WorldWideScience

Sample records for eigenfunctions

  1. Generation of genealogical spin eigenfunctions

    International Nuclear Information System (INIS)

    Grabenstetter, J.E.; Tseng, T.J.; Grein, F.

    1976-01-01

    A method is given for generating the Yamanouchi-Kotani genealogical spin eigenfunctions which requires neither storage of eigenfunctions for smaller numbers of electrons, nor summations of large order, nor explicit use of results from the theory of representations of the symmetric group. An explicit formula is given for the coefficients of expansion in terms of spin products

  2. Monte Carlo eigenfunction strategies and uncertainties

    International Nuclear Information System (INIS)

    Gast, R.C.; Candelore, N.R.

    1974-01-01

    Comparisons of convergence rates for several possible eigenfunction source strategies led to the selection of the ''straight'' analog of the analytic power method as the source strategy for Monte Carlo eigenfunction calculations. To insure a fair game strategy, the number of histories per iteration increases with increasing iteration number. The estimate of eigenfunction uncertainty is obtained from a modification of a proposal by D. B. MacMillan and involves only estimates of the usual purely statistical component of uncertainty and a serial correlation coefficient of lag one. 14 references. (U.S.)

  3. Eigenfunctions in chaotic quantum systems

    Energy Technology Data Exchange (ETDEWEB)

    Baecker, Arnd

    2007-07-01

    The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)

  4. Eigenfunctions in chaotic quantum systems

    International Nuclear Information System (INIS)

    Baecker, Arnd

    2007-01-01

    The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)

  5. Vertical motion and ''scarred'' eigenfunctions in the stadium billiard

    International Nuclear Information System (INIS)

    Christoffel, K.M.; Brumer, P.

    1985-01-01

    A subset of pseudoregular eigenfunctions of the classically chaotic stadium billiard is shown to participate strongly in vertically directed motion, supporting the conjectures of McDonald and of Heller regarding periodic orbits and pseudoregular eigenfunctions

  6. Eigenfunction statistics of Wishart Brownian ensembles

    International Nuclear Information System (INIS)

    Shukla, Pragya

    2017-01-01

    We theoretically analyze the eigenfunction fluctuation measures for a Hermitian ensemble which appears as an intermediate state of the perturbation of a stationary ensemble by another stationary ensemble of Wishart (Laguerre) type. Similar to the perturbation by a Gaussian stationary ensemble, the measures undergo a diffusive dynamics in terms of the perturbation parameter but the energy-dependence of the fluctuations is different in the two cases. This may have important consequences for the eigenfunction dynamics as well as phase transition studies in many areas of complexity where Brownian ensembles appear. (paper)

  7. Dynamical eigenfunction decomposition of turbulent channel flow

    Science.gov (United States)

    Ball, K. S.; Sirovich, L.; Keefe, L. R.

    1991-01-01

    The results of an analysis of low-Reynolds-number turbulent channel flow based on the Karhunen-Loeve (K-L) expansion are presented. The turbulent flow field is generated by a direct numerical simulation of the Navier-Stokes equations at a Reynolds number Re(tau) = 80 (based on the wall shear velocity and channel half-width). The K-L procedure is then applied to determine the eigenvalues and eigenfunctions for this flow. The random coefficients of the K-L expansion are subsequently found by projecting the numerical flow field onto these eigenfunctions. The resulting expansion captures 90 percent of the turbulent energy with significantly fewer modes than the original trigonometric expansion. The eigenfunctions, which appear either as rolls or shearing motions, possess viscous boundary layers at the walls and are much richer in harmonics than the original basis functions.

  8. Modified Poisson eigenfunctions for electrostatic Bernstein--Greene--Kruskal equilibria

    International Nuclear Information System (INIS)

    Ling, K.; Abraham-Shrauner, B.

    1981-01-01

    The stability of an electrostatic Bernstein--Greene--Kruskal equilibrium by Lewis and Symon's general linear stability analysis for spatially inhomogeneous Vlasov equilibria, which employs eigenfunctions and eigenvalues of the equilibrium Liouville operator and the modified Poisson operator, is considered. Analytic expressions for the Liouville eigenfuctions and eigenvalues have already been given; approximate analytic expressions for the dominant eigenfunction and eigenvalue of the modified Poisson operator are given. In the kinetic limit three methods are given: (i) the perturbation method, (ii) the Rayleigh--Ritz method, and (iii) a method based on a Hill's equation. In the fluid limit the Rayleigh--Ritz method is used. The dominant eigenfunction and eigenvalue are then substituted in the dispersion relation and the growth rate calculated. The growth rate agrees very well with previous results found by numerical simulation and by modified Poisson eigenfunctions calculated numerically

  9. Eigenfunction expansion for fractional Brownian motions

    International Nuclear Information System (INIS)

    Maccone, C.

    1981-01-01

    The fractional Brownian motions, a class of nonstationary stochastic processes defined as the Riemann-Liouville fractional integral/derivative of the Brownian motion, are studied. It is shown that these processes can be regarded as the output of a suitable linear system of which the input is the white noise. Their autocorrelation is then derived with a study of their standard-deviation curves. Their power spectra are found by resorting to the nonstationary spectral theory. And finally their eigenfunction expansion (Karhunen-Loeve expansion) is obtained: the eigenfunctions are proved to be suitable Bessel functions and the eigenvalues zeros of the Bessel functions. (author)

  10. Stability analysis of the Peregrine solution via squared eigenfunctions

    Science.gov (United States)

    Schober, C. M.; Strawn, M.

    2017-10-01

    A preliminary numerical investigation involving ensembles of perturbed initial data for the Peregrine soliton (the lowest order rational solution of the nonlinear Schrödinger equation) indicates that it is unstable [16]. In this paper we analytically investigate the linear stability of the Peregrine soliton, appealing to the fact that the Peregrine solution can be viewed as the singular limit of a single mode spatially periodic breathers (SPB). The "squared eigenfunction" connection between the Zakharov-Shabat (Z-S) system and the linearized NLS equation is employed in the stability analysis. Specifically, we determine the eigenfunctions of the Z-S system associated with the Peregrine soliton and construct a family of solutions of the associated linearized NLS (about the Peregrine) in terms of quadratic products of components of the eigenfunctions (i.e., the squared eigenfunction). We find there exist solutions of the linearization that grow exponentially in time, thus showing the Peregrine soliton is linearly unstable.

  11. From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport

    International Nuclear Information System (INIS)

    Ganapol, B.D.

    2001-01-01

    A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm

  12. Eigenfunction statistics on quantum graphs

    International Nuclear Information System (INIS)

    Gnutzmann, S.; Keating, J.P.; Piotet, F.

    2010-01-01

    We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.

  13. Anderson localization and ballooning eigenfunctions

    International Nuclear Information System (INIS)

    Dewar, R.L.; Cuthbert, P.

    1999-01-01

    In solving the ballooning eigenvalue for a low-aspect-ratio stellarator equilibrium it is found that the quasiperiodic behaviour of the equilibrium quantities along a typical magnetic field line can lead to localization of the ballooning eigenfunction (Anderson localization) even in the limit of zero shear. This localization leads to strong field-line dependence of the ballooning eigenvalue, with different branches attaining their maximum growth rates on different field lines. A method is presented of estimating the field-line dependence of various eigenvalue branches by using toroidal and poloidal symmetry operations on the shear-free ballooning equation to generate an approximate set of eigenfunctions. These zero-shear predictions are compared with accurate numerical solutions for the H-1 Heliac and are shown to give a qualitatively correct picture, but finite shear corrections will be needed to give quantitative predictions

  14. A simple eigenfunction convergence acceleration method for Monte Carlo

    International Nuclear Information System (INIS)

    Booth, Thomas E.

    2011-01-01

    Monte Carlo transport codes typically use a power iteration method to obtain the fundamental eigenfunction. The standard convergence rate for the power iteration method is the ratio of the first two eigenvalues, that is, k_2/k_1. Modifications to the power method have accelerated the convergence by explicitly calculating the subdominant eigenfunctions as well as the fundamental. Calculating the subdominant eigenfunctions requires using particles of negative and positive weights and appropriately canceling the negative and positive weight particles. Incorporating both negative weights and a ± weight cancellation requires a significant change to current transport codes. This paper presents an alternative convergence acceleration method that does not require modifying the transport codes to deal with the problems associated with tracking and cancelling particles of ± weights. Instead, only positive weights are used in the acceleration method. (author)

  15. Lax-pair operators for squared-sum and squared-difference eigenfunctions

    International Nuclear Information System (INIS)

    Ichikawa, Yoshihiko; Iino, Kazuhiro.

    1984-10-01

    Inter-relationship between various representations of the inverse scattering transformation is established by examining eigenfunctions of Lax-pair operators of the sine-Gordon equation and the modified Korteweg-de Vries equation. In particular, it is shown explicitly that there exists Lax-pair operators for the squared-sum and squared-difference eigenfunctions of the Ablowitz-Kaup-Newell-Segur inverse scattering transformation. (author)

  16. Quantum Ergodicity and L p Norms of Restrictions of Eigenfunctions

    Science.gov (United States)

    Hezari, Hamid

    2018-02-01

    We prove an analogue of Sogge's local L p estimates for L p norms of restrictions of eigenfunctions to submanifolds, and use it to show that for quantum ergodic eigenfunctions one can get improvements of the results of Burq-Gérard-Tzvetkov, Hu, and Chen-Sogge. The improvements are logarithmic on negatively curved manifolds (without boundary) and by o(1) for manifolds (with or without boundary) with ergodic geodesic flows. In the case of ergodic billiards with piecewise smooth boundary, we get o(1) improvements on L^∞ estimates of Cauchy data away from a shrinking neighborhood of the corners, and as a result using the methods of Ghosh et al., Jung and Zelditch, Jung and Zelditch, we get that the number of nodal domains of 2-dimensional ergodic billiards tends to infinity as λ \\to ∞. These results work only for a full density subsequence of any given orthonormal basis of eigenfunctions. We also present an extension of the L p estimates of Burq-Gérard-Tzvetkov, Hu, Chen-Sogge for the restrictions of Dirichlet and Neumann eigenfunctions to compact submanifolds of the interior of manifolds with piecewise smooth boundary. This part does not assume ergodicity on the manifolds.

  17. Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete Symmetries

    Directory of Open Access Journals (Sweden)

    Renato Lemus

    2012-11-01

    Full Text Available The eigenfunction approach used for discrete symmetries is deduced from the concept of quantum numbers. We show that the irreducible representations (irreps associated with the eigenfunctions are indeed a shorthand notation for the set of eigenvalues of the class operators (character table. The need of a canonical chain of groups to establish a complete set of commuting operators is emphasized. This analysis allows us to establish in natural form the connection between the quantum numbers and the eigenfunction method proposed by J.Q. Chen to obtain symmetry adapted functions. We then proceed to present a friendly version of the eigenfunction method to project functions.

  18. Lax-pair operators for squared eigenfunctions in the inverse scattering transformations

    International Nuclear Information System (INIS)

    Iino, Kazuhiro; Ichikawa, Yoshihiko.

    1982-05-01

    Modification of the algorithm of Chen, Lee and Liu enables us to construct alternative Lax-pair operators for the Korteweg-de Vries equation and the modified Korteweg-de Vries equation. These Lax-pair operators stand as the Lax-pair operators for the squared eigenfunction and the sum of squared eigenfunctions of the Ablowitz-Kaup-Newell-Segur inverse scattering transformation for these celebrated nonlinear evolution equations. (author)

  19. Eigenfunctions of the continuous spectrum of a two-dimensional periodic optical waveguide

    International Nuclear Information System (INIS)

    Derguzov, V.I.

    1986-01-01

    One proves the existence of the eigenfunctions of the continuous spectrum of a two-dimensional periodic optical waveguide. One gives a normalization of the eigenfunctions of the continuous spectrum relative to an indefinite inner product. One defines the concept of the genus of the multipliers of a Hamiltonian equation, corresponding to the continuous spectrum of the optical waveguide

  20. Eigenfunction expansions and scattering theory in rigged Hilbert spaces

    Energy Technology Data Exchange (ETDEWEB)

    Gomez-Cubillo, F [Dpt. de Analisis Matematico, Universidad de Valladolid. Facultad de Ciencias, 47011 Valladolid (Spain)], E-mail: fgcubill@am.uva.es

    2008-08-15

    The work reviews some mathematical aspects of spectral properties, eigenfunction expansions and scattering theory in rigged Hilbert spaces, laying emphasis on Lippmann-Schwinger equations and Schroedinger operators.

  1. Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model

    CERN Document Server

    Desrosiers, P; Mathieu, P; Desrosiers, Patrick; Lapointe, Luc; Mathieu, Pierre

    2003-01-01

    We present two constructions of the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement. These eigenfunctions are the superspace extension of the generalized Hermite (or Hi-Jack) polynomials. The conserved quantities of the rational supersymmetric model are first related to their trigonometric relatives through a similarity transformation. This leads to a simple expression for the generalized Hermite superpolynomials as a differential operator acting on the corresponding Jack superpolynomials. The second construction relies on the action of the Hamiltonian on the supermonomial basis. This translates into determinantal expressions for the Hamiltonian's eigenfunctions. As an aside, the maximal superintegrability of the supersymmetric rational Calogero-Moser-Sutherland model is demonstrated.

  2. Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

    International Nuclear Information System (INIS)

    Rabinovich, Vladimir S; Roch, Steffen

    2009-01-01

    This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z n which are discrete analogs of the Schroedinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of pseudodifference operators (i.e., pseudodifferential operators on the group Z n with analytic symbols), and the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schroedinger operators on Z n , Dirac operators on Z 3 and square root Klein-Gordon operators on Z n .

  3. Jordan blocks and Gamow-Jordan eigenfunctions associated to a double pole of the S-matrix

    International Nuclear Information System (INIS)

    Hernandez, E.; Mondragon, A.; Jauregui, A.

    2002-01-01

    An accidental degeneracy of resonances gives rise to a double pole in the scattering matrix, a double zero in the Jost function and a Jordan chain of length two of generalized Gamow-Jordan eigenfunctions of the radial Schrodinger equation. The generalized Gamow-Jordan eigenfunctions are basis elements of an expansion in bound and resonant energy eigenfunctions plus a continuum of scattering wave functions ol complex wave number. In this bi orthonormal basis, any operator f (H r (l) which is a regular function of the Hamiltonian is represented by a complex matrix which is diagonal except for a Jordan block of rank two. The occurrence of a double pole in the Green's function, as well as the non-exponential time evolution of the Gamow-Jordan generalized eigenfunctions are associated to the Jordan block in the complex energy representation. (Author)

  4. Computation of mode eigenfunctions in graded-index optical fibers by the propagating beam method

    International Nuclear Information System (INIS)

    Feit, M.D.; Fleck, J.A. Jr.

    1980-01-01

    The propagating beam method utilizes discrete Fourier transforms for generating configuration-space solutions to optical waveguide problems without reference to modes. The propagating beam method can also give a complete description of the field in terms of modes by a Fourier analysis with respect to axial distance of the computed fields. Earlier work dealt with the accurate determination of mode propagation constants and group delays. In this paper the method is extended to the computation of mode eigenfunctions. The method is efficient, allowing generation of a large number of eigenfunctions from a single propagation run. Computations for parabolic-index profiles show excellent agreement between analytic and numerically generated eigenfunctions

  5. An Explicit Formula for Symmetric Polynomials Related to the Eigenfunctions of Calogero-Sutherland Models

    Directory of Open Access Journals (Sweden)

    Martin Hallnäs

    2007-03-01

    Full Text Available We review a recent construction of an explicit analytic series representation for symmetric polynomials which up to a groundstate factor are eigenfunctions of Calogero-Sutherland type models. We also indicate a generalisation of this result to polynomials which give the eigenfunctions of so-called 'deformed' Calogero-Sutherland type models.

  6. A new formulation for the eigenvalue and the eigenfunction in the perturbation theory

    International Nuclear Information System (INIS)

    Korek, Mahmoud

    1999-01-01

    Full text.In infrared transitions, the problem of the ro vibrational eigenvalue and eigenfunction of a diatomic molecule is considered. It is shown that, for the transitions vJ↔v'J' the eigenvalues and the eigenfunctions of the two considered states can be expressed respectively in terms of one variable m (transition number), relating these two states, as E vm =Σ i=o e v (i) m i , Ψ vm =Σ i=0 φ v (i) m i and E v'm =Σ i=0 e v' (i) m i , Ψ v'm =Σ i=0 φ v' (i) m i , where m=[J'(J'+1)-J(J+1)]/2, and the coefficients e v (i) , φ v (i) , e v (i) , and φ v (i) , are given by analytical expressions. This m-representation of the eigenvalues and the eigenfunctions is more advantageous for the calculation of many factors in spectroscopy that are given in terms of m as the line intensities, the wave number of a transition, the Herman-Wallis coefficients,...etc. The numerical application to the ground state of the molecule CO shows that the present formulation provides a simple and accurate method for the calculation of the eigenvalues and the eigenfunctions for the two considered states

  7. Ground eigenvalue and eigenfunction of a spin-weighted spheroidal wave equation in low frequencies

    Institute of Scientific and Technical Information of China (English)

    Tang Wen-Lin; Tian Gui-Hua

    2011-01-01

    Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.

  8. Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation.

    Science.gov (United States)

    Marcotte, Christopher D; Grigoriev, Roman O

    2016-09-01

    This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.

  9. Eigenfunction statistics for Anderson model with Hölder continuous ...

    Indian Academy of Sciences (India)

    We consider random Schrödinger operators on l 2 ( Z d ) with α -Hölder continuous ( 0 < α ≤ 1 ) single site distribution. In localized regime, we study the distribution of eigenfunctions in space and energy simultaneously. In a certain scaling limit, we prove limit points are Poisson.

  10. Analytic families of eigenfunctions on a reductive symmetric space

    NARCIS (Netherlands)

    Ban, E.P. van den; Schlichtkrull, H.

    2000-01-01

    In harmonic analysis on a reductive symmetric space X an important role is played by families of generalized eigenfunctions for the algebra D (X) of invariant dierential operators. Such families arise for instance as matrix coeÆcients of representations that come in series, such as the (generalized)

  11. Measurements of the eigenfunction of reversed shear Alfvén eigenmodes that sweep downward in frequency

    International Nuclear Information System (INIS)

    Heidbrink, W. W.; Austin, M. E.; Spong, D. A.; Tobias, B. J.; Van Zeeland, M. A.

    2013-01-01

    Reversed shear Alfvén eigenmodes (RSAEs) usually sweep upward in frequency when the minimum value of the safety factor q min decreases in time. On rare occasions, RSAEs sweep downward prior to the upward sweep. Electron cyclotron emission measurements show that the radial eigenfunction during the downsweeping phase is similar to the eigenfunction of normal, upsweeping RSAEs

  12. Quantum and classical eigenfunctions in Calogero and Sutherland systems

    International Nuclear Information System (INIS)

    Loris, I; Sasaki, R

    2004-01-01

    An interesting observation was reported by Corrigan-Sasaki that all the frequencies of small oscillations around equilibrium are 'quantized' for Calogero and Sutherland (CS) systems, typical integrable multi-particle dynamics. We present an analytic proof by applying recent results. Explicit forms of 'classical' and quantum eigenfunctions are presented for CS systems based on any root system

  13. The Geometry of the Semiclassical Wave Front Set for Schrödinger Eigenfunctions on the Torus

    Energy Technology Data Exchange (ETDEWEB)

    Cardin, Franco, E-mail: cardin@math.unipd.it; Zanelli, Lorenzo, E-mail: lzanelli@math.unipd.it [University of Padova, Department of Mathematics “Tullio Levi Civita” (Italy)

    2017-06-15

    This paper deals with the phase space analysis for a family of Schrödinger eigenfunctions ψ{sub ℏ} on the flat torus #Mathematical Double-Struck Capital T#{sup n} = (ℝ/2πℤ){sup n} by the semiclassical Wave Front Set. We study those ψ{sub ℏ} such that WF{sub ℏ}(ψ{sub ℏ}) is contained in the graph of the gradient of some viscosity solutions of the Hamilton-Jacobi equation. It turns out that the semiclassical Wave Front Set of such Schrödinger eigenfunctions is stable under viscous perturbations of Mean Field Game kind. These results provide a further viewpoint, and in a wider setting, of the link between the smooth invariant tori of Liouville integrable Hamiltonian systems and the semiclassical localization of Schrödinger eigenfunctions on the torus.

  14. The extended-domain-eigenfunction method for solving elliptic boundary value problems with annular domains

    Energy Technology Data Exchange (ETDEWEB)

    Aarao, J; Bradshaw-Hajek, B H; Miklavcic, S J; Ward, D A, E-mail: Stan.Miklavcic@unisa.edu.a [School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095 (Australia)

    2010-05-07

    Standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely, if ever, obtainable. In this paper, we propose a solution technique wherein we embed the original domain into one with simple boundaries where the classical eigenfunction solution approach can be used. The solution in the larger domain, when restricted to the original domain, is then the solution of the original boundary value problem. We call this the extended-domain-eigenfunction method. To illustrate the method's strength and scope, we apply it to Laplace's equation on an annular-like domain.

  15. Laser modes as an eigenfunction of an operator equation

    International Nuclear Information System (INIS)

    Ripper, J.E.; Campos, M.D.; Pudensi, M.A.A.

    A new method is proposed of arriving to an approximate solution into mode problems which cannot be treated by the traditional methods. Basically the idea is to treat the laser mode as an eigenfunction of an operator equation so that the mathematical methods developed to treat the wave equations in quantum mechanics can be used as tools to solve the equation. (L.C.) [pt

  16. Generation of coherent states of photon-added type via pathway of eigenfunctions

    International Nuclear Information System (INIS)

    Gorska, K; Penson, K A; Duchamp, G H E

    2010-01-01

    We obtain and investigate the regular eigenfunctions of simple differential operators x r d r+1 /dx r+1 , r = 1, 2, ..., with the eigenvalues equal to 1. With the help of these eigenfunctions, we construct a non-unitary analogue of a boson displacement operator which will be acting on the vacuum. In this way, we generate collective quantum states of the Fock space which are normalized and equipped with the resolution of unity with the positive weight functions that we obtain explicitly. These states are thus coherent states in the sense of Klauder. They span the truncated Fock space without first r lowest-lying basis states: |0), |1), ..., |r - 1). These states are squeezed, sub-Poissonian in nature and reminiscent of photon-added states in Agarwal and Tara (1991 Phys. Rev. A 43 492).

  17. Rotational Parameters from Vibronic Eigenfunctions of Jahn-Teller Active Molecules

    Science.gov (United States)

    Garner, Scott M.; Miller, Terry A.

    2017-06-01

    The structure in rotational spectra of many free radical molecules is complicated by Jahn-Teller distortions. Understanding the magnitudes of these distortions is vital to determining the equilibrium geometric structure and details of potential energy surfaces predicted from electronic structure calculations. For example, in the recently studied {\\widetilde{A}^2E^{''} } state of the NO_3 radical, the magnitudes of distortions are yet to be well understood as results from experimental spectroscopic studies of its vibrational and rotational structure disagree with results from electronic structure calculations of the potential energy surface. By fitting either vibrationally resolved spectra or vibronic levels determined by a calculated potential energy surface, we obtain vibronic eigenfunctions for the system as linear combinations of basis functions from products of harmonic oscillators and the degenerate components of the electronic state. Using these vibronic eigenfunctions we are able to predict parameters in the rotational Hamiltonian such as the Watson Jahn-Teller distortion term, h_1, and compare with the results from the analysis of rotational experiments.

  18. Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

    Institute of Scientific and Technical Information of China (English)

    Tang Wen-Lin; Tian Gui-Hua

    2011-01-01

    The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.

  19. Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering

    Science.gov (United States)

    Pelinovsky, Dmitry E.; Sulem, Catherine

    A complete set of eigenfunctions is introduced within the Riemann-Hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations. In particular, we consider the time-independent and time-dependent Schrödinger problems which are related to the KdV and KPI equations possessing solitons and lumps, respectively. Non-standard scalar products, orthogonality and completeness relations are derived for these problems. The complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations. We classify two different types of bifurcations of new eigenvalues and analyze their characteristic features. One type corresponds to thresholdless generation of solitons in the KdV equation, while the other predicts a threshold for generation of lumps in the KPI equation.

  20. Numerical Aspects of Eigenvalue and Eigenfunction Computations for Chaotic Quantum Systems

    Science.gov (United States)

    Bäcker, A.

    Summary: We give an introduction to some of the numerical aspects in quantum chaos. The classical dynamics of two-dimensional area-preserving maps on the torus is illustrated using the standard map and a perturbed cat map. The quantization of area-preserving maps given by their generating function is discussed and for the computation of the eigenvalues a computer program in Python is presented. We illustrate the eigenvalue distribution for two types of perturbed cat maps, one leading to COE and the other to CUE statistics. For the eigenfunctions of quantum maps we study the distribution of the eigenvectors and compare them with the corresponding random matrix distributions. The Husimi representation allows for a direct comparison of the localization of the eigenstates in phase space with the corresponding classical structures. Examples for a perturbed cat map and the standard map with different parameters are shown. Billiard systems and the corresponding quantum billiards are another important class of systems (which are also relevant to applications, for example in mesoscopic physics). We provide a detailed exposition of the boundary integral method, which is one important method to determine the eigenvalues and eigenfunctions of the Helmholtz equation. We discuss several methods to determine the eigenvalues from the Fredholm equation and illustrate them for the stadium billiard. The occurrence of spurious solutions is discussed in detail and illustrated for the circular billiard, the stadium billiard, and the annular sector billiard. We emphasize the role of the normal derivative function to compute the normalization of eigenfunctions, momentum representations or autocorrelation functions in a very efficient and direct way. Some examples for these quantities are given and discussed.

  1. Classical limit for quantum mechanical energy eigenfunctions

    International Nuclear Information System (INIS)

    Sen, D.; Sengupta, S.

    2004-01-01

    The classical limit problem is discussed for the quantum mechanical energy eigenfunctions using the Wentzel-Kramers-Brillouin approximation, free from the problem at the classical turning points. A proper perspective of the whole issue is sought to appreciate the significance of the discussion. It is observed that for bound states in arbitrary potential, appropriate limiting condition is definable in terms of a dimensionless classical limit parameter leading smoothly to all observable classical results. Most important results are the emergence of classical phase space, keeping the observable distribution functions non-zero only within the so-called classical region at the limit point and resolution of some well-known paradoxes. (author)

  2. Commensurability effects in one-dimensional Anderson localization: Anomalies in eigenfunction statistics

    International Nuclear Information System (INIS)

    Kravtsov, V.E.; Yudson, V.I.

    2011-01-01

    Highlights: → Statistics of normalized eigenfunctions in one-dimensional Anderson localization at E = 0 is studied. → Moments of inverse participation ratio are calculated. → Equation for generating function is derived at E = 0. → An exact solution for generating function at E = 0 is obtained. → Relation of the generating function to the phase distribution function is established. - Abstract: The one-dimensional (1d) Anderson model (AM), i.e. a tight-binding chain with random uncorrelated on-site energies, has statistical anomalies at any rational point f=(2a)/(λ E ) , where a is the lattice constant and λ E is the de Broglie wavelength. We develop a regular approach to anomalous statistics of normalized eigenfunctions ψ(r) at such commensurability points. The approach is based on an exact integral transfer-matrix equation for a generating function Φ r (u, φ) (u and φ have a meaning of the squared amplitude and phase of eigenfunctions, r is the position of the observation point). This generating function can be used to compute local statistics of eigenfunctions of 1d AM at any disorder and to address the problem of higher-order anomalies at f=p/q with q > 2. The descender of the generating function P r (φ)≡Φ r (u=0,φ) is shown to be the distribution function of phase which determines the Lyapunov exponent and the local density of states. In the leading order in the small disorder we derived a second-order partial differential equation for the r-independent ('zero-mode') component Φ(u, φ) at the E = 0 (f=1/2 ) anomaly. This equation is nonseparable in variables u and φ. Yet, we show that due to a hidden symmetry, it is integrable and we construct an exact solution for Φ(u, φ) explicitly in quadratures. Using this solution we computed moments I m = N 2m > (m ≥ 1) for a chain of the length N → ∞ and found an essential difference between their m-behavior in the center-of-band anomaly and for energies outside this anomaly. Outside the

  3. Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.

    Science.gov (United States)

    Bardhan, Jaydeep P; Knepley, Matthew G; Brune, Peter

    2015-01-01

    In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson-Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.

  4. Quadratic Forms and Semiclassical Eigenfunction Hypothesis for Flat Tori

    Science.gov (United States)

    T. Sardari, Naser

    2018-03-01

    Let Q( X) be any integral primitive positive definite quadratic form in k variables, where {k≥4}, and discriminant D. For any integer n, we give an upper bound on the number of integral solutions of Q( X) = n in terms of n, k, and D. As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus {T^d} for {d≥ 5}. This conjecture is motivated by the work of Berry [2,3] on the semiclassical eigenfunction hypothesis.

  5. An eigenfunction method for reconstruction of large-scale and high-contrast objects.

    Science.gov (United States)

    Waag, Robert C; Lin, Feng; Varslot, Trond K; Astheimer, Jeffrey P

    2007-07-01

    A multiple-frequency inverse scattering method that uses eigenfunctions of a scattering operator is extended to image large-scale and high-contrast objects. The extension uses an estimate of the scattering object to form the difference between the scattering by the object and the scattering by the estimate of the object. The scattering potential defined by this difference is expanded in a basis of products of acoustic fields. These fields are defined by eigenfunctions of the scattering operator associated with the estimate. In the case of scattering objects for which the estimate is radial, symmetries in the expressions used to reconstruct the scattering potential greatly reduce the amount of computation. The range of parameters over which the reconstruction method works well is illustrated using calculated scattering by different objects. The method is applied to experimental data from a 48-mm diameter scattering object with tissue-like properties. The image reconstructed from measurements has, relative to a conventional B-scan formed using a low f-number at the same center frequency, significantly higher resolution and less speckle, implying that small, high-contrast structures can be demonstrated clearly using the extended method.

  6. Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

    Science.gov (United States)

    Bardhan, Jaydeep P.; Knepley, Matthew G.; Brune, Peter

    2015-01-01

    In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online. PMID:26273581

  7. Manifest rotation symmetric expressions for angular momentum eigenfunctions

    International Nuclear Information System (INIS)

    Eeg, J.O.; Wroldsen, J.

    1983-01-01

    Manifest rotation symmetric expressions for eigenfunctions for spin s, orbital angular momentum l and total angular momentum j = l+s, .... , /l-s/ in terms of (2j+1) x (2s+1) multipole transition matrices (MTM) is given. These matrices, which are irreducible tensor matrices, have an algebra together with ordinary spin matrices for spin s and spin j. Explicit expressions for MTM's and their algebra are given for angular momenta <-3. By means of some examples it is shown that within this formalism angular integrations in central field problems will be simplified considerably. Thus the formalism turns out to be very useful for instance for calculations within the MIT-bag and also within spin-spin interactions in atomic physics. (Auth.)

  8. One-dimensional unstable eigenfunction and manifold computations in delay differential equations

    International Nuclear Information System (INIS)

    Green, Kirk; Krauskopf, Bernd; Engelborghs, Koen

    2004-01-01

    In this paper we present a new numerical technique for computing the unstable eigenfunctions of a saddle periodic orbit in a delay differential equation. This is used to obtain the necessary starting data for an established algorithm for computing one-dimensional (1D) unstable manifolds of an associated saddle fixed point of a suitable Poincare map. To illustrate our method, we investigate an intermittent transition to chaos in a delay system describing a semiconductor laser subject to phase-conjugate feedback

  9. The critical slab problem for pure-triplet anisotropic scattering by singular eigenfunction method

    Energy Technology Data Exchange (ETDEWEB)

    Tuereci, R.G. [Kirikkale Univ. (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministery of Education, Ankara (Turkey). General Directorate of Secondary Education

    2017-12-15

    The infinite medium Green function can be written by using the jump condition, found Case's eigenfunctions. Thus, any reactor theory problem which is inplane geometry such the criticality problem as can be investigated by using the proper boundary conditions and suggested flux definitions. By using the criticality equation the critical thicknesses can be calculated as numerically. The selected numerical results can be tabulated.

  10. On the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_1^\\alpha ({T^N})

    Science.gov (United States)

    Ahmedov, Anvarjon; Materneh, Ehab; Zainuddin, Hishamuddin

    2017-09-01

    The relevance of waves in quantum mechanics naturally implies that the decomposition of arbitrary wave packets in terms of monochromatic waves plays an important role in applications of the theory. When eigenfunction expansions does not converge, then the expansions of the functions with certain smoothness should be considered. Such functions gained prominence primarily through their application in quantum mechanics. In this work we study the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_p^α ({T^N}), related to the self-adjoint extension of the Laplace operator in torus TN . The sufficient conditions for summability is obtained using the modified Poisson formula. Isomorphism properties of the elliptic differential operators is applied in order to obtain estimation for the Fourier series of the functions from the classes of Liouville L_p^α .

  11. Construction of six-quark states from parity eigenfunctions for n-n processes

    International Nuclear Information System (INIS)

    Stancu, F.; Wilets, L.

    1987-01-01

    The work presented is to classify and construct six-quark states as totally antisymmetric states of six fermions, each described by orbital, spin, isospin, and color degrees of freedom. A classification scheme is proposed based on parity eigenfunctions. The single-particle hamiltonian is assumed to be reflectionally and axially symmetric and can be obtained, for example, from constrained Hartree-Fock or solition mean field theories. The ultimate aim is to study N-N processes in the context of the (relativistic) soliton bag model

  12. Local and global properties of eigenfunctions and one-electron densities of Coulombic Schrödinger operators

    DEFF Research Database (Denmark)

    Fournais, Søren; Hoffmann-Ostenhof, Maria; Hoffmann-Ostenhof, Thomas

    2008-01-01

    We review recent results by the authors on the regularity of molecular eigenfunctions ψ and their corresponding one-electron densities ρ, as well as of the spherically averaged one-electron atomic density ρ. Furthermore, we prove an exponentially decreasing lower bound for ρ in the case when...

  13. Problem on eigenfunctions and eigenvalues for effective Hamiltonians in pair channels of four-particle systems

    International Nuclear Information System (INIS)

    Gurbanovich, N.S.; Zelenskaya, I.N.

    1976-01-01

    The solution for eigenfunction and eigenvalue for effective Hamiltonians anti Hsub(p) in two-particle channels corresponding to division of four particles into groups (3.1) and (2.2) is very essential in the four-body problem as applied to nuclear reactions. The interaction of anti√sub(p) in each channel may be written in the form of an integral operator which takes account of the structure of a target nucleus or of an incident particle and satisfying the integral equation. While assuming the two-particle potentials to be central, it is possible to expand the effective interactions anti√sub(p) in partial waves and write the radial equation for anti Hsub(p). In the approximation on a mass shell the radial equations for the eigenfunctions of Hsub(p) are reduced to an algebraic equations system. The coefficients of the latter are expressed through the Fourier images for products of wave functions of bound clusters and the two-particle central potential which are localized in a momentum space

  14. Phase space eigenfunctions of multidimensional quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Dodonov, V.V.; Man'ko, V.I.

    1986-01-01

    We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)

  15. The Solution of a Velocity-Dependent Slowing-Down Problem Using Case's Eigenfunction Expansion

    Energy Technology Data Exchange (ETDEWEB)

    Claesson, A

    1964-11-15

    The slowing-down of neutrons in a hydrogenous moderator is calculated assuming a plane source of monoenergetic neutrons. The scattering is regarded as spherically symmetric, but it is shown that a generalization to anisotropy is possible. The cross-section is assumed to be constant. The virgin neutrons are separated out, and it follows that the distribution of the remaining neutrons can be obtained by using an expansion in the eigenfunctions given by Case for the velocity-independent problem.

  16. Data-driven discovery of Koopman eigenfunctions using deep learning

    Science.gov (United States)

    Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan

    2017-11-01

    Koopman operator theory transforms any autonomous non-linear dynamical system into an infinite-dimensional linear system. Since linear systems are well-understood, a mapping of non-linear dynamics to linear dynamics provides a powerful approach to understanding and controlling fluid flows. However, finding the correct change of variables remains an open challenge. We present a strategy to discover an approximate mapping using deep learning. Our neural networks find this change of variables, its inverse, and a finite-dimensional linear dynamical system defined on the new variables. Our method is completely data-driven and only requires measurements of the system, i.e. it does not require derivatives or knowledge of the governing equations. We find a minimal set of approximate Koopman eigenfunctions that are sufficient to reconstruct and advance the system to future states. We demonstrate the method on several dynamical systems.

  17. Sub-cell balanced nodal expansion methods using S4 eigenfunctions for multi-group SN transport problems in slab geometry

    International Nuclear Information System (INIS)

    Hong, Ser Gi; Lee, Deokjung

    2015-01-01

    A highly accurate S 4 eigenfunction-based nodal method has been developed to solve multi-group discrete ordinate neutral particle transport problems with a linearly anisotropic scattering in slab geometry. The new method solves the even-parity form of discrete ordinates transport equation with an arbitrary S N order angular quadrature using two sub-cell balance equations and the S 4 eigenfunctions of within-group transport equation. The four eigenfunctions from S 4 approximation have been chosen as basis functions for the spatial expansion of the angular flux in each mesh. The constant and cubic polynomial approximations are adopted for the scattering source terms from other energy groups and fission source. A nodal method using the conventional polynomial expansion and the sub-cell balances was also developed to be used for demonstrating the high accuracy of the new methods. Using the new methods, a multi-group eigenvalue problem has been solved as well as fixed source problems. The numerical test results of one-group problem show that the new method has third-order accuracy as mesh size is finely refined and it has much higher accuracies for large meshes than the diamond differencing method and the nodal method using sub-cell balances and polynomial expansion of angular flux. For multi-group problems including eigenvalue problem, it was demonstrated that the new method using the cubic polynomial approximation of the sources could produce very accurate solutions even with large mesh sizes. (author)

  18. The Convergence Problems of Eigenfunction Expansions of Elliptic Differential Operators

    Science.gov (United States)

    Ahmedov, Anvarjon

    2018-03-01

    In the present research we investigate the problems concerning the almost everywhere convergence of multiple Fourier series summed over the elliptic levels in the classes of Liouville. The sufficient conditions for the almost everywhere convergence problems, which are most difficult problems in Harmonic analysis, are obtained. The methods of approximation by multiple Fourier series summed over elliptic curves are applied to obtain suitable estimations for the maximal operator of the spectral decompositions. Obtaining of such estimations involves very complicated calculations which depends on the functional structure of the classes of functions. The main idea on the proving the almost everywhere convergence of the eigenfunction expansions in the interpolation spaces is estimation of the maximal operator of the partial sums in the boundary classes and application of the interpolation Theorem of the family of linear operators. In the present work the maximal operator of the elliptic partial sums are estimated in the interpolation classes of Liouville and the almost everywhere convergence of the multiple Fourier series by elliptic summation methods are established. The considering multiple Fourier series as an eigenfunction expansions of the differential operators helps to translate the functional properties (for example smoothness) of the Liouville classes into Fourier coefficients of the functions which being expanded into such expansions. The sufficient conditions for convergence of the multiple Fourier series of functions from Liouville classes are obtained in terms of the smoothness and dimensions. Such results are highly effective in solving the boundary problems with periodic boundary conditions occurring in the spectral theory of differential operators. The investigations of multiple Fourier series in modern methods of harmonic analysis incorporates the wide use of methods from functional analysis, mathematical physics, modern operator theory and spectral

  19. Some applications of the particle-in-a-box eigenfunctions: fast-convergent variational and related calculations

    International Nuclear Information System (INIS)

    Pathak, R.K.; Chandra, A.K.; Bhattacharyya, K.

    1994-01-01

    Eigenfunctions of the quantum mechanical particle-in-a-box problem are shown to lead to a new trigonometric expansion scheme with good convergence properties. This hitherto unexplored expansion strategy is found to be quite efficient in variational calculations and as an alternative to the Fourier series. Demonstrative computations involve a few one-dimensional models of confining potentials for bound states and pulses of various shapes in signal analysis. ((orig.))

  20. Practical adjoint Monte Carlo technique for fixed-source and eigenfunction neutron transport problems

    International Nuclear Information System (INIS)

    Hoogenboom, J.E.

    1981-01-01

    An adjoint Monte Carlo technique is described for the solution of neutron transport problems. The optimum biasing function for a zero-variance collision estimator is derived. The optimum treatment of an analog of a non-velocity thermal group has also been derived. The method is extended to multiplying systems, especially for eigenfunction problems to enable the estimate of averages over the unknown fundamental neutron flux distribution. A versatile computer code, FOCUS, has been written, based on the described theory. Numerical examples are given for a shielding problem and a critical assembly, illustrating the performance of the FOCUS code. 19 refs

  1. The eigenfunction method and the mass operator in intense-field quantum electrodynamics

    International Nuclear Information System (INIS)

    Ritus, V.I.

    1987-01-01

    A method is given for calculating radiation effects in constant intense-field quantum electrodynamics; this method is based on the use of the eigenfunctions of the mass operator and diagonalization of the latter. A compact expression is found for the eigenvalue of the mass operator of the electron in a random constant field together with the corresponding elastic scattering amplitude. The anomalous electric moment that arises in the field with a pseudoscalar EH not equal to O is found and investigated in detail together with the anomalous magnetic moment in the electrical field that approaches the double Schwinger value with an increase in the field together with the mass shift and the rate of decay of the ground state of the electron in the electrical field

  2. Some results on the eigenfunctions of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra D4

    International Nuclear Information System (INIS)

    Fernandez Nunez, J.; Garcia Fuertes, W.; Perelomov, A.M.

    2003-01-01

    We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra D 4 in terms of a set of Weyl-invariant variables, namely, the characters of the fundamental representations of the Lie algebra. This parametrization allows us to solve for the energy eigenfunctions of the theory and to study properties of the system of orthogonal polynomials associated with them such as recurrence relations and generating functions

  3. On the completeness of systems of eigenfunctions of the Sturm-Liouville operator with a potential depending on the spectral parameter and a nonlinear problem

    International Nuclear Information System (INIS)

    Zhidkov, P.E.

    1996-01-01

    First, the eigenvalue problem on the segment [0,1] for the Sturm-Liouville operator with a potential depending on the spectral parameter with the zero Dirichlet boundary conditions is considered. For this problem, under some hypotheses on the potential, it is proved that the necessary and sufficient condition for an arbitrary system of eigenfunctions, possessing a unique function with n roots in the interval (0,1) for an arbitrary non-negative integer number n, being complete in the space L 2 (0,1) is the linear independence of the functions from this system in the space L 2 (0,1). Then, this result is applied to the investigation of an eigenvalue problem for a nonlinear operator on the Sturm-Liouville type. For this problem, the completeness of the system of its eigenfunctions in the space L 2 (0,1) is proved. (author). 12 refs

  4. Determination of a basic set of Eigen-functions and of the corresponding norm in the case of the one-velocity integral differential Boltzmann equation in spherical geometry

    International Nuclear Information System (INIS)

    Lafore, P.

    1965-01-01

    The object of the present work is to draw up a basic set of orthogonal eigenfunctions; resolution of the one-velocity integral-differential Boltzmann equation; this in the case of a spherical geometry system. (author) [fr

  5. Statistical distribution of components of energy eigenfunctions: from nearly-integrable to chaotic

    International Nuclear Information System (INIS)

    Wang, Jiaozi; Wang, Wen-ge

    2016-01-01

    We study the statistical distribution of components in the non-perturbative parts of energy eigenfunctions (EFs), in which main bodies of the EFs lie. Our numerical simulations in five models show that deviation of the distribution from the prediction of random matrix theory (RMT) is useful in characterizing the process from nearly-integrable to chaotic, in a way somewhat similar to the nearest-level-spacing distribution. But, the statistics of EFs reveals some more properties, as described below. (i) In the process of approaching quantum chaos, the distribution of components shows a delay feature compared with the nearest-level-spacing distribution in most of the models studied. (ii) In the quantum chaotic regime, the distribution of components always shows small but notable deviation from the prediction of RMT in models possessing classical counterparts, while, the deviation can be almost negligible in models not possessing classical counterparts. (iii) In models whose Hamiltonian matrices possess a clear band structure, tails of EFs show statistical behaviors obviously different from those in the main bodies, while, the difference is smaller for Hamiltonian matrices without a clear band structure.

  6. A study on current density distribution reproduction by bounded-eigenfunction expansion for a tokamak plasma

    International Nuclear Information System (INIS)

    Kurihara, Kenichi

    1997-11-01

    Plasma current density distribution is one of the most important controlled variables to determine plasma performance of energy confinement and stability in a tokamak. However, its reproduction by using magnetic measurements solely is recognized to yield an ill-posed problem. A method to presume the formulas giving profiles of plasma pressure and current has been adopted to regularize the ill-posedness, and hence it has been reported the current density distribution can be reproduced as a solution of Grad-Shafranov equation within a certain accuracy. In order to investigate its strict reproducibility from magnetic measurements in this inverse problem, a new method of 'bounded-eigenfunction expansion' is introduced, and it was found that the reproducibility directly corresponds to the independence of a series of the special function. The results from various investigations in an aspect of applied mathematics concerning this inverse problem are presented in detail. (author)

  7. Eigenfunction method and mass operator in the quantum electrodynamics of a constant field

    International Nuclear Information System (INIS)

    Ritus, V.I.

    1978-01-01

    A method is presented for the calculation of radiative effects in the quantum electrodynamics of an intense constant field. It is based on the application of the mass operator eigenfunctions and on diagonalization of the operator. A compact expression for the proper value of the electron mass operator in an arbitrary constant field and the corresponding elastic scattering amplitude are found. The imaginary part of the amplitude determines the decay rate of various states of the electron in the field; the real part contains the mass shift and the anomalous magnetic and electric moments as functions of the field and electron momentum. THe anomalous electric moment which arises in a field with a pseudoscalar EH not equal to 0 and the anomalous magnetic moment in an electric field which tends to the double Schwinger value with increase of the field strength are found and investigated in detail as are the mass shift and decay rate of the ground state of an electron in an electric field. In a weak field the mass shift contains the linear with respect to the field modulus classical term which characterizes the effect of acceleration on the structure of electron

  8. Equation of the fixed membrane in the n-dimensional space: some remarks on the maxima of the eigenfunctions subjected to various norms

    Directory of Open Access Journals (Sweden)

    Yves Biollay

    1979-01-01

    Full Text Available We show in this paper that the sequence {max|uk|}, where the uk are the eigenfunctions of the problem Δu+λu=0 in D⊂Rn and u=0 on ∂D, is not bounded generally if one imposes the norm ∫Du2p(xdx=1, p=(1,2,3,…. The same holds with the norm ∫D|gradu|2pdx=1 when n>4p−1. On the other hand, if D⊂R2, resp. R3 the norm ∫D|gradu|2dx=1 implies max|uk|→k→∞0, resp. max|uk|=0(1.

  9. Eigenfunctions of the invariant differential operators on symmetric spaces having A2 as a restricted root system

    International Nuclear Information System (INIS)

    Prati, M.C.

    1986-01-01

    The eigenfunctions psub(nm)sup(μ) (z, z-bar), n,m are elements of N, μ is an element of (-1/3, + infinity), z is an element of C, of two differential operators, which for some particular values of μ are the generators of the algebra of invariant differential operators on symmetric spaces, having A 2 as a restricted root system, are studied. The group-theoretic interpretation and the explicit form of these functions as polynomials of z , z-bar are given in the following cases: when μ = 0, 1 for every n, m belonging to N; when m = 0, for every n belonging to N and when μ is an element of (-1/3, +infinity). Furthermore, all solutions psub(nm)sup(μ) (z, z-bar) for every μ belonging to (-1/3, +infinity) and n + m <= 5 are explicitly written. This research has applications in quantum mechanics and in quantum field theory

  10. Recovering functions from the spherical mean transform with data on an ellipse using eigenfunction expansion in elliptical coordinates

    Science.gov (United States)

    Salman, Yehonatan

    2017-09-01

    The aim of this paper is to introduce a new inversion procedure for recovering functions, defined on R2 , from the spherical mean transform, which integrates functions on a prescribed family Λ of circles, where Λ consists of circles whose centers belong to a given ellipse E on the plane. The method presented here follows the same procedure which was used by Norton (J Acoust Soc Am 67:1266-1273, 1980) for recovering functions in case where Λ consists of circles with centers on a circle. However, at some point we will have to modify the method in [24] by using expansion in elliptical coordinates, rather than spherical coordinates, in order to solve the more generalized elliptical case. We will rely on a recent result obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the eigenfunction expansion of the Bessel function in elliptical coordinates.

  11. Ancestral informative marker selection and population structure visualization using sparse Laplacian eigenfunctions.

    Directory of Open Access Journals (Sweden)

    Jun Zhang

    Full Text Available Identification of a small panel of population structure informative markers can reduce genotyping cost and is useful in various applications, such as ancestry inference in association mapping, forensics and evolutionary theory in population genetics. Traditional methods to ascertain ancestral informative markers usually require the prior knowledge of individual ancestry and have difficulty for admixed populations. Recently Principal Components Analysis (PCA has been employed with success to select SNPs which are highly correlated with top significant principal components (PCs without use of individual ancestral information. The approach is also applicable to admixed populations. Here we propose a novel approach based on our recent result on summarizing population structure by graph laplacian eigenfunctions, which differs from PCA in that it is geometric and robust to outliers. Our approach also takes advantage of the priori sparseness of informative markers in the genome. Through simulation of a ring population and the real global population sample HGDP of 650K SNPs genotyped in 940 unrelated individuals, we validate the proposed algorithm at selecting most informative markers, a small fraction of which can recover the similar underlying population structure efficiently. Employing a standard Support Vector Machine (SVM to predict individuals' continental memberships on HGDP dataset of seven continents, we demonstrate that the selected SNPs by our method are more informative but less redundant than those selected by PCA. Our algorithm is a promising tool in genome-wide association studies and population genetics, facilitating the selection of structure informative markers, efficient detection of population substructure and ancestral inference.

  12. Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type

    International Nuclear Information System (INIS)

    Gorbachev, D V; Ivanov, V I

    2015-01-01

    Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles

  13. Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

    Energy Technology Data Exchange (ETDEWEB)

    Samin, Adib; Lahti, Erik; Zhang, Jinsuo, E-mail: zhang.3558@osu.edu [Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19" t" h Avenue, Columbus, Ohio 43210 (United States)

    2015-08-15

    Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.

  14. Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

    International Nuclear Information System (INIS)

    th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Samin, Adib; th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Lahti, Erik; th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Zhang, Jinsuo

    2015-01-01

    Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes

  15. Solution of the Helmholtz-Poincare Wave Equation using the coupled boundary integral equations and optimal surface eigenfunctions

    International Nuclear Information System (INIS)

    Werby, M.F.; Broadhead, M.K.; Strayer, M.R.; Bottcher, C.

    1992-01-01

    The Helmholtz-Poincarf Wave Equation (H-PWE) arises in many areas of classical wave scattering theory. In particular it can be found for the cases of acoustical scattering from submerged bounded objects and electromagnetic scattering from objects. The extended boundary integral equations (EBIE) method is derived from considering both the exterior and interior solutions of the H-PWECs. This coupled set of expressions has the advantage of not only offering a prescription for obtaining a solution for the exterior scattering problem, but it also obviates the problem of irregular values corresponding to fictitious interior eigenvalues. Once the coupled equations are derived, they can be obtained in matrix form by expanding all relevant terms in partial wave expansions, including a bi-orthogonal expansion of the Green's function. However some freedom in the choice of the surface expansion is available since the unknown surface quantities may be expanded in a variety of ways so long as closure is obtained. Out of many possible choices, we develop an optimal method to obtain such expansions which is based on the optimum eigenfunctions related to the surface of the object. In effect, we convert part of the problem (that associated with the Fredholms integral equation of the first kind) an eigenvalue problem of a related Hermitian operator. The methodology will be explained in detail and examples will be presented

  16. Particle in a uniform magnetic field under the symmetric gauge: the eigenfunctions and the time evolution of wave packets

    International Nuclear Information System (INIS)

    Brito, P E de; Nazareno, H N

    2007-01-01

    In the present work we treat the problem of a particle in a uniform magnetic field along the symmetric gauge, so chosen since the wavefunctions present the required cylindrical symmetry. It is our understanding that by means of this work we can make a contribution to the teaching of the present subject, as well as encourage students to use computer algebra systems in solving problems of quantum mechanics. We obtained the degeneracy of the spectrum of eigenvalues in a very clear way. Through the use of a computer algebra system we show graphs of the probability density associated with different eigenvalues as well as compare such functions for some degenerate states, which helps us to visualize the physics of the problem. We also present a semiclassical model which gives a physical insight regarding the paradoxical fact that eigenfunctions associated with opposite angular momenta and different energy eigenvalues have the same probability density. Finally, by solving the time-dependent Schroedinger equation we obtain the time evolution of a wave packet that at time zero was considered to be localized in a definite region of the lattice. The centroid of such a packet performs an orbit similar to that obtained in the classical treatment of a particle in a magnetic field

  17. Spectral algorithms for multiple scale localized eigenfunctions in infinitely long, slightly bent quantum waveguides

    Science.gov (United States)

    Boyd, John P.; Amore, Paolo; Fernández, Francisco M.

    2018-03-01

    A "bent waveguide" in the sense used here is a small perturbation of a two-dimensional rectangular strip which is infinitely long in the down-channel direction and has a finite, constant width in the cross-channel coordinate. The goal is to calculate the smallest ("ground state") eigenvalue of the stationary Schrödinger equation which here is a two-dimensional Helmholtz equation, ψxx +ψyy + Eψ = 0 where E is the eigenvalue and homogeneous Dirichlet boundary conditions are imposed on the walls of the waveguide. Perturbation theory gives a good description when the "bending strength" parameter ɛ is small as described in our previous article (Amore et al., 2017) and other works cited therein. However, such series are asymptotic, and it is often impractical to calculate more than a handful of terms. It is therefore useful to develop numerical methods for the perturbed strip to cover intermediate ɛ where the perturbation series may be inaccurate and also to check the pertubation expansion when ɛ is small. The perturbation-induced change-in-eigenvalue, δ ≡ E(ɛ) - E(0) , is O(ɛ2) . We show that the computation becomes very challenging as ɛ → 0 because (i) the ground state eigenfunction varies on both O(1) and O(1 / ɛ) length scales and (ii) high accuracy is needed to compute several correct digits in δ, which is itself small compared to the eigenvalue E. The multiple length scales are not geographically separate, but rather are inextricably commingled in the neighborhood of the boundary deformation. We show that coordinate mapping and immersed boundary strategies both reduce the computational domain to the uniform strip, allowing application of pseudospectral methods on tensor product grids with tensor product basis functions. We compared different basis sets; Chebyshev polynomials are best in the cross-channel direction. However, sine functions generate rather accurate analytical approximations with just a single basis function. In the down

  18. Internal parity symmetry and degeneracy of Bethe Ansatz strings in the isotropic heptagonal magnetic ring

    Energy Technology Data Exchange (ETDEWEB)

    Milewski, J., E-mail: jsmilew@wp.pl [Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań (Poland); Lulek, B., E-mail: barlulek@amu.edu.pl [East European State Higher School, ul. Tymona Terleckiego 6, 37-700 Przemyśl (Poland); Lulek, T., E-mail: tadlulek@prz.edu.pl [Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań (Poland); East European State Higher School, ul. Tymona Terleckiego 6, 37-700 Przemyśl (Poland); Łabuz, M., E-mail: labuz@univ.rzeszow.pl [University of Rzeszow, Institute of Physics, Rejtana 16a, 35-959 Rzeszów (Poland); Stagraczyński, R., E-mail: rstag@prz.edu.pl [Rzeszow University of Technology, The Faculty of Mathematics and Applied Physics, Powstańców Warszawy 6, 35-959 Rzeszów (Poland)

    2014-02-01

    The exact Bethe eigenfunctions for the heptagonal ring within the isotropic XXX model exhibit a doubly degenerated energy level in the three-deviation sector at the centre of the Brillouin zone. We demonstrate an explicit construction of these eigenfunctions by use of algebraic Bethe Ansatz, and point out a relation of degeneracy to parity conservation, applied to the configuration of strings for these eigenfunctions. Namely, the internal structure of the eigenfunctions (the 2-string and the 1-string, with opposite quasimomenta) admits generation of two mutually orthogonal eigenfunctions due to the fact that the strings which differ by their length are distinguishable objects.

  19. Handbook of mathematical techniques for wavestructure interactions

    CERN Document Server

    Linton, CM

    2001-01-01

    INTRODUCTIONThe Water-Wave ProblemThe Linearised EquationsInteraction of a Wave with a StructureReciprocity RelationsEnergy of the Fluid MotionEIGENFUNCTION EXPANSIONSIntroductionConstruction of Vertical EigenfunctionTwo-Dimensional ProblemsThree-Dimensional ProblemsMatched Eigenfunction ExpansionsMULTIPOLE EXPANSIONSIntroductionIsolated ObstaclesMultiple BodiesINTEGRAL EQUATIONSSource DistributionGreen's TheoremThin ObstaclesInterior ProblemsFree-Surface ProblemsNumerical Evaluation of Green's functions

  20. Separating variables in two-way diffusion equations

    International Nuclear Information System (INIS)

    Fisch, N.J.; Kruskal, M.D.

    1979-10-01

    It is shown that solutions to a class of diffusion equations of the two-way type may be found by a method akin to separation of variables. The difficulty with such equations is that the boundary data must be specified partly as initial and partly as final conditions. In contrast to the one-way diffusion equation, where the solution separates only into decaying eigenfunctions, the two-way equations separate into both decaying and growing eigenfunctions. Criteria are set forth for the existence of linear eigenfunctions, which may not be found directly by separating variables. A speculation with interesting ramifications is that the growing and decaying eigenfunctions are separately complete in an appropriate half of the problem domain

  1. Deep learning the quantum phase transitions in random two-dimensional electron systems

    International Nuclear Information System (INIS)

    Ohtsuki, Tomoki; Ohtsuki, Tomi

    2016-01-01

    Random electron systems show rich phases such as Anderson insulator, diffusive metal, quantum Hall and quantum anomalous Hall insulators, Weyl semimetal, as well as strong/weak topological insulators. Eigenfunctions of each matter phase have specific features, but owing to the random nature of systems, determining the matter phase from eigenfunctions is difficult. Here, we propose the deep learning algorithm to capture the features of eigenfunctions. Localization-delocalization transition, as well as disordered Chern insulator-Anderson insulator transition, is discussed. (author)

  2. Decoupling of the leading contribution in the discrete BFKL analysis of high-precision HERA data

    Energy Technology Data Exchange (ETDEWEB)

    Kowalski, H. [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany); Lipatov, L.N. [St. Petersburg State University, St. Petersburg (Russian Federation); Petersburg Nuclear Physics Institute, Gatchina (Russian Federation); Ross, D.A. [University of Southampton, School of Physics and Astronomy, Southampton (United Kingdom); Schulz, O. [Max Planck Institute for Physics, Munich (Germany)

    2017-11-15

    We analyse, in NLO, the physical properties of the discrete eigenvalue solution for the BFKL equation. We show that a set of eigenfunctions with positive eigenvalues, ω, together with a small contribution from a continuum of eigenfunctions with negative ω, provide an excellent description of high-precision HERA F{sub 2} data in the region, x < 0.001, Q{sup 2} > 6 GeV{sup 2}. The phases of the eigenfunctions can be obtained from a simple parametrisation of the pomeron spectrum, which has a natural motivation within BFKL. The data analysis shows that the first eigenfunction decouples completely or almost completely from the proton. This suggests that there exists an additional ground state, which is naturally saturated and may have the properties of the soft pomeron. (orig.)

  3. Accidental degeneracy of resonances

    International Nuclear Information System (INIS)

    Hernandez, E.; Mondragon, A.; Jauregui, A.

    2001-01-01

    Full text: It will be shown that a degeneracy of resonances is associated with a second rank pole in the scattering matrix and a Jordan cycle of generalized eigenfunctions of the radial Schrodinger equation. The generalized Gamow-Jordan eigenfunctions are basis elements of an expansion in complex resonance energy eigenfunctions. In this orthonormal basis, the Hamiltonian is represented by a non-diagonal complex matrix with a Jordan block of rank two. Some general properties of the degeneracy of resonances will be exhibited and discussed in an explicit example of degeneracy of resonant states and double poles in the scattering matrix of a double barrier potential. The cross section, scattering wave functions and Jordan-Gamow eigenfunctions are computed at degeneracy and their properties as functions of the control parameters of the system are discussed. (Author)

  4. Completeness in quantum mechanics and the Weyl-Titchmarsh-Kodaira theorem

    Energy Technology Data Exchange (ETDEWEB)

    Palma, G [Departamento de Fisica, Universidad de Santiago de Chile, Casilla 307, Santiago 2 (Chile); Prado, H; Reyes, E G, E-mail: guillermo.palma@usach.c, E-mail: humberto.prado@usach.c, E-mail: ereyes@fermat.usach.c [Departamento de Matematica y Ciencia de la Computacion, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago (Chile)

    2010-06-25

    We discuss the completeness of (generalized) eigenfunctions in quantum mechanics using the classical theory developed by Weyl, Titchmarsh, and Kodaira. As applications, we rigorously prove the completeness of generalized eigenfunctions for the step and well potentials.

  5. The eigenvalue problem for a singular quasilinear elliptic equation

    Directory of Open Access Journals (Sweden)

    Benjin Xuan

    2004-02-01

    Full Text Available We show that many results about the eigenvalues and eigenfunctions of a quasilinear elliptic equation in the non-singular case can be extended to the singular case. Among these results, we have the first eigenvalue is associated to a $C^{1,alpha}(Omega$ eigenfunction which is positive and unique (up to a multiplicative constant, that is, the first eigenvalue is simple. Moreover the first eigenvalue is isolated and is the unique positive eigenvalue associated to a non-negative eigenfunction. We also prove some variational properties of the second eigenvalue.

  6. Analyticity of the density of electronic wavefunctions

    DEFF Research Database (Denmark)

    Fournais, Søren; Hoffmann-Ostenhof, Maria; Hoffmann-Ostenhof, Thomas

    2004-01-01

    We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in R^3 away from the nuclei.......We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in R^3 away from the nuclei....

  7. Spectrum of the multigroup neutron transport operator for bounded spatial domains

    International Nuclear Information System (INIS)

    Larsen, E.W.

    1979-01-01

    The spectrum of the multigroup neutron transport operator A is studied for bounded spatial regions D which consist of a finite number of material subregions. Our main results provide simple conditions on the material cross sections which guarantee that (1) A possesses eigenvalues in the finite plane; (2) A possesses a ''leading'' eigenvalue lambda 0 which is real, not less than the real part of any other eigenvalue, and to which there corresponds at least one nonnegative eigenfunction psi/sub lambda/0; and (3) A possesses a ''dominant'' eigenvalue lambda 0 which is real, simple, greater than the real part of any other eigenvalue, and whose eigenfunction psi/sub lambda/0 satisfies psi/sub lambda/0> or =0 and ∫psi/sub lambda/0d 2 Ω>0. We give examples to illustrate the results and to show that a leading eigenvalue need not be simple, nor its eigenfunction(s) positive

  8. Hofstadter's butterfly in a two-dimensional lattice consisting of two sublattices

    International Nuclear Information System (INIS)

    Vugalter, G A; Pastukhov, A S

    2004-01-01

    Harper's equations for simple and complex two-dimensional lattices subject to a magnetic field have been derived in the tight-binding approximation. In our derivation we do not neglect the influence of the magnetic field on the electron eigenfunctions and eigenvalues in isolated atoms. Using a variational procedure for finding eigenfunctions and eigenvalues, we have self-consistently obtained Hofstadter's butterflies. Even for a simple square lattice Hofstadter's butterfly differs from the butterfly obtained in the case in which the influence of the magnetic field on the electron eigenvalues and eigenfunctions in isolated atoms is not taken into account

  9. A new approach to the BFKL mechanism. Application to high-precision HERA data

    International Nuclear Information System (INIS)

    Kowalski, H.; Lipatov, L.N.; Ross, D.A.

    2017-07-01

    We analyse here in NLO the physical properties of the discrete eigenvalue solution for the BFKL equation. We show that a set of positive ω eigenfunctions together with a small contribution from a continuum of negative ω's provide an excellent description of high-precision HERA F_2 data in the region, x 6 GeV"2. The phases of the eigenfunctions can be obtained from a simple parametrisation of the pomeron spectrum, which has a natural motivation within BFKL. The data analysis shows that the first eigenfunction decouples or nearly decouples from the proton. This suggests that there exist an additional ground state, which has no nodes.

  10. Hofstadter's butterfly in a two-dimensional lattice consisting of two sublattices

    Energy Technology Data Exchange (ETDEWEB)

    Vugalter, G A; Pastukhov, A S [Department of Physics, Nizhny Novgorod State University, 23 Gagarin Avenue, Nizhny Novgorod 603950 (Russian Federation)

    2004-06-04

    Harper's equations for simple and complex two-dimensional lattices subject to a magnetic field have been derived in the tight-binding approximation. In our derivation we do not neglect the influence of the magnetic field on the electron eigenfunctions and eigenvalues in isolated atoms. Using a variational procedure for finding eigenfunctions and eigenvalues, we have self-consistently obtained Hofstadter's butterflies. Even for a simple square lattice Hofstadter's butterfly differs from the butterfly obtained in the case in which the influence of the magnetic field on the electron eigenvalues and eigenfunctions in isolated atoms is not taken into account.

  11. Analytical Solution of the Schrödinger Equation with Spatially Varying Effective Mass for Generalised Hylleraas Potential

    International Nuclear Information System (INIS)

    Debnath, S.; Maji, Smarajit; Meyur, Sanjib

    2014-01-01

    We have obtained exact solution of the effective mass Schrödinger equation for the generalised Hylleraas potential. The exact bound state energy eigenvalues and corresponding eigenfunctions are presented. The bound state eigenfunctions are obtained in terms of the hypergeometric functions. Results are also given for the special case of potential parameter.

  12. A new approach to the BFKL mechanism. Application to high-precision HERA data

    Energy Technology Data Exchange (ETDEWEB)

    Kowalski, H. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Lipatov, L.N. [Sankt-Peterburgskij Univ., St. Petersburg (Russian Federation); Petersburg Nuclear Physics Institute, Gatchina (Russian Federation); Ross, D.A. [Southampton Univ. (United Kingdom). School of Physics and Astronomy; Schulz, O. [Max Planck Institute for Physics, Munich (Germany)

    2017-07-15

    We analyse here in NLO the physical properties of the discrete eigenvalue solution for the BFKL equation. We show that a set of positive ω eigenfunctions together with a small contribution from a continuum of negative ω's provide an excellent description of high-precision HERA F{sub 2} data in the region, x < 0.001, Q{sup 2} > 6 GeV{sup 2}. The phases of the eigenfunctions can be obtained from a simple parametrisation of the pomeron spectrum, which has a natural motivation within BFKL. The data analysis shows that the first eigenfunction decouples or nearly decouples from the proton. This suggests that there exist an additional ground state, which has no nodes.

  13. A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems

    Directory of Open Access Journals (Sweden)

    Muhammed I. Syam

    2017-11-01

    Full Text Available This article is devoted to both theoretical and numerical studies of eigenvalues of regular fractional $2\\alpha $-order Sturm-Liouville problem where $\\frac{1}{2}< \\alpha \\leq 1$. In this paper, we implement the reproducing kernel method RKM to approximate the eigenvalues. To find the eigenvalues, we force the approximate solution produced by the RKM satisfy the boundary condition at $x=1$. The fractional derivative is described in the Caputo sense. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the eigenfunctions of the proposed problem. Uniformly convergence of the approximate eigenfunctions produced by the RKM to the exact eigenfunctions is proven.

  14. An extended Harry Dym hierarchy

    International Nuclear Information System (INIS)

    Ma Wenxiu

    2010-01-01

    An extended Harry Dym hierarchy is constructed by using eigenfunctions and adjoint eigenfunctions of the spectral problems of the Harry Dym hierarchy associated with the pseudo-differential operator L = u∂ + u 0 + u 1 ∂ -1 + .... The corresponding Lax presentation possesses a self-consistent source involving squared eigenfunctions. The resulting extended Harry Dym hierarchy is reduced to the Harry Dym hierarchy with self-consistent sources under the n-reduction, L n = (L n ) ≥2 , and the k-constrained Harry Dym hierarchy under the k-constraint, L k = (L k ) ≥2 + Σ N i=1 q i ∂ -1 r i ∂ 2 . A few particular examples are computed, together with their Lax pairs.

  15. The q-deformed analogue of the Onsager algebra: Beyond the Bethe ansatz approach

    International Nuclear Information System (INIS)

    Baseilhac, Pascal

    2006-01-01

    The spectral properties of operators formed from generators of the q-Onsager non-Abelian infinite-dimensional algebra are investigated. Using a suitable functional representation, all eigenfunctions are shown to obey a second-order q-difference equation (or its degenerate discrete version). In the algebraic sector associated with polynomial eigenfunctions (or their discrete analogues), Bethe equations naturally appear. Beyond this sector, where the Bethe ansatz approach is not applicable in related massive quantum integrable models, the eigenfunctions are also described. The spin-half XXZ open spin chain with general integrable boundary conditions is reconsidered in light of this approach: all the eigenstates are constructed. In the algebraic sector which corresponds to special relations among the parameters, known results are recovered

  16. Three-body Coulomb systems using generalized angular-momentum S states

    Science.gov (United States)

    Whitten, R. C.; Sims, J. S.

    1974-01-01

    An expansion of the three-body Coulomb potential in generalized angular-momentum eigenfunctions developed earlier by one of the authors is used to compute energy eigenvalues and eigenfunctions of bound S states of three-body Coulomb systems. The results for He, H(-), e(-)e(+)e(-), and pmu(-)p are compared with the results of other computational approaches.

  17. On spectral resolutions of differential vector-operators

    International Nuclear Information System (INIS)

    Ashurov, R.R.; Sokolov, M.S.

    2004-04-01

    We show that spectral resolutions of differential vector-operators may be represented as a specific direct sum integral operator with a kernel written in terms of generalized vector-operator eigenfunctions. Then we prove that a generalized eigenfunction measurable with respect to the spectral parameter may be decomposed using a set of analytical defining systems of coordinate operators. (author)

  18. Explicit formulae for the generalized Hermite polynomials in superspace

    International Nuclear Information System (INIS)

    Desrosiers, Patrick; Lapointe, Luc; Mathieu, Pierre

    2004-01-01

    We provide explicit formulae for the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement, i.e., the generalized Hermite (or Hi-Jack) polynomials in superspace. The construction relies on the triangular action of the Hamiltonian on the supermonomial basis. This translates into determinantal expressions for the Hamiltonian's eigenfunctions

  19. Slab albedo for linearly and quadratically anisotropic scattering kernel with modified F{sub N} method

    Energy Technology Data Exchange (ETDEWEB)

    Tuereci, R. Goekhan [Kirikkale Univ. (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School

    2017-11-15

    One speed, time independent and homogeneous medium neutron transport equation is solved with the anisotropic scattering which includes both the linearly and the quadratically anisotropic scattering kernel. Having written Case's eigenfunctions and the orthogonality relations among of these eigenfunctions, slab albedo problem is investigated as numerically by using Modified F{sub N} method. Selected numerical results are presented in tables.

  20. Spectral properties of the massless relativistic quartic oscillator

    Science.gov (United States)

    Durugo, Samuel O.; Lőrinczi, József

    2018-03-01

    An explicit solution of the spectral problem of the non-local Schrödinger operator obtained as the sum of the square root of the Laplacian and a quartic potential in one dimension is presented. The eigenvalues are obtained as zeroes of special functions related to the fourth order Airy function, and closed formulae for the Fourier transform of the eigenfunctions are derived. These representations allow to derive further spectral properties such as estimates of spectral gaps, heat trace and the asymptotic distribution of eigenvalues, as well as a detailed analysis of the eigenfunctions. A subtle spectral effect is observed which manifests in an exponentially tight approximation of the spectrum by the zeroes of the dominating term in the Fourier representation of the eigenfunctions and its derivative.

  1. Unified heat kernel regression for diffusion, kernel smoothing and wavelets on manifolds and its application to mandible growth modeling in CT images.

    Science.gov (United States)

    Chung, Moo K; Qiu, Anqi; Seo, Seongho; Vorperian, Houri K

    2015-05-01

    We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel method is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, the method is applied to characterize the localized growth pattern of mandible surfaces obtained in CT images between ages 0 and 20 by regressing the length of displacement vectors with respect to a surface template. Copyright © 2015 Elsevier B.V. All rights reserved.

  2. Level density approach to perturbation theory and inverse-energy-weighted sum-rules

    International Nuclear Information System (INIS)

    Halemane, T.R.

    1983-01-01

    The terms in the familiar Rayleigh-Schroedinger perturbation series involve eigenvalues and eigenfunctions of the unperturbed operator. A level density formalism, that does not involve computation of eigenvalues and eigenfunctions, is given here for the perturbation series. In the CLT (central limit theorem) limit the expressions take very simple linear forms. The evaluation is in terms of moments and traces of operators and operator products. 3 references

  3. The effects of different expansions of the exit distribution on the extrapolation length for linearly anisotropic scattering

    International Nuclear Information System (INIS)

    Bulut, S.; Guelecyuez, M.C.; Kaskas, A.; Tezcan, C.

    2007-01-01

    H N and singular eigenfunction methods are used to determine the neutron distribution everywhere in a source-free half space with zero incident flux for a linearly anisotropic scattering kernel. The singular eigenfunction expansion of the method of elementary solutions is used. The orthogonality relations of the discrete and continuous eigenfunctions for linearly anisotropic scattering provides the determination of the expansion coefficients. Different expansions of the exit distribution are used: the expansion in powers of μ, the expansion in terms of Legendre polynomials and the expansion in powers of 1/(1+μ). The results are compared to each other. In the second part of our work, the transport equation and the infinite medium Green function are used. The numerical results of the extrapolation length obtained for the different expansions is discussed. (orig.)

  4. DCTNet and PCANet for acoustic signal feature extraction

    OpenAIRE

    Xian, Yin; Thompson, Andrew; Sun, Xiaobai; Nowacek, Douglas; Nolte, Loren

    2016-01-01

    We introduce the use of DCTNet, an efficient approximation and alternative to PCANet, for acoustic signal classification. In PCANet, the eigenfunctions of the local sample covariance matrix (PCA) are used as filterbanks for convolution and feature extraction. When the eigenfunctions are well approximated by the Discrete Cosine Transform (DCT) functions, each layer of of PCANet and DCTNet is essentially a time-frequency representation. We relate DCTNet to spectral feature representation method...

  5. A new approach to obtaining the roots of the dispersion equation for slab geometry multiplying media

    International Nuclear Information System (INIS)

    Silva, Davi J.M.; Barros, Ricardo C.; Alves Filho, Hermes

    2013-01-01

    In this work we describe an alternative approach for obtaining the roots of the dispersion equation. For the mathematical model, we used the slab-geometry neutron transport equation in the discrete ordinates (S N ), formulation, considering isotropic scattering and monoenergetic model. The basic idea is to find a basis for the kernel of the S N differential operator, whose elements are exponential eigenfunctions corresponding to distinct eigenvalues which are the roots of the dispersion equation. That strategy yields a gain in programming computational codes, including the strategy used to obtain the purely imaginary eigenvalues and their associated complex eigenfunctions, that appear in the spectral analysis of the S N equations in multiplying media. These eigenvalues and corresponding eigenfunctions are used to obtain the parameters of the auxiliary equations of the spectral nodal methods, e.g., the spectral diamond (SD) auxiliary equation. (author)

  6. Active feedback stabilization of axisymmetric modes in highly elongated tokamak plasmas

    International Nuclear Information System (INIS)

    Ward, D.J.; Hofmann, F.

    1993-07-01

    Active feedback stabilization of the vertical instability is studied for highly elongated tokamak plasmas (1≤κ≤3), and evaluated in particular for the TCV configuration. It is shown that the feedback can strongly affect the form of the eigenfunction for these highly elongated equilibria, and this can have detrimental effects on the ability of the feedback system to properly detect and stabilize the plasma. A calculation of the vertical displacement that uses poloidal flux measurements, poloidal magnetic field measurements, and corrections for the vessel eddy currents and active feedback currents was found to be effective even in the cases with the worst deformations of the eigenfunction. We also examine how these deformations affect differently shaped equilibria, and it is seen that the magnitude of the deformation of the eigenfunction is strongly function of the plasma elongation. (author) 15 figs., 13 refs

  7. Multiplicative formulation of quantum mechanics

    International Nuclear Information System (INIS)

    Voros, A.; Leboeuf, P.

    1991-01-01

    A general semi-classical description for the eigenfunctions of the multidimensional Schroedinger operator cannot be based on the WKB method which is incompatible with classically ergodic behavior. An alternative, more general multiplicative parametrization of quantum wave functions is suggested, whereby the semi-classical behavior of eigenfunctions can be traced in the presence of classical ergodicity, in the form of diffusive patterns of phase-space zeros in the quantum wave functions. (author) 24 refs.; 4 figs

  8. Advanced Variance Reduction for Global k-Eigenvalue Simulations in MCNP

    Energy Technology Data Exchange (ETDEWEB)

    Edward W. Larsen

    2008-06-01

    The "criticality" or k-eigenvalue of a nuclear system determines whether the system is critical (k=1), or the extent to which it is subcritical (k<1) or supercritical (k>1). Calculations of k are frequently performed at nuclear facilities to determine the criticality of nuclear reactor cores, spent nuclear fuel storage casks, and other fissile systems. These calculations can be expensive, and current Monte Carlo methods have certain well-known deficiencies. In this project, we have developed and tested a new "functional Monte Carlo" (FMC) method that overcomes several of these deficiencies. The current state-of-the-art Monte Carlo k-eigenvalue method estimates the fission source for a sequence of fission generations (cycles), during each of which M particles per cycle are processed. After a series of "inactive" cycles during which the fission source "converges," a series of "active" cycles are performed. For each active cycle, the eigenvalue and eigenfunction are estimated; after N >> 1 active cycles are performed, the results are averaged to obtain estimates of the eigenvalue and eigenfunction and their standard deviations. This method has several disadvantages: (i) the estimate of k depends on the number M of particles per cycle, (iii) for optically thick systems, the eigenfunction estimate may not converge due to undersampling of the fission source, and (iii) since the fission source in any cycle depends on the estimated fission source from the previous cycle (the fission sources in different cycles are correlated), the estimated variance in k is smaller than the real variance. For an acceptably large number M of particles per cycle, the estimate of k is nearly independent of M; this essentially takes care of item (i). Item (ii) can be addressed by taking M sufficiently large, but for optically thick systems a sufficiently large M can easily be unrealistic. Item (iii) cannot be accounted for by taking M or N sufficiently large; it is an inherent deficiency due

  9. The SU(1, 1) Perelomov number coherent states and the non-degenerate parametric amplifier

    Energy Technology Data Exchange (ETDEWEB)

    Ojeda-Guillén, D., E-mail: dojedag@ipn.mx; Granados, V. D. [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, C.P. 07738 México D. F. (Mexico); Mota, R. D. [Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacán, C.P. 04430, México D. F. (Mexico)

    2014-04-15

    We construct the Perelomov number coherent states for an arbitrary su(1, 1) group operation and study some of their properties. We introduce three operators which act on Perelomov number coherent states and close the su(1, 1) Lie algebra. By using the tilting transformation we apply our results to obtain the energy spectrum and eigenfunctions of the non-degenerate parametric amplifier. We show that these eigenfunctions are the Perelomov number coherent states of the two-dimensional harmonic oscillator.

  10. Ground state representation of the infinite one-dimensional Heisenberg ferromagnet. Pt. 2

    International Nuclear Information System (INIS)

    Babbitt, D.; Thomas, L.

    1977-01-01

    In its ground state representation, the infinite, spin 1/2 Heisenberg chain provides a model for spin wave scattering, which entails many features of the quantum mechanical N-body problem. Here, we give a complete eigenfunction expansion for the Hamiltonian of the chain in this representation, for all numbers of spin waves. Our results resolve the questions of completeness and orthogonality of the eigenfunctions given by Bethe for finite chains, in the infinite volume limit. (orig.) [de

  11. Born series for (2 cluster) → (2 cluster) scattering of two, three, and four particle Schroedinger operators

    International Nuclear Information System (INIS)

    Hagedorn, G.A.

    1979-01-01

    We investigate elastic and inelastic (2 cluster)→(2 cluster)scattering for classes of two, three, and four body Schroedinger operators H=H 0 +ΣVij. Formulas are derived for those generalized eigenfunctions of H which correspond asymptotically in the past to two freely moving clusters. With these eigenfunctions, we establish a formula for the (2 cluster)→(2 cluster) T-matrix and prove the convergence of a Born series for the T-matrix at high energy. (orig.) [de

  12. The Theory of Quantized Fields. III

    Science.gov (United States)

    Schwinger, J.

    1953-05-01

    In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transformation probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the intra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.

  13. Spin eigen-states of Dirac equation for quasi-two-dimensional electrons

    Energy Technology Data Exchange (ETDEWEB)

    Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)

    2015-10-15

    Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.

  14. Possibility of modifying the growth trajectory in Raeini Cashmere goat.

    Science.gov (United States)

    Ghiasi, Heydar; Mokhtari, M S

    2018-03-27

    The objective of this study was to investigate the possibility of modifying the growth trajectory in Raeini Cashmere goat breed. In total, 13,193 records on live body weight collected from 4788 Raeini Cashmere goats were used. According to Akanke's information criterion (AIC), the sing-trait random regression model included fourth-order Legendre polynomial for direct and maternal genetic effect; maternal and individual permanent environmental effect was the best model for estimating (co)variance components. The matrices of eigenvectors for (co)variances between random regression coefficients of direct additive genetic were used to calculate eigenfunctions, and different eigenvector indices were also constructed. The obtained results showed that the first eigenvalue explained 79.90% of total genetic variance. Therefore, changing the body weights applying the first eigenfunction will be obtained rapidly. Selection based on the first eigenvector will cause favorable positive genetic gains for all body weight considered from birth to 12 months of age. For modifying the growth trajectory in Raeini Cashmere goat, the selection should be based on the second eigenfunction. The second eigenvalue accounted for 14.41% of total genetic variance for body weights that is low in comparison with genetic variance explained by the first eigenvalue. The complex patterns of genetic change in growth trajectory observed under the third and fourth eigenfunction and low amount of genetic variance explained by the third and fourth eigenvalues.

  15. On a non-self adjoint eigenfunction expansion

    Directory of Open Access Journals (Sweden)

    D. Naylor

    1984-01-01

    Full Text Available This paper develops a formula of inversion for an integral transform similar to that associated with the names of Kontorovich and Lebedev. The kernel involves the Hankel function Hu(1(kr, in which r varies over a truncated infinite interval a≤r0 and the parameter k is complex. This kind of transform is useful in the investigation of functions that satisfy the Helmholtz equation and the condition of radiation.

  16. Application of eigenfunction orthogonalities to vibration problems

    CSIR Research Space (South Africa)

    Fedotov, I

    2009-07-01

    Full Text Available The modelling of vibration problems is of great importance in engineering. A popular method of analysing such problems is the variational method. The simplest vibration model is represented using the example of a long rod. Two kinds...

  17. Eigenfunctions of quadratic hamiltonians in Wigner representation

    International Nuclear Information System (INIS)

    Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.

    1984-01-01

    Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail

  18. Half-space albedo problem with modified F{sub N} method for linear and quadratic anisotropic scattering

    Energy Technology Data Exchange (ETDEWEB)

    Tuereci, R.G. [Kirikkale Univ., Kirikkale (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School

    2017-05-15

    One speed, time independent and homogeneous medium neutron transport equation can be solved with the anisotropic scattering which includes both the linear anisotropic and the quadratic anisotropic scattering properties. Having solved Case's eigenfunctions and the orthogonality relations among these eigenfunctions, some neutron transport problems such as albedo problem can be calculated as numerically by using numerical or semi-analytic methods. In this study the half-space albedo problem is investigated by using the modified F{sub N} method.

  19. The Schroedinger equation as a singular perturbation problem

    International Nuclear Information System (INIS)

    Jager, E.M. de; Kuepper, T.

    1978-01-01

    Comparisons are made of the eigenvalues and the corresponding eigenfunctions of the eigenvalue problem connected with the one dimensional Schroedinger equation in Hilbert space. The difference of the eigenvalues is estimated by applying Weyl's monotonicity principle and the minimum maximum principle. The difference of the eigenfunctions is estimated in L 2 norm and in maximum norm obtained by using simple tools from operator theory in Hilbert spaces. An application concerning perturbations of the Planck ideal linear oscillator is given. (author)

  20. EXCEPTIONAL POINTS IN OPEN AND PT-SYMMETRIC SYSTEMS

    Directory of Open Access Journals (Sweden)

    Hichem Eleuch

    2014-04-01

    Full Text Available Exceptional points (EPs determine the dynamics of open quantum systems and cause also PT symmetry breaking in PT symmetric systems. From a mathematical point of view, this is caused by the fact that the phases of the wavefunctions (eigenfunctions of a non-Hermitian Hamiltonian relative to one another are not rigid when an EP is approached. The system is therefore able to align with the environment to which it is coupled and, consequently, rigorous changes of the system properties may occur. We compare analytically as well as numerically the eigenvalues and eigenfunctions of a 2 × 2 matrix that is characteristic either of open quantum systems at high level density or of PT symmetric optical lattices. In both cases, the results show clearly the influence of the environment on the system in the neighborhood of EPs. Although the systems are very different from one another, the eigenvalues and eigenfunctions indicate the same characteristic features.

  1. The effects of plasma deformability on the feedback stabilization of axisymmetric modes in tokamak plasmas

    International Nuclear Information System (INIS)

    Ward, D.J.; Jardin, S.C.

    1991-09-01

    The effects of plasma deformability on the feedback stabilization of axisymmetric modes of tokamak plasmas are studied. It is seen that plasmas with strongly shaped cross sections have unstable motion different from a rigid shift. Furthermore, the placement of passive conductors is shown to modify the non-rigid components of the eigenfunction in a way that reduces the stabilizing eddy currents in these conductors. Passive feedback results using several equilibria of varying shape are presented. The eigenfunction is also modified under the effects of active feedback. This deformation is seen to depend strongly on the position of the flux loops which are used to determine plasma vertical position for the active feedback system. The variations of these non-rigid components of the eigenfunction always serve to reduce the stabilizing effect of the active feedback system by reducing the measurable poloidal flux at the flux-loop locations. Active feedback results are presented for the PBX-M tokamak configuration. (author) 19 figs., 2 tabs., 30 refs

  2. Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials

    Science.gov (United States)

    Horozov, Emil

    2016-05-01

    We construct new families of vector orthogonal polynomials that have the property to be eigenfunctions of some differential operator. They are extensions of the Hermite and Laguerre polynomial systems. A third family, whose first member has been found by Y. Ben Cheikh and K. Douak is also constructed. The ideas behind our approach lie in the studies of bispectral operators. We exploit automorphisms of associative algebras which transform elementary vector orthogonal polynomial systems which are eigenfunctions of a differential operator into other systems of this type.

  3. (Anti)symmetric multivariate exponential functions and corresponding Fourier transforms

    International Nuclear Information System (INIS)

    Klimyk, A U; Patera, J

    2007-01-01

    We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found

  4. THE BEHAVIOR OF TRANSVERSE WAVES IN NONUNIFORM SOLAR FLUX TUBES. I. COMPARISON OF IDEAL AND RESISTIVE RESULTS

    International Nuclear Information System (INIS)

    Soler, Roberto; Terradas, Jaume; Oliver, Ramón; Goossens, Marcel

    2013-01-01

    Magnetohydrodynamic (MHD) waves are ubiquitously observed in the solar atmosphere. Kink waves are a type of transverse MHD waves in magnetic flux tubes that are damped due to resonant absorption. The theoretical study of kink MHD waves in solar flux tubes is usually based on the simplification that the transverse variation of density is confined to a nonuniform layer much thinner than the radius of the tube, i.e., the so-called thin boundary approximation. Here, we develop a general analytic method to compute the dispersion relation and the eigenfunctions of ideal MHD waves in pressureless flux tubes with transversely nonuniform layers of arbitrary thickness. Results for kink waves are produced and compared with fully numerical resistive MHD eigenvalue computations in the limit of small resistivity. We find that the frequency and resonant damping rate are the same in both ideal and resistive cases. The actual results for thick nonuniform layers deviate from the behavior predicted in the thin boundary approximation and strongly depend on the shape of the nonuniform layer. The eigenfunctions in ideal MHD are very different from those in resistive MHD. The ideal eigenfunctions display a global character regardless of the thickness of the nonuniform layer, while the resistive eigenfunctions are localized around the resonance and are indistinguishable from those of ordinary resistive Alfvén modes. Consequently, the spatial distribution of wave energy in the ideal and resistive cases is dramatically different. This poses a fundamental theoretical problem with clear observational consequences

  5. SEARCH FOR GLOBAL f-MODES AND p-MODES IN THE {sup 8}B NEUTRINO FLUX

    Energy Technology Data Exchange (ETDEWEB)

    Lopes, Ilídio, E-mail: ilidio.lopes@ist.utl.pt, E-mail: ilopes@uevora.pt [Centro Multidisciplinar de Astrofísica, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Departamento de Física, Escola de Ciências e Tecnologia, Universidade de Évora, Colégio Luis António Verney, 7002-554 Évora (Portugal)

    2013-11-01

    The impact of global acoustic modes on the {sup 8}B neutrino flux time series is computed for the first time. It is shown that the time fluctuations of the {sup 8}B neutrino flux depend on the amplitude of acoustic eigenfunctions in the region where the {sup 8}B neutrino flux is produced: modes with low n (or order) that have eigenfunctions with a relatively large amplitude in the Sun's core strongly affect the neutrino flux; conversely, modes with high n that have eigenfunctions with a minimal amplitude in the Sun's core have a very small impact on the neutrino flux. It was found that the global modes with a larger impact on the {sup 8}B neutrino flux have a frequency of oscillation in the interval 250 μHz to 500 μHz (or a period in the interval 30 minutes to 70 minutes), such as the f-modes (n = 0) for the low degrees, radial modes of order n ≤ 3, and the dipole mode of order n = 1. Their corresponding neutrino eigenfunctions are very sensitive to the solar inner core and are unaffected by the variability of the external layers of the solar surface. If time variability of neutrinos is observed for these modes, it will lead to new ways of improving the sound speed profile inversion in the central region of the Sun.

  6. The driving mechanism of roAp stars

    Energy Technology Data Exchange (ETDEWEB)

    Dupret, M-A [Observatoire de Paris, LESIA, CNRS UMR 8109, 5 place J. Janssen, 92195 Meudon (France); Theado, S; Noels, A [Institut d' Astrophysique et Geophysique, Universite de Liege (Belgium)], E-mail: MA.dupret@obspm.fr

    2008-10-15

    We analyse in detail the driving mechanism of roAp stars and present the theoretical instability strip predicted by our models with solar metallicity. A particular attention is given to the interpretation of the role played by the different eigenfunctions in the stabilization of the modes at the red edge of the instability strip. The gradient of temperature in the H{sub I} opacity bump appears to play a major role in this context. We also consider the particular and complex role played by the shape of the eigenfunctions (location of the nodes, ...)

  7. Solving the Schroedinger equation using the finite difference time domain method

    International Nuclear Information System (INIS)

    Sudiarta, I Wayan; Geldart, D J Wallace

    2007-01-01

    In this paper, we solve the Schroedinger equation using the finite difference time domain (FDTD) method to determine energies and eigenfunctions. In order to apply the FDTD method, the Schroedinger equation is first transformed into a diffusion equation by the imaginary time transformation. The resulting time-domain diffusion equation is then solved numerically by the FDTD method. The theory and an algorithm are provided for the procedure. Numerical results are given for illustrative examples in one, two and three dimensions. It is shown that the FDTD method accurately determines eigenfunctions and energies of these systems

  8. Band theory of metals the elements

    CERN Document Server

    Altmann, Simon L

    1970-01-01

    Band Theory of Metals: The Elements focuses on the band theory of solids. The book first discusses revision of quantum mechanics. Topics include Heisenberg's uncertainty principle, normalization, stationary states, wave and group velocities, mean values, and variational method. The text takes a look at the free-electron theory of metals, including heat capacities, density of states, Fermi energy, core and metal electrons, and eigenfunctions in three dimensions. The book also reviews the effects of crystal fields in one dimension. The eigenfunctions of the translations; symmetry operations of t

  9. Spectral transform and orthogonality relations for the Kadomtsev-Petviashvili I equation

    Energy Technology Data Exchange (ETDEWEB)

    Boiti, M; Leon, J J.P.; Pempinelli, F [Montpellier-2 Univ., 34 (France). Lab. de Physique Mathematique

    1989-10-30

    We define a new spectral transform r(k,l) of the potential u in the time dependent Schroedinger equation (associated to the KPI equation). Orthogonality relations for the sectionally holomorphic eigenfunctions of the Schroedinger equation are used to express the spectral transform f(k,l) previously introduced by Manakov and Fokas and Ablowitz in terms of r(k,l). The main advantage of the new spectral transform r(k,l) is that its definition does not require to introduce an additional nonanalytic eigenfunction N. Characterization equations for r(k,l) are also obtained. (orig.).

  10. Application of the Asymptotic Taylor Expansion Method to Bistable Potentials

    Directory of Open Access Journals (Sweden)

    Okan Ozer

    2013-01-01

    Full Text Available A recent method called asymptotic Taylor expansion (ATEM is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistent with the existing literature.

  11. The driving mechanism of roAp stars

    International Nuclear Information System (INIS)

    Dupret, M-A; Theado, S; Noels, A

    2008-01-01

    We analyse in detail the driving mechanism of roAp stars and present the theoretical instability strip predicted by our models with solar metallicity. A particular attention is given to the interpretation of the role played by the different eigenfunctions in the stabilization of the modes at the red edge of the instability strip. The gradient of temperature in the H I opacity bump appears to play a major role in this context. We also consider the particular and complex role played by the shape of the eigenfunctions (location of the nodes, ...).

  12. Symmetry-adapted basis sets automatic generation for problems in chemistry and physics

    CERN Document Server

    Avery, John Scales; Avery, James Emil

    2012-01-01

    In theoretical physics, theoretical chemistry and engineering, one often wishes to solve partial differential equations subject to a set of boundary conditions. This gives rise to eigenvalue problems of which some solutions may be very difficult to find. For example, the problem of finding eigenfunctions and eigenvalues for the Hamiltonian of a many-particle system is usually so difficult that it requires approximate methods, the most common of which is expansion of the eigenfunctions in terms of basis functions that obey the boundary conditions of the problem. The computational effort needed

  13. Spectral transform and orthogonality relations for the Kadomtsev-Petviashvili I equation

    International Nuclear Information System (INIS)

    Boiti, M.; Leon, J.J.P.; Pempinelli, F.

    1989-01-01

    We define a new spectral transform r(k,l) of the potential u in the time dependent Schroedinger equation (associated to the KPI equation). Orthogonality relations for the sectionally holomorphic eigenfunctions of the Schroedinger equation are used to express the spectral transform f(k,l) previously introduced by Manakov and Fokas and Ablowitz in terms of r(k,l). The main advantage of the new spectral transform r(k,l) is that its definition does not require to introduce an additional nonanalytic eigenfunction N. Characterization equations for r(k,l) are also obtained. (orig.)

  14. Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model

    Science.gov (United States)

    Pont, Federico M.; Osenda, Omar; Serra, Pablo

    2018-05-01

    The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle regularised Calogero model is quasi-exactly solvable and that for certain values of the Hamiltonian parameters the eigenfunctions can be written in terms of Heun’s confluent polynomials. These eigenfunctions are such that the reduced density matrix of the two-particle density operator can be obtained exactly as well as its entanglement spectrum. We found that the number of non-zero eigenvalues of the reduced density matrix is finite in these cases. The limits for the cutoff distance going to zero (Calogero) and infinity are analysed and all the previously obtained results for the Calogero model are reproduced. Once the exact eigenfunctions are obtained, the exact von Neumann and Rényi entanglement entropies are studied to characterise the physical traits of the model. The quasi-exactly solvable character of the model is assessed studying the numerically calculated Rényi entropy and entanglement spectrum for the whole parameter space.

  15. Spectrum and Collapse of a Particle in a Nonlocal Field of Centrifugal Type

    CERN Document Server

    Pupyshev, V V

    2004-01-01

    The investigated problem is the one-dimensional Schrödinger equation with the zero boundary conditions at the ends of the segment $[0,\\pi/2]$, and the interaction equal to the product of the potential proportional to squared secant of the argument and the sum of the unity and integral operators. For this problem the dependence of the spectrum of real eigenvalues and the corresponding eigenfunctions on the real potential parameter is analyzed qualitatively and numerically. For analysis the Fourier- and spline-approximations of the searched eigenfunction are proposed and applied. Special attention is paid to the particle collapse.

  16. Comment on "Calculations for the one-dimensional soft Coulomb problem and the hard Coulomb limit".

    Science.gov (United States)

    Carrillo-Bernal, M A; Núñez-Yépez, H N; Salas-Brito, A L; Solis, Didier A

    2015-02-01

    In the referred paper, the authors use a numerical method for solving ordinary differential equations and a softened Coulomb potential -1/√[x(2)+β(2)] to study the one-dimensional Coulomb problem by approaching the parameter β to zero. We note that even though their numerical findings in the soft potential scenario are correct, their conclusions do not extend to the one-dimensional Coulomb problem (β=0). Their claims regarding the possible existence of an even ground state with energy -∞ with a Dirac-δ eigenfunction and of well-defined parity eigenfunctions in the one-dimensional hydrogen atom are questioned.

  17. A new approach to the Schrödinger equation with rational potentials

    Science.gov (United States)

    Dong, Ming-de; Chu, Jue-Hui

    1984-04-01

    A new analytic theory is established for the Schrödinger equation with a rational potential, including a complete classification of the regular eigenfunctions into three different types, an exact method of obtaining wavefunctions, an explicit formulation of the spectral equation (3 x 3 determinant) etc. All representations are exhibited in a unifying way via function-theoretic methods and therefore given in explicit form, in contrast to the prevailing discussion appealing to perturbation or variation methods or continued-fraction techniques. The irregular eigenfunctions at infinity can be obtained analogously and will be discussed separately as another solvable case for singular potentials.

  18. Destabilization of drift waves due to nonuniform density gradient

    International Nuclear Information System (INIS)

    Hirose, A.; Ishihara, O.

    1985-01-01

    It is shown that the conventional mode differential equation for low frequency electrostatic waves in a tokamak does not contain full ion dynamics. Both electrons and ions contribute to the ballooning term, which is subject to finite ion Larmor radius effects. Also, both fluid ion approximation and kinetic ion model yield the same correction. Reexamined are the density gradient universal mode and ion temperature gradient instability employing the lowest order Pearlstein-Berk type radial eigenfunctions. No unstable, bounded, energy outgoing eigenfunctions have been found. In particular, a large ion temperature gradient (eta/sub i/) tends to further stabilize the temperature gradient driven mode

  19. Analytic solution of boundary-value problems for nonstationary model kinetic equations

    International Nuclear Information System (INIS)

    Latyshev, A.V.; Yushkanov, A.A.

    1993-01-01

    A theory for constructing the solutions of boundary-value problems for non-stationary model kinetic equations is constructed. This theory was incorrectly presented equation, separation of the variables is used, this leading to a characteristic equation. Eigenfunctions are found in the space of generalized functions, and the eigenvalue spectrum is investigated. An existence and uniqueness theorem for the expansion of the Laplace transform of the solution with respect to the eigenfunctions is proved. The proof is constructive and gives explicit expressions for the expansion coefficients. An application to the Rayleigh problem is obtained, and the corresponding result of Cercignani is corrected

  20. Quantum influence of topological defects in Goedel-type space-times

    Energy Technology Data Exchange (ETDEWEB)

    Carvalho, Josevi [Universidade Federal de Campina Grande, Unidade Academica de Tecnologia de Alimentos, Centro de Ciencias e Tecnologia Agroalimentar, Pombal, PB (Brazil); Carvalho, M.; Alexandre, M. de [Universidade Federal de Alagoas, Instituto de Fisica, Maceio, AL (Brazil); Furtado, Claudio [Universidade Federal da Paraiba, Cidade Universitaria, Departamento de Fisica, CCEN, Joao Pessoa, PB (Brazil)

    2014-06-15

    In this contribution, some solutions of the Klein-Gordon equation in Goedel-type metrics with an embedded cosmic string are considered. The quantum dynamics of a scalar particle in three spaces whose metrics are described by different classes of Goedel solutions, with a cosmic string passing through the spaces, is found. The energy levels and eigenfunctions of the Klein-Gordon operator are obtained. We show that these eigenvalues and eigenfunctions depend on the parameter characterizing the presence of a cosmic string in the space-time. We note that the presence of topological defects breaks the degeneracy of energy levels. (orig.)

  1. Eigenfunctions in disordered systems near the mobility edge

    International Nuclear Information System (INIS)

    Brezini, A.

    1982-08-01

    A model is proposed to calculate the average probability and the average size of the localization domain for an electron being localized at a given site in a Cayley tree lattice. The numerical results are presented in the limit of weak disorder in the case of Cauchy distribution for site energies. Attention is paid to the states near the mobility edge in the localized regime. Particularly, features exhibited in the linear chain case are observed for the first time for higher dimensions. (author)

  2. Inertial modes of rigidly rotating neutron stars in Cowling approximation

    International Nuclear Information System (INIS)

    Kastaun, Wolfgang

    2008-01-01

    In this article, we investigate inertial modes of rigidly rotating neutron stars, i.e. modes for which the Coriolis force is dominant. This is done using the assumption of a fixed spacetime (Cowling approximation). We present frequencies and eigenfunctions for a sequence of stars with a polytropic equation of state, covering a broad range of rotation rates. The modes were obtained with a nonlinear general relativistic hydrodynamic evolution code. We further show that the eigenequations for the oscillation modes can be written in a particularly simple form for the case of arbitrary fast but rigid rotation. Using these equations, we investigate some general characteristics of inertial modes, which are then compared to the numerically obtained eigenfunctions. In particular, we derive a rough analytical estimate for the frequency as a function of the number of nodes of the eigenfunction, and find that a similar empirical relation matches the numerical results with unexpected accuracy. We investigate the slow rotation limit of the eigenequations, obtaining two different sets of equations describing pressure and inertial modes. For the numerical computations we only considered axisymmetric modes, while the analytic part also covers nonaxisymmetric modes. The eigenfunctions suggest that the classification of inertial modes by the quantum numbers of the leading term of a spherical harmonic decomposition is artificial in the sense that the largest term is not strongly dominant, even in the slow rotation limit. The reason for the different structure of pressure and inertial modes is that the Coriolis force remains important in the slow rotation limit only for inertial modes. Accordingly, the scalar eigenequation we obtain in that limit is spherically symmetric for pressure modes, but not for inertial modes

  3. A low dimensional dynamical system for the wall layer

    Science.gov (United States)

    Aubry, N.; Keefe, L. R.

    1987-01-01

    Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging.

  4. Improved statistical power with a sparse shape model in detecting an aging effect in the hippocampus and amygdala

    Science.gov (United States)

    Chung, Moo K.; Kim, Seung-Goo; Schaefer, Stacey M.; van Reekum, Carien M.; Peschke-Schmitz, Lara; Sutterer, Matthew J.; Davidson, Richard J.

    2014-03-01

    The sparse regression framework has been widely used in medical image processing and analysis. However, it has been rarely used in anatomical studies. We present a sparse shape modeling framework using the Laplace- Beltrami (LB) eigenfunctions of the underlying shape and show its improvement of statistical power. Tradition- ally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes as a form of Fourier descriptors. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we present a LB-based method to filter out only the significant eigenfunctions by imposing a sparse penalty. For dense anatomical data such as deformation fields on a surface mesh, the sparse regression behaves like a smoothing process, which will reduce the error of incorrectly detecting false negatives. Hence the statistical power improves. The sparse shape model is then applied in investigating the influence of age on amygdala and hippocampus shapes in the normal population. The advantage of the LB sparse framework is demonstrated by showing the increased statistical power.

  5. Mixed-mode loading of the structural elements with defect

    Directory of Open Access Journals (Sweden)

    Larisa V. Stepanova

    2015-06-01

    Full Text Available In the article the problem of determining the stress-strain state near the mixed-mode crack tip in a power-law material under plane stress conditions is considered. The eigenfunction method is used for the mixed-mode crack tip problem. It is shown that the eigenfunction expansion method results in the nonlinear eigenvalue problem. The numeric solution of the nonlinear eigenvalue problem formulated is obtained. The power of the distance from the crack tip is the eigenvalue of the nonlinear eigenvalue problem considered whereas the angular distributions of the stress components are the eigenfunctions. The new eigenvalues different from the eigenvalues of the Hutchinson–Rice–Rosengren are found. It is shown that the new asymptotic solution can be interpreted as the self-similar intermediate asymptotics of the stress field in the vicinity of the crack tip at distances which are very small compared to the crack length or the size of the specimen and at distances which are large compared to the length of the completely damaged zone. The developed method allows us to construct the geometry of the completely damaged zone in vicinity of the crack tip.

  6. Expressive body movement responses to music are coherent, consistent, and low dimensional.

    Science.gov (United States)

    Amelynck, Denis; Maes, Pieter-Jan; Martens, Jean Pierre; Leman, Marc

    2014-12-01

    Embodied music cognition stresses the role of the human body as mediator for the encoding and decoding of musical expression. In this paper, we set up a low dimensional functional model that accounts for 70% of the variability in the expressive body movement responses to music. With the functional principal component analysis, we modeled individual body movements as a linear combination of a group average and a number of eigenfunctions. The group average and the eigenfunctions are common to all subjects and make up what we call the commonalities. An individual performance is then characterized by a set of scores (the individualities), one score per eigenfunction. The model is based on experimental data which finds high levels of coherence/consistency between participants when grouped according to musical education. This shows an ontogenetic effect. Participants without formal musical education focus on the torso for the expression of basic musical structure (tempo). Musically trained participants decode additional structural elements in the music and focus on body parts having more degrees of freedom (such as the hands). Our results confirm earlier studies that different body parts move differently along with the music.

  7. Quantum nodal points as fingerprints of classical chaos

    International Nuclear Information System (INIS)

    Leboeuf, P.; Voros, A.

    1992-08-01

    Semiclassical analysis of the individual eigenfunctions in a quantum system is presented, especially when the classical dynamics is chaotic and the quantum bound states are considered. Quantum maps have emerged as ideal dynamical models for basic studies, with their ability to exhibit classical chaos within a single degree of freedom. On the other hand, phase space techniques have become recognized as extremely powerful for describing quantum states. It is argued that representations of eigenfunctions are essential for semiclassical analysis. An explicit realization of that program in one degree is overviewed, in which the crucial ingredient is a phase-space parametrization of 1-d wave-functions. (K.A.) 44 refs.; 6 figs

  8. Theoretical calculation of the spectra, the EPR g-factors and the magnetic susceptibilities of Cu2+ ion in Cs2CuCl4

    International Nuclear Information System (INIS)

    Shuen Wei Li.

    1991-08-01

    The crystal-field and spin-orbit matrix for d 1 or d 9 configuration with D 2 symmetry has been derived. By diagonalizing the matrix, the energy level of C 2+ u in Cs 2 CuCl 4 and its eigenfunctions have been obtained with the aid of the approximate SCF d-orbit. Furthermore, by suing the eigenfunctions, the EPR g-factors and the magnetic susceptibilities at different temperatures have been calculated. The calculated results are in good agreement with the experimental findings. The calculation only needs two adjustable parameters and can give more theoretical results than those of previous work which introduced 11 adjustable parameters. (author). 16 refs, 3 tabs

  9. Semi-analytic modeling of tokamak particle transport

    International Nuclear Information System (INIS)

    Shi Bingren; Long Yongxing; Li Jiquan

    2000-01-01

    The linear particle transport equation of tokamak plasma is analyzed. Particle flow consists of an outward diffusion and an inward convection. General solution is expressed in terms of a Green function constituted by eigen-functions of corresponding Sturm-Liouville problem. For a particle source near the plasma edge (shadow fueling), a well-behaved solution in terms of Fourier series can be constituted by using the complementarity relation. It can be seen from the lowest eigen-function that the particle density becomes peaked when the wall recycling reduced. For a transient point source in the inner region, a well-behaved solution can be obtained by the complementarity as well

  10. Generalized perturbation theory using two-dimensional, discrete ordinates transport theory

    International Nuclear Information System (INIS)

    Childs, R.L.

    1979-01-01

    Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using two-dimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions Λ and Λ*. Demonstration calculations were performed for changes in a reaction-rate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed to obtain these eigenfunctions

  11. Interbasis expansions for isotropic harmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Dong, Shi-Hai, E-mail: dongsh2@yahoo.com [Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, Mexico D.F. 07738 (Mexico)

    2012-03-12

    The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n. -- Highlights: ► Exact solutions of harmonic oscillator are reviewed in three coordinates. ► Interbasis expansions of the eigenfunctions is solved completely. ► This is occurred only for those degenerated states for given quantum number n.

  12. Fluctuations of wavefunctions about their classical average

    International Nuclear Information System (INIS)

    Benet, L; Flores, J; Hernandez-Saldana, H; Izrailev, F M; Leyvraz, F; Seligman, T H

    2003-01-01

    Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations of the quantum wavefunctions around the classical value are discussed. A simple random matrix model leads to a Gaussian distribution of the amplitudes whose width is determined by the classical shape of the eigenfunction. To compare this prediction with numerical calculations in chaotic models of coupled quartic oscillators, we develop a rescaling method for the components. The expectations are broadly confirmed, but deviations due to scars are observed. This effect is much reduced when both Hamiltonians have chaotic dynamics

  13. Closure of the squared Zakharov--Shabat eigenstates

    International Nuclear Information System (INIS)

    Kaup, D.J.

    1976-01-01

    By solution of the inverse scattering problem for a third-order (degenerate) eigenvalue problem, the closure of the squared eigenfunctions of the Zakharov--Shabat equations is found. The question of the completeness of squared eigenstates occurs in many aspects of ''inverse scattering transforms'' (solving nonlinear evolution equations exactly by inverse scattering techniques), as well as in various aspects of the inverse scattering problem. The method used here is quite suggestive as to how one might find the closure of the squared eigenfunctions of other eigenvalue equations, and the strong analogy between these results and the problem of finding the closure of the eigenvectors of a nonself-adjoint matrix is pointed out

  14. On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator

    Science.gov (United States)

    Korda, Milan; Mezić, Igor

    2018-04-01

    Extended dynamic mode decomposition (EDMD) (Williams et al. in J Nonlinear Sci 25(6):1307-1346, 2015) is an algorithm that approximates the action of the Koopman operator on an N-dimensional subspace of the space of observables by sampling at M points in the state space. Assuming that the samples are drawn either independently or ergodically from some measure μ , it was shown in Klus et al. (J Comput Dyn 3(1):51-79, 2016) that, in the limit as M→ ∞, the EDMD operator K_{N,M} converges to K_N, where K_N is the L_2(μ )-orthogonal projection of the action of the Koopman operator on the finite-dimensional subspace of observables. We show that, as N → ∞, the operator K_N converges in the strong operator topology to the Koopman operator. This in particular implies convergence of the predictions of future values of a given observable over any finite time horizon, a fact important for practical applications such as forecasting, estimation and control. In addition, we show that accumulation points of the spectra of K_N correspond to the eigenvalues of the Koopman operator with the associated eigenfunctions converging weakly to an eigenfunction of the Koopman operator, provided that the weak limit of the eigenfunctions is nonzero. As a by-product, we propose an analytic version of the EDMD algorithm which, under some assumptions, allows one to construct K_N directly, without the use of sampling. Finally, under additional assumptions, we analyze convergence of K_{N,N} (i.e., M=N), proving convergence, along a subsequence, to weak eigenfunctions (or eigendistributions) related to the eigenmeasures of the Perron-Frobenius operator. No assumptions on the observables belonging to a finite-dimensional invariant subspace of the Koopman operator are required throughout.

  15. Zero-range approximation for two-component boson systems

    International Nuclear Information System (INIS)

    Sogo, T.; Fedorov, D.V.; Jensen, A.S.

    2005-01-01

    The hyperspherical adiabatic expansion method is combined with the zero-range approximation to derive angular Faddeev-like equations for two-component boson systems. The angular eigenvalues are solutions to a transcendental equation obtained as a vanishing determinant of a 3 x 3 matrix. The eigenfunctions are linear combinations of Jacobi functions of argument proportional to the distance between pairs of particles. We investigate numerically the influence of two-body correlations on the eigenvalue spectrum, the eigenfunctions and the effective hyperradial potential. Correlations decrease or increase the distance between pairs for effectively attractive or repulsive interactions, respectively. New structures appear for non-identical components. Fingerprints can be found in the nodal structure of the density distributions of the condensates. (author)

  16. Method of local pointed function reduction of original shape in Fourier transformation

    International Nuclear Information System (INIS)

    Dosch, H.; Slavyanov, S.Yu.

    2002-01-01

    The method for analytical reduction of the original shape in the one-dimensional Fourier transformation by the fourier image modulus is proposed. The basic concept of the method consists in the presentation of the model shape in the form of the local peak functions sum. The eigenfunctions, generated by the linear differential equations with the polynomial coefficients, are selected as the latter ones. This provides for the possibility of managing the Fourier transformation without numerical integration. This reduces the reverse task to the nonlinear regression with a small number of the evaluated parameters and to the numerical or asymptotic study on the model peak functions - the eigenfunctions of the differential tasks and their fourier images [ru

  17. Nuclear spectroscopy and quantum chaos

    International Nuclear Information System (INIS)

    Sakata, Fumihiko; Marumori, Toshio; Hashimoto, Yukio; Yamamoto, Yoshifumi; Tsukuma, Hidehiko; Iwasawa, Kazuo.

    1990-05-01

    In this paper, a recent development of INS-TSUKUBA joint research project on large-amplitude collective motion is summerized. The classical theory of nuclear collective dynamics formulated within the time-dependent Hartree-Fock theory is recapitulated and decisive role of the level crossing in the single-particle dynamics on the order-to-chaos transition of collective motion is discussed in detail. Extending the basic idea of the classical theory, we discuss a quantum theory of nuclear collective dynamics which allows us to properly define a concept of quantum chaos for each eigenfunction. By using numerical calculation, we illustrate what the quantum chaos for each eigenfunction means and its relation to usual definition based on the random matrix theory. (author)

  18. Numerical analysis of quasiperiodic perturbations for the Alfven wave

    International Nuclear Information System (INIS)

    Yamakoshi, Y.; Muto, K.; Yoshida, Z.

    1994-01-01

    The Alfven wave may have a localized eigenfunction when it propagates on a chaotic magnetic field. The Arnold-Beltrami-Childress (ABC) flow is a paradigm of chaotic stream lines and is a simple exact solution to the three-dimensional force-free plasma equilibrium equations. The three-dimensional structure of the magnetic field is represented by sinusoidal quasiperiodic modulation. The short wavelength Alfven wave equation for the ABC-flow magnetic field has a quasiperiodic potential term, which induces interference among ''Bragg-reflected'' waves with irregular phases. Then the eigenfunction decays at long distance and a point spectrum occurs. Two different types of short wavelength modes have numerically analyzed to demonstrate the existence of localized Alfven wave eigenmodes

  19. Multi-group neutron transport theory

    International Nuclear Information System (INIS)

    Zelazny, R.; Kuszell, A.

    1962-01-01

    Multi-group neutron transport theory. In the paper the general theory of the application of the K. M. Case method to N-group neutron transport theory in plane geometry is given. The eigenfunctions (distributions) for the system of Boltzmann equations have been derived and the completeness theorem has been proved. By means of general solution two examples important for reactor and shielding calculations are given: the solution of a critical and albedo problem for a slab. In both cases the system of singular integral equations for expansion coefficients into a full set of eigenfunction distributions has been reduced to the system of Fredholm-type integral equations. Some results can be applied also to some spherical problems. (author) [fr

  20. The Pauli equation with differential operators for the spin

    International Nuclear Information System (INIS)

    Kern, E.

    1978-01-01

    The spin operator s = (h/2) sigma in the Pauli equation fulfills the commutation relation of the angular momentum and leads to half-integer eigenvalues of the eigenfunctions for s. If one tries to express s by canonically conjugated operators PHI and π = ( /i)delta/deltaPHI the formal angular momentum term s = PHIxπ fails because it leads only to whole-integer eigenvalues. However, the modification of this term in the form s = 1/2(π+PHI(PHI π)+PHIxπ) leads to the required result. The eigenfunction system belonging to this differential operator s(PHI, π) consists of (2s + 1) spin eigenfunctions xim(PHI) which are given explicitly. They form a basis for the wave functions of a particle of spin s. Applying this formalism to particles with s = 1/2, agreement is reached with Pauli's spin theory. The function s(PHI, π) follows from the theory of rotating rigid bodies. The continuous spin-variable PHI = ( x, y, z) can be interpreted classically as a 'turning vector' which defines the orientation in space of a rigid body. PHI is the positioning coordinate of the rigid body or the spin coordinate of the particle in analogy to the cartesian coordinate x. The spin s is a vector fixed to the body. (orig.) [de

  1. Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions

    Science.gov (United States)

    Prinari, Barbara; Demontis, Francesco; Li, Sitai; Horikis, Theodoros P.

    2018-04-01

    The inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m × m matrix nonlinear Schrödinger-type equation which, in the case m = 2, has been proposed as a model to describe hyperfine spin F = 1 spinor Bose-Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interactions and ferromagnetic spin-exchange interactions (self-focusing case). The IST for this system was first presented by Ieda et al. (2007) , using a different approach. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows to develop the IST on the standard complex plane, instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity of the scattering eigenfunctions and scattering data, symmetries, properties of the discrete spectrum, and asymptotics are derived. The inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided. In addition, the general behavior of the soliton solutions is analyzed in detail in the 2 × 2 self-focusing case, including some special solutions not previously discussed in the literature.

  2. Waves propagating over a two-layer porous barrier on a seabed

    Science.gov (United States)

    Lin, Qiang; Meng, Qing-rui; Lu, Dong-qiang

    2018-05-01

    A research of wave propagation over a two-layer porous barrier, each layer of which is with different values of porosity and friction, is conducted with a theoretical model in the frame of linear potential flow theory. The model is more appropriate when the seabed consists of two different properties, such as rocks and breakwaters. It is assumed that the fluid is inviscid and incompressible and the motion is irrotational. The wave numbers in the porous region are complex ones, which are related to the decaying and propagating behaviors of wave modes. With the aid of the eigenfunction expansions, a new inner product of the eigenfunctions in the two-layer porous region is proposed to simplify the calculation. The eigenfunctions, under this new definition, possess the orthogonality from which the expansion coefficients can be easily deduced. Selecting the optimum truncation of the series, we derive a closed system of simultaneous linear equations for the same number of the unknown reflection and transmission coefficients. The effects of several physical parameters, including the porosity, friction, width, and depth of the porous barrier, on the dispersion relation, reflection and transmission coefficients are discussed in detail through the graphical representations of the solutions. It is concluded that these parameters have certain impacts on the reflection and transmission energy.

  3. Inverse scattering transform for the KPI equation on the background of a one-line soliton*Inverse scattering transform for the KPI equation on the background of a one-line soliton

    Science.gov (United States)

    Fokas, A. S.; Pogrebkov, A. K.

    2003-03-01

    We study the initial value problem of the Kadomtsev-Petviashvili I (KPI) equation with initial data u(x1,x2,0) = u1(x1)+u2(x1,x2), where u1(x1) is the one-soliton solution of the Korteweg-de Vries equation evaluated at zero time and u2(x1,x2) decays sufficiently rapidly on the (x1,x2)-plane. This involves the analysis of the nonstationary Schrödinger equation (with time replaced by x2) with potential u(x1,x2,0). We introduce an appropriate sectionally analytic eigenfunction in the complex k-plane where k is the spectral parameter. This eigenfunction has the novelty that in addition to the usual jump across the real k-axis, it also has a jump across a segment of the imaginary k-axis. We show that this eigenfunction can be reconstructed through a linear integral equation uniquely defined in terms of appropriate scattering data. In turn, these scattering data are uniquely constructed in terms of u1(x1) and u2(x1,x2). This result implies that the solution of the KPI equation can be obtained through the above linear integral equation where the scattering data have a simple t-dependence.

  4. Eigenfunction statistics for Anderson model with Hölder continuous ...

    Indian Academy of Sciences (India)

    The Institute of Mathematical Sciences, Taramani, Chennai 600 113, India ... Anderson model; Hölder continuous measure; Poisson statistics. ...... [4] Combes J-M, Hislop P D and Klopp F, An optimal Wegner estimate and its application to.

  5. Linear augmented plane wave method for self-consistent calculations

    International Nuclear Information System (INIS)

    Takeda, T.; Kuebler, J.

    1979-01-01

    O.K. Andersen has recently introduced a linear augmented plane wave method (LAPW) for the calculation of electronic structure that was shown to be computationally fast. A more general formulation of an LAPW method is presented here. It makes use of a freely disposable number of eigenfunctions of the radial Schroedinger equation. These eigenfunctions can be selected in a self-consistent way. The present formulation also results in a computationally fast method. It is shown that Andersen's LAPW is obtained in a special limit from the present formulation. Self-consistent test calculations for copper show the present method to be remarkably accurate. As an application, scalar-relativistic self-consistent calculations are presented for the band structure of FCC lanthanum. (author)

  6. Model for Simulation Atmospheric Turbulence

    DEFF Research Database (Denmark)

    Lundtang Petersen, Erik

    1976-01-01

    A method that produces realistic simulations of atmospheric turbulence is developed and analyzed. The procedure makes use of a generalized spectral analysis, often called a proper orthogonal decomposition or the Karhunen-Loève expansion. A set of criteria, emphasizing a realistic appearance...... eigenfunctions and estimates of the distributions of the corresponding expansion coefficients. The simulation method utilizes the eigenfunction expansion procedure to produce preliminary time histories of the three velocity components simultaneously. As a final step, a spectral shaping procedure is then applied....... The method is unique in modeling the three velocity components simultaneously, and it is found that important cross-statistical features are reasonably well-behaved. It is concluded that the model provides a practical, operational simulator of atmospheric turbulence....

  7. (Weakly) three-dimensional caseology

    International Nuclear Information System (INIS)

    Pomraning, G.C.

    1996-01-01

    The singular eigenfunction technique of Case for solving one-dimensional planar symmetry linear transport problems is extended to a restricted class of three-dimensional problems. This class involves planar geometry, but with forcing terms (either boundary conditions or internal sources) which are weakly dependent upon the transverse spatial variables. Our analysis involves a singular perturbation about the classic planar analysis, and leads to the usual Case discrete and continuum modes, but modulated by weakly dependent three-dimensional spatial functions. These functions satisfy parabolic differential equations, with a different diffusion coefficient for each mode. Representative one-speed time-independent transport problems are solved in terms of these generalised Case eigenfunctions. Our treatment is very heuristic, but may provide an impetus for more rigorous analysis. (author)

  8. Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method

    Science.gov (United States)

    Zhou, Zhenhuan; Li, Yuejie; Fan, Junhai; Rong, Dalun; Sui, Guohao; Xu, Chenghui

    2018-05-01

    A new Hamiltonian-based approach is presented for finding exact solutions for transverse vibrations of double-nanobeam-systems embedded in an elastic medium. The continuum model is established within the frameworks of the symplectic methodology and the nonlocal Euler-Bernoulli and Timoshenko beam beams. The symplectic eigenfunctions are obtained after expressing the governing equations in a Hamiltonian form. Exact frequency equations, vibration modes and displacement amplitudes are obtained by using symplectic eigenfunctions and end conditions. Comparisons with previously published work are presented to illustrate the accuracy and reliability of the proposed method. The comprehensive results for arbitrary boundary conditions could serve as benchmark results for verifying numerically obtained solutions. In addition, a study on the difference between the nonlocal beam and the nonlocal plate is also included.

  9. Charge-changing transitions in an extended Lipkin-type model

    International Nuclear Information System (INIS)

    Mihut, I.; Stoica, S.; Suhonen, J.

    1997-01-01

    Charge-changing transition are considered in an extended Lipkin-Meshkov-Glick (LMG) model taking into account explicitly the proton and neutron degrees of freedom. The proton and neutron Hamiltonians are taken to be of the LMG form and in addition, a residual proton-neutron interaction is included. Model charge-changing operators and their action on eigenfunctions of the model Hamiltonian are defined. Transition amplitudes of these operators are calculated using exact eigenfunctions and then the RPA approximation. The best agreement between the two kinds of calculations was obtained when the correlated RPA ground state, instead of the uncorrelated HF ground state, is employed and when the proton-neutron residual interaction besides the proton-proton and neutron-neutron residual interactions is taken into account in the model Hamiltonian

  10. Towards a multigrid scheme in SU(2) lattice gauge theory

    International Nuclear Information System (INIS)

    Gutbrod, F.

    1992-12-01

    The task of constructing a viable updating multigrid scheme for SU(2) lattice gauge theory is discussed in connection with the classical eigenvalue problem. For a nonlocal overrelaxation Monte Carlo update step, the central numerical problem is the search for the minimum of a quadratic approximation to the action under nonlocal constraints. Here approximate eigenfunctions are essential to reduce the numerical work, and these eigenfunctions are to be constructed with multigrid techniques. A simple implementation on asymmetric lattices is described, where the grids are restricted to 3-dimensional hyperplanes. The scheme is shown to be moderately successful in the early stages of the updating history (starting from a cold configuration). The main results of another, less asymmetric scheme are presented briefly. (orig.)

  11. Inverse scattering transform for the vector nonlinear Schroedinger equation with nonvanishing boundary conditions

    International Nuclear Information System (INIS)

    Prinari, Barbara; Ablowitz, Mark J.; Biondini, Gino

    2006-01-01

    The inverse scattering transform for the vector defocusing nonlinear Schroedinger (NLS) equation with nonvanishing boundary values at infinity is constructed. The direct scattering problem is formulated on a two-sheeted covering of the complex plane. Two out of the six Jost eigenfunctions, however, do not admit an analytic extension on either sheet of the Riemann surface. Therefore, a suitable modification of both the direct and the inverse problem formulations is necessary. On the direct side, this is accomplished by constructing two additional analytic eigenfunctions which are expressed in terms of the adjoint eigenfunctions. The discrete spectrum, bound states and symmetries of the direct problem are then discussed. In the most general situation, a discrete eigenvalue corresponds to a quartet of zeros (poles) of certain scattering data. The inverse scattering problem is formulated in terms of a generalized Riemann-Hilbert (RH) problem in the upper/lower half planes of a suitable uniformization variable. Special soliton solutions are constructed from the poles in the RH problem, and include dark-dark soliton solutions, which have dark solitonic behavior in both components, as well as dark-bright soliton solutions, which have one dark and one bright component. The linear limit is obtained from the RH problem and is shown to correspond to the Fourier transform solution obtained from the linearized vector NLS system

  12. Algorithm for Stabilizing a POD-Based Dynamical System

    Science.gov (United States)

    Kalb, Virginia L.

    2010-01-01

    This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

  13. Many particle systems with inverse square potential, Riccatti equation and completely integrable systems connected with Schroedinger operator

    International Nuclear Information System (INIS)

    Chudnovsky, David; Chudnovsky, G.V.

    1978-01-01

    The relations between many particle problem with inverse square potential on the line and meromorphic eigenfunctions of Schroedinger operator are presented. This gives new type of Backlund transformations for many particle problem [fr

  14. An algebraic approach to the non-symmetric Macdonald polynomial

    International Nuclear Information System (INIS)

    Nishino, Akinori; Ujino, Hideaki; Wadati, Miki

    1999-01-01

    In terms of the raising and lowering operators, we algebraically construct the non-symmetric Macdonald polynomials which are simultaneous eigenfunctions of the commuting Cherednik operators. We also calculate Cherednik's scalar product of them

  15. Fermionic particles with position-dependent mass in the presence of ...

    Indian Academy of Sciences (India)

    2013-02-01

    Feb 1, 2013 ... Quantum mechanical systems with position-dependent mass are proved ... The relativistic energy eigenvalues of the Dirac equation with ... the exact eigenfunctions can be derived from the following wave function generator:.

  16. Supersymmetric quantum mechanics and new potentials

    International Nuclear Information System (INIS)

    Drigo Filho, E.

    1988-01-01

    Using the supersymmetric quantum mechanics the following potential are generalized. The particle in the box, Poeschl-Teller and Rosen-Morse. The new potentials are evaluated and their eigenfunctions and spectra are indicated. (author) [pt

  17. Vibration modes of 3n-gaskets and other fractals

    Energy Technology Data Exchange (ETDEWEB)

    Bajorin, N; Chen, T; Dagan, A; Emmons, C; Hussein, M; Khalil, M; Mody, P; Steinhurst, B; Teplyaev, A [Department of Mathematics, University of Connecticut, Storrs CT 06269 (United States)

    2008-01-11

    We rigorously study eigenvalues and eigenfunctions (vibration modes) on the class of self-similar symmetric finitely ramified fractals, which include the Sierpinski gasket and other 3n-gaskets. We consider the classical Laplacian on fractals which generalizes the usual one-dimensional second derivative, is the generator of the self-similar diffusion process, and has possible applications as the quantum Hamiltonian. We develop a theoretical matrix analysis, including analysis of singularities, which allows us to compute eigenvalues, eigenfunctions and their multiplicities exactly. We support our theoretical analysis by symbolic and numerical computations. Our analysis, in particular, allows the computation of the spectral zeta function on fractals and the limiting distribution of eigenvalues (i.e., integrated density of states). We consider such examples as the level-3 Sierpinski gasket, a fractal 3-tree, and the diamond fractal.

  18. Matrix-variational method: an efficient approach to bound state eigenproblems

    International Nuclear Information System (INIS)

    Gerck, E.; d'Oliveira, A.B.

    1978-11-01

    A new matrix-variational method for solving the radial Schroedinger equation is described. It consists in obtaining an adjustable matrix formulation for the boundary value differential equation, using a set of three functions that obey the boundary conditions. These functions are linearly combined at every three adjacents points to fit the true unknown eigenfunction by a variational technique. With the use of a new class of central differences, the exponential differences, tridiagonal or bidiagonal matrices are obtained. In the bidiagonal case, closed form expressions for the eigenvalues are given for the Coulomb, harmonic, linear, square-root and logarithmic potentials. The values obtained are within 0.1% of the true numerical value. The eigenfunction can be calculated using the eigenvectors to reconstruct the linear combination of the set functions [pt

  19. One-group transport theory calculation for three slabs cells

    International Nuclear Information System (INIS)

    Maia, C.R.M.

    1979-01-01

    As an idealized model of plate type fuel assemblies for nuclear reactors, three-slab cells are analysed numerically based on the exact solution of the transport equation in the one-group isotropic scattering model. From the equations describing the interface conditions, a set of regular integral equations for the coefficients of the singular eigenfunctions expansions is derived using the half-range orthogonality relations of the eigenfunctions and the recently developed method of regularization. Numerical solutions are obtained by solving this set of equations iteratively. The thermal utilization factor and thermal disadvantage factors as well as flux and current distributions are reported for the first time for various sets of parameters. The accuracy of the P sub(N) approximations is also analysed compared to the exact results. (Author) [pt

  20. An inverse Sturm–Liouville problem with a fractional derivative

    KAUST Repository

    Jin, Bangti; Rundell, William

    2012-01-01

    In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical

  1. Kinetic stability of field-reversed configurations

    International Nuclear Information System (INIS)

    Staudenmeier, J.L.; Hsiao, M.-Y.

    1991-01-01

    The internal tilt mode is considered to be the biggest threat to Field-Reversed Configuration (FRC) global stability. The tilt stability of the FRC is studied using the MHD, Hall MHD, and the Vlasov-fluid (Vlasov ions, cold massless fluid electrons) models. Nonlinear Hall MHD calculations showed that the FRC was stable to the tilt mode when the s value of the FRC was below a critical value that was dependent on plasma length. The critical s value is larger for longer plasma equilibria. The stability of FRC's with toroidal field was studied with a linear initial value MHD code. The calculations showed an axial perturbation wavelength of the most unstable eigenfunction that was consistent with internal probe measurements made on translated FRC's. Linear Vlasov-fluid eigenvalue calculations showed that kinetic ion effects can change both the growth rate and the structure of the eigenfunctions when compared to the corresponding MHD modes. Calculations on short FRC equilibria indicate that MHD is not the appropriate small gyroradius limit of the Vlasov-fluid model because the axial transit time of a thermal ion is approximately equal to an MHD growth time for the tilt mode. Calculations were done using a small number of unstable MHD eigenfunctions as basis functions in order to reduce the dimensionality of the stability problem. The results indicated that this basis set can produce inaccurate growth rates at large value for s for some equilibria

  2. F4 quantum integrable, rational and trigonometric models: space-of-orbits view

    International Nuclear Information System (INIS)

    Turbiner, A V; Vieyra, J C Lopez

    2014-01-01

    Algebraic-rational nature of the four-dimensional, F 4 -invariant integrable quantum Hamiltonians, both rational and trigonometric, is revealed and reviewed. It was shown that being written in F 4 Weyl invariants, polynomial and exponential, respectively, both similarity-transformed Hamiltonians are in algebraic form, they are quite similar the second order differential operators with polynomial coefficients; the flat metric in the Laplace-Beltrami operator has polynomial (in invariants) matrix elements. Their potentials are calculated for the first time: they are meromorphic (rational) functions with singularities at the boundaries of the configuration space. Ground state eigenfunctions are algebraic functions in a form of polynomials in some degrees. Both Hamiltonians preserve the same infinite flag of polynomial spaces with characteristic vector (1, 2, 2, 3), it manifests exact solvability. A particular integral common for both models is derived. The first polynomial eigenfunctions are presented explicitly.

  3. Wigner functions for fermions in strong magnetic fields

    Science.gov (United States)

    Sheng, Xin-li; Rischke, Dirk H.; Vasak, David; Wang, Qun

    2018-02-01

    We compute the covariant Wigner function for spin-(1/2) fermions in an arbitrarily strong magnetic field by exactly solving the Dirac equation at non-zero fermion-number and chiral-charge densities. The Landau energy levels as well as a set of orthonormal eigenfunctions are found as solutions of the Dirac equation. With these orthonormal eigenfunctions we construct the fermion field operators and the corresponding Wigner-function operator. The Wigner function is obtained by taking the ensemble average of the Wigner-function operator in global thermodynamical equilibrium, i.e., at constant temperature T and non-zero fermion-number and chiral-charge chemical potentials μ and μ_5, respectively. Extracting the vector and axial-vector components of the Wigner function, we reproduce the currents of the chiral magnetic and separation effect in an arbitrarily strong magnetic field.

  4. Spectral Solutions of Self-adjoint Elliptic Problems with Immersed Interfaces

    International Nuclear Information System (INIS)

    Auchmuty, G.; Klouček, P.

    2011-01-01

    This paper describes a spectral representation of solutions of self-adjoint elliptic problems with immersed interfaces. The interface is assumed to be a simple non-self-intersecting closed curve that obeys some weak regularity conditions. The problem is decomposed into two problems, one with zero interface data and the other with zero exterior boundary data. The problem with zero interface data is solved by standard spectral methods. The problem with non-zero interface data is solved by introducing an interface space H Γ (Ω) and constructing an orthonormal basis of this space. This basis is constructed using a special class of orthogonal eigenfunctions analogously to the methods used for standard trace spaces by Auchmuty (SIAM J. Math. Anal. 38, 894–915, 2006). Analytical and numerical approximations of these eigenfunctions are described and some simulations are presented.

  5. The toroidicity-induced Alfven eigenmode structure in DIII-D: Implications of soft x-ray and beam-ion loss data

    International Nuclear Information System (INIS)

    Carolipio, E. M.; Heidbrink, W. W.; Cheng, C. Z.; Chu, M. S.; Fu, G. Y.; Jaun, A.; Spong, D. A.; Turnbull, A. D.; White, R. B.

    2001-01-01

    The internal structure of the toroidicity-induced Alfven eigenmode (TAE) is studied by comparing soft x-ray profile and beam ion loss data taken during TAE activity in the DIII-D tokamak [W. W. Heidbrink , Nucl. Fusion 37, 1411 (1997)] with predictions from theories based on ideal magnetohydrodynamic (MHD), gyrofluid, and gyrokinetic models. The soft x-ray measurements indicate a centrally peaked eigenfunction, a feature which is closest to the gyrokinetic model's prediction. The beam ion losses are simulated using a guiding center code. In the simulations, the TAE eigenfunction calculated using the ideal MHD model acts as a perturbation to the equilibrium field. The predicted beam ion losses are an order of magnitude less than the observed ∼6%--8% losses at the peak experimental amplitude of {delta}B r /B 0 ≅2--5 x 10 -4

  6. How do we decide whether the first Born approximation applies to inelastic collisions of charged particles with an atom or molecule

    International Nuclear Information System (INIS)

    Inokuti, M.; Manson, S.T.

    1985-01-01

    A motivation of our study is to help resolve a general issue in atomic-collision physics. There are two major sources of uncertainties in the evaluation of cross sections. First, one uses an approximation for treating the collision process, e.g., the FBA, the distorted-wave approximation, or the close-coupling approximation. Second, explicit evaluation of cross sections within any of these approximations must use as input eigenfunctions for the target in the initial state and in the final state at least, and possibly in the intermediate states. It is important to distinguish these two sources of uncertainties as clearly as possible. For instance, once the authors are sure that the FBA holds, the uncertainties in the cross-section evaluation are fully attributable to the uncertainties in the target eigenfunctions. Strong plausibility arguments are given for the validity of the FBA

  7. Quantum maps from transfer operators

    International Nuclear Information System (INIS)

    Bogomolny, E.B.; Carioli, M.

    1992-09-01

    The Selberg zeta function ζ S (s) yields an exact relationship between the periodic orbits of a fully chaotic Hamiltonian system (the geodesic flow on surfaces of constant negative curvature) and the corresponding quantum system (the spectrum of the Laplace-Beltrami operator on the same manifold). It was found that for certain manifolds, ζ S (s) can be exactly rewritten as the Fredholm-Grothendieck determinant det(1-T s ), where T s is a generalization of the Ruelle-Perron-Frobenius transfer operator. An alternative derivation of this result is given, yielding a method to find not only the spectrum but also the eigenfunctions of the Laplace-Beltrami operator in terms of eigenfunctions of T s . Various properties of the transfer operator are investigated both analytically and numerically for several systems. (author) 30 refs.; 16 figs.; 2 tabs

  8. The Lagrangian and Hamiltonian Analysis of Integrable Infinite-Dimensional Dynamical Systems

    International Nuclear Information System (INIS)

    Bogolubov, Nikolai N. Jr.; Prykarpatsky, Yarema A.; Blackmorte, Denis; Prykarpatsky, Anatoliy K.

    2010-12-01

    The analytical description of Lagrangian and Hamiltonian formalisms naturally arising from the invariance structure of given nonlinear dynamical systems on the infinite- dimensional functional manifold is presented. The basic ideas used to formulate the canonical symplectic structure are borrowed from the Cartan's theory of differential systems on associated jet-manifolds. The symmetry structure reduced on the invariant submanifolds of critical points of some nonlocal Euler-Lagrange functional is described thoroughly for both differential and differential-discrete dynamical systems. The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integral-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Backlund transformation. The connection of this hierarchy with integrable by Lax spatially two-dimensional systems is studied. (author)

  9. Image denoising using the squared eigenfunctions of the Schrodinger operator

    KAUST Repository

    Kaisserli, Zineb; Laleg-Kirati, Taous-Meriem

    2015-01-01

    This study introduces a new image denoising method based on the spectral analysis of the semi-classical Schrodinger operator. The noisy image is considered as a potential of the Schrodinger operator, and the denoised image is reconstructed using the discrete spectrum of this operator. First results illustrating the performance of the proposed approach are presented and compared to the singular value decomposition method.

  10. Non-accretive Schrodinger operators and exponential decay of their eigenfunctions

    Czech Academy of Sciences Publication Activity Database

    Krejčiřík, David; Raymond, N.; Royer, J.; Siegl, Petr

    2017-01-01

    Roč. 221, č. 2 (2017), s. 779-802 ISSN 0021-2172 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : non-self-adjoint electromagnetic Schrodinger operators * Dirichlet realisation * Agmon-type exponential decay Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.796, year: 2016

  11. Image denoising using the squared eigenfunctions of the Schrodinger operator

    KAUST Repository

    Kaisserli, Zineb

    2015-02-02

    This study introduces a new image denoising method based on the spectral analysis of the semi-classical Schrodinger operator. The noisy image is considered as a potential of the Schrodinger operator, and the denoised image is reconstructed using the discrete spectrum of this operator. First results illustrating the performance of the proposed approach are presented and compared to the singular value decomposition method.

  12. Numerical calculation of the cross section by the solution of the wave equation

    International Nuclear Information System (INIS)

    Drewko, J.

    1982-01-01

    A numerical method of solving of the wave equation is described for chosen vibrational eigenfunctions. A prepared program calculates the total cross sections for the resonant vibrational excitation for diatomic molecules on the basis of introduced molecular data. (author)

  13. An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders

    DEFF Research Database (Denmark)

    Larsen, Niels Vesterdal; Breinbjerg, Olav

    2004-01-01

    Analytical Method of Auxiliary Sources solutions for plane wave scattering by circular impedance cylinders are derived by transformation of the exact eigenfunction series solutions employing the Hankel function wave transformation. The analytical Method of Auxiliary Sources solution thus obtained...

  14. On some asymptotic relations in the Boltzmann-Enskog model

    International Nuclear Information System (INIS)

    Sadovnikov, B.I.; Inozemtseva, N.G.

    1977-04-01

    The coefficients in the tsup(-3/2) asymptotics of the time autocorrelation functions are successively determined in the framework of the non-linear Boltzmann-Enskog model. The left and right eigenfunction systems are constructed for the Boltzmann-Enskog operator

  15. System and method for image reconstruction, analysis, and/or de-noising

    KAUST Repository

    Laleg-Kirati, Taous-Meriem; Kaisserli, Zineb

    2015-01-01

    A method and system can analyze, reconstruct, and/or denoise an image. The method and system can include interpreting a signal as a potential of a Schrödinger operator, decomposing the signal into squared eigenfunctions, reducing a design parameter

  16. The tunneling effect for a class of difference operators

    Science.gov (United States)

    Klein, Markus; Rosenberger, Elke

    We analyze a general class of self-adjoint difference operators H𝜀 = T𝜀 + V𝜀 on ℓ2((𝜀ℤ)d), where V𝜀 is a multi-well potential and 𝜀 is a small parameter. We give a coherent review of our results on tunneling up to new sharp results on the level of complete asymptotic expansions (see [30-35]).Our emphasis is on general ideas and strategy, possibly of interest for a broader range of readers, and less on detailed mathematical proofs. The wells are decoupled by introducing certain Dirichlet operators on regions containing only one potential well. Then the eigenvalue problem for the Hamiltonian H𝜀 is treated as a small perturbation of these comparison problems. After constructing a Finslerian distance d induced by H𝜀, we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by this distance to the well. It follows with microlocal techniques that the first n eigenvalues of H𝜀 converge to the first n eigenvalues of the direct sum of harmonic oscillators on ℝd located at several wells. In a neighborhood of one well, we construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low-lying eigenvalues of H𝜀. These are obtained from eigenfunctions or quasimodes for the operator H𝜀, acting on L2(ℝd), via restriction to the lattice (𝜀ℤ)d. Tunneling is then described by a certain interaction matrix, similar to the analysis for the Schrödinger operator (see [22]), the remainder is exponentially small and roughly quadratic compared with the interaction matrix. We give weighted ℓ2-estimates for the difference of eigenfunctions of Dirichlet-operators in neighborhoods of the different wells and the associated WKB-expansions at the wells. In the last step, we derive full asymptotic expansions for interactions between two “wells” (minima) of the potential energy, in particular for the discrete tunneling effect. Here we

  17. Continuation of connecting orbits in 3d-ODEs' (i) point-to-cycle connections.

    NARCIS (Netherlands)

    Doedel, E.J.; Kooi, B.W.; van Voorn, G.A.K.; Kuznetzov, Y.A.

    2008-01-01

    We propose new methods for the numerical continuation of point-to-cycle connecting orbits in three-dimensional autonomous ODE's using projection boundary conditions. In our approach, the projection boundary conditions near the cycle are formulated using an eigenfunction of the associated adjoint

  18. On a problem of Berenstein-Gay and its generalizations

    International Nuclear Information System (INIS)

    Volchkov, Valerii V; Volchkov, Vitaly V

    2010-01-01

    We obtain a solution of the Berenstein-Gay problem on the local analogue of spectral analysis on Riemannian symmetric spaces X of rank 1. The proof is based on constructing transmutation maps connected with eigenfunction expansions of the Laplace-Beltrami operator on X.

  19. Synchronization and matched filtering in time-frequency using the sunflower spiral

    NARCIS (Netherlands)

    Korevaar, C.W.; Kokkeler, Andre B.J.; de Boer, Pieter-Tjerk; Smit, Gerardus Johannes Maria

    2012-01-01

    Synchronization and matched filtering of signals in time dispersive, frequency dispersive and time-frequency dispersive channels are addressed in this paper. The ‘eigenfunctions’ of these channels form the signal sets under investigation. While using channel-eigenfunctions is a first requirement for

  20. Residual gauge invariance of Hamiltonian lattice gauge theories

    International Nuclear Information System (INIS)

    Ryang, S.; Saito, T.; Shigemoto, K.

    1984-01-01

    The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegengauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically. (orig.)

  1. Resonances and dipole moments in dielectric, magnetic, and magnetodielectric cylinders

    DEFF Research Database (Denmark)

    Dirksen, A.; Arslanagic, Samel; Breinbjerg, Olav

    2011-01-01

    An eigenfunction solution to the problem of plane wave scattering by dielectric, magnetic, and magnetodielectric cylinders is used for a systematic investigation of their resonances. An overview of the resonances with electric and magnetic dipole moments, needed in, e.g., the synthesis...

  2. Stable evaluation of Green's functions in cylindrically stratified regions with uniaxial anisotropic layers

    Science.gov (United States)

    Moon, H.; Donderici, B.; Teixeira, F. L.

    2016-11-01

    We present a robust algorithm for the computation of electromagnetic fields radiated by point sources (Hertzian dipoles) in cylindrically stratified media where each layer may exhibit material properties (permittivity, permeability, and conductivity) with uniaxial anisotropy. Analytical expressions are obtained based on the spectral representation of the tensor Green's function based on cylindrical Bessel and Hankel eigenfunctions, and extended for layered uniaxial media. Due to the poor scaling of these eigenfunctions for extreme arguments and/or orders, direct numerical evaluation of such expressions can produce numerical instability, i.e., underflow, overflow, and/or round-off errors under finite precision arithmetic. To circumvent these problems, we develop a numerically stable formulation through suitable rescaling of various expressions involved in the computational chain, to yield a robust algorithm for all parameter ranges. Numerical results are presented to illustrate the robustness of the formulation including cases of practical interest.

  3. A variational multi-scale method with spectral approximation of the sub-scales: Application to the 1D advection-diffusion equations

    KAUST Repository

    Chacó n Rebollo, Tomá s; Dia, Ben Mansour

    2015-01-01

    This paper introduces a variational multi-scale method where the sub-grid scales are computed by spectral approximations. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. This allows to element-wise calculate the sub-grid scales by means of the associated spectral expansion. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a finite number of modes. We apply this general framework to the convection-diffusion equation, by analytically computing the family of eigenfunctions. We perform a convergence and error analysis. We also present some numerical tests that show the stability of the method for an odd number of spectral modes, and an improvement of accuracy in the large resolved scales, due to the adding of the sub-grid spectral scales.

  4. Vibrational modes of thin oblate clouds of charge

    International Nuclear Information System (INIS)

    Jenkins, Thomas G.; Spencer, Ross L.

    2002-01-01

    A numerical method is presented for finding the eigenfunctions (normal modes) and mode frequencies of azimuthally symmetric non-neutral plasmas confined in a Penning trap whose axial thickness is much smaller than their radial size. The plasma may be approximated as a charged disk in this limit; the normal modes and frequencies can be found if the surface charge density profile σ(r) of the disk and the trap bounce frequency profile ω z (r) are known. The dependence of the eigenfunctions and equilibrium plasma shapes on nonideal components of the confining Penning trap fields is discussed. The results of the calculation are compared with the experimental data of Weimer et al. [Phys. Rev. A 49, 3842 (1994)] and it is shown that the plasma in this experiment was probably hollow and had mode displacement functions that were concentrated near the center of the plasma

  5. The Quantization of a Kerr-AdS Black Hole

    Directory of Open Access Journals (Sweden)

    Claus Gerhardt

    2018-01-01

    Full Text Available We apply our model of quantum gravity to a Kerr-AdS space-time of dimension 2m+1, m≥2, where all rotational parameters are equal, resulting in a wave equation in a quantum space-time which has a sequence of solutions that can be expressed as a product of stationary and temporal eigenfunctions. The stationary eigenfunctions can be interpreted as radiation and the temporal ones as gravitational waves. The event horizon corresponds in the quantum model to a Cauchy hypersurface that can be crossed by causal curves in both directions such that the information paradox does not occur. We also prove that the Kerr-AdS space-time can be maximally extended by replacing in a generalized Boyer-Lindquist coordinate system the r variable by ρ=r2 such that the extended space-time has a timelike curvature singularity in ρ=-a2.

  6. Vibrational treatment of the formic acid double minimum case in valence coordinates

    Science.gov (United States)

    Richter, Falk; Carbonnière, P.

    2018-02-01

    One single full dimensional valence coordinate HCOOH ground state potential energy surface accurate for both cis and trans conformers for all levels up to 6000 cm-1 relative to trans zero point energy has been generated at CCSD(T)-F12a/aug-cc-pVTZ level. The fundamentals and a set of eigenfunctions complete up to about 3120 and 2660 cm-1 for trans- and cis-HCOOH, respectively, have been calculated and assigned using the improved relaxation method of the Heidelberg multi-configuration time-dependent Hartree package and an exact expression for the kinetic energy in valence coordinates generated by the TANA program. The calculated trans fundamental transition frequencies agree with experiment to within 5 cm-1. A few reassignments are suggested. Our results discard any cis trans delocalization effects for vibrational eigenfunctions up to 3640 cm-1 relative to trans zero point energy.

  7. SU(1,1) coherent states for Dirac–Kepler–Coulomb problem in D+1 dimensions with scalar and vector potentials

    Energy Technology Data Exchange (ETDEWEB)

    Ojeda-Guillén, D., E-mail: dogphysics@gmail.com [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, C.P. 07738, México D.F. (Mexico); Mota, R.D. [Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacán, C.P. 04430, México D.F. (Mexico); Granados, V.D. [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, C.P. 07738, México D.F. (Mexico)

    2014-08-14

    We decouple the Dirac's radial equations in D+1 dimensions with Coulomb-type scalar and vector potentials through appropriate transformations. We study each of these uncoupled second-order equations in an algebraic way by using an su(1,1) algebra realization. Based on the theory of irreducible representations, we find the energy spectrum and the radial eigenfunctions. We construct the Perelomov coherent states for the Sturmian basis, which is the basis for the unitary irreducible representation of the su(1,1) Lie algebra. The physical radial coherent states for our problem are obtained by applying the inverse original transformations to the Sturmian coherent states. - Highlights: • We solve the most general Dirac–Kepler–Coulomb problem. • The eigenfunctions and energy spectrum are obtained in a purely algebraic way. • We construct the radial SU(1,1) coherent states for the Kepler–Coulomb problem.

  8. Solution of the Schroedinger equation by a spectral method

    International Nuclear Information System (INIS)

    Feit, M.D.; Fleck, J.A. Jr.; Steiger, A.

    1982-01-01

    A new computational method for determining the eigenvalues and eigenfunctions of the Schroedinger equation is described. Conventional methods for solving this problem rely on diagonalization of a Hamiltonian matrix or iterative numerical solutions of a time independent wave equation. The new method, in contrast, is based on the spectral properties of solutions to the time-dependent Schroedinger equation. The method requires the computation of a correlation function from a numerical solution psi(r, t). Fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system. Analysis of the location of these peaks reveals the eigenvalues with high accuracy. Additional Fourier transforms of psi(r, t) with respect to time generate the eigenfunctions. The effectiveness of the method is demonstrated for a one-dimensional asymmetric double well potential and for the two-dimensional Henon--Heiles potential

  9. Universal dynamics in the onset of a Hagen-Poiseuille flow

    DEFF Research Database (Denmark)

    Mortensen, Asger; Bruus, Henrik

    2006-01-01

    The dynamics in the onset of a Hagen-Poiseuille flow of an incompressible liquid in a channel of circular cross section is well-studied theoretically. We use an eigenfunction expansion in a Hilbert space formalism to generalize the results to channels of an arbitrary cross section. We find that t...... that the steady state is reached after a characteristic time scale tau=(A/P)(2)(1/nu), where A and P are the cross-sectional area and perimeter, respectively, and nu is the kinematic viscosity of the liquid. For the initial dynamics of the flow rate Q for t......The dynamics in the onset of a Hagen-Poiseuille flow of an incompressible liquid in a channel of circular cross section is well-studied theoretically. We use an eigenfunction expansion in a Hilbert space formalism to generalize the results to channels of an arbitrary cross section. We find...

  10. Stable evaluation of Green's functions in cylindrically stratified regions with uniaxial anisotropic layers

    Energy Technology Data Exchange (ETDEWEB)

    Moon, H., E-mail: haksu.moon@gmail.com [ElectroScience Laboratory, The Ohio State University, Columbus, OH 43212 (United States); Donderici, B., E-mail: burkay.donderici@halliburton.com [Sensor Physics & Technology, Halliburton Energy Services, Houston, TX 77032 (United States); Teixeira, F.L., E-mail: teixeira@ece.osu.edu [ElectroScience Laboratory, The Ohio State University, Columbus, OH 43212 (United States)

    2016-11-15

    We present a robust algorithm for the computation of electromagnetic fields radiated by point sources (Hertzian dipoles) in cylindrically stratified media where each layer may exhibit material properties (permittivity, permeability, and conductivity) with uniaxial anisotropy. Analytical expressions are obtained based on the spectral representation of the tensor Green's function based on cylindrical Bessel and Hankel eigenfunctions, and extended for layered uniaxial media. Due to the poor scaling of these eigenfunctions for extreme arguments and/or orders, direct numerical evaluation of such expressions can produce numerical instability, i.e., underflow, overflow, and/or round-off errors under finite precision arithmetic. To circumvent these problems, we develop a numerically stable formulation through suitable rescaling of various expressions involved in the computational chain, to yield a robust algorithm for all parameter ranges. Numerical results are presented to illustrate the robustness of the formulation including cases of practical interest.

  11. Using Peano Curves to Construct Laplacians on Fractals

    Science.gov (United States)

    Molitor, Denali; Ott, Nadia; Strichartz, Robert

    2015-12-01

    We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.

  12. Free harmonic oscillators, Jack polynomials, and Calogero-Sutherland systems

    International Nuclear Information System (INIS)

    Gurappa, N.; Panigrahi, Prasanta K.

    2000-01-01

    The algebraic structure and the relationships between the eigenspaces of the Calogero-Sutherland model (CSM) and the Sutherland model (SM) on a circle are investigated through the Cherednik operators. We find an exact connection between the simultaneous nonsymmetric eigenfunctions of the A N-1 Cherednik operators, from which the eigenfunctions of the CSM and SM are constructed, and the monomials. This construction allows us to simultaneously diagonalize both CSM and SM (after gauging away the Hamiltonians by suitable measures) and also enables us to write down a harmonic oscillator algebra involving the Cherednik operators, which yields the raising and lowering operators for both of these models. The connections of the CSM with free oscillators and the SM with free particles on a circle are established in a novel way. We also point out the subtle differences between the excitations of the CSM and the SM

  13. A variational multi-scale method with spectral approximation of the sub-scales: Application to the 1D advection-diffusion equations

    KAUST Repository

    Chacón Rebollo, Tomás

    2015-03-01

    This paper introduces a variational multi-scale method where the sub-grid scales are computed by spectral approximations. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. This allows to element-wise calculate the sub-grid scales by means of the associated spectral expansion. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a finite number of modes. We apply this general framework to the convection-diffusion equation, by analytically computing the family of eigenfunctions. We perform a convergence and error analysis. We also present some numerical tests that show the stability of the method for an odd number of spectral modes, and an improvement of accuracy in the large resolved scales, due to the adding of the sub-grid spectral scales.

  14. SU(1,1) coherent states for Dirac–Kepler–Coulomb problem in D+1 dimensions with scalar and vector potentials

    International Nuclear Information System (INIS)

    Ojeda-Guillén, D.; Mota, R.D.; Granados, V.D.

    2014-01-01

    We decouple the Dirac's radial equations in D+1 dimensions with Coulomb-type scalar and vector potentials through appropriate transformations. We study each of these uncoupled second-order equations in an algebraic way by using an su(1,1) algebra realization. Based on the theory of irreducible representations, we find the energy spectrum and the radial eigenfunctions. We construct the Perelomov coherent states for the Sturmian basis, which is the basis for the unitary irreducible representation of the su(1,1) Lie algebra. The physical radial coherent states for our problem are obtained by applying the inverse original transformations to the Sturmian coherent states. - Highlights: • We solve the most general Dirac–Kepler–Coulomb problem. • The eigenfunctions and energy spectrum are obtained in a purely algebraic way. • We construct the radial SU(1,1) coherent states for the Kepler–Coulomb problem

  15. Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

    Science.gov (United States)

    Guarnieri, F.; Moon, W.; Wettlaufer, J. S.

    2017-09-01

    Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with a negative constant drift, described by a Fokker-Planck equation with a potential V (x ) =-[b ln(x ) +a x ] , for b >0 and a finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schrödinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a constant negative drift. We conclude with a comparison to other analytical methods and with numerical solutions.

  16. Three-Body Protonium Formation in a Collision Between a Slow Antiproton ({barp}) and Muonic Hydrogen: {H_{μ}}—Low Energy {barp + (p μ^-)_{1s} → (barp p)_{1s} + μ^-} Reaction

    Science.gov (United States)

    Sultanov, Renat A.; Guster, D.; Adhikari, S. K.

    2015-12-01

    A bound state of a proton, p, and its counterpart antiproton, {barp}, is a protonium atom {Pn = (barp p)}. The following three-charge-particle reaction: {barp +(p μ^-)_{1s} → (barp {p})_{1s} + μ^-} is considered in this work, where {μ^-} is a muon. At low-energies muonic reaction {Pn} can be formed in the short range state with α = 1 s or in the first excited state: α = 2 s/2 p, where {barp} and p are placed close enough to each other and the effect of the {barp}-p nuclear interaction becomes significantly stronger. The cross sections and rates of the Pn formation reaction are computed in the framework of a few-body approach based on the two-coupled Faddeev-Hahn-type (FH-type) equations. Unlike the original three-body Faddeev method the FH-type equation approach is formulated in terms of only two but relevant components: {{Ψ}_1} and {Ψ_2}, of the system's three-body wave function {Ψ}, where {{Ψ}={Ψ}_1+{Ψ}_2}. In order to solve the FH-type equations {Ψ_1} is expanded in terms of the input channel target eigenfunctions, i.e. in this work in terms of the {({p} μ^-)} eigenfunctions. At the same time {Ψ_2} is expanded in terms of the output channel two-body wave function, that is in terms of the protonium {(bar{{p}} {p})} eigenfunctions. A total angular momentum projection procedure is performed, which leads to an infinite set of one-dimensional coupled integral-differential equations for unknown expansion coefficients.

  17. Exact solutions of the spherically symmetric multidimensional ...

    African Journals Online (AJOL)

    The complete orthonormalised energy eigenfunctions and the energy eigenvalues of the spherically symmetric isotropic harmonic oscillator in N dimensions, are obtained through the methods of separation of variables. Also, the degeneracy of the energy levels are examined. KEY WORDS: - Schrödinger Equation, Isotropic ...

  18. Unbounded planar domains whose second nodal line does not touch the boundary

    Czech Academy of Sciences Publication Activity Database

    Freitas, P.; Krejčiřík, David

    2007-01-01

    Roč. 14, č. 1 (2007), s. 107-111 ISSN 1073-2780 R&D Projects: GA MŠk LC06002 Institutional research plan: CEZ:AV0Z10480505 Keywords : Dirichlet Laplacian * eigenfunctions * nodal line Subject RIV: BA - General Mathematics Impact factor: 0.702, year: 2007

  19. Fermionic particles with position-dependent mass in the presence of ...

    Indian Academy of Sciences (India)

    Approximate solutions of the Dirac equation with position-dependent mass are presented for the inversely quadratic Yukawa potential and Coulomb-like tensor interaction by using the asymptotic iteration method. The energy eigenvalues and the corresponding normalized eigenfunctions are obtained in the case of ...

  20. Algebraic approach to the Kratzer potential

    International Nuclear Information System (INIS)

    Setare, Mohammad R; Karimi, Ebrahim

    2007-01-01

    In this paper, the energy eigenvalues and the corresponding eigenfunctions are calculated for the Kratzer potential. Then we obtain the ladder operators for the one-dimensional (1D) and 3D Kratzer potential. Finally, we show that these operators satisfy the SU(2) commutation relation

  1. Approximate Eigensolutions of the Deformed Woods—Saxon Potential via AIM

    International Nuclear Information System (INIS)

    Ikhdair, Sameer M.; Falaye Babatunde, J.; Hamzavi, Majid

    2013-01-01

    Using the Pekeris approximation, the Schrödinger equation is solved for the nuclear deformed Woods—Saxon potential within the framework of the asymptotic iteration method. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of hypergeometric function

  2. On matrix superpotential and three-component normal modes

    Energy Technology Data Exchange (ETDEWEB)

    Rodrigues, R. de Lima [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Lima, A.F. de [Universidade Federal de Campina Grande (UFCG), PB (Brazil). Dept. de Fisica; Mello, E.R. Bezerra de; Bezerra, V.B. [Universidade Federal da Paraiba (UFPB), Joao Pessoa, PB (Brazil). Dept. de Fisica]. E-mails: rafael@df.ufcg.edu.br; aerlima@df.ufcg.edu.br; emello@fisica.ufpb.br; valdir@fisica.ufpb.br

    2007-07-01

    We consider the supersymmetric quantum mechanics(SUSY QM) with three-component normal modes for the Bogomol'nyi-Prasad-Sommerfield (BPS) states. An explicit form of the SUSY QM matrix superpotential is presented and the corresponding three-component bosonic zero-mode eigenfunction is investigated. (author)

  3. Spectral analysis of the diffusion operator with random jumps from the boundary

    Czech Academy of Sciences Publication Activity Database

    Kolb, M.; Krejčiřík, David

    2016-01-01

    Roč. 284, 3-4 (2016), s. 877-900 ISSN 0025-5874 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : self-adjoint operators * eigenvalues * eigenfunctions Subject RIV: BE - Theoretical Physics Impact factor: 0.738, year: 2016

  4. On the Time-Dependent Analysis of Gamow Decay

    Science.gov (United States)

    Durr, Detlef; Grummt, Robert; Kolb, Martin

    2011-01-01

    Gamow's explanation of the exponential decay law uses complex "eigenvalues" and exponentially growing "eigenfunctions". This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wavefunctions. Observing that the time evolution of any…

  5. Pramana – Journal of Physics | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    Using the variational method and supersymmetric quantum mechanics we calculated, in an approximate way, the eigenvalues, eigenfunctions and wave functions at the origin of the Cornell potential. We compared results with numerical solutions for heavy quarkonia c c ¯ , b b ¯ and b c ¯ .

  6. A working model of incompatible quantum variables

    International Nuclear Information System (INIS)

    Matthews, J.C.; Sheard, F.W.

    1980-01-01

    An electronic device designed to simulate some of the features of incompatible observables is described which, it is stated, can play a useful role in aiding the student to digest the mathematics of noncommuting operators and their eigenfunctions as they appear in an introductory course. (U.K.)

  7. Pramana – Journal of Physics | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    Articles written in Pramana – Journal of Physics. Volume 58 Issue 2 February 2002 pp 333-341. From chaos to disorder: Statistics of the eigenfunctions ... the framework of nonlinear sigma models of supersymmetry. Volume 77 Issue 1 July 2011 pp 185-198. Magnetohydrodynamics turbulence: An astronomical perspective.

  8. R-matrix arising from affine Hecke algebras and its application to Macdonald's difference operators

    International Nuclear Information System (INIS)

    Kato, Shinichi

    1994-01-01

    We shall give a certain trigonometric R-matrix associated with each root system by using affine Hecke algebras. From this R-matrix, we derive a quantum Knizhnik-Zamolodchikov equation after Cherednik, and show that the solutions of this KZ equation yield eigenfunctions of Macdonald's difference operators. (orig.)

  9. The Embedding Method for Linear Partial Differential Equations

    Indian Academy of Sciences (India)

    The recently suggested embedding method to solve linear boundary value problems is here extended to cover situations where the domain of interest is unbounded or multiply connected. The extensions involve the use of complete sets of exterior and interior eigenfunctions on canonical domains. Applications to typical ...

  10. Linear problems and Baecklund transformations for the Hirota-Ohta system

    International Nuclear Information System (INIS)

    Adler, V.E.; Postnikov, V.V.

    2011-01-01

    The auxiliary linear problems are presented for all discretization levels of the Hirota-Ohta system. The structure of these linear problems coincides essentially with the structure of Nonlinear Schroedinger hierarchy. The squared eigenfunction constraints are found which relate Hirota-Ohta and Kulish-Sklyanin vectorial NLS hierarchies.

  11. On Properties of Impurity Spectrum in the Disordered Exactly Solvable Model

    CERN Document Server

    Grinshpun, V

    2006-01-01

    The random point interaction Hamiltonian (H) is considered on L^2(R^d), d=2, or d=3. Existence and certain bounds of the non-empty pure point component and exponential decay of the corresponding eigenfunctions with probability 1, within region of impurity spectrum of H, are rigorously established. In order to prove the localization result, the structure of the generalized eigenfunctions of H is explicitly described, and the relation between its spectral properties, and the properties of spectra of finite-difference infinite-order operators on l^2(Z^d), is established. The multiscale analysis scheme is applied to investigate the point spectrum of finite-difference operators. In addition, the generalized spectral theorem, and absolute continuity of the integrated density of states of H at the negative (impurity) part of the spectrum, rigorously proved. Applications of the new approximation scheme include straightforward analysis of absolutely continuous conductivity spectrum, subject to a possible separate publ...

  12. Symmetric tensor spherical harmonics on the N-sphere and their application to the de Sitter group SO(N,1)

    International Nuclear Information System (INIS)

    Higuchi, A.

    1987-01-01

    The symmetric tensor spherical harmonics (STSH's) on the N-sphere (S/sup N/), which are defined as the totally symmetric, traceless, and divergence-free tensor eigenfunctions of the Laplace--Beltrami (LB) operator on S/sup N/, are studied. Specifically, their construction is shown recursively starting from the lower-dimensional ones. The symmetric traceless tensors induced by STSH's are introduced. These play a crucial role in the recursive construction of STSH's. The normalization factors for STSH's are determined by using their transformation properties under SO(N+1). Then the symmetric, traceless, and divergence-free tensor eigenfunctions of the LB operator in the N-dimensional de Sitter space-time which are obtained by the analytic continuation of the STSH's on S/sup N/ are studied. Specifically, the allowed eigenvalues of the LB operator under the restriction of unitarity are determined. Our analysis gives a group-theoretical explanation of the forbidden mass range observed earlier for the spin-2 field theory in de Sitter space-time

  13. Study of the relaxation of electron velocity distributions in gases

    Energy Technology Data Exchange (ETDEWEB)

    Braglia, G L [Parma Univ. (Italy). Ist. di Fisica; Caraffini, G L; Diligenti, M [Parma Univ. (Italy). Ist. di Matematica

    1981-03-11

    The Fokker-Planck equation governing the relaxation of the electron speed (energy) distribution in gases is solved in a number of cases of special interest. The solution is given in terms of eigenfunctions of the Fokker-Planck operator, satisfying an orthonormalization condition in which the steady-state distribution is the weight function. The real cross-sections of the noble gases He, Ne, Ar, Kr and Xe, together with model collision frequencies of the form ..nu..(v) = ..cap alpha..vsup(n) with n = 0.5, 1, 1.5, 3 and 3.5, are used to calculate eigenvalues and eigenfunctions. The first fifteen eigenvalues are obtained in each case both in the absence and in the presence of a d.c. electric field and, in the latter case, both with atoms at rest and atoms in motion. Calculations of relaxation times and examples of evolutions towards their steady-state forms of given initial distributions are reported in several particular cases.

  14. On the theoretical analysis of the lowest many-electron states for cyclic zigzag graphene nano-ribbons

    International Nuclear Information System (INIS)

    Álvarez-Collado, José R; Cantarero, Andrés

    2014-01-01

    We have calculated the optical and magnetic properties of the four lowest many-body states for cyclic zigzag graphene nano-ribbons (GNRs). The results have been obtained within the semi-empirical restricted frozen Hartree–Fock approximation. Firstly, we obtained one-determinant numerical and analytical coincident results. We detected the existence of two degenerate open-shell molecular orbitals (MOs) o, o’. Due to this degeneracy, some of the mentioned results do depend on any (arbitrary) orthogonal transformation between these two MOs. We have improved these preliminary results by using linear combinations of two determinants, which are eigenfunctions of the operators, which commute with the electronic Hamiltonian. These eigenfunctions represent properly the wave functions of these four electronic states. These calculations show that there are two degenerate ground states. One of them is ferromagnetic and the other state is non magnetic. Finally, we have calculated these four states to full configuration interaction level studying the dependence of their properties on the size of the GNRs. (paper)

  15. On the theoretical analysis of the lowest many-electron states for cyclic zigzag graphene nano-ribbons

    Science.gov (United States)

    Álvarez-Collado, José R.; Cantarero, Andrés

    2014-09-01

    We have calculated the optical and magnetic properties of the four lowest many-body states for cyclic zigzag graphene nano-ribbons (GNRs). The results have been obtained within the semi-empirical restricted frozen Hartree-Fock approximation. Firstly, we obtained one-determinant numerical and analytical coincident results. We detected the existence of two degenerate open-shell molecular orbitals (MOs) o, o’. Due to this degeneracy, some of the mentioned results do depend on any (arbitrary) orthogonal transformation between these two MOs. We have improved these preliminary results by using linear combinations of two determinants, which are eigenfunctions of the operators, which commute with the electronic Hamiltonian. These eigenfunctions represent properly the wave functions of these four electronic states. These calculations show that there are two degenerate ground states. One of them is ferromagnetic and the other state is non magnetic. Finally, we have calculated these four states to full configuration interaction level studying the dependence of their properties on the size of the GNRs.

  16. Sum rules and other properties involving resonance projection operators. [for optical potential description of electron scattering from atoms and ions

    Science.gov (United States)

    Berk, A.; Temkin, A.

    1985-01-01

    A sum rule is derived for the auxiliary eigenvalues of an equation whose eigenspectrum pertains to projection operators which describe electron scattering from multielectron atoms and ions. The sum rule's right-hand side depends on an integral involving the target system eigenfunctions. The sum rule is checked for several approximations of the two-electron target. It is shown that target functions which have a unit eigenvalue in their auxiliary eigenspectrum do not give rise to well-defined projection operators except through a limiting process. For Hylleraas target approximations, the auxiliary equations are shown to contain an infinite spectrum. However, using a Rayleigh-Ritz variational principle, it is shown that a comparatively simple aproximation can exhaust the sum rule to better than five significant figures. The auxiliary Hylleraas equation is greatly simplified by conversion to a square root equation containing the same eigenfunction spectrum and from which the required eigenvalues are trivially recovered by squaring.

  17. On factorization of generalized Macdonald polynomials

    International Nuclear Information System (INIS)

    Kononov, Ya.; Morozov, A.

    2016-01-01

    A remarkable feature of Schur functions - the common eigenfunctions of cut-and-join operators from W ∞ - is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U q (SL N ) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization - on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding. (orig.)

  18. On factorization of generalized Macdonald polynomials

    Science.gov (United States)

    Kononov, Ya.; Morozov, A.

    2016-08-01

    A remarkable feature of Schur functions—the common eigenfunctions of cut-and-join operators from W_∞ —is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U_q(SL_N) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization—on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding.

  19. On factorization of generalized Macdonald polynomials

    Energy Technology Data Exchange (ETDEWEB)

    Kononov, Ya. [Landau Institute for Theoretical Physics, Chernogolovka (Russian Federation); HSE, Math Department, Moscow (Russian Federation); Morozov, A. [ITEP, Moscow (Russian Federation); Institute for Information Transmission Problems, Moscow (Russian Federation); National Research Nuclear University MEPhI, Moscow (Russian Federation)

    2016-08-15

    A remarkable feature of Schur functions - the common eigenfunctions of cut-and-join operators from W{sub ∞} - is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U{sub q}(SL{sub N}) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization - on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding. (orig.)

  20. High n ballooning modes in highly elongated tokamaks

    International Nuclear Information System (INIS)

    An, C.H.; Bateman, G.

    1980-02-01

    An analytic study of stability against high n ballooning modes in highly elongated axisymmetric plasmas is presented and compared with computational results. From the equation for the marginal pressure gradient, it is found that the local shear plays an important role on the stability of elongated and shifted plasma, and that high elongation deteriorates the stability by decreasing the stabilizing effects of field line bending and local shear. The net contribution of the local shear to stability decreases with elongation and shift for strongly ballooning modes (eigenfunctions strongly localized near the outer edge of the toroidal flux surfaces) but increases for interchange modes (eigenfunctions more uniform along the flux surfaces). The computational study of high n ballooning modes in a highly elongated plasma reveals that lowering the aspect ratio and broadening the pressure profile enhance the marginal beta for β/sub p/ less than unity but severely reduce the marginal beta for β/sub p/ larger than unity

  1. Behaviour of boundary functions for quantum billiards

    International Nuclear Information System (INIS)

    Baecker, A; Fuerstberger, S; Schubert, R; Steiner, F

    2002-01-01

    We study the behaviour of the normal derivative of eigenfunctions of the Helmholtz equation inside billiards with Dirichlet boundary condition. These boundary functions are of particular importance because they uniquely determine the eigenfunctions inside the billiard and also other physical quantities of interest. Therefore, they form a reduced representation of the quantum system, analogous to the Poincare section of the classical system. For the normal derivatives we introduce an equivalent to the standard Green function and derive an integral equation on the boundary. Based on this integral equation we compute the first two terms of the mean asymptotic behaviour of the boundary functions for large energies. The first term is universal and independent of the shape of the billiard. The second one is proportional to the curvature of the boundary. The asymptotic behaviour is compared with numerical results for the stadium billiard, different limacon billiards and the circle billiard, and good agreement is found. Furthermore, we derive an asymptotic completeness relation for the boundary functions

  2. Quantum field theory in spaces with closed time-like curves

    International Nuclear Information System (INIS)

    Boulware, D.G.

    1992-01-01

    Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon

  3. Multiple eigenmodes of the Rayleigh-Taylor instability observed for a fluid interface with smoothly varying density

    Science.gov (United States)

    Yu, C. X.; Xue, C.; Liu, J.; Hu, X. Y.; Liu, Y. Y.; Ye, W. H.; Wang, L. F.; Wu, J. F.; Fan, Z. F.

    2018-01-01

    In this article, multiple eigen-systems including linear growth rates and eigen-functions have been discovered for the Rayleigh-Taylor instability (RTI) by numerically solving the Sturm-Liouville eigen-value problem in the case of two-dimensional plane geometry. The system called the first mode has the maximal linear growth rate and is just extensively studied in literature. Higher modes have smaller eigen-values, but possess multi-peak eigen-functions which bring on multiple pairs of vortices in the vorticity field. A general fitting expression for the first four eigen-modes is presented. Direct numerical simulations show that high modes lead to appearances of multi-layered spike-bubble pairs, and lots of secondary spikes and bubbles are also generated due to the interactions between internal spikes and bubbles. The present work has potential applications in many research and engineering areas, e.g., in reducing the RTI growth during capsule implosions in inertial confinement fusion.

  4. Non-axial-symmetric Alfven waves in cylindrical, radial inhomogeneous plasmas

    International Nuclear Information System (INIS)

    Raeuchle, E.

    1978-08-01

    The propagation of nonaxialsymmetric Alfven waves is investigated theoretically. Eigenfunctions and dispersion relations are calculated numerically for radial inhomogeneous cylindrical plasmas. In the MHD treatment resistivity, neutral particle loading and ion cyclotron effects are included. The investigations are of importance for plasma heating by Alfven waves. (orig.) [de

  5. q-Deformed Kink solutions

    International Nuclear Information System (INIS)

    Lima, A.F. de

    2003-01-01

    The q-deformed kink of the λφ 4 -model is obtained via the normalisable ground state eigenfunction of a fluctuation operator associated with the q-deformed hyperbolic functions. The kink mass, the bosonic zero-mode and the q-deformed potential in 1+1 dimensions are found. (author)

  6. Fourier transforms related to a root system of rank 1.

    NARCIS (Netherlands)

    Groenevelt, W.G.M.

    2007-01-01

    Abstract : We introduce an algebra $\\mathcal H$ consisting of difference-reflection operators and multiplication operators that can be considered as a q = 1 analogue of Sahi's double affine Hecke algebra related to the affine root system of type $(C^\\vee_1, C_1)$ . We study eigenfunctions of a

  7. Orthonormal mode sets for the two-dimensional fractional Fourier transformation

    NARCIS (Netherlands)

    Alieva, T.; Bastiaans, M.J.

    2007-01-01

    A family of orthonormal mode sets arises when Hermite–Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an

  8. Quantum physics. 8. ed.

    International Nuclear Information System (INIS)

    Gasiorowicz, S.

    2002-01-01

    The following topics are dealt with: wave packets and uncertainty relation, Schroedinger equation, eigenfunctions and eigenvalues, one-dimensional potentials, wave mechanics, quantum operators, angular momentum, hydrogen atom, interaction of electrons with electromagnetic fields, operators, matrices and spin, perturbation theory, helium atom, molecules, atomic radiation, radiation theory, collision processes

  9. EXACT SOLUTION OF HEAT CONDUCTION IN A TWO-DOMAIN COMPOSITE CYLINDER WITH AN ORTHOTROPIC OUTER LAYER

    International Nuclear Information System (INIS)

    AVILES-RAMOS, C.; RUDY, C.

    2000-01-01

    The transient exact solution of heat conduction in a two-domain composite cylinder is developed using the separation of variables technique. The inner cylinder is isotropic and the outer cylindrical layer is orthotropic. Temperature solutions are obtained for boundary conditions of the first and second kinds at the outer surface of the orthotropic layer. These solutions are applied to heat flow calorimeters modeling assuming that there is heat generation due to nuclear reactions in the inner cylinder. Heat flow calorimeter simulations are carried out assuming that the inner cylinder is filled with plutonium oxide powder. The first objective in these simulations is to predict the onset of thermal equilibrium of the calorimeter with its environment. Two types of boundary conditions at the outer surface of the orthotropic layer are used to predict thermal equilibrium. The procedure developed to carry out these simulations can be used as a guideline for the design of calorimeters. Another important application of these solutions is on the estimation of thermophysical properties of orthotropic cylinders. The thermal conductivities in the vertical, radial and circumferential directions of the orthotropic outer layer can be estimated using this exact solution and experimental data. Simultaneous estimation of the volumetric heat capacity and thermal conductivities is also possible. Furthermore, this solution has potential applications to the solution of the inverse heat conduction problem in this cylindrical geometry. An interesting feature of the construction of this solution is that two different sets of eigenfunctions need to be considered in the eigenfunction expansion. These eigenfunctions sets depend on the relative values of the thermal diffusivity of the inner cylinder and the thermal diffusivity in the vertical direction of the outer cylindrical layer

  10. The propagation of charged particles in a focussing magnetic field with random components

    International Nuclear Information System (INIS)

    Pauls, H.L.

    1993-01-01

    Boltzmann's equation which describes the evolution of the particle distribution function in a focussing magnetic field with finite helicity, is solved by expanding the distribution function in terms of orthogonal focussing eigenfunctions. The present work advances upon previous work by carrying the expansion of the particle distribution function to a higher order (Ν=7 compared to Ν=3), the adding of magnetic helicity, and the injection of a delta function instead of a Gaussian as initial distribution. Results from this model compare very well with those from other known numerical models, provided that a time constraint, which is a direct consequence of the truncation of the eigenfunction expansion, is satisfied. This model, which gives the solution of Boltzmann's equation to a very high degree of accuracy, is used to evaluate the densities predicted by three lower order (and hence easier to implement) models. Two of these models, where the anisotropic component of the distribution function is approximated to first and second order respectively, follow from the Born approximation technique, while the third follows from a truncated eigenfunction expansion of the particle distribution function. It is shown that the latter two models, which include the effect of the dispersion of the so-called coherent pulses, give a better description of the isotropic density than the model which ignores the effect. The main use of this dispersionless model is that it provides a zeroth order approximation to the speed of the coherent pulses in the presence of helicity and focussing. When the dispersion in the pulse is small, its speed is shown to be predicted quite well by this simple model. (author). 67 refs

  11. Morphological evolution of Jinshan Trough in Hangzhou Bay (China) from 1960 to 2011

    Science.gov (United States)

    Liu, Yifei; Xia, Xiaoming; Chen, Shenliang; Jia, Jianjun; Cai, Tinglu

    2017-11-01

    An extensive system of tidal channels, starting with Jinshan Trough in the east, is located along the north shore of Hangzhou Bay, China. This contribution investigates the morphological evolution of Jinshan Trough by using 17 bathymetric charts from a series covering a period of 51 years from 1960 to 2011. Three stages of evolution during this period are distinguishable based on the morphology and annual mean volume data. The first stage (1960-1987) is characterized by extension of the trough; the second stage (1987-1996) is a relatively stable period with some adjustments in the trough morphology; the third stage (1996-2011) is marked by the processes of erosion and deposition in the beginning of the period and a subsequent slow erosion process. Spatio-temporal variability of the trough was evaluated by using empirical orthogonal function (EOF) analysis. The first eigenfunction indicates that erosion is the main evolution process and there exists three stages similar to those distinguished from volume variations. The second eigenfunction mainly reflects erosion and deposition in the northwest part of the trough located in the flood tidal current shadow area of the artificial headland in Jinshan. The third eigenfunction mainly reflects annual fluctuations of erosion and deposition in the side slope at the artificial headland in Jinshan. A particularly intense erosion process occurred between 1996 and 1998. The major effects on morphological evolution in Jinshan Trough from 1960 to 2011 were investigated and tentative conclusions were presented. Continuous coastal reclamations in Jinshan had the most pronounced effect on the morphological evolution during the first and the second stages. The storm surge had a pronounced effect on the evolution at the beginning of the third stage.

  12. Half-linear Sturm-Liouville problem with weights: asymptotic behavior of eigenfunctions

    Czech Academy of Sciences Publication Activity Database

    Drábek, P.; Kufner, Alois; Kuliev, K.

    2014-01-01

    Roč. 284, č. 1 (2014), s. 148-154 ISSN 0081-5438 Institutional support: RVO:67985840 Keywords : Sturm-Liouville problem * spectral problems * Hardy inequality Subject RIV: BA - General Mathematics Impact factor: 0.302, year: 2014 http://link.springer.com/article/10.1134%2FS008154381401009X

  13. Bounds on the order of vanishing of eigenfunctions of Schroedinger operators

    International Nuclear Information System (INIS)

    Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.

    1990-01-01

    We study L 2 -solutions of (-Δ+V-E)ψ = 0 in R n , n ≥ 2 and derive a sharp upper bound to l x 0 (ψ) in terms of x 0 , E and V under rather restrictive assumptions on V. We show for V smooth that an upper bound to l x 0 (ψ) implies an upper bound to the dimension of the eigenspace associated to E. 16 refs. (Authors)

  14. Non-Hermitian quantum mechanics and localization in physical systems

    International Nuclear Information System (INIS)

    Hatano, Naomichi

    1998-01-01

    Recent studies on a delocalization phenomenon of a non-Hermitian random system is reviewed. The complex spectrum of the system indicates delocalization transition of its eigenfunctions. It is emphasized that the delocalization is related to various physical phenomena such as flux-line pinning in superconductors and population biology of bacteria colony

  15. On solving the Schrödinger equation for a complex deictic potential ...

    Indian Academy of Sciences (India)

    Making use of an ansatz for the eigenfunction, we investigate closed-form solutions of the Schrödinger equation for an even power complex deictic potential and its variant in one dimension. For this purpose, extended complex phase-space approach is utilized and nature of the eigenvalue and the corresponding ...

  16. Alternative Form of the Hydrogenic Wave Functions for an Extended, Uniformly Charged Nucleus.

    Science.gov (United States)

    Ley-Koo, E.; And Others

    1980-01-01

    Presented are forms of harmonic oscillator attraction and Coulomb wave functions which can be explicitly constructed and which lead to numerical results for the energy eigenvalues and eigenfunctions of the atomic system. The Schrodinger equation and its solution and specific cases of muonic atoms illustrating numerical calculations are included.…

  17. Application of quasiexactly solvable potential method to the N-body ...

    Indian Academy of Sciences (India)

    The quasiexactly solvable potential method is used to determine the energies and the corresponding exact eigenfunctions for a system of N particles with equal mass interacting via an anharmonic potential. For systems with five and seven particles, we compute the ground state and the first excited state only, and compare ...

  18. Pramana – Journal of Physics | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    We study the statistics of the experimental eigenfunctions of chaotic and disordered microwave billiards in terms of the moments of their spatial distributions, such as the inverse participation ratio (IPR) and density-density auto-correlation. A path from chaos to disorder is described in terms of increasing IPR. In the chaotic ...

  19. Green's function for a neutral particle of spin 1/2 in a magnetic field

    International Nuclear Information System (INIS)

    Rodrigues, Rafael de Lima; Vaidya, Arvind Narayan

    2001-12-01

    Using the spectral theorema in context of Green's function in momentum space of neutrons in the magnetic field of a linear conductor with current the bound state energy spectrum and eigenfunctions are deduced. It's also pointed out that this problem present a new scenary of Green's function in non-relativistic quantum mechanics. (author)

  20. The quantum pendulum

    International Nuclear Information System (INIS)

    Aldrovandi, R.; Ferreira, P.L.

    1979-01-01

    The problem of the mathematical pendulum is treated in its classical, semi-classical and quantum aspects. The Schroedinger equation of the problem is reduced to a Mathieu equation. The energy spectrum and eigenfunctions are discussed, with the requirement of single-valuedness imposed on them. Physical limiting cases are also discussed. (author) [pt

  1. Pseudospectra in non-Hermitian quantum mechanics

    Science.gov (United States)

    Krejčiřík, D.; Siegl, P.; Tater, M.; Viola, J.

    2015-10-01

    We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

  2. Eigenstates of a particle in an array of hexagons with periodic boundary condition

    Directory of Open Access Journals (Sweden)

    A Nemati

    2013-10-01

    Full Text Available In this paper the problem of a particle in an array of hexagons with periodic boundary condition is solved. Using the projection operators, we categorize eigenfunctions corresponding to each of the irreducible representations of the symmetry group . Based on these results, the Dirichlet and Neumann boundary conditions are discussed.

  3. Note on the nodal line of the p-Laplacian

    Directory of Open Access Journals (Sweden)

    Abdel R. El Amrouss

    2006-09-01

    Full Text Available In this paper, we prove that the length of the nodal line of the eigenfunctions associated to the second eigenvalue of the problem $$ -Delta_p u = lambda ho (x |u|^{p-2}u quad hbox{in } Omega $$ with the Dirichlet conditions is not bounded uniformly with respect to the weight.

  4. Spatiotemporal multiscaling analysis of impurity transport in plasma turbulence using proper orthogonal decomposition

    International Nuclear Information System (INIS)

    Futatani, S.; Benkadda, S.; Del-Castillo-Negrete, D.

    2009-01-01

    The spatiotemporal multiscale dynamics of the turbulent transport of impurities is studied in the context of the collisional drift wave turbulence. Two turbulence regimes are considered: a quasihydrodynamic regime and a quasiadiabatic regime. The impurity is assumed to be a passive scalar advected by the corresponding ExB turbulent flow in the presence of diffusion. Two mixing scenarios are studied: a freely decaying case, and a forced case in which the scalar is forced by an externally imposed gradient. The results of the direct numerical simulations are analyzed using proper orthogonal decomposition (POD) techniques. The multiscale analysis is based on a space-time separable POD of the impurity field. The low rank spatial POD eigenfunctions capture the large scale coherent structures and the high rank eigenfunctions capture the small scale fluctuations. The temporal evolution at each scale is dictated by the corresponding temporal POD eigenfunctions. Contrary to the decaying case in which the POD spectrum decays fast, the spectrum in the forced case is relatively flat. The most striking difference between these two mixing scenarios is in the temporal dynamics of the small scale structures. In the decaying case the POD reveals the presence of 'bursty' dynamics in which successively small (high POD rank) scales are intermittently activated during the mixing process. On the other hand, in the forced simulations the temporal dynamics exhibits stationary fluctuations. Spatial intermittency or 'patchiness' in the mixing process characterizes the distribution of the passive tracer in the decaying quasihydrodynamic regime. In particular, in this case the probability distribution function of the low rank POD spatial reconstruction error is non-Gaussian. The spatiotemporal POD scales exhibit a diffusive-type scaling in the quasiadiabatic regime. However, this scaling seems to be absent in the quasihydrodynamic regime that shows no scaling (in the decaying case) or two

  5. Higher-order semiclassical energy expansions for potentials with ...

    Indian Academy of Sciences (India)

    global behavior of eigenfunctions and energy spectra of quantum mechanical systems are very important. ... where p, q and r are positive integers and contourC encloses points +1 and -1 on the real axis. Also these ... Derivation of AEE which is a relationship between quantum number k and the power series expansion of ...

  6. Resonances, resonance functions and spectral deformations

    International Nuclear Information System (INIS)

    Balslev, E.

    1984-01-01

    The present paper is aimed at an analysis of resonances and resonance states from a mathematical point of view. Resonances are characterized as singular points of the analytically continued Lippman-Schwinger equation, as complex eigenvalues of the Hamiltonian with a purely outgoing, exponentially growing eigenfunction, and as poles of the S-matrix. (orig./HSI)

  7. Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation

    OpenAIRE

    Li, Zhiyuan; Yamamoto, Masahiro

    2014-01-01

    This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace transform, we reduce the uniqueness for our inverse problems to the uniqueness of expansions of some special function and complete the proof.

  8. Influence of an anisotropic parabolic potential on the quantum dot qubit

    International Nuclear Information System (INIS)

    Zhao Cuilan; Cai Chunyu; Xiao Jingling

    2013-01-01

    To study the influence of an anisotropic parabolic potential (APP) on the properties of a quantum dot (QD) qubit, we obtain the eigenenergies and eigenfunctions of the ground and first excited state of an electron, which is strongly coupled to the bulk longitudinal optical (LO) phonons, in a QD under the influence of an APP by the celebrated Lee—Low—Pines (LLP) unitary transformation and the Pekar type variational (PTV) methods. Then, this kind of two-level quantum system can be excogitated to constitute a single qubit. When the electron locates at the superposition state of its related eigenfunctions, we get the time evolution of the electron's probability density. Finally, the influence of an APP on the QD qubit is investigated. The numerical calculations indicate that the probability density will oscillate periodically and it is a decreasing function of the effective confinement lengths of the APP in different directions. Whereas its oscillatory period is an increasing one and will diminish with enhancing the electron—phonon (EP) coupling strength. (semiconductor physics)

  9. Effect of wave-function localization on the time delay in photoemission from surfaces

    International Nuclear Information System (INIS)

    Zhang, C.-H.; Thumm, U.

    2011-01-01

    We investigate streaking time delays in the photoemission from a solid model surface as a function of the degree of localization of the initial-state wave functions. We consider a one-dimensional slab with lattice constant a latt of attractive Gaussian-shaped core potentials of width σ. The parameter σ/a latt thus controls the overlap between adjacent core potentials and localization of the electronic eigenfunctions on the lattice points. Small values of σ/a latt latt > or approx 0.4. By numerically solving the time-dependent Schroedinger equation, we calculate photoemission spectra from which we deduce a characteristic bimodal shape of the band-averaged photoemission time delay: as the slab eigenfunctions become increasingly delocalized, the time delay quickly decreases near σ/a latt =0.3 from relatively large values below σ/a latt ∼0.2 to much smaller delays above σ/a latt ∼0.4. This change in wave-function localization facilitates the interpretation of a recently measured apparent relative time delay between the photoemission from core and conduction-band levels of a tungsten surface.

  10. 基于平面离散曲线序列的三维几何结构识别%3D Geometrical Structure Recognition from Planar Discrete Curve Series

    Institute of Scientific and Technical Information of China (English)

    冯兰芳; 惠延波; 卢秉恒

    2002-01-01

    提出了一种由分层离散曲线序列识别物体三维特征的方法,定义了一些能够表达平面曲线基本特性的特征,设计了用于识别物体三维结构的特征函数,基于这些特征函数,物体被分解为柱体、锥体和曲线体的组合.给出了一些具体应用实例.%A method for feature recognition of 3D geometrical part from its slicing discrete curve series is studied. Some features of planar curve, which can represent its basic characteristics, are discussed. Furthermore, a number of eigenfunction used to recognize the 3D structure of geometrical part are constructed. Based on the eigenfunction, the geometrical part is decomposed into a combination of cylinder, taper as well as surface part. Some examples are given also.

  11. Numerical simulation of electronic properties of coupled quantum dots on wetting layers

    International Nuclear Information System (INIS)

    Betcke, M M; Voss, H

    2008-01-01

    Self-assembled quantum dots are grown on wetting layers and frequently in an array-like assembly of many similar but not exactly equal dots. Nevertheless, most simulations disregard these structural conditions and restrict themselves to simulating a pure single quantum dot. For reasons of numerical efficiency we advocate the effective one-band Hamiltonian with energy- and position-dependent effective mass approximation and a finite height hard-wall 3D confinement potential for computation of the energy levels of the electrons in the conduction band. Within this model we investigate the geometrical effects mentioned above on the electronic structure of a pyramidal InAs quantum dot embedded in a GaAs matrix. We find that the presence of a wetting layer may affect the electronic structure noticeably. Furthermore, we establish that, in spite of the large bandgap of the InAs/GaAs heterostructure, if the dots in a vertically aligned array are sufficiently close stacked there is considerable interaction between their eigenfunctions. Moreover, the eigenfunctions of such an array are quite sensitive to certain structural perturbations

  12. Two-stream sausage and hollowing instabilities in high-intensity particle beams

    International Nuclear Information System (INIS)

    Uhm, Han S.; Davidson, Ronald C.; Kaganovich, Igor

    2001-01-01

    Axisymmetric two-stream instabilities in high-intensity particle beams are investigated analytically by making use of the Vlasov-Maxwell equations in the smooth-focusing approximation. The eigenfunctions for the axisymmetric radial modes are calculated self-consistently in order to determine the dispersion relation describing collective stability properties. Stability properties for the sausage and hollowing modes, characterized by radial mode numbers n=1 and n=2, respectively, are investigated, and the dispersion relations are obtained for the complex eigenfrequency ω in terms of the axial wavenumber k and other system parameters. The eigenfunctions obtained self-consistently for the sausage and hollowing modes indicate that the perturbations exist only inside the beam. Therefore, the location of the conducting wall does not have an effect on stability behavior. The growth rates of the sausage and hollowing modes are of the same order of magnitude as that of the hose (dipole-mode) instability. Therefore, it is concluded that the axisymmetric sausage and hollowing instabilities may also be deleterious to intense ion beam propagation when a background component of electrons is presented

  13. SLIPM - a MAPLE package for numerical solution of Sturm-Liouville partial problems based on a continuous analog of Newton's method. II. Program realization

    International Nuclear Information System (INIS)

    Puzynin, I.V.; Puzynina, T.P.; Tkhak, V.Ch.

    2010-01-01

    SLIPM (Sturm-LIouville Problem in MAPLE) is a program complex written in the language of the computer algebras system MAPLE. It consists of the main program SLIPM.mw and of some procedures. It is intended for a numerical solution with the help of the continuous analog of Newton's method (CANM) of Sturm-Liouville partial problems, i.e. for calculating some eigenvalue of linear second-order differential operator and a corresponding eigenfunction satisfying homogeneous boundary conditions of the general type. SLIPM is the development of the program complexes SLIP1 and SLIPH4 written in the Fortran language. It is added by two new ways of calculating the initial value of iterative parameter τ 0 , by a procedure for calculating a higher precision solution (eigenvalue and corresponding eigenfunction) with the help of Richardson's extrapolation method, by graphical visualization procedures of intermediate and final results of the iterative process and by saving of the results on a disk file. The descriptions of the procedures purposes and their parameters are given

  14. Verification of gyrokinetic microstability codes with an LHD configuration

    Energy Technology Data Exchange (ETDEWEB)

    Mikkelsen, D. R. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Nunami, M. [National Inst. for Fusion Science (Japan); Watanabe, T. -H. [Nagoya Univ. (Japan); Sugama, H. [National Inst. for Fusion Science (Japan); Tanaka, K. [National Inst. for Fusion Science (Japan)

    2014-11-01

    We extend previous benchmarks of the GS2 and GKV-X codes to verify their algorithms for solving the gyrokinetic Vlasov-Poisson equations for plasma microturbulence. Code benchmarks are the most complete way of verifying the correctness of implementations for the solution of mathematical models for complex physical processes such as those studied here. The linear stability calculations reported here are based on the plasma conditions of an ion-ITB plasma in the LHD configuration. The plasma parameters and the magnetic geometry differ from previous benchmarks involving these codes. We find excellent agreement between the independently written pre-processors that calculate the geometrical coefficients used in the gyrokinetic equations. Grid convergence tests are used to establish the resolution and domain size needed to obtain converged linear stability results. The agreement of the frequencies, growth rates and eigenfunctions in the benchmarks reported here provides additional verification that the algorithms used by the GS2 and GKV-X codes are correctly finding the linear eigenvalues and eigenfunctions of the gyrokinetic Vlasov-Poisson equations.

  15. Wave dynamics of regular and chaotic rays

    International Nuclear Information System (INIS)

    McDonald, S.W.

    1983-09-01

    In order to investigate general relationships between waves and rays in chaotic systems, I study the eigenfunctions and spectrum of a simple model, the two-dimensional Helmholtz equation in a stadium boundary, for which the rays are ergodic. Statistical measurements are performed so that the apparent randomness of the stadium modes can be quantitatively contrasted with the familiar regularities observed for the modes in a circular boundary (with integrable rays). The local spatial autocorrelation of the eigenfunctions is constructed in order to indirectly test theoretical predictions for the nature of the Wigner distribution corresponding to chaotic waves. A portion of the large-eigenvalue spectrum is computed and reported in an appendix; the probability distribution of successive level spacings is analyzed and compared with theoretical predictions. The two principal conclusions are: 1) waves associated with chaotic rays may exhibit randomly situated localized regions of high intensity; 2) the Wigner function for these waves may depart significantly from being uniformly distributed over the surface of constant frequency in the ray phase space

  16. Spectral bisection algorithm for solving Schrodinger equation using upper and lower solutions

    Directory of Open Access Journals (Sweden)

    Qutaibeh Deeb Katatbeh

    2007-10-01

    Full Text Available This paper establishes a new criteria for obtaining a sequence of upper and lower bounds for the ground state eigenvalue of Schr"odinger equation $ -Deltapsi(r+V(rpsi(r=Epsi(r$ in $N$ spatial dimensions. Based on this proposed criteria, we prove a new comparison theorem in quantum mechanics for the ground state eigenfunctions of Schrodinger equation. We determine also lower and upper solutions for the exact wave function of the ground state eigenfunctions using the computed upper and lower bounds for the eigenvalues obtained by variational methods. In other words, by using this criteria, we prove that the substitution of the lower(upper bound of the eigenvalue in Schrodinger equation leads to an upper(lower solution. Finally, two proposed iteration approaches lead to an exact convergent sequence of solutions. The first one uses Raielgh-Ritz theorem. Meanwhile, the second approach uses a new numerical spectral bisection technique. We apply our results for a wide class of potentials in quantum mechanics such as sum of power-law potentials in quantum mechanics.

  17. Does quantum mechanics select out regularity and local mode behaviour in nonlinearly coupled vibrational systems?

    International Nuclear Information System (INIS)

    Yurtsever, E.; Brickmann, J.

    1990-01-01

    A two dimensional strongly nonharmonic vibrational system with nonlinear intermode coupling is studied both classically and quantum mechanically. The system was chosen such that there is a low lying transition (in energy) from a region where almost all trajectories move regularly to a region where chaotic dynamics strongly dominates. The corresponding quantum system is far away from the semiclassical limit. The eigenfunctions are calculated with high precision according to a linear variational scheme using conveniently chosen basis functions. It is the aim of this paper to check whether the prediction from semiclassical theory, namely that the measure of classically chaotic trajectories in phase space approaches the measure of irregular states in corresponding energy ranges, holds when the system is not close to the classical limit. It is also the aim to identify individual eigenfunctions with respect to regularity and to differentiate between local and normal vibrational states. It is found that there are quantitative and also qualitative differences between the quantum results and the semiclassical predictions. (orig./HK)

  18. Extraction and prediction of indices for monsoon intraseasonal oscillations: an approach based on nonlinear Laplacian spectral analysis

    Science.gov (United States)

    Sabeerali, C. T.; Ajayamohan, R. S.; Giannakis, Dimitrios; Majda, Andrew J.

    2017-11-01

    An improved index for real-time monitoring and forecast verification of monsoon intraseasonal oscillations (MISOs) is introduced using the recently developed nonlinear Laplacian spectral analysis (NLSA) technique. Using NLSA, a hierarchy of Laplace-Beltrami (LB) eigenfunctions are extracted from unfiltered daily rainfall data from the Global Precipitation Climatology Project over the south Asian monsoon region. Two modes representing the full life cycle of the northeastward-propagating boreal summer MISO are identified from the hierarchy of LB eigenfunctions. These modes have a number of advantages over MISO modes extracted via extended empirical orthogonal function analysis including higher memory and predictability, stronger amplitude and higher fractional explained variance over the western Pacific, Western Ghats, and adjoining Arabian Sea regions, and more realistic representation of the regional heat sources over the Indian and Pacific Oceans. Real-time prediction of NLSA-derived MISO indices is demonstrated via extended-range hindcasts based on NCEP Coupled Forecast System version 2 operational output. It is shown that in these hindcasts the NLSA MISO indices remain predictable out to ˜3 weeks.

  19. Spectral degeneracy and escape dynamics for intermittent maps with a hole

    International Nuclear Information System (INIS)

    Froyland, Gary; Stancevic, Ognjen; Murray, Rua

    2011-01-01

    We study intermittent maps from the point of view of metastability. Small neighbourhoods of an intermittent fixed point and their complements form pairs of almost-invariant sets. Treating the small neighbourhood as a hole, we first show that the absolutely continuous conditional invariant measures (ACCIMs) converge to the ACIM as the length of the small neighbourhood shrinks to zero. We then quantify how the escape dynamics from these almost-invariant sets are connected with the second eigenfunctions of Perron–Frobenius (transfer) operators when a small perturbation is applied near the intermittent fixed point. In particular, we describe precisely the scaling of the second eigenvalue with the perturbation size, provide upper and lower bounds and demonstrate L 1 convergence of the positive part of the second eigenfunction to the ACIM as the perturbation goes to zero. This perturbation and associated eigenvalue scalings and convergence results are all compatible with Ulam's method and provide a formal explanation for the numerical behaviour of Ulam's method in this nonuniformly hyperbolic setting. The main results of the paper are illustrated with numerical computations

  20. Sturm--Liouville eigenvalue problem

    International Nuclear Information System (INIS)

    Bailey, P.B.

    1977-01-01

    The viewpoint is taken that Sturn--Liouville problem is specified and the problem of computing one or more of the eigenvalues and possibly the corresponding eigenfunctions is presented for solution. The procedure follows the construction of a computer code, although such a code is not constructed, intended to solve Sturn--Liouville eigenvalue problems whether singular or nonsingular

  1. The Second Eigenvalue of the p-Laplacian as p Goes to 1

    Directory of Open Access Journals (Sweden)

    Enea Parini

    2010-01-01

    Full Text Available The asymptotic behaviour of the second eigenvalue of the p-Laplacian operator as p goes to 1 is investigated. The limit setting depends only on the geometry of the domain. In the particular case of a planar disc, it is possible to show that the second eigenfunctions are nonradial if p is close enough to 1.

  2. An efficient method for solving fractional Sturm-Liouville problems

    International Nuclear Information System (INIS)

    Al-Mdallal, Qasem M.

    2009-01-01

    The numerical approximation of the eigenvalues and the eigenfunctions of the fractional Sturm-Liouville problems, in which the second order derivative is replaced by a fractional derivative, is considered. The present results can be implemented on the numerical solution of the fractional diffusion-wave equation. The results show the simplicity and efficiency of the numerical method.

  3. Hamiltonian diagonalization in foliable space-times: A method to find the modes

    International Nuclear Information System (INIS)

    Castagnino, M.; Ferraro, R.

    1989-01-01

    A way to obtain modes diagonalizing the canonical Hamiltonian of a minimally coupled scalar quantum field, in a foliable space-time, is shown. The Cauchy data for these modes are found to be the eigenfunctions of a second-order differential operator that could be interpreted as the squared Hamiltonian for the first-quantized relativistic particle in curved space

  4. P-matrix description of charged particles interaction

    International Nuclear Information System (INIS)

    Babenko, V.A.; Petrov, N.M.

    1992-01-01

    The paper deals with formalism of the P-matrix description of two charged particles interaction. Separation in the explicit form of the background part corresponding to the purely Coulomb interaction in the P-matrix is proposed. Expressions for the purely Coulomb P-matrix, its poles, residues and purely Coulomb P-matrix approach eigenfunctions are obtained. (author). 12 refs

  5. Energy spectra of the hyperbolic and second Poeschl-Teller like potentials solved by new exact quantization rule

    International Nuclear Information System (INIS)

    Dong Shihai; Gonzalez-Cisneros, A.

    2008-01-01

    A new exact quantization rule simplifies the calculation of the energy levels for the exactly solvable quantum system. In this work we calculate the energy levels of the Schroedinger equation with the hyperbolic potential by this quantization rule. The corresponding eigenfunction is also derived for completeness. The second Poeschl-Teller like potential case is also carried out

  6. Simple One-Dimensional Quantum-Mechanical Model for a Particle Attached to a Surface

    Science.gov (United States)

    Fernandez, Francisco M.

    2010-01-01

    We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships…

  7. Green's function for a neutral particle of spin 1/2 in a magnetic field; Funcoes de Green para uma particula neutra de spin 1/2 num campo magnetico

    Energy Technology Data Exchange (ETDEWEB)

    Rodrigues, Rafael de Lima [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Vaidya, Arvind Narayan [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Fisica

    2001-12-01

    Using the spectral theorema in context of Green's function in momentum space of neutrons in the magnetic field of a linear conductor with current the bound state energy spectrum and eigenfunctions are deduced. It's also pointed out that this problem present a new scenary of Green's function in non-relativistic quantum mechanics. (author)

  8. Algebraic solution of an anisotropic nonquadratic potential

    International Nuclear Information System (INIS)

    Boschi Filho, H.; Vaidya, A.N.

    1990-06-01

    We show that an anisotropic nonquadratic potential, for which a path integral treatment had been recently discussed in the literature, possesses the (SO(2,1)xSO(2,1))ΛSO(2,1) dynamical symmetry and constructs its Green function algebraically. A particular case which generates new eigenvalues and eigenfunctions is also discussed. (author). 11 refs

  9. Escape rate from strange sets as an eigenvalue

    International Nuclear Information System (INIS)

    Tel, T.

    1986-06-01

    A new method is applied for calculating the escape rate from chaotic repellers or semi-attractors, based on the eigenvalue problem of the master equation of discrete dynamical systems. The corresponding eigenfunction is found to be smooth along unstable directions and to be, in general, a fractal measure. Examples of one and two dimensional maps are investigated. (author)

  10. Evolution kernel for the Dirac field

    International Nuclear Information System (INIS)

    Baaquie, B.E.

    1982-06-01

    The evolution kernel for the free Dirac field is calculated using the Wilson lattice fermions. We discuss the difficulties due to which this calculation has not been previously performed in the continuum theory. The continuum limit is taken, and the complete energy eigenfunctions as well as the propagator are then evaluated in a new manner using the kernel. (author)

  11. TRANSIENT ANOMALOUS SUB-DIFFUSION ON BOUNDED DOMAINS

    OpenAIRE

    MEERSCHAERT, MARK M.; NANE, ERKAN; VELLAISAMY, P.

    2012-01-01

    This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables, and eigenfunction expansions in time and space, are used to write strong solutions. Finally, stochastic solutions are written in terms of an inverse subordinator.

  12. Induced electric dipole in a quantum ring

    Energy Technology Data Exchange (ETDEWEB)

    Dantas, L.; Furtado, Claudio, E-mail: furtado@fisica.ufpb.br

    2013-12-02

    In this contribution, we investigate the quantum dynamics of a neutral particle confined in a quantum ring potential. We use two different field configurations for induced electric dipole in the presence of electric and magnetic fields and a general confining potential, for which we solve the Schrödinger equation and obtain the complete set of eigenfunctions and eigenvalues.

  13. Interrelation of alternative sets of Lax-pairs for a generalized nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Iino, Kazuhiro; Ichikawa, Yoshihiko; Wadati, Miki.

    1982-05-01

    Examination of the inverse scattering transformation schemes for a generalized nonlinear Schroedinger equation reveals the fact that the algorithm of Chen-Lee-Liu gives rise to the Lax-pairs for the squared eigenfunctions of the Wadati-Konno-Ichikawa scheme, which has been formulated as superposition of the Ablowitz-Kaup-Newell-Segur scheme and the Kaup-Newell scheme. (author)

  14. Track 4: basic nuclear science variance reduction for Monte Carlo criticality simulations. 2. Assessment of MCNP Statistical Analysis of keff Eigenvalue Convergence with an Analytical Criticality Verification Test Set

    International Nuclear Information System (INIS)

    Sood, Avnet; Forster, R. Arthur; Parsons, D. Kent

    2001-01-01

    Monte Carlo simulations of nuclear criticality eigenvalue problems are often performed by general purpose radiation transport codes such as MCNP. MCNP performs detailed statistical analysis of the criticality calculation and provides feedback to the user with warning messages, tables, and graphs. The purpose of the analysis is to provide the user with sufficient information to assess spatial convergence of the eigenfunction and thus the validity of the criticality calculation. As a test of this statistical analysis package in MCNP, analytic criticality verification benchmark problems have been used for the first time to assess the performance of the criticality convergence tests in MCNP. The MCNP statistical analysis capability has been recently assessed using the 75 multigroup criticality verification analytic problem test set. MCNP was verified with these problems at the 10 -4 to 10 -5 statistical error level using 40 000 histories per cycle and 2000 active cycles. In all cases, the final boxed combined k eff answer was given with the standard deviation and three confidence intervals that contained the analytic k eff . To test the effectiveness of the statistical analysis checks in identifying poor eigenfunction convergence, ten problems from the test set were deliberately run incorrectly using 1000 histories per cycle, 200 active cycles, and 10 inactive cycles. Six problems with large dominance ratios were chosen from the test set because they do not achieve the normal spatial mode in the beginning of the calculation. To further stress the convergence tests, these problems were also started with an initial fission source point 1 cm from the boundary thus increasing the likelihood of a poorly converged initial fission source distribution. The final combined k eff confidence intervals for these deliberately ill-posed problems did not include the analytic k eff value. In no case did a bad confidence interval go undetected. Warning messages were given signaling that

  15. Self-Commutators of Composition Operators with Monomial Symbols on the Dirichlet Space

    Directory of Open Access Journals (Sweden)

    A. Abdollahi

    2011-01-01

    Full Text Available Let (=,∈, for some positive integer and the composition operator on the Dirichlet space induced by . In this paper, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators ∗,∗ and self-commutators of , which expose that the spectrum and point spectrum coincide. We also find the eigenfunctions of the operators.

  16. The H-N method for solving linear transport equation: theory and application

    International Nuclear Information System (INIS)

    Kaskas, A.; Gulecyuz, M.C.; Tezcan, C.

    2002-01-01

    The system of singular integral equation which is obtained from the integro-differential form of the linear transport equation as a result of Placzec lemma is solved. Application are given using the exit distributions and the infinite medium Green's function. The same theoretical results are also obtained with the use of the singular eigenfunction of the method of elementary solutions

  17. Self-similar solutions for toroidal magnetic fields in a turbulent jet

    International Nuclear Information System (INIS)

    Komissarov, S.S.; Ovchinnikov, I.L.

    1989-01-01

    Self-similar solutions for weak toroidal magnetic fields transported by a turbulent jet of incompressible fluid are obtained. It is shown that radial profiles of the self-similar solutions form a discrete spectrum of eigenfunctions of a linear differential operator. The strong depatures from the magnetic flux conservation law, used frequently in turbulent jet models for extragalactic radio sources, are found

  18. Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

    Science.gov (United States)

    Bender, Carl M.; Brody, Dorje C.

    2018-04-01

    The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.

  19. About one Newell's result and the quantum mechanical check of the microcanonical distribution

    International Nuclear Information System (INIS)

    Zastavenko, L.G.

    1981-01-01

    G.F. Newell succeeded to prove for the eigenfunctions PSIsub(n)(x) of the k-dimensional Schroedinger equation (-Δsub(k)+q(xsub(1), xsub(2)..., xsub(k))-lambdasub(n))PSIsub(n)(x)=0, ∫/PSIsup(2)(x)/dsup(k)x=1, q(x)>=0, q(x)→+infinity at x→infinity the asymptotic relation (lambda→+infinity) Σsub(lambdasub(n) [ru

  20. A generalization of the virial theorem for strongly singular potentials

    International Nuclear Information System (INIS)

    Gesztesy, F.; Pittner, L.

    1978-09-01

    Using scale transformations the authors prove a generalization of the virial theorem for the eigenfunctions of non-relativistic Schroedinger Hamiltonians which are defined as the Friedrichs extension of strongly singular differential operators. The theorem also applies to situations where the ground state has divergent kinetic and potential energy and thus the usual version of the virial theorem becomes meaningless. (Auth.)

  1. An approximation theory for nonlinear partial differential equations with applications to identification and control

    Science.gov (United States)

    Banks, H. T.; Kunisch, K.

    1982-01-01

    Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

  2. Crystal field levels of tetravalent actinide ions in actinide dioxides UO2, NpO2 and PuO2

    International Nuclear Information System (INIS)

    Krupa, J.C.; Gajek, Z.

    1991-01-01

    Crystal-field parameters resulting from analysis of optical spectroscopy and neutron diffraction data recorded on UO 2 and NpO 2 as well as ab-initio calculated parameters were used to calculate the crystal-field eigenfunctions and eigenvalues for the J ground-state manifold of U 4+ , Np 4+ and Pu 4+ in UO 2 , NpO 2 and PuO 2

  3. Revisiting the quantum harmonic oscillator via unilateral Fourier transforms

    International Nuclear Information System (INIS)

    Nogueira, Pedro H F; Castro, Antonio S de

    2016-01-01

    The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions. (paper)

  4. The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

    Science.gov (United States)

    Yeon, Kyu Hwang; Um, Chung IN; George, T. F.

    1994-01-01

    The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

  5. Fermionic particles with positron-dependent mass in the presence of inversely quadratic Yukawa potential and tensor interaction

    International Nuclear Information System (INIS)

    Bahar, M.K.; Yasuk, F.

    2013-01-01

    Approximate solutions of the Dirac equation with positron-dependent mass are presented for the inversely quadratic Yukawa potential and Coulomb-like tensor interaction by using the asymptotic iteration method. The energy eigenvalues and the corresponding normalized eigenfunctions are obtained in the case of positron-dependent mass and arbitrary spin-orbit quantum number k state and approximation on the spin-orbit coupling term. (author)

  6. Properties of local equations for a separation column

    International Nuclear Information System (INIS)

    Hodor, I.

    1992-01-01

    An overall theory of column separation is developed. A general expression for fully-developed concentration fields is found. For close-separation processes, a simple method to derive the theoretical plate height and the stage efficiency from local equations are given. Application of separation-of-variables to linearized systems is discussed and a partial range completeness of the eigenfunctions is found. (author)

  7. The best of both worlds: Phylogenetic eigenvector regression and mapping

    Directory of Open Access Journals (Sweden)

    José Alexandre Felizola Diniz Filho

    2015-09-01

    Full Text Available Eigenfunction analyses have been widely used to model patterns of autocorrelation in time, space and phylogeny. In a phylogenetic context, Diniz-Filho et al. (1998 proposed what they called Phylogenetic Eigenvector Regression (PVR, in which pairwise phylogenetic distances among species are submitted to a Principal Coordinate Analysis, and eigenvectors are then used as explanatory variables in regression, correlation or ANOVAs. More recently, a new approach called Phylogenetic Eigenvector Mapping (PEM was proposed, with the main advantage of explicitly incorporating a model-based warping in phylogenetic distance in which an Ornstein-Uhlenbeck (O-U process is fitted to data before eigenvector extraction. Here we compared PVR and PEM in respect to estimated phylogenetic signal, correlated evolution under alternative evolutionary models and phylogenetic imputation, using simulated data. Despite similarity between the two approaches, PEM has a slightly higher prediction ability and is more general than the original PVR. Even so, in a conceptual sense, PEM may provide a technique in the best of both worlds, combining the flexibility of data-driven and empirical eigenfunction analyses and the sounding insights provided by evolutionary models well known in comparative analyses.

  8. Estimating amplitude ratios in boundary layer stability theory: a comparison between two approaches

    Science.gov (United States)

    Govindarajan, Rama; Narasimha, R.

    2001-07-01

    We first demonstrate that, if the contributions of higher-order mean flow are ignored, the parabolized stability equations (Bertolotti et al. 1992) and the ‘full’ non-parallel equation of Govindarajan & Narasimha (1995, hereafter GN95) are both equivalent to order R[minus sign]1 in the local Reynolds number R to Gaster's (1974) equation for the stability of spatially developing boundary layers. It is therefore of some concern that a detailed comparison between Gaster (1974) and GN95 reveals a small difference in the computed amplitude ratios. Although this difference is not significant in practical terms in Blasius flow, it is traced here to the approximation, in Gaster's method, of neglecting the change in eigenfunction shape due to flow non-parallelism. This approximation is not justified in the critical and the wall layers, where the neglected term is respectively O(R[minus sign]2/3) and O(R[minus sign]1) compared to the largest term. The excellent agreement of GN95 with exact numerical simulations, on the other hand, suggests that the effect of change in eigenfunction is accurately taken into account in that paper.

  9. Quantum finance Hamiltonian for coupon bond European and barrier options.

    Science.gov (United States)

    Baaquie, Belal E

    2008-03-01

    Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier option for a financial instrument is "knocked out" (terminated with zero value) if the price of the underlying instrument exceeds or falls below preset limits; the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates' Hamiltonian. The price of the European coupon bond option and the zero coupon bond barrier option are calculated. It is shown that, is general, the constraint function for a coupon bond barrier option can -- to a good approximation -- be linearized. A calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option, which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function.

  10. Periodical gas flow around a well in porous media

    International Nuclear Information System (INIS)

    Shnaid, I.; Olek, S.

    1996-01-01

    Analytical solutions of the linearized governing equation are presented for periodic gas flow around a well in porous media. Two cases are considered: a fully penetrating well and a partially penetrating well. For the first case, a closed form solution is obtained, whereas for the second case the solution is in the form of eigenfunctions expansions. The results have practical application in compressed air energy storage. (authors)

  11. Schroedinger operators - geometric estimates in terms of the occupation time

    International Nuclear Information System (INIS)

    Demuth, M.; Kirsch, W.; McGillivray, I.

    1995-01-01

    The difference of Schroedinger and Dirichlet semigroups is expressed in terms of the Laplace transform of the Brownian motion occupation time. This implies quantitative upper and lower bounds for the operator norms of the corresponding resolvent differences. One spectral theoretical consequence is an estimate for the eigenfunction for a Schroedinger operator in a ball where the potential is given as a cone indicator function. 12 refs

  12. Essentially isospectral transformations and their applications

    OpenAIRE

    Guliyev , Namig

    2017-01-01

    We define and study the properties of Darboux-type transformations between Sturm--Liouville problems with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary conditions). Using these transformations, we obtain various direct and inverse spectral results for these problems in a unified manner, such as asymptotics of eigenvalues and norming constants, oscillation of eigenfunctions, regularized trace formulas, and i...

  13. Time dependent formulation of the energy loss by an accelerated intense electron beam just emitted by the cathode of RF-FEL photoinjector

    Energy Technology Data Exchange (ETDEWEB)

    Salah, Wa' el [Physics Department, Hashemite University, Zarqa 13115 (Jordan)]. E-mail: wael_salahh@hotmail.com; Coacolo, J.-L. [Institut de Physique Nucleaire d' Orsay, 91406 Orsay Cedex (France); Hallak, A.B. [Physics Department, Hashemite University, Zarqa 13115 (Jordan); Al-Obaid, M. [Physics Department, Hashemite University, Zarqa 13115 (Jordan)

    2006-08-01

    The energy loss by an accelerated electron bunch of a conical shape propagating in the laser-driven RF-photoinjector is expressed in terms of an expansion of the vector and scalar potentials into a series of eigenfunctions of the empty unit 'pill-box' cavity. A versatile and simple analytical formula which can be easily applied to a bunch of any shape is obtained.

  14. Purely absolutely continuous spectrum for almost Mathieu operators

    International Nuclear Information System (INIS)

    Chulaevsky, V.; Delyon, F.

    1989-01-01

    Using a recent result of Sinai, the authors prove that the almost Mathieu operators acting on l 2 (Z), (H αλ Psi)(n) = Ψ(n + 1) + Ψ(n - 1) + λ cos(ωn + α) Ψ(n), have a purely absolutely continuous spectrum for almost all α provided that ω is a good irrational and λ is sufficiently small. Furthermore, the generalized eigenfunctions are quasiperiodic

  15. System and method for image reconstruction, analysis, and/or de-noising

    KAUST Repository

    Laleg-Kirati, Taous-Meriem

    2015-11-12

    A method and system can analyze, reconstruct, and/or denoise an image. The method and system can include interpreting a signal as a potential of a Schrödinger operator, decomposing the signal into squared eigenfunctions, reducing a design parameter of the Schrödinger operator, analyzing discrete spectra of the Schrödinger operator and combining the analysis of the discrete spectra to construct the image.

  16. Computation of cubic harmonics

    International Nuclear Information System (INIS)

    Fox, K.; Krohn, B.J.

    1977-01-01

    Symmetry-adapted functions (orthonormal linear combinations of angular-momentum eigenfunctions belonging to particular symmetry species) for the T/sub d/ and O/sub h/ point groups have been computed for J< or =100 using an algorithm of Fox and Ozier, and Cholesky factorization of idempotent matrices. The results of Cholesky factorization are compared with those of both symmetric elimination with pivoting and an EISPACK diagonalization routine

  17. Closed form solution for a double quantum well using Groebner basis

    Energy Technology Data Exchange (ETDEWEB)

    Acus, A [Institute of Theoretical Physics and Astronomy, Vilnius University, A Gostauto 12, LT-01108 Vilnius (Lithuania); Dargys, A, E-mail: dargys@pfi.lt [Center for Physical Sciences and Technology, Semiconductor Physics Institute, A Gostauto 11, LT-01108 Vilnius (Lithuania)

    2011-07-01

    Analytical expressions for the spectrum, eigenfunctions and dipole matrix elements of a square double quantum well (DQW) are presented for a general case when the potential in different regions of the DQW has different heights and the effective masses are different. This was achieved by using a Groebner basis algorithm that allowed us to disentangle the resulting coupled polynomials without explicitly solving the transcendental eigenvalue equation.

  18. Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method

    International Nuclear Information System (INIS)

    Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.

    2014-01-01

    By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained

  19. Some exactly solvable models in quantum mechanics and the low energy expansions

    International Nuclear Information System (INIS)

    Albeverio, S.; Hoeegh-Krohn, R.; Holden, H.; Gesztesy, F.

    We give an overview of recent results on exactly solvable models in quantum mechanics. In particular we discuss point interactions located at finitely or infinitely many centers, in one and three dimensions. Results about the resolvent, energy eigenvalues and resonances, scattering quantitites as well as eigenfunctions and corresponding low energy expansions are mentioned, with particular attention to the case of three-dimensional crystals. (orig.)

  20. Bender-Dunne Orthogonal Polynomials, Quasi-Exact Solvability and Asymptotic Iteration Method for Rabi Hamiltonian

    International Nuclear Information System (INIS)

    Yahiaoui, S.-A.; Bentaiba, M.

    2011-01-01

    We present a method for obtaining the quasi-exact solutions of the Rabi Hamiltonian in the framework of the asymptotic iteration method (AIM). The energy eigenvalues, the eigenfunctions and the associated Bender-Dunne orthogonal polynomials are deduced. We show (i) that orthogonal polynomials are generated from the upper limit (i.e., truncation limit) of polynomial solutions deduced from AIM, and (ii) prove to have nonpositive norm. (authors)

  1. On integral and finite Fourier transforms of continuous q-Hermite polynomials

    International Nuclear Information System (INIS)

    Atakishiyeva, M. K.; Atakishiyev, N. M.

    2009-01-01

    We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials H n (x vertical bar q) of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.

  2. Feasibility study on heterogeneous method in criticality calculations

    International Nuclear Information System (INIS)

    Prati, A.

    1977-01-01

    The criticality of finite heterogeneous assemblies is analysed by the heterogeneous methods employing the Eigen-function analysis. The moderation is treated by the Fermi age theory. The system is analysed in two dimensional rectangular coordinates. The criticality and the fluxes are determined for systems with small and large number of fuel rods. The convergence and the residual error in the modal analysis are discussed. (author)

  3. Medium energy probes and nuclear structure

    International Nuclear Information System (INIS)

    Ginocchio, J.N.

    1984-01-01

    In this paper we explore two topics. The first topic is the marriage of medium energy reaction theory with the interacting boson model of nuclei in such a way that the multiple scattering is summed to all orders. The second topic is an exactly solvable potential model which gives realistic shell model eigenfunctions which can be used to calculate static and transition nuclear densities. (orig./HSI)

  4. Tchebichef polynomials of the second kind and singular differential operators

    International Nuclear Information System (INIS)

    Onyango-Otieno, V.P.

    1985-10-01

    Our purpose in this paper is to study the so called right- and left-definite problems for the Tchebichef differential equation using the classical approach given in the book ''Eigenfunction expansions associated with second-order differential equations-I'' by Titchmarsh. We link the Titchmarsh method with operator theoretic results in the Hilbert function spaces Lsub(w) 2 (-1,1) and Hsub(p,q) 2 (-1,1)

  5. Investigations in the Spectral Properties of Operators with Distant Perturbations (survey

    Directory of Open Access Journals (Sweden)

    A. M. Golovina

    2015-01-01

    Full Text Available We propose a chronological overview of researches on operators with distant perturbations. Let us explain what "distant perturbations" mean. An elementary example of the operator with distant perturbations is a differential operator of the second order with two finite potentials. Supports of these operators are at a great distance from each other, i.e. they are \\distant".The study of such operators has been performed since the middle of the last century, mostly by foreign researchers see eg. R. Ahlrichs, T. Aktosun, M. Klaus, P. Aventini, P. Exner, E.B. Davies, V. Graffi, E.V. Harrell II, H.J. Silverstone, M. Mebkhout, R. Hoegh-Krohn, W. Hun ziker, V. Kostrykin, R. Schrader, J.D. Morgan (III, Y. Pinchover, O.K. Reity, H. Tamura, X. Wang, Y. Wang, S. Kondej, B. Simon, I. Veselic, D.I. Borisov, A.M. Golovina. The main objects of their investigation were the asymptotic behaviors of eigenvalues and corresponding eigenfunctions of perturbed operators. In several papers the research was focused on resolvents and eigenvalues of perturbed operator arising from the edge of the essential spectrum. The main results of the past century are the first members of the asymptotics of perturbed eigenvalues and the corresponding eigenfunctions and the first members of the asymptotics of resolvents of the perturbed operators. The main results of the last fifteen years are full asymptotic expansions for the eigenvalues and their corresponding functions and an explicit formula for the resolvent of the perturbed operator.In this paper, we also note that up to 2004 only different kind of potentials were considered as perturbing operators, and Laplace and Dirac operators were considered as unperturbed operators. Only since 2004, nonpotential perturbing operators appeared in the literature. Since 2012, an arbitrary elliptic differential operator is considered as an unperturbed operator.We propose a classification of investigations on distant perturbations, based on the

  6. Telecommunications with a relativistic spacecraft optimized via the Karhunen-Loève Transform (KLT)

    Science.gov (United States)

    Maccone, Claudio

    1999-01-01

    The subject of telecommunications between the Earth and a spacecraft moving at a relativistic speed has received little attention so far. This is probably because the best thoughts of scientists have usually been devoted to the relativistic spacecraft propulsion problems instead. In this paper we would like to give the basic equations for relativistic telecommunications in the form of the relativistic Karhunen-Loève Transform (KLT), investigated by this author for over 15 years (Maccone, 1994). Essentially, the KLT is something superior than the Fourier Transform (FT) inasmuch as: 1) The KLT applies to any non-stationary stochastic process (input noisy signal), whereas the FT rigorously applies to stationary processes only (the latter result is usually referred to as the ``Wiener-Khintchine Theorem'') 2) The KLT applies to any background noise distribution (i.e. to coloured noise in general) whereas the FT rigorously applies only when the background noise is white over the observing bandwidth; 3) The KLT is a more general filtering and compressing tool since it is a statistical procedure, rather than a deterministic procedure like the FT. This, unfortunately, makes the maths behind the KLT less easy to handle particularly in the case of the relativistic signals considered here. The KLT is a way of optimizing the signal processing of a given noisy signal by projecting the noisy signal itself onto the set of orthonormal basis functions spanned by the eigenfunctions of the autocorrelation of the noisy signal. Thus, the key problem in computing the KLT of a noisy signal is the computation of the eigenvalues and eigenfunctions of the autocorrelation of the noisy signal. For the special case of the Brownian motion (i.e. the basic Gaussian noisy signal) it can be proved that the KLT eigenfunctions are just sines, i.e. the KLT is the same as the FT. Let us now bring relativity into the KLT picture (this paper is confined to special relativity; general relativity can be

  7. Green function on product networks

    OpenAIRE

    Arauz Lombardía, Cristina; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos

    2012-01-01

    Our objective is to determine the Green function of product networks in terms of the Green function of one of the factor networks and the eigenvalues and eigenfunctions of the Schr odinger operator of the other factor network, which we consider that are known. Moreover, we use these results to obtain the Green function of spider networks in terms of Green functions over cicles and paths. Peer Reviewed

  8. Criteria for Second Stability for Ballooning Modes in Stellarators

    International Nuclear Information System (INIS)

    Hudson, S.R.; Hegna, C.C.

    2004-01-01

    An expression determining how variations in the pressure-gradient and average magnetic shear affect ballooning stability for a stellarator equilibrium is presented. The procedure for determining the marginal stability boundaries, for each field line, depends only on the equilibrium and a single ballooning eigenfunction calculation. This information is sufficient to determine if increasing pressure-gradient is stabilizing or destabilizing and to predict whether the configuration possess a second stable region

  9. Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain

    OpenAIRE

    Imbrie, John Z

    2016-01-01

    We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of eigenvalues. In a KAM-style construction, a sequence of local unitary transformations is used to diagonalize the Hamiltonian by deforming the initial tensor product basis into a complete set of exact many-body eigenfunctions.

  10. Exact quantum solutions for some asymmetrical two-well potentials

    International Nuclear Information System (INIS)

    Ley-Koo, E.

    1985-01-01

    We discuss several points of interest in the study of two-well potentials in quantum mechanics courses. In particular, we construct the solutions of the Schroedinger equation for rectangular-well, harmonic-oscillator and triangular-well potentials with a delta-function potential superimposed in different positions. The energy spectra and eigenfunctions of such systems are presented and analyzed for different intensities and positions of the delta-function potential. (author)

  11. A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion

    Energy Technology Data Exchange (ETDEWEB)

    Ojeda-Guillén, D., E-mail: dojedag@ipn.mx [Escuela Superior de Cómputo, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz esq. Av. Miguel Othón de Mendizábal, Col. Lindavista, Delegación Gustavo A. Madero, C.P. 07738 Ciudad de México (Mexico); Mota, R. D. [Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacán, C.P. 04430 Ciudad de México (Mexico); Granados, V. D. [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, Delegación Gustavo A. Madero, C.P. 07738 Ciudad de México (Mexico)

    2016-06-15

    We introduce a generalization of the Jaynes-Cummings model and study some of its properties. We obtain the energy spectrum and eigenfunctions of this model by using the tilting transformation and the squeezed number states of the one-dimensional harmonic oscillator. As physical applications, we connect this new model to two important and novelty problems: the relativistic parametric amplifier and the quantum simulation of a single trapped ion.

  12. A garden of orchids: a generalized Harper equation at quadratic irrational frequencies

    International Nuclear Information System (INIS)

    Mestel, B D; Osbaldestin, A H

    2004-01-01

    We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case

  13. Variational Multi-Scale method with spectral approximation of the sub-scales.

    KAUST Repository

    Dia, Ben Mansour

    2015-01-07

    A variational multi-scale method where the sub-grid scales are computed by spectral approximations is presented. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a nite number of modes.

  14. Stability equation and two-component Eigenmode for domain walls in scalar potential model

    International Nuclear Information System (INIS)

    Dias, G.S.; Graca, E.L.; Rodrigues, R. de Lima

    2002-08-01

    Supersymmetric quantum mechanics involving a two-component representation and two-component eigenfunctions is applied to obtain the stability equation associated to a potential model formulated in terms of two coupled real scalar fields. We investigate the question of stability by introducing an operator technique for the Bogomol'nyi-Prasad-Sommerfield (BPS) and non-BPS states on two domain walls in a scalar potential model with minimal N 1-supersymmetry. (author)

  15. Green's function method for perturbed Korteweg-de Vries equation

    International Nuclear Information System (INIS)

    Cai Hao; Huang Nianning

    2003-01-01

    The x-derivatives of squared Jost solution are the eigenfunctions with the zero eigenvalue of the linearized equation derived from the perturbed Korteweg-de Vries equation. A method similar to Green's function formalism is introduced to show the completeness of the squared Jost solutions in multi-soliton cases. It is not related to Lax equations directly, and thus it is beneficial to deal with the nonlinear equations with complicated Lax pair

  16. A model for the two-point velocity correlation function in turbulent channel flow

    International Nuclear Information System (INIS)

    Sahay, A.; Sreenivasan, K.R.

    1996-01-01

    A relatively simple analytical expression is presented to approximate the equal-time, two-point, double-velocity correlation function in turbulent channel flow. To assess the accuracy of the model, we perform the spectral decomposition of the integral operator having the model correlation function as its kernel. Comparisons of the empirical eigenvalues and eigenfunctions with those constructed from direct numerical simulations data show good agreement. copyright 1996 American Institute of Physics

  17. A garden of orchids: a generalized Harper equation at quadratic irrational frequencies

    Energy Technology Data Exchange (ETDEWEB)

    Mestel, B D [Department of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA (United Kingdom); Osbaldestin, A H [Department of Mathematics, University of Portsmouth, Portsmouth PO1 3HE (United Kingdom)

    2004-10-01

    We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case.

  18. Crystal field levels of tetravalent actinide ions in actinide dioxides UO sub 2 , NpO sub 2 and PuO sub 2

    Energy Technology Data Exchange (ETDEWEB)

    Krupa, J.C. (Paris-11 Univ., 91 - Orsay (FR). Inst. de Physique Nucleaire); Gajek, Z. (Polska Akademia Nauk, Wroclaw (PL). Inst. Niskich Temperatur i Badan Strukturalnych)

    1991-01-01

    Crystal-field parameters resulting from analysis of optical spectroscopy and neutron diffraction data recorded on UO{sub 2} and NpO{sub 2} as well as ab-initio calculated parameters were used to calculate the crystal-field eigenfunctions and eigenvalues for the J ground-state manifold of U{sup 4+}, Np{sup 4+} and Pu{sup 4+} in UO{sub 2}, NpO{sub 2} and PuO{sub 2}.

  19. Photoelectric atomic absorption cross sections for elements Z = 6 to 54 in the medium energy X-ray range (5 to 25 keV). Pt. 1

    International Nuclear Information System (INIS)

    Hildebrandt, G.; Stephenson, J.D.; Wagenfeld, H.

    1975-01-01

    Photoelectric atomic absorption cross sections have been calculated by means of hydrogen-like eigenfunctions for the atomic K, L, M and N sub-shells of the elements Z = 6 to 54, using revised screening constants and an extension of the theory. The absorption cross sections have been further separated into dipole and quadrupole components so that the numerical data can also be applied to the Borrmann effect. (orig.) [de

  20. SUSY QM from three domain walls in a scalar potential

    Energy Technology Data Exchange (ETDEWEB)

    Rodrigues, R. de Lima; Lima, A.F. de [Universidade Federal de Campina Grande (UFCG), Campina Grande, PB (Brazil). Centro de Tecnologia. Unidade Academica de Fisica]. E-mail: aerlima@df.ufcg.edu.br; Bezerra de Mello, E.R.; Bezerra, V.B. [Universidade Federal da Paraiba (UFPB), Joao Pessoa, PB (Brazil). Dept. de Fisica]. E-mails: emello@fisica.ufpb.br; valdir@fisica.ufpb.br

    2007-07-01

    We investigate the linear classical stability of Bogomol'nyi-Prasad-Sommerfield (BPS) on three domain wall solutions in a system of three coupled real scalar fields, for a general positive potential with a square form. From a field theoretic superpotential evaluated on the domain states, the connection between the supersymmetric quantum mechanics involving three-component eigenfunctions and the stability equation associated with three classical configurations is elaborated. (author)

  1. Approximate Solutions to the Dirac Equation with Effective Mass for the Manning-Rosen Potential in N Dimensions

    International Nuclear Information System (INIS)

    Bahar, M.K.; Yasuk, F.

    2012-01-01

    The solutions of the effective mass Dirac equation for the Manning-Rosen potential with the centrifugal term are studied approximately in N dimension. The relativistic energy spectrum and two-component spinor eigenfunctions are obtained by the asymptotic iteration method. We have also investigated eigenvalues of the effective mass Dirac-Manning-Rosen problem for α = 0 or α = 1. In this case, the Manning-Rosen potential reduces to the Hulthen potential. (author)

  2. The basis property of eigenfunctions in the problem of a nonhomogeneous damped string

    Directory of Open Access Journals (Sweden)

    Łukasz Rzepnicki

    2017-01-01

    Full Text Available The equation which describes the small vibrations of a nonhomogeneous damped string can be rewritten as an abstract Cauchy problem for the densely defined closed operator \\(i A\\. We prove that the set of root vectors of the operator \\(A\\ forms a basis of subspaces in a certain Hilbert space \\(H\\. Furthermore, we give the rate of convergence for the decomposition with respect to this basis. In the second main result we show that with additional assumptions the set of root vectors of the operator \\(A\\ is a Riesz basis for \\(H\\.

  3. A singular-value method for reconstruction of nonradial and lossy objects.

    Science.gov (United States)

    Jiang, Wei; Astheimer, Jeffrey; Waag, Robert

    2012-03-01

    Efficient inverse scattering algorithms for nonradial lossy objects are presented using singular-value decomposition to form reduced-rank representations of the scattering operator. These algorithms extend eigenfunction methods that are not applicable to nonradial lossy scattering objects because the scattering operators for these objects do not have orthonormal eigenfunction decompositions. A method of local reconstruction by segregation of scattering contributions from different local regions is also presented. Scattering from each region is isolated by forming a reduced-rank representation of the scattering operator that has domain and range spaces comprised of far-field patterns with retransmitted fields that focus on the local region. Methods for the estimation of the boundary, average sound speed, and average attenuation slope of the scattering object are also given. These methods yielded approximations of scattering objects that were sufficiently accurate to allow residual variations to be reconstructed in a single iteration. Calculated scattering from a lossy elliptical object with a random background, internal features, and white noise is used to evaluate the proposed methods. Local reconstruction yielded images with spatial resolution that is finer than a half wavelength of the center frequency and reproduces sound speed and attenuation slope with relative root-mean-square errors of 1.09% and 11.45%, respectively.

  4. The Direct Effect of Toroidal Magnetic Fields on Stellar Oscillations: An Analytical Expression for the General Matrix Element

    Energy Technology Data Exchange (ETDEWEB)

    Kiefer, René; Schad, Ariane; Roth, Markus [Kiepenheuer-Institut für Sonnenphysik, Schöneckstraße 6, D-79104 Freiburg (Germany)

    2017-09-10

    Where is the solar dynamo located and what is its modus operandi? These are still open questions in solar physics. Helio- and asteroseismology can help answer them by enabling us to study solar and stellar internal structures through global oscillations. The properties of solar and stellar acoustic modes are changing with the level of magnetic activity. However, until now, the inference on subsurface magnetic fields with seismic measures has been very limited. The aim of this paper is to develop a formalism to calculate the effect of large-scale toroidal magnetic fields on solar and stellar global oscillation eigenfunctions and eigenfrequencies. If the Lorentz force is added to the equilibrium equation of motion, stellar eigenmodes can couple. In quasi-degenerate perturbation theory, this coupling, also known as the direct effect, can be quantified by the general matrix element. We present the analytical expression of the matrix element for a superposition of subsurface zonal toroidal magnetic field configurations. The matrix element is important for forward calculations of perturbed solar and stellar eigenfunctions and frequency perturbations. The results presented here will help to ascertain solar and stellar large-scale subsurface magnetic fields, and their geometric configuration, strength, and change over the course of activity cycles.

  5. Revisiting the Low-Frequency Dipolar Perturbation by an Impenetrable Ellipsoid in a Conductive Surrounding

    Directory of Open Access Journals (Sweden)

    Panayiotis Vafeas

    2017-01-01

    Full Text Available This contribution deals with the scattering by a metallic ellipsoidal target, embedded in a homogeneous conductive medium, which is stimulated when a 3D time-harmonic magnetic dipole is operating at the low-frequency realm. The incident, the scattered, and the total three-dimensional electromagnetic fields, which satisfy Maxwell’s equations, yield low-frequency expansions in terms of positive integral powers of the complex-valued wave number of the exterior medium. We preserve the static Rayleigh approximation and the first three dynamic terms, while the additional terms of minor contribution are neglected. The Maxwell-type problem is transformed into intertwined potential-type boundary value problems with impenetrable boundary conditions, whereas the environment of a genuine ellipsoidal coordinate system provides the necessary setting for tackling such problems in anisotropic space. The fields are represented via nonaxisymmetric infinite series expansions in terms of harmonic eigenfunctions, affiliated with the ellipsoidal system, obtaining analytical closed-form solutions in a compact fashion. Until nowadays, such problems were attacked by using the very few ellipsoidal harmonics exhibiting an analytical form. In the present article, we address this issue by incorporating the full series expansion of the potentials and utilizing the entire subspace of ellipsoidal harmonic eigenfunctions.

  6. Analyzing self-similar and fractal properties of the C. elegans neural network.

    Directory of Open Access Journals (Sweden)

    Tyler M Reese

    Full Text Available The brain is one of the most studied and highly complex systems in the biological world. While much research has concentrated on studying the brain directly, our focus is the structure of the brain itself: at its core an interconnected network of nodes (neurons. A better understanding of the structural connectivity of the brain should elucidate some of its functional properties. In this paper we analyze the connectome of the nematode Caenorhabditis elegans. Consisting of only 302 neurons, it is one of the better-understood neural networks. Using a Laplacian Matrix of the 279-neuron "giant component" of the network, we use an eigenvalue counting function to look for fractal-like self similarity. This matrix representation is also used to plot visualizations of the neural network in eigenfunction coordinates. Small-world properties of the system are examined, including average path length and clustering coefficient. We test for localization of eigenfunctions, using graph energy and spacial variance on these functions. To better understand results, all calculations are also performed on random networks, branching trees, and known fractals, as well as fractals which have been "rewired" to have small-world properties. We propose algorithms for generating Laplacian matrices of each of these graphs.

  7. Efficient solution of 3D Ginzburg-Landau problem for mesoscopic superconductors

    International Nuclear Information System (INIS)

    Pereira, Paulo J; Moshchalkov, Victor V; Chibotaru, Liviu F

    2014-01-01

    The recently proposed approach for the solution of Ginzburg-Landau (GL) problem for 2D samples of arbitrary shape is, in this article, extended over 3D samples having the shape of (i) a prism with arbitrary base and (ii) a solid of revolution with arbitrary profile. Starting from the set of Laplace operator eigenfunctions of a 2D object, we construct an approximation to or the exact eigenfunctions of the Laplace operator of a 3D structure by applying an extrusion or revolution to these solutions. This set of functions is used as the basis to construct the solutions of the linearized GL equation. These solutions are then used as basis for the non-linear GL equation much like the famous LCAO method. To solve the non-linear equation, we used the Newton-Raphson method starting from the solution of the linear equation, i.e., the nucleation distribution of superconducting condensate. The vector potential approximations typically used in 2D cases, i.e., considering it as corresponding to applied constant field, are in the 3D case harder to justify. For that reason, we use a locally corrected Nystrom method to solve the second Ginzburg-Landau equation. The complete solution of GL problem is then achieved by solving self-consistently both equations

  8. The lie-algebraic structures and integrability of differential and differential-difference nonlinear dynamical systems

    International Nuclear Information System (INIS)

    Prykarpatsky, A.K.; Blackmore, D.L.; Bogolubov, N.N. Jr.

    2007-05-01

    The infinite-dimensional operator Lie algebras of the related integrable nonlocal differential-difference dynamical systems are treated as their hidden symmetries. As a result of their dimerization the Lax type representations for both local differential-difference equations and nonlocal ones are obtained. An alternative approach to the Lie-algebraic interpretation of the integrable local differential-difference systems is also proposed. The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the centrally extended Lie algebra of integro-differential operators with matrix-valued coefficients coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is obtained by means of a specially constructed Baecklund transformation. The Hamiltonian description for the corresponding set of additional symmetry hierarchies is represented. The relation of these hierarchies with Lax type integrable (3+1)-dimensional nonlinear dynamical systems and their triple Lax type linearizations is analyzed. The Lie-algebraic structures, related with centrally extended current operator Lie algebras are discussed with respect to constructing new nonlinear integrable dynamical systems on functional manifolds and super-manifolds. Special Poisson structures and related with them factorized integrable operator dynamical systems having interesting applications in modern mathematical physics, quantum computing mathematics and other fields are constructed. The previous purely computational results are explained within the approach developed. (author)

  9. Mathematical modeling of two phase stratified flow in a microchannel with curved interface

    Science.gov (United States)

    Dandekar, Rajat; Picardo, Jason R.; Pushpavanam, S.

    2017-11-01

    Stratified or layered two-phase flows are encountered in several applications of microchannels, such as solvent extraction. Assuming steady, unidirectional creeping flow, it is possible to solve the Stokes equations by the method of eigenfunctions, provided the interface is flat and meets the wall with a 90 degree contact angle. However, in reality the contact angle depends on the pair of liquids and the material of the channel, and differs significantly from 90 degrees in many practical cases. For unidirectional flow, this implies that the interface is a circular arc (of constant curvature). We solve this problem within the framework of eigenfunctions, using the procedure developed by Shankar. We consider two distinct cases: (a) the interface meets the wall with the equilibrium contact angle; (b) the interface is pinned by surface treatment of the walls, so that the flow rates determine the apparent contact angle. We show that the contact angle appreciably affects the velocity profile and the volume fractions of the liquids, while limiting the range of flow rates that can be sustained without the interface touching the top/bottom walls. Non-intuitively, we find that the pressure drop is reduced when the more viscous liquid wets the wall.

  10. Electronic states in a quantum lens

    International Nuclear Information System (INIS)

    Rodriguez, Arezky H.; Trallero-Giner, C.; Ulloa, S. E.; Marin-Antuna, J.

    2001-01-01

    We present a model to find analytically the electronic states in self-assembled quantum dots with a truncated spherical cap (''lens'') geometry. A conformal analytical image is designed to map the quantum dot boundary into a dot with semispherical shape. The Hamiltonian for a carrier confined in the quantum lens is correspondingly mapped into an equivalent operator and its eigenvalues and eigenfunctions for the corresponding Dirichlet problem are analyzed. A modified Rayleigh-Schro''dinger perturbation theory is presented to obtain analytical expressions for the energy levels and wave functions as a function of the spherical cap height b and radius a of the circular cross section. Calculations for a hard wall confinement potential are presented, and the effect of decreasing symmetry on the energy values and eigenfunctions of the lens-shape quantum dot is studied. As the degeneracies of a semicircular geometry are broken for b≠a, our perturbation approach allows tracking of the split states. Energy states and electronic wave functions with m=0 present the most pronounced influence on the reduction of the lens height. The method and expressions presented here can be straightforwardly extended to deal with more general Hamiltonians, including strains and valence-band coupling effects in Group III--V and Group II--VI self-assembled quantum dots

  11. A Laplace transform certified reduced basis method; application to the heat equation and wave equation

    OpenAIRE

    Knezevic, David; Patera, Anthony T.; Huynh, Dinh Bao Phuong

    2010-01-01

    We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary “modal” truncation; RB eigenfunction decomposition and contour integration for Offline–Online decomposition. We present numerical results to demonstrate the accura...

  12. Evolution of the pulsation properties of hot pre-white dwarf stars

    Energy Technology Data Exchange (ETDEWEB)

    Kawaler, S.D.; Winget, D.E.; Hansen, C.J.

    1985-08-01

    After solving the equations of linear, nonradial adiabatic oscillation for evolutionary pre-white dwarf (PWD) models, calculations are made for the periods, eigenfunctions, weight functions and rates of period change for high order dipole and quadrupole gravity mode oscillations in spherical nonrotating PWD models. The results obtained place stringent upper limits on the absolute magnitude of the rates of period change expected in stars represented by this class of models. 43 references.

  13. Normal and adjoint integral and integrodifferential neutron transport equations. Pt. 2

    International Nuclear Information System (INIS)

    Velarde, G.

    1976-01-01

    Using the simplifying hypotheses of the integrodifferential Boltzmann equations of neutron transport, given in JEN 334 report, several integral equations, and theirs adjoint ones, are obtained. Relations between the different normal and adjoint eigenfunctions are established and, in particular, proceeding from the integrodifferential Boltzmann equation it's found out the relation between the solutions of the adjoint equation of its integral one, and the solutions of the integral equation of its adjoint one (author)

  14. A novel algorithm for image representation using discrete spectrum of the Schrödinger operator

    KAUST Repository

    Kaisserli, Zineb; Laleg-Kirati, Taous-Meriem; Lahmar-Benbernou, Amina

    2015-01-01

    This paper extends the recent signal analysis method based on the spectral analysis of the semi-classical Schrödinger operator to two dimensions. An algorithm based on the tensor product approach when writing the eigenfunctions of the semi-classical Schrödinger operator is proposed. The algorithm is described and the effect of some parameters on the convergence of this method are numerically studied. The performance of the algorithm is illustrated through some examples.

  15. Third All-Union Symposium on Wave Diffraction.

    Science.gov (United States)

    1982-08-02

    the field takes the form of cylindrical wave where U=Cos 0 , aCosO , (5) * - angle between the direction to observation point and x axis, and 0. - angle...numerous regions in the cylindrical coordinate systems. In many instances instead of the labor -consuming integration of the squares of eigenfunctions for...Bola, Miklovich, etc. The calculation of contour integrals by integration for the coasts of shear/sections proved to be very labor -consuming, but for

  16. A high-order q-difference equation for q-Hahn multiple orthogonal polynomials

    DEFF Research Database (Denmark)

    Arvesú, J.; Esposito, Chiara

    2012-01-01

    A high-order linear q-difference equation with polynomial coefficients having q-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation coincides with the number of orthogonality conditions that these polynomials satisfy. Some limiting situations when are studie....... Indeed, the difference equation for Hahn multiple orthogonal polynomials given in Lee [J. Approx. Theory (2007), ), doi: 10.1016/j.jat.2007.06.002] is obtained as a limiting case....

  17. A novel algorithm for image representation using discrete spectrum of the Schrödinger operator

    KAUST Repository

    Kaisserli, Zineb

    2015-05-01

    This paper extends the recent signal analysis method based on the spectral analysis of the semi-classical Schrödinger operator to two dimensions. An algorithm based on the tensor product approach when writing the eigenfunctions of the semi-classical Schrödinger operator is proposed. The algorithm is described and the effect of some parameters on the convergence of this method are numerically studied. The performance of the algorithm is illustrated through some examples.

  18. Scaling properties of localized quantum chaos

    International Nuclear Information System (INIS)

    Izrailev, F.M.

    1991-01-01

    Statistical properties of spectra and eigenfunctions are studied for the model of quantum chaos in the presence of dynamical localization. The main attention is paid to the scaling properties of localization length and level spacing distribution in the intermediate region between Poissonian and Wigner-Dyson statistics. It is shown that main features of such localized quantum chaos are well described by the introduced ensemble of band random matrices. 28 refs.; 7 figs

  19. The technique of the modified hamiltonian for construction of the spin-projected wave function

    International Nuclear Information System (INIS)

    Tsaune, A.Ya.; Glushkov, V.N.

    1991-01-01

    A method is suggested to construct the wave function, which is an eigenfunction for operator S 2 . A combination of Lowdin's projection operators and the method of taking into account the orthogonality conditions in variational problems previously developed by the authors is used for determination of the spin-current wave functions component. It is shown that the suggested method gives better results for the energies that the traditional restricted Hartee-Fock scheme

  20. DNS and the theory of receptivity of a supersonic boundary layer to free-stream disturbances

    International Nuclear Information System (INIS)

    Soudakov, Vitaly; Fedorov, Alexander; Ryzhov, Alexander

    2011-01-01

    Direct numerical simulation (DNS) of receptivity of a boundary layer over flat plate is carried out. The free stream Mach number is equal to 6. The following two-dimensional disturbances are introduced into the free-stream flow: fast and slow acoustic waves, temperature spottiness. A theoretical model describing the excitation of unstable waves in the boundary layer is developed using the biorthogonal eigenfunction decomposition method. The DNS results agree with the theoretical predictions.

  1. Reply to Comment on 'Excited states in the infinite quantum lens potential: conformal mapping and moment quantization methods'

    International Nuclear Information System (INIS)

    RodrIguez, Arezky H; Handy, Carlos R; Trallero-Giner, C

    2004-01-01

    The suitability of conformal transformation (CT) analysis, and the eigenvalue moment method (EMM), for determining the eigenenergies and eigenfunctions of a quantum particle confined within a lens geometry, is reviewed and compared to the recent results by Even and Loualiche (2003 J. Phys.: Condens. Matter 15 8465). It is shown that CT and EMM define two accurate and versatile analytical/computational methods relevant to lens shaped regions of varying geometrical aspect ratios. (reply)

  2. Transport properties of a piecewise linear transformation and deterministic Levy flights

    International Nuclear Information System (INIS)

    Miyaguchi, Tomoshige

    2006-01-01

    The transport properties of a 1-dimensional piecewise linear dynamical system are investigated through the spectrum of its Frobenius-Perron operator. For a class of initial densities, eigenvalues and eigenfunctions of the Frobenius-Perron operator are obtained explicitly. It is also found that in the long length wave limit, this system exhibits normal diffusion and super diffusion called Levy flight. The diffusion constant and stable index are derived from the eigenvalues. (author)

  3. Jack superpolynomials: physical and combinatorial definitions

    International Nuclear Information System (INIS)

    Desrosiers, P.; Mathieu, P.; Lapointe, L.

    2004-01-01

    Jack superpolynomials are eigenfunctions of the supersymmetric extension of the quantum trigonometric Calogero-Moser-Sutherland Hamiltonian. They are orthogonal with respect to the scalar product, dubbed physical, that is naturally induced by this quantum-mechanical problem. But Jack superpolynomials can also be defined more combinatorially, starting from the multiplicative bases of symmetric superpolynomials, enforcing orthogonality with respect to a one-parameter deformation of the combinatorial scalar product. Both constructions turn out to be equivalent. (author)

  4. Current relaxation time scales in toroidal plasmas

    International Nuclear Information System (INIS)

    Mikkelsen, D.R.

    1987-02-01

    An approximate normal mode analysis of plasma current diffusion in tokamaks is presented. The work is based on numerical solutions of the current diffusion equation in cylindrical geometry. Eigenvalues and eigenfunctions are shown for a broad range of plasma conductivity profile shapes. Three classes of solutions are considered which correspond to three types of tokamak operation. Convenient approximations to the three lowest eigenvalues in each class are presented and simple formulae for the current relaxation time scales are given

  5. Relativistic configuration-interaction calculation of the correlation energies of heliumlike ions. Revision 1

    International Nuclear Information System (INIS)

    Cheng, K.T.; Chen, M.H.; Johnson, W.R.

    1994-04-01

    A new relativistic configuration-interaction (CI) method using B-spline basis functions has been developed to study the correlation energies of two-electron heliumlike ions. Based on the relativistic no-pair Hamiltonian, the CI equation leads to a symmetric eigenvalue problem involving large, dense matrices. Davidson's method is used to obtain the lowest few eigenenergies and eigenfunctions. Results on transition energies and finite structure splittings for heliumlike ions are in very good agreement with experiment throughout the periodic table

  6. Hydrogen atom and the H+2 and HeH++ molecular ions inside prolate spheroidal boxes

    International Nuclear Information System (INIS)

    Ley-Koo, E.; Cruz, S.A.

    1981-01-01

    We formulate the exact solution of the Schroedinger equation for systems of one electron in the Coulomb field of one or two fixed nuclei at the foci inside prolate spheroidal boxes. Numerical results are obtained for the energy eigenvalues and eigenfunctions of the lowest states of the hydrogen atom and the H + 2 and HeH ++ molecular ions for boxes of different sizes and eccentricities. We also evaluate the hyperfine splitting of atomic hydrogen and of H + 2

  7. On some Hermite series identities and their applications to Gabor analysis

    DEFF Research Database (Denmark)

    Lemvig, Jakob

    2016-01-01

    We prove some infinite series identities for the Hermite functions. From these identities we disprove the Gabor frame set conjecture for Hermite functions of order (Formula presented.) and (Formula presented.) for (Formula presented.). The results hold not only for Hermite functions, but for two ...... large classes of eigenfunctions of the Fourier transform associated with the eigenvalues (Formula presented.) and i, and the results indicate that the Gabor frame set of all such functions must have a rather complicated structure....

  8. Spectral Analysis and Dirichlet Forms on Barlow-Evans Fractals

    OpenAIRE

    Steinhurst, Benjamin; Teplyaev, Alexander

    2012-01-01

    We show that if a Barlow-Evans Markov process on a vermiculated space is symmetric, then one can study the spectral properties of the corresponding Laplacian using projective limits. For some examples, such as the Laakso spaces and a Spierpinski P\\^ate \\`a Choux, one can develop a complete spectral theory, including the eigenfunction expansions that are analogous to Fourier series. Also, one can construct connected fractal spaces isospectral to the fractal strings of Lapidus and van Frankenhu...

  9. Maximization of energy in the output of a linear system

    International Nuclear Information System (INIS)

    Dudley, D.G.

    1976-01-01

    A time-limited signal which, when passed through a linear system, maximizes the total output energy is considered. Previous work has shown that the solution is given by the eigenfunction associated with the maximum eigenvalue in a Hilbert-Schmidt integral equation. Analytical results are available for the case where the transfer function is a low-pass filter. This work is extended by obtaining a numerical solution to the integral equation which allows results for reasonably general transfer functions

  10. Matrix elements of u and p for the modified Poeschl-Teller potential

    International Nuclear Information System (INIS)

    Gomez-Camacho, J; Lemus, R; Arias, J M

    2004-01-01

    Closed analytical expressions in terms of a single sum are obtained for the matrix elements of the momentum and the natural variable u tanh(αx) in the basis of the modified Poeschl-Teller (MPT) bound eigenstates. These matrix elements are first expressed in terms of Franck-Condon factors, which thereafter are substituted for analytic expressions. Expansions of the variables p and u in terms of creation and annihilation operators associated with the MPT bound eigenfunctions are also presented

  11. Two-dimensional simulation of the MHD stability, (2)

    International Nuclear Information System (INIS)

    Kurita, Gen-ichi; Amano, Tsuneo.

    1977-09-01

    Growth rate and eigen-function of the MHD instability of a toroidal plasma were calculated numerically as an initial-boundary value problem. When a conducting shell is away from the plasma, toroidicity hardly influences growth rate of the external kink modes in a slender tokamak, but it stabilizes the modes in a fat tokamak. On the other hand, when the shell is near to the plasma, the unstable external modes are stabilized by both toroidicity and shell effect. (auth.)

  12. Inverse participation ratio and localization in topological insulator phase transitions

    International Nuclear Information System (INIS)

    Calixto, M; Romera, E

    2015-01-01

    Fluctuations of Hamiltonian eigenfunctions, measured by the inverse participation ratio (IPR), turn out to characterize topological-band insulator transitions occurring in 2D Dirac materials like silicene, which is isostructural with graphene but with a strong spin–orbit interaction. Using monotonic properties of the IPR, as a function of a perpendicular electric field (which provides a tunable band gap), we define topological-like quantum numbers that take different values in the topological-insulator and band-insulator phases. (paper)

  13. In-medium covariant propagator of baryons under a strong magnetic field: Effect of the intrinsic magnetic moments

    Energy Technology Data Exchange (ETDEWEB)

    Aguirre, R.M.; Paoli, A.L. de [Universidad Nacional de La Plata, and IFLP, Departamento de Fisica, Facultad de Ciencias Exactas, La Plata (Argentina)

    2016-11-15

    We obtain the covariant propagator at finite temperature for interacting baryons immersed in a strong magnetic field. The effect of the intrinsic magnetic moments on the Green function are fully taken into account. We make an expansion in terms of eigenfunctions of a Dirac field, which leads us to a compact form of its propagator. We present some simple applications of these propagators, where the statistical averages of nuclear currents and energy density are evaluated. (orig.)

  14. Numerical methods for studying anharmonic oscillator approximations to the phi super 4 sub 2 quantum field theory

    Science.gov (United States)

    Isaacson, D.; Marchesin, D.; Paes-Leme, P. J.

    1980-01-01

    This paper is an expanded version of a talk given at the 1979 T.I.C.O.M. conference. It is a self-contained introduction, for applied mathematicians and numerical analysts, to quantum mechanics and quantum field theory. It also contains a brief description of the authors' numerical approach to the problems of quantum field theory, which may best be summarized by the question; Can we compute the eigenvalues and eigenfunctions of Schrodinger operators in infinitely many variables.

  15. On choice of trial functions in integro-differential variational principles of transport theory

    International Nuclear Information System (INIS)

    Loyalka, S.K.; Cipolla, J.W. Jr.

    1988-01-01

    In several problems of particle transport, quantities of macroscopic interest can be related to stationary values of variational functionals based on general integro-differential equations and boundary conditions. Within the context of the jump (Milne's) problem, it is shown how highly accurate results can be obtained by using trial functions based on the eigenfunctions of the relevant integrodifferential equations. Such choices of trial functions should apply equally effectively to problems in curved geometries, both internal and external

  16. Time rescaling and Gaussian properties of the fractional Brownian motions

    International Nuclear Information System (INIS)

    Maccone, C.

    1981-01-01

    The fractional Brownian motions are proved to be a class of Gaussian (normal) stochastic processes suitably rescaled in time. Some consequences affecting their eigenfunction expansion (Karhunen-Loeve expansion) are inferred. A known formula of Cameron and Martin is generalized. The first-passage time probability density is found. The partial differential equation of the fractional Brownian diffusion is obtained. And finally the increments of the fractional Brownian motions are proved to be independent for nonoverlapping time intervals. (author)

  17. Calculations of wavefunctions and energies of electron system in Coulomb potential by variational method without a basis set

    International Nuclear Information System (INIS)

    Bykov, V.P.; Gerasimov, A.V.

    1992-08-01

    A new variational method without a basis set for calculation of the eigenvalues and eigenfunctions of Hamiltonians is suggested. The expansion of this method for the Coulomb potentials is given. Calculation of the energy and charge distribution in the two-electron system for different values of the nuclear charge Z is made. It is shown that at small Z the Coulomb forces disintegrate the electron cloud into two clots. (author). 3 refs, 4 figs, 1 tab

  18. Quantum Stephani exact cosmological solutions and the selection of time variable

    International Nuclear Information System (INIS)

    Pedram, P; Jalalzadeh, S; Gousheh, S S

    2007-01-01

    We study a perfect fluid Stephani quantum cosmological model. In the present work, the Schutz's variational formalism which recovers the notion of time is applied. This gives rise to a Wheeler-DeWitt equation for the scale factor. We use the eigenfunctions in order to construct wave packets for each case. We study the time-dependent behavior of the expectation value of the scale factor, using many-worlds and de Broglie-Bohm interpretations of quantum mechanics

  19. Transferring strong boundedness among Laguerre orthogonal ...

    Indian Academy of Sciences (India)

    the multiplier operator associated with the sequence mk = k. √( k + α+1. 2. )( ... Theorem 2.9 (Multiplier theorem). Let −1 < α, 1 < p < ∞ and .... −αLα k (y2), where Lα k. (y) are the functions defined in (1.2). The functions ψα k are eigenfunctions for the operator Lα = −1. 4. { d2 dy2 +. (2α+1 y. ) d dy − y2}. , in effect. Lα(ψα k ) =.

  20. Integrability in the theory of Schroedinger operator and harmonic analysis

    International Nuclear Information System (INIS)

    Chalykh, O.A.; Veselov, A.P.

    1993-01-01

    The algebraic integrability for the Schroedinger equation in R n and the role of the quantum Calogero-Sutherland problem and root systems in this context are discussed. For the special values of the parameters in the potential the explicit formula for the eigenfunction of the corresponding Sutherland operator is found. As an application the explicit formula for the zonal spherical functions on the symmetric spaces SU 2 * n /Sp n (type A II in Cartan notations) is presented. (orig.)

  1. Initial-boundary value problems for multi-term time-fractional diffusion equations with x-dependent coefficients

    OpenAIRE

    Li, Zhiyuan; Huang, Xinchi; Yamamoto, Masahiro

    2018-01-01

    In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffler functions and the eigenfunction expansion, we reduce the IBVP to an equivalent integral equation to show the unique existence and the analyticity of the solution for the equation. Especially, in the case where all the coefficients of the time-fractional derivatives are non-negative, by the Laplace and inversion L...

  2. Eigenvalue-eigenfunction problem for Steklov's smoothing operator and differential-difference equations of mixed type

    Directory of Open Access Journals (Sweden)

    Serguei I. Iakovlev

    2013-01-01

    Full Text Available It is shown that any \\(\\mu \\in \\mathbb{C}\\ is an infinite multiplicity eigenvalue of the Steklov smoothing operator \\(S_h\\ acting on the space \\(L^1_{loc}(\\mathbb{R}\\. For \\(\\mu \

  3. Microscopic theory of nuclear collective dynamics

    International Nuclear Information System (INIS)

    Sakata, Fumihiko; Marumori, Toshio; Hashimoto, Yukio; Tsukuma, Hidehiko; Yamamoto, Yoshifumi; Iwasawa, Kazuo.

    1990-10-01

    A recent development of the INS-TSUKUBA joint research project on large-amplitude collective motion is summarized by putting special emphasis on an inter-relationship between quantum chaos and nuclear spectroscopy. Aiming at introducing various concepts used in this lecture, we start with recapitulating the semi-classical theory of nuclear collective dynamics formulated within the time-dependent Hartree-Fock (TDHF) theory. The central part of the semi-classical theory is provided by the self-consistent collective coordinate (SCC) method which has been developed to properly take account of the non-linear dynamics specific for the finite many-body quantum system. A decisive role of the level crossing dynamics on the order-to-chaos transition of collective motion is discussed in detail. Extending the basic idea of the semi-classical theory, we discuss a full quantum theory of nuclear collective dynamics which allows us to properly define a concept of the quantum integrability as well as the quantum chaoticity for each eigenfunction. The lecture is arranged so as to clearly show the similar structure between the semi-classical and quantum theories of nuclear collective dynamics. Using numerical calculations, we illustrate what the quantum chaos for each eigenfunction means and relate it to the usual definition of quantum chaos for nearest neighbor level spacing statistics based on the random matrix theory. (author)

  4. Landau quantized dynamics and spectra for group-VI dichalcogenides, including a model quantum wire

    Science.gov (United States)

    Horing, Norman J. M.

    2017-06-01

    This work is concerned with the derivation of the Green's function for Landau-quantized carriers in the Group-VI dichalcogenides. In the spatially homogeneous case, the Green's function is separated into a Peierls phase factor and a translationally invariant part which is determined in a closed form integral representation involving only elementary functions. The latter is expanded in an eigenfunction series of Laguerre polynomials. These results for the retarded Green's function are presented in both position and momentum representations, and yet another closed form representation is derived in circular coordinates in terms of the Bessel wave function of the second kind (not to be confused with the Bessel function). The case of a quantum wire is also addressed, representing the quantum wire in terms of a model one-dimensional δ (x ) -potential profile. This retarded Green's function for propagation directly along the wire is determined exactly in terms of the corresponding Green's function for the system without the δ (x ) -potential, and the Landau quantized eigenenergy dispersion relation is examined. The thermodynamic Green's function for the dichalcogenide carriers in a normal magnetic field is formulated here in terms of its spectral weight, and its solution is presented in a momentum/integral representation involving only elementary functions, which is subsequently expanded in Laguerre eigenfunctions and presented in both momentum and position representations.

  5. Landau quantized dynamics and spectra for group-VI dichalcogenides, including a model quantum wire

    Directory of Open Access Journals (Sweden)

    Norman J. M. Horing

    2017-06-01

    Full Text Available This work is concerned with the derivation of the Green’s function for Landau-quantized carriers in the Group-VI dichalcogenides. In the spatially homogeneous case, the Green’s function is separated into a Peierls phase factor and a translationally invariant part which is determined in a closed form integral representation involving only elementary functions. The latter is expanded in an eigenfunction series of Laguerre polynomials. These results for the retarded Green’s function are presented in both position and momentum representations, and yet another closed form representation is derived in circular coordinates in terms of the Bessel wave function of the second kind (not to be confused with the Bessel function. The case of a quantum wire is also addressed, representing the quantum wire in terms of a model one-dimensional δ(x-potential profile. This retarded Green’s function for propagation directly along the wire is determined exactly in terms of the corresponding Green’s function for the system without the δ(x-potential, and the Landau quantized eigenenergy dispersion relation is examined. The thermodynamic Green’s function for the dichalcogenide carriers in a normal magnetic field is formulated here in terms of its spectral weight, and its solution is presented in a momentum/integral representation involving only elementary functions, which is subsequently expanded in Laguerre eigenfunctions and presented in both momentum and position representations.

  6. Wave excited motion of a body floating on water confined between two semi-infinite ice sheets

    Science.gov (United States)

    Ren, K.; Wu, G. X.; Thomas, G. A.

    2016-12-01

    The wave excited motion of a body floating on water confined between two semi-infinite ice sheets is investigated. The ice sheet is treated as an elastic thin plate and water is treated as an ideal and incompressible fluid. The linearized velocity potential theory is adopted in the frequency domain and problems are solved by the method of matched eigenfunctions expansion. The fluid domain is divided into sub-regions and in each sub-region the velocity potential is expanded into a series of eigenfunctions satisfying the governing equation and the boundary conditions on horizontal planes including the free surface and ice sheets. Matching is conducted at the interfaces of two neighbouring regions to ensure the continuity of the pressure and velocity, and the unknown coefficients in the expressions are obtained as a result. The behaviour of the added mass and damping coefficients of the floating body with the effect of the ice sheets and the excitation force are analysed. They are found to vary oscillatorily with the wave number, which is different from that for a floating body in the open sea. The motion of the body confined between ice sheets is investigated, in particular its resonant behaviour with extremely large motion found to be possible under certain conditions. Standing waves within the polynya are also observed.

  7. Generalized hybrid Monte Carlo - CMFD methods for fission source convergence

    International Nuclear Information System (INIS)

    Wolters, Emily R.; Larsen, Edward W.; Martin, William R.

    2011-01-01

    In this paper, we generalize the recently published 'CMFD-Accelerated Monte Carlo' method and present two new methods that reduce the statistical error in CMFD-Accelerated Monte Carlo. The CMFD-Accelerated Monte Carlo method uses Monte Carlo to estimate nonlinear functionals used in low-order CMFD equations for the eigenfunction and eigenvalue. The Monte Carlo fission source is then modified to match the resulting CMFD fission source in a 'feedback' procedure. The two proposed methods differ from CMFD-Accelerated Monte Carlo in the definition of the required nonlinear functionals, but they have identical CMFD equations. The proposed methods are compared with CMFD-Accelerated Monte Carlo on a high dominance ratio test problem. All hybrid methods converge the Monte Carlo fission source almost immediately, leading to a large reduction in the number of inactive cycles required. The proposed methods stabilize the fission source more efficiently than CMFD-Accelerated Monte Carlo, leading to a reduction in the number of active cycles required. Finally, as in CMFD-Accelerated Monte Carlo, the apparent variance of the eigenfunction is approximately equal to the real variance, so the real error is well-estimated from a single calculation. This is an advantage over standard Monte Carlo, in which the real error can be underestimated due to inter-cycle correlation. (author)

  8. Warm-fluid description of intense beam equilibrium and electrostatic stability properties

    International Nuclear Information System (INIS)

    Lund, S.M.; Davidson, R.C.

    1998-01-01

    A nonrelativistic warm-fluid model is employed in the electrostatic approximation to investigate the equilibrium and stability properties of an unbunched, continuously focused intense ion beam. A closed macroscopic model is obtained by truncating the hierarchy of moment equations by the assumption of negligible heat flow. Equations describing self-consistent fluid equilibria are derived and elucidated with examples corresponding to thermal equilibrium, the Kapchinskij endash Vladimirskij (KV) equilibrium, and the waterbag equilibrium. Linearized fluid equations are derived that describe the evolution of small-amplitude perturbations about an arbitrary equilibrium. Electrostatic stability properties are analyzed in detail for a cold beam with step-function density profile, and then for axisymmetric flute perturbations with ∂/∂θ=0 and ∂/∂z=0 about a warm-fluid KV beam equilibrium. The radial eigenfunction describing axisymmetric flute perturbations about the KV equilibrium is found to be identical to the eigenfunction derived in a full kinetic treatment. However, in contrast to the kinetic treatment, the warm-fluid model predicts stable oscillations. None of the instabilities that are present in a kinetic description are obtained in the fluid model. A careful comparison of the mode oscillation frequencies associated with the fluid and kinetic models is made in order to delineate which stability features of a KV beam are model-dependent and which may have general applicability. copyright 1998 American Institute of Physics

  9. Modes in a nonneutral plasma column of finite length

    International Nuclear Information System (INIS)

    Rasband, S. Neil; Spencer, Ross L.

    2002-01-01

    A Galerkin, finite-element, nonuniform mesh computation of the mode equation for waves in a non-neutral plasma of finite length in a Cold-Fluid model gives an accurate calculation of the mode eigenfrequencies and eigenfunctions. We report on studies of the following: (1) finite-length Trivelpiece-Gould modes with flat-top and realistic density profiles, (2) finite-length diocotron modes with flat density profiles. We compare with the frequency equation of Fine and Driscoll [Phys Plasmas 5, 601 (1998)

  10. Linear mode conversion in a toroidal plasma

    International Nuclear Information System (INIS)

    Hellsten, T.

    1980-05-01

    Linear mode conversion at the perpendicular ion cyclotron resonance has been treated for an axially symmetric toroidal plasma. The mode conversion appears between a fast electromagnetic wave and a slow-quasi electrostatic wave, due to finite electron inertia. The problem reduces to the Orr-Sommerfeld equation where the coefficients determining the reflectron, transmission and conversion are functions of the arc length along a poloidal intersection of the resonance surface. These coefficients can be determined from eigenfunctions of an ordinary differential equation. (author)

  11. On field line resonances of hydromagnetic Alfven waves in dipole magnetic field

    International Nuclear Information System (INIS)

    Chen, Liu; Cowley, S.C.

    1989-07-01

    Using the dipole magnetic field model, we have developed the theory of field line resonances of hydromagnetic Alfven waves in general magnetic field geometries. In this model, the Alfven speed thus varies both perpendicular and parallel to the magnetic field. Specifically, it is found that field line resonances do persist in the dipole model. The corresponding singular solutions near the resonant field lines as well as the natural definition of standing shear Alfven eigenfunctions have also been systematically derived. 11 refs

  12. Ray and wave optics of integrable and stochastic systems

    International Nuclear Information System (INIS)

    McDonald, S.W.; Kaufman, A.N.

    1979-07-01

    The generalization of WKB methods to more than one dimension is discussed in terms of the integrability or non-integrability of the geometrical optics (ray Hamiltonian) system derived in the short-wave approximation. In the two-dimensional case the ray trajectories are either regular or stochastic, and the qualitative differences between these types of motion are manifested in the characteristics of the spectra and eigenfunctions. These are examined for a model system which may be integrable or stochastic, depending on a single parameter

  13. Some problems in steady-state thermal conductivity with variable heat transfer rate

    International Nuclear Information System (INIS)

    Malov, Yu.I.; Martinson, L.K.; Pavlov, K.B.

    1975-01-01

    Some boundary-value problems of steady heat conductivity with an alternating heat exchange coefficient have been solved for a cylindrical region. The solutions have been performed as expansion in series with respect to eigenfunctions with the coefficients consistent with infinite systems of linear algebraic equations. A reduction method has been substantiated for those systems. The paper presents results of calculation of the temperature distribution inside the infinite cylinder with concrete tasks of heat exchange coefficient variations on the cylinder surface

  14. Preliminary analysis of resonance effect by Helmholtz-Schrödinger method

    International Nuclear Information System (INIS)

    Er-Yan, Yan; Fan-Bao, Meng; Hong-Ge, Ma; Chao-Yang, Chen

    2010-01-01

    The Helmholtz-Schrödinger method is employed to study the electric field standing wave caused by coupling through a simple slot. There is a good agreement between the numerical results and the resonant conditions presented by the Helmholtz—Schrödinger method. Thus, it can be used in similar cases where the amplitude of the electric field is the important quantity or eigenfunctions of the Schrödinger equation are needed for complicated quantum structures with hard wall boundary conditions. (general)

  15. Unstable drift eigenmode in slab geometry

    International Nuclear Information System (INIS)

    Tsotsonis, S.; Hirose, A.

    1986-01-01

    The unstable Pearlstein-Berk mode of drift waves in plane, sheared slab geometry has later been shown to be stable when electron Landau resonance is rigorously treated. Based on the variational method previously developed the authors have found that in addition to the absolutely stable Pearlstein-Berk mode, there exists an absolutely unstable eigenfunction characterized by ω ≤ ω/sub chemical bonde/, and weak ''radial'' dependence. Also, the growth rate, only weakly depends on the magnetic shear and ion/electron temperature ratio

  16. Spectral theory of Sturm-Liouville differential operators: proceedings of the 1984 workshop

    Energy Technology Data Exchange (ETDEWEB)

    Kaper, H.G.; Zettl, A. (eds.)

    1984-12-01

    This report contains the proceedings of the workshop which was held at Argonne during the period May 14 through June 15, 1984. The report contains 22 articles, authored or co-authored by the participants in the workshop. Topics covered at the workshop included the asymptotics of eigenvalues and eigenfunctions; qualitative and quantitative aspects of Sturm-Liouville eigenvalue problems with discrete and continuous spectra; polar, indefinite, and nonselfadjoint Sturm-Liouville eigenvalue problems; and systems of differential equations of Sturm-Liouville type.

  17. On Perturbative Cubic Nonlinear Schrodinger Equations under Complex Nonhomogeneities and Complex Initial Conditions

    Directory of Open Access Journals (Sweden)

    Magdy A. El-Tawil

    2009-01-01

    Full Text Available A perturbing nonlinear Schrodinger equation is studied under general complex nonhomogeneities and complex initial conditions for zero boundary conditions. The perturbation method together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the symbolic solution algorithm is tested through computing the possible approximations under truncation procedures. The method of solution is illustrated through case studies and figures.

  18. Saddle point avoidance in barrier crossing problems

    Energy Technology Data Exchange (ETDEWEB)

    Talkner, P.; Drozdov, A.N. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)

    1997-06-01

    The long-time behavior of the stochastic dynamics of a two-dimensional system having two metastable states is investigated by means of the low-lying part of the corresponding two-dimensional Smoluchowski operator. In particular, its dependence on three parameters describing the strength of the noise, the coupling of the degrees of freedom and a ratio of relaxation-times is considered. Further information characterizing the transition process between the metastable states is gained from the corresponding eigenfunctions. (author) 9 refs.

  19. Applications of Green's functions in science and engineering

    CERN Document Server

    Greenberg, Michael D

    2015-01-01

    Concise and highly regarded, this treatment of Green's functions and their applications in science and engineering is geared toward undergraduate and graduate students with only a moderate background in ordinary differential equations and partial differential equations. The text also includes a wealth of information of a more general nature on boundary value problems, generalized functions, eigenfunction expansions, partial differential equations, and acoustics. The two-part treatment begins with an overview of applications to ordinary differential equations. Topics include the adjoint operato

  20. Dynamical invariants for variable quadratic Hamiltonians

    International Nuclear Information System (INIS)

    Suslov, Sergei K

    2010-01-01

    We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.

  1. Harmonic Analysis and Group Representation

    CERN Document Server

    Figa-Talamanca, Alessandro

    2011-01-01

    This title includes: Lectures - A. Auslander, R. Tolimeri - Nilpotent groups and abelian varieties, M Cowling - Unitary and uniformly bounded representations of some simple Lie groups, M. Duflo - Construction de representations unitaires d'un groupe de Lie, R. Howe - On a notion of rank for unitary representations of the classical groups, V.S. Varadarajan - Eigenfunction expansions of semisimple Lie groups, and R. Zimmer - Ergodic theory, group representations and rigidity; and, Seminars - A. Koranyi - Some applications of Gelfand pairs in classical analysis.

  2. Quantum mechanics in Grassmann space

    International Nuclear Information System (INIS)

    Mankoc Borstnik, N.

    1991-10-01

    The representations of the infinitesimal operators of Lorentz rotations and translation and the corresponding carriers for a scalar, spinor and vector case in the Grassmann space as well as the eigenfunctions of the Hamilton function for a free particle, are presented. Functions are orthogonalized. The mass appears after compactification from 5 to 4 dimensions in the ordinary space-time, while in the Grassmann space the particle lives in five dimensions, so that a boost can be performed. (author). 5 refs

  3. Hartree-Fock calculations for strongly deformed and highly excited nuclei using the Skyrme force

    International Nuclear Information System (INIS)

    Zint, P.G.

    1975-01-01

    It has been shown that in CHF-calculations the Skyrme-force is usefull to describe strongly deformed nuclei with even proton and neutron number till separation. Thereby the eigenfunctions of the two-centre Hamiltonian form an adequate basis. With this procedure, we obtain the correct deformation of the 32 S-system. Induding the spurious energy of relative motion between the 16 O-fragments, the energy curve is a good approximation for the real potential, extracted form scattering experiments. (orig./WL) [de

  4. Dynamics and symmetries of a field partitioned by an accelerated frame

    OpenAIRE

    Gerlach, Ulrich H.

    1999-01-01

    The canonical evolution and symmetry generators are exhibited for a Klein-Gordon (K-G) system which has been partitioned by an accelerated coordinate frame into a pair of subsystems. This partitioning of the K-G system is conveyed to the canonical generators by the eigenfunction property of the Minkowski Bessel (M-B) modes. In terms of the M-B degrees of freedom, which are unitarily related to those of the Minkowski plane waves, a near complete diagonalization of these generators can be reali...

  5. An inverse Sturm–Liouville problem with a fractional derivative

    KAUST Repository

    Jin, Bangti

    2012-05-01

    In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical reconstructions of the potential with a Newton method from finite spectral data are presented. Surprisingly, it allows very satisfactory reconstructions for both smooth and discontinuous potentials, provided that the order . α∈. (1,. 2) of fractional derivative is sufficiently away from 2. © 2012 Elsevier Inc.

  6. On the Discrete Spectrum of the Nonstationary Schrödinger Equation and Multipole Lumps of the Kadomtsev-Petviashvili I Equation

    Science.gov (United States)

    Villarroel, Javier; Ablowitz, Mark J.

    The discrete spectrum of the nonstationary Schrödinger equation and localized solutions of the Kadomtsev-Petviashvili-I (KPI) equation are studied via the inverse scattering transform. It is shown that there exist infinitely many real and rationally decaying potentials which correspond to a discrete spectrum whose related eigenfunctions have multiple poles in the spectral parameter. An index or winding number is asssociated with each of these solutions. The resulting localized solutions of KPI behave as collection of individual humps with nonuniform dynamics.

  7. Discrete spectrum of the two-center problem of p bar He+ atomcule

    International Nuclear Information System (INIS)

    Pavlov, D.V.; Puzynin, I.V.; Vinitskij, S.I.

    1999-01-01

    A discrete spectrum of the two-center Coulomb problem of p bar He + system is studied. For solving this problem the finite-difference scheme of the 4th-order and the continuous analog of Newton's method are applied. The algorithm for calculation of eigenvalues and eigenfunctions with optimization of the parameter of the fractional-rational transformation of the quasiradial variable to a finite interval is developed. The specific behaviour of the solutions in a vicinity of the united and separated atoms is discussed

  8. Covariance operator of functional measure in P(φ)2-quantum field theory

    International Nuclear Information System (INIS)

    Lobanov, Yu.Yu.; Zhidkov, E.P.

    1988-01-01

    Functional integration measure in the Euclidean quantum field theory with polynomial interactions of boson fields with zero spin in two-dimensional space-time is investigated. The representation for the kernal of the measure covariance operator is obtained in the form of expansion over the eigenfunctions of some boundary problem for the heat equation. Two cases of the integration domains with different configurations are considered. Some trends and perspectives of employing the functional integration method in quantum field theory are also discussed. 43 refs

  9. Wigner functions of s waves

    International Nuclear Information System (INIS)

    Dahl, J. P.; Varro, S.; Wolf, A.; Schleich, W. P.

    2007-01-01

    We derive explicit expressions for the Wigner function of wave functions in D dimensions which depend on the hyperradius--that is, of s waves. They are based either on the position or the momentum representation of the s wave. The corresponding Wigner function depends on three variables: the absolute value of the D-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary s wave and the energy eigenfunction of a free particle

  10. Alternating multivariate trigonometric functions and corresponding Fourier transforms

    International Nuclear Information System (INIS)

    Klimyk, A U; Patera, J

    2008-01-01

    We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group A n , which is a subgroup of the permutation (symmetric) group S n . These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel

  11. Two New Multi-component BKP Hierarchies

    International Nuclear Information System (INIS)

    Wu Hongxia; Liu Xiaojun; Zeng Yunbo

    2009-01-01

    We firstly propose two kinds of new multi-component BKP (mcBKP) hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources whose Lax representations are presented. The two mcBKP hierarchies both admit reductions to the k-constrained BKP hierarchy and to integrable (1+1)-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of bi-directional SK equations with self-consistent sources.

  12. Physical properties of scalar and spinor field states with the Rindler-Milne (hyperbolic) symmetry

    International Nuclear Information System (INIS)

    Ritus, V.I.

    2001-01-01

    It is shown that right and left combinations of the positive- and negative-frequency hyperbolically symmetric solutions of the Klein-Fock-Gordon equation possess an everywhere timelike current density vector with a definite Lorentz-invariant sing of the charge density, and similar combinations of solutions to the Dirac equation possess the energy-momentum tensor with everywhere real eigenvalues and a definite Lorentz-invariant sing of the energy density. These right and left modes, just as their ±-frequency components, are eigenfunctions of the Lorentz generator [ru

  13. Vertical propagation of baroclinic Kelvin waves along the west coast of India

    Digital Repository Service at National Institute of Oceanography (India)

    Nethery, D; Shankar, D

    ; monsoon current; equatorial oceanography; remote forcing; modelling; monsoons; oceanography. J. Earth Syst. Sci. 116, No. 4, August 2007, pp. 331?339 ? Printed in India. 331 332 D Nethery and D Shankar Figure 1. The stability or buoyancy frequency squared... and rho represents (dimen- sionless) density anomaly. The vertical modes psin are the eigenfunctions of the equation parenleftbigg (psi n)z N2b parenrightbigg z = - 1c2 n psin, (3) subject to the boundary conditions (psin)z =0 at z = -D and z = 0, where...

  14. Spectrum of resistive MHD modes in cylindrical plasmas

    International Nuclear Information System (INIS)

    Ryu, C.M.; Grimm, R.C.

    1983-07-01

    A numerical study of the normal modes of a compressible resistive MHD fluid in cylindrical geometry is presented. Resistivity resolves the shear Alfven and slow magnetosonic continua of ideal MHD into discrete spectra and gives rise to heavily damped modes whose frequencies lie on specific lines in the complex plane. Fast magnetosonic waves are less affected but are also damped. Overstable modes arise from the shear Alfven spectrum. The stabilizing effect of favorable average curvature is shown. Eigenfunctions illustrating the nature of typical normal modes are displayed

  15. Optimally localized Wannier functions for quasi one-dimensional nonperiodic insulators

    DEFF Research Database (Denmark)

    Cornean, Horia; Nenciu, A.; Nenciu, Gheorghe

    2008-01-01

    It is proved that for general, not necessarily periodic, quasi one-dimensional systems the band position operator corresponding to an isolated part of the energy spectrum has discrete spectrum and its eigenfunctions have the same spatial localization as the corresponding spectral projection....... As a consequence, an eigenbasis of the band position operator provides a basis of optimally localized (generalized) Wannier functions for quasi one-dimensional systems, and this proves the strong Marzari-Vanderbilt conjecture. If the system has some translation symmetries (e.g. usual translations, screw...

  16. Optimally localized Wannier functions for quasi one-dimensional nonperiodic insulators

    DEFF Research Database (Denmark)

    Cornean, Horia; Nenciu, A.; Nenciu, Gheorghe

    It is proved that for general, not necessarily periodic quasi one dimensional systems, the band position operator corresponding to an isolated part of the energy spectrum has discrete spectrum and its eigenfunctions have the same spatial localization as the corresponding spectral projection....... As a consequence, an eigenbasis of the band position operator provides a basis of optimally localized (generalized) Wannier functions for quasi one dimensional systems. If the system has some translation symmetries (e.g. usual translations, screw transformations), they are "inherited" bythe Wannier basis....

  17. Para-bosons and Para-fermions in Quantum Mechanics

    International Nuclear Information System (INIS)

    Cattani, M.S.D.; Fernandes, N.C.

    1982-01-01

    Within the framework of the ordinary quantum mechanics, a detailed study of the energy eigenfunctions of N identical particles using the irreducible representations of the permutation group in the Hilbert space is performed. It is shown that the para-states, as occurs with the boson and fermion states, are compatible with the postulates of quantum mechanics and with the principle of indistinguishability. A mathematical support for the existence of para-bosons and para-fermions is given. Gentile's quantum statistics is, in a certain sense, justified. (Author) [pt

  18. Toward precise potential energy curves for diatomic molecules, derived from experimental line positions

    International Nuclear Information System (INIS)

    Helm, H.

    1984-01-01

    An inverted, first-order perturbation approach is used to derive potential energy curves for diatomic molecules from experimental line positions of molecular bands. The concept adopted here is based on the inverted perturbation analysis (IPA) proposed by Kozman and Hinze, but uses radial eigenfunctions of the trial potential energy curves as basis sets for the perturbation correction. Using molecular linepositions rather than molecular energy levels we circumvent the necessity of defining molecular constants for the molecule prior to the derivation of the potential energy curves. (Author)

  19. Obtaining the Wakefield Due to Cell-to-Cell Misalignments in a Linear Accelerator Structure

    OpenAIRE

    Bane, Karl L. F.; Li, Zenghai

    2001-01-01

    A linear accelerator structure, such as will be used in the linacs of the JLC/NLC collider, is composed of on the order of 100 cells. The cells are constructed as individual cups that are brazed together to form a structure. Fabrication error will result in slight cell-to-cell misalignments along the finished structure. In this report we derive an approximation to the transverse wakefield of a structure with cell-to-cell misalignments in terms of the eigenfunctions and eigenvalues of the erro...

  20. Infinite families of superintegrable systems separable in subgroup coordinates

    International Nuclear Information System (INIS)

    Lévesque, Daniel; Post, Sarah; Winternitz, Pavel

    2012-01-01

    A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials. (paper)

  1. Normal modes and continuous spectra

    International Nuclear Information System (INIS)

    Balmforth, N.J.; Morrison, P.J.

    1994-12-01

    The authors consider stability problems arising in fluids, plasmas and stellar systems that contain singularities resulting from wave-mean flow or wave-particle resonances. Such resonances lead to singularities in the differential equations determining the normal modes at the so-called critical points or layers. The locations of the singularities are determined by the eigenvalue of the problem, and as a result, the spectrum of eigenvalues forms a continuum. They outline a method to construct the singular eigenfunctions comprising the continuum for a variety of problems

  2. The Berry phase in GaAs semiconductor with a quantized field

    International Nuclear Information System (INIS)

    Chen Gang; Chen Zidong; Yu Lixian

    2007-01-01

    In this paper we investigate the Berry phase in GaAs semiconductor with a quantized magnetic field in the rotating wave approximation. The eigenfunctions of the nuclear spin in the quantized external field are obtained and thus the Berry phase is evaluated explicitly in terms of the introduction of the phase shift. It is shown that the Berry phase can be easily controlled by the coupling strength, the anisotropy constant and the frequency of the electromagnetic wave, which can be important in applications in geometric quantum computing

  3. Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations

    Directory of Open Access Journals (Sweden)

    Winfried Auzinger

    2006-01-01

    Full Text Available We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.

  4. Fourier analysis and its applications

    CERN Document Server

    Folland, Gerald B

    2009-01-01

    This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern ana

  5. 2005 Program of Study: Fast Times and Fine Scales

    Science.gov (United States)

    2006-07-01

    effect of the O(E) mean flow is simply a phase shift determined by the angular procession of rays around the cylinder . 173 Shadow boundary GTD...for the Magnus force due to flow past a cylinder . 177 7.2 Force calculation by eigenfunction solution We can also calculate the force using the...However, the only 0(c) contribution to the force turns out to be a Magnus force due to the mean Eulerian flow 719T-I2 past the cylinder . To solve the 0

  6. Study of electron-related intersubband optical properties in three coupled quantum wells wires with triangular transversal section

    Science.gov (United States)

    Tiutiunnyk, A.; Tulupenko, V.; Akimov, V.; Demediuk, R.; Morales, A. L.; Mora-Ramos, M. E.; Radu, A.; Duque, C. A.

    2015-11-01

    This work concerns theoretical study of confined electrons in a low-dimensional structure consisting of three coupled triangular GaAs/AlxGa1-xAs quantum wires. Calculations have been made in the effective mass and parabolic band approximations. In the calculations a diagonalization method to find the eigenfunctions and eigenvalues of the Hamiltonian was used. A comparative analysis of linear and nonlinear optical absorption coefficients and the relative change in the refractive index was made, which is tied to the intersubband electron transitions.

  7. Some mathematical methods of physics

    CERN Document Server

    Goertzel, Gerald

    2014-01-01

    This well-rounded, thorough treatment for advanced undergraduates and graduate students introduces basic concepts of mathematical physics involved in the study of linear systems. The text emphasizes eigenvalues, eigenfunctions, and Green's functions. Prerequisites include differential equations and a first course in theoretical physics.The three-part presentation begins with an exploration of systems with a finite number of degrees of freedom (described by matrices). In part two, the concepts developed for discrete systems in previous chapters are extended to continuous systems. New concepts u

  8. Spin eigenmodes of magnetic skyrmions and the problem of the effective skyrmion mass

    Science.gov (United States)

    Kravchuk, Volodymyr P.; Sheka, Denis D.; Rößler, Ulrich K.; van den Brink, Jeroen; Gaididei, Yuri

    2018-02-01

    The properties of magnon modes localized on a ferromagnetic skyrmion are studied. Mode eigenfrequencies display three types of asymptotic behavior for large skyrmion radius Rs, namely, ω0∝Rs-2 for the breathing mode and ω-|μ |∝Rs-1 and ω|μ |∝Rs-3 for modes with negative and positive azimuthal quantum numbers, respectively. A number of properties of the magnon eigenfunctions are determined. This enables us to demonstrate that the skyrmion dynamics for a traveling-wave ansatz obeys the massless Thiele equation.

  9. κ-deformed Dirac oscillator in an external magnetic field

    Science.gov (United States)

    Chargui, Y.; Dhahbi, A.; Cherif, B.

    2018-04-01

    We study the solutions of the (2 + 1)-dimensional κ-deformed Dirac oscillator in the presence of a constant transverse magnetic field. We demonstrate how the deformation parameter affects the energy eigenvalues of the system and the corresponding eigenfunctions. Our findings suggest that this system could be used to detect experimentally the effect of the deformation. We also show that the hidden supersymmetry of the non-deformed system reduces to a hidden pseudo-supersymmetry having the same algebraic structure as a result of the κ-deformation.

  10. Banana regime pressure anisotropy in a bumpy cylinder magnetic field

    International Nuclear Information System (INIS)

    Garcia-Perciante, A.L.; Callen, J.D.; Shaing, K.C.; Hegna, C.C.

    2006-01-01

    The pressure anisotropy is calculated for a plasma in a bumpy cylindrical magnetic field in the low collisionality (banana) regime for small magnetic-field modulations (ε≡ΔB/2B parallel is then calculated and is shown to exceed the flux-surface-averaged parallel viscous force parallel > by a factor of O(1/ε). A high-frequency limit (ω>>ν) for the pressure anisotropy is also determined and the calculation is then extended to include the full frequency dependence by using an expansion in Cordey eigenfunctions

  11. Wigner functions of s waves

    DEFF Research Database (Denmark)

    Dahl, Jens Peder; Varro, S.; Wolf, A.

    2007-01-01

    We derive explicit expressions for the Wigner function of wave functions in D dimensions which depend on the hyperradius-that is, of s waves. They are based either on the position or the momentum representation of the s wave. The corresponding Wigner function depends on three variables......: the absolute value of the D-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary s wave and the energy eigenfunction of a free particle....

  12. Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems

    Directory of Open Access Journals (Sweden)

    Misha V. Feigin

    2009-09-01

    Full Text Available We consider trigonometric solutions of WDVV equations and derive geometric conditions when a collection of vectors with multiplicities determines such a solution. We incorporate these conditions into the notion of trigonometric Veselov system (v-system and we determine all trigonometric v-systems with up to five vectors. We show that generalized Calogero-Moser-Sutherland operator admits a factorized eigenfunction if and only if it corresponds to the trigonometric v-system; this inverts a one-way implication observed by Veselov for the rational solutions.

  13. On the equisummability of Hermite and Fourier expansions

    Indian Academy of Sciences (India)

    is the Fourier transform on Rn. Let ب ; 2 Nn be the n-dimensional Hermite functions which are eigenfunctions of the Hermite operator H ¼ ہء jxj. 2 with the eigenvalue. ً2j j nق where j j ¼ 1 ءءء n. Let Pk be the orthogonal projection of L 2ًRnق onto the kth eigenspace spanned by ب ; j j ¼ k. More precisely,. Pk fًxق ¼. X j j¼k. Z.

  14. Passive control of coherent structures in a modified backwards-facing step flow

    Science.gov (United States)

    Ormonde, Pedro C.; Cavalieri, André V. G.; Silva, Roberto G. A. da; Avelar, Ana C.

    2018-05-01

    We study a modified backwards-facing step flow, with the addition of two different plates; one is a baseline, impermeable plate and the second a perforated one. An experimental investigation is carried out for a turbulent reattaching shear layer downstream of the two plates. The proposed setup is a model configuration to study how the plate characteristics affect the separated shear layer and how turbulent kinetic energies and large-scale coherent structures are modified. Measurements show that the perforated plate changes the mean flow field, mostly by reducing the intensity of reverse flow close to the bottom wall. Disturbance amplitudes are significantly reduced up to five step heights downstream of the trailing edge of the plate, more specifically in the recirculation region. A loudspeaker is then used to introduce phase-locked, low-amplitude perturbations upstream of the plates, and phase-averaged measurements allow a quantitative study of large-scale structures in the shear-layer. The evolution of such coherent structures is evaluated in light of linear stability theory, comparing the eigenfunction of the Kelvin-Helmholtz mode to the experimental results. We observe a close match of linear-stability eigenfunctions with phase-averaged amplitudes for the two tested Strouhal numbers. The perforated plate is found to reduce the amplitude of the Kelvin-Helmholtz coherent structures in comparison to the baseline, impermeable plate, a behavior consistent with the predicted amplification trends from linear stability.

  15. High-energy localized eigenstates in a Fabry-Perot graphene resonator in a magnetic field

    Science.gov (United States)

    Zalipaev, V. V.

    2012-06-01

    A semiclassical analysis of the high-energy eigenstates of Dirac fermions inside a graphene monolayer nanoribbon resonator of Fabry-Perot type in a magnetic field with zigzag boundary conditions is discussed. A semiclassical asymptotic method of construction of Maslov spectral series of energy spectrum and eigenfunctions, localized in an asymptotically small neighborhood of a periodic orbit, is developed for the graphene Dirac system. The isolated periodic orbit is confined between two flat boundaries. The analysis involves constructing a localized asymptotic solution to the Dirac system (electron-hole Gaussian beam). Then, the stability of a continuous family of periodic orbits (POs) confined between reflecting boundaries of the resonator is studied. The asymptotics of the eigenfunctions are constructed as a superposition of two Gaussian beams propagating in opposite directions between two reflecting points of the periodic orbit. The asymptotics of the energy spectrum are obtained by means of the generalized Bohr-Sommerfeld quantization condition only for stable POs. It provides two parts of semiclassical Maslov spectral series with positive and negative energies, for electrons and holes, correspondingly, with two different Hamiltonian dynamics and families of classical trajectories. The presence of electrostatic potential is vital as it makes a family of periodic orbit stable. For one subclass of lens-shaped periodic orbits, for a piecewise linear potential, localized eigenstates were computed numerically by the finite element method using COMSOL, and proved to be in very good agreement with the ones computed semiclassically.

  16. Application of biorthogonal eigenfunction system for extraction of Tollmien-Schlichting waves in acoustic receptivity simulations

    OpenAIRE

    Shahriari, Nima; Hanifi, Ardeshir; Henningson, Dan S.

    2016-01-01

    Acoustic receptivity of a two-dimensional boundary layer on a flat plate with elliptic leading edge is studied through direct numerical simulation (DNS). Sound waves are modelled by a uniform oscillation of freestream boundaries in time which results to an infinite-wavelength acoustic wave. Acoustic disturbances interact with strong streamwise gradients at the leading edge or surface non- homogeneities and create Tollmien-Schlichting (TS) waves inside the boundary layer. Measuring amplitude o...

  17. Squeezing a wave packet with an angular-dependent mass

    Energy Technology Data Exchange (ETDEWEB)

    Schmidt, Alexandre G M [Departamento de Ciencias Exatas, Universidade Federal Fluminense, Av. dos Trabalhadores 420, Volta Redonda RJ, CEP 27255-125 (Brazil)], E-mail: agmschmidt@gmail.com, E-mail: agmschmidt@pq.cnpq.br

    2009-06-19

    We present a new effect of position-dependent mass (PDM) systems: the possibility of creating squeezed wave packets at the partial revival times. We solve exactly the PDM Schroedinger equation for the two-dimensional quantum rotor with two effective masses {mu}({theta}), both free and interacting with a uniform electric field, and present their energy eigenvalues and eigenfunctions in terms of Mathieu functions. For the first one, in order to squeeze the wave packet it is necessary to apply an electric field; for the second one such an effect can be achieved without the field.

  18. Squeezing a wave packet with an angular-dependent mass

    International Nuclear Information System (INIS)

    Schmidt, Alexandre G M

    2009-01-01

    We present a new effect of position-dependent mass (PDM) systems: the possibility of creating squeezed wave packets at the partial revival times. We solve exactly the PDM Schroedinger equation for the two-dimensional quantum rotor with two effective masses μ(θ), both free and interacting with a uniform electric field, and present their energy eigenvalues and eigenfunctions in terms of Mathieu functions. For the first one, in order to squeeze the wave packet it is necessary to apply an electric field; for the second one such an effect can be achieved without the field

  19. Two-photon transitions in hydrogen atoms embedded in weakly coupled plasmas

    International Nuclear Information System (INIS)

    Paul, S.; Ho, Y. K.

    2008-01-01

    The pseudostate method has been applied to calculate energy eigenvalues and corresponding eigenfunctions of the hydrogen atom in Debye plasma environments. Resonant two-photon transition rates from the ground state of atomic hydrogen to 2s and 3s excited states have been computed as a function of photon frequency in the length and velocity gauges for different Debye lengths. A two-photon transparency is found in correspondence to each resonance for 1s-3s. The transparency frequency and resonance enhancement frequency vary significantly with the Debye length.

  20. Spectrum of the linearized operator for the Ginzburg-Landau equation

    Directory of Open Access Journals (Sweden)

    Tai-Chia Lin

    2000-06-01

    Full Text Available We study the spectrum of the linearized operator for the Ginzburg-Landau equation about a symmetric vortex solution with degree one. We show that the smallest eigenvalue of the linearized operator has multiplicity two, and then we describe its behavior as a small parameter approaches zero. We also find a positive lower bound for all the other eigenvalues, and find estimates of the first eigenfunction. Then using these results, we give partial results on the dynamics of vortices in the nonlinear heat and Schrodinger equations.

  1. Quantum scattering via the discretisation of Schroedinger's equation

    Energy Technology Data Exchange (ETDEWEB)

    Alexopoulos, A. [Electronic Warfare and Radar Division, Defence Science and Technology Organisation (DSTO), PO Box 1500, Edinburgh 5111 (Australia)]. E-mail: aris.alexopoulos@dsto.defence.gov.au

    2007-03-19

    We obtain the scattering matrix for particles that encounter a quantum potential by discretising Schroedinger's time independent differential equation without the need to resort to the manipulation of the eigenfunctions directly. The singularities that arise in some solutions by other methods are handled with ease including the effects of resonances while convergence is excellent in all limits with only a small number of orders required to give accurate results. Our method compares the tunnelling probability with that of the WKB theory, exact numerical solutions and the modified Airy function method.

  2. The critical behavior of PHI41

    International Nuclear Information System (INIS)

    Isaacson, D.

    1977-01-01

    The eigenvalues, eigenfunctions, and Schwinger functions of the ordinary differential operator H(Λ,m) = 1/2[p 2 + Λq 4 + (m 2 - Λm -1 )q 2 ] are studied as Λ → infinity. It is shown that the scaling limit of the Schwinger functions equals the scaling limit of a one dimensional Ising model. Critical exponents of H(Λ,m) are shown to equal critical exponents of the Ising model, while critical exponents of the renormalized theory are shown to agree with those of a harmonic oscillator. (orig.) [de

  3. Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis

    International Nuclear Information System (INIS)

    Fillion-Gourdeau, F.; Lorin, E.; Bandrauk, A.D.

    2016-01-01

    A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron–molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.

  4. A rigorous approach to relativistic corrections of bound state energies for spin-1/2 particles

    International Nuclear Information System (INIS)

    Gesztesy, F.; Thaller, B.; Grosse, H.

    1983-01-01

    Under fairly general conditions on the interactions we prove holomorphy of the Dirac resolvent around its nonrelativistic limit. As a consequences, perturbation theory in terms of resolvents (instead of Hamiltonians) yields holomorphy of Dirac eigenvalues and eigenfunctions with respect to c - 1 and a new method of calculating relativistic corrections to bound state energies. Due to a formulation in an abstract setting our method is applicable in many different concrete situation. In particular our approach covers the case of the relavistic hydrogen atom in external electromagnetic fields. (Author)

  5. Hydrogen atom within spherical boxes with penetrable walls

    International Nuclear Information System (INIS)

    Ley-Koo, E.; Rubinstein, S.

    1979-01-01

    We study a model for the hydrogen atom confined within spherical boxes with penetrable walls. The potential consists of the Coulomb potential inside the box and a constant potential outside the box; the Schroedinger equation admits analytical solutions in both regions. The energy eigenvalues and eigenfunctions for the lowest states of the system are determined numerically for boxes of different sizes and penetrabilities. In addition, we also evaluate the hyperfine splitting, nuclear magnetic shielding, polarizability and pressure of the system and investigate the effect of the confinement on these atomic properties

  6. Modelling dynamic processes in a nuclear reactor by state change modal method

    Science.gov (United States)

    Avvakumov, A. V.; Strizhov, V. F.; Vabishchevich, P. N.; Vasilev, A. O.

    2017-12-01

    Modelling of dynamic processes in nuclear reactors is carried out, mainly, using the multigroup neutron diffusion approximation. The basic model includes a multidimensional set of coupled parabolic equations and ordinary differential equations. Dynamic processes are modelled by a successive change of the reactor states. It is considered that the transition from one state to another occurs promptly. In the modal method the approximate solution is represented as eigenfunction expansion. The numerical-analytical method is based on the use of dominant time-eigenvalues of a group diffusion model taking into account delayed neutrons.

  7. Electric-line-source illumination of a circular cylinder of lossless double-negative material: an investigation of near field, directivity, and radiation resistance

    DEFF Research Database (Denmark)

    Arslanagic, Samel; Breinbjerg, Olav

    2006-01-01

    the properties of the near field, inside as well as outside the cylinder, and the far-field. Third, the variations of these fields are examined, as well as the radiation resistance and radiation pattern, as functions of the geometrical and electromagnetic parameters of the configuration. It is demonstrated......This work investigates the properties of an antenna-like configuration with an electric line source radiating in the presence of a double-negative circular cylinder. First, the analytical eigenfunction-series solution is derived. Second, this solution is employed in numerical calculations to study...

  8. Sturm-Liouville operators and applications

    CERN Document Server

    Marchenko, Vladimir A

    2011-01-01

    The spectral theory of Sturm-Liouville operators is a classical domain of analysis, comprising a wide variety of problems. Besides the basic results on the structure of the spectrum and the eigenfunction expansion of regular and singular Sturm-Liouville problems, it is in this domain that one-dimensional quantum scattering theory, inverse spectral problems, and the surprising connections of the theory with nonlinear evolution equations first become related. The main goal of this book is to show what can be achieved with the aid of transformation operators in spectral theory as well as in their

  9. Solution of Schroedinger Equation for Two-Dimensional Complex Quartic Potentials

    International Nuclear Information System (INIS)

    Singh, Ram Mehar; Chand, Fakir; Mishra, S. C.

    2009-01-01

    We investigate the quasi-exact solutions of the Schroedinger wave equation for two-dimensional non-hermitian complex Hamiltonian systems within the frame work of an extended complex phase space characterized by x = x 1 + ip 3 , y = x 2 + ip 4 , p x = p 1 + ix 3 , p y = p 2 + ix 4 . Explicit expressions of the energy eigenvalues and the eigenfunctions for ground and first excited states for a complex quartic potential are obtained. Eigenvalue spectra of some variants of the complex quartic potential, including PT-symmetric one, are also worked out. (general)

  10. Self-similar solutions for poloidal magnetic field in turbulent jet

    International Nuclear Information System (INIS)

    Komissarov, S.S.; Ovchinnikov, I.L.

    1990-01-01

    Evolution of a large-scale magnetic field in a turbulent extragalactic source radio jets is considered. Self-similar solutions for a weak poloidal magnetic field transported by turbulent jet of incompressible fluid are found. It is shown that the radial profiles of the solutions are the eigenfunctions of a linear differential operator. In all the solutions, the strength of a large-scale field decreases more rapidly than that of a small-scale turbulent field. This can be understood as a decay of a large-scale field in the turbulent jet

  11. Modelling Acoustic Wave Propagation in Axisymmetric Varying-Radius Waveguides

    DEFF Research Database (Denmark)

    Bæk, David; Willatzen, Morten

    2008-01-01

    A computationally fast and accurate model (a set of coupled ordinary differential equations) for fluid sound-wave propagation in infinite axisymmetric waveguides of varying radius is proposed. The model accounts for fluid heat conduction and fluid irrotational viscosity. The model problem is solved...... by expanding solutions in terms of cross-sectional eigenfunctions following Stevenson’s method. A transfer matrix can be easily constructed from simple model responses of a given waveguide and later used in computing the response to any complex wave input. Energy losses due to heat conduction and viscous...

  12. Properties of solar gravity mode signals in total irradiance observations

    International Nuclear Information System (INIS)

    Kroll, R.J.; Chen, J.; Hill, H.A.

    1988-01-01

    Further evidence has been found that a significant fraction of the gravity mode power density in the total irradiance observations appears in sidebands of classified eigenfrequencies. These sidebands whose amplitudes vary from year to year are interpreted as harmonics of the rotational frequencies of the nonuniform solar surface. These findings are for non axisymmetric modes and corroborate the findings of Kroll, Hill and Chen for axisymmetric modes. It is demonstrated the the generation of the sidebands lifts the usual restriction on the parity of the eigenfunctions for modes detectable in total irradiance observations. 14 refs

  13. Heisenberg representation for secondary-quantized fields in nonstationary external fields and dielectric nonlinear medium

    International Nuclear Information System (INIS)

    Lobashev, A.A.; Mostepanenko, V.M.

    1993-01-01

    Heisenberg formalism is developed for creation-annihilation operators of quantum fields propagating in nonstationary external fields. Quantum fields with spin 0,1/2, 1 are considered in the presence of such external fields as electromagnetic, scalar and the field of nonstationary dielectric properties of nonlinear medium. Elliptic operator parametrically depending on time is constructed. In Heisenberg representation field variables are decomposed over eigenfunction of this operator. The relation between Heisenberg creation-annihilation operators and the operators obtained in the frame of diagonalization of Hamiltonian with Bogoliubov transformations is set up

  14. Trace formulae for arithmetical systems

    International Nuclear Information System (INIS)

    Bogomolny, E.B.; Georgeot, B.; Giannoni, M.J.; Schmit, C.

    1992-09-01

    For quantum problems on the pseudo-sphere generated by arithmetic groups there exist special trace formulae, called trace formulae for Hecke operators, which permit the reconstruction of wave functions from the knowledge of periodic orbits. After a short discussion of this subject, the Hecke operators trace formulae are presented for the Dirichlet problem on the modular billiard, which is a prototype of arithmetical systems. The results of numerical computations for these semiclassical type relations are in good agreement with the directly computed eigenfunctions. (author) 23 refs.; 2 figs

  15. Comparison of Austin Research Associates and Los Alamos Scientific Laboratory loop-drive boundary conditions. Informal report

    International Nuclear Information System (INIS)

    Shanahan, W.R.

    1979-02-01

    A comparison of two different models for boundary conditions appropriate to the resonant-loop-drive slow-wave structure is presented. The first model is based on a low-frequency approximation in which a capacitive field--current relationship is invoked. The second model is essentially a rigorous field theory approach in which no such low-frequency assumption is made. Significantly lower growth rates are obtained from the latter approach than from the former. Reasons for this difference are sought in an examination of the radial eigenfunctions of the azimuthal electric field. 3 figures

  16. Modal Ring Method for the Scattering of Electromagnetic Waves

    Science.gov (United States)

    Baumeister, Kenneth J.; Kreider, Kevin L.

    1993-01-01

    The modal ring method for electromagnetic scattering from perfectly electric conducting (PEC) symmetrical bodies is presented. The scattering body is represented by a line of finite elements (triangular) on its outer surface. The infinite computational region surrounding the body is represented analytically by an eigenfunction expansion. The modal ring method effectively reduces the two dimensional scattering problem to a one-dimensional problem similar to the method of moments. The modal element method is capable of handling very high frequency scattering because it has a highly banded solution matrix.

  17. The exact wavefunction factorization of a vibronic coupling system

    International Nuclear Information System (INIS)

    Chiang, Ying-Chih; Klaiman, Shachar; Otto, Frank; Cederbaum, Lorenz S.

    2014-01-01

    We investigate the exact wavefunction as a single product of electronic and nuclear wavefunction for a model conical intersection system. Exact factorized spiky potentials and nodeless nuclear wavefunctions are found. The exact factorized potential preserves the symmetry breaking effect when the coupling mode is present. Additionally nodeless wavefunctions are found to be closely related to the adiabatic nuclear eigenfunctions. This phenomenon holds even for the regime where the non-adiabatic coupling is relevant, and sheds light on the relation between the exact wavefunction factorization and the adiabatic approximation

  18. Algebra with polynomial commutation relations for Zeeman effect in Coulomb-Dirac field

    International Nuclear Information System (INIS)

    Karasev, M.V.; Novikova, E.M.

    2005-01-01

    One studies a model of a particle motion in the field of electromagnetic monopole (the Coulomb-Dirac field) disturbed by homogeneous magnetic and inhomogeneous electric fields. The quantum averaging is followed by occurrence of the integrated system the Hamiltonian of which is represented by the algebra elements with polynomial commutation relations. One forms irreducible representations of the mentioned algebra and its hypergeometric coherent states. One obtains the representation of the eigenfunction of the assumption problem and specifies the asymptotics of eigenvalues in the first order of perturbation theory [ru

  19. Shape Analysis Using the Auto Diffusion Function

    DEFF Research Database (Denmark)

    Gebal, Katarzyna; Bærentzen, Jakob Andreas; Aanæs, Henrik

    2009-01-01

    Scalar functions defined on manifold triangle meshes is a starting point for many geometry processing algorithms such as mesh parametrization, skeletonization, and segmentation. In this paper, we propose the Auto Diffusion Function (ADF) which is a linear combination of the eigenfunctions......, it is controlled by a single parameter which can be interpreted as feature scale, and, finally, the ADF is invariant to rigid and isometric deformations. We describe the ADF and its properties in detail and compare it to other choices of scalar functions on manifolds. As an example of an application, we present...

  20. On the construction of coherent states of position dependent mass Schroedinger equation endowed with effective potential

    International Nuclear Information System (INIS)

    Chithiika Ruby, V.; Senthilvelan, M.

    2010-01-01

    In this paper, we propose an algorithm to construct coherent states for an exactly solvable position dependent mass Schroedinger equation. We use point canonical transformation method and obtain ground state eigenfunction of the position dependent mass Schroedinger equation. We fix the ladder operators in the deformed form and obtain explicit expression of the deformed superpotential in terms of mass distribution and its derivative. We also prove that these deformed operators lead to minimum uncertainty relations. Further, we illustrate our algorithm with two examples, in which the coherent states given for the second example are new.

  1. Renormalized two-body low-energy scattering

    DEFF Research Database (Denmark)

    Skibsted, Erik

    For a class of long-range potentials, including ultra-strong perturbations of the attractive Coulomb potential in dimension d≥3, we introduce a stationary scattering theory for Schrödinger operators which is regular at zero energy. In particular it is well defined at this energy, and we use it to...... it to establish a characterization there of the set of generalized eigenfunctions in an appropriately adapted Besov space generalizing parts of [DS1]. Principal tools include global solutions to the eikonal equation and strong radiation condition bounds....

  2. Sum rules for the quarkonium systems

    International Nuclear Information System (INIS)

    Burnel, A.; Caprasse, H.

    1980-01-01

    In the framework of the radial Schroedinger equation we derive in a very simple way sum rules relating the potential to physical quantities such as the energy eigenvalues and the square of the lth derivative of the eigenfunctions at the origin. These sum rules contain as particular cases well-known results such as the quantum version of the Clausius theorem in classical mechanics as well as Kramers's relations for the Coulomb potential. Several illustrations are given and the possibilities of applying them to the quarkonium systems are considered

  3. Unitarity and irreversibility in chaotic systems

    International Nuclear Information System (INIS)

    Hasegawa, H.H.; Saphir, W.C.

    1992-01-01

    We analyze the spectral properties of the Perron-Frobenius operator U, associated with some simple highly chaotic maps. We obtain a spectral decomposition of U in terms of generalized eigenfunctions of U and its adjoint. The corresponding eigenvalues are related to the decay rates of correlation functions and have magnitude less than one, so that physically measurable quantities manifestly approach equilibrium. To obtain decaying eigenstates of unitary and isometric operators it is necessary to extend the Hilbert-space formulation of dynamical systems. We describe and illustrate a method to obtain the decomposition explicitly

  4. On the spectrum of a periodic operator with a small localized perturbation

    International Nuclear Information System (INIS)

    Borisov, D I; Gadyl'shin, R R

    2008-01-01

    The paper deals with the spectrum of a periodic self-adjoint differential operator on the real axis perturbed by a small localized non-self-adjoint operator. We show that the continuous spectrum does not depend on the perturbation, the residual spectrum is empty, and the point spectrum has no finite accumulation points. We study the problem of the existence of eigenvalues embedded in the continuous spectrum, obtain necessary and sufficient conditions for the existence of eigenvalues, construct asymptotic expansions of the eigenvalues and corresponding eigenfunctions and consider some examples

  5. Effects of a weakly 3-D equilibrium on ideal magnetohydrodynamic instabilities

    Energy Technology Data Exchange (ETDEWEB)

    Hegna, C. C. [Departments of Engineering Physics and Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States)

    2014-07-15

    The effect of a small three-dimensional equilibrium distortion on an otherwise axisymmetric configuration is shown to be destabilizing to ideal magnetohydrodynamic modes. The calculations assume that the 3-D fields are weak and that shielding physics is present so that no islands appear in the resulting equilibrium. An eigenfunction that has coupled harmonics of different toroidal mode number is constructed using a perturbation approach. The theory is applied to the case of tokamak H-modes with shielded resonant magnetic perturbations (RMPs) present indicating RMPs can be destabilizing to intermediate-n peeling-ballooning modes.

  6. Reciprocity principle in stochastic quantum mechanics

    International Nuclear Information System (INIS)

    Brooke, J.A.; Guz, W.; Prugovecki, E.

    1982-01-01

    Born's reciprocity theory can be combined with a recently proposed framework for quantum spacetime by requiring that the free test particle propagators obey the Born-Lande equation in addition to the Klein-Gordon equation. If, furthermore, the coordinate transition amplitudes in between various standards are required to be eigenfunctions of Born's metric operator, then a mass formula results which predicts linear dependence on spin of the squared rest mass of elementary particles. This procedure also leads to a guage and reciprocally invariant formulation of the relativistic canonical commutation relations

  7. Matrix-exponential description of radiative transfer

    International Nuclear Information System (INIS)

    Waterman, P.C.

    1981-01-01

    By appling the matrix-exponential operator technique to the radiative-transfer equation in discrete form, new analytical solutions are obtained for the transmission and reflection matrices in the limiting cases x >1, where x is the optical depth of the layer. Orthongonality of the eigenvectors of the matrix exponential apparently yields new conditions for determining. Chandrasekhar's characteristic roots. The exact law of reflection for the discrete eigenfunctions is also obtained. Finally, when used in conjuction with the doubling method, the matrix exponential should result in reduction in both computation time and loss of precision

  8. On the partitioning method and the perturbation quantum theory - discrete spectra

    International Nuclear Information System (INIS)

    Logrado, P.G.

    1982-05-01

    Lower and upper bounds to eigenvalues of the Schroedinger equation H Ψ = E Ψ (H = H 0 + V) and the convergence condition, in Schonberg's perturbation theory, are presented. These results are obtained using the partitioning technique. It is presented for the first time a perturbation treatment obtained when the reference function in the partitioning technique is chosen to be a true eigenfunction Ψ. The convergence condition and upper and lower bounds for the true eigenvalues E are derived in this formulation. The concept of the reaction and wave operators is also discussed. (author)

  9. Data-Driven Model Reduction and Transfer Operator Approximation

    Science.gov (United States)

    Klus, Stefan; Nüske, Feliks; Koltai, Péter; Wu, Hao; Kevrekidis, Ioannis; Schütte, Christof; Noé, Frank

    2018-06-01

    In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis, dynamic mode decomposition, and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods.

  10. Stable pseudoanalytical computation of electromagnetic fields from arbitrarily-oriented dipoles in cylindrically stratified media

    Science.gov (United States)

    Moon, Haksu; Teixeira, Fernando L.; Donderici, Burkay

    2014-09-01

    Computation of electromagnetic fields due to point sources (Hertzian dipoles) in cylindrically stratified media is a classical problem for which analytical expressions of the associated tensor Green's function have been long known. However, under finite-precision arithmetic, direct numerical computations based on the application of such analytical (canonical) expressions invariably lead to underflow and overflow problems related to the poor scaling of the eigenfunctions (cylindrical Bessel and Hankel functions) for extreme arguments and/or high-order, as well as convergence problems related to the numerical integration over the spectral wavenumber and to the truncation of the infinite series over the azimuth mode number. These problems are exacerbated when a disparate range of values is to be considered for the layers' thicknesses and material properties (resistivities, permittivities, and permeabilities), the transverse and longitudinal distances between source and observation points, as well as the source frequency. To overcome these challenges in a systematic fashion, we introduce herein different sets of range-conditioned, modified cylindrical functions (in lieu of standard cylindrical eigenfunctions), each associated with nonoverlapped subdomains of (numerical) evaluation to allow for stable computations under any range of physical parameters. In addition, adaptively-chosen integration contours are employed in the complex spectral wavenumber plane to ensure convergent numerical integration in all cases. We illustrate the application of the algorithm to problems of geophysical interest involving layer resistivities ranging from 1000 Ω m to 10-8 Ω m, frequencies of operation ranging from 10 MHz down to the low magnetotelluric range of 0.01 Hz, and for various combinations of layer thicknesses.

  11. K-scrambling in a near-symmetric top molecule containing an excited noncoaxial internal rotor

    International Nuclear Information System (INIS)

    Ortigoso, Juan; Hougen, Jon T.

    2000-01-01

    Classical trajectories on rotational energy surfaces and coherent-state quantum projections have been used to study an asymmetric-top molecule containing a freely rotating internal symmetric top whose symmetry axis is not coincident with a principal axis of the molecule. Stationary points on the rotational energy surface, which strongly influence the trajectories, increase in number from two to four to six as J/n increases from zero to infinity (where J is the total and n is the free-internal-rotor angular momentum). For some J/n values trajectories can arise that sample a large fraction of K values (where K is the z-axis projection of J), corresponding in quantum wave functions to extensive K mixing in the symmetric-top basis set |J,K>. When such mixing cannot be made small for any choice of z axis, we call it K scrambling. For typical values of the torsion-rotation coupling parameter ρ, rotational eigenfunctions for a given J and torsional state turn out to be quite different from eigenfunctions for the same J in some other torsional state. Nonzero rotational overlap integrals are then distributed among many rotational functions for each (n,n ' ) pair, which may, in turn, contribute to internal rotation enhancement of intramolecular vibrational energy redistribution. We have also examined near-free-rotor levels of our test molecule acetaldehyde, which arise for excitation of ten or more quanta of methyl group torsion, and find that barrier effects do not change the qualitative picture obtained from the free-rotor treatment. (c) 2000 American Institute of Physics

  12. Analysis of high-speed rotating flow inside gas centrifuge casing

    Science.gov (United States)

    Pradhan, Sahadev

    2017-11-01

    The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ωi while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

  13. From Jack to Double Jack Polynomials via the Supersymmetric Bridge

    Science.gov (United States)

    Lapointe, Luc; Mathieu, Pierre

    2015-07-01

    The Calogero-Sutherland model occurs in a large number of physical contexts, either directly or via its eigenfunctions, the Jack polynomials. The supersymmetric counterpart of this model, although much less ubiquitous, has an equally rich structure. In particular, its eigenfunctions, the Jack superpolynomials, appear to share the very same remarkable combinatorial and structural properties as their non-supersymmetric version. These super-functions are parametrized by superpartitions with fixed bosonic and fermionic degrees. Now, a truly amazing feature pops out when the fermionic degree is sufficiently large: the Jack superpolynomials stabilize and factorize. Their stability is with respect to their expansion in terms of an elementary basis where, in the stable sector, the expansion coefficients become independent of the fermionic degree. Their factorization is seen when the fermionic variables are stripped off in a suitable way which results in a product of two ordinary Jack polynomials (somewhat modified by plethystic transformations), dubbed the double Jack polynomials. Here, in addition to spelling out these results, which were first obtained in the context of Macdonal superpolynomials, we provide a heuristic derivation of the Jack superpolynomial case by performing simple manipulations on the supersymmetric eigen-operators, rendering them independent of the number of particles and of the fermionic degree. In addition, we work out the expression of the Hamiltonian which characterizes the double Jacks. This Hamiltonian, which defines a new integrable system, involves not only the expected Calogero-Sutherland pieces but also combinations of the generators of an underlying affine {widehat{sl}_2} algebra.

  14. A Dynamic BI–Orthogonal Field Equation Approach to Efficient Bayesian Inversion

    Directory of Open Access Journals (Sweden)

    Tagade Piyush M.

    2017-06-01

    Full Text Available This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen-Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.

  15. Inverse-scattering-theory approach to the exact n→∞ solutions of O(n) ϕ⁴ models on films and semi-infinite systems bounded by free surfaces.

    Science.gov (United States)

    Rutkevich, Sergei B; Diehl, H W

    2015-06-01

    The O(n) ϕ(4) model on a strip bounded by a pair of planar free surfaces at separation L can be solved exactly in the large-n limit in terms of the eigenvalues and eigenfunctions of a self-consistent one-dimensional Schrödinger equation. The scaling limit of a continuum version of this model is considered. It is shown that the self-consistent potential can be eliminated in favor of scattering data by means of appropriately extended methods of inverse scattering theory. The scattering data (Jost function) associated with the self-consistent potential are determined for the L=∞ semi-infinite case in the scaling regime for all values of the temperature scaling field t=(T-T(c))/T(c) above and below the bulk critical temperature T(c). These results are used in conjunction with semiclassical and boundary-operator expansions and a trace formula to derive exact analytical results for a number of quantities such as two-point functions, universal amplitudes of two excess surface quantities, the universal amplitude difference associated with the thermal singularity of the surface free energy, and potential coefficients. The asymptotic behaviors of the scaled eigenenergies and eigenfunctions of the self-consistent Schrödinger equation as function of x=t(L/ξ(+))(1/ν) are determined for x→-∞. In addition, the asymptotic x→-∞ forms of the universal finite-size scaling functions Θ(x) and ϑ(x) of the residual free energy and the Casimir force are computed exactly to order 1/x, including their x(-1)ln|x| anomalies.

  16. Harmonic maps of V-manifolds

    International Nuclear Information System (INIS)

    Chiang, Yuan-Jen.

    1989-01-01

    Harmonic maps between manifolds are described as the critical maps of their associated energy functionals. By using Sampson's method [Sam1], the author constructs a Sobolev's chain on a compact V-manifold and obtain Rellich's Theorem (Theorem 3.1), Sobolev's Theorem (Theorem 3.2), the regularity theorem (Theorem 3.3), the property of the eigenspaces for the Laplacian (Theorem 3.5) and the solvability of Laplacian (Theorem 3.6). Then, with these results, he constructs the Green's functions for the Laplacian on a compact V-manifold M in Proposition 4.1; and obtain an orthonormal basis for L 2 (M) formed by the eigenfunctions of the Laplacian corresponding to the eigenvalues in Proposition 4.2. He also estimates the eigenvalues and eigenfunctions of the Laplacian in Theorem 4.3, which is used to construct the heat kernel on a compact V-manifold in Proposition 5.1. Afterwards, he compares the G-invariant heat kernel functions with the G-invariant fundamental solutions of heat equations in the finite V-charts of a compact V-manifold in Theorem 6.1, and then study two integral operators associated to the heat kernel on a compact V-manifold in section 7. With all the preceding results established, in Theorem 8.3 he uses successive approximations to prove the existence of the solutions of parabolic equations on V-manifolds. Finally, he uses Theorem 8.3 to show the existence of harmonic maps from compact V-manifolds into compact Riemannian manifolds in Theorem 9.1 which extends Eells-Sampson's results [E-S

  17. INTRODUCING CAFein, A NEW COMPUTATIONAL TOOL FOR STELLAR PULSATIONS AND DYNAMIC TIDES

    International Nuclear Information System (INIS)

    Valsecchi, F.; Farr, W. M.; Willems, B.; Rasio, F. A.; Kalogera, V.

    2013-01-01

    Here we present CAFein, a new computational tool for investigating radiative dissipation of dynamic tides in close binaries and of non-adiabatic, non-radial stellar oscillations in isolated stars in the linear regime. For the latter, CAFein computes the non-adiabatic eigenfrequencies and eigenfunctions of detailed stellar models. The code is based on the so-called Riccati method, a numerical algorithm that has been successfully applied to a variety of stellar pulsators, and which does not suffer from the major drawbacks of commonly used shooting and relaxation schemes. Here we present an extension of the Riccati method to investigate dynamic tides in close binaries. We demonstrate CAFein's capabilities as a stellar pulsation code both in the adiabatic and non-adiabatic regimes, by reproducing previously published eigenfrequencies of a polytrope, and by successfully identifying the unstable modes of a stellar model in the β Cephei/SPB region of the Hertzsprung-Russell diagram. Finally, we verify CAFein's behavior in the dynamic tides regime by investigating the effects of dynamic tides on the eigenfunctions and orbital and spin evolution of massive main sequence stars in eccentric binaries, and of hot Jupiter host stars. The plethora of asteroseismic data provided by NASA's Kepler satellite, some of which include the direct detection of tidally excited stellar oscillations, make CAFein quite timely. Furthermore, the increasing number of observed short-period detached double white dwarfs (WDs) and the observed orbital decay in the tightest of such binaries open up a new possibility of investigating WD interiors through the effects of tides on their orbital evolution

  18. Non-linear effects in the Boltzmann equation

    International Nuclear Information System (INIS)

    Barrachina, R.O.

    1985-01-01

    The Boltzmann equation is studied by defining an integral transformation of the energy distribution function for an isotropic and homogeneous gas. This transformation may be interpreted as a linear superposition of equilibrium states with variable temperatures. It is shown that the temporal evolution features of the distribution function are determined by the singularities of said transformation. This method is applied to Maxwell and Very Hard Particle interaction models. For the latter, the solution of the Boltzmann equation with the solution of its linearized version is compared, finding out many basic discrepancies and non-linear effects. This gives a hint to propose a new rational approximation method with a clear physical meaning. Applying this technique, the relaxation features of the BKW (Bobylev, Krook anf Wu) mode is analyzed, finding a conclusive counter-example for the Krook and Wu conjecture. The anisotropic Boltzmann equation for Maxwell models is solved as an expansion in terms of the eigenfunctions of the corresponding linearized collision operator, finding interesting transient overpopulation and underpopulation effects at thermal energies as well as a new preferential spreading effect. By analyzing the initial collision, a criterion is established to deduce the general features of the final approach to equilibrium. Finally, it is shown how to improve the convergence of the eigenfunction expansion for high energy underpopulated distribution functions. As an application of this theory, the linear cascade model for sputtering is analyzed, thus finding out that many differences experimentally observed are due to non-linear effects. (M.E.L.) [es

  19. Singular solution of the Feller diffusion equation via a spectral decomposition

    Science.gov (United States)

    Gan, Xinjun; Waxman, David

    2015-01-01

    Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

  20. Energy of surface states for 3D magnetic Schrödinger operators

    DEFF Research Database (Denmark)

    Nasrallah, Marwa

    In this dissertation, we study the Schrödinger operator with magnetic field in a three dimensional domain with compact smooth boundary. Functions in the domain of the operator satisfy (magnetic) Neumann condition on the boundary. The operator depends on the semi-classical parameter....... As this parameter becomes small, certain eigenfunctions of the operator are localized near the boundary of the domain, hence they will be called surface states. The main result of this dissertation is the calculation of the leading order terms of the energy and the number of surface states when the semi-classical...

  1. On the Analytical and Numerical Properties of the Truncated Laplace Transform II

    Science.gov (United States)

    2015-05-29

    La,b)∗ ◦ La,b) (un)) (t) = ∫ b a 1 t+ s un(s)ds = α 2 nun (t). (32) Similarly, the left singular functions vn of La,b are eigenfunctions of the...odd in the sense that Un(s) = (−1) nUn (−s). (83) 3.5 Decay of the coefficients Since the left singular function vn (defined in (27)) is a smooth...is associated with the right singular function un via (41) and (42) and it is studied in [12]. Lemma 3.13. Suppose that un be the n+ 1-th right

  2. The Green function in the secondary model of thermalization; La funcion de GREEN en el Modelo secundario de Termalizacion

    Energy Technology Data Exchange (ETDEWEB)

    Guasp, J

    1972-07-01

    The Green Function of the thermalization problem is studied in the secondary model case through the spatial Fourier transform. A relation between singularities and eigenvalues allows the determination of the analyticity dominion. The eigenvalue spectrum has a purely discrete part, laying on an interval of the imaginary axis of the K complex plane (the Fourier parameter), and another part, purely continuous, laying in the reminder of the imaginary axis. A correspondence between discrete eigenvalues and exponential modes of the Green Function, extemal properties for the eigenvalues and some remarkable properties of the eigenfunctions are established. (Author) 32 refs.

  3. Discussion of various flow calculation methods in high-speed centrifuges

    International Nuclear Information System (INIS)

    Louvet, P.; Cortet, C.

    1979-01-01

    The flow in high-speed centrifuges for the separation of uranium isotopes has been studied in the frame of linearized theory for long years. Three different methods have been derived for viscous compressible flow with small Ekman numbers and high Mach numbers: - numerical solution of flow equation by finite element method and Gaussian elimination (Centaure Code), - boundary layer theory using matched asymptotic expansions, - the so called eigenfunction method slightly modified. The mathematical assumptions, the easiness and the accuracy of the computations are compared. Numerical applications are performed successively for thermal countercurrent centrifuges with or without injections

  4. Dirac particle in a box, and relativistic quantum Zeno dynamics

    International Nuclear Information System (INIS)

    Menon, Govind; Belyi, Sergey

    2004-01-01

    After developing a complete set of eigenfunctions for a Dirac particle restricted to a box, the quantum Zeno dynamics of a relativistic system is considered. The evolution of a continuously observed quantum mechanical system is governed by the theorem put forth by Misra and Sudarshan. One of the conditions for quantum Zeno dynamics to be manifest is that the Hamiltonian is semi-bounded. This Letter analyzes the effects of continuous observation of a particle whose time evolution is generated by the Dirac Hamiltonian. The theorem by Misra and Sudarshan is not applicable here since the Dirac operator is not semi-bounded

  5. Scattering by a conducting elliptic cylinder with a multilayer dielectric coating

    Science.gov (United States)

    Caorsi, Salvatore; Pastorino, Matteo; Raffetto, Mirco

    1997-11-01

    A solution to the electromagnetic scattering of a transverse magnetic plane wave due to a perfectly conducting elliptic cylinder coated by a lossless, nonmagnetic, and elliptic multilayer dielectric is proposed. Despite the lack of orthogonality of the eigenfunctions of the field inside different layers, an efficient recursive procedure for the computation of the solution is devised. It is based on series expansions of the fields in terms of Mathieu functions and on a Galerkin approach. An outline of the procedure is given, and some numerical results, concerning both the field quantities and the radar cross section per unit length, are provided.

  6. Drift waves in a stellarator

    International Nuclear Information System (INIS)

    Bhattacharjee, A.; Sedlak, J.E.; Similon, P.L.; Rosenbluth, M.N.; Ross, D.W.

    1982-11-01

    We investigate the eigenmode structure of drift waves in a straight stellarator using the ballooning mode formalism. The electrons are assumed to be adiabatic and the ions constitute a cold, magnetized fluid. The effective potential has an overall parabolic envelope but is modulated strongly by helical ripples along B. We have found two classes of solutions: those that are strongly localized in local helical wells, and those that are weakly localized and have broad spatial extent. The weakly localized modes decay spatially due to the existence of Mathieu resonances between the periods of the eigenfunction and the effective potential

  7. Wentzel-Kramers-Brillouin method in the Bargmann representation. [of quantum mechanics

    Science.gov (United States)

    Voros, A.

    1989-01-01

    It is demonstrated that the Bargmann representation of quantum mechanics is ideally suited for semiclassical analysis, using as an example the WKB method applied to the bound-state problem in a single well of one degree of freedom. For the harmonic oscillator, this WKB method trivially gives the exact eigenfunctions in addition to the exact eigenvalues. For an anharmonic well, a self-consistent variational choice of the representation greatly improves the accuracy of the semiclassical ground state. Also, a simple change of scale illuminates the relationship of semiclassical versus linear perturbative expansions, allowing a variety of multidimensional extensions.

  8. Quantum Waveguide Properties of Bethe Lattices with a Ring

    International Nuclear Information System (INIS)

    Zhi-Ping, Lin; Zhi-Lin, Hou; You-Yan, Liu

    2008-01-01

    Based on waveguide theory we investigate electronic transport properties of Bethe lattices with a mesoscopic ring threaded by a magnetic flux. The generalized eigen-function method (GEM) is used to calculate the transmission and reflection coefficients up to the fifth generation of Bethe lattices. The relationships among the transmission coefficient T, magnetic flux φ and wave vector kl are investigated in detail. The numerical results are shown by the three-dimensional plots and contour maps. Some resonant-transmission features and the symmetry of the transmission coefficient T to flux φ are observed and discussed. (condensed matter: electronic structure, electrical, magnetic, and optical properties)

  9. ON THE USE OF FIELD THEORETICAL MODELS IN STRONG INTERACTION PHYSICS

    Energy Technology Data Exchange (ETDEWEB)

    Fubini, Sergio

    1963-06-15

    The effects of the short-range behavior in potential scattering upon the asymptotic behavior of the stronginteraction scattering amplitude and upon the validity of the methods of solution are discussed, using models. In particular, it is found that for certain singular potentials, the bound-state problem cannot be solved by a plane-wave expansion. For these singular potentials, an irtegral equation must be set up by means of an expansion in terms of eigenfunctions having the correct behavior at small distances. The study makes use of both the Schroedinger and Bethe-Salpeter equations. (T.F.H.)

  10. Test of the fermion dynamical symmetry model microscopy in the sd shell

    International Nuclear Information System (INIS)

    Halse, P.

    1987-01-01

    The recently formulated fermion dynamical symmetry model treats low-lying collective levels as states classified in a pseudo-orbit pseudo-spin (k-i) basis having either k = 1 and zero i seniority, or i = (3/2) and zero k seniority. The validity of this suggestion, which has not previously been subjected to a microscopic examination, is determined for even-even nuclei in the sd shell, for which the model is phenomenologically successful, by comparing these states with the eigenfunctions of a realistic Hamiltonian. Most low-lying levels are almost orthogonal to the fermion dynamical symmetry model zero seniority subspaces

  11. Canonically conjugate pairs and phase operators

    International Nuclear Information System (INIS)

    Schoenhammer, K.

    2002-01-01

    For quantum mechanics on a lattice the position ('particle number') operator and the quasimomentum ('phase') operator obey canonical commutation relations (CCRs) only on a dense set of the Hilbert space. We compare exact numerical results for a particle in a linear and a quadratic potential on the lattice with the expectations, when the CCRs are assumed to be strictly obeyed. Only for sufficiently smooth eigenfunctions does this lead to reasonable results. In the long time limit the use of the CCRs can lead to a qualitatively wrong dynamics even if the initial state is in the dense set

  12. Three identical particles on a line: comparison of some exact and approximate calculations

    International Nuclear Information System (INIS)

    Chuluunbaatar, O.; Gusev, A.A.; Vinitsky, S.I.; Larsen, S.Y.

    2002-01-01

    The three-body scattering problem is formulated in the adiabatic representation as a multi-channel spectral problem for a set of coupled one-dimensional integral equations. New stable variational-iteration schemes are developed to calculate the Hamiltonian eigenfunctions and energy eigenvalues, as well as the reaction matrix in the eigenphase shift representation, with prescribed accuracy. The convergence and efficiency of the method are demonstrated in the vicinity of the three-body threshold in the exactly solvable model of three identical particles fixed on a line and coupled with pair-repulsive or attractive zero-range potentials. (author). Letter-to-the-editor

  13. Hydrogen atoms in the presence of a homogeneous magnetic field

    International Nuclear Information System (INIS)

    Brandi, H.S.; Koiller, B.

    1978-01-01

    A variational scheme to obtain the spectrum of the hydrogen atom in the presence of an external homogeneous magnetic field is proposed. Two different sets of basis function to diagonalize the Hamiltonian describing the system are used, namely the eigenfunctions of the free hydrogen atom and of the three-dimensional harmonic oscillator; both having their radial coordinates properly scaled by a variational parammeter. Because of its characteristics, the present approach is suitable to describe the ground state as well as an infinite number of excited states also for a wide range of magnetic field strengths [pt

  14. Investigation of band structure of {sup 103,105}Rh using microscopic computational technique

    Energy Technology Data Exchange (ETDEWEB)

    Kumar, Amit, E-mail: akbcw2@gmail.com [Research Scholar, Department of Physics and Electronics, University of Jammu, Jammu-180006 (India); Singh, Suram, E-mail: suramsingh@gmail.com [Assistant Professor, Department of Physics Govt. Degree College, Kathua-184142 (India); Bharti, Arun, E-mail: arunbharti-2003@yahoo.co.in [Professor, Department of Physics and Electronics, University of Jammu, Jammu-180006 (India)

    2015-08-28

    The high-spin structure in {sup 61}Cu nucleus is studied in terms of effective two body interaction. In order to take into account the deformed BCS basis, the basis states are expanded in terms of the core eigenfunctions. Yrast band with some other bands havew been obtained and back-bending in moment of inertia has also been calculated and compared with the available experimental data for {sup 61}Cu nucleus. On comparing the available experimental as well as other theoretical data, it is found that the treatment with PSM provides a satisfactory explanation of the available data.

  15. Plane waves and structures in turbulent channel flow

    Science.gov (United States)

    Sirovich, L.; Ball, K. S.; Keefe, L. R.

    1990-01-01

    A direct simulation of turbulent flow in a channel is analyzed by the method of empirical eigenfunctions (Karhunen-Loeve procedure, proper orthogonal decomposition). This analysis reveals the presence of propagating plane waves in the turbulent flow. The velocity of propagation is determined by the flow velocity at the location of maximal Reynolds stress. The analysis further suggests that the interaction of these waves appears to be essential to the local production of turbulence via bursting or sweeping events in the turbulent boundary layer, with the additional suggestion that the fast acting plane waves act as triggers.

  16. Stark effect in a hydrogenic atom or ion treated by the phase-integral method with adjoined papers by A. Hökback and P. O. Fröman

    CERN Document Server

    Fröman, Nanny

    2008-01-01

    This book treats the Stark effect of a hydrogenic atom or ion in a homogeneous electric field. It begins with a thorough review of previous work in this field since 1926. After the Schrödinger equation has been separated with respect to time dependence, centre of mass motion and internal motion, followed by a discussion of its eigenfunctions, the exact development in time of the probability amplitude for a decaying state is obtained by means of a formula analogous to the Fock-Krylov theorem. From this formula one obtains by means of the phase-integral approximation generated from a particular

  17. Criticality problems in energy dependent neutron transport theory

    International Nuclear Information System (INIS)

    Victory, H.D. Jr.

    1979-01-01

    The criticality problem is considered for energy dependent neutron transport in an isotropically scattering, homogeneous slab. Under a positivity assumption on the scattering kernel, an expression can be found relating the thickness of the slab to a parameter characterizing production by fission. This is accomplished by exploiting the Perron-Frobenius-Jentsch characterization of positive operators (i.e. those leaving invariant a normal, reproducing cone in a Banach space). It is pointed out that those techniques work for classes of multigroup problems were the Case singular eigenfunction approach is not as feasible as in the one-group theory, which is also analyzed

  18. Superintegrability of d-dimensional conformal blocks

    International Nuclear Information System (INIS)

    Isachenkov, Mikhail

    2016-02-01

    We observe that conformal blocks of scalar 4-point functions in a d-dimensional conformal field theory can mapped to eigenfunctions of a 2-particle hyperbolic Calogero-Sutherland Hamiltonian. The latter describes two coupled Poeschl-Teller particles. Their interaction, whose strength depends smoothly on the dimension d, is known to be superintegrable. Our observation enables us to exploit the rich mathematical literature on Calogero-Sutherland models in deriving various results for conformal field theory. These include an explicit construction of conformal blocks in terms of Heckman-Opdam hypergeometric functions and a remarkable duality that relates the blocks of theories in different dimensions.

  19. Perturbation methods for power and reactivity reconstruction

    International Nuclear Information System (INIS)

    Palmiotti, G.; Salvatores, M.; Estiot, J.C.; Broccoli, U.; Bruna, G.; Gomit, J.M.

    1987-01-01

    This paper deals with recent developments and applications in perturbation methods. Two types of methods are used. The first one is an explicit method, which allows the explicit reconstruction of a perturbed flux using a linear combination of a library of functions. In our application, these functions are the harmonics (i.e. the high order eigenfunctions of the system). The second type is based on the Generalized Perturbation Theory GPT and needs the calculation of an importance function for each integral parameter of interest. Recent developments of a particularly useful high order formulation allows to obtain satisfactory results also for very large perturbations

  20. Adaptively Learning an Importance Function Using Transport Constrained Monte Carlo

    International Nuclear Information System (INIS)

    Booth, T.E.

    1998-01-01

    It is well known that a Monte Carlo estimate can be obtained with zero-variance if an exact importance function for the estimate is known. There are many ways that one might iteratively seek to obtain an ever more exact importance function. This paper describes a method that has obtained ever more exact importance functions that empirically produce an error that is dropping exponentially with computer time. The method described herein constrains the importance function to satisfy the (adjoint) Boltzmann transport equation. This constraint is provided by using the known form of the solution, usually referred to as the Case eigenfunction solution