculations and with data from charge-exchange reactions on {sup 48}Ti. It is the first time that μ-capture and charge-exchange reaction data are being compared in the context of ββ decay.
OMC studies for the matrix elements in Î²Î² decay
Zinatulina, D.; Brudanin, V.; Briançon, Ch.; Egorov, V.; Petitjean, C.; Shirchenko, M.; Vasiliev, R.; Yyutlandov, I.
2013-12-01
Energy and time spectra of gamma-rays following μ-capture in natural Kr, Se, Cd and Sm, as well as isotopic enriched 82Kr, 76Se, 106Cd and 150Sm, have been measured. Total life-times of muons in different isotopes, as well as partial μ-capture rates to the excited states of 48Sc, 76As and 106Ag, were extracted. These results are discussed in the context of the double-beta decay matrix elements. The data are also compared with data from theoretical calculations and with data from charge-exchange reactions on 48Ti. It is the first time that μ-capture and charge-exchange reaction data are being compared in the context of ββ decay.
Spin dipole nuclear matrix elements for double beta decay nuclei by charge-exchange reactions
Ejiri, H.; Frekers, D.
2016-11-01
Spin dipole (SD) strengths for double beta-decay (DBD) nuclei were studied experimentally for the first time by using measured cross sections of (3He, t) charge-exchange reactions (CERs). Then SD nuclear matrix elements (NMEs) {M}α ({{SD}}) for low-lying 2- states were derived from the experimental SD strengths by referring to the experimental α = GT (Gamow-Teller) and α = F (Fermi) strengths. They are consistent with the empirical NMEs M({{SD}}) based on the quasi-particle model with the empirical effective SD coupling constant. The CERs are used to evaluate the SD NME, which is associated with one of the major components of the neutrino-less DBD NME.
Nucleon distribution apmlitudes and proton decay matrix elements on the lattice
Braun, Vladimir M.; Goeckeler, Meinulf [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Horsley, Roger [Edinburgh Univ. (GB). School of Physics] (and others)
2008-11-15
Baryon distribution amplitudes (DAs) are crucial for the theory of hard exclusive reactions. We present a calculation of the first few moments of the leading-twist nucleon DA within lattice QCD. In addition we deal with the normalization of the next-to-leading (twist-four) DAs. The matrix elements determining the latter quantities are also responsible for proton decay in Grand Unified Theories. Our lattice evaluation makes use of gauge field configurations generated with two flavors of clover fermions. The relevant operators are renormalized nonperturbatively with the final results given in the MS scheme. We find that the deviation of the leading-twist nucleon DA from its asymptotic form is less pronounced than sometimes claimed in the literature. (orig.)
Haddouche, Issam; Cherbi, Lynda
2017-01-01
In this paper, we investigate Surface Plasmon Polaritons (SPPs) in the visible regime at a metal/dielectric interface within two different waveguide structures, the first is a Photonic Crystal Fiber where the Full Vector Finite Element Method (FVFEM) is used and the second is a slab waveguide where the transfer matrix method (TMM) is used. Knowing the diversities between the two methods in terms of speed, simplicity, and scope of application, computation is implemented with respect to wavelength and metal layer thickness in order to analyze and compare the performances of the two methods. Simulation results show that the TMM can be a good approximation for the FVFEM and that SPPs behave more like modes propagating in a semi infinite metal/dielectric structure as metal thickness increases from about 150 nm.
Ablinger, J; Blümlein, J; De Freitas, A; von Manteuffel, A; Schneider, C
2015-01-01
Three loop ladder and $V$-topology diagrams contributing to the massive operator matrix element $A_{Qg}$ are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable $N$ and the dimensional parameter $\\varepsilon$. Given these representations, the desired Laurent series expansions in $\\varepsilon$ can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural ...
Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms
Ablinger, Jakob; Raab, Clemens; Schneider, Carsten; Wißbrock, Fabian
2014-01-01
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist $\\tau =2$ local operator insertions corresponding to spin $N$. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version to the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and $V$-type graphs, belonging to the genuine 3-loop topologies. In case of the $V$-type graphs with five massive propagators new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of $\\sim 30$ square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for $N \\in...
Measurement of the Top Quark Mass Using the Matrix Element Technique in Dilepton Final States
Abazov, Victor Mukhamedovich; Acharya, Bannanje Sripath; Adams, Mark Raymond; Adams, Todd; Agnew, James P; Alexeev, Guennadi D; Alkhazov, Georgiy D; Alton, Andrew K; Askew, Andrew Warren; Atkins, Scott; Augsten, Kamil; Aushev, Volodymyr; Aushev, Yegor; Avila, Carlos A; Badaud, Frederique; Bagby, Linda F; Baldin, Boris; Bandurin, Dmitry V; Banerjee, Sunanda; Barberis, Emanuela; Baringer, Philip S; Bartlett, JFrederick; Bassler, Ursula Rita; Bazterra, Victor; Bean, Alice L; Begalli, Marcia; Bellantoni, Leo; Beri, Suman B; Bernardi, Gregorio; Bernhard, Ralf Patrick; Bertram, Iain A; Besancon, Marc; Beuselinck, Raymond; Bhat, Pushpalatha C; Bhatia, Sudeep; Bhatnagar, Vipin; Blazey, Gerald Charles; Blessing, Susan K; Bloom, Kenneth A; Boehnlein, Amber S; Boline, Daniel Dooley; Boos, Edward E; Borissov, Guennadi; Borysova, Maryna; Brandt, Andrew; Brandt, Oleg; Brochmann, Michelle; Brock, Raymond L; Bross, Alan D; Brown, Duncan Paul; Bu, Xue-Bing; Buehler, Marc; Buescher, Volker; Bunichev, Viacheslav Yevgenyevich; Burdin, Sergey; Buszello, Claus Peter; Camacho-Perez, Enrique; Casey, Brendan Cameron Kieran; Castilla-Valdez, Heriberto; Caughron, Seth Aaron; Chakrabarti, Subhendu; Chan, Kwok Ming Leo; Chandra, Avdhesh; Chapon, Emilien; Chen, Guo; Cho, Sung-Woong; Choi, Suyong; Choudhary, Brajesh C; Cihangir, Selcuk; Claes, Daniel R; Clutter, Justace Randall; Cooke, Michael P; Cooper, William Edward; Corcoran, Marjorie D; Couderc, Fabrice; Cousinou, Marie-Claude; Cuth, Jakub; Cutts, David; Das, Amitabha; Davies, Gavin John; de Jong, Sijbrand Jan; De La Cruz-Burelo, Eduard; Deliot, Frederic; Demina, Regina; Denisov, Dmitri S; Denisov, Sergei P; Desai, Satish Vijay; Deterre, Cecile; DeVaughan, Kayle Otis; Diehl, HThomas; Diesburg, Michael; Ding, Pengfei; Dominguez, DAaron M; Dubey, Abhinav Kumar; Dudko, Lev V; Duperrin, Arnaud; Dutt, Suneel; Eads, Michael T; Edmunds, Daniel L; Ellison, John A; Elvira, VDaniel; Enari, Yuji; Evans, Harold G; Evdokimov, Anatoly V; Evdokimov, Valeri N; Faure, Alexandre; Feng, Lei; Ferbel, Thomas; Fiedler, Frank; Filthaut, Frank; Fisher, Wade Cameron; Fisk, HEugene; Fortner, Michael R; Fox, Harald; Franc, Jiri; Fuess, Stuart C; Garbincius, Peter H; Garcia-Bellido, Aran; Garcia-Gonzalez, Jose Andres; Gavrilov, Vladimir B; Geng, Weigang; Gerber, Cecilia Elena; Gershtein, Yuri S; Ginther, George E; Gogota, Olga; Golovanov, Georgy Anatolievich; Grannis, Paul D; Greder, Sebastien; Greenlee, Herbert B; Grenier, Gerald Jean; Gris, Phillipe Luc; Grivaz, Jean-Francois; Grohsjean, Alexander; Gruenendahl, Stefan; Gruenewald, Martin Werner; Guillemin, Thibault; Gutierrez, Gaston R; Gutierrez, Phillip; Haley, Joseph Glenn Biddle; Han, Liang; Harder, Kristian; Harel, Amnon; Hauptman, John Michael; Hays, Jonathan M; Head, Tim; Hebbeker, Thomas; Hedin, David R; Hegab, Hatim; Heinson, Ann; Heintz, Ulrich; Hensel, Carsten; Heredia-De La Cruz, Ivan; Herner, Kenneth Richard; Hesketh, Gavin G; Hildreth, Michael D; Hirosky, Robert James; Hoang, Trang; Hobbs, John D; Hoeneisen, Bruce; Hogan, Julie; Hohlfeld, Mark; Holzbauer, Jenny Lyn; Howley, Ian James; Hubacek, Zdenek; Hynek, Vlastislav; Iashvili, Ia; Ilchenko, Yuriy; Illingworth, Robert A; Ito, Albert S; Jabeen, Shabnam; Jaffre, Michel J; Jayasinghe, Ayesh; Jeong, Min-Soo; Jesik, Richard L; Jiang, Peng; Johns, Kenneth Arthur; Johnson, Emily; Johnson, Marvin E; Jonckheere, Alan M; Jonsson, Per Martin; Joshi, Jyoti; Jung, Andreas Werner; Juste, Aurelio; Kajfasz, Eric; Karmanov, Dmitriy Y; Katsanos, Ioannis; Kaur, Manbir; Kehoe, Robert Leo Patrick; Kermiche, Smain; Khalatyan, Norayr; Khanov, Alexander; Kharchilava, Avto; Kharzheev, Yuri N; Kiselevich, Ivan Lvovich; Kohli, Jatinder M; Kozelov, Alexander V; Kraus, James Alexander; Kumar, Ashish; Kupco, Alexander; Kurca, Tibor; Kuzmin, Valentin Alexandrovich; Lammers, Sabine Wedam; Lebrun, Patrice; Lee, Hyeon-Seung; Lee, Seh-Wook; Lee, William M; Lei, Xiaowen; Lellouch, Jeremie; Li, Dikai; Li, Hengne; Li, Liang; Li, Qi-Zhong; Lim, Jeong Ku; Lincoln, Donald W; Linnemann, James Thomas; Lipaev, Vladimir V; Lipton, Ronald J; Liu, Huanzhao; Liu, Yanwen; Lobodenko, Alexandre; Lokajicek, Milos; Lopes de Sa, Rafael; Luna-Garcia, Rene; Lyon, Adam Leonard; Maciel, Arthur KA; Madar, Romain; Magana-Villalba, Ricardo; Malik, Sudhir; Malyshev, Vladimir L; Mansour, Jason; Martinez-Ortega, Jorge; McCarthy, Robert L; Mcgivern, Carrie Lynne; Meijer, Melvin M; Melnitchouk, Alexander S; Menezes, Diego D; Mercadante, Pedro Galli; Merkin, Mikhail M; Meyer, Arnd; Meyer, Jorg Manfred; Miconi, Florian; Mondal, Naba K; Mulhearn, Michael James; Nagy, Elemer; Narain, Meenakshi; Nayyar, Ruchika; Neal, Homer A; Negret, Juan Pablo; Neustroev, Petr V; Nguyen, Huong Thi; Nunnemann, Thomas P; Hernandez Orduna, Jose de Jesus; Osman, Nicolas Ahmed; Pal, Arnab; Parashar, Neeti; Parihar, Vivek; Park, Sung Keun; Partridge, Richard A; Parua, Nirmalya; Patwa, Abid; Penning, Bjoern; Perfilov, Maxim Anatolyevich; Peters, Reinhild Yvonne Fatima; Petridis, Konstantinos; Petrillo, Gianluca; Petroff, Pierre; Pleier, Marc-Andre; Podstavkov, Vladimir M; Popov, Alexey V; Prewitt, Michelle; Price, Darren; Prokopenko, Nikolay N; Qian, Jianming; Quadt, Arnulf; Quinn, Gene Breese; Ratoff, Peter N; Razumov, Ivan A; Ripp-Baudot, Isabelle; Rizatdinova, Flera; Rominsky, Mandy Kathleen; Ross, Anthony; Royon, Christophe; Rubinov, Paul Michael; Ruchti, Randal C; Sajot, Gerard; Sanchez-Hernandez, Alberto; Sanders, Michiel P; Santos, Angelo Souza; Savage, David G; Savitskyi, Mykola; Sawyer, HLee; Scanlon, Timothy P; Schamberger, RDean; Scheglov, Yury A; Schellman, Heidi M; Schott, Matthias; Schwanenberger, Christian; Schwienhorst, Reinhard H; Sekaric, Jadranka; Severini, Horst; Shabalina, Elizaveta K; Shary, Viacheslav V; Shaw, Savanna; Shchukin, Andrey A; Simak, Vladislav J; Skubic, Patrick Louis; Slattery, Paul F; Snow, Gregory R; Snow, Joel Mark; Snyder, Scott Stuart; Soldner-Rembold, Stefan; Sonnenschein, Lars; Soustruznik, Karel; Stark, Jan; Stefaniuk, Nazar; Stoyanova, Dina A; Strauss, Michael G; Suter, Louise; Svoisky, Peter V; Titov, Maxim; Tokmenin, Valeriy V; Tsai, Yun-Tse; Tsybychev, Dmitri; Tuchming, Boris; Tully, Christopher George T; Uvarov, Lev; Uvarov, Sergey L; Uzunyan, Sergey A; Van Kooten, Richard J; van Leeuwen, Willem M; Varelas, Nikos; Varnes, Erich W; Vasilyev, Igor A; Verkheev, Alexander Yurievich; Vertogradov, Leonid S; Verzocchi, Marco; Vesterinen, Mika; Vilanova, Didier; Vokac, Petr; Wahl, Horst D; Wang, Michael HLS; Warchol, Jadwiga; Watts, Gordon Thomas; Wayne, Mitchell R; Weichert, Jonas; Welty-Rieger, Leah Christine; Williams, Mark Richard James; Wilson, Graham Wallace; Wobisch, Markus; Wood, Darien Robert; Wyatt, Terence R; Xie, Yunhe; Yamada, Ryuji; Yang, Siqi; Yasuda, Takahiro; Yatsunenko, Yuriy A; Ye, Wanyu; Ye, Zhenyu; Yin, Hang; Yip, Kin; Youn, Sungwoo; Yu, Jiaming; Zennamo, Joseph; Zhao, Tianqi Gilbert; Zhou, Bing; Zhu, Junjie; Zielinski, Marek; Zieminska, Daria; Zivkovic, Lidija
2016-01-01
We present a measurement of the top quark mass in ppbar collisions at a center-of-mass energy of 1.96 TeV at the Fermilab Tevatron collider. The data were collected by the D0 experiment corresponding to an integrated luminosity of 9.7 fb-1. The matrix element technique is applied to ttbar events in the final state containing leptons (electrons or muons) with high transverse momenta and at least two jets. The calibration of the jet energy scale determined in the lepton + jets final state of ttbar decays is applied to jet energies. This correction provides a substantial reduction in systematic uncertainties. We obtain a top quark mass of mt = 173.93 +- 1.84 GeV.
HELAC-Onia: an automatic matrix element generator for heavy quarkonium physics
Shao, Hua-Sheng
2013-01-01
By the virtues of the Dyson-Schwinger equations, we upgrade the published code \\mtt{HELAC} to be capable to calculate the heavy quarkonium helicity amplitudes in the framework of NRQCD factorization, which we dub \\mtt{HELAC-Onia}. We rewrote the original \\mtt{HELAC} to make the new program be able to calculate helicity amplitudes of multi P-wave quarkonium states production at hadron colliders and electron-positron colliders by including new P-wave off-shell currents. Therefore, besides the high efficiencies in computation of multi-leg processes within the Standard Model, \\mtt{HELAC-Onia} is also sufficiently numerical stable in dealing with P-wave quarkonia (e.g. $h_{c,b},\\chi_{c,b}$) and P-wave color-octet intermediate states. To the best of our knowledge, it is a first general-purpose automatic quarkonium matrix elements generator based on recursion relations on the market.
Top Quark Mass Measurement Using a Matrix Element Method with Quasi-Monte Carlo Integration
Lujan, Paul J
2008-01-01
We report an updated measurement of the top quark mass obtained from ppbar collisions at sqrt(s) = 1.96 TeV at the Fermilab Tevatron using the CDF II detector. Our measurement uses a matrix element integration method to obtain a signal likelihood, with a neural network used to identify background events and a likelihood cut applied to reduce the effect of badly reconstructed events. We use a 2.7 fb^-1 sample and observe 422 events passing all of our cuts. We find m_t = 172.2 +/- 1.0 (stat.) +/- 0.9 (JES) +/- 1.0 (syst.) GeV/c^2, or m_t = 172.2 +/- 1.7 (total) GeV/c^2.
Measurement of spin correlation in tt production using a matrix element approach.
Abazov, V M; Abbott, B; Acharya, B S; Adams, M; Adams, T; Alexeev, G D; Alkhazov, G; Alton, A; Alverson, G; Alves, G A; Ancu, L S; Aoki, M; Arov, M; Askew, A; Åsman, B; Atramentov, O; Avila, C; BackusMayes, J; Badaud, F; Bagby, L; Baldin, B; Bandurin, D V; Banerjee, S; Barberis, E; Baringer, P; Barreto, J; Bartlett, J F; Bassler, U; Bazterra, V; Beale, S; Bean, A; Begalli, M; Begel, M; Belanger-Champagne, C; Bellantoni, L; Beri, S B; Bernardi, G; Bernhard, R; Bertram, I; Besançon, M; Beuselinck, R; Bezzubov, V A; Bhat, P C; Bhatnagar, V; Blazey, G; Blessing, S; Bloom, K; Boehnlein, A; Boline, D; Boos, E E; Borissov, G; Bose, T; Brandt, A; Brandt, O; Brock, R; Brooijmans, G; Bross, A; Brown, D; Brown, J; Bu, X B; Buehler, M; Buescher, V; Bunichev, V; Burdin, S; Burnett, T H; Buszello, C P; Calpas, B; Camacho-Pérez, E; Carrasco-Lizarraga, M A; Casey, B C K; Castilla-Valdez, H; Chakrabarti, S; Chakraborty, D; Chan, K M; Chandra, A; Chen, G; Chevalier-Théry, S; Cho, D K; Cho, S W; Choi, S; Choudhary, B; Cihangir, S; Claes, D; Clutter, J; Cooke, M; Cooper, W E; Corcoran, M; Couderc, F; Cousinou, M-C; Croc, A; Cutts, D; Das, A; Davies, G; De, K; de Jong, S J; De la Cruz-Burelo, E; Déliot, F; Demarteau, M; Demina, R; Denisov, D; Denisov, S P; Desai, S; Deterre, C; DeVaughan, K; Diehl, H T; Diesburg, M; Dominguez, A; Dorland, T; Dubey, A; Dudko, L V; Duggan, D; Duperrin, A; Dutt, S; Dyshkant, A; Eads, M; Edmunds, D; Ellison, J; Elvira, V D; Enari, Y; Evans, H; Evdokimov, A; Evdokimov, V N; Facini, G; Ferbel, T; Fiedler, F; Filthaut, F; Fisher, W; Fisk, H E; Fortner, M; Fox, H; Fuess, S; Garcia-Bellido, A; Gavrilov, V; Gay, P; Geng, W; Gerbaudo, D; Gerber, C E; Gershtein, Y; Ginther, G; Golovanov, G; Goussiou, A; Grannis, P D; Greder, S; Greenlee, H; Greenwood, Z D; Gregores, E M; Grenier, G; Gris, Ph; Grivaz, J-F; Grohsjean, A; Grünendahl, S; Grünewald, M W; Guillemin, T; Guo, F; Gutierrez, G; Gutierrez, P; Haas, A; Hagopian, S; Haley, J; Han, L; Harder, K; Harel, A; Hauptman, J M; Hays, J; Head, T; Hebbeker, T; Hedin, D; Hegab, H; Heinson, A P; Heintz, U; Hensel, C; Heredia-De la Cruz, I; Herner, K; Hesketh, G; Hildreth, M D; Hirosky, R; Hoang, T; Hobbs, J D; Hoeneisen, B; Hohlfeld, M; Hubacek, Z; Huske, N; Hynek, V; Iashvili, I; Illingworth, R; Ito, A S; Jabeen, S; Jaffré, M; Jamin, D; Jayasinghe, A; Jesik, R; Johns, K; Johnson, M; Johnston, D; Jonckheere, A; Jonsson, P; Joshi, J; Jung, A W; Juste, A; Kaadze, K; Kajfasz, E; Karmanov, D; Kasper, P A; Katsanos, I; Kehoe, R; Kermiche, S; Khalatyan, N; Khanov, A; Kharchilava, A; Kharzheev, Y N; Khatidze, D; Kirby, M H; Kohli, J M; Kozelov, A V; Kraus, J; Kulikov, S; Kumar, A; Kupco, A; Kurča, T; Kuzmin, V A; Kvita, J; Lammers, S; Landsberg, G; Lebrun, P; Lee, H S; Lee, S W; Lee, W M; Lellouch, J; Li, L; Li, Q Z; Lietti, S M; Lim, J K; Lincoln, D; Linnemann, J; Lipaev, V V; Lipton, R; Liu, Y; Liu, Z; Lobodenko, A; Lokajicek, M; Lopes de Sa, R; Lubatti, H J; Luna-Garcia, R; Lyon, A L; Maciel, A K A; Mackin, D; Madar, R; Magaña-Villalba, R; Malik, S; Malyshev, V L; Maravin, Y; Martínez-Ortega, J; McCarthy, R; McGivern, C L; Meijer, M M; Melnitchouk, A; Menezes, D; Mercadante, P G; Merkin, M; Meyer, A; Meyer, J; Miconi, F; Mondal, N K; Muanza, G S; Mulhearn, M; Nagy, E; Naimuddin, M; Narain, M; Nayyar, R; Neal, H A; Negret, J P; Neustroev, P; Novaes, S F; Nunnemann, T; Obrant, G; Orduna, J; Osman, N; Osta, J; Otero y Garzón, G J; Padilla, M; Pal, A; Parashar, N; Parihar, V; Park, S K; Parsons, J; Partridge, R; Parua, N; Patwa, A; Penning, B; Perfilov, M; Peters, K; Peters, Y; Petridis, K; Petrillo, G; Pétroff, P; Piegaia, R; Piper, J; Pleier, M-A; Podesta-Lerma, P L M; Podstavkov, V M; Polozov, P; Popov, A V; Prewitt, M; Price, D; Prokopenko, N; Protopopescu, S; Qian, J; Quadt, A; Quinn, B; Rangel, M S; Ranjan, K; Ratoff, P N; Razumov, I; Renkel, P; Rijssenbeek, M; Ripp-Baudot, I; Rizatdinova, F; Rominsky, M; Ross, A; Royon, C; Rubinov, P; Ruchti, R; Safronov, G; Sajot, G; Salcido, P; Sánchez-Hernández, A; Sanders, M P; Sanghi, B; Santos, A S; Savage, G; Sawyer, L; Scanlon, T; Schamberger, R D; Scheglov, Y; Schellman, H; Schliephake, T; Schlobohm, S; Schwanenberger, C; Schwienhorst, R; Sekaric, J; Severini, H; Shabalina, E; Shary, V; Shchukin, A A; Shivpuri, R K; Simak, V; Sirotenko, V; Skubic, P; Slattery, P; Smirnov, D; Smith, K J; Snow, G R; Snow, J; Snyder, S; Söldner-Rembold, S; Sonnenschein, L; Soustruznik, K; Stark, J; Stolin, V; Stoyanova, D A; Strauss, M; Strom, D; Stutte, L; Suter, L; Svoisky, P; Takahashi, M; Tanasijczuk, A; Taylor, W; Titov, M; Tokmenin, V V; Tsai, Y-T; Tsybychev, D; Tuchming, B; Tully, C; Uvarov, L; Uvarov, S; Uzunyan, S; Van Kooten, R; van Leeuwen, W M; Varelas, N; Varnes, E W; Vasilyev, I A; Verdier, P; Vertogradov, L S; Verzocchi, M; Vesterinen, M; Vilanova, D; Vokac, P; Wahl, H D; Wang, M H L S; Warchol, J; Watts, G; Wayne, M; Weber, M; Welty-Rieger, L; White, A; Wicke, D; Williams, M R J; Wilson, G W; Wobisch, M; Wood, D R; Wyatt, T R; Xie, Y; Xu, C; Yacoob, S; Yamada, R; Yang, W-C; Yasuda, T; Yatsunenko, Y A; Ye, Z; Yin, H; Yip, K; Youn, S W; Yu, J; Zelitch, S; Zhao, T; Zhou, B; Zhu, J; Zielinski, M; Zieminska, D; Zivkovic, L
2011-07-15
We determine the fraction of tt events with spin correlation, assuming that the spin of the top quark is either correlated with the spin of the top antiquark as predicted by the standard model or is uncorrelated. For the first time we use a matrix-element-based approach to study tt spin correlation. We use tt → W+ b W- b → ℓ+ νbℓ- ν b final states produced in pp collisions at a center-of-mass energy sqrt(s)=1.96 TeV, where ℓ denotes an electron or a muon. The data correspond to an integrated luminosity of 5.4 fb(-1) and were collected with the D0 detector at the Fermilab Tevatron collider. The result agrees with the standard model prediction. We exclude the hypothesis that the spins of the tt are uncorrelated at the 97.7% C.L.
Determination of the CKM Matrix Element |V_cb| from Semileptonic B Decays
Luth, V G
2004-01-01
We report studies of semileptonic decays, B --> X_c l nu, based on a sample of 88 million BB events recorded with the BABAR detector. We have measured four moments of the electron energy distribution and four moments of the hadronic mass distribution, each as a function of the minimum electron energy. From these moments we determine the inclusive branching fraction, the CKM matrix element |V_cb|, and other heavy quark parameters, using Heavy Quark Expansions (HQE) to order 1/m_b^3 in the kinetic mass scheme. In addition, we have studied a large sample of exclusive B^0 --> D^*- l^+ nu decays. This sample is used to extract the vector and axial form factors, the normalization and slope of the HQET form factor to determine |V_cb|.
The Matrix Element Method at the LHC: status and prospects for Run II
Wertz, Sébastien
2016-10-01
The Matrix Element Method (MEM) is a powerful multivariate method allowing to maximally exploit the experimental and theoretical information available to an analysis. Applications of the MEM at LHC experiments are discussed, such as searches for rare processes and measurements of properties of the Standard Model Higgs boson. The MadWeight software, allowing for a fast and automated computation of MEM weights for any user- specified process, is briefly reviewed. A new implementation of the MEM in the C++ language, MoMEMta, is presented. Building on MadWeight's tricks to accelerate the calculations, it aims at a much improved modularity and maintainability. Examples of this modularity are discussed: the possibility to compute several weights in parallel (propagation of systematic uncertainties), the Differential MEM (DMEM), and a novel way to search for lion-resonant. New Physics.
Lattice matrix elements and CP violation in and physics: Status and outlook
Amarjit Soni
2004-02-01
Status of lattice calculations of hadron matrix elements along with CP violation in $B$ and in $K$ systems is reviewed. Lattice has provided useful input which, in conjunction with experimental data, leads to the conclusion that CP-odd phase in the CKM matrix plays the dominant role in the observed asymmetry in $B→ K_{s}$. It is now quite likely that any beyond the SM, CP-odd, phase will cause only small deviations in $B$-physics. Search for the effects of the new phase(s) will consequently require very large data samples as well as very precise theoretical predictions. Clean determination of all the angles of the unitarity triangle therefore becomes essential. In this regard $B→ KD^{0}$ processes play a unique role. Regarding $K$-decays, remarkable progress made by theory with regard to maintenance of chiral symmetry on the lattice is briefly discussed. First application already provide quantitative information on $B_{K}$ and the $ I=1/2$ rule. In the lattice calculation, the enhancement in Re $A_{0}$ appears to arise solely from tree operators, esp. $Q_{2}$; penguin contribution to Re $A_{0}$ appears to be very small. However, improved calculations are necessary for $'/$ as the contributions of QCD penguins and electroweak penguins largely seem to cancel. There are good reasons, though, to believe that these cancellations will not survive improvements that are now underway. Importance of determining the unitarity triangle purely from $K$-decays is also emphasized.
Open-Ended Recursive Approach for the Calculation of Multiphoton Absorption Matrix Elements.
Friese, Daniel H; Beerepoot, Maarten T P; Ringholm, Magnus; Ruud, Kenneth
2015-03-10
We present an implementation of single residues for response functions to arbitrary order using a recursive approach. Explicit expressions in terms of density-matrix-based response theory for the single residues of the linear, quadratic, cubic, and quartic response functions are also presented. These residues correspond to one-, two-, three- and four-photon transition matrix elements. The newly developed code is used to calculate the one-, two-, three- and four-photon absorption cross sections of para-nitroaniline and para-nitroaminostilbene, making this the first treatment of four-photon absorption in the framework of response theory. We find that the calculated multiphoton absorption cross sections are not very sensitive to the size of the basis set as long as a reasonably large basis set with diffuse functions is used. The choice of exchange-correlation functional, however, significantly affects the calculated cross sections of both charge-transfer transitions and other transitions, in particular, for the larger para-nitroaminostilbene molecule. We therefore recommend the use of a range-separated exchange-correlation functional in combination with the augmented correlation-consistent double-ζ basis set aug-cc-pVDZ for the calculation of multiphoton absorption properties.
Minimizing matrix effect by femtosecond laser ablation and ionization in elemental determination.
Zhang, Bochao; He, Miaohong; Hang, Wei; Huang, Benli
2013-05-07
Matrix effect is unavoidable in direct solid analysis, which usually is a leading cause of the nonstoichiometric effect in quantitative analysis. In this research, experiments were carried out to study the overall characteristics of atomization and ionization in laser-solid interaction. Both nanosecond (ns) and femtosecond (fs) lasers were applied in a buffer-gas-assisted ionization source coupled with an orthogonal time-of-flight mass spectrometer. Twenty-nine solid standards of ten different matrices, including six metals and four dielectrics, were analyzed. The results indicate that the fs-laser mode offers more stable relative sensitivity coefficients (RSCs) with irradiance higher than 7 × 10(13) W·cm(-2), which could be more reliable in the determination of element composition of solids. The matrix effect is reduced by half when the fs-laser is employed, owing to the fact that the fs-laser ablation and ionization (fs-LAI) incurs an almost heat-free ablation process and creates a dense plasma for the stable ionization.
Covariant Hamiltonian field theory
Giachetta, G; Sardanashvily, G
1999-01-01
We study the relationship between the equations of first order Lagrangian field theory on fiber bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. The main peculiarity of these Hamilton equations lies in the fact that, for degenerate systems, they contain additional gauge fixing conditions. We develop the BRST extension of the covariant Hamiltonian formalism, characterized by a Lie superalgebra of BRST and anti-BRST symmetries.
Sergiu Ciprian Catinas
2015-07-01
Full Text Available A detailed theoretical and practical investigation of the reinforced concrete elements is due to recent techniques and method that are implemented in the construction market. More over a theoretical study is a demand for a better and faster approach nowadays due to rapid development of the calculus technique. The paper above will present a study for implementing in a static calculus the direct stiffness matrix method in order capable to address phenomena related to different stages of loading, rapid change of cross section area and physical properties. The method is a demand due to the fact that in our days the FEM (Finite Element Method is the only alternative to such a calculus and FEM are considered as expensive methods from the time and calculus resources point of view. The main goal in such a method is to create the moment-curvature diagram in the cross section that is analyzed. The paper above will express some of the most important techniques and new ideas as well in order to create the moment curvature graphic in the cross sections considered.
Heavy-ion double charge exchange reactions: A tool toward 0 νββ nuclear matrix elements
Cappuzzello, F.; Bondi, M. [Universita di Catania, Dipartimento di Fisica e Astronomia, Catania (Italy); INFN, Laboratori Nazionali del Sud, Catania (Italy); Cavallaro, M.; Agodi, C.; Carbone, D.; Cunsolo, A. [INFN, Laboratori Nazionali del Sud, Catania (Italy); Foti, A. [Universita di Catania, Dipartimento di Fisica e Astronomia, Catania (Italy); INFN, Sezione di Catania, Catania (Italy)
2015-11-15
The knowledge of the nuclear matrix elements for the neutrinoless double beta decay is fundamental for neutrino physics. In this paper, an innovative technique to extract information on the nuclear matrix elements by measuring the cross section of a double charge exchange nuclear reaction is proposed. The basic point is that the initial- and final-state wave functions in the two processes are the same and the transition operators are similar. The double charge exchange cross sections can be factorized in a nuclear structure term containing the matrix elements and a nuclear reaction factor. First pioneering experimental results for the {sup 40}Ca({sup 18}O,{sup 18}Ne){sup 40}Ar reaction at 270 MeV incident energy show that such cross section factorization reasonably holds for the crucial 0{sup +} → 0{sup +} transition to {sup 40}Ar{sub gs}, at least at very forward angles. (orig.)
Poreda, R. J.; Basu, A. R.; Chakrabarti, R.; Becker, L.
2004-12-01
We report on geochemical and petrographic analysis of separated matrix glass from Lagrange-1 and Bedout-1 drill cores that penetrated the Bedout structure offshore NW Australia. The results support the conclusion that the Bedout structure was produced by a a major ET impact at the end-Permian that generated shock melted glass and impact breccias (Becker et al., Science, v.304, p.1469, 2004) The Bedout structure is a 30 km, circular, 1.5 km uplifted basment high that occurs on the passive margin offshore NW Australia. The isolated feature, covered by 3 km of Triassic to Recent sediments,is not consistent with any typical volcanic province (i.e. arc or hotspot volcanism). This hypothesis is supported by the unique mineralogy and chemistry of the matrix glass. At Lagrange, major elements crudely resemble low-K, Fe-Ti basalts while the trace element patterns have two distinct signatures. The lower 250 m of Lagrange (3260 - 3010 m depth) have essentially flat REE and "spider" patterns that superficially resemble some E-MORB; a signal not typically found in arc, hotspot or continental margin settings. The upper 150 meters (3000 - 2850m) of Lagrange and the entire Bedout core (3030 - 3070m) have similar light REE-enriched patterns but low levels of alkalis, alkaline-earths and high field strength elements. Again, the chemistry is not consistent with an arc or hotspot setting, based on the low Ba and extremely low Sr (30-110 ppm) concentrations. Based on the geophysical, chemical and petrologic evidence, we hypothesize that the Bedout structure formed as the result` of an ET impact with Permian age rift margin basalts and continental sediment. The basalts did not completely melt as evidenced by the abundance of large (1 mm) An50 plagioclase,that exist as both crystalline plag and shock melted maskelynite. Plagioclase is the major repository of Sr in basalts and the lack of a plagioclase contribution to the melt glass is reflected in the low Sr abundance. Shock
Matrix elements in the coupled-cluster approach - With application to low-lying states in Li
Martensson-Pendrill, Ann-Marie; Ynnerman, Anders
1990-01-01
A procedure is suggested for evaluating matrix elements of an operator between wavefunctions in the coupled-cluster form. The use of the exponential ansatz leads to compact exponential expressions also for matrix elements. Algorithms are developed for summing all effects of one-particle clusters and certain chains of two-particle clusters (containing the well-known random-phase approximation as a subset). The treatment of one-particle perturbations in single valence states is investigated in detail. As examples the oscillator strength for the 2s-2p transition in Li as well as the hyperfine structure for the two states are studied and compared to earlier work.
Random Matrix Approach to a Special Kind of Quantum Random Hopping
杨森; 翟荟
2002-01-01
We use the random matrix method to study one kind of quantum random hopping. The Hamiltonian is a nonHermitian matrix with some negative subdiagonal elements. Using potential theory, we calculate the eigenvalue density of an N x N matrix when N goes to infinity. We also obtain a least upper bound of the module of ejgenvalues. In view of phase strjng theory in high-temperature superconductors, this model connects with localization-delocalization transition.
Dynamic-stiffness matrix of embedded and pile foundations by indirect boundary-element method
Wolf, J.P.; Darbre, G.R. (Electrowatt Engineering Services Ltd., Zurich (Switzerland))
1984-08-01
The boundary-integral equation method is well suited for the calculation of the dynamic-stiffness matrix of foundations embedded in a layered visco-elastic halfspace (or a transmitting boundary of arbitrary shape), which represents an unbounded domain. It also allows pile groups to be analyzed, taking pile-soil-pile interaction into account. The discretization of this boundary-element method is restricted to the structure-soil interface. All trial functions satisfy exactly the field equations and the radiation condition at infinity. In the indirect boundary-element method distributed source loads of initially unknown intensities act on a source line located in the excavated part of the soil and are determined such that the prescribed boundary conditions on the structure-soil interface are satisfied in an average sense. In the two-dimensional case the variables are expanded in a Fourier integral in the wave number domain, while in three dimensions, Fourier series in the circumferential direction and Bessel functions of the wave number domain, while in three dimensions, Fourier series in the circumferential direction and Bessel functions of the wave number in the radial direction are selected. Accurate results arise with a small number of parameters of the loads acting on a source line which should coincide with the structure-soil interface. In a parametric study the dynamic-stiffness matrices of rectangular foundations of various aspect ratios embedded in a halfplane and in a layer built-in at its base are calculated. For the halfplane, the spring coefficients for the translational directions hardly depend on the embedment, while the corresponding damping coefficients increase for larger embedments, this tendency being more pronounced in the horizontal direction.
Bubin, Sergiy; Adamowicz, Ludwik
2008-03-21
In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.
Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.
2016-05-01
Three loop ladder and V-topology diagrams contributing to the massive operator matrix element AQg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V-topologies.
Fatchurrohman, N.; Marini, C. D.; Suraya, S.; Iqbal, AKM Asif
2016-02-01
The increasing demand of fuel efficiency and light weight components in automobile sectors have led to the development of advanced material parts with improved performance. A specific class of MMCs which has gained a lot of attention due to its potential is aluminium metal matrix composites (Al-MMCs). Product performance investigation of Al- MMCs is presented in this article, where an Al-MMCs brake disc is analyzed using finite element analysis. The objective is to identify the potentiality of replacing the conventional iron brake disc with Al-MMCs brake disc. The simulation results suggested that the MMCs brake disc provided better thermal and mechanical performance as compared to the conventional cast iron brake disc. Although, the Al-MMCs brake disc dissipated higher maximum temperature compared to cast iron brake disc's maximum temperature. The Al-MMCs brake disc showed a well distributed temperature than the cast iron brake disc. The high temperature developed at the ring of the disc and heat was dissipated in circumferential direction. Moreover, better thermal dissipation and conduction at brake disc rotor surface played a major influence on the stress. As a comparison, the maximum stress and strain of Al-MMCs brake disc was lower than that induced on the cast iron brake disc.
A measurement of the top quark mass with a matrix element method
Gibson, Adam Paul [Univ. of California, Berkeley, CA (United States)
2006-01-01
The authors present a measurement of the mass of the top quark. The event sample is selected from proton-antiproton collisions, at 1.96 TeV center-of-mass energy, observed with the CDF detector at Fermilab's Tevatron. They consider a 318 pb^{-1} dataset collected between March 2002 and August 2004. They select events that contain one energetic lepton, large missing transverse energy, exactly four energetic jets, and at least one displaced vertex b tag. The analysis uses leading-order t$\\bar{t}$ and background matrix elements along with parameterized parton showering to construct event-by-event likelihoods as a function of top quark mass. From the 63 events observed with the 318 pb^{-1} dataset they extract a top quark mass of 172.0 ± 2.6(stat) ± 3.3(syst) GeV/c^{2} from the joint likelihood. The mean expected statistical uncertainty is 3.2 GeV/c^{2} for m $\\bar{t}$ = 178 GTeV/c^{2} and 3.1 GeV/c^{2} for m $\\bar{t}$ = 172.5 GeV/c^{2}. The systematic error is dominated by the uncertainty of the jet energy scale.
FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS
CHENG Daizhan; XI Zairong
2002-01-01
This paper investigates the relationship between state feedback and Hamiltonian realizatiou. First, it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization. Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural outpnt. Then some conditions for an affine nonlinear system to have a Hamiltonian realization arc given.For generalized outputs, the conditions of the feedback, keeping Hamiltonian, are discussed. Finally, the admissible feedback controls for generalized Hamiltonian systems are considered.
FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS
CHENGDaizhan; XIZairong
2002-01-01
This paper investigates the relationship between state feedback and Hamiltonican realization.Firest,it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization.Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural output.Then some conditions for an affine nonlinear system to have a Hamiltonian realization are given.some conditions for an affine nonlinear system to have a Hamiltonian realization are given.For generalized outputs,the conditions of the feedback,keeping Hamiltonian,are discussed.Finally,the admissible feedback controls for generalized Hamiltonian systems are considered.
Landau levels in 2D materials using Wannier Hamiltonians obtained by first principles
Lado, J. L.; Fernández-Rossier, J.
2016-09-01
We present a method to calculate the Landau levels and the corresponding edge states of two dimensional (2D) crystals using as a starting point their electronic structure as obtained from standard density functional theory (DFT). The DFT Hamiltonian is represented in the basis of maximally localized Wannier functions. This defines a tight-binding Hamiltonian for the bulk that can be used to describe other structures, such as ribbons, provided that atomic scale details of the edges are ignored. The effect of the orbital magnetic field is described using the Peierls substitution in the hopping matrix elements. Implementing this approach in a ribbon geometry, we obtain both the Landau levels and the dispersive edge states for a series of 2D crystals, including graphene, Boron Nitride, MoS2, Black Phosphorous, Indium Selenide and MoO3. Our procedure can readily be used in any other 2D crystal, and provides an alternative to effective mass descriptions.
Asymptotic freedom in the Hamiltonian approach to binding of color
Gómez-Rocha María
2017-01-01
Full Text Available We derive asymptotic freedom and the SU(3 Yang-Mills β-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size s is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian Hs, which is a matrix written in a basis that depend on the scale (or size parameter s. The effective Hamiltonians Hs and the (regularized canonical Hamiltonian H0 are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
Asymptotic freedom in the Hamiltonian approach to binding of color
Gómez-Rocha, María
2016-01-01
We derive asymptotic freedom and the $SU(3)$ Yang-Mills $\\beta$-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size $s$ is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian $H_s$, which is a matrix written in a basis that depend on the scale (or size) parameter $s$. The effective Hamiltonians $H_s$ and the (regularized) canonical Hamiltonian $H_{0}$ are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
Oberhofer, Harald; Blumberger, Jochen
2010-12-01
We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q-) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, ( { } )^{1/2} = 6.7 {mH}, is significantly higher than the value obtained for the minimum energy structure, | {H_ab } | = 3.8 {mH}. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q- in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.
Image-based visual servo control using the port-Hamiltonian Approach
Muñoz Arias, Mauricio; El Hawwary, Mohamed; Scherpen, Jacquelien M.A.
2015-01-01
This work is devoted to an image-based visual servo control strategy for standard mechanical systems in the port-Hamiltonian framework. We utilize a change of variables that transforms the port-Hamiltonian system into one with constant mass-inertia matrix, and we use an interaction matrix that inclu
Remarks on hamiltonian digraphs
Gutin, Gregory; Yeo, Anders
2001-01-01
This note is motivated by A.Kemnitz and B.Greger, Congr. Numer. 130 (1998)127-131. We show that the main result of the paper by Kemnitz and Greger is an easy consequence of the characterization of hamiltonian out-locally semicomplete digraphs by Bang-Jensen, Huang, and Prisner, J. Combin. Theory...... of Fan's su#cient condition [5] for an undirected graph to be hamiltonian. In this note we give another, more striking, example of this kind, which disproves a conjecture from [6]. We also show that the main result of [6] 1 is an easy consequence of the characterization of hamiltonian out......-tournaments by Bang-Jensen, Huang and Prisner [4]. For further information and references on hamiltonian digraphs, see e.g. the chapter on hamiltonicity in [1] as well as recent survey papers [2, 8]. We use the standard terminology and notation on digraphs as described in [1]. A digraph D has vertex set V (D) and arc...
Microscopic plasma Hamiltonian
Peng, Y.-K. M.
1974-01-01
A Hamiltonian for the microscopic plasma model is derived from the Low Lagrangian after the dual roles of the generalized variables are taken into account. The resulting Hamilton equations are shown to agree with the Euler-Lagrange equations of the Low Lagrangian.
Gates, S. James; Guyton, Forrest; Harmalkar, Siddhartha; Kessler, David S.; Korotkikh, Vadim; Meszaros, Victor A.
2017-06-01
We examine values of the Adinkra Holoraumy-induced Gadget representation space metric over all possible four-color, four-open node, and four-closed node adinkras. Of the 1,358,954,496 gadget matrix elements, only 226,492,416 are non-vanishing and take on one of three values: -1/3, 1/3, or 1 and thus a subspace isomorphic to a description of a body-centered tetrahedral molecule emerges.
Alimonti, Luca; Atalla, Noureddine; Berry, Alain; Sgard, Franck
2014-05-01
Modeling complex vibroacoustic systems including poroelastic materials using finite element based methods can be unfeasible for practical applications. For this reason, analytical approaches such as the transfer matrix method are often preferred to obtain a quick estimation of the vibroacoustic parameters. However, the strong assumptions inherent within the transfer matrix method lead to a lack of accuracy in the description of the geometry of the system. As a result, the transfer matrix method is inherently limited to the high frequency range. Nowadays, hybrid substructuring procedures have become quite popular. Indeed, different modeling techniques are typically sought to describe complex vibroacoustic systems over the widest possible frequency range. As a result, the flexibility and accuracy of the finite element method and the efficiency of the transfer matrix method could be coupled in a hybrid technique to obtain a reduction of the computational burden. In this work, a hybrid methodology is proposed. The performances of the method in predicting the vibroacoutic indicators of flat structures with attached homogeneous acoustic treatments are assessed. The results prove that, under certain conditions, the hybrid model allows for a reduction of the computational effort while preserving enough accuracy with respect to the full finite element solution.
Khokhar, Zahid R.; Ashcroft, Ian A.; Silberschmidt, Vadim V.
2011-02-01
Two main damage mechanisms of laminates—matrix cracking and inter-ply delaminationare closely linked together (Joshi and Sun 1). This paper is focussed on interaction between matrix cracking and delamination failure mechanisms in CFRP cross-ply laminates under quasi-static tensile loading. In the first part of the work, a transverse crack is introduced in 90o layers of the cross-ply laminate [01/904/01], and the stresses and strains that arise due to tensile loading are analyzed. In the second part, the cohesive zone modelling approach where the constitutive behaviour of the cohesive elements is governed by traction-displacement relationship is employed to deal with the problem of delamination initiation from the matrix crack introduced in the 90o layers of the laminate specimen. Additionally, the effect of microstructural randomness, exhibited by CFRP laminates on the damage behaviour of these laminates is also accounted for in simulations. This effect is studied in numerical finite-element simulations by introducing stochastic cohesive zone elements. The proposed damage modelling effectively simulated the interaction between the matrix crack and delamination and the variations in the stresses, damage and crack lengths of the laminate specimen due to the microstructural randomness.
Transformation design and nonlinear Hamiltonians
Brougham, Thomas; Jex, Igor
2009-01-01
We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple `beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons.
Reanalysis of nuclear spin matrix elements for dark matter spin-dependent scattering
Cannoni, M.
2013-04-01
We show how to include in the existing calculations for nuclei other than Xe129 and Xe131 the corrections to the isovector coupling arising in chiral effective field theory recently found in Menendez et al. [Phys. Rev. D 86, 103511 (2012)PRVDAQ1550-7998]. The dominant, momentum-independent, two-body current effect can be taken into account by formally redefining the static spin matrix elements ⟨Sp,n⟩. By further using the normalized form factor at q≠0 built with the one-body level structure functions, we show that the weakly interacting massive particles (WIMP)-nucleus cross section and the upper limits on the WIMP-nucleon cross sections coincide with the ones derived by using the exact functions at the two-body level. We explicitly show it in the case of XENON100 limits on the WIMP-neutron cross section, and we recalculate the limits on the WIMP-proton spin-dependent cross section set by COUPP. We also give practical formulas to obtain ⟨Sp,n⟩ given the structure functions in the various formalisms and notations existing in the literature. We argue that the standard treatment of the spin-dependent cross section in terms of three independent isospin functions, S00(q), S11(q), and S01(q), is redundant in the sense that the interference function S01(q) is the double product |S01(q)|=2S00(q)S11(q) even when including the new effective field theory corrections.
Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Behring, A.; Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Manteuffel, A. von [Mainz Univ. (Germany). Inst. fuer Physik
2015-09-15
Three loop ladder and V-topology diagrams contributing to the massive operator matrix element A{sub Qg} are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V-topologies.
Robust H∞ Control of Hamiltonian System with Uncertainty
薛安成; 梅生伟; 胡伟; 周原
2003-01-01
This paper investigates the robust H∞ problem for a class of generalized forced Hamiltonian systems with uncertainties. The robust L2-gain was proved for the Hamiltonian with a sufficient condition for stable control of multimachine power systems expressed as a matrix algebraic inequality. A similar sufficient condition was then extended to the robust H∞ control of Hamiltonian systems to construct the state feedback H∞ control law. A numerical example is given to verify the validity of the proposed control scheme, which shows the effectiveness and promising application of the method.
ZHONG Yi-feng; WANG Rui; YING Xue-gang; CHEN Huai
2006-01-01
In this paper, we established a finite element (FEM) model to analyze the dynamic characteristics of arch bridges. In this model, the effects of adjustment to the length of a suspender on its geometry stiffness matrix are stressed. The FEM equations of mechanics characteristics, natural frequency and main mode are set up based on the first order matrix perturbation theory. Applicantion of the proposed model to analyze a real arch bridge proved the improvement in the simulation precision of dynamical characteristics of the arch bridge by considering the effects of suspender length variation.
Hamiltonian Forms for a Hierarchy of Discrete Integrable Coupling Systems
XU Xi-Xiang; YANG Hong-Xiang; LU Rong-Wu
2008-01-01
A semi-direct sum of two Lie algebras of four-by-four matrices is presented, and a discrete four-by-fore matrix spectral problem is introduced. A hierarchy of discrete integrable coupling systems is derived. The obtained integrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity. Finally, we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discrete Hamiltonian systems.
Adya Prasad Mishra; T K Balasubramanian
2001-10-01
Rovibrational matrix elements of the multipole moments ℓ up to rank 10 and of the linear polarizability of the H2 molecule in the condensed phase have been computed taking into account the effect of the intermolecular potential. Comparison with gas phase matrix elements shows that the effect of solid state interactions is marginal.
Ender, I A; Flegontova, E Yu; Gerasimenko, A B
2016-01-01
An algorithm for sequential calculation of non-isotropic matrix elements of the collision integral which are necessary for the solution of the non-linear Boltzmann equation by moment method is proposed. Isotropic matrix elements that we believe are known, are starting ones. The procedure is valid for any interaction law and any mass ratio of the colliding particles.
Swain, J D
1999-01-01
We present a new method for the determination of the Cabibbo- Kobayashi-Maskawa quark mixing matrix element V/sub tb/ from electroweak loop corrections, in particular those affecting the process Z to bb. From a combined analysis of results from the LEP, SLC, Tevatron, and neutrino scattering experiments we determine V /sub tb/=0.77/sub -0.24//sup +18/. We comment briefly on the implications of this measurement for the mass of the top quark and Higgs boson, alpha /sub s/, and CKM unitarity. (19 refs).
Subsystem's dynamics under random Hamiltonian evolution
Vinayak,
2011-01-01
We study time evolution of a subsystem's density matrix under a unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian. We exactly calculate all coherences, purity and fluctuations. The reduced density matrix is described in terms of a noncentral correlated Wishart ensemble. Our description accounts for a transition from an arbitrary initial state towards a random state at large times, enabling us to determine the convergence time after which random states are reached. We identify and describe a number of other interesting features, like a series of collisions between the largest eigenvalue and the bulk, accompanied by a phase transition in its distribution function.
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...
Wieland, Wolfgang M
2013-01-01
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
Whiting, Daniel J.; Keaveney, James; Adams, Charles S.; Hughes, Ifan G.
2016-04-01
Applying large magnetic fields to gain access to the hyperfine Paschen-Back regime can isolate three-level systems in a hot alkali metal vapors, thereby simplifying usually complex atom-light interactions. We use this method to make the first direct measurement of the || matrix element in 87Rb. An analytic model with only three levels accurately models the experimental electromagnetically induced transparency spectra and extracted Rabi frequencies are used to determine the dipole matrix element. We measure || =(2.290 ±0 .002stat±0 .04syst) e a0 , which is in excellent agreement with the theoretical calculations of Safronova, Williams, and Clark [Phys. Rev. A 69, 022509 (2004), 10.1103/PhysRevA.69.022509].
Whiting, Daniel J; Adams, Charles S; Hughes, Ifan G
2016-01-01
Applying large magnetic fields to gain access to the hyperfine Paschen-Back regime can isolate three-level systems in a hot alkali metal vapors, thereby simplifying usually complex atom-light interactions. We use this method to make the first direct measurement of the $|\\langle\\mathrm{5P}| er||\\mathrm{5D}\\rangle|$ matrix element in $^{87}$Rb. An analytic model with only three-levels accurately models the experimental electromagnetically induced transparency spectra and extracted Rabi-frequencies are used to determine the dipole matrix element. We measure $|\\langle\\mathrm{5P}_{3/2}|er||\\mathrm{5D}_{5/2}\\rangle| = (2.290\\pm0.002_{\\rm stat}\\pm0.05_{\\rm syst})~ea_{0}$ which is in excellent agreement with the theoretical calculations of Safronova, Williams and Clark, Phys. Rev. A 69(2), 022509 (2004).
Meister, Matthias
2005-10-01
In a recent publication it has been shown how to generate derivatives with respect to atom coordinates of Slater-Koster matrix elements for the tight binding modeling of a system. For the special case of a mixed second partial derivative at coordinate singularities only the results were stated in that publication. In this work, the derivation of these results is given in detail. Though it may seem rather technical and only applicable to a very special case, atomic configurations where the connecting vector between the two atoms involved in a two-center matrix element is aligned along the z axis (in the usual approach) require results for precisely this case. The expressions derived in this work have been implemented in the DINAMO code.
Quantum Hamiltonian Complexity
2014-01-01
Constraint satisfaction problems are a central pillar of modern computational complexity theory. This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems. Over the past decade and a half, this field has witnessed fundamental breakthroughs, ranging from the establishment of a "Quantum Cook-Levin Theorem" to deep insights into the structure of 1D low-temperature quantum systems via s...
Exploring the Hamiltonian inversion landscape.
Donovan, Ashley; Rabitz, Herschel
2014-08-07
The identification of quantum system Hamiltonians through the use of experimental data remains an important research goal. Seeking a Hamiltonian that is consistent with experimental measurements constitutes an excursion over a Hamiltonian inversion landscape, which is the quality of reproducing the data as a function of the Hamiltonian parameters. Recent theoretical work showed that with sufficient experimental data there should be local convexity about the true Hamiltonian on the landscape. The present paper builds on this result and performs simulations to test whether such convexity is observed. A gradient-based Hamiltonian search algorithm is incorporated into an inversion routine as a means to explore the local inversion landscape. The simulations consider idealized noise-free as well as noise-ridden experimental data. The results suggest that a sizable convex domain exists about the true Hamiltonian, even with a modest amount of experimental data and in the presence of a reasonable level of noise.
FANHong－Yi
2002-01-01
We show that the Wigner function W=Tr(Δρ)( an ensemble average of the density operator ρ，Δis the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states.In doing so,converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise,The entangled states are defined in the enlarged Fock space with a fictitious freedom.
Matsumoto, Takuma; Ogata, Kazuyuki; Yahiro, Masanobu
2009-01-01
We present a practical way of smoothing discrete breakup S-matrix elements calculated by the continuum-discretized coupled-channel method (CDCC). This method makes the smoothing procedure much easier. The reliability of the smoothing method is confirmed for the three-body breakup reactions, 58Ni(d,pn) at 80 MeV and 12C(6He,4He2n) at 229.8 MeV.
FAN Hong-Yi
2002-01-01
We show that the Wigner function W = Tr(△ρ) (an ensemble average of the density operator ρ, △ is theWigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting fromquantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangledstates are defined in the enlarged Fock space with a fictitious freedom.
Gautam Pennathur
2010-06-01
Full Text Available Abstract Background Chromatin in the nucleus of all eukaryotes is organized into a system of loops and domains. These loops remain fastened at their bases to the fundamental framework of the nucleus, the matrix or the scaffold. The DNA sequences which anchor the bases of the chromatin loops to the matrix are known as Scaffold/Matrix Attachment Regions or S/MARs. Though S/MARs have been studied in yeast and higher eukaryotes and they have been found to be associated with gene organization and regulation of gene expression, they have not been reported in protists like Giardia. Several tools have been discovered and formulated to predict S/MARs from a genome of a higher eukaryote which take into account a number of features. However, the lack of a definitive consensus sequence in S/MARs and the randomness of the protozoan genome in general, make it a challenge to predict and identify such sequences from protists. Results Here, we have analysed the Giardia genome for the probable S/MARs predicted by the available computational tools; and then shown these sequences to be physically associated with the nuclear matrix. Our study also reflects that while no single computational tool is competent to predict such complex elements from protist genomes, a combination of tools followed by experimental verification is the only way to confirm the presence of these elements from these organisms. Conclusion This is the first report of S/MAR elements from the protozoan parasite Giardia lamblia. This initial work is expected to lay a framework for future studies relating to genome organization as well as gene regulatory elements in this parasite.
Brunner, T; Andreoiu, C; Brodeur, M; Delheji, P; Ettenauer, S; Frekers, D; Gallant, A T; Gernhäuser, R; Grossheim, A; Krücken, R; Lennarz, A; Lunney, D; Mücher, D; Ringle, R; Simon, M C; Simon, V V; Sjue, S K L; Zuber, K; Dilling, J
2013-01-01
A new technique has been developed at TRIUMF's TITAN facility to perform in-trap decay spectroscopy. The aim of this technique is to eventually measure weak electron capture branching ratios (ECBRs) and by this to consequently determine GT matrix elements of $\\beta\\beta$ decaying nuclei. These branching ratios provide important input to the theoretical description of these decays. The feasibility and power of the technique is demonstrated by measuring the ECBR of $^{124}$Cs.
The transition matrix element Agq(N) of the variable flavor number scheme at O(αs3)
Ablinger, J.; Blümlein, J.; De Freitas, A.; Hasselhuhn, A.; von Manteuffel, A.; Round, M.; Schneider, C.; Wißbrock, F.
2014-05-01
We calculate the massive unpolarized operator matrix element Agq(3)(N) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N. This is the first complete transition function needed in the variable flavor number scheme obtained at O(αs3). A first independent recalculation is performed for the contributions ∝NF of the 3-loop anomalous dimension γgq(2)(N).
The Transition Matrix Element A_{gq}(N) of the Variable Flavor Number Scheme at O(\\alpha_s^3)
Ablinger, J; De Freitas, A; Hasselhuhn, A; von Manteuffel, A; Schneider, M Round C; Wissbrock, F
2014-01-01
We calculate the massive operator matrix element $A_{gq}^{(3)}(N)$ to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable $N$. This is the first complete transition function needed in the variable flavor number scheme obtained at $O(\\alpha_s^3)$. A first independent recalculation is performed for the contributions $\\propto N_F$ of the 3-loop anomalous dimension $\\gamma_{gq}^{(2)}(N)$.
Heavy quark spectroscopy and matrix elements: A lattice study using the static approximation
Ewing, A.K.; Flynn, J.M.; Sachrajda, C.T.; Stella, N.; Wittig, H. [Physics Department, The University, Southampton SO17 1BJ (United Kingdom); Bowler, K.C.; Kenway, R.D.; Mehegan, J.; Richards, D.G. [Department of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3JZ (Scotland); Michael, C. [DAMTP, University of Liverpool, Liverpool L69 3BX, United Kingdom (UKQCD Collaboration)
1996-09-01
We present results of a lattice analysis of the {ital B} parameter {ital B}{sub {ital B}}, the decay constant {ital f}{sub {ital B}}, and several mass splittings using the static approximation. Results were obtained for 60 quenched gauge configurations computed at {beta}=6.2 on a lattice size of 24{sup 3}{times}48. Light quark propagators were calculated using the {ital O}({ital a})-improved Sheikholeslami-Wohlert action. We find {ital B}{sub {ital B}}{sup static}({ital m}{sub {ital b}})=0.69{sub {minus}4}{sup +3}(stat){sub {minus}1}{sup +2} (syst), corresponding to {ital B}{sub {ital B}}{sup static}=1.02{sub {minus}6 {minus}2}{sup +5 +3}, {ital f}{sub {ital B}}{sup static}=266{sub {minus}20 {minus}27}{sup +18 +28} MeV, and {ital f}{sub {ital B}}{sub {ital s}}{sup 2}{ital B}{sub {ital B}}{sub {ital s}}/{ital f}{sub {ital B}}{ital i}{sup 2}{ital B}{sub {ital B}}=1.34{sub {minus}8 {minus}3}{sup +9 +5}, where a variational fitting technique was used to extract {ital f}{sup 2}{sub {ital B{sub s}}}{ital B}{sub {ital B{sub {ital s}}}}{sub B{sup static}}. For the mass splittings we obtain {ital M}{sub {ital B{sub {ital s}}}}{minus}{ital M}{sub {ital B{sub {ital d}}}}=87{sub {minus}12 {minus}12}{sup +15 +6} MeV, {ital M}{sub {Lambda}{sub {ital b}}}{minus}{ital M}{sub {ital B}}{sub {ital d}}=420{sub {minus}90 {minus}30}{sup +100 +30} MeV, and {ital M}{sub {ital B}{asterisk}}{sup 2}{minus}{ital M}{sup 2}{sub {ital B}}=0.281{sub {minus}16 {minus}37}{sup +15 +40} GeV{sup 2}. We compare different smearing techniques intended to improve the signal/noise ratio. From a detailed assessment of systematic effects, we conclude that the main systematic uncertainties are associated with the renormalization constants relating a lattice matrix element to its continuum counterpart. The dependence of our findings on lattice artifacts is to be investigated in the future. {copyright} {ital 1996 The American Physical Society.}
Kaldamäe, L; Körner, J G
2016-01-01
We provide analytical results for the $O(\\alpha_s)$ corrections to the double-spin density matrix elements in the reaction $e^+e^-\\to t\\bar t$. These concern the elements $ll$, $lt$, $ln$, $tt$, $tn$, and $nn$ of the double-spin density matrix elements where $l,t,n$ stand for longitudinal, transverse and normal orientations with respect to the beam frame spanned by the electron and the top quark momentum.
Energy levels and transition probability matrix elements of ruby for maser applications
Berwin, R. W.
1971-01-01
Program computes fine structure energy levels of ruby as a function of magnetic field. Included in program is matrix formulation, each row of which contains a magnetic field and four corresponding energy levels.
YANZHIJIANG; RUOLANQIAN
1998-01-01
The nuclear matrix attachment regions(MARs) and the binding nuclear matrix proteins in the 5'-flanking cisacting elements of the human ε-globin gene have been examined.Using in vitro DNA-matrix binding assay,it has been shown that the positive stage-specific regulatory element (ε-PREII,-446bp- -419bp) upstream of this gene could specifically associate with the nuclear matrix from K562 cells,indicating that ε-PREII may be an erythroidspecific facultative MAR.In gel mobility shift assay and Southwestern blotting assay,an erythroid-specific nuclear matrix protein (ε-NMPk) in K562 cells has been revealed to bind to this positive regulatory element (ε-PREII).Furthermore,we demonstrated that the silencer (-392bp- -177bp) upstream of the human ε-globin gene could associate with the nuclear matrices from K562,HEL and Raji cells.In addition,the nuclear matrix proteins prepared from these three cell lines could also bind to this silencer,suggesting that this silencer element might be a constitutive nuclear matrix attachment region(constitutive MAR).Our results demonstrated that the nuclear matrix and nuclear matrix proteins might play an important role in the regulation of the human ε-globin gene expression.
Lenzi, P
2009-01-01
We study Matrix Element corrections as implemented in four popular event generators for hadron collisions. We compare PYTHIA, HERWIG, ALPGEN and SHERPA in the Z/gamma* inclusive production at LHC. PYTHIA and HERWIG are able to correct the first emission from the shower taking the Matrix Element calculation for one additional parton into account. SHERPA and ALPGEN are able to take into account Matrix Element corrections not only for one, but rather for several hard emissions from the incoming partons. This can be done at the price of introducing a separation cut to distinguish a Matrix Element and a Parton Shower populated regions. In this paper we check the effect of Matrix Element corrections in PYTHIA and HERWIG and we check that results from these two generators are consistent. Then we turn to SHERPA and ALPGEN, that implement two different methods to match Matrix Element calculations and Parton Shower. If we constraint them so that no more than one parton can emerge from the Matrix Element calculations th...
Kim, Jeong Soo; Kyum Kim, Moon
2012-08-01
In this study, finite element analysis of beam on elastic foundation, which received great attention of researchers due to its wide applications in engineering, is performed for estimating dynamic responses of shallow foundation using exact stiffness matrix. First, element stiffness matrix based on the closed solution of beam on elastic foundation is derived. Then, we performed static finite element analysis included exact stiffness matrix numerically, comparing results from the analysis with some exact analysis solutions well known for verification. Finally, dynamic finite element analysis is performed for a shallow foundation structure under rectangular pulse loading using trapezoidal method. The dynamic analysis results exist in the reasonable range comparing solution of single degree of freedom problem under a similar condition. The results show that finite element analysis using exact stiffness matrix is evaluated as a good tool of estimating the dynamic response of structures on elastic foundation.
Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices
Habib, K. M. Masum; Sajjad, Redwan N.; Ghosh, Avik W.
2016-03-01
Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.
Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems
Szederkenyi, Gabor; Hangos, Katalin M
2004-04-26
We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.
The extracellular matrix - the under-recognized element in lung disease?
Burgess, Janette K.; Mauad, Thais; Tjin, Gavin; Karlsson, Jenny C.; Westergren-Thorsson, Gunilla
2016-01-01
The lung is composed of airways and lung parenchyma, and the extracellular matrix (ECM) contains the main building blocks of both components. The ECM provides physical support and stability to the lung, and as such it has in the past been regarded as an inert structure. More recent research has
Raj, Vivek [Indian Institute of Technology-Kanpur, Kanpur (India); Mistarihi, Qusai M.; Ryu, Ho Jin [KAIST, Daejeon (Korea, Republic of)
2015-10-15
The improvement of thermal properties of ZrO{sub 2} has been investigated in many ways to enhance the performance of inert matrix fuel (IMF). Inert matrix fuel is a useful concept to burn transuranic elements (TRU) without increasing extra plutonium. The addition of reinforcements with a high thermal conductivity has been proposed in the previous studies. Molybdenum and silicon carbide are good candidate materials for the reinforcement because of their high thermal conductivities and low neutron absorption cross sections. Recently, ZrO{sub 2}-based composites reinforced with Mo-wire mesh or carbon foam were fabricated by spark plasma sintering. When the effects of the structures of reinforcements were compared, interconnected structures provided more enhanced thermal conductivity than discrete structures. The effective thermal conductivity of composite materials with various reinforcement structures can be calculated by using the finite element analyses. The finite element analyses presented a good agreement with theoretical models in estimating the effects of the reinforcement on the thermal conductivities of discrete Mo reinforced ZrO{sub 2} nanocomposites. It is found that the effects of interconnected thermal reinforcements on the effective thermal conductivity can be estimated by using the percolation model.
Yelnykov, O V
2005-01-01
This thesis addresses three topics: calculation of the invariant measure for the pure Yang-Mills configuration space in (3 + 1) dimensions, Hamiltonian analysis of the pure Chern-Simons theory on the noncommutative plane and noncommutative quantum mechanics in the presence of singular potentials. In Chapter 1 we consider a gauge-invariant Hamiltonian analysis for Yang-Mills theories in three spatial dimensions. The gauge potentials are parameterized in terms of a matrix variable which facilitates the elimination of the gauge degrees of freedom. We develop an approximate calculation of the volume element on the gauge-invariant configuration space. We also make a rough estimate of the ratio of 0++ glueball mass and the square root of string tension by comparison with (2 + 1)-dimensional Yang-Mills theory. In Chapter 2 the Hamiltonian analysis of the pure Chern- Simons theory on the noncommutative plane is performed. We use the techniques of geometric quantization to show that the classical reduced phase space o...
Papas, Brian N; Schuurman, Michael S; Yarkony, David R
2008-09-28
A self-consistent procedure for constructing a quasidiabatic Hamiltonian representing N(state) coupled electronic states in the vicinity of an arbitrary point in nuclear coordinate space is described. The matrix elements of the Hamiltonian are polynomials of arbitrary order. Employing a crude adiabatic basis, the coefficients of the linear terms are determined exactly using analytic gradient techniques. The remaining polynomial coefficients are determined from the normal form of a system of pseudolinear equations, which uses energy gradient and derivative coupling information obtained from reliable multireference configuration interaction wave functions. In a previous implementation energy gradient and derivative coupling information were employed to limit the number of nuclear configurations at which ab initio data were required to determine the unknown coefficients. Conversely, the key aspect of the current approach is the use of ab initio data over an extended range of nuclear configurations. The normal form of the system of pseudolinear equations is introduced here to obtain a least-squares fit to what would have been an (intractable) overcomplete set of data in the previous approach. This method provides a quasidiabatic representation that minimizes the residual derivative coupling in a least-squares sense, a means to extend the domain of accuracy of the diabatic Hamiltonian or refine its accuracy within a given domain, and a way to impose point group symmetry and hermiticity. These attributes are illustrated using the 1 (2)A(1) and 1 (2)E states of the 1-propynyl radical, CH(3)CC.
Haxton, Wick; Lunardini, Cecilia
2008-09-01
Semi-leptonic electroweak interactions in nuclei—such as β decay, μ capture, charged- and neutral-current neutrino reactions, and electron scattering—are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order |p→|/M, where p→ and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q, where q is the magnitude of the three-momentum transfer. While results for such matrix elements are available in tabular form, with certain restriction on quantum numbers, the task of determining the analytic form of a response function can still be quite tedious, requiring the folding of the tabulated matrix elements with the nuclear density matrix, and subsequent algebra to evaluate products of operators. Here we provide a Mathematica script for generating these matrix elements, which will allow users to carry out all such calculations by symbolic manipulation. This will eliminate the errors that may accompany hand calculations and speed the calculation of electroweak nuclear cross sections and rates. We illustrate the use of the new script by calculating the cross sections for charged- and neutral-current neutrino scattering in 12C. Program summaryProgram title: SevenOperators Catalogue identifier: AEAY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Gazmeh, Meisam; Bahreini, Maryam; Tavassoli, Seyed Hassan; Asnaashari, Mohammad
2015-01-01
Introduction: In this study, laser induced breakdown spectroscopy (LIBS) is used for qualitative analysis of healthy and carious teeth. The technique of laser ablation is receiving increasing attention for applications in dentistry, specifically for the treatment of teeth such as drilling of micro-holes and plaque removal. Methods: A quality-switched (Q-switched) Neodymium-Doped Yttrium Aluminium Garnet (Nd:YAG) laser operating at wavelength of 1064 nm, pulse energy of 90 mJ/pulse, repetition rate of 2Hz and pulse duration of 6 ns was used in this analysis. In the process of ablation a luminous micro-plasma is normally generated which may be exploited for on-line elemental analysis via laser induced breakdown spectroscopy technique. We propose laser induced breakdown spectroscopy as a rapid, in situ and easy method for monitoring drilling process. Results: The results of elemental analysis show the presence of some trace elements in teeth including P, Ca, Mg, Zn, K, Sr, C, Na, H, O and the permeability of some amalgam (teeth filling materials) elements including Hg, Ag, Cu and Sn into dental matrix. Conclusion: This study addresses the ability of LIBS in elemental analysis of teeth and its feasibility in acute identification of healthy and carious teeth during drilling process for future clinical applications. PMID:25987971
Wu, Yueqian; Yang, Minglin; Sheng, Xinqing; Ren, Kuan Fang
2015-05-01
Light scattering properties of absorbing particles, such as the mineral dusts, attract a wide attention due to its importance in geophysical and environment researches. Due to the absorbing effect, light scattering properties of particles with absorption differ from those without absorption. Simple shaped absorbing particles such as spheres and spheroids have been well studied with different methods but little work on large complex shaped particles has been reported. In this paper, the surface Integral Equation (SIE) with Multilevel Fast Multipole Algorithm (MLFMA) is applied to study scattering properties of large non-spherical absorbing particles. SIEs are carefully discretized with piecewise linear basis functions on triangle patches to model whole surface of the particle, hence computation resource needs increase much more slowly with the particle size parameter than the volume discretized methods. To improve further its capability, MLFMA is well parallelized with Message Passing Interface (MPI) on distributed memory computer platform. Without loss of generality, we choose the computation of scattering matrix elements of absorbing dust particles as an example. The comparison of the scattering matrix elements computed by our method and the discrete dipole approximation method (DDA) for an ellipsoid dust particle shows that the precision of our method is very good. The scattering matrix elements of large ellipsoid dusts with different aspect ratios and size parameters are computed. To show the capability of the presented algorithm for complex shaped particles, scattering by asymmetry Chebyshev particle with size parameter larger than 600 of complex refractive index m = 1.555 + 0.004 i and different orientations are studied.
STATISTIC MODELING OF THE CREEP BEHAVIOR OF METAL MATRIX COMPOSITES BASED ON FINITE ELEMENT ANALYSIS
岳珠峰
2002-01-01
The aim of the paper is to discover the general creep mechanisms for the short fiber reinforcement matrix composites (MMCs) under uniaxial stress states and to build a relationship between the macroscopic steady creep behavior and the material micro geometric parameters. The unit cell models were used to calculate the macroscopic creep behavior with different micro geometric parameters of fibers on different loading directions. The influence of the geometric parameters of the fibers and loading directions on the macroscopic creep behavior had been obtained, and described quantitatively. The matrix/fiber interface had been considered by a third layer, matrix/fiber interlayer, in the unit cells with different creep properties and thickness. Based on the numerical results of the unit cell models, a statistic model had been presented for the plane randomly-distributed-fiber MMCs. The fiber breakage had been taken into account in the statistic model for it starts experimentally early in the creep life. With the distribution of the geometric parameters of the fibers, the results of the statistic model agree well with the experiments. With the statistic model, the influence of the geometric parameters and the breakage of the fibers as well as the properties and thickness of the interlayer on the macroscopic steady creep rate have been discussed.
Lax operator algebras and Hamiltonian integrable hierarchies
Sheinman, Oleg K
2009-01-01
We consider the theory of Lax equations in complex simple and reductive classical Lie algebras with the spectral parameter on a Riemann surface of finite genus. Our approach is based on the new objects -- the Lax operator algebras, and develops the approach of I.Krichever treating the $\\gl(n)$ case. For every Lax operator considered as the mapping sending a point of the cotangent bundle on the space of extended Tyrin data to an element of the corresponding Lax operator algebra we construct the hierarchy of mutually commuting flows given by Lax equations and prove that those are Hamiltonian with respect to the Krichever-Phong symplectic structure. The corresponding Hamiltonians give integrable finite-dimensional Hitchin-type systems. For example we derive elliptic $A_n$, $C_n$, $D_n$ Calogero-Moser systems in frame of our approach.
Lax operator algebras and Hamiltonian integrable hierarchies
Sheinman, Oleg K [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2011-02-28
This paper considers the theory of Lax equations with a spectral parameter on a Riemann surface, proposed by Krichever in 2001. The approach here is based on new objects, the Lax operator algebras, taking into consideration an arbitrary complex simple or reductive classical Lie algebra. For every Lax operator, regarded as a map sending a point of the cotangent bundle on the space of extended Tyurin data to an element of the corresponding Lax operator algebra, a hierarchy of mutually commuting flows given by the Lax equations is constructed, and it is proved that they are Hamiltonian with respect to the Krichever-Phong symplectic structure. The corresponding Hamiltonians give integrable finite-dimensional Hitchin-type systems. For example, elliptic A{sub n}, C{sub n}, and D{sub n} Calogero-Moser systems are derived in the framework of our approach. Bibliography: 13 titles.
3-Loop massive O(T{sub 2}{sup F}) contributions to the DIS operator matrix element A{sub gg}
Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Hasselhuhn, A.; Round, M. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Inst. for Symbolic Computation (RISC); Manteuffel, A. von [Mainz Univ. (Germany). PRISMA Cluster of Excellence
2014-09-15
Contributions to heavy flavour transition matrix elements in the variable flavour number scheme are considered at 3-loop order. In particular a calculation of the diagrams with two equal masses that contribute to the massive operator matrix element A{sup (3)}{sub gg,Q} is performed. In the Mellin space result one finds finite nested binomial sums. In x-space these sums correspond to iterated integrals over an alphabet containing also square-root valued letters.
Pascual, J.
1987-12-01
An X-ray fluorescence method for determining trace elements in silicate rock samples was studied. The procedure focused on the application of the pertinent matrix corrections. Either the Compton peak or the reciprocal of the mass absorption coefficient of the sample was used as internal standard for this purpose. X-ray tubes with W or Cr anodes were employed, and the W L..beta.. and Cr K..cap alpha.. Compton intensities scattered by the sample were measured. The mass absorption coefficients at both sides of the absorption edge for Fe (1.658 and 1.936 A) were calculated. The elements Zr, Y, Rb, Zn, Ni, Cr and V were determined in 15 international reference rocks covering wide ranges of concentration. Relative mean errors were in many cases less than 10%.
Oktay Demirdaǧ
2008-02-01
This paper deals with the free vibration of Timoshenko columns with attached masses having rotary inertia. The support of the model is elastically restrained against rotation. The concept of ﬁxity factor is used to deﬁne the stiffness of the elastic connection relative to that of the column. The governing equation of the column elements is solved by applying the separation of variables method in the transfer matrix method (TMM) algorithm. The same problems are solved, also, by ﬁnite element method (FEM) algorithm in which the matrices in equation of motion are obtained for Timoshenko column, and the results are compared with the ones of TMM. The comparison graphs are presented in numerical analysis to show the effectiveness of the considered methods, and it is resulted that FEM gives closer results to TMM.
Kopp, Wassja A.; Leonhard, Kai
2016-12-01
We show how inverse metric tensors and rovibrational kinetic energy operators in terms of internal bond-angle coordinates can be obtained analytically following a factorization of the Jacobian worked out by Frederick and Woywod. The structure of these Jacobians is exploited in two ways: On one hand, the elements of the metric tensor as well as its determinant all have the form ∑rmsin (αn) cos (βo) . This form can be preserved by working with the adjugate metric tensor that can be obtained without divisions. On the other hand, the adjugate can be obtained with less effort by exploiting the lower triangular structure of the Jacobians. Together with a suitable choice of the wavefunction, we avoid singularities and show how to obtain analytical expressions for the rovibrational kinetic energy matrix elements.
Stanišić Svetlana M.
2012-01-01
Full Text Available The single agent extractions of major and trace metals from soil sample were conducted by means of rotary mixer and ultrasonic bath with sonication time of 10, 20, 30, 40 and 50 min. The sequential extraction according to the BCR scheme was undertaken. The obtained soil extracts were analyzed by ICP-OES and according to the results the rotary mixer assisted extraction was more efficient in the case of alkaline-earth elements. However, by the use of ultrasound several times higher amounts of matrix elements (Fe, Al and Mn and heavy metals predominantly associated with Fe, Al and Mn oxyhydroxides were extracted. The increase of the sonication time failed to improve extraction yields. The changes of the conductivity, pH, oxidoreduction potential, particle size diameter and zeta potential of colloid particles, with the sonication time increase were measured. The extraction mechanism and expressed selectivity of ultrasound is discussed and explanation is suggested.
Riccati group invariants of linear hamiltonian systems
Garzia, M. R.; Loparo, K. A.; Martin, C. F.
1983-01-01
The action of the Riccati group on the Riccati differential equation is associated with the action of a subgroup of the symplectic group on a set of hamiltonian matrices. Within this framework various sets of canonical forms are developed for the matrix coefficients of the Riccati differential equation. The canonical forms presented are valid for arbitrary Kronecker indices, and it is shown that the Kronecker indices are invariants for this group action. These canonical forms are useful for studying problems arising in the areas of optimal decentralized control and the spectral theory of optimal control problems.
Port-Hamiltonian description and analysis of the LuGre friction model
Koopman, J.; Jeltsema, D.; Verhaegen, M.H.G.
2010-01-01
A port-Hamiltonian formulation of the LuGre friction model is presented that can be used as a building block in the physical modelling of systems with friction. Based on the dissipation structure matrix of this port-Hamiltonian LuGre model, an alternative proof can be given for the passivity conditi
Chromatic roots and hamiltonian paths
Thomassen, Carsten
2000-01-01
We present a new connection between colorings and hamiltonian paths: If the chromatic polynomial of a graph has a noninteger root less than or equal to t(n) = 2/3 + 1/3 (3)root (26 + 6 root (33)) + 1/3 (3)root (26 - 6 root (33)) = 1.29559.... then the graph has no hamiltonian path. This result...
Reta, Daniel; Moreira, Ibério de P R; Illas, Francesc
2016-07-12
In the most general case of three electrons in three symmetry unrelated centers with Ŝ1 = Ŝ2 = Ŝ3 = 1/2 localized magnetic moments, the low energy spectrum consists of one quartet (Q) and two doublet (D1, D2) pure spin states. The energy splitting between these spin states can be described with the well-known Heisenberg-Dirac-Van Vleck (HDVV) model spin Hamiltonian, and their corresponding energy expressions are expressed in terms of the three different two-body magnetic coupling constants J12, J23, and J13. However, the values of all three magnetic coupling constants cannot be extracted using the calculated energy of the three spin-adapted states since only two linearly independent energy differences between pure spin states exist. This problem has been recently investigated by Reta et al. (J. Chem. Theory Comput. 2015, 11, 3650), resulting in an alternative proposal to the original Noodleman's broken symmetry mapping approach. In the present work, this proposal is validated by means of ab initio effective Hamiltonian theory, which allows a direct extraction of all three J values from the one-to-one correspondence between the matrix elements of both effective and HDVV Hamiltonian. The effective Hamiltonian matrix representation has been constructed from configuration interaction wave functions for the three spin states obtained for two model systems showing a different degree of delocalization of the unpaired electrons. These encompass a trinuclear Cu(II) complex and a π-conjugated purely organic triradical.
Quantization of noncommutative completely integrable Hamiltonian systems
Giachetta, G; Sardanashvily, G
2007-01-01
Integrals of motion of a Hamiltonian system need not be commutative. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as an abelian completely integrable Hamiltonian system.
A static analysis of metal matrix composite spur gear by three-dimensional finite element method
Ganesan, N.; Vijayarangan, S.
1993-03-01
A number of engineering components have recently been made using metal matrix composite (MMC) materials, due to their overwhelming advantages, such as light weight high strength, higher dimensional stability and minimal attack by environment, when compared with polymer-based composite materials, even though the cost of MMCs are very high. Power transmission gears are one such area able to make use of MMC materials. Here an attempt is made to study and compare the performance of gears made of MMC materials with that of conventional steel material gears. It may be concluded from this study that MMC materials are highly suitable for making gears that are to transmit even fairly large power.
Hu, Anguang; Chan, Nora W. C.; Dunlap, Brett I.
2017-08-01
The computation of s-type Gaussian pseudopotential matrix elements involving low powers of the distance from the pseudopotential center using Gaussian orbitals can be reduced to familiar integrals. They may be directly expressed as either simple three-center overlap integrals for even powers of the radial distance from the pseudopotential center or related to the three-center nuclear integrals of a Gaussian charge distribution for odd powers. Orbital angular momentum about each atom is added to these integrals by solid-harmonic differentiation with respect to its center. The solid-harmonic addition theorem allows all the integrals to be factored into products of invariant one-dimensional integrals involving the Gaussian exponents and angular factors that contain the azimuthal quantum numbers but are independent of all Gaussian exponents. Precomputing the angular factors allow looping over all Gaussian exponents about the three centers. The fact that solid harmonics are eigenstates of angular momentum removes the singularities seen in previous treatments of pseudopotential matrix elements.
Kicošev Vesna
2015-01-01
Full Text Available Salt steppes and marshes represent the most valuable ecosystems in the world, providing numerous ecosystem services that are extremely vulnerable to anthropogenic influences. These types of habitat in the territory of Serbia are most dominant in Banat and a significant portion of them is under protection or in the process of becoming protected. The section surrounding the protected areas of Slano Kopovo Special Nature Reserve, Rusanda Nature Park and Okanj Bara Special Nature Reserve with the non-building area of Novi Bečej, Kumane, Melenci, Elemir and Taraš cadastral municipalities, has been chosen for the analysis. The aim of this paper was to assess the influence of specific anthropogenic factors on the elements of an ecological network using the analytical method that can generate the required results in a manner suitable for presentation to various stakeholders. To achieve this aim, the Leopold matrix model, used for assessing anthropogenic influence on the environment, has been chosen. The specificity of this issue of protecting and preserving elements of an ecological network resulted in the need to isolate and evaluate the factors affecting the preservation of habitats and functionality of ecosystems, unlike the concept of Leopold matrix, which treats all factors as equally important in the process of evaluation. Evaluation results indicate significant effects of historical, perennial manner of using the area and other resources in the non-building area.
Alimonti, Luca; Atalla, Noureddine; Berry, Alain; Sgard, Franck
2015-02-01
Practical vibroacoustic systems involve passive acoustic treatments consisting of highly dissipative media such as poroelastic materials. The numerical modeling of such systems at low to mid frequencies typically relies on substructuring methodologies based on finite element models. Namely, the master subsystems (i.e., structural and acoustic domains) are described by a finite set of uncoupled modes, whereas condensation procedures are typically preferred for the acoustic treatments. However, although accurate, such methodology is computationally expensive when real life applications are considered. A potential reduction of the computational burden could be obtained by approximating the effect of the acoustic treatment on the master subsystems without introducing physical degrees of freedom. To do that, the treatment has to be assumed homogeneous, flat, and of infinite lateral extent. Under these hypotheses, simple analytical tools like the transfer matrix method can be employed. In this paper, a hybrid finite element-transfer matrix methodology is proposed. The impact of the limiting assumptions inherent within the analytical framework are assessed for the case of plate-cavity systems involving flat and homogeneous acoustic treatments. The results prove that the hybrid model can capture the qualitative behavior of the vibroacoustic system while reducing the computational effort.
Measurement of the top quark mass in the lepton+jets final state with the matrix element method
Abazov, V M; Abolins, M; Acharya, B S; Adams, M; Adams, T; Agelou, M; Aguiló, E; Ahn, S H; Ahsan, M; Alexeev, G D; Alkhazov, G; Alton, A; Alverson, G; Alves, G A; Anastasoaie, M; Andeen, T; Anderson, S; Andrieu, B; Anzelc, M S; Arnoud, Y; Arov, M; Askew, A; Åsman, B; Assis-Jesus, A C S; Atramentov, O; Autermann, C; Avila, C; Ay, C; Badaud, F; Baden, A; Bagby, L; Baldin, B; Bandurin, D V; Banerjee, P; Banerjee, S; Barberis, E; Bargassa, P; Baringer, P; Barnes, C; Barreto, J; Bartlett, J F; Bassler, U; Bauer, D; Beale, S; Bean, A; Begalli, M; Begel, M; Belanger-Champagne, C; Bellantoni, L; Bellavance, A; Benítez, J A; Beri, S B; Bernardi, G; Bernhard, R; Berntzon, L; Bertram, I; Besançon, M; Beuselinck, R; Bezzubov, V A; Bhat, P C; Bhatnagar, V; Binder, M; Biscarat, C; Black, K M; Blackler, I; Blazey, G; Blekman, F; Blessing, S; Bloch, D; Bloom, K; Blumenschein, U; Böhnlein, A; Boeriu, O; Bolton, T A; Borissov, G; Bos, K; Bose, T; Brandt, A; Brock, R; Brooijmans, G; Bross, A; Brown, D; Buchanan, N J; Buchholz, D; Bühler, M; Büscher, V; Burdin, S; Burke, S; Burnett, T H; Busato, E; Buszello, C P; Butler, J M; Calfayan, P; Calvet, S; Cammin, J; Caron, S; Carvalho, W; Casey, B C K; Cason, N M; Castilla-Valdez, H; Chakrabarti, S; Chakraborty, D; Chan, K M; Chandra, A; Charles, F; Cheu, E; Chevallier, F; Cho, D K; Choi, S; Choudhary, B; Christofek, L; Claes, D; Clement, B; Clément, C; Coadou, Y; Cooke, M; Cooper, W E; Coppage, D; Corcoran, M; Cousinou, M C; Cox, B; Crepe-Renaudin, S; Cutts, D; Cwiok, M; Da Motta, H; Das, A; Das, M; Davies, B; Davies, G; Davis, G A; De, K; de Jong, P; De Jong, S J; De La Cruz-Burelo, E; De Oliveira Martins, C; Degenhardt, J D; Déliot, F; Demarteau, M; Demina, R; Demine, P; Denisov, D; Denisov, S P; Desai, S; Diehl, H T; Diesburg, M; Doidge, M; Dominguez, A; Dong, H; Dudko, L V; Duflot, L; Dugad, S R; Duggan, D; Duperrin, A; Dyer, J; Dyshkant, A; Eads, M; Edmunds, D; Edwards, T; Ellison, J; Elmsheuser, J; Elvira, V D; Eno, S; Ermolov, P; Evans, H; Evdokimov, A; Evdokimov, V N; Fatakia, S N; Feligioni, L; Ferapontov, A V; Ferbel, T; Fiedler, F; Filthaut, F; Fisher, W; Fisk, H E; Fleck, I; Ford, M; Fortner, M; Fox, H; Fu, S; Fuess, S; Gadfort, T; Galea, C F; Gallas, E; Galyaev, E; García, C; García-Bellido, A; Gardner, J; Gavrilov, V; Gay, A; Gay, P; Gelé, D; Gelhaus, R; Gerber, C E; Gershtein, Yu; Gillberg, D; Ginther, G; Gollub, N; Gómez, B; Goussiou, A; Grannis, P D; Greenlee, H; Greenwood, Z D; Gregores, E M; Grenier, G; Gris, P; Grivaz, J F; Grünendahl, S; Grünewald, M W; Guo, F; Guo, J; Gutíerrez, G; Gutíerrez, P; Haas, A; Hadley, N J; Haefner, P; Hagopian, S; Haley, J; Hall, I; Hall, R E; Han, L; Hanagaki, K; Hansson, P; Harder, K; Harel, A; Harrington, R; Hauptman, J M; Hauser, R; Hays, J; Hebbeker, T; Hedin, D; Hegeman, J G; Heinmiller, J M; Heinson, A P; Heintz, U; Hensel, C; Herner, K; Hesketh, G; Hildreth, M D; Hirosky, R; Hobbs, J D; Hoeneisen, B; Hoeth, H; Hohlfeld, M; Hong, S J; Hooper, R; Houben, P; Hu, Y; Hubacek, Z; Hynek, V; Iashvili, I; Illingworth, R; Ito, A S; Jabeen, S; Jaffré, M; Jain, S; Jakobs, K; Jarvis, C; Jenkins, A; Jesik, R; Johns, K; Johnson, C; Johnson, M; Jonckheere, A; Jonsson, P; Juste, A; Käfer, D; Kahn, S; Kajfasz, E; Kalinin, A M; Kalk, J M; Kalk, J R; Kappler, S; Karmanov, D; Kasper, J; Kasper, P; Katsanos, I; Kau, D; Kaur, R; Kehoe, R; Kermiche, S; Khalatyan, N; Khanov, A; Kharchilava, A I; Kharzheev, Yu M; Khatidze, D; Kim, H; Kim, T J; Kirby, M H; Klima, B; Kohli, J M; Konrath, J P; Kopal, M; Korablev, V M; Kotcher, J; Kothari, B; Koubarovsky, A; Kozelov, A V; Kroninger, K; Krop, D; Kryemadhi, A; Kühl, T; Kumar, A; Kunori, S; Kupco, A; Kurca, T; Kvita, J; Lammers, S; Landsberg, G L; Lazoflores, J; Le Bihan, A C; Lebrun, P; Lee, W M; Leflat, A; Lehner, F; Lesne, V; Lévêque, J; Lewis, P; Li, J; Li, Q Z; Lima, J G R; Lincoln, D; Linnemann, J; Lipaev, V V; Lipton, R; Liu, Z; Lobo, L; Lobodenko, A; Lokajícek, M; Lounis, A; Love, P; Lubatti, H J; Lynker, M; Lyon, A L; Maciel, A K A; Madaras, R J; Mättig, P; Magass, C; Magerkurth, A; Magnan, A M; Makovec, N; Mal, P K; Malbouisson, H B; Malik, S; Malyshev, V L; Mao, H S; Maravin, Y; Martens, M; McCarthy, R; Meder, D; Melnitchouk, A; Mendes, A; Mendoza, L; Merkin, M; Merritt, K W; Meyer, A; Meyer, J; Michaut, M; Miettinen, H; Millet, T; Mitrevski, J; Molina, J; Mondal, N K; Monk, J; Moore, R W; Moulik, T; Muanza, G S; Mulders, M; Mulhearn, M; Mundal, O; Mundim, L; Mutaf, Y D; Nagy, E; Naimuddin, M; Narain, M; Naumann, N A; Neal, H A; Negret, J P; Neustroev, P; Nöding, C; Nomerotski, A; Novaes, S F; Nunnemann, T; O'Dell, V; O'Neil, D C; Obrant, G; Oguri, V; Oliveira, N; Onoprienko, D; Oshima, N; Otec, R; Oteroy-Garzon, G J; Owen, M; Padley, P; Parashar, N; Park, S J; Park, S K; Parsons, J; Partridge, R; Parua, N; Patwa, A; Pawloski, G; Perea, P M; Pérez, E; Peters, K; Petroff, P; Petteni, M; Piegaia, R; Piper, J; Pleier, M A; Podesta-Lerma, P L M; Podstavkov, V M; Pogorelov, Y; Pol, M E; Pompos, A; Pope, B G; Popov, A V; Potter, C; Prado da Silva, W L; Prosper, H B; Protopopescu, S D; Qian, J; Quadt, A; Quinn, B; Rangel, M S; Rani, K J; Ranjan, K; Ratoff, P N; Renkel, P; Reucroft, S; Rijssenbeek, M; Ripp-Baudot, I; Rizatdinova, F K; Robinson, S; Rodrigues, R F; Royon, C; Rubinov, P; Ruchti, R; Rud, V I; Sajot, G; Sánchez-Hernández, A; Sanders, M P; Santoro, A F S; Savage, G; Sawyer, L; Scanlon, T; Schaile, A D; Schamberger, R D; Scheglov, Y; Schellman, H; Schieferdecker, P; Schmitt, C; Schwanenberger, C; Schwartzman, A; Schwienhorst, R; Sekaric, J; Sen-Gupta, S; Severini, H; Shabalina, E; Shamim, M; Shary, V; Shchukin, A A; Shephard, W D; Shivpuri, R K; Shpakov, D; Siccardi, V; Sidwell, R A; Simák, V; Sirotenko, V I; Skubic, P L; Slattery, P F; Smith, R P; Snow, G R; Snow, J; Snyder, S; Söldner-Rembold, S; Song, X; Sonnenschein, L; Sopczak, A; Sosebee, M; Soustruznik, K; Souza, M; Spurlock, B; Stark, J; Steele, J; Stolin, V; Stone, A; Stoyanova, D A; Strandberg, J; Strandberg, S; Strang, M A; Strauss, M; Ströhmer, R; Strom, D; Strovink, M; Stutte, L; Sumowidagdo, S; Svoisky, P; Sznajder, A; Talby, M; Tamburello, P; Taylor, W; Telford, P; Temple, J; Tiller, B; Titov, M; Tokmenin, V V; Tomoto, M; Toole, T; Torchiani, I; Towers, S; Trefzger, T; Trincaz-Duvoid, S; Tsybychev, D; Tuchming, B; Tully, C; Turcot, A S; Tuts, P M; Unalan, R; Uvarov, L; Uvarov, S; Uzunyan, S; Vachon, B; vanden Berg, P J; Van Kooten, R; Van Leeuwen, W M; Varelas, N; Varnes, E W; Vartapetian, A H; Vasilyev, I A; Vaupel, M; Verdier, P; Vertogradov, L S; Verzocchi, M; Villeneuve-Séguier, F; Vint, P; Vlimant, J R; Von Törne, E; Voutilainen, M; Vreeswijk, M; Wahl, H D; Wang, L; Wang, M H L; Warchol, J; Watts, G; Wayne, M; Weber, G; Weber, M; Weerts, H; Wermes, N; Wetstein, M; White, A; Wicke, D; Wilson, G W; Wimpenny, S J; Wobisch, M; Womersley, J; Wood, D R; Wyatt, T R; Xie, Y; Xuan, N; Yacoob, S; Yamada, R; Yan, M; Yasuda, T; Yatsunenko, Y A; Yip, K; Yoo, H D; Youn, S W; Yu, C; Yu, J; Yurkewicz, A; Zatserklyaniy, A; Zeitnitz, C; Zhang, D; Zhao, T; Zhou, B; Zhu, J; Zielinski, M; Zieminska, D; Zieminski, A; Zutshi, V; Zverev, E G; al, et
2006-01-01
We present a measurement of the top quark mass with the Matrix Element method in the lepton+jets final state. As the energy scale for calorimeter jets represents the dominant source of systematic uncertainty, the Matrix Element likelihood is extended by an additional parameter, which is defined as a global multiplicative factor applied to the standard energy scale. The top quark mass is obtained from a fit that yields the combined statistical and systematic jet energy scale uncertainty. Using a data set of 370 pb-1 taken with the D0 experiment at Run II of the Fermilab Tevatron Collider, the mass of the top quark is measured using topological information to be: mtop(topo) = 169.2 +5.0-7.4 (stat.+JES) +1.5-1.4 (syst.) GeV, and when information about identified $b$ jets is included: mtop(b-tag) = 170.3 +4.1-4.5 (stat.+JES) +1.2-1.8 (syst.) GeV. The measurements yield a jet energy scale consistent with the reference scale.
Short-distance matrix elements for D-meson mixing for 2+1 flavor lattice QCD
Chang, Chia Cheng
We study the short-distance hadronic matrix elements for D-meson mixing with partially quenched Nf = 2+1 lattice QCD. We use a large set of the MIMD Lattice Computation Collaboration's gauge configurations with a2 tadpole-improved staggered sea quarks and tadpole-improved Luscher-Weisz gluons. We use the a2 tadpole-improved action for valence light quarks and the Sheikoleslami-Wohlert action with the Fermilab interpretation for the valence charm quark. Our calculation covers the complete set of five operators needed to constrain new physics models for D-meson mixing. We match our matrix elements to the MS-NDR scheme evaluated at 3GeV. We report values for the Beneke-Buchalla-Greub-Lenz-Nierste choice of evanescent operators and obtain / mD = 0.042(4)GeV3, /mD = -0.078(4)GeV3, /mD = 0.033(2)GeV 3, /mD = 0.155(10)GeV3, /mD = 0.058(6)GeV3.
Linear Hamiltonian systems - The Riccati group and its invariants
Garzia, M. R.; Martin, C. F.; Loparo, K. A.
1982-01-01
The action of the Riccati group on the Riccati differential equation is associated with the action of a subgroup of the symplectic group on a set of Hamiltonian matrices. Within this framework canonical forms are developed for the matrix coefficients of the Riccati differential equation.
Two-dimensional point spread matrix of layered metal-dielectric imaging elements
Kotynski, Rafal; Krol, Karol; Panajotov, Krassimir
2010-01-01
We describe the change of the spatial distribution of the state of polarisation occurring during two-dimensional imaging through a multilayer and in particular through a layered metallic flat lens. Linear or circular polarisation of incident light is not preserved due to the difference in the amplitude transfer functions for the TM and TE polarisations. In effect, the transfer function and the point spread function that characterize 2D imaging through a multilayer both have a matrix form and cross-polarisation coupling is observed for spatially modulated beams with a linear or circular incident polarisation. The point spread function in a matrix form is used to characterise the resolution of the superlens for different polarisation states. We demonstrate how the 2D PSF may be used to design a simple diffractive nanoelement consisting of two radial slits. The structure assures the separation of non-diffracting radial beams originating from two slits in the mask and exhibits an interesting property of a backwar...
Time Averaged Quantum Dynamics and the Validity of the Effective Hamiltonian Model
Gamel, Omar
2010-01-01
We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an Effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the general equation to harmonic Hamiltonians, we confirm a previous formula for the Effective Hamiltonian together with a new decoherence term which should in general be included, and whose vanishing provides the criteria for validity of the Effective Hamiltonian approach. Finally, we apply the theory to examples of the AC Stark Shift and Three- Level Raman Transitions, recovering a new decoherence effect in the latter.
Cwik, T. [California Institute of Technology, Pasadena, CA (United States); Katz, D.S. [Cray Research, El Segundo, CA (United States)
1996-12-31
Finite element modeling has proven useful for accurately simulating scattered or radiated electromagnetic fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of an electrical wavelength. An unstructured finite element model of realistic objects leads to a large, sparse, system of equations that needs to be solved efficiently with regard to machine memory and execution time. Both factorization and iterative solvers can be used to produce solutions to these systems of equations. Factorization leads to high memory requirements that limit the electrical problem size of three-dimensional objects that can be modeled. An iterative solver can be used to efficiently solve the system without excessive memory use and in a minimal amount of time if the convergence rate is controlled.
Yuan, Ji-hai; Zhan, Xiu-chun; Hu, Ming-yue; Zhao, Ling-hao; Sun, Dong-yang
2015-02-01
Matrix effect between reference materials and samples is one of the major factors affecting the accuracy of analytical results by laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS). However, there is no method or calculation formula to quantify matrix effect between standards and samples up to date. In this paper, the linear correlation coefficient r of the Ii/I(is-Ci)/Cis graphs of element pairs were used to characterize the matrix effect, which took the ratios of concentrations (ci/ c(is)) and intensities (Ii/Iis) of the analytical element and internal standard element as x-axis and gamma-axis, respectively. Matrix effects of 6 element pairs in 13 glass reference materials, 2 sulfide reference materials and 2 sulfide minerals using Fe as internal standard was studied, with the linear correlation coefficient r of Fe-Cu, Fe-Zn element pairs both less than 0. 999 and trace Fe--Mn, Fe--Co, Fe--Ga, Fe--Pb element pairs all better than 0.999. Matrix effects of 3 major element pairs in 2 sulfide ref- erence materials and 6 sulfide minerals using S as internal standard was also studied, with the linear correlation coefficient r of S--Fe, S--Cu, S--Zn all less than 0.999. The great majority of relative errors of EMPA analytical results for major elements in sulfide minerals were greater than 10%, whether analyzed using Fe as internal standard with glass reference materials as external standard, or S as internal standard with sulfide reference materials MASS-1, IMER-1 as external standard, respectively. But the most analytical results for trace elements calibrated by glass reference materials using Fe as internal standard were well agreed with sulfide standard MASS-1, with the relative errors less than 15%. The results showed that matrix effects existed in glass reference materials, sulfide reference materials and sulfide minerals, and it also proved a certain rationality and practicability for quantification of matrix effect using the linear
Guliar O.
2015-12-01
Full Text Available On the basis of virtual work variations a new finite element with a variable crosssectional area along a generation, which due to numerical integration takes into account the variability of mechanical and geometrical parameters in cross-section was developed. In the process of test problem solving the correctness of the results, which allows to get this version of FE, was confirmed.
Haque, A.; Ahmed, L.; Ware, T.; Jeelani, S.; Verrilli, Michael J. (Technical Monitor)
2001-01-01
The stress concentrations associated with circular notches and subjected to uniform tensile loading in woven ceramic matrix composites (CMCs) have been investigated for high-efficient turbine engine applications. The CMC's were composed of Nicalon silicon carbide woven fabric in SiNC matrix manufactured through polymer impregnation process (PIP). Several combinations of hole diameter/plate width ratios and ply orientations were considered in this study. In the first part, the stress concentrations were calculated measuring strain distributions surrounding the hole using strain gages at different locations of the specimens during the initial portion of the stress-strain curve before any microdamage developed. The stress concentration was also calculated analytically using Lekhnitskii's solution for orthotropic plates. A finite-width correction factor for anisotropic and orthotropic composite plate was considered. The stress distributions surrounding the circular hole of a CMC's plate were further studied using finite element analysis. Both solid and shell elements were considered. The experimental results were compared with both the analytical and finite element solutions. Extensive optical and scanning electron microscopic examinations were carried out for identifying the fracture behavior and failure mechanisms of both the notched and notched specimens. The stress concentration factors (SCF) determined by analytical method overpredicted the experimental results. But the numerical solution underpredicted the experimental SCF. Stress concentration factors are shown to increase with enlarged hole size and the effects of ply orientations on stress concentration factors are observed to be negligible. In all the cases, the crack initiated at the notch edge and propagated along the width towards the edge of the specimens.
Prokhin Egor Anatol’evich
2016-10-01
Full Text Available In the modern conditions innovatization of construction is of great necessity, though it is associated with a number of problems of first of all institutional genesis. The development of green construction in Russia is on its first stages, though its necessity is growing according to the tendency for energy efficiency and sustainable development. The innovative process of ecological construction has a network model and requires its optimization with the aim of further development by advancing the institutional platform. The author proposed a conceptual scheme for an institutional platform of the innovative process of green construction and conducted systematization of institutional structures. The unique role of innovative and ecological institutes is substantiated. The author recommends an optimization method for institutional interaction of the subjects using the stakeholder theory and the theory of matrix games aimed at activation of innovative green technologies. Practical application of the offered algorithms and methods will allow increasing the efficiency of green construction development.
Dynamics of Hamiltonian Systems and Memristor Circuits
Itoh, Makoto; Chua, Leon
In this paper, we show that any n-dimensional autonomous systems can be regarded as subsystems of 2n-dimensional Hamiltonian systems. One of the two subsystems is identical to the n-dimensional autonomous system, which is called the driving system. Another subsystem, called the response system, can exhibit interesting behaviors in the neighborhood of infinity. That is, the trajectories approach infinity with complicated nonperiodic (chaotic-like) behaviors, or periodic-like behavior. In order to show the above results, we project the trajectories of the Hamiltonian systems onto n-dimensional spheres, or n-dimensional balls by using the well-known central projection transformation. Another interesting behavior is that the transient regime of the subsystems can exhibit Chua corsage knots. We next show that generic memristors can be used to realize the above Hamiltonian systems. Finally, we show that the internal state of two-element memristor circuits can have the same dynamics as n-dimensional autonomous systems.
A general nuclear motion Hamiltonian and non-internal curvilinear coordinates.
Strobusch, D; Scheurer, Ch
2013-03-07
An exact Hamiltonian for nuclear motions in general curvilinear coordinates is derived. It is demonstrated how this Hamiltonian transforms into well-established expressions, such as the Wilson Howard Hamiltonian or the Meyer Günthard Hamiltonian, if the general coordinates are restricted to be rectilinear or internal. Furthermore, a compact expression for the Hamiltonian expressed in non-internal curvilinear coordinates is provided, which makes this coordinate class available for applications in a simple way, since only the Jacobian matrix with respect to the rotating frame coordinates must be calculated. An example, employing a water model potential, exemplifies how different coordinate systems from all three coordinate classes (rectilinear, internal, and non-internal) lead to vibrational spectra, which are in excellent agreement. Thereby, the applicability of the general Hamiltonian is demonstrated and also its correctness is confirmed.
On the Reaction Path Hamiltonian
孙家钟; 李泽生
1994-01-01
A vector-fiber bundle structure of the reaction path Hamiltonian, which has been introduced by Miller, Handy and Adams, is explored with respect to molecular vibrations orthogonal to the reaction path. The symmetry of the fiber bundle is characterized by the real orthogonal group O(3N- 7) for the dynamical system with N atoms. Under the action of group O(3N- 7). the kinetic energy of the reaction path Hamiltonian is left invariant. Furthermore , the invariant behaviour of the Hamiltonian vector fields is investigated.
Weak Hamiltonian, CP Violation and Rare Decays
Buras, Andrzej J
1998-01-01
These lectures describe in detail the effective Hamiltonians for weak decays of mesons constructed by means of the operator product expansion and the renormalization group method. We calculate Wilson coeffcients of local operators, discuss mixing of operators under renormalization, the anomalous dimensions of operators and anomalous dimension matrices. We elaborate on the renormalzation scheme and renormalization scale dependences and their cancellations in physical amplitudes. In particular we discuss the issue of gamma-5 in D-dimensions and the role of evanescent operators in the calculation of two-loop anomalous dimensions. We present an explicit calculation of the 6 times 6 one-loop anomalous dimension matrix involving current-current and QCD-penguin operators and we give some hints how to properly calculate two-loop anomalous dimensions of these operators. In the phenonomenological part of these lectures we discuss in detail: CKM matrix, the unitarity triangle and its determination, two-body non-leptonic...
A Class of Asymmetric Gapped Hamiltonians on Quantum Spin Chains and its Characterization II
Ogata, Yoshiko
2016-12-01
We give a characterization of the class of gapped Hamiltonians introduced in Part I (Ogata, A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015). The Hamiltonians in this class are given as MPS (Matrix product state) Hamiltonians. In Ogata (A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015), we list up properties of ground state structures of Hamiltonians in this class. In this Part II, we show the converse. Namely, if a (not necessarily MPS) Hamiltonian H satisfies five of the listed properties, there is a Hamiltonian H' from the class by Ogata (A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015), satisfying the following: The ground state spaces of the two Hamiltonians on the infinite interval coincide. The spectral projections onto the ground state space of H on each finite intervals are approximated by that of H' exponentially well, with respect to the interval size. The latter property has an application to the classification problem with open boundary conditions.
A Class of Asymmetric Gapped Hamiltonians on Quantum Spin Chains and its Characterization II
Ogata, Yoshiko
2016-06-01
We give a characterization of the class of gapped Hamiltonians introduced in Part I (Ogata, A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015). The Hamiltonians in this class are given as MPS (Matrix product state) Hamiltonians. In Ogata (A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015), we list up properties of ground state structures of Hamiltonians in this class. In this Part II, we show the converse. Namely, if a (not necessarily MPS) Hamiltonian H satisfies five of the listed properties, there is a Hamiltonian H' from the class by Ogata (A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification I, 2015), satisfying the following: The ground state spaces of the two Hamiltonians on the infinite interval coincide. The spectral projections onto the ground state space of H on each finite intervals are approximated by that of H' exponentially well, with respect to the interval size. The latter property has an application to the classification problem with open boundary conditions.
Cline, Douglas; Wu, Ching-Yen
2001-10-01
Measured E2 properties are a sensitive and unambiguous probe of the collective shape parameters for quadrupole collective motion in nuclei. Collective motion produces strong correlations of the measured E2 matrix elements that can be related to the E2 properties in the principal axis frame of the rotating nucleus. By analogy with Bohr's quadrupole shape parameters (β,γ), the instantaneous principal axis frame E2 tensor can be expressed in terms of two parameters, Q,δ where E2(2,0)=Q\\cosδ, and E2(2,± 2)=fracQ√2sinδ. The E2 properties can be used to extract the E2 triaxiality parameter δ which can be related to γ by use of a geometrical collective model. The 1965 measurement [1] of the Q_2^+ state in ^114Cd provoked considerable interest in collective triaxial deformation in nuclei and stimulated measurement of Q_2^+ values in many other nuclei in order to probe the centroid of the E2 triaxial deformation. The heavy-ion Coulomb excitation experimental technique, plus the Coulomb excitation least-squares search code GOSIA, made it possible to measure rather complete sets of E2 matrix elements adding a new dimension to the study of triaxiality in nuclear collective motion [2]. This development also made it possible to exploit the rotational invariant technique [3-6] to extract directly from the measured E2 matrix elements, the expectation values of the centroids and fluctuation widths of principal axis E2 parameters for any state. The usefulness, range of validity, and results of this technique for determining the centroids and fluctuation widths for the triaxiality degree of freedom δ in a range of nuclei will be presented. The completeness required is a disadvantage of the rotational invariant technique. A comparison will be made of the use of the full rotational invariant technique with results obtained using restricted E2 data in conjunction with model-dependent analyses or truncation schemes. [1] J. de Boer et al, Phys. Rev. Lett. 14 (1965) 564; [2] D
Gardiner, Bruce S; Wong, Kelvin K L; Joldes, Grand R; Rich, Addison J; Tan, Chin Wee; Burgess, Antony W; Smith, David W
2015-10-01
This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus) and extracellular matrix (e.g. collagen) are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties). Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings). Each particle is in effect an 'agent', meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory.
Bruce S Gardiner
2015-10-01
Full Text Available This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus and extracellular matrix (e.g. collagen are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties. Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings. Each particle is in effect an 'agent', meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory.
Effective Hamiltonian for a microwave billiard with attached waveguide.
Stöckmann, H-J; Persson, E; Kim, Y-H; Barth, M; Kuhl, U; Rotter, I
2002-06-01
In a recent work the resonance widths in a microwave billiard with attached waveguide were studied in dependence on the coupling strength [E. Persson et al., Phys. Rev. Lett. 85, 2478 (2000)], and resonance trapping was experimentally found. In the present paper an effective Hamiltonian is derived that depends exclusively on billiard and waveguide geometry. Its eigenvalues give the poles of the scattering matrix provided that the system and environment are defined adequately. Further, we present the results of resonance trapping measurements where, in addition to our previous work, the position of the slit aperture within the waveguide was varied. Numerical simulations with the derived Hamiltonian qualitatively reproduce the experimental data.
Average quantum dynamics of closed systems over stochastic Hamiltonians
Yu, Li
2011-01-01
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in closed system dynamics, in addition to the usual unitary evolution. We then show that, for an important class of problems in which the Hamiltonian is proportional to a Gaussian random process, the 2nd-order master equation yields exact dynamics. The general formalism is applied to study the examples of a two-level system, two atoms in a stochastic magnetic field and the heating of a trapped ion.
Kuramoto dynamics in Hamiltonian systems.
Witthaut, Dirk; Timme, Marc
2014-09-01
The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony (phase locking). Here we present a classical Hamiltonian (and thus conservative) system with 2N state variables that in its action-angle representation exactly yields Kuramoto dynamics on N-dimensional invariant manifolds. We show that locking of the phase of one oscillator on a Kuramoto manifold to the average phase emerges where the transverse Hamiltonian action dynamics of that specific oscillator becomes unstable. Moreover, the inverse participation ratio of the Hamiltonian dynamics perturbed off the manifold indicates the global synchronization transition point for finite N more precisely than the standard Kuramoto order parameter. The uncovered Kuramoto dynamics in Hamiltonian systems thus distinctly links dissipative to conservative dynamics.
Continuum Hamiltonian Hopf Bifurcation II
Hagstrom, G I
2013-01-01
Building on the development of [MOR13], bifurcation of unstable modes that emerge from continuous spectra in a class of infinite-dimensional noncanonical Hamiltonian systems is investigated. Of main interest is a bifurcation termed the continuum Hamiltonian Hopf (CHH) bifurcation, which is an infinite-dimensional analog of the usual Hamiltonian Hopf (HH) bifurcation. Necessary notions pertaining to spectra, structural stability, signature of the continuous spectra, and normal forms are described. The theory developed is applicable to a wide class of 2+1 noncanonical Hamiltonian matter models, but the specific example of the Vlasov-Poisson system linearized about homogeneous (spatially independent) equilibria is treated in detail. For this example, structural (in)stability is established in an appropriate functional analytic setting, and two kinds of bifurcations are considered, one at infinite and one at finite wavenumber. After defining and describing the notion of dynamical accessibility, Kre\\u{i}n-like the...
Hamiltonian Structure of PI Hierarchy
Kanehisa Takasaki
2007-03-01
Full Text Available The string equation of type (2,2g+1 may be thought of as a higher order analogue of the first Painlevé equation that corresponds to the case of g = 1. For g > 1, this equation is accompanied with a finite set of commuting isomonodromic deformations, and they altogether form a hierarchy called the PI hierarchy. This hierarchy gives an isomonodromic analogue of the well known Mumford system. The Hamiltonian structure of the Lax equations can be formulated by the same Poisson structure as the Mumford system. A set of Darboux coordinates, which have been used for the Mumford system, can be introduced in this hierarchy as well. The equations of motion in these Darboux coordinates turn out to take a Hamiltonian form, but the Hamiltonians are different from the Hamiltonians of the Lax equations (except for the lowest one that corresponds to the string equation itself.
Alternative Hamiltonian representation for gravity
Rosas-RodrIguez, R [Instituto de Fisica, Universidad Autonoma de Puebla, Apdo. Postal J-48, 72570, Puebla, Pue. (Mexico)
2007-11-15
By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity.
Nonabelian N=2 Superstrings: Hamiltonian Structure
Isaev, A P
2009-01-01
We examine the Hamiltonian structure of nonabelian N=2 superstrings 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 choices of the background.
Hamiltonian analysis of interacting fluids
Banerjee, Rabin; Mitra, Arpan Krishna [S. N. Bose National Centre for Basic Sciences, Kolkata (India); Ghosh, Subir [Indian Statistical Institute, Kolkata (India)
2015-05-15
Ideal fluid dynamics is studied as a relativistic field theory with particular stress on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary roles of the canonical (Noether) stress tensor and the symmetric one obtained by metric variation are discussed. (orig.)
When are vector fields hamiltonian?
Crehan, P
1994-01-01
Dynamical systems can be quantised only if they are Hamiltonian. This prompts the question from which our talk gets its title. We show how the simple predator-prey equation and the damped harmonic oscillator can be considered to be Hamiltonian with respect to an infinite number of non-standard Poisson brackets. This raises some interesting questions about the nature of quantisation. Questions which are valid even for flows which possess a canonical structure.
Averett, Rodney D; Scogin, Tyler; Walker, Mitchell L R
2016-01-01
Blood clots occur in the human body when they are required to prevent bleeding. In pathological states such as diabetes and sickle cell disease, blood clots can also form undesirably due to hypercoagulable plasma conditions. With the continued effort in developing fibrin therapies for potential life-saving solutions, more mechanical modeling is needed to understand the properties of fibrin structures with inclusions. In this study, a fibrin matrix embedded with magnetic micro particles was subjected to a magnetic field to determine the plastic deformation of the clot. Using finite element analysis, we estimate the magnetic force from an electromagnet at a sample space located approximately 3 cm away from the coil center. This electromagnetic force along with gravity is applied on a fibrin sub model to calculate the stresses and displacements. Initial analyses show the forces are not sufficient to create fibrinolysis and hence we extended the study using parametric sweep analysis and redesign the coil paramete...
Yordanov, D., E-mail: yordanov@phys.uni-sofia.bg; Lishev, St.; Shivarova, A. [Faculty of Physics, Sofia University, BG-1164 Sofia (Bulgaria)
2016-02-15
Combining measurements of the extracted currents with probe and laser-photodetachment diagnostics, the study is an extension of recent tests of factors and gas-discharge conditions stimulating the extraction of volume produced negative ions. The experiment is in a single element of a rf source with the design of a matrix of small-radius inductively driven discharges. The results are for the electron and negative-ion densities, for the plasma potential and for the electronegativity in the vicinity of the plasma electrode as well as for the currents of the extracted negative ions and electrons. The plasma-electrode bias and the rf power have been varied. Necessity of a high bias to the plasma electrode and stable linear increase of the extracted currents with the rf power are the main conclusions.
Gupta, Rajan; Joseph, Anosh; Lin, Huey-Wen; Cohen, Saul D
2012-01-01
We motivate undertaking precision analyses of neutron decays to look for signatures of new scalar and tensor interactions that can arise in extensions of the Standard Model at the TeV scale. The key ingrediant needed to connect experimental data with theoretical analysis are high-precision calculations of matrix elements of isovector bilinear operators between the decaying neutron and final state proton. We describe the status of our Lattice QCD program of using valence clover fermions on dynamical N_f=2+1+1 HISQ configurations generated by the MILC Collaboration. On the theoretical side we use the effective field theory method and provide both model independent and dependent analyses to obtain bounds on possible scalar and tensor interactions, both from low energy experiments and LHC data.
Al Saleh, Salwa
2016-10-01
This paper completes a previous published work that calculated analytically the relativistic wavefunctions for bound electron in a Compton diffusion process. This work calculates the relativistic propagator and the Wronskian of the two associated Feynman diagrams of Compton diffusion (emission first and absorption first). Then find an explicit expression for the covariant matrix elements separated into two parts: spin-angular part and radial part. Using these explicit expressions, the effective cross-section for Compton diffusion in the most general form is obtained in terms of basic dynamical and static quantities, like electron's and photon's 4-momenta and atomic number. The form of the cross-section is put ready for numerical calculations.
The nuclear matrix elements of 0vββ decay and the NUMEN project at INFN-LNS
Cappuzzello, F.; Agodi, C.; Aciksoz, E.; Acosta, L.; Aslanouglou, X.; Auerbach, N.; Bijker, R.; Bonanno, D.; Bongiovanni, D.; Borello, T.; Boudhaim, S.; Bouhssa, M. L.; Boztosun, I.; Calabretta, L.; Calanna, A.; Carbone, D.; Cavallaro, M.; Calvo, D.; Chávez Lomelí, E. R.; Colonna, M.; D'Agostino, G.; Deshmukh, N.; de Faria, P. N.; Ferrero, A.; Foti, A.; Finocchiaro, P.; Gomes, P. R. S.; Greco, V.; Hacisalihoglu, A.; Housni, Z.; Khouaja, A.; Inchaou, J.; Lanzalone, G.; La Via, F.; Lay, J. A.; Lenske, H.; Linares, R.; Lubian, J.; Iazzi, F.; Introzzi, R.; Lavagno, A.; Lo Presti, D.; Medina, N.; Mendes, D. R.; Muoio, A.; Oliveira, J. R. B.; Pakou, A.; Pandola, L.; Rifuggiato, D.; Rodrigues, M. R. D.; Santagati, G.; Santopinto, E.; Scaltrito, L.; Sgouros, O.; Solakcı, S. O.; Soukeras, V.; Tudisco, S.; Vsevolodovna, R. I. M.; Zagatto, V.
2016-07-01
An innovative technique to access the nuclear matrix elements entering the expression of the life time of the double beta decay by relevant cross section measurements of double charge exchange reactions is proposed. A key aspect of the project is the use of the MAGNEX large acceptance magnetic spectrometer, for the detection of the ejectiles, and of the LNS K800 Superconducting Cyclotron (CS), for the acceleration of the required high resolution and low emittance heavy-ion beams, already in operation at INFN Laboratory Nazionali del Sud in Catania (Italy). However, a major upgrade is foreseen for the INFN-LNS research infrastructure to cope with beam currents as high as several ppA required by the project.
The O(\\alpha_s^3 T_F^2) Contributions to the Gluonic Operator Matrix Element
Ablinger, J; De Freitas, A; Hasselhuhn, A; von Manteuffel, A; Round, M; Schneider, C
2014-01-01
The $O(\\alpha_s^3 T_F^2 C_F (C_A))$ contributions to the transition matrix element $A_{gg,Q}$ relevant for the variable flavor number scheme at 3--loop order are calculated. The corresponding graphs contain two massive fermion lines of equal mass leading to terms given by inverse binomially weighted sums beyond the usual harmonic sums. In $x$-space two root-valued letters contribute in the iterated integrals in addition to those forming the harmonic polylogarithms. We outline technical details needed in the calculation of graphs of this type, which are as well of importance in the case of two different internal massive lines.
Abbiendi, G; Abramowicz, H; Acosta, D; Adamczyk, L; Adamus, M; Ahn, S H; Amelung, C; An Shiz Hong; Anselmo, F; Antonioli, P; Arneodo, M; Bacon, Trevor C; Badgett, W F; Bailey, D C; Bailey, D S; Bamberger, A; Barbagli, G; Bari, G; Barreiro, F; Barret, O; Bashindzhagian, G L; Bashkirov, V; Basile, M; Bauerdick, L A T; Bednarek, B; Behrens, U; Bellagamba, L; Bertolin, A; Bhadra, S; Bienlein, J K; Blaikley, H E; Bohnet, I; Bokel, C; Boogert, S; Bornheim, A; Borzemski, P; Boscherini, D; Botje, M; Breitweg, J; Brock, I; Brook, N H; Brugnera, R; Bruni, A; Bruni, G; Brümmer, N; Burgard, C; Burow, B D; Bussey, P J; Butterworth, J M; Bylsma, B; Caldwell, A; Capua, M; Cara Romeo, G; Carlin, R; Cartiglia, N; Cashmore, R J; Castellini, G; Catterall, C D; Chapin, D; Chekanov, S; Chwastowski, J; Ciborowski, J; Cifarelli, Luisa; Cindolo, F; Cirio, R; Cloth, P; Coboken, K; Coldewey, C; Cole, J E; Contin, A; Cooper-Sarkar, A M; Coppola, N; Cor, M; Cormack, C; Corriveau, F; Costa, M; Cottingham, W N; Crittenden, J; Cross, R; D'Agostini, G; Dagan, S; Dal Corso, F; Dardo, M; De Pasquale, S; De Wolf, E; Deffner, R; Del Peso, J; Deppe, O; Derrick, M; Deshpande, Abhay A; Desler, K; Devenish, R C E; Dhawan, S; Dolgoshein, B A; Dondana, S; Dosselli, U; Doyle, A T; Drews, G; Dulinski, Z; Durkin, L S; Dusini, S; Eckert, M; Edmonds, J K; Eisenberg, Y; Eisenhardt, S; Engelen, J; Epperson, D E; Ermolov, P F; Eskreys, Andrzej; Fagerstroem, C P; Fernández, J P; Ferrero, M I; Figiel, J; Filges, D; Foster, B; Foudas, C; Fox-Murphy, A; Fricke, U; Frisken, W R; Fusayasu, T; Gadaj, T; Galea, R; Gallo, E; García, G; Garfagnini, A; Gendner, N; Gialas, I; Gilmore, J; Ginsburg, C M; Giusti, P; Gladilin, L K; Glasman, C; Göbel, F; Golubkov, Yu A; Grabosch, H J; Graciani, R; Grosse-Knetter, J; Grzelak, G; Göttlicher, P; Haas, T; Hain, W; Hall-Wilton, R; Hamatsu, R; Hanna, D S; Harnew, N; Hart, H; Hart, J C; Hartmann, J; Hartner, G F; Hasell, D; Hayes, M E; Heaphy, E A; Heath, G P; Heath, H F; Hebbel, K; Heinloth, K; Heinz, L; Hernández, J M; Heusch, C A; Hilger, E; Hirose, T; Hochman, D; Holm, U; Homma, K; Hong, S J; Howell, G; Hughes, V W; Iacobucci, G; Iannotti, L; Iga, Y; Inuzuka, M; Ishii, T; Jakob, H P; Jelen, K; Jeoung, H Y; Jing, Z; Johnson, K F; Jones, T W; Kananov, S; Kappes, A; Karshon, U; Kasemann, M; Katz, U F; Kcira, D; Kerger, R; Khakzad, M; Khein, L A; Kim, C L; Kim, J Y; Kisielewska, D; Kitamura, S; Klanner, Robert; Klimek, K; Ko, I A; Koch, W; Koffeman, E; Kooijman, P; Koop, T; Korotkova, N A; Kotanski, A; Kowal, A M; Kowalski, H; Kowalski, T; Krakauer, D; Kreisel, A; Kuze, M; Kuzmin, V A; Kötz, U; Labarga, L; Lamberti, L; Lane, J B; Laurenti, G; Lee, J H; Lee, S B; Lee, S W; Levi, G; Levman, G M; Levy, A; Lim, H; Lim, I T; Limentani, S; Lindemann, L; Ling, T Y; Liu, W; Lohrmann, E; Long, K R; Lopez-Duran Viani, A; Lukina, O Yu; Löhr, B; Ma, K J; MacDonald, N; Maccarrone, G; Magill, S; Mallik, U; Margotti, A; Marini, G; Markun, P; Martin, J F; Martínez, M; Maselli, S; Massam, Thomas; Mastroberardino, A; Matsushita, T; Mattingly, M C K; Mattingly, S E K; McCance, G J; McCubbin, N A; McFall, J D; Mellado, B; Menary, S R; Meyer, A; Meyer-Larsen, A; Milewski, J; Milite, M; Miller, D B; Monaco, V; Monteiro, T; Morandin, M; Moritz, M; Murray, W N; Musgrave, B; Mönig, K; Nagano, K; Nam, S W; Nania, R; Nigro, A; Nishimura, T; Notz, D; Nowak, R J; Noyes, V A; Nylander, P; Ochs, A; Oh, B Y; Okrasinski, J R; Olkiewicz, K; Orr, R S; Pac, M Y; Padhi, S; Palmonari, F; Park, I H; Park, S K; Parsons, J A; Paul, E; Pavel, N; Pawlak, J M; Pawlak, R; Pelfer, Pier Giovanni; Pellegrino, A; Pelucchi, F; Peroni, C; Pesci, A; Petrucci, M C; Pfeiffer, M; Pic, D; Piotrzkowski, K; Poelz, G; Polenz, S; Polini, A; Posocco, M; Prinias, A; Proskuryakov, A S; Przybycien, M B; Puga, J; Quadt, A; Raach, H; Raso, M; Rautenberg, J; Re, J; Redondo, I; Reeder, D D; Ritz, S; Riveline, M; Rohde, M; Rulikowska-Zarebska, E; Ruske, O; Ruspa, M; Sabetfakhri, A; Sacchi, R; Sadrozinski, H F W; Saint-Laurent, M; Salehi, H; Samp, S; Sartorelli, G; Saull, P R B; Savin, A A; Saxon, D H; Schechter, A; Schioppa, M; Schlenstedt, S; Schmidke, W B; Schneekloth, U; Schnurbusch, H; Schwarzer, O; Sciulli, F; Scott, J; Sedgbeer, J K; Seiden, A; Selonke, F; Shah, T P; Shcheglova, L M; Sideris, D; Sievers, M; Simmons, D; Sinclair, L E; Skillicorn, I O; Smalska, B; Smith, W H; Solano, A; Solomin, A N; Son, D; Staiano, A; Stairs, D G; Stanco, L; Stanek, R; Stifutkin, A; Stonjek, S; Straub, P B; Strickland, E; Stroili, R; Susinno, G; Suszycki, L; Sutton, M R; Suzuki, I; Tandler, J; Tapper, A D; Tapper, R J; Tassi, E; Terron, J; Tiecke, H G; Tokushuku, K; Toothacker, W S; Tsurugai, T; Tuning, N; Tymieniecka, T; Umemori, K; Vaiciulis, A W; Van Sighem, A; Velthuis, J J; Verkerke, W; Voci, C; Vossebeld, Joost Herman; Votano, L; Walczak, R; Walker, R; Wang, S M; Waters, D S; Waugh, R; Weber, A; Whitmore, J J; Wichmann, R; Wick, K; Wieber, H; Wiggers, L; Wildschek, T; Williams, D C; Wing, M; Wodarczyk, M; Wolf, G; Wollmer, U; Wróblewski, A K; Wölfle, S; Yamada, S; Yamashita, T; Yamauchi, K; Yamazaki, Y; Yoshida, R; Youngman, C; Zajac, J; Zakrzewski, J A; Zamora Garcia, Y; Zawiejski, L; Zetsche, F; Zeuner, W; Zhu, Q; Zichichi, A; Zotkin, S A
2000-01-01
Exclusive electroproduction of rho^0 mesons has been measured using the ZEUS detector at HERA in two Q^2 ranges, 0.25matrix elements which completely define the angular distributions are presented and discussed.
Interchange graphs and the Hamiltonian cycle polytope
Sierksma, G
1998-01-01
This paper answers the (non)adjacency question for the whole spectrum of Hamiltonian cycles on the Hamiltonian cycle polytope (HC-polytope), also called the symmetric traveling salesman polytope, namely from Hamiltonian cycles that differ in only two edges through Hamiltonian cycles that are edge di
Hamiltonian description of the ideal fluid
Morrison, P.J.
1994-01-01
Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems.
Regueiro, R. A.; Yu, S.
2010-12-01
The paper models grain-scale micro-cracking in shale at grain-matrix interfaces, assuming constituents are composed of quart silt grains and compacted clay matrix for a typical shale. The influence of grain-matrix-grain interaction on micro-crack patterns is investigated. Elasto-plastic pressure-sensitive cohesive-surface models are inserted at grain-matrix interfaces and intra-clay-matrix finite element facets, while a bulk elasto-plasticity model with bifurcation is employed for the clay matrix to compare to the intra-clay-matrix cohesive-surface model. Numerical examples are presented under two-dimensional plane strain condition at small strains. A procedure is proposed to upscale grain-scale micro-cracking to predict macro-fracture nucleation and propagation in shale and other bound particulate materials. It is shown that using cohesive surface elements (CSEs) at all finite element facets in the clay matrix mesh to simulate micro-cracking in the clay matrix leads to mesh-dependent results. Using CSEs at grain-clay-matrix interfaces is physical and not mesh dependent. We also considered using bulk pressure-sensitive elasto-plasticity with bifurcation condition within the clay matrix to attempt to predict onset of localization around grains in the simulations. It was encouraging to see that for both the single grain and multiple grain simulations, the finite element region in the clay matrix meshes where bifurcation was first detected around the grains was nearly the same. This gives us confidence that once a proper post-bifurcation constitutive model is implemented within an embedded discontinuity formulation, micro-cracking nucleation and propagation at the grain-scale in shale can be properly simulated, which will provide the basis for up-scaling to macro-cracks within a multiscale method for fracture in shale. Other items to address in future research are: (i) include transverse isotropy (elastic and plastic) for the bulk clay matrix elasto-plasticity model
Holas, A.; Cinal, M.
2005-09-01
Three approximate exchange potentials of high accuracy vxY(r) , Y=A ,B,C, for the density-functional theory applications are obtained by replacing the matrix elements of the exact potential between the Kohn-Sham (KS) orbitals with such elements of the Fock exchange operator (within the virtual-occupied subset only) in three representations found for any local potential. A common identity is the base of these representations. The potential vxC happens to be the same as that derived by Harbola and Sahni, and vxA as that derived by Gritsenko and Baerends, and Della Sala and Görling. The potentials obtained can be expressed in terms of occupied KS orbitals only. At large r , their asymptotic form -1/r is the same as that of the exact potential. The high quality of these three approximations is demonstrated by direct comparison with the exact potential and using various consistency tests. A common root established for the three approximations could be helpful in finding new and better approximations via modification of identities employed in the present investigation.
Kwiatkowski, A A; Holt, J D; Chaudhuri, A; Chowdhury, U; Eibach, M; Engel, J; Gallant, A T; Grossheim, A; Horoi, M; Lennarz, A; Macdonald, T D; Pearson, M R; Schultz, B E; Simon, M C; Senkov, R A; Simon, V V; Zuber, K; Dilling, J
2013-01-01
We report a direct measurement of the Q-value of the neutrinoless double-beta-decay candidate 48Ca at the TITAN Penning-trap mass spectrometer, with the result that Q = 4267.98(32) keV. We measured the masses of both the mother and daughter nuclides, and in the latter case found a 1 keV deviation from the literature value. In addition to the Q-value, we also present results of a new calculation of the neutrinoless double-beta-decay nuclear matrix element of 48Ca. Using diagrammatic many-body perturbation theory to second order to account for physics outside the valence space, we constructed an effective shell-model double-beta-decay operator, which increased the nuclear matrix element by about 75% compared with that produced by the bare operator. The new Q-value and matrix element strengthen the case for a 48Ca double-beta-decay experiment.
Abdul-Aziz, Ali; Baaklini, George Y.; Bhatt, Ramakrishna T.
2003-01-01
Most reverse engineering approaches involve imaging or digitizing an object and then creating a computerized reconstruction that can be integrated, in three dimensions, into a particular design environment. The rapid prototyping technique builds high-quality physical prototypes directly from computer-aided design files. This fundamental technique for interpreting and interacting with large data sets is being used here via Velocity2 (an integrated image-processing software, ref. 1) using computed tomography (CT) data to produce a prototype three-dimensional test specimen model for analyses. A study at the NASA Glenn Research Center proposes to use these capabilities to conduct a combined nondestructive evaluation (NDE) and finite element analysis (FEA) to screen pretest and posttest structural anomalies in structural components. A tensile specimen made of silicon nitrite (Si3N4) ceramic matrix composite was considered to evaluate structural durability and deformity. Ceramic matrix composites are being sought as candidate materials to replace nickel-base superalloys for turbine engine applications. They have the unique characteristics of being able to withstand higher operating temperatures and harsh combustion environments. In addition, their low densities relative to metals help reduce component mass (ref. 2). Detailed three-dimensional volume rendering of the tensile test specimen was successfully carried out with Velocity2 (ref. 1) using two-dimensional images that were generated via computed tomography. Subsequent, three-dimensional finite element analyses were performed, and the results obtained were compared with those predicted by NDE-based calculations and experimental tests. It was shown that Velocity2 software can be used to render a three-dimensional object from a series of CT scan images with a minimum level of complexity. The analytical results (ref. 3) show that the high-stress regions correlated well with the damage sites identified by the CT scans
Gu, Zhiping
This paper extends Riccati transfer matrix method to the transient and stability analysis of large scale rotor-bearing systems with strong nonlinear elements, and proposes a mode summation-transfer matrix method, in which the field transfer matrix of a distributed mass uniform shaft segment is obtained with the aid of the idea of mode summation and Newmark beta formulation, and the Riccati transfer matrix method is adopted to stablize the boundary value problem of the nonlinear systems. In this investigation, the real nonlinearity of the strong nonlinear elements is considered, not linearized, and the advantages of the Riccati transfer matrix are retained. So, this method is especially applicable to analyze the transient response and stability of large-scale rotor-bear systems with strong nonlinear elements. One example, a single-spool rotating system with strong nonlinear elements, is given. The obtained results show that this method is superior to that of Gu and Chen (1990) in accuracy, stability, and economy.
Krebs, Derek; Budynas, Richard G.
A common procedure for performing a cross orthogonality check for the purpose of modal correlation between the test and the finite element analysis results incorporates the Guyan reduction method to obtain a reduced mass matrix. This paper describes a procedure which uses NASTRAN's Generalized Dynamic Reduction solution routine which is much more accurate than the standard Guyan reduction solution and which offers the advantage of not requiring the selection of mdof. Using NASTRAN's DMAP programming methods, a modal reduction of the full analytical mass matrix is performed based on the accelerometer locations and the analytical modal matrix results. The accuracy of the procedure is illustrated in two case studies.
Effective Hamiltonian of strained graphene.
Linnik, T L
2012-05-23
Based on the symmetry properties of the graphene lattice, we derive the effective Hamiltonian of graphene under spatially nonuniform acoustic and optical strains. Comparison with the published results of the first-principles calculations allows us to determine the values of some Hamiltonian parameters, and suggests the validity of the derived Hamiltonian for acoustical strain up to 10%. The results are generalized for the case of graphene with broken plane reflection symmetry, which corresponds, for example, to the case of graphene placed on a substrate. Here, essential modifications to the Hamiltonian give rise, in particular, to the gap opening in the spectrum in the presence of the out-of-plane component of optical strain, which is shown to be due to the lifting of the sublattice symmetry. The developed effective Hamiltonian can be used as a convenient tool for analysis of a variety of strain-related effects, including electron-phonon interaction or pseudo-magnetic fields induced by the nonuniform strain.
Eliav, Ephraim; Vilkas, Marius J; Ishikawa, Yasuyuki; Kaldor, Uzi
2005-06-08
The intermediate Hamiltonian (IH) coupled-cluster method makes possible the use of very large model spaces in coupled-cluster calculations without running into intruder states. This is achieved at the cost of approximating some of the IH matrix elements, which are not taken at their rigorous effective Hamiltonian (EH) value. The extrapolated intermediate Hamiltonian (XIH) approach proposed here uses a parametrized IH and extrapolates it to the full EH, with model spaces larger by several orders of magnitude than those possible in EH coupled-cluster methods. The flexibility and resistance to intruders of the IH approach are thus combined with the accuracy of full EH. Various extrapolation schemes are described. A pilot application to the electron affinities (EAs) of alkali atoms is presented, where converged EH results are obtained by XIH for model spaces of approximately 20,000 determinants; direct EH calculations converge only for a one-dimensional model space. Including quantum electrodynamic effects, the average XIH error for the EAs is 0.6 meV and the largest error is 1.6 meV. A new reference estimate for the EA of Fr is proposed at 486+/-2 meV.
Hamiltonian Dynamics of Preferential Attachment
Zuev, Konstantin; Krioukov, Dmitri
2015-01-01
Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment, known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evolution of a dynamical system is described by Hamilton's equations. We derive the explicit form of the Hamiltonian that governs network growth in preferential attachment. This Hamiltonian turns out to be nearly identical to graph energy in the configuration model, which shows that the ensemble of random graphs generated by preferential attachment is nearly identical to the ensemble of random graphs with scale-free degree d...
First principles of Hamiltonian medicine.
Crespi, Bernard; Foster, Kevin; Úbeda, Francisco
2014-05-19
We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease.
Unified Hamiltonian for conducting polymers
Leitão Botelho, André; Shin, Yongwoo; Li, Minghai; Jiang, Lili; Lin, Xi
2011-11-01
Two transferable physical parameters are incorporated into the Su-Schrieffer-Heeger Hamiltonian to model conducting polymers beyond polyacetylene: the parameter γ scales the electron-phonon coupling strength in aromatic rings and the other parameter ɛ specifies the heterogeneous core charges. This generic Hamiltonian predicts the fundamental band gaps of polythiophene, polypyrrole, polyfuran, poly-(p-phenylene), poly-(p-phenylene vinylene), and polyacenes, and their oligomers of all lengths, with an accuracy exceeding time-dependent density functional theory. Its computational costs for moderate-length polymer chains are more than eight orders of magnitude lower than first-principles approaches.
Hamiltonian systems as selfdual equations
2008-01-01
Hamiltonian systems with various time boundary conditions are formulated as absolute minima of newly devised non-negative action func-tionals obtained by a generalization of Bogomolnyi's trick of 'completing squares'. Reminiscent of the selfdual Yang-Mills equations, they are not derived from the fact that they are critical points (i.e., from the correspond- ing Euler-Lagrange equations) but from being zeroes of the corresponding non-negative Lagrangians. A general method for resolving such variational problems is also described and applied to the construction of periodic solutions for Hamiltonian systems, but also to study certain Lagrangian intersections.
A systematic construction of completely integrable Hamiltonians from coalgebras
Ballesteros, A; Ballesteros, Angel; Ragnisco, Orlando
1998-01-01
A universal algorithm to construct N-particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum deformations can be interpreted as generating structures for integrable deformations of Hamiltonian systems with coalgebra symmetry. In order to illustrate this general method, the $so(2,1)$ algebra and the oscillator algebra $h_4$ are used to derive new classical integrable systems including a generalization of Gaudin-Calogero systems and oscillator chains. Quantum deformations are then used to obtain some explicit integrable deformations of the previous long-range interacting systems and a (non-coboundary) deformation of the $(1+1)$ Poincaré algebra is shown to provide a new Ruijsenaars-Schneider-like Hamiltonian.
Raychev, P P; Lo-Iudice, N; Roussev, R P; Terziev, P A
1997-01-01
A simplified boson realization of the $so_q(3)$ subalgebra of $u_q(3)$ is constructed. A simplified form of the corresponding $so_q(3)$ basis states is obtained. The reduced matrix elements of a special second-rank tensor operator (quadrupole operator) are calculated in the $so_q(3)$ basis.
Noaki, J I; Aoki, Y; Burkhalter, R; Ejiri, S; Fukugita, M; Hashimoto, S; Ishizuka, N; Iwasaki, Y; Izubuchi, T; Kanaya, K; Kaneko, T; Kuramashi, Y; Lesk, V I; Nagai, K I; Okawa, M; Taniguchi, Y; Ukawa, A; Yoshié, T
2001-01-01
We explore application of the domain wall fermion formalism of lattice QCD to calculate the $K\\to\\pi\\pi$ decay amplitudes in terms of the $K\\to\\pi$ and $K\\to 0$ hadronic matrix elements through relations derived in chiral perturbation theory. Numerical simulations are carried out in quenched QCD using domain-wall fermion action for quarks and an RG-improved gauge action for gluons on a $16^3\\times 32\\times 16$ and $24^3\\times 32\\times 16$ lattice at $\\beta=2.6$ corresponding to the lattice spacing $1/a\\approx 2$GeV. Quark loop contractions which appear in Penguin diagrams are calculated by the random noise method, and the $\\Delta I=1/2$ matrix elements which require subtractions with the quark loop contractions are obtained with a statistical accuracy of about 10%. We confirm the chiral properties required of the $K\\to\\pi$ matrix elements. Matching the lattice matrix elements to those in the continuum at $\\mu=1/a$ using the perturbative renormalization factor to one loop order, and running to the scale $\\mu=m...
Chackerian, C., Jr.
1976-01-01
The electric dipole moment function of the ground electronic state of carbon monoxide has been determined by combining numerical solutions of the radial Schrodinger equation with absolute intensity data of vibration-rotation bands. The derived dipole moment function is used to calculate matrix elements of interest to stellar astronomy and of importance in the carbon monoxide laser.
Determination of the Form Factors for the Decay B0 --> D*-l+nu_l and of the CKM Matrix Element |Vcb|
Aubert, B; Bóna, M; Boutigny, D; Couderc, F; Karyotakis, Yu; Lees, J P; Poireau, V; Tisserand, V; Zghiche, A; Graugès-Pous, E; Palano, A; Chen, J C; Qi, N D; Rong, G; Wang, P; Zhu, Y S; Eigen, G; Ofte, I; Stugu, B; Abrams, G S; Battaglia, M; Brown, D N; Button-Shafer, J; Cahn, R N; Charles, E; Gill, M S; Groysman, Y; Jacobsen, R G; Kadyk, J A; Kerth, L T; Kolomensky, Y G; Kukartsev, G; Lynch, G; Mir, L M; Orimoto, T J; Pripstein, M; Roe, N A; Ronan, M T; Wenzel, W A; Del Amo-Sánchez, P; Barrett, M; Ford, K E; Hart, A J; Harrison, T J; Hawkes, C M; Morgan, S E; Watson, A T; Held, T; Koch, H; Lewandowski, B; Pelizaeus, M; Peters, K; Schröder, T; Steinke, M; Boyd, J T; Burke, J P; Cottingham, W N; Walker, D; Asgeirsson, D J; Çuhadar-Dönszelmann, T; Fulsom, B G; Hearty, C; Knecht, N S; Mattison, T S; McKenna, J A; Khan, A; Kyberd, P; Saleem, M; Sherwood, D J; Teodorescu, L; Blinov, V E; Bukin, A D; Druzhinin, V P; Golubev, V B; Onuchin, A P; Serednyakov, S I; Skovpen, Yu I; Solodov, E P; Todyshev, K Y; Best, D S; Bondioli, M; Bruinsma, M; Chao, M; Curry, S; Eschrich, I; Kirkby, D; Lankford, A J; Lund, P; Mandelkern, M A; Mommsen, R K; Röthel, W; Stoker, D P; Abachi, S; Buchanan, C; Foulkes, S D; Gary, J W; Long, O; Shen, B C; Wang, K; Zhang, L; Hadavand, H K; Hill, E J; Paar, H P; Rahatlou, S; Sharma, V; Berryhill, J W; Campagnari, C; Cunha, A; Dahmes, B; Hong, T M; Kovalskyi, D; Richman, J D; Beck, T W; Eisner, A M; Flacco, C J; Heusch, C A; Kroseberg, J; Lockman, W S; Nesom, G; Schalk, T; Schumm, B A; Seiden, A; Spradlin, P; Williams, D C; Wilson, M G; Albert, J; Chen, E; Dvoretskii, A; Fang, F; Hitlin, D G; Narsky, I; Piatenko, T; Porter, F C; Ryd, A; Samuel, A; Mancinelli, G; Meadows, B T; Mishra, K; Sokoloff, M D; Blanc, F; Bloom, P C; Chen, S; Ford, W T; Hirschauer, J F; Kreisel, A; Nagel, M; Nauenberg, U; Olivas, A; Ruddick, W O; Smith, J G; Ulmer, K A; Wagner, S R; Zhang, J; Chen, A; Eckhart, E A; Soffer, A; Toki, W H; Wilson, R J; Winklmeier, F; Zeng, Q; Altenburg, D D; Feltresi, E; Hauke, A; Jasper, H; Merkel, J; Petzold, A; Spaan, B; Brandt, T; Klose, V; Lacker, H M; Mader, W F; Nogowski, R; Schubert, J; Schubert, K R; Schwierz, R; Sundermann, J E; Volk, A; Bernard, D; Bonneaud, G R; Latour, E; Thiebaux, C; Verderi, M; Clark, P J; Gradl, W; Muheim, F; Playfer, S; Robertson, A I; Xie, Y; Andreotti, M; Bettoni, D; Bozzi, C; Calabrese, R; Cibinetto, G; Luppi, E; Negrini, M; Petrella, A; Piemontese, L; Prencipe, E; Anulli, F; Baldini-Ferroli, R; Calcaterra, A; De Sangro, R; Finocchiaro, G; Pacetti, S; Patteri, P; Peruzzi, I M; Piccolo, M; Rama, M; Zallo, A; Buzzo, A; Capra, R; Contri, R; Lo Vetere, M; Macri, M M; Monge, M R; Passaggio, S; Patrignani, C; Robutti, E; Santroni, A; Tosi, S; Brandenburg, G; Chaisanguanthum, K S; Morii, M; Wu, J; Dubitzky, R S; Marks, J; Schenk, S; Uwer, U; Bard, D J; Bhimji, W; Bowerman, D A; Dauncey, P D; Egede, U; Flack, R L; Nash, J A; Nikolich, M B; Panduro-Vazquez, W; Behera, P K; Chai, X; Charles, M J; Mallik, U; Meyer, N T; Ziegler, V; Cochran, J; Crawley, H B; Dong, L; Eyges, V; Meyer, W T; Prell, S; Rosenberg, E I; Rubin, A E; Gritsan, A V; Denig, A G; Fritsch, M; Schott, G; Arnaud, N; Davier, M; Grosdidier, G; Höcker, A; Le Diberder, F R; Lepeltier, V; Lutz, A M; Oyanguren, A; Pruvot, S; Rodier, S; Roudeau, P; Schune, M H; Stocchi, A; Wang, W F; Wormser, G; Cheng, C H; Lange, D J; Wright, D M; Chavez, C A; Forster, I J; Fry, J R; Gabathuler, E; Gamet, R; George, K A; Hutchcroft, D E; Payne, D J; Schofield, K C; Touramanis, C; Bevan, A J; Di Lodovico, F; Menges, W; Sacco, R; Cowan, G; Flächer, H U; Hopkins, D A; Jackson, P S; McMahon, T R; Ricciardi, S; Salvatore, F; Wren, A C; Davis, C L; Allison, J; Barlow, N R; Barlow, R J; Chia, Y M; Edgar, C L; Lafferty, G D; Naisbit, M T; Williams, J C; Yi, J I; Chen, C; Hulsbergen, W D; Jawahery, A; Lae, C K; Roberts, D A; Simi, G; Blaylock, G; Dallapiccola, C; Hertzbach, S S; Li, X; Moore, T B; Saremi, S; Stängle, H; Cowan, R; Sciolla, G; Sekula, S J; Spitznagel, M; Taylor, F; Yamamoto, R K; Kim, H; Mclachlin, S E; Patel, P M; Robertson, S H; Lazzaro, A; Lombardo, V; Palombo, F; Bauer, J M; Cremaldi, L; Eschenburg, V; Godang, R; Kroeger, R; Sanders, D A; Summers, D J; Zhao, H W; Brunet, S; Côte, D; Simard, M; Taras, P; Viaud, F B; Nicholson, H; Cavallo, N; De Nardo, Gallieno; Fabozzi, F; Gatto, C; Lista, L; Monorchio, D; Paolucci, P; Piccolo, D; Sciacca, C; Baak, M A; Raven, G; Snoek, H L; Jessop, C P; LoSecco, J M; Allmendinger, T; Benelli, G; Corwin, L A; Gan, K K; Honscheid, K; Hufnagel, D; Jackson, P D; Kagan, H; Kass, R; Rahimi, A M; Regensburger, J J; Ter-Antonian, R; Wong, Q K; Blount, N L; Brau, J E; Frey, R; Igonkina, O; Kolb, J A; Lu, M; Rahmat, R; Sinev, N B; Strom, D; Strube, J; Torrence, E; Gaz, A; Margoni, M; Morandin, M; Pompili, A; Posocco, M; Rotondo, M; Simonetto, F; Stroili, R; Voci, C; Benayoun, M; Briand, H; Chauveau, J; David, P; Del Buono, L; La Vaissière, C de; Hamon, O; Hartfiel, B L; John, M J J; Leruste, P; Malcles, J; Ocariz, J; Roos, L; Therin, G; Gladney, L; Panetta, J; Biasini, M; Covarelli, R; Angelini, C; Batignani, G; Bettarini, S; Bucci, F; Calderini, G; Carpinelli, M; Cenci, R; Forti, F; Giorgi, M A; Lusiani, A; Marchiori, G; Mazur, M A; Morganti, M; Neri, N; Paoloni, E; Rizzo, G; Walsh, J J; Haire, M; Judd, D; Wagoner, D E; Biesiada, J; Danielson, N; Elmer, P; Lau, Y P; Lü, C; Olsen, J; Smith, A J S; Telnov, A V; Bellini, F; Cavoto, G; D'Orazio, A; Del Re, D; Di Marco, E; Faccini, R; Ferrarotto, F; Ferroni, F; Gaspero, M; Li Gioi, L; Mazzoni, M A; Morganti, S; Piredda, G; Polci, F; Safai-Tehrani, F; Voena, C; Ebert, M; Schröder, H; Waldi, R; Adye, T; De Groot, N; Franek, B; Olaiya, E O; Wilson, F F; Aleksan, R; Emery, S; Gaidot, A; Ganzhur, S F; Hamel de Monchenault, G; Kozanecki, Witold; Legendre, M; Vasseur, G; Yéche, C; Zito, M; Chen, X R; Liu, H; Park, W; Purohit, M V; Wilson, J R; Allen, M T; Aston, D; Bartoldus, R; Bechtle, P; Berger, N; Claus, R; Coleman, J P; Convery, M R; Cristinziani, M; Dingfelder, J C; Dorfan, J; Dubois-Felsmann, G P; Dujmic, D; Dunwoodie, W M; Field, R C; Glanzman, T; Gowdy, S J; Graham, M T; Grenier, P; Halyo, V; Hast, C; Hrynóva, T; Innes, W R; Kelsey, M H; Kim, P; Leith, D W G S; Li, S; Luitz, S; Lüth, V; Lynch, H L; MacFarlane, D B; Marsiske, H; Messner, R; Müller, D R; O'Grady, C P; Ozcan, V E; Perazzo, A; Perl, M; Pulliam, T; Ratcliff, B N; Roodman, A; Salnikov, A A; Schindler, R H; Schwiening, J; Snyder, A; Stelzer, J; Su, D; Sullivan, M K; Suzuki, K; Swain, S K; Thompson, J M; Vavra, J; Van Bakel, N; Weaver, M; Weinstein, A J R; Wisniewski, W J; Wittgen, M; Wright, D H; Yarritu, A K; Yi, K; Young, C C; Burchat, P R; Edwards, A J; Majewski, S A; Petersen, B A; Roat, C; Wilden, L; Ahmed, S; Alam, M S; Bula, R; Ernst, J A; Jain, V; Pan, B; Saeed, M A; Wappler, F R; Zain, S B; Bugg, W; Krishnamurthy, M; Spanier, S M; Eckmann, R; Ritchie, J L; Satpathy, A; Schilling, C J; Schwitters, R F; Izen, J M; Lou, X C; Ye, S; Bianchi, F; Gallo, F; Gamba, D; Bomben, M; Bosisio, L; Cartaro, C; Cossutti, F; Della Ricca, G; Dittongo, S; Lanceri, L; Vitale, L; Azzolini, V; Lopez-March, N; Martínez-Vidal, F; Banerjee, S; Bhuyan, B; Brown, C M; Fortin, D; Hamano, K; Kowalewski, R V; Nugent, I M; Roney, J M; Sobie, R J; Back, J J; Harrison, P F; Latham, T E; Mohanty, G B; Pappagallo, M; Band, H R; Chen, X; Cheng, B; Dasu, S; Datta, M; Flood, K T; Hollar, J J; Kutter, P E; Mellado, B; Mihályi, A; Pan, Y; Pierini, M; Prepost, R; Wu, S L; Yu, Z; Neal, H
2006-01-01
We present a combined measurement of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ and of the parameters $\\rho^2$, $R_1$, and $R_2$, which fully characterize the form factors of the $B^0 \\to D^{*-}\\ell^{+}\
Vladimirov, Igor G
2012-01-01
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations with non-quadratic Hamiltonians. The linearization proceeds by approximating the actual Hamiltonian of the quantum system by a quadratic function of its observables which corresponds to the Hamiltonian of a quantum harmonic oscillator. This approximation is carried out in a mean square optimal sense with respect to a Gaussian reference quantum state and leads to a self-consistent linearization procedure where the mean vector and quantum covariance matrix of the system observables evolve in time according to the effective linear dynamics. We demonstrate the proposed Hamiltonian-based Gaussian linearization for the quantum Duffing oscillator whose Hamiltonian is a quadro-quartic polynomial of the momentum and position operators. The results of the paper are applicable t...
Maxwell consideration of polaritonic quasi-particle Hamiltonians in multi-level systems
Richter, Steffen; Michalsky, Tom; Fricke, Lennart; Sturm, Chris; Franke, Helena; Grundmann, Marius; Schmidt-Grund, Rüdiger [Institut für Experimentelle Physik II, Universität Leipzig, Linnéstr. 5, 04103 Leipzig (Germany)
2015-12-07
We address the problem of the correct description of light-matter coupling for excitons and cavity photons in the case of systems with multiple photon modes or excitons, respectively. In the literature, two different approaches for the phenomenological coupling Hamiltonian can be found: Either one single Hamiltonian with a basis whose dimension equals the sum of photonic modes and excitonic resonances is used. Or a set of independent Hamiltonians, one for each photon mode, is chosen. Both are usually used equivalently for the same kind of multi-photonic systems which cannot be correct. However, identifying the suitable Hamiltonian is difficult when modeling experimental data. By means of numerical transfer matrix calculations, we demonstrate the scope of application of each approach: The first one holds only for the coupling of a single photon state to several excitons, while in the case of multiple photon modes, separate Hamiltonians must be used for each photon mode.
Search for rare processes with a Z+bb signature at the LHC, with the matrix element method
Beluffi, Camille; Lemaitre, Vincent
This thesis presents a detailed study of the final state with the Z boson decaying into two leptons, produced in the CMS detector at the LHC. In order to tag this topology, sophisticated b jet tagging algorithms have been used, and the calibration of one of them, the Jet Probability (JP) tagger is exposed. A study of the tagger degradation at high energy has been done and led to a small gain of performance. This investigation is followed by the search for the associated production of the standard model (SM) Higgs boson with a Z boson and decaying into two b quarks (ZH channel), using the Matrix Element Method (MEM) and two b-taggers: JP and Combined Secondary Vertex (CSV). The MEM is an advanced tool that produces an event-by-event discriminating variable, called weight. To apply it, several sets of transfer function have been produced. The final results give an observed limit on the ZH production cross section with the H → bb branching ratio of 5.46xσSM when using the CSV tagger and 4.89xσSM when using t...
Kaon matrix elements and CP violation from lattice QCD with 2+1 flavors of domain wall fermions
Li, Shu
Low energy constants describing the weak, two-pion decays of K mesons in chiral perturbation theory are computed using 2+1 flavors of domain wall fermions in a finite volume with spatial extent 2.74 fm and for a single inverse lattice spacing 1/a = 1.73 GeV. Partially quenched perturbation theory is used in both leading and next-to-leading order. The non-perturbative regularization independent RI/MOM renormalization scheme is employed to determine these low energy constants in the continuum, RI normalization scheme with 20% statistical errors but systematic errors which are estimated to lie between 50 and 100% depending on the operator. These low energy constants are then used to estimate the DeltaI = 1/2 and DeltaI = 3/2 K → pipi decay matrix elements and epsilon'/epsilon. The poor convergence of chiral perturbation theory for quark masses as large as that of the strange quark severely limits the accuracy of these results.
Della Morte, Michele
2011-01-01
We make use of the global symmetries of the Yang-Mills theory on the lattice to design a new computational strategy for extracting glueball masses and matrix elements which achieves an exponential reduction of the statistical error with respect to standard techniques. By generalizing our previous work on the parity symmetry, the partition function of the theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated to parity, charge conjugation, translations, rotations and central conjugations Z_N^3. Ratios of path integrals and correlation functions can then be computed with a multi-level Monte Carlo integration scheme whose numerical cost, at a fixed statistical precision and at asymptotically large times, increases power-like with the time extent of the lattice. The strategy is implemented for the SU(3) Yang--Mills theory, and a full-fledged computation of the mass and multiplicity of the lightest glueball with vacuum quantum ...
Della Morte, Michele; Giusti, Leonardo
2011-05-01
We make use of the global symmetries of the Yang-Mills theory on the lattice to design a new computational strategy for extracting glueball masses and matrix elements which achieves an exponential reduction of the statistical error with respect to standard techniques. By generalizing our previous work on the parity symmetry, the partition function of the theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated to parity, charge conjugation, translations, rotations and central conjugations Z N 3. Ratios of path integrals and correlation functions can then be computed with a multi-level Monte Carlo integration scheme whose numerical cost, at a fixed statistical precision and at asymptotically large times, increases power-like with the time extent of the lattice. The strategy is implemented for the SU(3) Yang-Mills theory, and a full-fledged computation of the mass and multiplicity of the lightest glueball with vacuum quantum numbers is carried out at a lattice spacing of 0.17 fm.
LIU,Ji-Feng(刘继凤); ZHU,Quan(朱权); LI,Xiang-Yuan(李象远); YANG,Sheng-Yong(杨胜勇)
2002-01-01
As a successive work of our previous paper, 1 the electron transfer matrix element ( Vrp) in the oxidation of the simplified model molecule of α-amino carbon-centered radical by O2 has been investigated with ab initio calculation at the level of UHF/6-31 + + G * * . Based on the optimized geometries of the reactant and the ion-pair complex obtained previously, the reaction heat and the inner reorganization energy have been obrained by constructing the potential energy curves of reactant and product states considering the solvent effect with the conductor-like screening model (COSMO). The solvent reorganization energy has been estimated using Lippert-Mataga relationship. The calculated results show that the value of Vrp is several times larger than that of RT, which means that the model reaction is an adiabatic one. Theoretical investigation indicates that the solvent effect on the direct electron transfer (ET) process of oxidation of α-amino carbon-centered radical by oxygen is remarkable.
胡圣虹; 胡兆初; 刘勇胜; 林守麟; 高山
2003-01-01
A simple method for the determination of Sc, Y and Ln in carbonate at sub-μg*g-1 levels by ICP-MS with inter-elements matrix-matched technique was developed. A series of matrix-matched standard solution were prepared by adopting the normalized concentration values, which were calculated the statistic average compositions of reference values of REEs in carbonate standard reference materials. The matrix effects of Ca and Mg on REEs were studied in detail and the results show that the matrix effect of Ca and Mg can be ignored when the dilution factors are more than 1000. The combination of 115In and 103Rh as internal standard was selected to compensate the drift of analytical signals. The method proposed was applied to the analysis of ultra-trace REEs in carbonate references materials GSR-6, GSR-12 and real samples.
Efficient variational diagonalization of fully many-body localized Hamiltonians
Pollmann, Frank; Khemani, Vedika; Cirac, J. Ignacio; Sondhi, S. L.
2016-07-01
We introduce a variational unitary matrix product operator based variational method that approximately finds all the eigenstates of fully many-body localized one-dimensional Hamiltonians. The computational cost of the variational optimization scales linearly with system size for a fixed depth of the UTN ansatz. We demonstrate the usefulness of our approach by considering the Heisenberg chain in a strongly disordered magnetic field for which we compare the approximation to exact diagonalization results.
New Interval Oscillation Criteria for Certain Linear Hamiltonian Systems
Jing Shao
2013-01-01
Full Text Available Using a generalized Riccati transformation and the general integral means technique, some new interval oscillation criteria for the linear matrix Hamiltonian system U'=(A(t-λ(tIU+B(tV, V'=C(tU+(μ(tI-A*(tV, t≥t0 are obtained. These results generalize and improve the oscillation criteria due to Zheng (2008. An example is given to dwell upon the importance of our results.
Parry, A. O.; Boulter, C. J.
1995-02-01
We study the pair correlation function for an inhomogeneous fluid or Ising-type spin system near a wall with particular attention to the complete wetting phase transition. We show that one can unify a generalized interfacial Hamiltonian theory with a mean-field treatment of correlations provided we follow a systematic scheme for reconstructing order-parameter fluctuations. Near a complete wetting transition it is necessary to use a model effective Hamiltonian HI(2) [ l1, l2] which is a functional of two collective coordinates in order to properly describe the coupling between fluctuations near the wall and the depinning fluid (αβ) interface. This gives an accurate description of the Ornstein-Zernike-like fluctuations of particles located near the αβ interface and the non-Ornstein-Zernike behavior of correlations near the wall. We show that the off-diagonal elements of the stiffness matrix characterizing HI(2) [ l1, l2] are related to singular behaviour of the free-energy.
Graphical calculus of volume, inverse volume and Hamiltonian operators in loop quantum gravity
Yang, Jinsong; Ma, Yongge
2017-04-01
To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In this paper, the graphical calculus based on the original Brink graphical method is applied to loop quantum gravity along the line of previous work. The graphical method provides a very powerful technique for simplifying complicated calculations. The closed formula of the volume operator and the actions of the Euclidean Hamiltonian constraint operator and the so-called inverse volume operator on spin-network states with trivalent vertices are derived via the graphical method. By employing suitable and non-ambiguous graphs to represent the action of operators as well as the spin-network states, we use the simple rules of transforming graphs to obtain the resulting formula. Comparing with the complicated algebraic derivation in some literature, our procedure is more concise, intuitive and visual. The resulting matrix elements of the volume operator is compact and uniform, fitting for both gauge-invariant and gauge-variant spin-network states. Our results indicate some corrections to the existing results for the Hamiltonian operator and inverse volume operator in the literature.
Balabin, I. A.; Onichic, J. N.
1997-03-01
Understanding how the protein molecular structure controls the electron transfer (ET) rate is critical for both achieving an insight into vital bioenergetic reactions and designing new ET proteins. We develop and test a new approach for computing ET tunneling matrix elements. Our goal is to provide quantitative results for large molecules with limited computer resources. This connection between simple models and more detailed atomistic models will also provide a better understanding of the basic features that control the ET mechanism. We introduce a series of simple Hamiltonians that incorporate effects of complex molecular structure on the ET rate. Electronic orbital interactions are categorized as classes, and only the most important of them are included. The remaining orbitals are incorporated by means of effective (dependent on the tunneling energy) interaction parameters. Calculations with these Hamiltonians are compared with ``exact'' extended Huckel-level results for several biological and chemically-designed systems. The suggested approach integrates quantum chemical and pathway-like methods. Quantitative calculations with limited computer resources and identification of the domains dominating ET are now in reach. This new developed approach integrates quantum chemistry and pathway-like methods.
Graphical calculus of volume, inverse volume and Hamiltonian operators in loop quantum gravity
Yang, Jinsong [Guizhou University, Department of Physics, Guiyang (China); Academia Sinica, Institute of Physics, Taipei (China); Ma, Yongge [Beijing Normal University, Department of Physics, Beijing (China)
2017-04-15
To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In this paper, the graphical calculus based on the original Brink graphical method is applied to loop quantum gravity along the line of previous work. The graphical method provides a very powerful technique for simplifying complicated calculations. The closed formula of the volume operator and the actions of the Euclidean Hamiltonian constraint operator and the so-called inverse volume operator on spin-network states with trivalent vertices are derived via the graphical method. By employing suitable and non-ambiguous graphs to represent the action of operators as well as the spin-network states, we use the simple rules of transforming graphs to obtain the resulting formula. Comparing with the complicated algebraic derivation in some literature, our procedure is more concise, intuitive and visual. The resulting matrix elements of the volume operator is compact and uniform, fitting for both gauge-invariant and gauge-variant spin-network states. Our results indicate some corrections to the existing results for the Hamiltonian operator and inverse volume operator in the literature. (orig.)
Skurnick, Ronald; Davi, Charles; Skurnick, Mia
2005-01-01
Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…
Hamiltonian monodromy as lattice defect
Zhilinskii, B.
2003-01-01
The analogy between monodromy in dynamical (Hamiltonian) systems and defects in crystal lattices is used in order to formulate some general conjectures about possible types of qualitative features of quantum systems which can be interpreted as a manifestation of classical monodromy in quantum finite particle (molecular) problems.
Maslov index for Hamiltonian systems
Alessandro Portaluri
2008-01-01
Full Text Available The aim of this article is to give an explicit formula for computing the Maslov index of the fundamental solutions of linear autonomous Hamiltonian systems in terms of the Conley-Zehnder index and the map time one flow.
Dynamical stability of Hamiltonian systems
无
2000-01-01
Dynamical stability has become the center of study on Hamiltonian system. In this article we intro-duce the recent development in some areas closely related to this topic, such as the KAM theory, Mather theory, Arnolddiffusion and non-singular collision of n-body problem.
Derivation of Hamiltonians for accelerators
Symon, K.R.
1997-09-12
In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.
Time-reversible Hamiltonian systems
Schaft, Arjan van der
1982-01-01
It is shown that transfer matrices satisfying G(-s) = G(s) = G^T(-s) have a minimal Hamiltonian realization with an energy which is the sum of potential and kinetic energy, yielding the time reversibility of the equations. Furthermore connections are made with an associated gradient system. The
On third order integrable vector Hamiltonian equations
Meshkov, A. G.; Sokolov, V. V.
2017-03-01
A complete list of third order vector Hamiltonian equations with the Hamiltonian operator Dx having an infinite series of higher conservation laws is presented. A new vector integrable equation on the sphere is found.
Hamiltonian realizations of nonlinear adjoint operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2002-01-01
This paper addresses the issue of state-space realizations for nonlinear adjoint operators. In particular, the relationships between nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are established. Then, characterizations of the adjoints of control
Hamiltonian Realizations of Nonlinear Adjoint Operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel ope
Quantum Jacobi fields in Hamiltonian mechanics
Giachetta, G; Sardanashvily, G
2000-01-01
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
Quantization of noncommutative completely integrable Hamiltonian systems
Giachetta, G. [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino (Italy); Mangiarotti, L. [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino (Italy); Sardanashvily, G. [Department of Theoretical Physics, Moscow State University, 117234 Moscow (Russian Federation)]. E-mail: gennadi.sardanashvily@unicam.it
2007-02-26
Integrals of motion of a Hamiltonian system need not commute. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as the Abelian one.
Two-Component Super AKNS Equations and Their Finite-Dimensional Integrable Super Hamiltonian System
Jing Yu; Jingwei Han
2014-01-01
Starting from a matrix Lie superalgebra, two-component super AKNS system is constructed. By making use of monononlinearization technique of Lax pairs, we find that the obtained two-component super AKNS system is a finite-dimensional integrable super Hamiltonian system. And its Lax representation and $r$ -matrix are also given in this paper.
Two-Component Super AKNS Equations and Their Finite-Dimensional Integrable Super Hamiltonian System
Jing Yu
2014-01-01
Full Text Available Starting from a matrix Lie superalgebra, two-component super AKNS system is constructed. By making use of monononlinearization technique of Lax pairs, we find that the obtained two-component super AKNS system is a finite-dimensional integrable super Hamiltonian system. And its Lax representation and r-matrix are also given in this paper.
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.
Dridi, G; Julien, R; Hliwa, M; Joachim, C
2015-08-28
The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.
Port-Hamiltonian systems: an introductory survey
Schaft, van der Arjan; Sanz-Sole, M.; Soria, J.; Varona, J.L.; Verdera, J.
2006-01-01
The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian
New sufficient conditions for Hamiltonian paths.
Rahman, M Sohel; Kaykobad, M; Firoz, Jesun Sahariar
2014-01-01
A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph.
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
Geometric Hamiltonian structures and perturbation theory
Omohundro, S.
1984-08-01
We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging.
Driving Hamiltonian in a Quantum Search Problem
Oshima, K
2001-01-01
We examine the driving Hamiltonian in the analog analogue of Grover's algorithm by Farhi and Gutmann. For a quantum system with a given Hamiltonian $E|w> $ from an initial state $|s>$, the driving Hamiltonian $E^{\\prime}|s> < s|(E^{\\prime} \
Generic construction of efficient matrix product operators
Hubig, C.; McCulloch, I. P.; Schollwöck, U.
2017-01-01
Matrix product operators (MPOs) are at the heart of the second-generation density matrix renormalization group (DMRG) algorithm formulated in matrix product state language. We first summarize the widely known facts on MPO arithmetic and representations of single-site operators. Second, we introduce three compression methods (rescaled SVD, deparallelization, and delinearization) for MPOs and show that it is possible to construct efficient representations of arbitrary operators using MPO arithmetic and compression. As examples, we construct powers of a short-ranged spin-chain Hamiltonian, a complicated Hamiltonian of a two-dimensional system and, as proof of principle, the long-range four-body Hamiltonian from quantum chemistry.
Least-Squares Solutions of the Equation AX = B Over Anti-Hermitian Generalized Hamiltonian Matrices
无
2006-01-01
Upon using the denotative theorem of anti-Hermitian generalized Hamiltonian matrices, we solve effectively the least-squares problem min ‖AX - B‖ over anti-Hermitian generalized Hamiltonian matrices. We derive some necessary and sufficient conditions for solvability of the problem and an expression for general solution of the matrix equation AX = B. In addition, we also obtain the expression for the solution of a relevant optimal approximate problem.
胡志强; 林皋; 王毅; 刘俊
2011-01-01
The scaled boundary finite element method（SBFEM） is a semi-analytical and semi-numerical solution approach for solving partial differential equation.For problem in elasticity,the governing equations can be obtained by mechanically based formulation,Weighted residual formulation and principle of virtual work based on Scaled-boundary-transformation.These formulations are described in the frame of Lagrange system and the unknowns are displacements.In this paper,the discretization of the SBFEM and the dual system to solve elastic problem proposed by W.X.Zhong are combined to derive the governing equations in the frame of Hamilton system by introducing the dual variables.Then the algebraic Riccati equations of the static boundary stiffness matrix for the bounded and unbounded domain are derived based on the hybrid energy and Hamilton variational principle in the interval.The eigen-vector method and precise integration method can be employed to solve the algebraic Riccati equations for static boundary stiffness matrice.%比例边界有限元方法是求解偏微分方程的一种半解析半数值解法。对于弹性力学问题,可采用基于力学相似性、基于比例坐标相似变换的加权余量法和虚功原理得到以位移为未知量的系统控制方程,属于Lagrange体系。但在求解时,又引入了表面力为未知量,控制方程属于Hamilton体系。因而,本文提出在比例边界有限元离散方法的基础上,利用钟万勰教授提出的弹性力学对偶（辛）体系求解方法,通过引入对偶变量,直接在Hamil-ton体系框架内建立控制方程。再利用区段混合能和对偶方程得到了有限域、无限域边界静力刚度所满足的代数Ri
Goodmanson, David M.
2000-09-01
This paper describes a recursion relation for matrix elements of the quantum bouncer. The relation provides an exact expression for the normalization integral, and allows recursive calculation of matrix elements of the form , where z is the spatial coordinate and |m>,|n> are quantum bouncer eigenstates.
ZHANG Zhong-zhi; HAN Xu-li
2005-01-01
By using the characteristic properties of the anti-Hermitian generalized anti-Hamiltonian matrices, we prove some necessary and sufficient conditions of the solvability for algebra inverse eigenvalue problem of anti-Hermitian generalized anti-Hamiltonian matrices, and obtain a general expression of the solution to this problem. By using the properties of the orthogonal projection matrix, we also obtain the expression of the solution to optimal approximate problem of an n× n complex matrix under spectral restriction.
Hamiltonian dynamics of extended objects
Capovilla, R [Departamento de FIsica, Centro de Investigacion y de Estudios Avanzados del IPN, Apdo Postal 14-740, 07000 Mexico, DF (Mexico); Guven, J [School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4 (Ireland); Rojas, E [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo Postal 70-543, 04510 Mexico, DF (Mexico)
2004-12-07
We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations.
Lowest Eigenvalues of Random Hamiltonians
Shen, J J; Arima, A; Yoshinaga, N
2008-01-01
In this paper we present results of the lowest eigenvalues of random Hamiltonians for both fermion and boson systems. We show that an empirical formula of evaluating the lowest eigenvalues of random Hamiltonians in terms of energy centroids and widths of eigenvalues are applicable to many different systems (except for $d$ boson systems). We improve the accuracy of the formula by adding moments higher than two. We suggest another new formula to evaluate the lowest eigenvalues for random matrices with large dimensions (20-5000). These empirical formulas are shown to be applicable not only to the evaluation of the lowest energy but also to the evaluation of excited energies of systems under random two-body interactions.
On Hamiltonian formulation of cosmologies
K D Krori; S Dutta
2000-03-01
Novello et al [1,2] have shown that it is possible to ﬁnd a pair of canonically conjugate variables (written in terms of gauge-invariant variables) so as to obtain a Hamiltonian that describes the dynamics of a cosmological system. This opens up the way to the usual technique of quantization. Elbaz et al [4] have applied this method to the Hamiltonian formulation of FRW cosmological equations. This note presents a generalization of this approach to a variety of cosmologies. A general Schrödinger wave equation has been derived and exact solutions have been worked out for the stiff matter era for some cosmological models. It is argued that these solutions appear to hint at their possible relevance in the early phase of cosmological evolution.
A Hamiltonian approach to Thermodynamics
Baldiotti, M.C., E-mail: baldiotti@uel.br [Departamento de Física, Universidade Estadual de Londrina, 86051-990, Londrina-PR (Brazil); Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br [Universidade Federal do ABC, Av. dos Estados 5001, 09210-580, Santo André-SP (Brazil); Molina, C., E-mail: cmolina@usp.br [Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Bettio 1000, CEP 03828-000, São Paulo-SP (Brazil)
2016-10-15
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.
Hamiltonian mechanics of stochastic acceleration.
Burby, J W; Zhmoginov, A I; Qin, H
2013-11-08
We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.
Hamiltonian chaos and fractional dynamics
Zaslavsky, George M
2008-01-01
The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image ...
Freeman, John [Univ. of California, Berkeley, CA (United States)
2007-01-01
A measurement of the top quark mass in t$\\bar{t}$ → l + jets candidate events, obtained from p$\\bar{p}$ collisions at √s = 1.96 TeV at the Fermilab Tevatron using the CDF II detector, is presented. The measurement approach is that of a matrix element method. For each candidate event, a two dimensional likelihood is calculated in the top pole mass and a constant scale factor, 'JES', where JES multiplies the input particle jet momenta and is designed to account for the systematic uncertainty of the jet momentum reconstruction. As with all matrix element techniques, the method involves an integration using the Standard Model matrix element for t$\\bar{t}$ production and decay. However, the technique presented is unique in that the matrix element is modified to compensate for kinematic assumptions which are made to reduce computation time. Background events are dealt with through use of an event observable which distinguishes signal from background, as well as through a cut on the value of an event's maximum likelihood. Results are based on a 955 pb^{-1} data sample, using events with a high-p_{T} lepton and exactly four high-energy jets, at least one of which is tagged as coming from a b quark; 149 events pass all the selection requirements. They find M_{meas} = 169.8 ± 2.3(stat.) ± 1.4(syst.) GeV/c^{2}.
Raychev, P. P.; Roussev, R. P.; Terziev, P. A.; Bonatsos, D.; Iudice, N. Lo
1997-04-01
A simplified boson realization of the soq subalgebra of u_q(3) is constructed. A simplified form of the corresponding so_q(3) basis states is obtained. The reduced matrix elements of a special second-rank tensor operator (quadrupole operator) are calculated in the so_q(3) basis (P. P. Raychev, R. P. Roussev, P. A. Terziev, D. Bonatsos and N. Lo Iudice, J. Phys. A (1996) in press).
Canelli, Florencia [University of Chicago, Fermi National Accelerator Laboratory - Fermilab, P.O. Box 500, Batavia, IL 60510-5011 (United States)
2010-07-01
The matrix element technique developed over the last decade has improved precision measurements and also helped establish new processes. This is in great part possible due to the availability of CPU and to the improved modeling of the Monte Carlo tools. W+jets physics has given strong SM foundation for beyond SM: Top quark mass measurements; Top quark coupling probes; Single top observation; di-boson w/jets observation; Higgs searches; Heavy quark searches
Kroeninger, Kevin Alexander; /Bonn U.
2004-04-01
Using a data set of 158 and 169 pb{sup -1} of D0 Run-II data in the electron and muon plus jets channel, respectively, the top quark mass has been measured using the Matrix Element Method. The method and its implementation are described. Its performance is studied in Monte Carlo using ensemble tests and the method is applied to the Moriond 2004 data set.
Kroeninger, Kevin Alexander; /Bonn U.
2004-04-01
Using a data set of 158 and 169 pb{sup -1} of D0 Run-II data in the electron and muon plus jets channel, respectively, the top quark mass has been measured using the Matrix Element Method. The method and its implementation are described. Its performance is studied in Monte Carlo using ensemble tests and the method is applied to the Moriond 2004 data set.
Freeman, John C [Univ. of California, Berkeley, CA (United States)
2007-01-01
A measurement of the top quark mass in t$\\bar{t}$ → l + jets candidate events, obtained from p$\\bar{p}$ collisions at √s = 1.96 TeV at the Fermilab Tevatron using the CDF II detector, is presented. The measurement approach is that of a matrix element method. For each candidate event, a two dimensional likelihood is calculated in the top pole mass and a constant scale factor, 'JES', where JES multiplies the input particle jet momenta and is designed to account for the systematic uncertainty of the jet momentum reconstruction. As with all matrix elements techniques, the method involves an integration using the Standard Model matrix element for tt production and decay. however, the technique presented is unique in that the matrix element is modified to compensate for kinematic assumptions which are made to reduce computation time. Background events are dealt with through use of an event observable which distinguishes signal from background, as well as through a cut on the value of an event's maximum likelihood. Results are based on a 955 pb^{-1 }data sample, using events with a high-p_{T} lepton and exactly four high-energy jets, at least one of which is tagged as coming from a b quark; 149 events pass all the selection requirements. They find M_{meas} = 169.8 ± 2.3(stat.) ± 1.4(syst.) GeV/c^{2}.
Lin Yan Chang; Lai Wan Chang; Zhou Si Chun
2002-01-01
Dot matrix LCD based on T6963C is a low power supply module. It needs no complex interface circuits connecting with MCU. Application in text and graphics is easy. Application of this LCD in multi-element portable XRF spectrometry is show. How to use it in Chinese, pull-down menu, spectrum and how to design the interface circuits with embedded computer are shown as well
Ablinger, J.; Hasselhuhn, A.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Manteuffel, A. von [Mainz Univ. (Germany). PRISMA Cluster of Excellence; Mainz Univ. (Germany). Inst. fuer Physik; Round, M.; Wissbrock, F. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2014-01-15
We calculate the massive operator matrix element A{sup (3)}{sub gq}(N) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N. This is the first complete transition function needed in the variable flavor number scheme obtained at O({alpha}{sup 3}{sub s}). A fist independent recalculation is performed for the contributions {proportional_to} N{sub F} of the 3-loop anomalous dimension {gamma}{sup (2)}{sub gq}(N).
Ablinger, J. [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Blümlein, J.; De Freitas, A. [Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany); Hasselhuhn, A. [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Manteuffel, A. von [PRISMA Cluster of Excellence and Institute of Physics, J. Gutenberg University, D-55099 Mainz (Germany); Round, M. [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany); Schneider, C. [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Wißbrock, F. [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz (Austria); Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany)
2014-05-15
We calculate the massive unpolarized operator matrix element A{sub gq}{sup (3)}(N) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N. This is the first complete transition function needed in the variable flavor number scheme obtained at O(α{sub s}{sup 3}). A first independent recalculation is performed for the contributions ∝N{sub F} of the 3-loop anomalous dimension γ{sub gq}{sup (2)}(N)
Ablikim, M.; Achasov, M. N.; Ai, X.C.; Albayrak, O.; Albrecht, M.; Ambrose, D. J.; Amoroso, A.; Haddadi, Z.; Kalantar-Nayestanaki, N.; Kavatsyuk, M.; Loehner, H.; Messchendorp, J.G.; Tiemens, M.
2015-01-01
Based on a sample of 1.31 x 10(9) J/psi events collected with the BESIII detector at the BEPCII collider, Dalitz plot analyses of selected 79,625 eta -> pi(+)pi(-)pi(0) events, 33,908 eta -> pi(0)pi(0)pi(0) events, and 1,888 eta' -> pi(0)pi(0)pi(0) events are performed. The measured matrix elements
Ablikim, M.; Achasov, M. N.; Ai, X.C.; Albayrak, O.; Albrecht, M.; Ambrose, D. J.; Amoroso, A.; Haddadi, Z.; Kalantar-Nayestanaki, N.; Kavatsyuk, M.; Loehner, H.; Messchendorp, J.G.; Tiemens, M.
2015-01-01
Based on a sample of 1.31 x 10(9) J/psi events collected with the BESIII detector at the BEPCII collider, Dalitz plot analyses of selected 79,625 eta -> pi(+)pi(-)pi(0) events, 33,908 eta -> pi(0)pi(0)pi(0) events, and 1,888 eta' -> pi(0)pi(0)pi(0) events are performed. The measured matrix elements
Gardner, David [Lawrence Livermore National Laboratory (LLNL); Woodward, Carol S. [Lawrence Livermore National Laboratory (LLNL); Evans, Katherine J [ORNL
2015-01-01
Efficient solution of global climate models requires effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a time step dictated by accuracy of the processes of interest rather than by stability governed by the fastest of the time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton s method is applied for these systems. Each iteration of the Newton s method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but this Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite-difference which may show a loss of accuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite-difference approximations of these matrix-vector products for climate dynamics within the spectral-element based shallow-water dynamical-core of the Community Atmosphere Model (CAM).
Haefner, Petra
2008-07-31
The top quark plays a special role in the Standard Model of Particle Physics. With its enormous mass of about 170 GeV it is as heavy as a gold atom and is the only quark with a mass near the electroweak scale. Together with the W boson mass, the top quark mass allows indirect constraints on the mass of the hypothetical Higgs boson, which might hold the clue to the origin of mass. Top pair production with a semileptonic decay t anti t{yields}W{sup {+-}}W{sup -+}b anti b{yields}q anti ql{nu}b anti b is the ''golden channel'' for mass measurements, due to a large branching fraction and a relatively low background contamination compared to other decay channels. Top mass measurements based on this decay, performed with the matrix element method, have always been among the single best measurements in the world. In 2007, the top mass world average broke the 1% level of precision. Its measurement is no longer dominated by statistical but instead by systematic uncertainties. The reduction of systematic uncertainties has therefore become a key issue for further progress. This thesis introduces two new developments in the treatment of b jets. The first improvement is an optimization in the way b identification information is used. It leads to an enhanced separation between signal and background processes and reduces the statistical uncertainty by about 16%. The second improvement determines differences in the detector response and thus the energy scales of light jets and b jets. Thereby, it addresses the major source of systematic uncertainty in the latest top mass measurements. The method was validated on Monte Carlo events at the generator level, calibrated with fully simulated events, including detector simulation, and applied to D0 Run II data corresponding to 1 fb{sup -1} of integrated luminosity. Possible sources of systematic uncertainties were studied. The top mass is measured to be: m{sub t}=(169.2{+-}3.5(stat.){+-}1.0(syst.)) GeV. The
Matrix-model dualities in the collective field formulation
Andric, I
2005-01-01
We establish a strong-weak coupling duality between two types of free matrix models. In the large-N limit, the real-symmetric matrix model is dual to the quaternionic-real matrix model. Using the large-N conformal invariant collective field formulation, the duality is displayed in terms of the generators of the conformal group. The conformally invariant master Hamiltonian is constructed and we conjecture that the master Hamiltonian corresponds to the hermitian matrix model.
Kirsch, Matthias [RWTH Aachen Univ. (Germany)
2009-06-29
At particle accelerators the Standard Model has been tested and will be tested further to a great precision. The data analyzed in this thesis have been collected at the world's highest energetic-collider, the Tevatron, located at the Fermi National Accelerator Laboratory (FNAL) in the vicinity of Chicago, IL, USA. There, protons and antiprotons are collided at a center-of-mass energy of {radical}s = 1.96 TeV. The discovery of the top quark was one of the remarkable results not only for the CDF and D0 experiments at the Tevatron collider, but also for the Standard Model, which had predicted the existence of the top quark because of symmetry arguments long before already. Still, the Tevatron is the only facility able to produce top quarks. The predominant production mechanism of top quarks is the production of a top-antitop quark pair via the strong force. However, the Standard Model also allows the production of single top quarks via the electroweak interaction. This process features the unique opportunity to measure the |V_{tb}| matrix element of the Cabbibo-Kobayashi-Maskawa (CKM) matrix directly, without assuming unitarity of the matrix or assuming that the number of quark generations is three. Hence, the measurement of the cross section of electroweak top quark production is more than the technical challenge to extract a physics process that only occurs one out of ten billion collisions. It is also an important test of the V-A structure of the electroweak interaction and a potential window to physics beyond the Standard Model in the case where the measurement of |V{sub tb}| would result in a value significantly different from 1, the value predicted by the Standard Model. At the Tevatron two production processes contribute significantly to the production of single top quarks: the production via the t-channel, also called W-gluon fusion, and the production via the s-channel, known as well as W* process. This analysis searches for the combined s
Kirsch, Matthias [RWTH Aachen Univ. (Germany)
2009-06-29
At particle accelerators the Standard Model has been tested and will be tested further to a great precision. The data analyzed in this thesis have been collected at the world's highest energetic-collider, the Tevatron, located at the Fermi National Accelerator Laboratory (FNAL) in the vicinity of Chicago, IL, USA. There, protons and antiprotons are collided at a center-of-mass energy of {radical}s = 1.96 TeV. The discovery of the top quark was one of the remarkable results not only for the CDF and D0 experiments at the Tevatron collider, but also for the Standard Model, which had predicted the existence of the top quark because of symmetry arguments long before already. Still, the Tevatron is the only facility able to produce top quarks. The predominant production mechanism of top quarks is the production of a top-antitop quark pair via the strong force. However, the Standard Model also allows the production of single top quarks via the electroweak interaction. This process features the unique opportunity to measure the |V_{tb}| matrix element of the Cabbibo-Kobayashi-Maskawa (CKM) matrix directly, without assuming unitarity of the matrix or assuming that the number of quark generations is three. Hence, the measurement of the cross section of electroweak top quark production is more than the technical challenge to extract a physics process that only occurs one out of ten billion collisions. It is also an important test of the V-A structure of the electroweak interaction and a potential window to physics beyond the Standard Model in the case where the measurement of |V{sub tb}| would result in a value significantly different from 1, the value predicted by the Standard Model. At the Tevatron two production processes contribute significantly to the production of single top quarks: the production via the t-channel, also called W-gluon fusion, and the production via the s-channel, known as well as W* process. This analysis searches for the combined s
Paredes, Eduardo [Departamento de Quimica Analitica, Nutricion y Bromatologia, University of Alicante, 03080 Alicante (Spain); Maestre, Salvador E. [Departamento de Quimica Analitica, Nutricion y Bromatologia, University of Alicante, 03080 Alicante (Spain); Todoli, Jose L. [Departamento de Quimica Analitica, Nutricion y Bromatologia, University of Alicante, 03080 Alicante (Spain)]. E-mail: jose.todoli@ua.es
2006-03-15
A stirred tank was used for the first time to elucidate the mechanism responsible for inductively coupled plasma atomic emission spectroscopy (ICP-AES) matrix effects caused by inorganic, acids and easily ionized elements (EIEs), as well as organic, ethanol and acetic acid, compounds. In order to gradually increase the matrix concentration, a matrix solution was introduced inside a stirred container (tank) initially filled with an aqueous multielement standard. PolyTetraFluoroEthylene (PTFE) tubing was used to deliver the resulting solution to the liquid sample introduction system. Matrix concentration ranged from 0 to 2 mol l{sup -1} in the case of inorganic acids (i.e., nitric, sulfuric, hydrochloric and a mixture of them), from 0 to about 2500 mg l{sup -1} for EIEs (i.e., sodium, calcium and mixtures of both) and from 0% to 15%, w/w for organic compounds. Up to 40-50 different solutions were prepared and measured in a period of time shorter than 6-7 min. This investigation was carried out in terms of emission intensity and tertiary aerosols characteristics. The experimental setup used in the present work allowed to thoroughly study the effect of matrix concentration on analytical signal. Generally speaking, the experiments concerning tertiary aerosol characterization revealed that, in the case of inorganic acids and EIEs, the mechanism responsible for changes in aerosol characteristics was the droplet fission. In contrast, for organic matrices it was found that the interference was caused by a change in both aerosol transport and plasma thermal characteristics. The extent of the interferences caused by organic as well as inorganic compounds was compared for a set of 14 emission lines through a wide range of matrix concentrations. With a stirred tank, it is possible to choose an efficient internal standard for any given matrix composition. The time required to complete this procedure was shorter than 7 min.
Entanglement hamiltonians in two-dimensional conformal field theory
Cardy, John
2016-01-01
We enumerate the cases in 2d conformal field theory where the logarithm of the reduced density matrix (the entanglement or modular hamiltonian) may be written as an integral over the energy-momentum tensor times a local weight. These include known examples and new ones corresponding to the time-dependent scenarios of a global and local quench. In these latter cases the entanglement hamiltonian depends on the momentum density as well as the energy density. In all cases the entanglement spectrum is that of the appropriate boundary CFT. We emphasize the role of boundary conditions at the entangling surface and the appearance of boundary entropies as universal O(1) terms in the entanglement entropy.
Hamiltonian identification through enhanced observability utilizing quantum control
Leghtas, Zaki; Rabitz, Herschel; Rouchon, Pierre
2011-01-01
This paper considers Hamiltonian identification for a controllable quantum system with non-degenerate transitions and a known initial state. We assume to have at our disposal a single scalar control input and the population measure of only one state at an (arbitrarily large) final time T. We prove that the quantum dipole moment matrix is locally observable in the following sense: for any two close but distinct dipole moment matrices, we construct discriminating controls giving two different measurements. Such discriminating controls are constructed to have three well defined temporal components, as inspired by Ramsey interferometry. This result suggests that what may appear at first to be very restrictive measurements are actually rich for identification, when combined with well designed discriminating controls, to uniquely identify the complete dipole moment of such systems. The assessment supports the employment of quantum control as a promising means to achieve high quality identification of a Hamiltonian.
Comparative index and Sturmian theory for linear Hamiltonian systems
Šepitka, Peter; Šimon Hilscher, Roman
2017-01-01
The comparative index was introduced by J. Elyseeva (2007) as an efficient tool in matrix analysis, which has fundamental applications in the discrete oscillation theory. In this paper we implement the comparative index into the theory of continuous time linear Hamiltonian systems, study its properties, and apply it to obtain new Sturmian separation theorems as well as new and optimal estimates for left and right proper focal points of conjoined bases of these systems on bounded intervals. We derive our results for general possibly abnormal (or uncontrollable) linear Hamiltonian systems. The results turn out to be new even in the case of completely controllable systems. We also provide several examples, which illustrate our new theory.
Diagonalization of the XXZ Hamiltonian by Vertex Operators
Davies, B; Jimbo, M; Miwa, T; Nakayashiki, A; Davies, Brian; Foda, Omar; Jimbo, Michio; Miwa, Tetsuji; Nakayashiki, Atsushi
1993-01-01
We diagonalize the anti-ferroelectric XXZ-Hamiltonian directly in the thermodynamic limit, where the model becomes invariant under the action of affine U_q( sl(2) ). Our method is based on the representation theory of quantum affine algebras, the related vertex operators and KZ equation, and thereby bypasses the usual process of starting from a finite lattice, taking the thermodynamic limit and filling the Dirac sea. From recent results on the algebraic structure of the corner transfer matrix of the model, we obtain the vacuum vector of the Hamiltonian. The rest of the eigenvectors are obtained by applying the vertex operators, which act as particle creation operators in the space of eigenvectors. We check the agreement of our results with those obtained using the Bethe Ansatz in a number of cases, and with others obtained in the scaling limit --- the $su(2)$-invariant Thirring model.
Element stiffness matrix for Timoshenko beam with variable cross-section%变截面 Timoshenko 梁的单元刚度矩阵
传光红; 陈以一; 童根树
2014-01-01
The variable cross-section members have been widely used in engineering practice for many years ,thus it is necessary to investigate their element stiffness matrixes .In this paper ,based on the prin-ciple of potential energy ,the element stiffness matrix with approximation to second order are obtained , w here the change rates of both the flexural and shear stiffness are treated as infinitesimal quantities (or Infinitesimal) .It is noted that the effects of geometric nonlinearity due to axial force as well as shear de-formation is considered in the matrix .In addition ,based on the differential equilibrium equations of the members ,the flexural and shear displacements modes with approximation to second order ,expressed as cubic and quintic polynomial respectively ,are also obtained .Moreover ,the singularity of the element stiffness matrix and the expression of axial stiffness are discussed in detail .By comparing the obtained matrix results with some exact solutions ,it is indicated that the accuracy of the obtained element stiff-ness matrix can be guaranteed .Finally ,the convergence of this method is discussed by comparing with other methods in a case study .%变截面构件在工程中应用广泛，在对变截面梁进行数值计算时，需要建立变截面梁单元的刚度矩阵。该文采用势能驻值原理，考虑了轴力引起的几何非线性和剪切变形的影响，将梁截面刚度的变化率作为小量，得到了近似到二阶的单元刚度矩阵。在构造位移模式时，从梁的微分平衡方程出发，得到同样近似到二阶、分别以三次和五次多项式表示的剪切和弯曲位移模式。该文还证明了单元刚度矩阵的奇异性，给出了轴压刚度的表达式，定量论证了与某些精确解的误差，表明在一定范围内，该文的结果具有足够的精度。最后以一个计算实例说明该文的单元刚度矩阵具有较快的收敛性。
van Oers, Alexander M.; Maas, Leo R. M.; Bokhove, Onno
2017-02-01
The linear equations governing internal gravity waves in a stratified ideal fluid possess a Hamiltonian structure. A discontinuous Galerkin finite element method has been developed in which this Hamiltonian structure is discretized, resulting in conservation of discrete analogs of phase space and energy. This required (i) the discretization of the Hamiltonian structure using alternating flux functions and symplectic time integration, (ii) the discretization of a divergence-free velocity field using Dirac's theory of constraints and (iii) the handling of large-scale computational demands due to the 3-dimensional nature of internal gravity waves and, in confined, symmetry-breaking fluid domains, possibly its narrow zones of attraction.
Monte Carlo Hamiltonian: Linear Potentials
LUO Xiang-Qian; LIU Jin-Jiang; HUANG Chun-Qing; JIANG Jun-Qin; Helmut KROGER
2002-01-01
We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. Weconsider two quantum mechanical models: a symmetric one V(x) = |x|/2; and an asymmetric one V(x) = ∞, forx ＜ 0 and V(x) = x, for x ≥ 0. The results for the spectrum, wave functions and thermodynamical observables are inagreement with the analytical or Runge-Kutta calculations.
LOCALIZATION THEOREM ON HAMILTONIAN GRAPHS
无
2000-01-01
Let G be a 2-connected graph of order n( 3).If I(u,v) S(u,v) or max {d(u),d(v)} n/2 for any two vertices u,v at distance two in an induced subgraph K1,3 or P3 of G,then G is hamiltonian.Here I(u,v) = ｜N(u)∩ N(v)｜,S(u,v) denotes thenumber of edges of maximum star containing u,v as an induced subgraph in G.
Discrete Hamiltonian for General Relativity
Ziprick, Jonathan
2015-01-01
Beginning from canonical general relativity written in terms of Ashtekar variables, we derive a discrete phase space with a physical Hamiltonian for gravity. The key idea is to define the gravitational fields within a complex of three-dimensional cells such that the dynamics is completely described by discrete boundary variables, and the full theory is recovered in the continuum limit. Canonical quantization is attainable within the loop quantum gravity framework, and we believe this will lead to a promising candidate for quantum gravity.
Chasing Hamiltonian structure in gyrokinetic theory
Burby, J W
2015-01-01
Hamiltonian structure is pursued and uncovered in collisional and collisionless gyrokinetic theory. A new Hamiltonian formulation of collisionless electromagnetic theory is presented that is ideally suited to implementation on modern supercomputers. The method used to uncover this structure is described in detail and applied to a number of examples, where several well-known plasma models are endowed with a Hamiltonian structure for the first time. The first energy- and momentum-conserving formulation of full-F collisional gyrokinetics is presented. In an effort to understand the theoretical underpinnings of this result at a deeper level, a \\emph{stochastic} Hamiltonian modeling approach is presented and applied to pitch angle scattering. Interestingly, the collision operator produced by the Hamiltonian approach is equal to the Lorentz operator plus higher-order terms, but does not exactly conserve energy. Conversely, the classical Lorentz collision operator is provably not Hamiltonian in the stochastic sense.
Samsonov, Boris F
2013-04-28
One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the eigenfunctions of a Hermitian Hamiltonian equivalent to the given non-Hermitian one is found. As a result, the corresponding scattering matrix and cross section are given explicitly. It is demonstrated that the possible presence of a spectral singularity in the spectrum of the non-Hermitian Hamiltonian may be detected as a resonance in the scattering cross section of its Hermitian counterpart. Nevertheless, just at the singular point, the equivalent Hermitian Hamiltonian becomes undetermined.
Cairns, Warren R.L.; Cozzi, Giulio [Institute for the Dynamics of Environmental Processes-CNR, Venice (Italy); De Boni, Antonella; Gabrieli, Jacopo [University of Venice, Department of Environmental Science, Venice (Italy); Asti, Massimo; Merlone Borla, Edoardo; Parussa, Flavio [Centro Ricerche Fiat, Orbassano (Italy); Moretto, Ezio [FIAT Powertrain Technologies S.p.A, Turin (Italy); Cescon, Paolo; Barbante, Carlo [University of Venice, Department of Environmental Science, Venice (Italy); Institute for the Dynamics of Environmental Processes-CNR, Venice (Italy); Boutron, Claude [Laboratoire de Glaciologie et Geophysique de l' Environnement, UMR CNRS 5183, B.P. 96, Saint Martin d' Heres Cedex (France)
2011-03-15
Inductively coupled plasma-mass spectrometry coupled with cation exchange matrix separation has been optimised for the direct determination of platinum group element (PGE) and trace element emissions from a diesel engine car. After matrix separation method detection limits of 1.6 ng g{sup -1} for Pd, 0.4 ng g{sup -1} for Rh and 4.3 ng g{sup -1} for Pt were achieved, the method was validated against the certified reference material BCR 723, urban road dust. The test vehicle was fitted with new and aged catalytic converters with and without diesel particulate filters (DPF). Samples were collected after three consecutive New European Driving Cycle (NEDC) of the particulate and ''soluble'' phases using a home-made sampler optimised for trace element analysis. Emission factors for the PGEs ranged from 0.021 ng km{sup -1} for Rh to 70.5 ng km{sup -1} for Pt; when a DPF was fitted, the emission factors for the PGEs actually used in the catalysts dropped by up to 97% (for Pt). Trace element emission factors were found to drop by a maximum of 92% for Ni to a minimum of 18% for Y when a DPF was fitted; a new DPF was also found to cause a reduction of up to 86% in the emission of particulate matter. (orig.)
Haefner, Petra [Ludwig Maximilian Univ., Munich (Germany)
2008-07-31
The top quark plays a special role in the Standard Model of Particle Physics. With its enormous mass of about 170 GeV it is as heavy as a gold atom and is the only quark with a mass near the electroweak scale. Together with theW boson mass, the top quark mass allows indirect constraints on the mass of the hypothetical Higgs boson, which might hold the clue to the origin of mass. Top pair production with a semileptonic decay t $\\bar{t}$ →W^{±}W^{∓} b$\\bar{b}$ →q $\\bar{t}$lnb$\\bar{b}$ is the ”golden channel” for mass measurements, due to a large branching fraction and a relatively low background contamination compared to other decay channels. Top mass measurements based on this decay, performed with the matrix element method, have always been among the single best measurements in the world. In 2007, the top mass world average broke the 1% level of precision. Its measurement is no longer dominated by statistical but instead by systematic uncertainties. The reduction of systematic uncertainties has therefore become a key issue for further progress. This thesis introduces two new developments in the treatment of b jets. The first improvement is an optimization in the way b identification information is used. It leads to an enhanced separation between signal and background processes and reduces the statistical uncertainty by about 16%. The second improvement determines differences in the detector response and thus the energy scales of light jets and b jets. Thereby, it addresses the major source of systematic uncertainty in the latest top mass measurements. The method was validated on Monte Carlo events at the generator level, calibrated with fully simulated events, including detector simulation, and applied to D0 Run II data corresponding to 1 fb^{-1} of integrated luminosity. Possible sources of systematic uncertainties were studied. The top mass is measured to be: m_{t} = (169.2±3.5(stat.)±1.0(syst.)) GeV . The
Stochastic averaging of quasi-Hamiltonian systems
朱位秋
1996-01-01
A stochastic averaging method is proposed for quasi-Hamiltonian systems (Hamiltonian systems with light dampings subject to weakly stochastic excitations). Various versions of the method, depending on whether the associated Hamiltonian systems are integrable or nonintegrable, resonant or nonresonant, are discussed. It is pointed out that the standard stochastic averaging method and the stochastic averaging method of energy envelope are special cases of the stochastic averaging method of quasi-Hamiltonian systems and that the results obtained by this method for several examples prove its effectiveness.