Full Operator Research Articles

Deformations of [formula omitted] SYM and integrable spin chain models

Beginning with the planar limit of N = 4 SYM theory, we study planar diagrams for field theory deformations of N = 4 which are marginal at the free field theory level. We show that the requirement of integrability of the full one-loop dilatation operator in the scalar sector, places very strong constraints on the field theory, so that the only soluble models correspond essentially to orbifolds of N = 4 SYM. For these, the associated spin chain model gets twisted boundary conditions that depend on the length of the chain, but which are still integrable. We also show that theories with integrable subsectors appear quite generically, and it is possible to engineer integrable subsectors to have some specific symmetry, however these do not generally lead to full integrability. We also try to construct a theory whose spin chain has quantum group symmetry SO q ( 6 ) as a deformation of the SO ( 6 ) R-symmetry structure of N = 4 SYM. We show that it is not possible to obtain a spin chain with that symmetry from deformations of the scalar potential of N = 4 SYM. We also show that the natural context for these questions can be better phrased in terms of multi-matrix quantum mechanics rather than in four-dimensional field theories.

Nonequilibrium electron transport using the density matrix renormalization group method

We extended the Density Matrix Renormalization Group method to study the real time dynamics of interacting one dimensional spinless Fermi systems by applying the full time evolution operator to an initial state. As an example we describe the propagation of a density excitation in an interacting clean system and the transport through an interacting nano structure.

AN INVESTIGATION INTO THE PERCEIVED FARM MANAGEMENT AND MARKETING EDUCATIONAL NEEDS OF FARM OPERATORS IN JORDAN

The study aimed to investigate the educational needs of producers on farm management and marketing skills using two 5-point Likert scales. Data were collected from a sample of 120 producers in the main irrigated area in Jordan, and non-parametric tests were used to analyze the data. Producers were largely commercial, but the majority does not perceive the need to participate in training activities on farm management and marketing skills. Higher scores on both scales were observed for full time operators, renters, the risk-averse, the more dependent on farm income and hired-labor; those who make use of sources of information more intensively; those who preferred group extension; and those who use computers in business management. Efforts have to be made to investigate the educational needs of operators with low ratings, and to develop an understanding of the importance of farm management. The more positive operators have to be targeted through group extension techniques to initiate simple book keeping, and financial analysis tools to promote business-like farming. While the educational role of improving the managerial abilities of the producers remains an important task for state extension, the public and private sector can cooperate in areas where the private companies can benefit from activities such as book-keeping and technical and financial management software.

Limit theorems for continuous-time random walks with infinite mean waiting times

A continuous-time random walk is a simple random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has infinite mean, the scaling limit is an operator Lévy motion subordinated to the hitting time process of a classical stable subordinator. Density functions for the limit process solve a fractional Cauchy problem, the generalization of a fractional partial differential equation for Hamiltonian chaos. We also establish a functional limit theorem for random walks with jumps in the strict generalized domain of attraction of a full operator stable law, which is of some independent interest.

Limit theorems for continuous-time random walks with infinite mean waiting times

A continuous-time random walk is a simple random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has infinite mean, the scaling limit is an operator Lévy motion subordinated to the hitting time process of a classical stable subordinator. Density functions for the limit process solve a fractional Cauchy problem, the generalization of a fractional partial differential equation for Hamiltonian chaos. We also establish a functional limit theorem for random walks with jumps in the strict generalized domain of attraction of a full operator stable law, which is of some independent interest.

Doppler-limited FTIR spectrum of the v 3(a′)/v 8 (a″) Coriolis resonance dyad of CHC1F2: analysis and comparison with ab initio calculations

The Doppler-limited FTIR spectrum of the band system in the region 1070–1170 cm−1 (Doppler width ≈ 0.0015 cm−1, FWHM) was measured with our new Bruker IFS 120 HR Zürich prototype (ZP2001) spectrometer. This instrument allows for an unapodized resolution of 0.0007 cm−1 (FWHM). This is the highest resolution realized so far by a commercial FTIR spectrometer system. It allows high-resolution analysis of the room temperature spectra of the strongly coupled modes v 3(a′) and v 8 (a″), corresponding to the symmetric and antisymmetric CF-stretching vibrations, including also further couplings not analysed previously. The present analysis is based on effective rotational Hamiltonians for the v 3=1 and v 8=1 states, including all terms up to sextic, and involves the full first-order Coriolis interaction operator Consideration of both the and first-order Coriolis terms proved essential in order to obtain good line-by-line agreement between observed and calculated rovibrational structures over the full band system. In addition, the analysis of two local resonances allowed us to determine the vibrational wavenumbers of the 3v 9 and v 6+2v 9) levels with good accuracy. We describe possible approaches to the analysis. The final analysis involves both chlorine isotopomers and includes all hybrid components which are allowed by symmetry. It results in the band centres cm−1, cm−1, cm−1 and (v 6+2v 9)0=1144.32 cm−1, where the last digit is rounded, relating to the first digits differing in two types of analyses and data sets from our work. The main Coriolis interaction parameters are cm−1 and cm−1. In addition, smaller interactions could also be determined quantitatively. Our results are in essential agreement with the original analysis of Luckhaus and Quack (1989, Molec. Phys., 68, 745), which was, however, much less complete and precise. We discuss the comparison of different types of analyses and further recent results on this band system. We report ab initio calculations for this molecule on the MP2 level of theory with an aug-cc-pVDZ or an aug-cc-pVTZ basis set. Various subspaces of the potential energy and electric dipole moment hypersurface have been calculated in reduced normal coordinates including up to three dimensions. With these hypersurfaces we determined the corresponding vibrational absorption spectra, comprising transition wave- numbers and intensities. An analysis of the vibrational levels with an effective Hamiltonian was used to derive anharmonic constants. We also derived Coriolis coupling constants and integrated absorption intensities ab initio, which are compared with the present and previous experimental and theoretical results. The complete set of data as analysed is tabulated in Appendix A of this publication [61].

Does chlorine peroxide absorb below 250 nm?

Low-lying singlet and triplet electronic excited states of ClOOCl are presented. Calculations of the excitation energies and oscillator strengths are reported using excited state coupled cluster response methods, as well as the complete active space self-consistent field method with the full Breit-Pauli spin-orbit operator. These calculations predict that for ClOOCl there should be a weakly absorbing triplet state lying below the lowest absorbing singlet excited state. This state is predicted to have an absorption maximum at about 385 +/- 25 nm. This lowest triplet state is calculated to be dissociative and leads to ClOO+Cl.

Bicircular projections on some matrix and operator spaces

A projection on a complex Banach space is bicircular if its linear combinations with the complementary projection having coefficients of modulus one are isometries. Such projections are always bicontractive. In this paper we prove structure theorems for bicircular projections acting on the spaces of the full operator algebra, symmetric operators and antisymmetric operators.

Bicircular projections on some matrix and operator spaces

A projection on a complex Banach space is bicircular if its linear combinations with the complementary projection having coefficients of modulus one are isometries. Such projections are always bicontractive. In this paper we prove structure theorems for bicircular projections acting on the spaces of the full operator algebra, symmetric operators and antisymmetric operators.

Split Full Tensor Discretization Operators for General Hexahedral Grids

Summary A major assumption in many simulators is that the pressure equation always has a diagonal tensor. However, in many cases of practical interest, a full tensor matrix occurs. Three contributing factors that can give rise to a full tensor pressure equation are anisotropic media, upscaling (with cross-flow effects), and non-K-orthogonal structured and unstructured grids. The introduction of a full tensor approximation typically increases the support of the standard scheme on a logically rectangular grid from 7 to 27 nodes in 3D, which can increase 3D simulation costs by over 100%. In this paper, 3D full tensor operator splitting schemes are presented. These schemes maintain consistent full tensor approximations while only requiring diagonal tensor inversion.

APPLICATION OF ENTANGLED STATE IN QUANTIZING SUPERCONDUCTING CAPACITOR MODEL IN THE PRESENCE OF A VOLTAGE BIAS AND A CURRENT BIAS

Based on the entangled state representation and the appropriate bosonic phase operator we develop the superconducting capacitor model in the presence of a voltage bias and a current bias. In so doing, the full Hamiltonian operator theory for a superconducting barrier is established.

Influence of the non-linearity of the collision operator on ion cyclotron resonance heating

The distribution function of ions heated in the ion cyclotron range of frequencies is obtained by solving the Fokker–Planck equation. For non-minority heating scenarios, the full non-linear Coulomb collision operator must be used in this equation. A method of resolution accounting for the complexity of this operator is presented. We consider a plasma immersed in a homogeneous magnetic field. The adopted method of resolution is based on an expansion of the distribution function in a series of Legendre polynomials. Results of the corresponding code non-linear Fokker–Planck in two-dimensional velocity space (NLFP-2D) are discussed for experimentally relevant JET-like parameters. The convergence of the Legendre expansion has been tested and the importance of the non-linear effects has been shown. Three different regimes, characterized by different modes of indirect ion heating and depending on the absorbed RF power density as well as the minority concentration, were identified. The NLFP-2D code has been used to study the validity of the Maxwellian approximation of the self-collision operator. One finds that this model is only correct in a very limited range of parameters, and leads mostly to an overestimation of the indirect ion heating.

Dsr‐Based Wave Equation 3‐D Prestack Depth Migration

AbstractStarting from the double square root (DSR) based wave equation, and based on the survey‐sinking concept and the perturbation theory, we introduce a prestack depth full migration operator and an approach to construct common imaging gathers (CIGs). Considering the azimuthal characteristics of 3‐D prestack data, three DSR migration operators for common azimuth sections, cross‐line common offset sections and common offset vector sections are developed respectively by the stationary phase method. Among them the cross‐line common offset migration is a theoretically new DSR‐based method. The theoretic analysis and examples on synthetic datasets prove that, the full migration operator and common azimuth migration operator have good performance in the case of strong velocity variation, while the other two operators work only when the velocity varies gentlely.

Beyond the long-wavelength approximation in electromagnetic Rydberg–Rydberg couplings

We give a method, to a great extent analytical, for calculating the high- n intrashell (Δ n=0) and intershell (Δ n≠0) Rydberg–Rydberg matrix elements of the full electric operator of the multipolar Hamiltonian for the atom – electromagnetic radiation interaction. Our method is an alternative to the recent approach of Komninos, Mercouris and Nicolaides [Phys. Rev. A 65 (2002) 043412] being predominantly a numerical one. Wherever a comparison has been possible, the two approaches are shown to give the same results. Within our approach we give a number of examples which should discourage the use of the electric-dipole approximation, and generally the long-wavelength approximation, in some problems of high- n Rydberg state physics.

The rovibrational levels of ammonia

In this paper we report variational rovibrational studies on ammonia and its isotopomers. We use six internal coordinates (one of which describes the umbrella motion). The expansion functions are products of one-dimensional functions of these internal coordinates, multiplied by appropriate functions of the Euler angles to describe the rotational motion. We use a previously published high accuracy six-dimensional potential energy surface [LEONARD, C., HANDY, N. C., CARTER, S., and BOWMAN, J. M., 2002, Spectrachim. Acta, 58, 825]. We derive the full kinetic energy operator for the rovibrational motion in these coordinates. This operator has been completely checked to give a hermitian secular matrix. All matrix elements are evaluated numerically by quadrature. The symmetry of the expansion functions is fully described in D3h, C2v and Cs. It is not possible to perform the calculations in D3h, but complete degeneracy in the appropriate levels is obtained with the C2v program. The algebraic complexity of this program has been far greater than for any other variational study we have undertaken for a tetra-atomic molecule. We present J = 0, 1, 2 energy levels for the experimentally observed band origins of NH3, and J = 0, 1 energy levels for the ground state and fundamentals of NH2D, ND2H and ND3. For the asymmetric isotopomers, identical results are obtained for both C2v and Cs, thus confirming the validity of the method. The levels we obtain are completely converged. Agreement with observation is of the order of 0.5% (of course being dependent upon the accuracy of the potential energy surface); therefore the ordering of the rotational levels and their splitting is completely predicted and understood.

The calculation of triple-differential cross sections of hydrogen atom single-io nization by electrons

A simple model is proposed to study the ionization of the atomic hydrogen by fast election impact in coplanar asymmetric geometry, making use of the post form of the enery shell transition matrix element and the two-potential formula. By virtue of dividing the full kinetic energy operator, we obtain an approximate solution of the three body problem through the canceling of the motion of two-election mass and exponent factor of relative motion and the approximation of projectile plane wave. TDCS(triple differential cross section) is expressed by the product of two factors,the structure factor T2 and correlation one T12. In this article, the contribution of these factors is investigated using the method of asymptotic series and method.

Limit of maximum entropy for the damped Jaynes Cummings model

Employing projection methods from kinetic theory, we study the non-Markovian quantum evolution of a two-level atom that is coupled to a single mode of the electromagnetic field. The interaction between the atom and field mode is described by the damped Jaynes–Cummings model. The general case is considered, in which dissipation is generated by both a photonic and an atomic reservoir of finite temperature. Only one special choice is made. The frequencies of the atom and field mode are in the same ratio as the temperatures of the atomic and the photonic reservoirs. Making use of Laplace transformation, we show that the atomic density matrix evolves to the state of maximum von Neumann entropy if the time, the cube of the initial electromagnetic energy density, the inverse of the photonic damping parameter and the inverse of the atomic damping parameter tend to infinity equally fast. We propose a large class of states from which the full density operator for the atom and field may start. This class includes entangled states. Expansion of the time-dependent exponential of the Laplace backtransform enables us to derive the limit of maximum entropy directly, without explicit evaluation of the atomic density matrix. We interchange limits and sums without proof, so our derivation is not entirely rigorous. Next, we remove the photonic reservoir. Then the damping process gets a sequential character. The field mode is assumed to start from a photon-number state. For the special choice of zero temperature and detuning we verify that the limit of maximum entropy survives the qualitative modification of the model. The only consequence is a slightly different scaling between the parameters that become large. Finally, we argue that our case study could be of value in finding out to what extent quantum dissipative processes obey the general principles of thermodynamics.

Local automorphisms of operator algebras on Banach spaces

In this paper we extend a result of Šemrl stating that every 2-local automorphism of the full operator algebra on a separable infinite dimensional Hilbert space is an automorphism. In fact, besides separable Hilbert spaces, we obtain the same conclusion for the much larger class of Banach spaces with Schauder bases. The proof rests on an analogous statement concerning the 2-local automorphisms of matrix algebras for which we present a short proof. The need to get such a proof was formulated in Šemrl’s paper.

Wavelets for multichannel signals

In this paper, we introduce and investigate multichannel wavelets, which are wavelets for vector fields, based on the concept of full rank subdivision operators. We prove that, like in the scalar and multiwavelet case, the existence of a scaling function with orthogonal integer translates guarantees the existence of a wavelet function, also with orthonormal integer translates. In this context, however, scaling functions as well as wavelets turn out to be matrix-valued functions.

Quantum electron transport beyond linear response

After a brief historical survey and summary of previous work involving the linear response theory (LRT) Hamiltonian, H= H( system)− AF( t), where the latter part refers to the effect of an applied field F( t) as in Kubo's theory, we deal with the nonlinear problem in which the applied electric field of arbitrary strength, as well as a possible magnetic field, are included in the system Hamiltonian, H= H[ system( E, B)]. In Part A of this study we deal with the general formalism on the many-body level. Projection operators are applied to the Von Neumann equation in the interaction picture, H( system)= H 0+ λV, which after the Van Hove limit, λ→0, t→∞, λ 2t finite, leads to the master equation for ∂ρ/ ∂t, containing both the Pauli–Van Hove diagonal part involving the transitions W γγ′ , and a nondiagonal quantum-interference part, as obtained by us previously. Likewise, the full many-body current operator J A is obtained by manipulation of the Heisenberg equation of motion for d A/d t in the interaction picture. The second division, Part B, concerns the quantum Boltzmann theory. Employing the formalism of second quantization ( c †,c fermion operators, a †,a boson operators) we obtain a general quantum Boltzmann equation for an electron gas in interaction with phonons or impurities in the adiabatic approximation (no phonon drag). On the ‘one-body’-level the current operator leads to a generalized Calecki form for arbitrary electric and magnetic fields. For extended states this transport equation yields the Boltzmann transport equation (BTE) for the Wigner occupancy function f( k, r, t) of a Fermi gas, thus furnishing a definitive proof, fully rooted in the quantum description, for Boltzmann's much criticized irreversible BTE of 1871. For localized states Titeica's foreseen ‘collisional current’ (1935) is established in terms of the matrix elements of the state-centers and the hopping probabilities w ζ ζ′ . Also, for the limiting case of small fields, |qE ΔR ζ ζ′ |⪡kT , our previous LRT results as well as the well-known results for the magneto-conductivity by Adams and Holstein and by Argyres and Roth, are recovered.