Non-diagonal Terms Research Articles

Multiple reference states and complete spectrum of the [formula omitted] Belavin model with open boundaries

The multiple reference state structure of the Z n Belavin model with non-diagonal boundary terms is discovered. It is found that there exist n reference states, each of them yields a set of eigenvalues and Bethe Ansatz equations of the transfer matrix. These n sets of eigenvalues together constitute the complete spectrum of the model. In the quasi-classic limit, they give the complete spectrum of the corresponding Gaudin model.

Identification of clearances and stability analysis for a rotor-journal bearing system

Abstract Significant wear occurs on the surface of bearings, which support rotating shafts for long periods of time. Therefore, the need for a new clearance identification method is required. Furthermore, having identified these new clearances, the investigation of gauging reliable future operation with regards to stability is also an important task. The rotor is modeled here using the finite element method with 4DOF’s per node, including the gyroscopic effect. The dynamic coefficients of the bearing are calculated by solving the Reynolds equation, thus obtaining the pressure distribution of the oil film, and by finding the equilibrium position. The 4 × 4 stiffness and damping matrices, including the force-moment and displacement-rotation relations with all non-diagonal coupling terms, are taken into account for the analysis. Here, an identification method for the bearing radial clearances is presented theoretically, using response measurements of the rotor at a particular point (usually the midpoint of the rotor). These “measurements” should be taken at two different speeds and from different wear effects. The present theoretical work on this particular problem needs to be verified experimentally as well. The sum of the squares of the differences between the measured and the computed responses at the abovementioned particular point and for two different speeds is used as an objective function to be minimized. The stability of the system as a function of the rotational speed and the wear is also examined.

Finite-size correction and bulk hole-excitations for special case of an open XXZ chain with nondiagonal boundary terms at roots of unity

Using our solution for the open spin-1/2 XXZ quantum spin chain with N spins and two arbitrary boundary parameters at roots of unity, the central charge and the conformal dimensions for bulk hole excitations are derived from the 1/N correction to the energy (Casimir energy).

On the second reference state and complete eigenstates of the open XXZ chain

The second reference state of the open XXZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz. In the quasi-classical limit, two sets of Bethe states give the complete eigenstates of the associated Gaudin model.

Spectrum of the supersymmetric [formula omitted] model with non-diagonal open boundaries

In this work we diagonalize the double-row transfer matrix of the supersymmetric t – J model with non-diagonal boundary terms by means of the algebraic Bethe ansatz. The corresponding reflection equations are studied and two distinct classes of solutions are found, one diagonal solution and other non-diagonal. Except for the case of two non-diagonal boundaries, the eigenvalues are given for arbitrary values of the boundary parameters.

Low-lying zeros of L-functions with orthogonal symmetry

We investigate the moments of a smooth counting function of the zeros near the central point of L-functions of weight k cuspidal newforms of prime level N. We split by the sign of the functional equations and show that for test functions whose Fourier transform is supported in (−1/n,1/n), as N→∞ the first n centered moments are Gaussian. By extending the support to (−1/(n−1),1/(n−1)), we see non-Gaussian behavior; in particular, the odd-centered moments are nonzero for such test functions. If we do not split by sign, we obtain Gaussian behavior for support in (−2/n,2/n) if 2k≥n. The nth-centered moments agree with random matrix theory in this extended range, providing additional support for the Katz-Sarnak conjectures. The proof requires calculating multidimensional integrals of the nondiagonal terms in the Bessel-Kloosterman expansion of the Petersson formula. We convert these multidimensional integrals to one-dimensional integrals already considered in the work of Iwaniec, Luo, and Sarnak [ILS] and derive a new and more tractable expression for the nth-centered moments for such test functions. This new formula facilitates comparisons between number theory and random matrix theory for test functions supported in (−1/(n−1),1/(n−1)) by simplifying the combinatorial arguments. As an application we obtain bounds for the percentage of such cusp forms with a given order of vanishing at the central point

SuSpect: A Fortran code for the Supersymmetric and Higgs particle spectrum in the MSSM

We present the Fortran code SuSpect version 2.3, which calculates the Supersymmetric and Higgs particle spectrum in the Minimal Supersymmetric Standard Model (MSSM). The calculation can be performed in constrained models with universal boundary conditions at high scales such as the gravity (mSUGRA), anomaly (AMSB) or gauge (GMSB) mediated supersymmetry breaking models, but also in the non-universal MSSM case with R-parity and CP conservation. Care has been taken to treat important features such as the renormalization group evolution of parameters between low and high energy scales, the consistent implementation of radiative electroweak symmetry breaking and the calculation of the physical masses of the Higgs bosons and supersymmetric particles taking into account the dominant radiative corrections. Some checks of important theoretical and experimental features, such as the absence of non-desired minima, large fine-tuning in the electroweak symmetry breaking condition, as well as agreement with precision measurements can be performed. The program is simple to use, self-contained and can easily be linked to other codes; it is rather fast and flexible, thus allowing scans of the parameter space with several possible options and choices for model assumptions and approximations. Program summary Title of program:SuSpect Catalogue identifier:ADYR_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYR_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:none Programming language used:FORTRAN 77 Computer:Unix machines, PC No. of lines in distributed program, including test data, etc.:21 821 No. of bytes in distributed program, including test data, etc.:249 657 Distribution format:tar.gz Operating system:Unix (or Linux) RAM:approximately 2500 Kbytes Number of processors used:1 processor Nature of problem: SuSpect calculates the supersymmetric and Higgs particle spectrum (masses and some other relevant parameters) in the unconstrained Minimal Supersymmetric Standard Model (MSSM), as well as in constrained models (cMSSMs) such as the minimal Supergravity (mSUGRA), the gauge mediated (GMSB) and anomaly mediated (AMSB) Supersymmetry breaking scenarii. The following features and ingredients are included: renormalization group evolution between low and high energy scales, consistent implementation of radiative electroweak symmetry breaking, calculation of the physical particle masses with radiative corrections at the one- and two-loop level. Solution method:The main methods used in the code are: (1) an (adaptative fourth-order) Runge–Kutta type algorithm (following a standard algorithm described in “Numerical Recipes”), used to solve numerically a set of coupled differential equations resulting from the renormalization group equations at the two-loop level of the perturbative expansions; (2) diagonalizations of mass matrices; (3) some mathematical (Spence, etc) functions resulting from the evaluation of one and two-loop integrals using the Feynman graphs techniques for radiative corrections to the particle masses; (4) finally, some fixed-point iterative algorithms to solve non-linear equations for some of the relevant output parameters. Restrictions:(1) The code is limited at the moment to real input parameters. (2) It also does not include flavor non-diagonal terms which are possible in the most general soft supersymmetry breaking Lagrangian. (3) There are some (mild) limitations on the possible range of values of input parameter, i.e. not any arbitrary values of some input parameters are allowed: these limitations are essentially based on physical rather than algorithmic issues, and warning flags and other protections are installed to avoid as much as possible execution failure if unappropriate input values are used. Running time:between 1 and 3 seconds depending on options, with a 1 GHz processor.

Boundary Energy of the Open XXZ Chain from New Exact Solutions

Bethe Ansatz solutions of the open spin-\(\frac{1}{2}\) integrable XXZ quantum spin chain at roots of unity with nondiagonal boundary terms containing two free boundary parameters have recently been proposed.We use these solutions to compute the boundary energy (surface energy) in the thermodynamic limit.

Electron Transport through Double Quantum Dots with Interdot Coulomb Repulsion

We consider electron tunnelling through double quantum dots (DQD) attached to external leads. Systems of quantum dots coupled in series and in parallel configuration are investigated. Tunnelling coupling between the two dots in series is described by V and it is treated as a tunable parameter A single dot in the system is described by the one-level Anderson Hamiltonian with infinite intradot Coulomb repulsion. Accordingly, only a single state on each dot can be expected and the double occupancy of each dot can be ignored. The interdot Coulomb interaction is taken into account and it is described via Hubbard-like term. Strong and weak correlation regimes are studied. Tunneling rates between the dots and reservoirs are assumed to be weak, so the Kondo effect is not observed in the system. The non-equilibrium Green function (GF) formalism is introduced to describe electron transport in the non-linear regime. The retarded r G and advanced a G GFs are calculated within the framework of the Hartree-Fock approximation with use of the equation of motion method. For a DQD system GFs are represented by 2 x 2 matrices. In the present approach diagonal and non-diagonal terms are taken into account and are calculated in a self-consistent way. Note, that for steady-state transport one does not need to find an appropriate formula for lesser GF < G itself (see Ref. [1]). Occupation numbers and electric current can be expressed by ( ) ∫ < e e d G and retarded (advanced) GF only. This approach allows us to omit

A novel perturbation expansion method for coupled system of acoustics and structures

We formulate a coupled vibration problem between a structure and an acoustic field in a mathematically rigorous fashion. A typical example of the structure is a car body that can be modeled by a cluster of thin plates. The problem leads to a nonstandard eigenvalue problem in a function space. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the nondiagonal coupling terms. A natural interpretation of this parameter is given. We represent an eigenpair for the coupled system by a perturbation series with respect to ε which enable us to express the eigenpair for the coupled case by those for the decoupled case. We prove that the series consists only of even order terms of ε. In some practical applications, by using this perturbation series, it would become unnecessary to perform time consuming computations to get coupled eigenvalues, and hence the present results obtained by the perturbation analysis might have considerable engineering importance. We confirm the adequacy of this perturbation analysis by investigating some numerical examples. The results are given for a two-dimensional coupled problem. Without loss of generality, the same operator theoretical approach applies to the eigenvalue problems of the coupled vibration problem in a more general three-dimensional acoustic region with a plate for a part of its boundary.

Formula omitted] relation and exact solution for the XYZ chain with general non-diagonal boundary terms

We propose that the Baxter's Q-operator for the quantum XYZ spin chain with open boundary conditions is given by the j → ∞ limit of the corresponding transfer matrix with spin- j (i.e., ( 2 j + 1 ) -dimensional) auxiliary space. The associated T – Q relation is derived from the fusion hierarchy of the model. We use this relation to determine the Bethe Ansatz solution of the eigenvalues of the fundamental transfer matrix. The solution yields the complete spectrum of the Hamiltonian.

Intramolecular Vibrational Energy Redistribution Involving the Torsion in CF3CH3: A Molecular Dynamics Study

Classical trajectory calculations on intramolecular vibrational energy redistribution (IVR) involving the torsion in 1,1,1-trifluoroethane (TFE) are reported. Two potential energy functions (PEFs) are used to describe the potential energy surface. The "full" PEF gives excellent agreement with the experimental vibrational frequencies. The "simple" PEF omits nondiagonal interaction terms, but still gives very good agreement with the experimental frequencies. The "simple" PEF is intended to minimize mode-mode coupling. Neither PEF includes the HF elimination reaction. Calculations are carried out both with nominal microcanonical selection of initial coordinates and momenta, and with a modified selection method that places controlled amounts of energy in the torsion. Total (classical) vibrational energies from 0.005 to 140 kcal mol(-1) are investigated. The calculated time constants describing energy flow out of the torsional mode are <10 ps for classical vibrational energies near the classical reaction threshold energy (approximately 75 kcal mol(-1)) and greater. It is found that the rate of decay from the torsion largely depends on the amount of energy in the other vibrational modes. Analysis using power spectra shows that the torsional mode in TFE is strongly coupled to the other vibrational modes. These results strongly suggest that vibrational energy in TFE will not be sequestered in the torsion for time periods greater than a few tens of picoseconds when the molecule has enough energy to react via HF elimination.

Spectral equivalences and symmetry breaking in integrableSUq(N) spin chains with boundaries

We consider the SUq(N) invariant spin chain with diagonal and non-diagonal integrable boundary terms.The algebraic study of spin chains with different kinds of boundary terms is used to motivate aset of spectral equivalences between integrable chains with purely diagonal boundary termsand ones with an arbitrary non-diagonal term at one end. For each choice of diagonalboundary terms there is an iso-spectral one-boundary problem and vice versa. The casesN = 2, 3, 4 are used as examples throughout to illustrate the general structure.The quantum group SUq(N) symmetry is broken by the presence of a non-diagonal boundary term; however, onecan use the spectral equivalence with the diagonal chain to easily understandthe residual symmetries of the system. This is described in detail for the case ofSU(3).

An improvement of the lattice theory of dislocation for a two-dimensional triangular crystal

The structure of dislocation in a two-dimensional triangular crystal has been studied theoretically on the basis of atomic interaction and lattice statics. The theory presented in this paper is an improvement to that published previously. Within a reasonable interaction approximation, a new dislocation equation is obtained, which remedies a fault existing in the lattice theory of dislocation. A better simplification of non-diagonal terms of the kernel is given. The solution of the new dislocation equation asymptotically becomes the same as that obtained in the elastic theory and agrees with experimental data. It is found that the solution is formally identical with that proposed phenomenologically by Foreman et al, where the parameter can be chosen freely, but cannot uniquely determined from theory. Indeed, if the parameter in the expression of the solution is selected suitably, the expression can be well applied to describe the fine structure of the dislocation.

Brillouin light scattering investigation of magnetostatic modes in symmetric and asymmetricNiFe∕Cu∕NiFetrilayered wires

The peculiarities of magnetostatic resonances of trilayered wires ($700\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ wide) consisting of two ferromagnetic permalloy layers, coupled by dipolar interaction across a nonmagnetic Cu spacer, have been comprehensively studied both experimentally and theoretically. Both a symmetric structure, $\mathrm{Ni}\mathrm{Fe}(30\phantom{\rule{0.3em}{0ex}}\mathrm{nm})∕\mathrm{Cu}(10\phantom{\rule{0.3em}{0ex}}\mathrm{nm})∕\mathrm{Ni}\mathrm{Fe}(30\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$, and an asymmetric one, $\mathrm{Ni}\mathrm{Fe}(10\phantom{\rule{0.3em}{0ex}}\mathrm{nm})∕\mathrm{Cu}(10\phantom{\rule{0.3em}{0ex}}\mathrm{nm})∕\mathrm{Ni}\mathrm{Fe}(30\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$, were analyzed. Brillouin light scattering (BLS) from thermally excited spin waves, has been performed as a function of the incidence angle of light and of the intensity of the external applied field. A number of discrete peaks, corresponding to the resonant frequencies of the trilayered structures have been observed in BLS spectra. To achieve a satisfactory interpretation of the experimental results, substantial improvements of previous theoretical models were necessary. In this case, in fact, due to the rather large value of the ferromagnetic layers thickness, the dipole interaction between magnetic layers associated with the nondiagonal terms of the tensorial Green's functions (describing a dynamic dipolar magnetic field induced by one magnetic layer in the other one) gives significant contributions to the resonant frequencies.

Modification of electron-hole excitations for a quantum well embedded in an asymmetric dielectric structure

Starting from the conventional quantum electrodynamical formulation in Coulomb gauge we show that the Coulomb interaction of an electronhole in a quantum well (QW) embedded in an asymmetric dielectric structure with different dielectric constants in barrier regions yields a nondiagonal term of electron-hole pair excitation and the electron-hole vacuum state cannot be longer than the ground state of the system. A Bogoliubov transformation with a representation of new quasiparticles is provided to eliminate the nondiagonal term. The linear response function describing the modified exciton-polariton effect of the system is obtained. Analytical expressions are found for the effective mass of quasiparticles, the modified band gap, and the exciton coupling potential for a quasi-electron-hole pair. The exciton-polariton coupling turns out to contain an additional term originating from intraband processes. It is shown that the effect is significant for QW's with small thicknesses and for semiconductors with narrow band gaps.

Addendum to Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms

Addendum to Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms

A Study of Raman Excitation Profiles for Soluble cis-Polyacetylene

A quantitative analysis of the Raman excitation profiles (REPs) for soluble cis-polyacetylene, cis-(CH)x, in toluene observed by Sassi et al. was undertaken. This analysis took two approaches, namely improved vibronic interaction theory and resonance-Raman scattering theory for solute molecules coupled homogeneously and strongly to a continuum of environmental nuclear modes. For the former theory, a ‘static’ approach, the effect of inhomogeneous environmental broadening of REPs of a solute molecule due to the solvent–molecule interactions was investigated as well as the role of diagonal and non-diagonal terms of the scattering matrix. For the latter theory, a ‘dynamic’ approach which rests on vibrational density matrices including both molecular and solvent modes in the ground and excited electronic states, the solvent effects are regarded as dynamic and homogeneous. The values of the equilibrium coordinate shifts for the Raman-active mode and the homogeneous and inhomogeneous broadening parameters derived from the REPs by both approaches are compared with theoretical results of previous studies of soluble and of solid cis- and trans-(CH)x.

Bethe ansatz solution of the open XXZ chain with nondiagonal boundary terms

We consider the integrable open XX quantum spin chain with non-diagonal boundary terms. We derive an exact inversion identity, by which we obtain the eigenvalues of the transfer matrix and the Bethe ansatz equations. For generic values of the boundary parameters, the Bethe ansatz solution is formulated in terms of the Jacobian elliptic functions.

The practice of Delta–Gamma VaR: Implementing the quadratic portfolio model

This paper intends to critically evaluate state-of-the-art methodologies for calculating the value-at-risk (VaR) of non-linear portfolios from the point of view of computational accuracy and efficiency. We focus on the quadratic portfolio model, also known as “Delta–Gamma”, and, as a working assumption, we model risk factor returns as multi-normal random variables. We present the main approaches to Delta–Gamma VaR weighing their merits and accuracy from an implementation-oriented standpoint. One of our main conclusions is that the Delta–Gamma-Normal VaR may be less accurate than even Delta VaR. On the other hand, we show that methods that essentially take into account the non-linearity (hence gammas and third or higher moments) of the portfolio values may present significant advantages over full Monte Carlo revaluations. The role of non-diagonal terms in the Gamma matrix as well as the sensitivity to correlation is considered both for accuracy and computational effort. We also qualitatively examine the robustness of Delta–Gamma methodologies by considering a highly non-quadratic portfolio value function.