Methods and applications of analytical perturbation theory
International Nuclear Information System (INIS)
Kirchgraber, U.; Stiefel, E.
1978-01-01
This monograph on perturbation theory is based on various courses and lectures held by the authors at the ETH, Zurich and at the University of Texas, Austin. Its principal intention is to inform application-minded mathematicians, physicists and engineers about recent developments in this field. The reader is not assumed to have mathematical knowledge beyond what is presented in standard courses on analysis and linear algebra. Chapter I treats the transformations of systems of differential equations and the integration of perturbed systems in a formal way. These tools are applied in Chapter II to celestial mechanics and to the theory of tops and gyroscopic motion. Chapter III is devoted to the discussion of Hamiltonian systems of differential equations and exposes the algebraic aspects of perturbation theory showing also the necessary modifications of the theory in case of singularities. The last chapter gives the mathematical justification for the methods developed in the previous chapters and investigates important questions such as error estimations for the solutions and asymptotic stability. Each chapter ends with useful comments and an extensive reference to the original literature. (HJ) [de
International Nuclear Information System (INIS)
Bartlett, R.; Kirtman, B.; Davidson, E.R.
1978-01-01
After noting some advantages of using perturbation theory some of the various types are related on a chart and described, including many-body nonlinear summations, quartic force-field fit for geometry, fourth-order correlation approximations, and a survey of some recent work. Alternative initial approximations in perturbation theory are also discussed. 25 references
Generalized perturbation theory (GPT) methods. A heuristic approach
International Nuclear Information System (INIS)
Gandini, A.
1987-01-01
Wigner first proposed a perturbation theory as early as 1945 to study fundamental quantities such as the reactivity worths of different materials. The first formulation, CPT, for conventional perturbation theory is based on universal quantum mechanics concepts. Since that early conception, significant contributions have been made to CPT, in particular, Soodak, who rendered a heuristic interpretation of the adjoint function, (referred to as the GPT method for generalized perturbation theory). The author illustrates the GPT methodology in a variety of linear and nonlinear domains encountered in nuclear reactor analysis. The author begins with the familiar linear neutron field and then generalizes the methodology to other linear and nonlinear fields, using heuristic arguments. The author believes that the inherent simplicity and elegance of the heuristic derivation, although intended here for reactor physics problems might be usefully adopted in collateral fields and includes such examples
Variational configuration interaction methods and comparison with perturbation theory
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Pople, J.A.; Seeger, R.; Krishnan, R.
1977-01-01
A configuration interaction (CI) procedure which includes all single and double substitutions from an unrestricted Hartree-Fock single determinant is described. This has the feature that Moller-Plesset perturbation results to second and third order are obtained in the first CI iterative cycle. The procedure also avoids the necessity of a full two-electron integral transformation. A simple expression for correcting the final CI energy for lack of size consistency is proposed. Finally, calculations on a series of small molecules are presented to compare these CI methods with perturbation theory
Foundations of quantum chromodynamics: Perturbative methods in gauge theories
International Nuclear Information System (INIS)
Muta, T.
1986-01-01
This volume develops the techniques of perturbative QCD in great detail starting with field theory. Aside from extensive treatments of the renormalization group technique, the operator product expansion formalism and their applications to short-distance reactions, this book provides a comprehensive introduction to gauge field theories. Examples and exercises are provided to amplify the discussions on important topics. Contents: Introduction; Elements of Quantum Chromodynamics; The Renormalization Group Method; Asymptotic Freedom; Operator Product Expansion Formalism; Applications; Renormalization Scheme Dependence; Factorization Theorem; Further Applications; Power Corrections; Infrared Problem. Power Correlations; Infrared Problem
Developments in perturbation theory
International Nuclear Information System (INIS)
Greenspan, E.
1976-01-01
Included are sections dealing with perturbation expressions for reactivity, methods for the calculation of perturbed fluxes, integral transport theory formulations for reactivity, generalized perturbation theory, sensitivity and optimization studies, multigroup calculations of bilinear functionals, and solution of inhomogeneous Boltzmann equations with singular operators
Developing feasible loading patterns using perturbation theory methods
International Nuclear Information System (INIS)
White, J.R.; Avila, K.M.
1990-01-01
This work illustrates an approach to core reload design that combines the power of integer programming with the efficiency of generalized perturbation theory. The main use of the method is as a tool to help the design engineer identify feasible loading patterns with minimum time and effort. The technique is highly successful for the burnable poison (BP) loading problem, but the unpredictable behavior of the branch-and-bound algorithm degrades overall performance for large problems. Unfortunately, the combined fuel shuffling plus BP optimization problem falls into this latter classification. Overall, however, the method shows great promise for significantly reducing the manpower time required for the reload design process. And it may even give the further benefit of better designs and improved performance
Numerical perturbative methods in the quantum theory of physical systems
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Adam, G.
1980-01-01
During the last two decades, development of digital electronic computers has led to the deployment of new, distinct methods in theoretical physics. These methods, based on the advances of modern numerical analysis as well as on specific equations describing physical processes, enabled to perform precise calculations of high complexity which have completed and sometimes changed our image of many physical phenomena. Our efforts have concentrated on the development of numerical methods with such intrinsic performances as to allow a successful approach of some Key issues in present theoretical physics on smaller computation systems. The basic principle of such methods is to translate, in numerical analysis language, the theory of perturbations which is suited to numerical rather than to analytical computation. This idea has been illustrated by working out two problems which arise from the time independent Schroedinger equation in the non-relativistic approximation, within both quantum systems with a small number of particles and systems with a large number of particles, respectively. In the first case, we are led to the numerical solution of some quadratic ordinary differential equations (first section of the thesis) and in the second case, to the solution of some secular equations in the Brillouin area (second section). (author)
An Introduction to Perturbative Methods in Gauge Theories
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T Muta
1998-01-01
This volume develops the techniques of perturbative QCD in great pedagogical detail starting with field theory. Aside from extensive treatments of the renormalization group technique, the operator product expansion formalism and their applications to short-distance reactions, this book provides a comprehensive introduction to gauge theories. Examples and exercises are provided to amplify the discussions on important topics. This is an ideal textbook on the subject of quantum chromodynamics and is essential for researchers and graduate students in high energy physics, nuclear physics and mathematical physics
Lattice field theories: non-perturbative methods of analysis
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Weinstein, M.
1978-01-01
A lecture is given on the possible extraction of interesting physical information from quantum field theories by studying their semiclassical versions. From the beginning the problem of solving for the spectrum states of any given continuum quantum field theory is considered as a giant Schroedinger problem, and then some nonperturbative methods for diagonalizing the Hamiltonian of the theory are explained without recourse to semiclassical approximations. The notion of a lattice appears as an artifice to handle the problems associated with the familiar infrared and ultraviolet divergences of continuum quantum field theory and in fact for all but gauge theories. 18 references
Generalized perturbation theory based on the method of cyclic characteristics
Energy Technology Data Exchange (ETDEWEB)
Assawaroongruengchot, M.; Marleau, G. [Institut de Genie Nucleaire, Departement de Genie Physique, Ecole Polytechnique de Montreal, 2900 Boul. Edouard-Montpetit, Montreal, Que. H3T 1J4 (Canada)
2006-07-01
A GPT algorithm for estimation of eigenvalues and reaction-rate ratios is developed for the neutron transport problems in 2D fuel assemblies with isotropic scattering. In our study the GPT formulation is based on the integral transport equations. The mathematical relationship between the generalized flux importance and generalized source importance functions is applied to transform the generalized flux importance transport equations into the integro-differential forms. The resulting adjoint and generalized adjoint transport equations are then solved using the method of cyclic characteristics (MOCC). Because of the presence of negative adjoint sources, a biasing/decontamination scheme is applied to make the generalized adjoint functions positive in such a way that it can be used for the multigroup re-balance technique. To demonstrate the efficiency of the algorithms, perturbative calculations are performed on a 17 x 17 PWR lattice. (authors)
Generalized perturbation theory based on the method of cyclic characteristics
International Nuclear Information System (INIS)
Assawaroongruengchot, M.; Marleau, G.
2006-01-01
A GPT algorithm for estimation of eigenvalues and reaction-rate ratios is developed for the neutron transport problems in 2D fuel assemblies with isotropic scattering. In our study the GPT formulation is based on the integral transport equations. The mathematical relationship between the generalized flux importance and generalized source importance functions is applied to transform the generalized flux importance transport equations into the integro-differential forms. The resulting adjoint and generalized adjoint transport equations are then solved using the method of cyclic characteristics (MOCC). Because of the presence of negative adjoint sources, a biasing/decontamination scheme is applied to make the generalized adjoint functions positive in such a way that it can be used for the multigroup re-balance technique. To demonstrate the efficiency of the algorithms, perturbative calculations are performed on a 17 x 17 PWR lattice. (authors)
International Nuclear Information System (INIS)
Killingbeck, J.
1979-01-01
By using the methods of perturbation theory it is possible to construct simple formulae for the numerical integration of the Schroedinger equation, and also to calculate expectation values solely by means of simple eigenvalue calculations. (Auth.)
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Santos, Adimir dos; Borges, A.A.
2000-01-01
A new method for the calculation of sensitivity coefficients is developed. The new method is a combination of two methodologies used for calculating these coefficients, which are the differential and the generalized perturbation theory methods. The proposed method utilizes as integral parameter the average flux in an arbitrary region of the system. Thus, the sensitivity coefficient contains only the component corresponding to the neutron flux. To obtain the new sensitivity coefficient, the derivates of the integral parameter, φ(ξ), with respect to σ are calculated using the perturbation method and the functional derivates of this generic integral parameter with respect to σ and φ are calculated using the differential method. The new method merges the advantages of the differential and generalized perturbation theory methods and eliminates their disadvantages. (author)
New numerical method for iterative or perturbative solution of quantum field theory
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Hahn, S.C.; Guralnik, G.S.
1999-01-01
A new computational idea for continuum quantum Field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating fermions on a relatively symmetric footing with bosons. As a spin-off of the technology developed for 'exact' solutions, the numerical methods used have a special case application to perturbation theory. We are in the process of developing an entirely numerical approach to evaluating graphs to high perturbative order. (authors)
International Nuclear Information System (INIS)
Borges, Antonio Andrade
1998-01-01
A new method for the calculation of sensitivity coefficients is developed. The new method is a combination of two methodologies used for calculating theses coefficients, which are the differential and the generalized perturbation theory methods. The method utilizes as integral parameter the average flux in an arbitrary region of the system. Thus, the sensitivity coefficient contains only the component corresponding to the neutron flux. To obtain the new sensitivity coefficient, the derivatives of the integral parameter, Φ, with respect to σ are calculated using the perturbation method and the functional derivatives of this generic integral parameter with respect to σ and Φ are calculated using the differential method. (author)
The method of rigged spaces in singular perturbation theory of self-adjoint operators
Koshmanenko, Volodymyr; Koshmanenko, Nataliia
2016-01-01
This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadra...
A computational chemistry analysis of six unique tautomers of cyromazine, a pesticide used for fly control, was performed with density functional theory (DFT) and canonical second order Møller–Plesset perturbation theory (MP2) methods to gain insight into the contributions of molecular structure to ...
Generalized chiral perturbation theory
International Nuclear Information System (INIS)
Knecht, M.; Stern, J.
1994-01-01
The Generalized Chiral Perturbation Theory enlarges the framework of the standard χPT (Chiral Perturbation Theory), relaxing certain assumptions which do not necessarily follow from QCD or from experiment, and which are crucial for the usual formulation of the low energy expansion. In this way, experimental tests of the foundations of the standard χPT become possible. Emphasis is put on physical aspects rather than on formal developments of GχPT. (author). 31 refs
Superfield perturbation theory and renormalization
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Delbourgo, R.
1975-01-01
The perturbation theory graphs and divergences in super-symmetric Lagrangian models are studied by using superfield techniques. In super PHI 3 -theory very little effort is needed to arrive at the single infinite (wave function) renormalization counterterm, while in PHI 4 -theory the method indicates the counter-Lagrangians needed at the one-loop level and possibly beyond
Perturbation theory from stochastic quantization
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Hueffel, H.
1984-01-01
By using a diagrammatical method it is shown that in scalar theories the stochastic quantization method of Parisi and Wu gives the usual perturbation series in Feynman diagrams. It is further explained how to apply the diagrammatical method to gauge theories, discussing the origin of ghost effects. (Author)
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Ecker, G.
1996-06-01
After a general introduction to the structure of effective field theories, the main ingredients of chiral perturbation theory are reviewed. Applications include the light quark mass ratios and pion-pion scattering to two-loop accuracy. In the pion-nucleon system, the linear σ model is contrasted with chiral perturbation theory. The heavy-nucleon expansion is used to construct the effective pion-nucleon Lagrangian to third order in the low-energy expansion, with applications to nucleon Compton scattering. (author)
String perturbation theory diverges
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Gross, D.J.; Periwal, V.
1988-01-01
We prove that perturbation theory for the bosonic string diverges for arbitrary values of the coupling constant and is not Borel summable. This divergence is independent of the existence of the infinities that occur in the theory due to the presence of tachyons and dilaton tadpoles. We discuss the physical implications of such a divergence
Instantaneous stochastic perturbation theory
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Lüscher, Martin
2015-01-01
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.
Large-order perturbation theory
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Wu, T.T.
1982-01-01
The original motivation for studying the asymptotic behavior of the coefficients of perturbation series came from quantum field theory. An overview is given of some of the attempts to understand quantum field theory beyond finite-order perturbation series. At least is the case of the Thirring model and probably in general, the full content of a relativistic quantum field theory cannot be recovered from its perturbation series. This difficulty, however, does not occur in quantum mechanics, and the anharmonic oscillator is used to illustrate the methods used in large-order perturbation theory. Two completely different methods are discussed, the first one using the WKB approximation, and a second one involving the statistical analysis of Feynman diagrams. The first one is well developed and gives detailed information about the desired asymptotic behavior, while the second one is still in its infancy and gives instead information about the distribution of vertices of the Feynman diagrams
Nayfeh, Ali H
2008-01-01
1. Introduction 1 2. Straightforward Expansions and Sources of Nonuniformity 23 3. The Method of Strained Coordinates 56 4. The Methods of Matched and Composite Asymptotic Expansions 110 5. Variation of Parameters and Methods of Averaging 159 6. The Method of Multiple Scales 228 7. Asymptotic Solutions of Linear Equations 308 References and Author Index 387 Subject Index 417
DeVille, R. E. Lee; Harkin, Anthony; Holzer, Matt; Josić, Krešimir; Kaper, Tasso J.
2008-06-01
For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. E. 49 (1994) 4502-4511] has been shown to be an effective general approach for deriving reduced or amplitude equations that govern the long time dynamics of the system. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the Poincaré-Lindstedt method, the method of averaging, and others. In this article, we show how the RG method may be used to generate normal forms for large classes of ordinary differential equations. First, we apply the RG method to systems with autonomous perturbations, and we show that the reduced or amplitude equations generated by the RG method are equivalent to the classical Poincaré-Birkhoff normal forms for these systems up to and including terms of O(ɛ2), where ɛ is the perturbation parameter. This analysis establishes our approach and generalizes to higher order. Second, we apply the RG method to systems with nonautonomous perturbations, and we show that the reduced or amplitude equations so generated constitute time-asymptotic normal forms, which are based on KBM averages. Moreover, for both classes of problems, we show that the main coordinate changes are equivalent, up to translations between the spaces in which they are defined. In this manner, our results show that the RG method offers a new approach for deriving normal forms for nonautonomous systems, and it offers advantages since one can typically more readily identify resonant terms from naive perturbation expansions than from the nonautonomous vector fields themselves. Finally, we establish how well the solution to the RG equations approximates the solution of the original equations on time scales of O(1/ɛ).
Core design and operation optimization methods based on time-dependent perturbation theory
International Nuclear Information System (INIS)
Greenspan, E.
1983-08-01
A general approach for the optimization of nuclear reactor core design and operation is outlined; it is based on two cornerstones: a newly developed time-dependent (or burnup-dependent) perturbation theory for nonlinear problems and a succesive iteration technique. The resulting approach is capable of handling realistic reactor models using computational methods of any degree of sophistication desired, while accounting for all the constraints imposed. Three general optimization strategies, different in the way for handling the constraints, are formulated. (author)
Nonperturbative perturbation theory
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Bender, C.M.
1989-01-01
In this talk we describe a recently proposed graphical perturbative calculational scheme for quantum field theory. The basic idea is to expand in the power of the interaction term. For example, to solve a λφ 4 theory in d-dimensional space-time, we introduce a small parameter δ and consider a λ(φ 2 ) 1+δ field theory. We show how to expand such a theory as a series in powers of δ. The resulting perturbation series appears to have a finite radius of convergence and numerical results for low-dimensional models are good. We have computed the two-point and four-point Green's functions to second order in powers of δ and the 2n-point Green's functions (n>2) to order δ. We explain how to renormalize the theory and show that, to first order in powers of δ, when δ>0 and d≥4 the theory is free. This conclusion remains valid to second order in powers of δ, and we believe that it remains valid to all orders in powers of δ. The new perturbative scheme is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not know of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0. (orig.)
The theory of singular perturbations
De Jager, E M
1996-01-01
The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat
Principles of chiral perturbation theory
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Leutwyler, H.
1995-01-01
An elementary discussion of the main concepts used in chiral perturbation theory is given in textbooks and a more detailed picture of the applications may be obtained from the reviews. Concerning the foundations of the method, the literature is comparatively scarce. So, I will concentrate on the basic concepts and explain why the method works. (author)
Perturbative method for the derivation of quantum kinetic theory based on closed-time-path formalism
International Nuclear Information System (INIS)
Koide, Jun
2002-01-01
Within the closed-time-path formalism, a perturbative method is presented, which reduces the microscopic field theory to the quantum kinetic theory. In order to make this reduction, the expectation value of a physical quantity must be calculated under the condition that the Wigner distribution function is fixed, because it is the independent dynamical variable in the quantum kinetic theory. It is shown that when a nonequilibrium Green function in the form of the generalized Kadanoff-Baym ansatz is utilized, this condition appears as a cancellation of a certain part of contributions in the diagrammatic expression of the expectation value. Together with the quantum kinetic equation, which can be derived in the closed-time-path formalism, this method provides a basis for the kinetic-theoretical description
Optimization of Candu fuel management with gradient methods using generalized perturbation theory
International Nuclear Information System (INIS)
Chambon, R.; Varin, E.; Rozon, D.
2005-01-01
CANDU fuel management problems are solved using time-average representation of the core. Optimization problems based on this representation have been defined in the early nineties. The mathematical programming using the generalized perturbation theory (GPT) that was developed has been implemented in the reactor code DONJON. The use of the augmented Lagrangian (AL) method is presented and evaluated in this paper. This approach is mandatory for new constraint problems. Combined with the classical Lemke method, it proves to be very efficient to reach optimal solution in a very limited number of iterations. (authors)
Perturbation theory in large order
International Nuclear Information System (INIS)
Bender, C.M.
1978-01-01
For many quantum mechanical models, the behavior of perturbation theory in large order is strikingly simple. For example, in the quantum anharmonic oscillator, which is defined by -y'' + (x 2 /4 + ex 4 /4 - E) y = 0, y ( +- infinity) = 0, the perturbation coefficients, A/sub n/, in the expansion for the ground-state energy, E(ground state) approx. EPSILON/sub n = 0//sup infinity/ A/sub n/epsilon/sup n/, simplify dramatically as n → infinity: A/sub n/ approx. (6/π 3 )/sup 1/2/(-3)/sup n/GAMMA(n + 1/2). Methods of applied mathematics are used to investigate the nature of perturbation theory in quantum mechanics and show that its large-order behavior is determined by the semiclassical content of the theory. In quantum field theory the perturbation coefficients are computed by summing Feynman graphs. A statistical procedure in a simple lambda phi 4 model for summing the set of all graphs as the number of vertices → infinity is presented. Finally, the connection between the large-order behavior of perturbation theory in quantum electrodynamics and the value of α, the charge on the electron, is discussed. 7 figures
Perturbative coherence in field theory
International Nuclear Information System (INIS)
Aldrovandi, R.; Kraenkel, R.A.
1987-01-01
A general condition for coherent quantization by perturbative methods is given, because the basic field equations of a fild theory are not always derivable from a Lagrangian. It's seen that non-lagrangian models way have well defined vertices, provided they satisfy what they call the 'coherence condition', which is less stringent than the condition for the existence of a Lagrangian. They note that Lagrangian theories are perturbatively coherent, in the sense that they have well defined vertices, and that they satisfy automatically that condition. (G.D.F.) [pt
Geometric Hamiltonian structures and perturbation theory
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Omohundro, S.
1984-08-01
We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging
Renormalized Lie perturbation theory
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Rosengaus, E.; Dewar, R.L.
1981-07-01
A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another
International Nuclear Information System (INIS)
Harada, Masayasu
2009-01-01
Chiral perturbation theory has been used for great number of phenomenological analyses in low energy QCD as well as the lattice QCD analyses since the creation of the theory by Weinberg in 1979 followed by its consolidation by Gasser and Leutwyler in 1984 and 85. The theory is now the highly established one as the approach based on the effective field theory to search for Green function including quantum correlations in the frame of the systematic expansion technique using Lagrangian which includes all of the terms allowed by the symmetry. This review has been intended to describe how systematically physical quantities are calculated in the framework of the chiral symmetry. Consequently many of the various phenomenological analyses are not taken up here for which other reports are to be referred. Further views are foreseen to be developed based on the theory in addition to numbers of results reported up to the present. Finally π-π scattering is taken up to discuss to what energy scale the theory is available. (S. Funahashi)
Perturbation theory with instantons
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Carruthers, P.; Pinsky, S.S.; Zachariasen, F.
1977-05-01
''Perturbation theory'' rules are developed for calculating the effect of instantons in a pure Yang-Mills theory with no fermions, in the ''dilute gas'' approximation in which the N-instanton solution is assumed to be the sum of N widely separated one-instanton solutions. These rules are then used to compute the gluon propagator and proper vertex function including all orders of the instanton interaction but only to lowest order in the gluon coupling. It is to be expected that such an approximation is valid only for momenta q larger than the physical mass μ. The result is that in this regime instantons cause variations in the propagator and vertex of the form (μ 2 /q 2 )/sup -8π 2 b/ where b is the coefficient in the expansion of the β function: β = bg 3 +...
Analysis of 2D reactor core using linear perturbation theory and nodal finite element methods
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Adrian Mugica; Edmundo del Valle
2005-01-01
In this work the multigroup steady state neutron diffusion equations are solved using the nodal finite element method (NFEM) and the Linear Perturbation Theory (LPT) for XY geometry. The NFEM used corresponds to the Raviart-Thomas schemes RT0 and RT1, interpolating 5 and 12 parameters respectively in each node of the space discretization. The accuracy of these methods is related with the dimension of the space approximation and the mesh size. Therefore, using fine meshes and the RT0 or RT1 nodal methods leads to a large an interesting eigenvalue problem. The finite element method used to discretize the weak formulation of the diffusion equations is the Galerkin one. The algebraic structure of the discrete eigenvalue problem is obtained and solved using the Wielandt technique and the BGSTAB iterative method using the SPARSKIT package developed by Yousef Saad. The results obtained with LPT show good agreement with the results obtained directly for the perturbed problem. In fact, the cpu time to solve a single problem, the unperturbed and the perturbed one, is practically the same but when one is focused in shuffling many times two different assemblies in the core then the LPT technique becomes quite useful to get good approximations in a short time. This particular problem was solved for one quarter-core with NFEM. Thus, the computer program based on LPT can be used to perform like an analysis tool in the fuel reload optimization or combinatory analysis to get reload patterns in nuclear power plants once that it had been incorporated with the thermohydraulic aspects needed to simulate accurately a real problem. The maximum differences between the NFEM and LPT for the three LWR reactor cores are about 250 pcm. This quantity is considered an acceptable value for this kind of analysis. (authors)
Instantons and large N an introduction to non-perturbative methods in quantum field theory
Marino, Marcos
2015-01-01
This highly pedagogical textbook for graduate students in particle, theoretical and mathematical physics, explores advanced topics of quantum field theory. Clearly divided into two parts; the first focuses on instantons with a detailed exposition of instantons in quantum mechanics, supersymmetric quantum mechanics, the large order behavior of perturbation theory, and Yang-Mills theories, before moving on to examine the large N expansion in quantum field theory. The organised presentation style, in addition to detailed mathematical derivations, worked examples and applications throughout, enables students to gain practical experience with the tools necessary to start research. The author includes recent developments on the large order behaviour of perturbation theory and on large N instantons, and updates existing treatments of classic topics, to ensure that this is a practical and contemporary guide for students developing their understanding of the intricacies of quantum field theory.
International Nuclear Information System (INIS)
Rossi, Lubianka Ferrari Russo
2014-01-01
The main target of this study is to introduce a new method for calculating the coefficients of sensibility through the union of differential method and generalized perturbation theory, which are the two methods generally used in reactor physics to obtain such variables. These two methods, separated, have some issues turning the sensibility coefficients calculation slower or computationally exhaustive. However, putting them together, it is possible to repair these issues and build a new equation for the coefficient of sensibility. The method introduced in this study was applied in a PWR reactor, where it was performed the sensibility analysis for the production and 239 Pu conversion rate during 120 days (1 cycle) of burnup. The computational code used for both burnup and sensibility analysis, the CINEW, was developed in this study and all the results were compared with codes widely used in reactor physics, such as CINDER and SERPENT. The new mathematical method for calculating the sensibility coefficients and the code CINEW provide good numerical agility and also good efficiency and security, once the new method, when compared with traditional ones, provide satisfactory results, even when the other methods use different mathematical approaches. The burnup analysis, performed using the code CINEW, was compared with the code CINDER, showing an acceptable variation, though CINDER presents some computational issues due to the period it was built. The originality of this study is the application of such method in problems involving temporal dependence and, not least, the elaboration of the first national code for burnup and sensitivity analysis. (author)
Application of perturbation theory to lattice calculations based on method of cyclic characteristics
Assawaroongruengchot, Monchai
Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the
Application of perturbation theory to lattice calculations based on method of cyclic characteristics
Energy Technology Data Exchange (ETDEWEB)
Assawaroongruengchot, M
2007-07-01
Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the
Application of perturbation theory to lattice calculations based on method of cyclic characteristics
International Nuclear Information System (INIS)
Assawaroongruengchot, M.
2007-01-01
Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the
Lattice regularized chiral perturbation theory
International Nuclear Information System (INIS)
Borasoy, Bugra; Lewis, Randy; Ouimet, Pierre-Philippe A.
2004-01-01
Chiral perturbation theory can be defined and regularized on a spacetime lattice. A few motivations are discussed here, and an explicit lattice Lagrangian is reviewed. A particular aspect of the connection between lattice chiral perturbation theory and lattice QCD is explored through a study of the Wess-Zumino-Witten term
Continual integral in perturbation theory
International Nuclear Information System (INIS)
Slavnov, A.A.
1975-01-01
It is shown that all results obtained by means of continual integration within the framework of perturbation theory are completely equivalent to those obtained by the usual diagram technique and are therfore just as rigorous. A rigorous justification is given for the rules for operating with continual integrals in perturbation theory. (author)
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)
Perturbation theory corrections to the two-particle reduced density matrix variational method.
Juhasz, Tamas; Mazziotti, David A
2004-07-15
In the variational 2-particle-reduced-density-matrix (2-RDM) method, the ground-state energy is minimized with respect to the 2-particle reduced density matrix, constrained by N-representability conditions. Consider the N-electron Hamiltonian H(lambda) as a function of the parameter lambda where we recover the Fock Hamiltonian at lambda=0 and we recover the fully correlated Hamiltonian at lambda=1. We explore using the accuracy of perturbation theory at small lambda to correct the 2-RDM variational energies at lambda=1 where the Hamiltonian represents correlated atoms and molecules. A key assumption in the correction is that the 2-RDM method will capture a fairly constant percentage of the correlation energy for lambda in (0,1] because the nonperturbative 2-RDM approach depends more significantly upon the nature rather than the strength of the two-body Hamiltonian interaction. For a variety of molecules we observe that this correction improves the 2-RDM energies in the equilibrium bonding region, while the 2-RDM energies at stretched or nearly dissociated geometries, already highly accurate, are not significantly changed. At equilibrium geometries the corrected 2-RDM energies are similar in accuracy to those from coupled-cluster singles and doubles (CCSD), but at nonequilibrium geometries the 2-RDM energies are often dramatically more accurate as shown in the bond stretching and dissociation data for water and nitrogen. (c) 2004 American Institute of Physics.
Perturbation Theory of Embedded Eigenvalues
DEFF Research Database (Denmark)
Engelmann, Matthias
project gives a general and systematic approach to analytic perturbation theory of embedded eigenvalues. The spectral deformation technique originally developed in the theory of dilation analytic potentials in the context of Schrödinger operators is systematized by the use of Mourre theory. The group...... of dilations is thereby replaced by the unitary group generated y the conjugate operator. This then allows to treat the perturbation problem with the usual Kato theory.......We study problems connected to perturbation theory of embedded eigenvalues in two different setups. The first part deals with second order perturbation theory of mass shells in massive translation invariant Nelson type models. To this end an expansion of the eigenvalues w.r.t. fiber parameter up...
Discrete state perturbation theory via Green's functions
International Nuclear Information System (INIS)
Rubinson, W.
1975-01-01
The exposition of stationary-state perturbation theory via the Green's function method in Goldberger and Watson's Collision Theory is reworked in a way that makes explicit its mathematical basis. It is stressed that the theory consists of the construction of, and manipulations on, a mathematical identity. The perturbation series fall out of the identity almost immediately. The logical status of the method is commented on
Review of chiral perturbation theory
Indian Academy of Sciences (India)
Abstract. A review of chiral perturbation theory and recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.
Introduction to perturbation methods
Holmes, M
1995-01-01
This book is an introductory graduate text dealing with many of the perturbation methods currently used by applied mathematicians, scientists, and engineers. The author has based his book on a graduate course he has taught several times over the last ten years to students in applied mathematics, engineering sciences, and physics. The only prerequisite for the course is a background in differential equations. Each chapter begins with an introductory development involving ordinary differential equations. The book covers traditional topics, such as boundary layers and multiple scales. However, it also contains material arising from current research interest. This includes homogenization, slender body theory, symbolic computing, and discrete equations. One of the more important features of this book is contained in the exercises. Many are derived from problems of up- to-date research and are from a wide range of application areas.
Perturbation theory of effective Hamiltonians
International Nuclear Information System (INIS)
Brandow, B.H.
1975-01-01
This paper constitutes a review of the many papers which have used perturbation theory to derive ''effective'' or ''model'' Hamiltonians. It begins with a brief review of nondegenerate and non-many-body perturbation theory, and then considers the degenerate but non-many-body problem in some detail. It turns out that the degenerate perturbation problem is not uniquely defined, but there are some practical criteria for choosing among the various possibilities. Finally, the literature dealing with the linked-cluster aspects of open-shell many-body systems is reviewed. (U.S.)
Basics of QCD perturbation theory
International Nuclear Information System (INIS)
Soper, D.E.
1997-01-01
This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs
Basics of QCD perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Soper, D.E. [Univ. of Oregon, Eugene, OR (United States). Inst. of Theoretical Science
1997-06-01
This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs.
The power of perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Serone, Marco [SISSA International School for Advanced Studies and INFN Trieste, Via Bonomea 265, 34136, Trieste (Italy); Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy); Spada, Gabriele [SISSA International School for Advanced Studies and INFN Trieste, Via Bonomea 265, 34136, Trieste (Italy); Villadoro, Giovanni [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy)
2017-05-10
We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach based on the Picard-Lefschetz theory we characterize the conditions under which perturbative expansions lead to exact results. Even when such conditions are not met, we explain how to define a different perturbative expansion that reproduces the full answer without the need of transseries, i.e. non-perturbative effects, such as real (or complex) instantons. Applications to several quantum mechanical systems are presented.
Perturbation theory in light-cone gauge
International Nuclear Information System (INIS)
Vianello, Eliana
2000-01-01
Perturbation calculations are presented for the light-cone gauge Schwinger model. Eigenstates can be calculated perturbatively but the perturbation theory is nonstandard. We hope to extend the work to QCD 2 to resolve some outstanding issues in those theories
International Nuclear Information System (INIS)
Sabouri, Pouya
2013-01-01
This thesis presents a comprehensive study of sensitivity/uncertainty analysis for reactor performance parameters (e.g. the k-effective) to the base nuclear data from which they are computed. The analysis starts at the fundamental step, the Evaluated Nuclear Data File and the uncertainties inherently associated with the data they contain, available in the form of variance/covariance matrices. We show that when a methodical and consistent computation of sensitivity is performed, conventional deterministic formalisms can be sufficient to propagate nuclear data uncertainties with the level of accuracy obtained by the most advanced tools, such as state-of-the-art Monte Carlo codes. By applying our developed methodology to three exercises proposed by the OECD (Uncertainty Analysis for Criticality Safety Assessment Benchmarks), we provide insights of the underlying physical phenomena associated with the used formalisms. (author)
Status of chiral perturbation theory
International Nuclear Information System (INIS)
Ecker, G.
1996-10-01
A survey is made of semileptonic and nonleptonic kaon decays in the framework of chiral perturbation theory. The emphasis is on what has been done rather than how it was done. The theoretical predictions are compared with available experimental results. (author)
Cosmological perturbation theory and quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Brunetti, Romeo [Dipartimento di Matematica, Università di Trento,Via Sommarive 14, 38123 Povo TN (Italy); Fredenhagen, Klaus [II Institute für Theoretische Physik, Universität Hamburg,Luruper Chaussee 149, 22761 Hamburg (Germany); Hack, Thomas-Paul [Institute für Theoretische Physik, Universität Leipzig,Brüderstr. 16, 04103 Leipzig (Germany); Pinamonti, Nicola [Dipartimento di Matematica, Università di Genova,Via Dodecaneso 35, 16146 Genova (Italy); INFN, Sezione di Genova,Via Dodecaneso 33, 16146 Genova (Italy); Rejzner, Katarzyna [Department of Mathematics, University of York,Heslington, York YO10 5DD (United Kingdom)
2016-08-04
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.
Application of linear and higher perturbation theory in reactor physics
International Nuclear Information System (INIS)
Woerner, D.
1978-01-01
For small perturbations in the material composition of a reactor according to the first approximation of perturbation theory the eigenvalue perturbation is proportional to the perturbation of the system. This assumption is true for the neutron flux not influenced by the perturbance. The two-dimensional code LINESTO developed for such problems in this paper on the basis of diffusion theory determines the relative change of the multiplication constant. For perturbations varying the neutron flux in the space of energy and position the eigenvalue perturbation is also influenced by this changed neutron flux. In such cases linear perturbation theory yields larger errors. Starting from the methods of calculus of variations there is additionally developed in this paper a perturbation method of calculation permitting in a quick and simple manner to assess the influence of flux perturbation on the eigenvalue perturbation. While the source of perturbations is evaluated in isotropic approximation of diffusion theory the associated inhomogeneous equation may be used to determine the flux perturbation by means of diffusion or transport theory. Possibilities of application and limitations of this method are studied in further systematic investigations on local perturbations. It is shown that with the integrated code system developed in this paper a number of local perturbations may be checked requiring little computing time. With it flux perturbations in first approximation and perturbations of the multiplication constant in second approximation can be evaluated. (orig./RW) [de
Geometric perturbation theory and plasma physics
International Nuclear Information System (INIS)
Omohundro, S.M.
1985-01-01
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory, and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure in five different ways. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle-group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a long-standing question posed by Kruskal about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no adhoc elements, which is then applied to gyromotion. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A theory motivated by free electron lasers gives new restrictions on the change of area of projected parallelepipeds under canonical transformations
Chiral perturbation theory with nucleons
International Nuclear Information System (INIS)
Meissner, U.G.
1991-09-01
I review the constraints posed on the interactions of pions, nucleons and photons by the spontaneously broken chiral symmetry of QCD. The framework to perform these calculations, chiral perturbation theory, is briefly discussed in the meson sector. The method is a simultaneous expansion of the Greens functions in powers of external moments and quark masses around the massless case, the chiral limit. To perform this expansion, use is made of a phenomenological Lagrangian which encodes the Ward-identities and pertinent symmetries of QCD. The concept of chiral power counting is introduced. The main part of the lectures of consists in describing how to include baryons (nucleons) and how the chiral structure is modified by the fact that the nucleon mass in the chiral limit does not vanish. Particular emphasis is put on working out applications to show the strengths and limitations of the methods. Some processes which are discussed are threshold photopion production, low-energy compton scattering off nucleons, πN scattering and the σ-term. The implications of the broken chiral symmetry on the nuclear forces are briefly described. An alternative approach, in which the baryons are treated as very heavy fields, is touched upon
Infrared problems in field perturbation theory
International Nuclear Information System (INIS)
David, Francois.
1982-12-01
The work presented mainly covers questions related to the presence of ''infrared'' divergences in perturbation expansions of the Green functions of certain massless field theories. It is important to determine the mathematical status of perturbation expansions in field theory in order to define the region in which they are valid. Renormalization and the symmetry of a theory are important factors in infrared problems. The main object of this thesis resides in the mathematical techniques employed: integral representations of the Feynman amplitudes; methods for desingularization, regularization and dimensional renormalization. Nonlinear two dimensional space-time sigma models describing Goldstone's low energy boson dynamics associated with a breaking of continuous symmetry are studied. Random surface models are then investigated followed by infrared divergences in super-renormalizable theories. Finally, nonperturbation effects in massless theories are studied by expanding the two-dimensional nonlinear sigma model in 1/N [fr
New perturbative approach to renormalizable field theories
International Nuclear Information System (INIS)
Dhar, A.; Gupta, V.
1984-01-01
A new method for obtaining perturbative predictions in quantum field theory is developed. Our method gives finite predictions, which are free from scheme ambiguities, for any quantity of interest (like a cross section or a Green's function) starting directly from the bare regularized Lagrangian. The central idea in our approach is to incorporate directly the consequences of dimensional transmutation for the predictions of the theory. We thus completely bypass the conventional renormalization procedure and the ambiguities associated with it. The case of massless theories with a single dimensionless coupling constant is treated in detail to illustrate our approach
Geometric perturbation theory and plasma physics
Energy Technology Data Exchange (ETDEWEB)
Omohundro, S.M.
1985-04-04
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.
Geometric perturbation theory and plasma physics
International Nuclear Information System (INIS)
Omohundro, S.M.
1985-01-01
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism
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
"Phonon" scattering beyond perturbation theory
Qiu, WuJie; Ke, XueZhi; Xi, LiLi; Wu, LiHua; Yang, Jiong; Zhang, WenQing
2016-02-01
Searching and designing materials with intrinsically low lattice thermal conductivity (LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical- bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T -1 relationship ( T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.
Perturbation theory for Alfven wave
International Nuclear Information System (INIS)
Yoshida, Z.; Mahajan, S.M.
1995-01-01
The Alfven wave is the dominant low frequency transverse mode of a magnetized plasma. The Alfven wave propagation along the magnetic field, and displays a continuous spectrum even in a bounded plasma. This is essentially due to the degeneracy of the wave characteristics, i.e. the frequency (ω) is primarily determined by the wave number in the direction parallel to the ambient magnetic field (k parallel ) and is independent of the perpendicular wavenumbers. The characteristics, that are the direction along which the wave energy propagates, are identical to the ambient magnetic field lines. Therefore, the spectral structure of the Alfven wave has a close relationship with the geometric structure of the magnetic field lines. In an inhomogeneous plasma, the Alfven resonance constitutes a singularity for the defining wave equation; this results in a singular eigenfunction corresponding to the continuous spectrum. The aim of this review is to present an overview of the perturbation theory for the Alfven wave. Emphasis is placed on those perturbations of the continuous spectrum which lead to the creation of point spectra. Such qualitative changes in the spectrum are relevant to many plasma phenomena
Gravitational perturbation theory and synchrotron radiation
Energy Technology Data Exchange (ETDEWEB)
Breuer, R A [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany). Inst. fuer Astrophysik
1975-01-01
This article presents methods and results for a gravitational perturbation theory which treats massless fields as linearized perturbations of an arbitrary gravitational vacuum background spacetime. The formalism is outlined for perturbations of type (22) spacetimes. As an application, high-frequency radiation emitted by particles moving approximately on relativistic circular geodesic orbits is computed. More precisely, the test particle assumption is made; throughout it is therefore assumed that the reaction of the radiation on the particle motion is negligible. In particular, these orbits are studied in the gravitational field of a spherically symmetric (Schwarzschild-) black hole as well as of a rotating (Kerr-) black hole. In this model, the outgoing radiation is highly focussed and of much higher fequency than the orbital frequency, i.e. one is dealing with 'gravitational synchrotron radiation'.
Gribov ambiguity, perturbation theory, and confinement
International Nuclear Information System (INIS)
Greensite, J.P.
1978-01-01
The generating functional proposed for gauge theories by Bender, Eguchi, and Pagels (BEP) is shown to be equivalent to a truncated form of the functional integral, in which only one field configuration from each gauge-equivalent Gribov set contributes to the functional integration. The standard perturbation technique provides a method of realizing this truncation condition. It is shown that any gauge-covariant quantity (such as the quark N-point functions), evaluated by perturbating around a field configuration gauge-equivalent to A = 0, is related by a gauge transformation to the same quantity evaluated perturbatively around the trivial vacuum. It follows that, contrary to the conclusion of BEP, the existence of degeneracies in the Coulomb gauge-fixing condition (the Gribov ambiguity) is not directly related to the physics of confinement
Acoustic anisotropic wavefields through perturbation theory
Alkhalifah, Tariq Ali
2013-09-01
Solving the anisotropic acoustic wave equation numerically using finite-difference methods introduces many problems and media restriction requirements, and it rarely contributes to the ability to resolve the anisotropy parameters. Among these restrictions are the inability to handle media with η<0 and the presence of shear-wave artifacts in the solution. Both limitations do not exist in the solution of the elliptical anisotropic acoustic wave equation. Using perturbation theory in developing the solution of the anisotropic acoustic wave equation allows direct access to the desired limitation-free solutions, that is, solutions perturbed from the elliptical anisotropic background medium. It also provides a platform for parameter estimation because of the ability to isolate the wavefield dependency on the perturbed anisotropy parameters. As a result, I derive partial differential equations that relate changes in the wavefield to perturbations in the anisotropy parameters. The solutions of the perturbation equations represented the coefficients of a Taylor-series-type expansion of the wavefield as a function of the perturbed parameter, which is in this case η or the tilt of the symmetry axis. The expansion with respect to the symmetry axis allows use of an acoustic transversely isotropic media with a vertical symmetry axis (VTI) kernel to estimate the background wavefield and the corresponding perturbation coefficients. The VTI extrapolation kernel is about one-fourth the cost of the transversely isotropic model with a tilt in the symmetry axis kernel. Thus, for a small symmetry axis tilt, the cost of migration using a first-order expansion can be reduced. The effectiveness of the approach was demonstrated on the Marmousi model.
Solitonic Integrable Perturbations of Parafermionic Theories
Fernández-Pousa, C R; Hollowood, Timothy J; Miramontes, J L
1997-01-01
The quantum integrability of a class of massive perturbations of the parafermionic conformal field theories associated to compact Lie groups is established by showing that they have quantum conserved densities of scale dimension 2 and 3. These theories are integrable for any value of a continuous vector coupling constant, and they generalize the perturbation of the minimal parafermionic models by their first thermal operator. The classical equations-of-motion of these perturbed theories are the non-abelian affine Toda equations which admit (charged) soliton solutions whose semi-classical quantization is expected to permit the identification of the exact S-matrix of the theory.
Perturbation theories for the dipolar fluids
International Nuclear Information System (INIS)
Lee, L.L.; Chung, T.H.
1983-01-01
We derive here four different perturbation equations for the calculation of the angular pair correlation functions of dipolar fluids; namely, the first order y-expansion, the modified Percus--Yevik (MPY) expansion, the modified hypernetted chain (MHNC) expansion, and the modified linearized hypernetted chain (MLHNC) equation. Both the method of the functional expansion and the method of the cluster integrals are utilized. Comparison with other perturbation theories (e.g., the Melnyk--Smith equation) is made. While none of the theories is exact, as shown by the cluster diagrams, the MLHNC and the MHNC contain more diagrams than, say, the MPY and y-expansion. The y-expansion equation can be improved by including the correction terms to the Kirkwood superposition approximation for the triplet correlation function. For example, the inclusion of the correction term rho∫d4h(14)h(24)h(34) in a formula given by Henderson, is shown to improve substantially the y-expansion equation. We examine the performance of two of the theories: the y-expansion and the MLHNC equation for a Stockmayer (dipolar) fluid with a reduced dipole moment μ/sup asterisk2/ [ = μ 2 /(epsilonsigma 3 )] = 1.0. Comparison with Monte Carlo simulation results of Adams et al. and with other theories (e.g., the QHNC equation) shows that our results are reasonable. Further improvements of the equations are also pointed out
Application of depletion perturbation theory to fuel cycle burnup analysis
International Nuclear Information System (INIS)
White, J.R.
1979-01-01
Over the past several years static perturbation theory methods have been increasingly used for reactor analysis in lieu of more detailed and costly direct computations. Recently, perturbation methods incorporating time dependence have also received attention, and several authors have demonstrated their applicability to fuel burnup analysis. The objective of the work described here is to demonstrate that a time-dependent perturbation method can be easily and accurately applied to realistic depletion problems
Perturbative spacetimes from Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Luna, Andrés [School of Physics and Astronomy, University of Glasgow,Glasgow G12 8QQ, Scotland (United Kingdom); Monteiro, Ricardo [Theoretical Physics Department, CERN,Geneva (Switzerland); Nicholson, Isobel; Ochirov, Alexander; O’Connell, Donal [Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); Westerberg, Niclas [Institute of Photonics and Quantum Sciences,School of Engineering and Physical Sciences, Heriot-Watt University,Edinburgh (United Kingdom); Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); White, Chris D. [Centre for Research in String Theory,School of Physics and Astronomy, Queen Mary University of London,327 Mile End Road, London E1 4NS (United Kingdom)
2017-04-12
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Tunnelling instability via perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Graffi, S. (Bologna Univ. (Italy). Dip. di Matematica); Grecchi, V. (Moderna Univ. (Italy). Dip. di Matematica); Jona-Lasinio, G. (Paris-11 Univ., 91 - Orsay (France). Lab. de Physique Theorique et Hautes Energies)
1984-10-21
The semiclassical limit of low lying states in a multiwell potential is studied by rigorous perturbative techniques. In particular tunnelling instability and localisation of wave functions is obtained in a simple way under small deformations of symmetric potentials.
Perturbation theory of quantum resonances
Czech Academy of Sciences Publication Activity Database
Durand, P.; Paidarová, Ivana
2016-01-01
Roč. 135, č. 7 (2016), s. 159 ISSN 1432-2234 Institutional support: RVO:61388955 Keywords : Partitioning technique * Analytic continuation * Perturbative expansion Subject RIV: CF - Physical ; Theoretical Chemistry
International Nuclear Information System (INIS)
Passos, E.M.J. de
1976-01-01
The relationship between the Johnson-Baranger time-dependent folded diagram (JBFD) expansion, and the time independent methods of perturbation theory, are investigated. In the nondegenerate case, the JBFD expansion and the Rayleigh-Schroedinger perturbation expansion, for the ground state energy, are identical. On the other hand, in the degenerate case, for the nonhermitian effective interaction considered, the JBFD expansion, of the effective interaction, is equal to the perturbative expansion of the effective interaction of the nonhermitian eigenvalue problem of Bloch and Brandow-Des Cloizeaux. For the two hermitian effective interactions, the JBFD expansion of the effective interaction differs from the perturbation expansion of the effective interaction of the hermitian eigenvalue problem of Des Cloizeaux [pt
Perturbation theory in nuclear fuel management optimization
International Nuclear Information System (INIS)
Ho, L.W.; Rohach, A.F.
1982-01-01
Perturbation theory along with a binary fuel shuffling technique is applied to predict the effects of various core configurations and, hence, the optimization of in-core fuel management. The computer code FULMNT has been developed to shuffle the fuel assemblies in search of the lowest possible power peaking factor. An iteration approach is used in the search routine. A two-group diffusion theory method is used to obtain the power distribution for the iterations. A comparison of the results of this method with other methods shows that this approach can save computer time and obtain better power peaking factors. The code also has a burnup capability that can be used to check power peaking throughout the core life
On perturbation theory for distance dependent statistics.
Energy Technology Data Exchange (ETDEWEB)
Mashkevich, S V
1994-12-31
It is known that perturbation theory for anyons has to be modified near Bose statistics in order to get correct finite results. For ``distance dependent statistics`` or anyons with smeared flux tubes, perturbation theory is in principle applicable directly but gives results which hold for too small values of the statistical parameter and, in particular, are not valid as the flux tube radius tends to zero. In this paper we discuss the way to modify perturbation theory for this situation, which allows to obtain the appropriate results. (author). 6 refs.
Closed form bound-state perturbation theory
Directory of Open Access Journals (Sweden)
Ollie J. Rose
1980-01-01
Full Text Available The perturbed Schrödinger eigenvalue problem for bound states is cast into integral form using Green's Functions. A systematic algorithm is developed and applied to the resulting equation giving rise to approximate solutions expressed as functions of the given perturbation parameter. As a by-product, convergence radii for the traditional Rayleigh-Schrödinger and Brillouin-Wigner perturbation theories emerge in a natural way.
Factorization theorems in perturbative quantum field theory
International Nuclear Information System (INIS)
Date, G.D.
1982-01-01
This dissertation deals with factorization properties of Green functions and cross-sections in perturbation theory. It consists of two parts. Part I deals with the factorization theorem for the Drell-Yan cross-section. The new approach developed for this purpose is based upon a renormalization group equation with a generalized anomalous dimension. Using an alternate form of factorization for the Drell-Yan cross-section, derived in perturbation theory, a corresponding generalized anomalous dimension is defined, and explicit Feynman rules for its calculation are given. The resultant renormalization group equation is solved by a formal solution which is exhibited explicitly. Simple, explicit calculations are performed which verify Mueller's conjecture for the recovery of the usual parton model results for the Drell-Yan cross-section. The approach developed in this work offers a general framework to analyze the role played by the group factors in the cancellation of the soft divergences, and study their influence on the asymptotic behavior. Part II deals with factorization properties of the Green functions in position space. In this part, a Landau equation analysis is carried out for the singularities of the position space Green fucntions, in perturbation theory with the theta 4 interaction Lagrangian. A physical picture interpretation is given for the corresponding Landau equations. It is used to suggest a light-cone expansion. Using a power counting method, a formal derivation of the light-cone expansion for the two point function, the three point function and a product of two currents, is given without assuming a short distance expansion. Possible extensions to other theories is also considered
Homological Perturbation Theory for Nonperturbative Integrals
Johnson-Freyd, Theo
2015-11-01
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In particular, we explain that phenomena usually thought of as particular to asymptotic integrals in fact also occur exactly: integrals of the type appearing in quantum field theory can be reduced in a totally algebraic fashion to integrals over an Euler-Lagrange locus, provided this locus is understood in the scheme-theoretic sense, so that imaginary critical points and multiplicities of degenerate critical points contribute.
Cumulants in perturbation expansions for non-equilibrium field theory
International Nuclear Information System (INIS)
Fauser, R.
1995-11-01
The formulation of perturbation expansions for a quantum field theory of strongly interacting systems in a general non-equilibrium state is discussed. Non-vanishing initial correlations are included in the formulation of the perturbation expansion in terms of cumulants. The cumulants are shown to be the suitable candidate for summing up the perturbation expansion. Also a linked-cluster theorem for the perturbation series with cumulants is presented. Finally a generating functional of the perturbation series with initial correlations is studied. We apply the methods to a simple model of a fermion-boson system. (orig.)
Massive states in chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Mallik, S [Saha Inst. of Nuclear Physics, Calcutta (India)
1995-08-01
It is shown that the chiral nonanalytic terms generated by {Delta}{sub 33} resonance in the nucleon self-energy is reproduced in chiral perturbation theory by perturbing appropriate local operators contained in the pion-nucleon effective Lagrangian itself. (orig.)
Scalar Quantum Electrodynamics: Perturbation Theory and Beyond
International Nuclear Information System (INIS)
Bashir, A.; Gutierrez-Guerrero, L. X.; Concha-Sanchez, Y.
2006-01-01
In this article, we calculate scalar propagator in arbitrary dimensions and gauge and the three-point scalar-photon vertex in arbitrary dimensions and Feynman gauge, both at the one loop level. We also discuss constraints on their non perturbative structure imposed by requirements of gauge invariance and perturbation theory
Transport perturbation theory in nuclear reactor analysis
International Nuclear Information System (INIS)
Nishigori, Takeo; Takeda, Toshikazu; Selvi, S.
1985-01-01
Perturbation theory is formulated on the basis of transport theory to obtain a formula for the reactivity changes due to possible variations of cross sections. Useful applications to cell homogenization are presented for the whole core calculation in transport and in diffusion theories. (author)
Inflation and the theory of cosmological perturbations
International Nuclear Information System (INIS)
Riotto, A.
2003-01-01
These lectures provide a pedagogical introduction to inflation and the theory of cosmological perturbations generated during inflation which are thought to be the origin of structure in the universe. (author)
Energy Technology Data Exchange (ETDEWEB)
Faisal, F H.M. [Bielefeld Univ. (Germany, F.R.). Fakultaet fuer Physik
1976-06-11
In this work the perturbation theory for multiphoton processes at high intensities is investigated and it is described an analytical method of summing the perturbation series to extract the contribution from all terms that give rise to the absorption of N photons by an atomic system. The method is first applied to the solution of a simple model problem and the result is confirmed by direct integration of the model Schroedinger equation. The usual lowest (nonvanishing)-order perturbation-theoretical calculation is also carried out for this model to demonstrate explicitly that the full result correctly reproduces that of the lowest-order theory in the limit of low intensity. The method is then extended to the case of an atomic system with well-developed spectrum (e.g. H atom) and the N-photon T-matrix is derived in terms of a ''photon matrix'' asub(N), for which a three-term recurrence relation is established. Next, from the vantage point of the general result obtained here, A probe is made into the nature of several approximate nonperturbative solutions that have appeared in the literature in the past. It is shown here that their applicability is severely restricted by the requirement of the essential spectral degeneracy of the atomic system. Finally, appendix A outlines a prescription of computing the photon matrix asub(N), which (as in the usual lowest-order perturbation-theoretical calculation)requires a knowledge of the eigenfunctions and eigenvalues of the atomic Hamiltonian only.
Coupling-parameter expansion in thermodynamic perturbation theory.
Ramana, A Sai Venkata; Menon, S V G
2013-02-01
An approach to the coupling-parameter expansion in the liquid state theory of simple fluids is presented by combining the ideas of thermodynamic perturbation theory and integral equation theories. This hybrid scheme avoids the problems of the latter in the two phase region. A method to compute the perturbation series to any arbitrary order is developed and applied to square well fluids. Apart from the Helmholtz free energy, the method also gives the radial distribution function and the direct correlation function of the perturbed system. The theory is applied for square well fluids of variable ranges and compared with simulation data. While the convergence of perturbation series and the overall performance of the theory is good, improvements are needed for potentials with shorter ranges. Possible directions for further developments in the coupling-parameter expansion are indicated.
't Hooft loops and perturbation theory
De Forcrand, Philippe; Noth, D; Forcrand, Philippe de; Lucini, Biagio; Noth, David
2005-01-01
We show that high-temperature perturbation theory describes extremely well the area law of SU(N) spatial 't Hooft loops, or equivalently the tension of the interface between different Z_N vacua in the deconfined phase. For SU(2), the disagreement between Monte Carlo data and lattice perturbation theory for sigma(T)/T^2 is less than 2%, down to temperatures O(10) T_c. For SU(N), N>3, the ratios of interface tensions, (sigma_k/sigma_1)(T), agree with perturbation theory, which predicts tiny deviations from the ratio of Casimirs, down to nearly T_c. In contrast, individual tensions differ markedly from the perturbative expression. In all cases, the required precision Monte Carlo measurements are made possible by a simple but powerful modification of the 'snake' algorithm.
Supersymmetry restoration in superstring perturbation theory
International Nuclear Information System (INIS)
Sen, Ashoke
2015-01-01
Superstring perturbation theory based on the 1PI effective theory approach has been useful for addressing the problem of mass renormalization and vacuum shift. We derive Ward identities associated with space-time supersymmetry transformation in this approach. This leads to a proof of the equality of renormalized masses of bosons and fermions and identities relating fermionic amplitudes to bosonic amplitudes after taking into account the effect of mass renormalization. This also relates unbroken supersymmetry to a given order in perturbation theory to absence of tadpoles of massless scalars to higher order. The results are valid at the perturbative vacuum as well as in the shifted vacuum when the latter describes the correct ground state of the theory. We apply this to SO(32) heterotic string theory on Calabi-Yau 3-folds where a one loop Fayet-Iliopoulos term apparently breaks supersymmetry at one loop, but analysis of the low energy effective field theory indicates that there is a nearby vacuum where supersymmetry is restored. We explicitly prove that the perturbative amplitudes of this theory around the shifted vacuum indeed satisfy the Ward identities associated with unbroken supersymmetry. We also test the general arguments by explicitly verifying the equality of bosonic and fermionic masses at one loop order in the shifted vacuum, and the appearance of two loop dilaton tadpole in the perturbative vacuum where supersymmetry is expected to be broken.
Supersymmetry restoration in superstring perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Sen, Ashoke [Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India)
2015-12-14
Superstring perturbation theory based on the 1PI effective theory approach has been useful for addressing the problem of mass renormalization and vacuum shift. We derive Ward identities associated with space-time supersymmetry transformation in this approach. This leads to a proof of the equality of renormalized masses of bosons and fermions and identities relating fermionic amplitudes to bosonic amplitudes after taking into account the effect of mass renormalization. This also relates unbroken supersymmetry to a given order in perturbation theory to absence of tadpoles of massless scalars to higher order. The results are valid at the perturbative vacuum as well as in the shifted vacuum when the latter describes the correct ground state of the theory. We apply this to SO(32) heterotic string theory on Calabi-Yau 3-folds where a one loop Fayet-Iliopoulos term apparently breaks supersymmetry at one loop, but analysis of the low energy effective field theory indicates that there is a nearby vacuum where supersymmetry is restored. We explicitly prove that the perturbative amplitudes of this theory around the shifted vacuum indeed satisfy the Ward identities associated with unbroken supersymmetry. We also test the general arguments by explicitly verifying the equality of bosonic and fermionic masses at one loop order in the shifted vacuum, and the appearance of two loop dilaton tadpole in the perturbative vacuum where supersymmetry is expected to be broken.
Higher order perturbation theory - An example for discussion
International Nuclear Information System (INIS)
Lewins, J.D.; Parks, G.; Babb, A.L.
1986-01-01
Higher order perturbation theory is developed in the form of a Taylor series expansion to third order to calculate the thermal utilization of a nonuniform cell. The development takes advantage of the self-adjoint property of the diffusion operator to provide a simple development of this illustration of generalized perturbation theory employing scalar perturbation parameters. The results show how a designer might employ a second-order theory to quantify proposed design improvements, together with the limitations of second- and third-order theory. The chosen example has an exact optimization solution and thus provides a clear understanding of the role of perturbation theory at its various orders. Convergence and the computational advantages and disadvantages of the method are discussed
The use of perturbation theory in density-functional theory
International Nuclear Information System (INIS)
Goerling, A.
1996-01-01
Perturbation theory with respect to the electron-electron interaction leads to expressions for the exchange and correlation energies and potentials in terms of Kohn-Sham orbitals and Kohn-Sham eigenvalues. An exact open-quote exchange-only close-quote procedure for solids is introduced. Results for several semiconductors are presented. Perturbation theory expansions for the hardness of molecules and the bad gap of solids are given. Density-functional exchange and correlation energies for excited states are defined and a perturbation theory based Kohn-Sham formalism to treat excited states within density-functional theory is introduced
Operator Decomposition Framework for Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Abdel-Khalik, Hany S.; Wang, Congjian; Bang, Young Suk [North Carolina State University, Raleigh (United States)
2012-05-15
This summary describes a new framework for perturbation theory intended to improve its performance, in terms of the associated computational cost and the complexity of implementation, for routine reactor calculations in support of design, analysis, and regulation. Since its first introduction in reactor analysis by Winger, perturbation theory has assumed an aura of sophistication with regard to its implementation and its capabilities. Only few reactor physicists, typically mathematically proficient, have contributed to its development, with the general body of the nuclear engineering community remaining unaware of its current status, capabilities, and challenges. Given its perceived sophistication and the small body of community users, the application of perturbation theory has been limited to investigatory analyses only. It is safe to say that the nuclear community is split into two groups, a small one which understands the theory and, and a much bigger group with the perceived notion that perturbation theory is nothing but a fancy mathematical approach that has very little use in practice. Over the past three years, research has demonstrated two goals. First, reduce the computational cost of perturbation theory in order to enable its use for routine reactor calculations. Second, expose some of the myth about perturbation theory and present it in a form that is simple and relatable in order to stimulate the interest of nuclear practitioners, especially those who are currently working on the development of next generation reactor design and analysis tools. The operator decomposition approach has its roots in linear algebra and can be easily understood by code developers, especially those involved in the design of iterative numerical solution strategies
Kato expansion in quantum canonical perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Nikolaev, Andrey, E-mail: Andrey.Nikolaev@rdtex.ru [Institute of Computing for Physics and Technology, Protvino, Moscow Region, Russia and RDTeX LTD, Moscow (Russian Federation)
2016-06-15
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.
Kato expansion in quantum canonical perturbation theory
International Nuclear Information System (INIS)
Nikolaev, Andrey
2016-01-01
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.
Perturbative and global anomalies in supergravity theories
International Nuclear Information System (INIS)
Sezgin, E.
1986-09-01
Perturbative and global anomalies in supergravity theories are reviewed. The existence of a matter and gauge coupled supergravity theory in six dimensions with E 6 xE 7 xU(1) symmetry and highly nontrivial anomaly cancellations is emphasised. The possible string origin of this theory is posed as an open problem, study of which may lead to discovery of new ways to construct/compactify heterotic superstrings. (author)
Perturbation theory for continuous stochastic equations
International Nuclear Information System (INIS)
Chechetkin, V.R.; Lutovinov, V.S.
1987-01-01
The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)
The classification of diagrams in perturbation theory
International Nuclear Information System (INIS)
Phillips, D.R.; Afnan, I.R.
1995-01-01
The derivation of scattering equations connecting the amplitudes obtained from diagrammatic expansions is of interest in many branches of physics. One method for deriving such equations is the classification-of-diagrams technique of Taylor. However, as we shall explain in this paper, there are certain points of Taylor's method which require clarification. First, it is not clear whether Taylor's original method is equivlant to the simpler classification-of-diagrams scheme used by Thomas, Rinat, Afnan, and Blankleider (TRAB). Second, when the Taylor method is applied to certain problems in a time-dependent perturbation theory it leads to the over-counting of some diagrams. This paper first restates Taylor's method, in the process uncovering reasons why certain diagrams might be double-counted in the Taylor method. In then explores how far Taylor's method is equivalent to the simpler TRAB method. Finally, it examines precisely why the double-counting occurs in Taylor's method and derives corrections which compensate for this double-counting. copyright 1995 Academic Press, Inc
Fedosov quantization and perturbative quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Collini, Giovanni
2016-12-12
Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold (''phase space''). His algorithm gives a non-commutative, but associative, product (a so-called ''star-product'') between smooth phase space functions parameterized by Planck's constant ℎ, which is treated as a deformation parameter. In the limit as ℎ goes to zero, the star product commutator goes to ℎ times the Poisson bracket, so in this sense his method provides a quantization of the algebra of classical observables. In this work, a generalization of Fedosov's method is developed which applies to the infinite-dimensional symplectic ''manifolds'' that occur in Lagrangian field theories. We show that the procedure remains mathematically well-defined, and we explain the relationship of the method to more standard perturbative quantization schemes in quantum field theory.
Perturbative analysis in higher-spin theories
Energy Technology Data Exchange (ETDEWEB)
Didenko, V.E. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation); Misuna, N.G. [Moscow Institute of Physics and Technology,Institutsky lane 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Vasiliev, M.A. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation)
2016-07-28
A new scheme of the perturbative analysis of the nonlinear HS equations is developed giving directly the final result for the successive application of the homotopy integrations which appear in the standard approach. It drastically simplifies the analysis and results from the application of the standard spectral sequence approach to the higher-spin covariant derivatives, allowing us in particular to reduce multiple homotopy integrals resulting from the successive application of the homotopy trick to a single integral. Efficiency of the proposed method is illustrated by various examples. In particular, it is shown how the Central on-shell theorem of the free theory immediately results from the nonlinear HS field equations with no intermediate computations.
Perturbation theory in nuclear fuel management optimization
International Nuclear Information System (INIS)
Ho, L.W.
1981-01-01
Nuclear in-core fuel management involves all the physical aspects which allow optimal operation of the nuclear fuel within the reactor core. In most nuclear power reactors, fuel loading patterns which have a minimum power peak are economically desirable to allow the reactors to operate at the highest power density and to minimize the possibility of fuel failure. In this study, perturbation theory along with a binary fuel shuffling technique is applied to predict the effects of various core configurations, and hence, the optimization of in-core fuel management. The computer code FULMNT has been developed to shuffle the fuel assemblies in search of the lowest possible power peaking factor. An iteration approach is used in the search routine. A two-group diffusion theory method is used to obtain the power distribution for the iterations. A comparison of the results of this method with other methods shows that this approach can save computer time. The code also has a burnup capability which can be used to check power peaking throughout the core life
On the domain of string perturbation theory
International Nuclear Information System (INIS)
Davis, S.
1989-06-01
For a large class of effectively closed surfaces, it is shown that the only divergences in string scattering amplitudes at each order in perturbation theory are those associated with the coincidence of vertex operators and the boundary of moduli space. This class includes all closed surfaces of finite genus, and infinite-genus surfaces which can be uniformized by a group of Schottky type. While the computation is done explicitly for bosonic strings in their ground states, it can also be extended to excited states and to superstrings. The properties of these amplitudes lead to a definition of the domain of perturbation theory as the set of effectively closed surfaces. The implications of the restriction to effectively closed surfaces on the behavior of the perturbation series are discussed. (author). 20 refs, 6 figs
Quenched Chiral Perturbation Theory to one loop
Colangelo, G.; Pallante, E.
The divergences of the generating functional of quenched Chiral Perturbation theory (qCHPT) to one loop are computed in closed form. We show how the quenched chiral logarithms can be reabsorbed in the renormalization of the B0 parameter of the leading order Lagrangian. Finally, we do the chiral
Acoustic anisotropic wavefields through perturbation theory
Alkhalifah, Tariq Ali
2013-01-01
these restrictions are the inability to handle media with η<0 and the presence of shear-wave artifacts in the solution. Both limitations do not exist in the solution of the elliptical anisotropic acoustic wave equation. Using perturbation theory in developing
Guo, Yang; Becker, Ute; Neese, Frank
2018-03-01
Local correlation theories have been developed in two main flavors: (1) "direct" local correlation methods apply local approximation to the canonical equations and (2) fragment based methods reconstruct the correlation energy from a series of smaller calculations on subsystems. The present work serves two purposes. First, we investigate the relative efficiencies of the two approaches using the domain-based local pair natural orbital (DLPNO) approach as the "direct" method and the cluster in molecule (CIM) approach as the fragment based approach. Both approaches are applied in conjunction with second-order many-body perturbation theory (MP2) as well as coupled-cluster theory with single-, double- and perturbative triple excitations [CCSD(T)]. Second, we have investigated the possible merits of combining the two approaches by performing CIM calculations with DLPNO methods serving as the method of choice for performing the subsystem calculations. Our cluster-in-molecule approach is closely related to but slightly deviates from approaches in the literature since we have avoided real space cutoffs. Moreover, the neglected distant pair correlations in the previous CIM approach are considered approximately. Six very large molecules (503-2380 atoms) were studied. At both MP2 and CCSD(T) levels of theory, the CIM and DLPNO methods show similar efficiency. However, DLPNO methods are more accurate for 3-dimensional systems. While we have found only little incentive for the combination of CIM with DLPNO-MP2, the situation is different for CIM-DLPNO-CCSD(T). This combination is attractive because (1) the better parallelization opportunities offered by CIM; (2) the methodology is less memory intensive than the genuine DLPNO-CCSD(T) method and, hence, allows for large calculations on more modest hardware; and (3) the methodology is applicable and efficient in the frequently met cases, where the largest subsystem calculation is too large for the canonical CCSD(T) method.
Effective field theory of cosmological perturbations
International Nuclear Information System (INIS)
Piazza, Federico; Vernizzi, Filippo
2013-01-01
The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu–Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry—that allows us to write down the most general Lagrangian—and of the Stückelberg ‘trick’—that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy. (paper)
Where does cosmological perturbation theory break down?
International Nuclear Information System (INIS)
Armendariz-Picon, Cristian; Fontanini, Michele; Penco, Riccardo; Trodden, Mark
2009-01-01
It is often assumed that initial conditions for the evolution of a cosmological mode should be set at the time its physical wavelength reaches a cut-off of the order of the Planck length. Beyond that scale, trans-Planckian corrections to the dispersion relation are supposed to become dominant, leading to the breakdown of cosmological perturbation theory. In this paper, we apply the effective field theory approach to the coupled metric-inflaton system in order to calculate the corrections to the power spectrum of scalar and tensor perturbations induced by higher-dimension operators at short wavelengths. These corrections can be interpreted as modifications of the dispersion relation, and thus open a window to probe the validity of cosmological perturbation theory. Both for scalars and tensors, the modifications become important when the Hubble parameter is of the order of the Planck mass, or when the physical wave number of a cosmological perturbation mode approaches the square of the Planck mass divided by the Hubble constant. Thus, the cut-off length at which such a breakdown occurs is finite, but much smaller than the Planck length.
Effective field theory of cosmological perturbations
Piazza, Federico; Vernizzi, Filippo
2013-11-01
The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry—that allows us to write down the most general Lagrangian—and of the Stückelberg ‘trick’—that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy.
A primer for Chiral Perturbative Theory
International Nuclear Information System (INIS)
Scherer, Stefan; Schindler, Matthias R.; George Washington Univ., Washington, DC
2012-01-01
Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques. (orig.)
A primer for chiral perturbation theory
Scherer, Stefan
2012-01-01
Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques.
Implementation of static generalized perturbation theory for LWR design applications
International Nuclear Information System (INIS)
Byron, R.F.; White, J.R.
1987-01-01
A generalized perturbation theory (GPT) formulation is developed for application to light water reactor (LWR) design. The extensions made to standard generalized perturbation theory are the treatment of thermal-hydraulic and fission product poisoning feedbacks, and criticality reset. This formulation has been implemented into a standard LWR design code. The method is verified by comparing direct calculations with GPT calculations. Data are presented showing that feedback effects need to be considered when using GPT for LWR problems. Some specific potential applications of this theory to the field of LWR design are discussed
New Methods in Non-Perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Unsal, Mithat [North Carolina State Univ., Raleigh, NC (United States)
2017-01-31
In this work, we investigate the properties of quantum chromodynamics (QCD), by using newly developing mathematics and physics formalisms. Almost all of the mass in the visible universe emerges from a quantum chromodynamics (QCD), which has a completely negligible microscopic mass content. An intimately related issue in QCD is the quark confinement problem. Answers to non-perturbative questions in QCD remained largely elusive despite much effort over the years. It is also believed that the usual perturbation theory is inadequate to address these kinds of problems. Perturbation theory gives a divergent asymptotic series (even when the theory is properly renormalized), and there are non-perturbative phenomena which never appear at any order in perturbation theory. Recently, a fascinating bridge between perturbation theory and non-perturbative effects has been found: a formalism called resurgence theory in mathematics tells us that perturbative data and non-perturbative data are intimately related. Translating this to the language of quantum field theory, it turns out that non-perturbative information is present in a coded form in perturbation theory and it can be decoded. We take advantage of this feature, which is particularly useful to understand some unresolved mysteries of QCD from first principles. In particular, we use: a) Circle compactifications which provide a semi-classical window to study confinement and mass gap problems, and calculable prototypes of the deconfinement phase transition; b) Resurgence theory and transseries which provide a unified framework for perturbative and non-perturbative expansion; c) Analytic continuation of path integrals and Lefschetz thimbles which may be useful to address sign problem in QCD at finite density.
Perturbative algebraic quantum field theory at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Lindner, Falk
2013-08-15
We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.
Perturbative algebraic quantum field theory at finite temperature
International Nuclear Information System (INIS)
Lindner, Falk
2013-08-01
We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.
Perturbative quantum field theory via vertex algebras
International Nuclear Information System (INIS)
Hollands, Stefan; Olbermann, Heiner
2009-01-01
In this paper, we explain how perturbative quantum field theory can be formulated in terms of (a version of) vertex algebras. Our starting point is the Wilson-Zimmermann operator product expansion (OPE). Following ideas of a previous paper (S. Hollands, e-print arXiv:0802.2198), we consider a consistency (essentially associativity) condition satisfied by the coefficients in this expansion. We observe that the information in the OPE coefficients can be repackaged straightforwardly into 'vertex operators' and that the consistency condition then has essentially the same form as the key condition in the theory of vertex algebras. We develop a general theory of perturbations of the algebras that we encounter, similar in nature to the Hochschild cohomology describing the deformation theory of ordinary algebras. The main part of the paper is devoted to the question how one can calculate the perturbations corresponding to a given interaction Lagrangian (such as λφ 4 ) in practice, using the consistency condition and the corresponding nonlinear field equation. We derive graphical rules, which display the vertex operators (i.e., OPE coefficients) in terms of certain multiple series of hypergeometric type.
Non-hard sphere thermodynamic perturbation theory.
Zhou, Shiqi
2011-08-21
A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established. © 2011 American Institute of Physics
Baryon form factors in chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Kubis, B.; Meissner, U.G. [Forschungszentrum Juelich GmbH (Germany). Inst. fuer Kernphysik
2001-01-01
We analyze the electromagnetic form factors of the ground state baryon octet to fourth order in relativistic baryon chiral perturbation theory. Predictions for the {sigma}{sup -} charge radius and the {lambda}-{sigma}{sup 0} transition moment are found to be in excellent agreement with the available experimental information. Furthermore, the convergence behavior of the hyperon charge radii is shown to be more than satisfactory. (orig.)
Perturbation theory for arbitrary coupling strength?
Mahapatra, Bimal P.; Pradhan, Noubihary
2018-03-01
We present a new formulation of perturbation theory for quantum systems, designated here as: “mean field perturbation theory” (MFPT), which is free from power-series-expansion in any physical parameter, including the coupling strength. Its application is thereby extended to deal with interactions of arbitrary strength and to compute system-properties having non-analytic dependence on the coupling, thus overcoming the primary limitations of the “standard formulation of perturbation theory” (SFPT). MFPT is defined by developing perturbation about a chosen input Hamiltonian, which is exactly solvable but which acquires the nonlinearity and the analytic structure (in the coupling strength) of the original interaction through a self-consistent, feedback mechanism. We demonstrate Borel-summability of MFPT for the case of the quartic- and sextic-anharmonic oscillators and the quartic double-well oscillator (QDWO) by obtaining uniformly accurate results for the ground state of the above systems for arbitrary physical values of the coupling strength. The results obtained for the QDWO may be of particular significance since “renormalon”-free, unambiguous results are achieved for its spectrum in contrast to the well-known failure of SFPT in this case.
Thermal gluons beyond pure perturbation theory
International Nuclear Information System (INIS)
Reinbach, J.
2000-01-01
The perturbative treatment of non-abelian gauge theory at high temperature leads to a threshold in calculation because of chromomagnetic effects. Infinitely many terms of the same order of magnitude arise. The numerical series to be summed is contained in the part of the theory reduced on 3D, which was recently treated non-perturbative as 2+1D Yang-Mills theory at T=0 by Karabali, Kim and Nair. In the thesis in question the exact 3D results are combined with the thermal 4D diagrammatic. In particular the splitting of the space-part of the transverse self-energy in the static limit is treated. As expected, the 3D subsystem can separate as regularized 3D Yang-Mills theory from the 4D structure. In 1-loop order the regulators are received explicit. For 2-loop order it can be shown amongst other things, that the generic contribution with hard inner momenta vanishes. It is examined, how the magnetic mass could follow. Under pressure it is possible to separate the 3D part in 1- and 2-loop order and to receive regulators [de
Quasi-degenerate perturbation theory using matrix product states
International Nuclear Information System (INIS)
Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali
2016-01-01
In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner’s 2n + 1 rule. Further, our formulation satisfies Granovsky’s requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost
Quasi-degenerate perturbation theory using matrix product states
Energy Technology Data Exchange (ETDEWEB)
Sharma, Sandeep, E-mail: sanshar@gmail.com; Jeanmairet, Guillaume [Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart (Germany); Alavi, Ali, E-mail: a.alavi@fkf.mpg.de [Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart (Germany); Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW (United Kingdom)
2016-01-21
In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner’s 2n + 1 rule. Further, our formulation satisfies Granovsky’s requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.
Quasi-degenerate perturbation theory using matrix product states
Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali
2016-01-01
In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner's 2n + 1 rule. Further, our formulation satisfies Granovsky's requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.
Perturbative Quantum Gravity and its Relation to Gauge Theory
Directory of Open Access Journals (Sweden)
Bern Zvi
2002-01-01
Full Text Available In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on $D$-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input thegravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.
Perturbation Theory for Open Two-Level Nonlinear Quantum Systems
International Nuclear Information System (INIS)
Zhang Zhijie; Jiang Dongguang; Wang Wei
2011-01-01
Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r = C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results. (general)
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
Chiral perturbation theory for lattice QCD
International Nuclear Information System (INIS)
Baer, Oliver
2010-01-01
The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed. (orig.)
Perturbation theory for plasmonic modulation and sensing
Raman, Aaswath
2011-05-25
We develop a general perturbation theory to treat small parameter changes in dispersive plasmonic nanostructures and metamaterials. We specifically apply it to dielectric refractive index and metallic plasma frequency modulation in metal-dielectric nanostructures. As a numerical demonstration, we verify the theory\\'s accuracy against direct calculations for a system of plasmonic rods in air where the metal is defined by a three-pole fit of silver\\'s dielectric function. We also discuss new optical behavior related to plasma frequency modulation in such systems. Our approach provides new physical insight for the design of plasmonic devices for biochemical sensing and optical modulation and future active metamaterial applications. © 2011 American Physical Society.
Chiral perturbation theory for lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Baer, Oliver
2010-07-21
The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed. (orig.)
Inflationary perturbations in no-scale theories
Energy Technology Data Exchange (ETDEWEB)
Salvio, Alberto [CERN, Theoretical Physics Department, Geneva (Switzerland)
2017-04-15
We study the inflationary perturbations in general (classically) scale-invariant theories. Such scenario is motivated by the hierarchy problem and provides natural inflationary potentials and dark matter candidates. We analyse in detail all sectors (the scalar, vector and tensor perturbations) giving general formulae for the potentially observable power spectra, as well as for the curvature spectral index n{sub s} and the tensor-to-scalar ratio r. We show that the conserved Hamiltonian for all perturbations does not feature negative energies even in the presence of the Weyl-squared term if the appropriate quantisation is performed and argue that this term does not lead to phenomenological problems at least in some relevant setups. The general formulae are then applied to a concrete no-scale model, which includes the Higgs and a scalar, ''the planckion'', whose vacuum expectation value generates the Planck mass. Inflation can be triggered by a combination of the planckion and the Starobinsky scalar and we show that no tension with observations is present even in the case of pure planckion inflation, if the coefficient of the Weyl-squared term is large enough. In general, even quadratic inflation is allowed in this case. Moreover, the Weyl-squared term leads to an isocurvature mode, which currently satisfies the observational bounds, but it may be detectable with future experiments. (orig.)
Canonical perturbation theory in linearized general relativity theory
International Nuclear Information System (INIS)
Gonzales, R.; Pavlenko, Yu.G.
1986-01-01
Canonical perturbation theory in linearized general relativity theory is developed. It is shown that the evolution of arbitrary dynamic value, conditioned by the interaction of particles, gravitation and electromagnetic fields, can be presented in the form of a series, each member of it corresponding to the contribution of certain spontaneous or induced process. The main concepts of the approach are presented in the approximation of a weak gravitational field
SMD-based numerical stochastic perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Dalla Brida, Mattia [Universita di Milano-Bicocca, Dipartimento di Fisica, Milan (Italy); INFN, Sezione di Milano-Bicocca (Italy); Luescher, Martin [CERN, Theoretical Physics Department, Geneva (Switzerland); AEC, Institute for Theoretical Physics, University of Bern (Switzerland)
2017-05-15
The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schroedinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit. (orig.)
SMD-based numerical stochastic perturbation theory
International Nuclear Information System (INIS)
Dalla Brida, Mattia; Luescher, Martin
2017-01-01
The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schroedinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit. (orig.)
SMD-based numerical stochastic perturbation theory
Dalla Brida, Mattia; Lüscher, Martin
2017-05-01
The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schrödinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit.
Adiabatic perturbation theory in quantum dynamics
Teufel, Stefan
2003-01-01
Separation of scales plays a fundamental role in the understanding of the dynamical behaviour of complex systems in physics and other natural sciences. A prominent example is the Born-Oppenheimer approximation in molecular dynamics. This book focuses on a recent approach to adiabatic perturbation theory, which emphasizes the role of effective equations of motion and the separation of the adiabatic limit from the semiclassical limit. A detailed introduction gives an overview of the subject and makes the later chapters accessible also to readers less familiar with the material. Although the general mathematical theory based on pseudodifferential calculus is presented in detail, there is an emphasis on concrete and relevant examples from physics. Applications range from molecular dynamics to the dynamics of electrons in a crystal and from the quantum mechanics of partially confined systems to Dirac particles and nonrelativistic QED.
Advances in heuristically based generalized perturbation theory
International Nuclear Information System (INIS)
Gandini, A.
1994-01-01
A distinctive feature of heuristically based generalized perturbation theory methodology consists in the systematic use of importance conservation concepts. As well known, this use leads to fundamental reciprocity relationship. Instead, the alternative variational and differential one approaches make a consistent use of the properties and adjoint functions. The equivalence between the importance and the adjoint functions have been demonstrated in important cases. There are some instances, however, in which the commonly known operator governing the adjoint function are not adequate. In this paper ways proposed to generalize this rules, as adopted with the heuristic generalized perturbation theory methodology, are illustrated. When applied to the neutron/nuclide field characterizing the core evolution in a power reactor system, in which also an intensive control variable (ρ) is defined, these rules leas to an orthogonality relationship connected to this same control variable. A set of ρ-mode eigenfunctions may be correspondingly defined and an extended concept of reactivity (generalizing that commonly associated with the multiplication factor) proposed as more directly indicative of the controllability of a critical reactor system. (author). 25 refs
Dissipative motion perturbation theory and exact solutions
International Nuclear Information System (INIS)
Lodder, J.J.
1976-06-01
Dissipative motion of classical and quantum systems is described. In particular, attention is paid to systems coupled to the radiation field. A dissipative equation of motion for a particle in an arbitrary potential coupled to the radiation field is derived by means of perturbation theory. The usual divrgencies associated with the radiation field are eliminated by the application of a theory of generalized functions. This theory is developed as a subject in its own right and is presented independently. The introduction of classical zero-point energy makes the classical equa tion of motion for the phase density formally the same as its quantum counterpart. In particular, it is shown that the classical zero-point energy prevents the collapse of a classical H-atom and gives rise to a classical ground state. For systems with a quadratic Hamiltoian, the equation of motion can be solved exactly, even in the continuum limit for the radiation field, by means of the new generalized functions. Classically, the Fokker-Planck equation is found without any approximations, and quantum mechanically, the only approximation is the neglect of the change in the ground state caused by the interaction. The derivation is valid even for strong damping and arbitrarily short times. There is no transient time. For harmonic oscillators complete equivalence is shown to exist between quantum mechanics and classical mechanics with zero-point energy. A discussion of the derivation of the Pauli equation is given and perturbation theory is compared with the exact derivation. The exactly solvable models are used to calculate the Langevin force of the radiation field. The result is that the classical Langevin force is exactly delta-correlated, while the quantum Langevin force is not delta-correlated at all. The fluctuation-dissipation theorem is shown to be an exact consequence of the solution to the equations of motion
New Approaches and Applications for Monte Carlo Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Aufiero, Manuele; Bidaud, Adrien; Kotlyar, Dan; Leppänen, Jaakko; Palmiotti, Giuseppe; Salvatores, Massimo; Sen, Sonat; Shwageraus, Eugene; Fratoni, Massimiliano
2017-02-01
This paper presents some of the recent and new advancements in the extension of Monte Carlo Perturbation Theory methodologies and application. In particular, the discussed problems involve Brunup calculation, perturbation calculation based on continuous energy functions, and Monte Carlo Perturbation Theory in loosely coupled systems.
Perturbation Theory of the Cosmological Log-Density Field
DEFF Research Database (Denmark)
Wang, Xin; Neyrinck, Mark; Szapudi, István
2011-01-01
, motivating an analytic study of it. In this paper, we develop cosmological perturbation theory for the power spectrum of this field. Our formalism is developed in the context of renormalized perturbation theory, which helps to regulate the convergence behavior of the perturbation series, and of the Taylor...
A finite element formulation for perturbation theory calculations
International Nuclear Information System (INIS)
Ozgener, B.; Kaluc, S.
2004-01-01
Full text: When the introduced change in the configuration of a nuclear system is neutronically not too significant, the use of the perturbation theory approximation ('the perturbation theory method' or PTM) is usually considered as an alternative to the recalculation of the effective multiplication factor (K eff ) of the modified system ('the diffusion theory method' or DTM) for the determination of the ensuing change in reactivity. In the DTM, the change in reactivity due to the introduced change can be calculated by the multigroup diffusion theory by performing two K eff determinations, one for the original and one for the modified system. The accuracy of this method is only limited by the approximations inherent in the multigroup diffusion theory and the numerical method employed for its solution. The error stemming from the numerical approximation can be nearly eliminated by utilizing a fine enough spatial mesh ad an 'exact' solution is nearly possible. Its basic disadvantage relative to the PTM is the necessity of a new K eff calculation for every change in the configuration no matter how small. On the other hand, if we use PTM, with an only one-time calculation of the flux and the adjoint flux of the original system, the change in reactivity due to any kind of perturbation can be approximately calculated using the changes in the cross section data in the perturbation theory reactivity formula. The accuracy of the PTM is restricted by the size and location of the induced change. In this work, our aim is to assess the accuracy of PTM relative to the DTM and determine criteria for the justification of its use. For all required solutions of the normal and adjoint multigroup diffusion equations, we choose the finite element method (FEM) as our numerical method and a 1-D cylindrical geometry model. The underlying theory is implemented in our FORTRAN program PERTURB. The validation of PERTURB is carried out via comparisons with analytical solutions for bare and
Algebraic quantum field theory, perturbation theory, and the loop expansion
International Nuclear Information System (INIS)
Duetsch, M.; Fredenhagen, K.
2001-01-01
The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system A (n) of observables ''up to n loops'', where A (0) is the Poisson algebra of the classical field theory. Finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of Green's functions. (orig.)
Alien calculus and non perturbative effects in Quantum Field Theory
Bellon, Marc P.
2016-12-01
In many domains of physics, methods for dealing with non-perturbative aspects are required. Here, I want to argue that a good approach for this is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean Écalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.
A general-model-space diagrammatic perturbation theory
International Nuclear Information System (INIS)
Hose, G.; Kaldor, U.
1980-01-01
A diagrammatic many-body perturbation theory applicable to arbitrary model spaces is presented. The necessity of having a complete model space (all possible occupancies of the partially-filled shells) is avoided. This requirement may be troublesome for systems with several well-spaced open shells, such as most atomic and molecular excited states, as a complete model space spans a very broad energy range and leaves out states within that range, leading to poor or no convergence of the perturbation series. The method presented here would be particularly useful for such states. The solution of a model problem (He 2 excited Σ + sub(g) states) is demonstrated. (Auth.)
Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation
Directory of Open Access Journals (Sweden)
Samuel Friot
2010-10-01
Full Text Available Using a method mixing Mellin-Barnes representation and Borel resummation we show how to obtain hyperasymptotic expansions from the (divergent formal power series which follow from the perturbative evaluation of arbitrary ''N-point'' functions for the simple case of zero-dimensional φ4 field theory. This hyperasymptotic improvement appears from an iterative procedure, based on inverse factorial expansions, and gives birth to interwoven non-perturbative partial sums whose coefficients are related to the perturbative ones by an interesting resurgence phenomenon. It is a non-perturbative improvement in the sense that, for some optimal truncations of the partial sums, the remainder at a given hyperasymptotic level is exponentially suppressed compared to the remainder at the preceding hyperasymptotic level. The Mellin-Barnes representation allows our results to be automatically valid for a wide range of the phase of the complex coupling constant, including Stokes lines. A numerical analysis is performed to emphasize the improved accuracy that this method allows to reach compared to the usual perturbative approach, and the importance of hyperasymptotic optimal truncation schemes.
Photoionization cross sections and Auger rates calculated by many-body perturbation theory
International Nuclear Information System (INIS)
Kelly, H.P.
1976-01-01
Methods for applying the many body perturbation theory to atomic calculations are discussed with particular emphasis on calculation of photoionization cross sections and Auger rates. Topics covered include: Rayleigh--Schroedinger theory; many body perturbation theory; calculations of photoionization cross sections; and Auger rates
Calculations in perturbative string field theory
International Nuclear Information System (INIS)
Thorn, C.B.
1987-01-01
The author discusses methods for evaluating the Feynman diagrams of string field theory, with particular emphasis on Witten's version of open string field theory. It is explained in some detail how the rules states by Giddings and Martinec for relating a given diagram to a Polyakov path integral emerge from the Feynman rules
Nucleon parton distributions in chiral perturbation theory
International Nuclear Information System (INIS)
Moiseeva, Alena
2013-01-01
Properties of the chiral expansion of nucleon light-cone operators have been studied. In the framework of the chiral perturbation theory we have demonstrated that convergency of the chiral expansion of nucleon parton distributions strongly depends on the value of the variable x. Three regions in x with essentially different analytical properties of the resulting chiral expansion for parton distributions were found. For each of the regions we have elaborated special power counting rules corresponding to the partial resummation of the chiral series. The nonlocal effective operators for the vector and the axial nucleon parton distributions have been constructed at the zeroth and the first chiral order. Using the derived nonlocal operators and the derived power counting rules we have obtained the second order expressions for the nucleon GPDs H(x,ξ,Δ 2 ), H(x,ξ,Δ 2 ),E(x,ξ,Δ 2 ) valid in the region x>or similar a 2 χ .
Baryon mass splittings in chiral perturbation theory
International Nuclear Information System (INIS)
Banerjee, M.K.; Milana, J.
1995-01-01
Baryon masses are calculated in chiral perturbation theory at the one-loop O(p 3 ) level in chiral expansion and to leading order in the heavy baryon expansion. Ultraviolet divergences occur requiring the introduction of counterterms. Despite this necessity, no knowledge of the counterterms is required to determine the violations of the Gell-Mann--Okubo mass relation for the baryon octet or of the decuplet equal-mass-spacing rule, as all divergences cancel exactly at this order. For the same reason all references to an arbitrary scale μ are absent. Neither of these features continue to higher powers in the chiral expansion. We also discuss critically the absolute necessity of simultaneously going beyond the leading-order heavy baryon expansion, if one goes beyond the one-loop O(p 3 ) level. We point out that these corrections in 1/M B generate new divergences ∝m 4 /M 10 . These divergences together with the divergences occurring in one-loop O(p 4 ) graphs of chiral perturbation theory are taken care of by the same set of counterterms. Because of these unknown counterterms one cannot predict the baryon mass splittings at the one-loop O(p 4 ) level even if the parameters of all scrL 1 πN terms are known. We point out another serious problem of going to the one-loop O(p 4 ) level. When the decuplet is off its mass shell there are additional πNΔ and πΔΔ interaction terms. These interactions contribute to the divergent terms ∝(m 4 /M 10 ), and also to nonanalytic terms such as ∝(m 4 /M 10 )ln(m/M 10 ). Without knowledge of the coupling constants appearing in these interactions, one cannot carry out a consistent one-loop O(p 4 ) level calculation
Generalized perturbation theory in DRAGON: application to CANDU cell calculations
International Nuclear Information System (INIS)
Courau, T.; Marleau, G.
2001-01-01
Generalized perturbation theory (GPT) in neutron transport is a means to evaluate eigenvalue and reaction rate variations due to small changes in the reactor properties (macroscopic cross sections). These variations can be decomposed in two terms: a direct term corresponding to the changes in the cross section themselves and an indirect term that takes into account the perturbations in the neutron flux. As we will show, taking into account the indirect term using a GPT method is generally straight forward since this term is the scalar product of the unperturbed generalized adjoint with the product of the variation of the transport operator and the unperturbed flux. In the case where the collision probability (CP) method is used to solve the transport equation, evaluating the perturbed transport operator involves calculating the variations in the CP matrix for each change in the reactor properties. Because most of the computational effort is dedicated to the CP matrix calculation the gains expected form the GPT method would therefore be annihilated. Here we will present a technique to approximate the variations in the CP matrices thereby replacing the variations in the transport operator with source term variations. We will show that this approximation yields errors fully compatible with the standard generalized perturbation theory errors. Results for 2D CANDU cell calculations will be presented. (author)
Energy Technology Data Exchange (ETDEWEB)
Blanchard, P [European Organization for Nuclear Research, Geneva (Switzerland); Seneor, R [European Organization for Nuclear Research, Geneva (Switzerland); Ecole Polytechnique, 75 - Paris (France). Centre de Physique Theorique)
1975-01-01
With the method of perturbative renormalization developed by Epstein and Glaser it is shown that Green's functions exist for theories with massless particles such as Q.E.D. and lambda:PHI/sup 2n/ theories. Growth properties are given in momentum space. In the case of Q.E.D., it is also shown that one can perform the physical mass renormalization.
Energy Technology Data Exchange (ETDEWEB)
Borges, Antonio Andrade
1998-07-01
A new method for the calculation of sensitivity coefficients is developed. The new method is a combination of two methodologies used for calculating theses coefficients, which are the differential and the generalized perturbation theory methods. The method utilizes as integral parameter the average flux in an arbitrary region of the system. Thus, the sensitivity coefficient contains only the component corresponding to the neutron flux. To obtain the new sensitivity coefficient, the derivatives of the integral parameter, {phi}, with respect to {sigma} are calculated using the perturbation method and the functional derivatives of this generic integral parameter with respect to {sigma} and {phi} are calculated using the differential method. (author)
Matsubara, Takahiko
2003-02-01
We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields and provide useful formulae for application of the perturbation theory to various statistics. This formalism is an extensive generalization of the method used by Matsubara, who derived a weakly nonlinear formula of the genus statistic in a three-dimensional density field. After describing the general method, we apply the formalism to a series of statistics, including genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clarified. These statistics can be applied to several cosmic fields, including three-dimensional density field, three-dimensional velocity field, two-dimensional projected density field, and so forth. The results are detailed for second-order theory of the formalism. The effect of the bias is discussed. The statistics of smoothed cosmic fields as functions of rescaled threshold by volume fraction are discussed in the framework of second-order perturbation theory. In CDM-like models, their functional deviations from linear predictions plotted against the rescaled threshold are generally much smaller than that plotted against the direct threshold. There is still a slight meatball shift against rescaled threshold, which is characterized by asymmetry in depths of troughs in the genus curve. A theory-motivated asymmetry factor in the genus curve is proposed.
Convergence of perturbation theory expansion for the Yukawa interaction
International Nuclear Information System (INIS)
Basuev, A.G.
1975-01-01
It is shown that the perturbation theory series in the translational-invariant case and upon removal of the boson propagator cut-off for euclidian Green's functions converges when gsup(2)/2 2 is the mass of the boson and Δ(o) is the fermion propagator in the zero of kappa-space. This problem was previously considered by other methods in respect of pseudo-euclidian functions (for the S-matrix) and of euclidian Green's functions. (author)
de Sitter limit of inflation and nonlinear perturbation theory
DEFF Research Database (Denmark)
R. Jarnhus, Philip; Sloth, Martin Snoager
2007-01-01
We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gaug...
Driven similarity renormalization group: Third-order multireference perturbation theory.
Li, Chenyang; Evangelista, Francesco A
2017-03-28
A third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N 6 ) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F 2 , H 2 O 2 , C 2 H 6 , and N 2 along the F-F, O-O, C-C, and N-N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbation theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (Δ ST =E T -E S ) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic Δ ST is 3.9 kcal mol -1 , a value that is within 0.1 kcal mol -1 from multireference coupled cluster results.
Very high order lattice perturbation theory for Wilson loops
International Nuclear Information System (INIS)
Horsley, R.
2010-10-01
We calculate perturbativeWilson loops of various sizes up to loop order n=20 at different lattice sizes for pure plaquette and tree-level improved Symanzik gauge theories using the technique of Numerical Stochastic Perturbation Theory. This allows us to investigate the behavior of the perturbative series at high orders. We observe differences in the behavior of perturbative coefficients as a function of the loop order. Up to n=20 we do not see evidence for the often assumed factorial growth of the coefficients. Based on the observed behavior we sum this series in a model with hypergeometric functions. Alternatively we estimate the series in boosted perturbation theory. Subtracting the estimated perturbative series for the average plaquette from the non-perturbative Monte Carlo result we estimate the gluon condensate. (orig.)
Modified method of perturbed stationary states. I
International Nuclear Information System (INIS)
Green, T.A.
1978-10-01
The reaction coordinate approach of Mittleman is used to generalize the method of Perturbed Stationary States. A reaction coordinate is defined for each state in the scattering expansion in terms of parameters which depend on the internuclear separation. These are to be determined from a variational principle described by Demkov. The variational result agrees with that of Bates and McCarroll in the limit of separated atoms, but is generally different elsewhere. The theory is formulated for many-electron systems, and the construction of the scattering expansion is discussed for simple one-, two-, and three-electron systsm. The scattering expansion and the Lagrangian for the radial scattering functions are given in detail for a heteronuclear one-electron system. 2 figures
Perturbative Quantum Gravity from Gauge Theory
Carrasco, John Joseph
In this dissertation we present the graphical techniques recently developed in the construction of multi-loop scattering amplitudes using the method of generalized unitarity. We construct the three-loop and four-loop four-point amplitudes of N = 8 supergravity using these methods and the Kawaii, Lewellen and Tye tree-level relations which map tree-level gauge theory amplitudes to tree-level gravity theory amplitudes. We conclude by extending a tree-level duality between color and kinematics, generic to gauge theories, to a loop level conjecture, allowing the easy relation between loop-level gauge and gravity kinematics. We provide non-trivial evidence for this conjecture at three-loops in the particular case of maximal supersymmetry.
The Schroedinger equation and canonical perturbation theory
International Nuclear Information System (INIS)
Graffi, S.; Paul, T.
1987-01-01
Let T 0 (ℎ,ω)+εV be the Schroedinger operator corresponding to the classical Hamiltonian H 0 (ω)+εV, where H 0 (ω) is the d-dimensional harmonic oscillator with non-resonant frequencies ω=(ω 1 ..., ω d ) and the potential V(q 1 , ..., q d ) is an entire function of order (d+l) -1 . We prove that the algorithm of classical, canonical perturbation theory can be applied to the Schroedinger equation in the Bargmann representation. As a consequence, each term of the Rayleigh-Schroedinger series near any eigenvalue of T 0 (ℎ,ω) admits a convergent expansion in powers of ℎ of initial point the corresponding term of the classical Birkhoff expansion. Moreover if V is an even polynomial, the above result and the KAM theorem show that all eigenvalues λ n (ℎ,ε) of T 0 +εV such that nℎ coincides with a KAM torus are given, up to order ε ∞ , by a quantization formula which reduces to the Bohr-Sommerfeld one up to first order terms in ℎ. (orig.)
The tension as perturbative parameter in string theory
International Nuclear Information System (INIS)
Gamboa, J.
1990-01-01
We propose an approach to string theory where the zero theory is the null string. We find an explicit form of the propagator for the null string in the momentum space. We show that considering the tension as perturbative parameter, the perturbative series is completely summable and we find the propagator of the bosonic open string with tension T. (author) [pt
Sensitivity calculations of integral parameters by a generalyzed perturbation theory
International Nuclear Information System (INIS)
Santo, A.C.F. de.
1981-12-01
In this work, we first revise some concepts, concerning the neutron transport in nuclear systems. We derive the balance and importance equation. Then we discuss the neutron importance in subcritical, critical and supercritical systems. The adjoint flux is estabilished as the neutron importance for the fission process. The conventional perturbation theory is later presented. We developed a sistematic perturbative formulation in the first order variation in the distribution functions calculate the reactivity due to a system perturbation. We present in detail the flux difference and generalized functions methos. The above formulation is then extended for altered systems. We consider integral parameters of the type ratio of bilinear functionals (for which the reactivity is a particular case). We define sensitivity coeficients, for any integral parameter, corresponding to a especific system alterations. Possible aplication of the method are also discussed. In the last part of this work, we apply the perturbative formulation to the doppler reacitivity sensibility calculation, utilizing the generalized functions method. We describe in detail the compiler program written for this and some other possible aplications. (Author) [pt
Perturbation method for fuel evolution and shuffling analysis
International Nuclear Information System (INIS)
Gandini, A.
1987-01-01
A perturbation methodology is described by which the behaviour of a reactor system during burnup can be analyzed making use of Generalized Perturbation Theory (GPT) codes already available in the linear domain. Typical quantities that can be studied with the proposed methodology are the amount of a specified material at the end of cycle, the fluence in a specified region, the residual reactivity at end of reactor life cycle. The potentiality of the method for fuel shuffling studies is also described. (author)
On the resolvents methods in quantum perturbation calculations
International Nuclear Information System (INIS)
Burzynski, A.
1979-01-01
This paper gives a systematic review of resolvent methods in quantum perturbation calculations. The case of discrete spectrum of hamiltonian is considered specially (in the literature this is the fewest considered case). The topics of calculations of quantum transitions by using of the resolvent formalism, quantum transitions between states from particular subspaces, the shifts of energy levels, are shown. The main ideas of stationary perturbation theory developed by Lippmann and Schwinger are considered too. (author)
Efficient perturbation theory to improve the density matrix renormalization group
Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej
2017-02-01
The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j= ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.
Divergence of perturbation theory in large scale structures
Pajer, Enrico; van der Woude, Drian
2018-05-01
We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for which exact solutions before shell crossing are known. We review the convergence of perturbation theory for the power spectrum, recently proven by McQuinn and White [1], and extend it to non-Gaussian initial conditions and the bispectrum. In contrast, we prove that perturbation theory diverges for the real space two-point correlation function and for the probability density function (PDF) of the density averaged in cells and all the cumulants derived from it. We attribute these divergences to the statistical averaging intrinsic to cosmological observables, which, even on very large and "perturbative" scales, gives non-vanishing weight to all extreme fluctuations. Finally, we discuss some general properties of non-perturbative effects in real space and Fourier space.
Solving the open bosonic string in perturbation theory
International Nuclear Information System (INIS)
Samuel, S.
1990-01-01
The integrand and integration region for the N-point amplitude in the open oriented bosonic string are obtained to all orders in perturbation theory. The result is derived from the Witten covariant string field theory by using on-shell and off-shell conformal methods and Riemann surface mathematics. Although only the off-shell g-loop tachyon amplitudes are computed explicitly, the methods generalize to other external states. We derive the g-loop ghost-Jacobi identity in which the ghost correlation function cancels the jacobian factor in changing from second-quantized to first-quantized variables. Moduli space is discussed from several viewpoints and it is shown that string field theory provides an algorithm for its determination. (orig.)
Fuel management optimization based on generalized perturbation theory
International Nuclear Information System (INIS)
White, J.R.; Chapman, D.M.; Biswas, D.
1986-01-01
A general methodology for optimization of assembly shuffling and burnable poison (BP) loadings for LWR reload design has been developed. The uniqueness of this approach lies in the coupling of Generalized Perturbation Theory (GPT) methods and standard Integer Programming (IP) techniques. An IP algorithm can simulate the discrete nature of the fuel shuffling and BP loading problems, and the use of GPT sensitivity data provides an efficient means for modeling the behavior of the important core performance parameters. The method is extremely flexible since the choice of objective function and the number and mix of constraints depend only on the ability of GPT to determine the appropriate sensitivity functions
Adler function for light quarks in analytic perturbation theory
International Nuclear Information System (INIS)
Milton, K. A.; Solovtsov, I. L.; Solovtsova, O. P.
2001-01-01
The method of analytic perturbation theory, which avoids the problem of ghost-pole-type singularities and gives a self-consistent description of both spacelike and timelike regions, is applied to describe the 'light' Adler function corresponding to the nonstrange vector channel of the inclusive decay of the τ lepton. The role of threshold effects is investigated. The behavior of the quark-antiquark system near threshold is described by using a new relativistic resummation factor. It is shown that the method proposed leads to good agreement with the 'experimental' Adler function down to the lowest energy scale
Perturbative Gravity and Gauge Theory Relations: A Review
Directory of Open Access Journals (Sweden)
Thomas Søndergaard
2012-01-01
Full Text Available This paper is dedicated to the amazing Kawai-Lewellen-Tye relations, connecting perturbative gravity and gauge theories at tree level. The main focus is on n-point derivations and general properties both from a string theory and pure field theory point of view. In particular, the field theory part is based on some very recent developments.
Renormalization scheme-invariant perturbation theory
International Nuclear Information System (INIS)
Dhar, A.
1983-01-01
A complete solution to the problem of the renormalization scheme dependence of perturbative approximants to physical quantities is presented. An equation is derived which determines any physical quantity implicitly as a function of only scheme independent variables. (orig.)
Fermi interaction. Conservation of vector current and modified perturbation theory
International Nuclear Information System (INIS)
Rochev, V.E.
1983-01-01
The Fermi interaction (anti psi ysub(n) psi)sup(2) is investigated with the method of auxilary field. The analogues of the Ward-Takahashi electrodynamical identities and the gauge transformations of Green functions, that are the consequence of the conservation of vector current, have been obtained. The gauge function for the spinor propagator is the exponential superpropagator. The arguments are given in favour of the existence of a modified perturbation theory, which is finite in every order and non-analytical over its coupling constant, for the four-fermion interaction. The non-analytical part is defined unambiguously, and the analytical part contains a set of finite dimensionless constants to define which non-perturbative information is needed. The simplest model (the chain approximation) for the non-stable vector bound state is considered
Renewal theory for perturbed random walks and similar processes
Iksanov, Alexander
2016-01-01
This book offers a detailed review of perturbed random walks, perpetuities, and random processes with immigration. Being of major importance in modern probability theory, both theoretical and applied, these objects have been used to model various phenomena in the natural sciences as well as in insurance and finance. The book also presents the many significant results and efficient techniques and methods that have been worked out in the last decade. The first chapter is devoted to perturbed random walks and discusses their asymptotic behavior and various functionals pertaining to them, including supremum and first-passage time. The second chapter examines perpetuities, presenting results on continuity of their distributions and the existence of moments, as well as weak convergence of divergent perpetuities. Focusing on random processes with immigration, the third chapter investigates the existence of moments, describes long-time behavior and discusses limit theorems, both with and without scaling. Chapters fou...
A simple extrapolation of thermodynamic perturbation theory to infinite order
International Nuclear Information System (INIS)
Ghobadi, Ahmadreza F.; Elliott, J. Richard
2015-01-01
Recent analyses of the third and fourth order perturbation contributions to the equations of state for square well spheres and Lennard-Jones chains show trends that persist across orders and molecular models. In particular, the ratio between orders (e.g., A 3 /A 2 , where A i is the ith order perturbation contribution) exhibits a peak when plotted with respect to density. The trend resembles a Gaussian curve with the peak near the critical density. This observation can form the basis for a simple recursion and extrapolation from the highest available order to infinite order. The resulting extrapolation is analytic and therefore cannot fully characterize the critical region, but it remarkably improves accuracy, especially for the binodal curve. Whereas a second order theory is typically accurate for the binodal at temperatures within 90% of the critical temperature, the extrapolated result is accurate to within 99% of the critical temperature. In addition to square well spheres and Lennard-Jones chains, we demonstrate how the method can be applied semi-empirically to the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT)
Communication: Random phase approximation renormalized many-body perturbation theory
International Nuclear Information System (INIS)
Bates, Jefferson E.; Furche, Filipp
2013-01-01
We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations
Wilson loops in very high order lattice perturbation theory
International Nuclear Information System (INIS)
Ilgenfritz, E.M.; Nakamura, Y.; Perlt, H.; Schiller, A.; Rakow, P.E.L.; Schierholz, G.; Regensburg Univ.
2009-10-01
We calculate Wilson loops of various sizes up to loop order n=20 for lattice sizes of L 4 (L=4,6,8,12) using the technique of Numerical Stochastic Perturbation Theory in quenched QCD. This allows to investigate the behaviour of the perturbative series at high orders. We discuss three models to estimate the perturbative series: a renormalon inspired fit, a heuristic fit based on an assumed power-law singularity and boosted perturbation theory. We have found differences in the behavior of the perturbative series for smaller and larger Wilson loops at moderate n. A factorial growth of the coefficients could not be confirmed up to n=20. From Monte Carlo measured plaquette data and our perturbative result we estimate a value of the gluon condensate left angle (α)/(π)GG right angle. (orig.)
Numerical stochastic perturbation theory in the Schroedinger functional
International Nuclear Information System (INIS)
Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk; Dalla Brida, Mattia; Sint, Stefan; Deutsches Elektronen-Synchrotron
2013-11-01
The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.
Numerical stochastic perturbation theory in the Schroedinger functional
Energy Technology Data Exchange (ETDEWEB)
Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk [Parma Univ. (Italy); INFN, Parma (Italy); Dalla Brida, Mattia [Trinity College Dublin (Ireland). School of Mathematics; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2013-11-15
The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.
Ferromagnetism in the Hubbard model: a modified perturbation theory
International Nuclear Information System (INIS)
Gangadhar Reddy, G.; Ramakanth, A.; Nolting, W.
2005-01-01
We study the possibility of ferromagnetism in the Hubbard model using the modified perturbation theory. In this approach an Ansatz is made for the self-energy of the electron which contains the second order contribution developed around the Hartree-Fock solution and two parameters. The parameters are fixed by using a moment method. This self energy satisfies several known exact limiting cases. Using this self energy, the Curie temperature T c as a function of band filling n is investigated. It is found that T c falls off abruptly as n approaches half filling. The results are in qualitative agreement with earlier calculations using other approximation schemes. (author)
Cosmological Perturbation Theory Using the Schrödinger Equation
Szapudi, István; Kaiser, Nick
2003-01-01
We introduce the theory of nonlinear cosmological perturbations using the correspondence limit of the Schrödinger equation. The resulting formalism is equivalent to using the collisionless Boltzmann (or Vlasov) equations, which remain valid during the whole evolution, even after shell crossing. Other formulations of perturbation theory explicitly break down at shell crossing, e.g., Eulerean perturbation theory, which describes gravitational collapse in the fluid limit. This Letter lays the groundwork by introducing the new formalism, calculating the perturbation theory kernels that form the basis of all subsequent calculations. We also establish the connection with conventional perturbation theories, by showing that third-order tree-level results, such as bispectrum, skewness, cumulant correlators, and three-point function, are exactly reproduced in the appropriate expansion of our results. We explicitly show that cumulants up to N=5 predicted by Eulerian perturbation theory for the dark matter field δ are exactly recovered in the corresponding limit. A logarithmic mapping of the field naturally arises in the Schrödinger context, which means that tree-level perturbation theory translates into (possibly incomplete) loop corrections for the conventional perturbation theory. We show that the first loop correction for the variance is σ2=σ2L+(-1.14- n)σ4L for a field with spectral index n. This yields 1.86 and 0.86 for n=-3 and -2, respectively, to be compared with the exact loop order corrections 1.82 and 0.88. Thus, our tree-level theory recovers the dominant part of first-order loop corrections of the conventional theory, while including (partial) loop corrections to infinite order in terms of δ.
Granovsky, Alexander A
2011-06-07
The distinctive desirable features, both mathematically and physically meaningful, for all partially contracted multi-state multi-reference perturbation theories (MS-MR-PT) are explicitly formulated. The original approach to MS-MR-PT theory, called extended multi-configuration quasi-degenerate perturbation theory (XMCQDPT), having most, if not all, of the desirable properties is introduced. The new method is applied at the second order of perturbation theory (XMCQDPT2) to the 1(1)A(')-2(1)A(') conical intersection in allene molecule, the avoided crossing in LiF molecule, and the 1(1)A(1) to 2(1)A(1) electronic transition in cis-1,3-butadiene. The new theory has several advantages compared to those of well-established approaches, such as second order multi-configuration quasi-degenerate perturbation theory and multi-state-second order complete active space perturbation theory. The analysis of the prevalent approaches to the MS-MR-PT theory performed within the framework of the XMCQDPT theory unveils the origin of their common inherent problems. We describe the efficient implementation strategy that makes XMCQDPT2 an especially useful general-purpose tool in the high-level modeling of small to large molecular systems. © 2011 American Institute of Physics
Perturbation theory and coupling constant analyticity in two-dimensional field theories
International Nuclear Information System (INIS)
Simon, B.
1973-01-01
Conjectural material and results over a year old are presented in the discussion of perturbation theory and coupling constant analyticity in two-dimensional field theories. General properties of perturbation series are discussed rather than questions of field theory. The question is interesting for two reasons: First, one would like to understand why perturbation theory is such a good guide (to show that perturbation theory determines the theory in some way). Secondly, one hopes to prove that some or all of the theories are nontrivial. (U.S.)
Application of generalized perturbation theory to flux disadvantage factor calculations
International Nuclear Information System (INIS)
Sallam, O.H.; Akimov, I.S.; Naguib, K.; Hamouda, I.
1979-01-01
The possibility of using the generalized perturbation theory to calculate the perturbation of the flux disadvantage factors of reactor cell, resulting from the variation of the cell parameters, is studied. For simplicity the one-group diffusion approximation is considered. All necessary equations are derived for variations both of the cell dimensions. Numerical results are presented in the paper
Theory of deep inelastic neutron scattering: Hard-core perturbation theory
International Nuclear Information System (INIS)
Silver, R.N.
1988-01-01
Details are presented of a new many-body theory for deep inelastic neutron scattering (DINS) experiments to measure momentum distributions in quantum fluids and solids. The high-momentum and energy-transfer scattering law in helium is shown to be a convolution of the impulse approximation with a final-state broadening function which depends on the scattering phase shifts and the radial distribution function. The predicted broadening satisfies approximate Y scaling, is neither Lorentzian nor Gaussian, and obeys the f, ω 2 , and ω 3 sum rules. The derivation uses a combination of Liouville perturbation theory, projection superoperators, and semiclassical methods which I term ''hard-core perturbation theory.'' A review is presented of the predictions of prior theories for DINS experiments in relation to the present work. A subsequent paper will present massive numerical predictions and a discussion of DINS experiments on superfluid 4 He
Non-perturbative Heavy Quark Effective Theory
DEFF Research Database (Denmark)
Della Morte, Michele; Heitger, Jochen; Simma, Hubert
2015-01-01
We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/m_h-corrections. We also discuss recent preliminary results on the form factors parameterizing semi-leptonic B...
Energy momentum tensor in local causal perturbation theory
International Nuclear Information System (INIS)
Prange, D.
2001-01-01
We study the energy momentum tensor in the Bogolyubov-Epstein-Glaser approach to perturbation theory. It is found to be locally conserved for a class of theories containing to derivated fields in the interaction. For the massless φ 4 -theory we derive the trace anomaly of the improved tensor. (orig.)
Quasipotential in the fourth order of perturbation theory
International Nuclear Information System (INIS)
Bojkova, N.A.; Dvoeglazov, V.V.; Tyukhtyaev, Yu.N.; Faustov, R.N.
1992-01-01
The quasipotential in the fourth order of perturbation theory is calculated in the Coulomb gauge for the unequal mass particles. It could be used for the future calculations of energy spectra in two-body systems. 15 refs.; 1 fig
Perturbation theory instead of large scale shell model calculations
International Nuclear Information System (INIS)
Feldmeier, H.; Mankos, P.
1977-01-01
Results of large scale shell model calculations for (sd)-shell nuclei are compared with a perturbation theory provides an excellent approximation when the SU(3)-basis is used as a starting point. The results indicate that perturbation theory treatment in an SU(3)-basis including 2hω excitations should be preferable to a full diagonalization within the (sd)-shell. (orig.) [de
A direct derivation of polynomial invariants from perturbative Chern-Simons gauge theory
International Nuclear Information System (INIS)
Ochiai, Tomoshiro
2003-01-01
There have been several methods to show that the expectation values of Wilson loop operators in the SU(N) Chern-Simons gauge theory satisfy the HOMFLY skein relation. We shall give another method from the perturbative method of the SU(N) Chern-Simons gauge theory in the light-cone gauge, which is more direct than already known methods
Perturbation theory and collision probability formalism. Vol. 2
Energy Technology Data Exchange (ETDEWEB)
Nasr, M [National Center for Nuclear Safety and Radiation Control, Atomic Energy Authority, Cairo (Egypt)
1996-03-01
Perturbation theory is commonly used in evaluating the activity effects, particularly those resulting from small and localized perturbation in multiplying media., e.g. in small sample reactivity measurements. The Boltzmann integral transport equation is generally used for evaluating the direct and adjoint fluxes in the heterogenous lattice cells to be used in the perturbation equations. When applying perturbation theory in this formalism, a term involving the perturbation effects on the special transfer kernel arises. This term is difficult to evaluate correctly, since it involves an integration all over the entire system. The main advantage of the perturbation theory which is the limitation of the integration procedure on the perturbation region is found to be of no practical use in such cases. In the present work, the perturbation equation in the collision probability formalism is analyzed. A mathematical treatment of the term in question is performed. A new mathematical expression for this term is derived. The new expression which can be estimated easily is derived.
On estimating perturbative coefficients in quantum field theory and statistical physics
International Nuclear Information System (INIS)
Samuel, M.A.; Stanford Univ., CA
1994-05-01
The authors present a method for estimating perturbative coefficients in quantum field theory and Statistical Physics. They are able to obtain reliable error-bars for each estimate. The results, in all cases, are excellent
On the meaning of perturbation expansions in quantum field theory
International Nuclear Information System (INIS)
Burdik, C.; Chyla, J.
1987-01-01
We reformulate perturbation expansions in renormalized quantum field theories in a way that allows straightforward handling of situations when in the conventional approach (i.e. in fixed renormalization scheme) these expansions are divergent. In our approach the results of perturbation calculations of physical quantities appear in the form of (under certain circumstances) convergent expansions in powers of a free parameter χ, characterising the procedure involved. This inherent ambiguity of perturbative calculations is conjectures to be an expression of the underlaying ambiguity in the separation of the full theory into its perturbative and nonperturbative parts. The close connection of our results with the Borel summation technique is demonstrated and their relation to conventional perturbation expansions in fixed renormalization scheme is clarified
Theory of cosmological perturbations with cuscuton
Energy Technology Data Exchange (ETDEWEB)
Boruah, Supranta S.; Kim, Hyung J.; Geshnizjani, Ghazal, E-mail: ssarmabo@uwaterloo.ca, E-mail: h268kim@uwaterloo.ca, E-mail: ggeshniz@uwaterloo.ca [Department of Applied Mathematics, University of Waterloo, 200 University Ave W., Waterloo, ON N2L 3G1 (Canada)
2017-07-01
This paper presents the first derivation of the quadratic action for curvature perturbations, ζ, within the framework of cuscuton gravity. We study the scalar cosmological perturbations sourced by a canonical single scalar field in the presence of cuscuton field. We identify ζ as comoving curvature with respect to the source field and we show that it retains its conservation characteristic on super horizon scales. The result provides an explicit proof that cuscuton modification of gravity around Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is ghost free. We also investigate the potential development of other instabilities in cuscuton models. We find that in a large class of these models, there is no generic instability problem. However, depending on the details of slow-roll parameters, specific models may display gradient instabilities.
Perturbing the ground ring of 2D string theory
Barbón, José L F
1992-01-01
We use free field techniques in D=2 string theory to calculate the perturbation of the special state algebras when the cosmologi- cal constant is turned on. In particular, we find that the "ground cone" preserved by the ring structure is promoted to a three dimen- sional hyperboloid as conjectured by Witten. On the other hand, the perturbed (1,1) a three dimensional hyperboloid as conjectured by Witten. On the other hand, the perturbed (1,1) current algebra of moduli deformations is computed completely, and no simple geometrical inter- pretation is found. We also quote some facts concerning the Liouville/matrix model dictio- nary in this class of theories.
Growth rate, population entropy, and perturbation theory.
Demetrius, L.
1989-01-01
This paper is concerned with the connection between two classes of population variables: measures of population growth rate—the Malthusian parameter, the net reproduction rate, the gross reproduction rate, and the mean life expectancy; and measures of demographic heterogeneity—population entropy. It is shown that the entropy functions predict the response of the growth rate parameters to perturbations in the age-specific fecundity and mortality schedule. These results are invoked to introduce...
Monte Carlo perturbation theory in neutron transport calculations
International Nuclear Information System (INIS)
Hall, M.C.G.
1980-01-01
The need to obtain sensitivities in complicated geometrical configurations has resulted in the development of Monte Carlo sensitivity estimation. A new method has been developed to calculate energy-dependent sensitivities of any number of responses in a single Monte Carlo calculation with a very small time penalty. This estimation typically increases the tracking time per source particle by about 30%. The method of estimation is explained. Sensitivities obtained are compared with those calculated by discrete ordinates methods. Further theoretical developments, such as second-order perturbation theory and application to k/sub eff/ calculations, are discussed. The application of the method to uncertainty analysis and to the analysis of benchmark experiments is illustrated. 5 figures
Convergent perturbation expansions for Euclidean quantum field theory
International Nuclear Information System (INIS)
Mack, G.; Pordt, A.
1984-09-01
Mayer perturbation theory is designed to provide computable convergent expansions which permit calculation of Greens functions in Euclidean Quantum Field Theory to arbitrary accuracy, including 'nonperturbative' contributions from large field fluctuations. Here we describe the expansions at the example of 3-dimensional lambdaphi 4 -theory (in continuous space). They are not essentially more complicated than standard perturbation theory. The n-th order term is expressed in terms of 0(n)-dimensional integrals, and is of order lambda 4 if 4k-3<=n<=4k. (orig.)
Wilson loops to 20th order numerical stochastic perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Hotzel, G.; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Ilgenfritz, E.M. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Joint Institute for Nuclear Research, VBLHEP, Dubna (Russian Federation); Millo, R.; Rakow, P.E.L. [Liverpool Univ. (Germany). Theoretical Physics Div.; Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Kobe, Hyogo (Japan); Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-05-15
We calculate Wilson loops of various sizes up to 20 loops in SU(3) pure lattice gauge theory at different lattice sizes for Wilson gauge action using the technique of numerical stochastic perturbation theory. This allows us to investigate the perturbative series for various Wilson loops at high loop orders. We observe differences in the behavior of those series as function of the loop order. Up to n=20 we do not find evidence for the factorial growth of the expansion coefficients often assumed to characterize an asymptotic series. Based on the actually observed behavior we sum the series in a model parametrized by hypergeometric functions. Alternatively we estimate the total series in boosted perturbation theory using information from the first 14 loops. We introduce generalized ratios of Wilson loops of different sizes. Together with the corresponding Wilson loops from standard Monte Carlo measurements they enable us to assess their non-perturbative parts.
Perturbation theory for water with an associating reference fluid
Marshall, Bennett D.
2017-11-01
The theoretical description of the thermodynamics of water is challenged by the structural transition towards tetrahedral symmetry at ambient conditions. As perturbation theories typically assume a spherically symmetric reference fluid, they are incapable of accurately describing the liquid properties of water at ambient conditions. In this paper we address this problem by introducing the concept of an associated reference perturbation theory (APT). In APT we treat the reference fluid as an associating hard sphere fluid which transitions to tetrahedral symmetry in the fully hydrogen bonded limit. We calculate this transition in a theoretically self-consistent manner without appealing to molecular simulations. This associated reference provides the reference fluid for a second order Barker-Henderson perturbative treatment of the long-range attractions. We demonstrate that this approach gives a significantly improved description of water as compared to standard perturbation theories.
Evolution of curvature perturbation in generalized gravity theories
International Nuclear Information System (INIS)
Matsuda, Tomohiro
2009-01-01
Using the cosmological perturbation theory in terms of the δN formalism, we find the simple formulation of the evolution of the curvature perturbation in generalized gravity theories. Compared with the standard gravity theory, a crucial difference appears in the end-boundary of the inflationary stage, which is due to the non-ideal form of the energy-momentum tensor that depends explicitly on the curvature scalar. Recent study shows that ultraviolet-complete quantum theory of gravity (Horava-Lifshitz gravity) can be approximated by using a generalized gravity action. Our paper may give an important step in understanding the evolution of the curvature perturbation during inflation, where the energy-momentum tensor may not be given by the ideal form due to the corrections from the fundamental theory.
Perturbation theory and importance functions in integral transport formulations
International Nuclear Information System (INIS)
Greenspan, E.
1976-01-01
Perturbation theory expressions for the static reactivity derived from the flux, collision density, birth-rate density, and fission-neutron density formulations of integral transport theory, and from the integro-differential formulation, are intercompared. The physical meaning and relation of the adjoint functions corresponding to each of the five formulations are established. It is found that the first-order approximation of the perturbation expressions depends on the transport theory formulation and on the adjoint function used. The approximations of the integro-differential formulation corresponding to different first-order approximations of the integral transport theory formulations are identified. It is found that the accuracy of all first-order approximations of the integral transport formulations examined is superior to the accuracy of first-order integro-differential perturbation theory
Mercier Franco, Luís Fernando; Castier, Marcelo; Economou, Ioannis G
2017-12-07
We show that the Zwanzig first-order perturbation theory can be obtained directly from a truncated Taylor series expansion of a two-body perturbation theory and that such truncation provides a more accurate prediction of thermodynamic properties than the full two-body perturbation theory. This unexpected result is explained by the quality of the resulting approximation for the fluid radial distribution function. We prove that the first-order and the two-body perturbation theories are based on different approximations for the fluid radial distribution function. To illustrate the calculations, the square-well fluid is adopted. We develop an analytical expression for the two-body perturbed Helmholtz free energy for the square-well fluid. The equation of state obtained using such an expression is compared to the equation of state obtained from the first-order approximation. The vapor-liquid coexistence curve and the supercritical compressibility factor of a square-well fluid are calculated using both equations of state and compared to Monte Carlo simulation data. Finally, we show that the approximation for the fluid radial distribution function given by the first-order perturbation theory provides closer values to the ones calculated via Monte Carlo simulations. This explains why such theory gives a better description of the fluid thermodynamic behavior.
On-Shell Methods in Perturbative QCD
International Nuclear Information System (INIS)
Bern, Zvi; Dixon, Lance J.; Kosower, David A.
2007-01-01
We review on-shell methods for computing multi-parton scattering amplitudes in perturbative QCD, utilizing their unitarity and factorization properties. We focus on aspects which are useful for the construction of one-loop amplitudes needed for phenomenological studies at the Large Hadron Collider
Many-body perturbation theory for ab initio nuclear structure
International Nuclear Information System (INIS)
Tichai, Alexander
2017-01-01
The solution of the quantum many-body problem for medium-mass nuclei using realistic nuclear interactions poses a superbe challenge for nuclear structure research. Because an exact solution can only be provided for the lightest nuclei, one has to rely on approximate solutions when proceeding to heavier systems. Over the past years, tremendous progress has been made in the development and application of systematically improvable expansion methods and an accurate description of nuclear observables has become viable up to mass number A ∼ 100. While closed-shell systems are consistently described via a plethora of different many-body methods, the extension to genuine open-shell systems still remains a major challenge and up to now there is no ab initio many-body method which applies equally well to systems with even and odd mass numbers. The goal of this thesis is the development and implementation of innovative perturbative approaches with genuine open-shell capabilities. This requires the extension of well-known single-reference approaches to more general vacua. In this work we choose two complementary routes for the usage of generalized reference states. First, we derive a new ab initio approach based on multi-configurational reference states that are conveniently derived from a prior no-core shell model calculation. Perturbative corrections are derived via second-order many-body perturbation theory, thus, merging configuration interaction and many-body perturbation theory. The generality of this ansatz enables for a treatment of medium-mass systems with arbitrary mass number, as well as the extension to low-lying excited states such that ground and excited states are treated on an equal footing. In a complementary approach, we use reference states that break a symmetry of the underlying Hamiltonian. In the simplest case this corresponds to the expansion around a particle-number-broken Hartree-Fock-Bogolyubov vacuum which is obtained from a mean-field calculation
Stochastic many-body perturbation theory for anharmonic molecular vibrations
Energy Technology Data Exchange (ETDEWEB)
Hermes, Matthew R. [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); Hirata, So, E-mail: sohirata@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan)
2014-08-28
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
Quark disconnected diagrams in chiral perturbation theory
Della Morte, Michele
2010-01-01
We show how quark-disconnected and quark-connected contributions to hadronic n-point functions can be written as independent correlators for which one can derive expressions in partially quenched chiral effective theory. As an example we apply the idea to the case of the hadronic vacuum polarisation. In particular, we consider the cases of the Nf = 2 theory without and with a partially quenched strange quark and also the Nf = 2 + 1 theory. In the latter two cases a parameter-free prediction for the disconnected contribution at NLO in the effective theory is given. Finally we show how twisted boundary conditions can then be used in lattice QCD to improve the q^2 resolution in the connected contributions even when flavour singlet operators are considered.
A new perturbative approximation applied to supersymmetric quantum field theory
International Nuclear Information System (INIS)
Bender, C.M.; Milton, K.A.; Pinsky, S.S.; Simmons, L.M. Jr.; Los Alamos National Lab.
1988-01-01
We show that a recently proposed graphical perturbative calculational scheme in quantum field theory is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not known of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0. (orig.)
Analysis of observables in Chern-Simons perturbation theory
International Nuclear Information System (INIS)
Alvarez, M.; Labastida, J.M.F.
1993-01-01
Chern-Simons theory with gauge group SU(N) is analyzed from a perturbation theory point of view. Computations up to order g 6 of the vacuum expectation value of the unknot are carried out and it is shown that agreement with the exact result by Witten implies no quantum correction at two loops for the two-point function. In addition, it is shown from a perturbation theory point of view that the framing dependence of the vacuum expectation value of an arbitrary knot factorizes in the form predicted by Witten. (orig.)
Scheme (in?) dependence in perturbative Lagrangian quantum field theory
International Nuclear Information System (INIS)
Slavnov, D.A.
1995-01-01
A problem of renormalization - scheme ambiguity in perturbation quantum field theory is investigated. A procedure is described that makes it possible to express uniquely all observable quantities in terms of a set base observables. Renormalization group equations for the base observable are constructed. The case of mass theory is treated. 9 refs
Perturbation Theory of Massive Yang-Mills Fields
Veltman, M.
1968-08-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.
Perturbation theory via Feynman diagrams in classical mechanics
Penco, R.; Mauro, D.
2006-01-01
In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like path integrals and generating functionals.
The SU(3) beta function from numerical stochastic perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Perlt, H. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Bonn Univ. (Germany). Helmholtz Inst. fuer Strahlen- und Kernphysik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Div.; Schierholz, G.; Schiller, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-09-15
The SU(3) beta function is derived from Wilson loops computed to 20th order in numerical stochastic perturbation theory. An attempt is made to include massless fermions, whose contribution is known analytically to 4th order. The question whether the theory admits an infrared stable fixed point is addressed.
Degenerate R-S perturbation theory
Hirschfelder, J. O.; Certain, P. R.
1973-01-01
A concise, systematic procedure is given for determining the Rayleigh-Schrodinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n+1)st order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite order operators which are determined by the successive resolution of the space of the zeroth order functions.
The Operator Product Expansion Beyond Perturbation Theory in QCD
International Nuclear Information System (INIS)
Dominguez, C. A.
2011-01-01
The Operator Product Expansion (OPE) of current correlators at short distances beyond perturbation theory in QCD, together with Cauchy's theorem in the complex energy plane, are the pillars of the method of QCD sum rules. This technique provides an analytic tool to relate QCD with hadronic physics at low and intermediate energies. It has been in use for over thirty years to determine hadronic parameters, form factors, and QCD parameters such as the quark masses, and the running strong coupling at the scale of the τ-lepton. QCD sum rules provide a powerful complement to numerical simulations of QCD on the lattice. In this talk a short review of the method is presented for non experts, followed by three examples of recent applications.
Non-perturbative field theory/field theory on a lattice
International Nuclear Information System (INIS)
Ambjorn, J.
1988-01-01
The connection between the theory of critical phenomena in statistical mechanics and the renormalization of field theory is briefly outlined. The way of using this connection is described to get information about non-perturbative quantities in QCD and about more intelligent ways of doing the Monte Carlo (MC) simulations. The (MC) method is shown to be a viable one in high energy physics, but it is not a good substitute for an analytic understanding. MC-methods will be very valuable both for getting out hard numbers and for testing the correctness of new ideas
Non-perturbative heavy quark effective theory. Introduction and status
International Nuclear Information System (INIS)
Sommer, Rainer; Humboldt-Universitaet, Berlin
2015-01-01
We give an introduction to Heavy Quark Effective Theory (HQET). Our emphasis is on its formulation non-perturbative in the strong coupling, including the non-perturbative determination of the parameters in the HQET Lagrangian. In a second part we review the present status of HQET on the lattice, largely based on work of the ALPHA collaboration in the last few years. We finally discuss opportunities and challenges.
Perturbation theory around the Wess-Zumino-Witten model
International Nuclear Information System (INIS)
Hasseln, H. v.
1991-05-01
We consider a perturbation of the Wess-Zumino-Witten model in 2D by a current-current interaction. The β-function is computed to third order in the coupling constant and a nontrivial fixedpoint is found. By non-abelian bosonization, this perturbed WZW-model is shown to have the same β-function (at least to order g 2 ) as the fermionic theory with a four-fermion interaction. (orig.) [de
String perturbation theory and effective Lagrangians
International Nuclear Information System (INIS)
Klebanov, I.
1987-09-01
We isolate logarithmic divergences from bosonic string amplitudes on a disc. These divergences are compared with 'tadpole' divergences in the effective field theory with a cosmological term, which also contains an effective potential for the dilation. Also, corrections to β-functions are compared with variations of the effective action. In both cases we find an inconsistency between the two. This is a serious problem which could undermine our ability to remove divergences from the bosonic string
Perturbed period-doubling bifurcation. I. Theory
DEFF Research Database (Denmark)
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1990-01-01
-defined way that is a function of the amplitude and the frequency of the signal. New scaling laws between the amplitude of the signal and the detuning δ are found; these scaling laws apply to a variety of quantities, e.g., to the shift of the bifurcation point. It is also found that the stability...... of a microwave-driven Josephson junction confirm the theory. Results should be of interest in parametric-amplification studies....
The accuracy of QCD perturbation theory at high energies
Dalla Brida, Mattia; Korzec, Tomasz; Ramos, Alberto; Sint, Stefan; Sommer, Rainer
2016-01-01
We discuss the determination of the strong coupling $\\alpha_\\mathrm{\\overline{MS}}^{}(m_\\mathrm{Z})$ or equivalently the QCD $\\Lambda$-parameter. Its determination requires the use of perturbation theory in $\\alpha_s(\\mu)$ in some scheme, $s$, and at some energy scale $\\mu$. The higher the scale $\\mu$ the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the $\\Lambda$-parameter in three-flavor QCD, we perform lattice computations in a scheme which allows us to non-perturbatively reach very high energies, corresponding to $\\alpha_s = 0.1$ and below. We find that perturbation theory is very accurate there, yielding a three percent error in the $\\Lambda$-parameter, while data around $\\alpha_s \\approx 0.2$ is clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.
Variational cluster perturbation theory for Bose-Hubbard models
International Nuclear Information System (INIS)
Koller, W; Dupuis, N
2006-01-01
We discuss the application of the variational cluster perturbation theory (VCPT) to the Mott-insulator-to-superfluid transition in the Bose-Hubbard model. We show how the VCPT can be formulated in such a way that it gives a translation invariant excitation spectrum-free of spurious gaps-despite the fact that it formally breaks translation invariance. The phase diagram and the single-particle Green function in the insulating phase are obtained for one-dimensional systems. When the chemical potential of the cluster is taken as a variational parameter, the VCPT reproduces the dimensional dependence of the phase diagram even for one-site clusters. We find a good quantitative agreement with the results of the density-matrix renormalization group when the number of sites in the cluster becomes of order 10. The extension of the method to the superfluid phase is discussed
Recent advances in multireference-based perturbation theory
International Nuclear Information System (INIS)
Nakano, Haruyuki; Hirao, Kimihiko
2003-01-01
Accurate ab initio computational chemistry has evolved dramatically. In particular, the development of multireference-based approaches has opened up a completely new area, and has had a profound impact on the potential of theoretical chemistry. Multireference-based perturbation theory (MRPT) is an extension of the closed-shell single reference Moeller-Plesset method, and has been successfully applied to many chemical and spectroscopic problems. MRPT has established itself as an efficient technique for treating nondynamical and dynamical correlations. Usually, a complete active space self-consistent field (CASSCF) wave function is chosen as a reference function of MRPT. However, CASSCF often generates too many configurations, and the size of the active space can outgrow the capacity of the present technology. Many attempts have been proposed to reduce the dimension of CASSCF and to widen the range of applications of MRPT. This review focuses on our recent development in MRPT
Time-dependent perturbation theory for nonequilibrium lattice models
International Nuclear Information System (INIS)
Jensen, I.; Dickman, R.
1993-01-01
The authors develop a time-dependent perturbation theory for nonequilibrium interacting particle systems. They focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles. At a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state, which is absorbing. They present several methods for deriving series for the evolution starting from a single seed particle, including expansions for the ultimate survival probability in the super- and subcritical regions, expansions for the average number of particles in the subcritical region, and short-time expansions. Algorithms for computer generation of the various expansions are presented. Rather long series (24 terms or more) and precise estimates of critical parameters are presented. 45 refs., 4 figs., 9 tabs
International Nuclear Information System (INIS)
Randriamisy, H.D.E.
2014-01-01
Nowadays, the study of scattering and production of particles occupies an important place in subatomic physics research. The main ongoing experiments concern high-energy scattering in the colliders, the scattering theory based on quantum field theory is used for the theoretical study. The work presented in this thesis is located in this framework, in fact it concerns a study on the scattering theory and Perturbative Quantum Chromodynamics. We used the path integral formalism of quantum field theory and perturbation theory. As we considered the higher order corrections in perturbative developments, the renormalization theory with the method of dimensional regularization was also used. As an application, the case of the Top quark production was considered. As main results, we can quote the obtention of the cross section of quark-antiquark top pair production up to second order. [fr
Khoshgoftar, M. J.; Mirzaali, M. J.; Rahimi, G. H.
2015-11-01
Recently application of functionally graded materials(FGMs) have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.
A global numerical solution of the radial Schroedinger equation by second-order perturbation theory
International Nuclear Information System (INIS)
Adam, G.
1979-01-01
A global numerical method, which uses second-order perturbation theory, is described for the solution of the radial Schroedinger equation. The perturbative numerical (PN) solution is derived in two stages: first, the original potential is approximated by a piecewise continuous parabolic function, and second, the resulting Schroedinger equation is solved on each integration step by second-order perturbation theory, starting with a step function reference approximation for the parabolic potential. We get a manageable PN algorithm, which shows an order of accuracy equal to six in the solution of the original Schroedinger equation, and is very stable against round off errors. (author)
Perturbing the ground ring of 2D string theory
International Nuclear Information System (INIS)
Barbon, J.L.F.
1992-01-01
In this paper, the authors use free field techniques in D = 2 string theory t calculate the perturbation of the special state algebras when the cosmological constant is turned on. In particular, the authors find that the 'ground cone' preserved by the ring structure is promoted to a three-dimensional hyperboloid as conjectured by Witten. On the other hand, the perturbed (1,1) current algebra of moduli deformations is computed completely, and no simple geometrical interpretation is found. The authors also quote some facts concerning the Liouville matrix a model dictionary in this class of theories
Lie transforms and their use in Hamiltonian perturbation theory
International Nuclear Information System (INIS)
Cary, J.R.
1978-06-01
A review is presented of the theory of Lie transforms as applied to Hamiltonian systems. We begin by presenting some general background on the Hamiltonian formalism and by introducing the operator notation for canonical transformations. We then derive the general theory of Lie transforms. We derive the formula for the new Hamiltonian when one uses a Lie transform to effect a canonical transformation, and we use Lie transforms to prove a very general version of Noether's theorem, or the symmetry-equals-invariant theorem. Next we use the general Lie transform theory to derive Deprit's perturbation theory. We illustrate this perturbation theory by application to two well-known problems in classical mechanics. Finally we present a chapter on conventions. There are many ways to develop Lie transforms. The last chapter explains the reasons for the choices made here
Perturbative string theory in BRST invariant formalism
International Nuclear Information System (INIS)
Di Vecchia, P.; Hornfeck, K.; Frau, M.; Lerda, A.
1988-01-01
In this talk we present a constructive and very explicit way of calculating multiloop amplitudes in string theories. The main ingredients are the BRST invariant N String Vertex and the BRST invariant twisted propagator. This approach naturally leads to the Schottky parametrization of moduli space in terms of multipliers and fixed points of the g projective transformations which characterize a Riemann surface of genus g. The complete expression (including measure) of the multiloop corrections to the N String Vertex for the bosonic string is exhibited. (orig.)
An ambiguity in fermionic string perturbation theory
International Nuclear Information System (INIS)
Atick, J.J.; Rabin, J.M.
1988-01-01
Recent investigation by Verlinde and Verlinde has shown that the fermionic string loop amplitudes change by a total derivative term in the moduli space under a change of basis of the supermoduli. This ambiguity is addressed in the context of the heterotic string theory, and shown to be a consequence of an inherent ambiguity in defining integration over the variables of a Grassmann algebra - in this case the Grassmann-valued coordinates of the supermoduli space. A resolution of this ambiguity in genus-two within this formalism is also presented. (orig.)
Perturbation theory for quantized string fields
International Nuclear Information System (INIS)
Thorn, C.B.; Florida Univ., Gainesville
1987-01-01
We discuss the problem of gauge fixing in string field theory. We show that BRST invariance requires the gauge-fixed action to contain terms cubic in the ghost... of ghost of ghost fields. The final BRST invariant gauge-fixed action for the gauge b 0 A=0 is extremely simple: with the proper interpretation (as given in this article), it is essentially the one anticipated earlier in the work of Giddings, Martinec, and Witten in their analysis of the BRST invariant world-sheet approach to string theory. We derive the Feynman rules from this action and explain in detail how the sum over sufaces of the BRST first-quantized string is reproduced. This result depends crucially on the correct assignment for the Grassmann character of the string field and its ghost... of ghost of ghost string fields. If all these fields are unified in a single string field Φ containing all ghost numbers, the requirements is that Φ be uniformly Grassmann odd. Finally, we do some sample calculations which provide some simple checks on our general results. (orig.)
Some global issues in string perturbation theory
International Nuclear Information System (INIS)
Atick, J.J.; Moore, G.; Sen, Ashoke
1988-01-01
Calculations of type II string vacuum amplitude using the picture changing prescription have been shown to lead, in general, to a positive cosmological constant. We show that there is a global obstruction to the choices of gauge slice for super-Teichmueller space that lead to such measures. We discuss the general restrictions on gauge slices appropriate for use in explicit fermionic string calculations. We also discuss the relation of the functional determinant and conformal field theory versions of the path integral measure, and show that, at arbitrary genus and in arbitrary backgrounds preserving tree level N=1 supersymmetry, the measure is an exact differential. We evaluate the boundary integrals of this total derivative at genus two in two ways for target space R 10 to show that the integrals are zero. Finally, we use the factorization hypothesis to show that in appropriate compactified spacetimes the boundary integrals continue to vanish. (orig.)
Non-perturbative aspects of string theory from elliptic curves
International Nuclear Information System (INIS)
Reuter, Jonas
2015-08-01
We consider two examples for non-perturbative aspects of string theory involving elliptic curves. First, we discuss F-theory on genus-one fibered Calabi-Yau manifolds with the fiber being a hypersurface in a toric fano variety. We discuss in detail the fiber geometry in order to find the gauge groups, matter content and Yukawa couplings of the corresponding supergravity theories for the four examples leading to gauge groups SU(3) x SU(2) x U(1), SU(4) x SU(2) x SU(2)/Z 2 , U(1) and Z 3 . The theories are connected by Higgsings on the field theory side and conifold transitions on the geometry side. We extend the discussion to the network of Higgsings relating all theories stemming from the 16 hypersurface fibrations. For the models leading to gauge groups SU(3) x SU(2) x U(1), SU(4) x SU(2) x SU(2)/Z 2 and U(1) we discuss the construction of vertical G 4 fluxes. Via the D3-brane tadpole cancelation condition we can restrict the minimal number of families in the first two of these models to be at least three. As a second example for non-perturbative aspects of string theory we discuss a proposal for a non-perturbative completion of topological string theory on local B-model geometries. We discuss in detail the computation of quantum periods for the examples of local F 1 , local F 2 and the resolution of C 3 /Z 5 . The quantum corrections are calculated order by order using second order differential operators acting on the classical periods. Using quantum geometry we calculate the refined free energies in the Nekrasov-Shatashvili limit. Finally we check the non-perturbative completion of topological string theory for the geometry of local F 2 against numerical calculations.
An improved thermodynamic perturbation theory for Mercedes-Benz water.
Urbic, T; Vlachy, V; Kalyuzhnyi, Yu V; Dill, K A
2007-11-07
We previously applied Wertheim's thermodynamic perturbation theory for associative fluids to the simple Mercedes-Benz model of water. We found that the theory reproduced well the physical properties of hot water, but was less successful in capturing the more structured hydrogen bonding that occurs in cold water. Here, we propose an improved version of the thermodynamic perturbation theory in which the effective density of the reference system is calculated self-consistently. The new theory is a significant improvement, giving good agreement with Monte Carlo simulations of the model, and predicting key anomalies of cold water, such as minima in the molar volume and large heat capacity, in addition to giving good agreement with the isothermal compressibility and thermal expansion coefficient.
Reactor perturbation calculations by Monte Carlo methods
International Nuclear Information System (INIS)
Gubbins, M.E.
1965-09-01
Whilst Monte Carlo methods are useful for reactor calculations involving complicated geometry, it is difficult to apply them to the calculation of perturbation worths because of the large amount of computing time needed to obtain good accuracy. Various ways of overcoming these difficulties are investigated in this report, with the problem of estimating absorbing control rod worths particularly in mind. As a basis for discussion a method of carrying out multigroup reactor calculations by Monte Carlo methods is described. Two methods of estimating a perturbation worth directly, without differencing two quantities of like magnitude, are examined closely but are passed over in favour of a third method based on a correlation technique. This correlation method is described, and demonstrated by a limited range of calculations for absorbing control rods in a fast reactor. In these calculations control rod worths of between 1% and 7% in reactivity are estimated to an accuracy better than 10% (3 standard errors) in about one hour's computing time on the English Electric KDF.9 digital computer. (author)
Dynamical affine symmetry and covariant perturbation theory for gravity
International Nuclear Information System (INIS)
Pervushin, V.N.
1975-01-01
The covariant perturbation theory for gravity with the simplest reduction properties is formulated. The main points are as follows: fundamental fields are the normal coordinates of ten-dimensional space of the gravitational field, and the fields are separated into the classical (background) and quantum ones in the generating functional along geodesics of this space
The precession of mercury's perihelion via perturbation theory
International Nuclear Information System (INIS)
Rosales, M.H.; Castro-Quilantan, J.L.
1984-01-01
Perturbation theory is used to solve the problem of the precession of Mercury's perihelion, this phenomenon being a relativistic effect. The expansion parameter appears naturally when the orbit equation is written in an appropriate form and it completely justifies the use of the first order approximation. (author)
Renormalization and scaling behaviour of eikonal perturbation theories. [Eikonal approximation
Energy Technology Data Exchange (ETDEWEB)
Din, A M [Chalmers Tekniska Hoegskola, Goeteborg (Sweden). Institutionen foer Teoretisk Fysik; Nielsen, N K [Aarhus Univ. (Denmark)
1975-01-04
Some observations on the renormalization and scaling behaviour of the charged-particle propagator in scalar quantum electrodynamics, in the ordinary eikonal approximation as well as in the eikonal perturbation theory, are reported. The conclusions indicate that scaling behaviour is not realized in the simple sense.
Improved Fluid Perturbation Theory: Equation of state for Fluid Xenon
Li, Qiong; Liu, Hai-Feng; Zhang, Gong-Mu; Zhao, Yan-Hong; Tian, Ming-Feng; Song, Hai-Feng
2016-01-01
The traditional fluid perturbation theory is improved by taking electronic excitations and ionizations into account, in the framework of average ion spheres. It is applied to calculate the equation of state for fluid Xenon, which turns out in good agreement with the available shock data.
Perturbation theory for Markov chains via Wasserstein distance
Rudolf, Daniel; Schweizer, Nikolaus
2017-01-01
Perturbation theory for Markov chains addresses the question of how small differences in the transition probabilities of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the nth step distributions of two Markov chains
Finite volume at two-loops in chiral perturbation theory
International Nuclear Information System (INIS)
Bijnens, Johan; Rössler, Thomas
2015-01-01
We calculate the finite volume corrections to meson masses and decay constants in two and three flavour Chiral Perturbation Theory to two-loop order. The analytical results are compared with the existing result for the pion mass in two-flavour ChPT and the partial results for the other quantities. We present numerical results for all quantities.
Chiral perturbation theory for nucleon generalized parton distributions
Energy Technology Data Exchange (ETDEWEB)
Diehl, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Manashov, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik]|[Sankt-Petersburg State Univ. (Russian Federation). Dept. of Theoretical Physics; Schaefer, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik
2006-08-15
We analyze the moments of the isosinglet generalized parton distributions H, E, H, E of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. We discuss in detail the construction of the operators in the effective theory that are required to obtain all corrections to a given order in the chiral power counting. The results will serve to improve the extrapolation of lattice results to the chiral limit. (orig.)
International Nuclear Information System (INIS)
Seregin, A.S.
2000-01-01
In the paper the formulae for perturbation theory functionals calculation are given and equations are based on improved coarse mesh discretization of diffusion problem in 3-dimensional geometry (Hex-Z). Expressions for the reactivity effect components and reactivity coefficients, written in the framework of the first order perturbation theory, are presented. On this basis the formulae for estimation of the sensitivity coefficients of different reactivity effects group cross-sections were derived. Expressions for the reactivity effect and its components obtained in the framework of the strict perturbation theory, are also presented in the paper. (author)
Hybrid perturbation methods based on statistical time series models
San-Juan, Juan Félix; San-Martín, Montserrat; Pérez, Iván; López, Rosario
2016-04-01
In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or semianalytical theory, generates an initial approximation that contains some inaccuracies derived from the fact that, in order to simplify the expressions and subsequent computations, not all the involved forces are taken into account and only low-order terms are considered, not to mention the fact that mathematical models of perturbations not always reproduce physical phenomena with absolute precision. The prediction technique, which can be based on either statistical time series models or computational intelligence methods, is aimed at modelling and reproducing missing dynamics in the previously integrated approximation. This combination results in the precision improvement of conventional numerical, analytical and semianalytical theories for determining the position and velocity of any artificial satellite or space debris object. In order to validate this methodology, we present a family of three hybrid orbit propagators formed by the combination of three different orders of approximation of an analytical theory and a statistical time series model, and analyse their capability to process the effect produced by the flattening of the Earth. The three considered analytical components are the integration of the Kepler problem, a first-order and a second-order analytical theories, whereas the prediction technique is the same in the three cases, namely an additive Holt-Winters method.
Singular perturbation theory for interacting fermions in two dimensions
International Nuclear Information System (INIS)
Chubukov, A.V.; Maslov, D.L.; Gangadharaiah, S.; Glazman, L.I.
2004-11-01
We consider a system of interacting fermions in two dimensions beyond the second-order perturbation theory in the interaction. It is shown that the mass-shell singularities in the self-energy, arising already at the second order of the perturbation theory, manifest a nonperturbative effect: an interaction with the zero-sound mode. Resuming the perturbation theory for a weak, short-range interaction and accounting for a finite curvature of the fermion spectrum, we eliminate the singularities and obtain the results for the quasi-particle self-energy and the spectral function to all orders in the interaction with the zero-sound mode. A threshold for emission of zero-sound waves leads a non-monotonic variation of the self-energy with energy (or momentum) near the mass shell. Consequently, the spectral function has a kink-like feature. We also study in detail a non-analytic temperature dependence of the specific heat, C(T) ∝T 2 . It turns out that although the interaction with the collective mode results in an enhancement of the fermion self-energy, this interaction does not affect the non-analytic term in C(T) due to a subtle cancellation between the contributions from the real and imaginary parts of the self-energy. For a short-range and weak interaction, this implies that the second-order perturbation theory suffices to determine the non-analytic part of C(T). We also obtain a general form of the non-analytic term in C(T), valid for the case of a generic Fermi liquid, i.e., beyond the perturbation theory. (author)
Nonperturbative Quantum Physics from Low-Order Perturbation Theory.
Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K
2015-10-02
The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.
Determination of partial molar volumes from free energy perturbation theory.
Vilseck, Jonah Z; Tirado-Rives, Julian; Jorgensen, William L
2015-04-07
Partial molar volume is an important thermodynamic property that gives insights into molecular size and intermolecular interactions in solution. Theoretical frameworks for determining the partial molar volume (V°) of a solvated molecule generally apply Scaled Particle Theory or Kirkwood-Buff theory. With the current abilities to perform long molecular dynamics and Monte Carlo simulations, more direct methods are gaining popularity, such as computing V° directly as the difference in computed volume from two simulations, one with a solute present and another without. Thermodynamically, V° can also be determined as the pressure derivative of the free energy of solvation in the limit of infinite dilution. Both approaches are considered herein with the use of free energy perturbation (FEP) calculations to compute the necessary free energies of solvation at elevated pressures. Absolute and relative partial molar volumes are computed for benzene and benzene derivatives using the OPLS-AA force field. The mean unsigned error for all molecules is 2.8 cm(3) mol(-1). The present methodology should find use in many contexts such as the development and testing of force fields for use in computer simulations of organic and biomolecular systems, as a complement to related experimental studies, and to develop a deeper understanding of solute-solvent interactions.
An analytic approach to sunset diagrams in chiral perturbation theory: Theory and practice
Energy Technology Data Exchange (ETDEWEB)
Ananthanarayan, B.; Ghosh, Shayan [Indian Institute of Science, Centre for High Energy Physics, Karnataka (India); Bijnens, Johan [Lund University, Department of Astronomy and Theoretical Physics, Lund (Sweden); Hebbar, Aditya [Indian Institute of Science, Centre for High Energy Physics, Karnataka (India); University of Delaware, Department of Physics and Astronomy, Newark, DE (United States)
2016-12-15
We demonstrate the use of several code implementations of the Mellin-Barnes method available in the public domain to derive analytic expressions for the sunset diagrams that arise in the two-loop contribution to the pion mass and decay constant in three-flavoured chiral perturbation theory. We also provide results for all possible two mass configurations of the sunset integral, and derive a new one-dimensional integral representation for the one mass sunset integral with arbitrary external momentum. Thoroughly annotated Mathematica notebooks are provided as ancillary files in the Electronic Supplementary Material to this paper, which may serve as pedagogical supplements to the methods described in this paper. (orig.)
An analytic approach to sunset diagrams in chiral perturbation theory: Theory and practice
International Nuclear Information System (INIS)
Ananthanarayan, B.; Ghosh, Shayan; Bijnens, Johan; Hebbar, Aditya
2016-01-01
We demonstrate the use of several code implementations of the Mellin-Barnes method available in the public domain to derive analytic expressions for the sunset diagrams that arise in the two-loop contribution to the pion mass and decay constant in three-flavoured chiral perturbation theory. We also provide results for all possible two mass configurations of the sunset integral, and derive a new one-dimensional integral representation for the one mass sunset integral with arbitrary external momentum. Thoroughly annotated Mathematica notebooks are provided as ancillary files in the Electronic Supplementary Material to this paper, which may serve as pedagogical supplements to the methods described in this paper. (orig.)
Optimized Perturbation Theory for Wave Functions of Quantum Systems
International Nuclear Information System (INIS)
Hatsuda, T.; Tanaka, T.; Kunihiro, T.
1997-01-01
The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave functions. This leads to a condition similar to that obtained from the principle of minimal sensitivity. Applications of the method to the quantum anharmonic oscillator and the double well potential show that uniformly valid wave functions with correct asymptotic behavior are obtained in the first-order optimized perturbation even for strong couplings. copyright 1997 The American Physical Society
Invariant exchange perturbation theory for multicenter systems: Time-dependent perturbations
International Nuclear Information System (INIS)
Orlenko, E. V.; Evstafev, A. V.; Orlenko, F. E.
2015-01-01
A formalism of exchange perturbation theory (EPT) is developed for the case of interactions that explicitly depend on time. Corrections to the wave function obtained in any order of perturbation theory and represented in an invariant form include exchange contributions due to intercenter electron permutations in complex multicenter systems. For collisions of atomic systems with an arbitrary type of interaction, general expressions are obtained for the transfer (T) and scattering (S) matrices in which intercenter electron permutations between overlapping nonorthogonal states belonging to different centers (atoms) are consistently taken into account. The problem of collision of alpha particles with lithium atoms accompanied by the redistribution of electrons between centers is considered. The differential and total charge-exchange cross sections of lithium are calculated
Cosmological perturbation theory at three-loop order
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-09-15
We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.
Cosmological perturbation theory at three-loop order
International Nuclear Information System (INIS)
Blas, Diego; Garny, Mathias; Konstandin, Thomas
2013-09-01
We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.
Convergence and analytic properties of manifestly finite perturbation theory
International Nuclear Information System (INIS)
Mtingwa, S.K.
1979-01-01
The author discusses more carefully the ultraviolet convergence properties of Feynman diagrams in recently proposed manifestly finite perturbation expansions. Speccifically, he refines one of the constraints on the γ's-the noncanonical dimensions-such that, when satisfied, any general product-type interaction of massive scalar, fermion and vector fields yields finite perturbation expansions requiring no conventional renormalization procedure. Moreover, the analytic properties of the Feynman integrals in the theory are discussed and concluded with remarks on the necessity of a modified Kaellen-Lehmann representation
International Nuclear Information System (INIS)
Takac, S.M.
1972-01-01
The method is based on perturbation of the reactor cell from a few up to few tens of percent. Measurements were performed for square lattice calls of zero power reactors Anna, NORA and RB, with metal uranium and uranium oxide fuel elements, water, heavy water and graphite moderators. Character and functional dependence of perturbations were obtained from the experimental results. Zero perturbation was determined by extrapolation thus obtaining the real physical neutron flux distribution in the reactor cell. Simple diffusion theory for partial plate cell perturbation was developed for verification of the perturbation method. The results of these calculation proved that introducing the perturbation sample in the fuel results in flattening the thermal neutron density dependent on the amplitude of the applied perturbation. Extrapolation applied for perturbed distributions was found to be justified
S-matrices for perturbations of certain conformal field theories
International Nuclear Information System (INIS)
Freund, P.G.O.; Klassen, T.R.; Melzer, E.; Chicago Univ., IL
1989-01-01
We present a family of factorizable S-matrix theories in 1+1 dimensions with an arbitrary number N of particles of distinct masses, and find the conservation laws of these theories. An analysis of the conservation laws of the family of nonunitary CFTs with central charge c=c 2,2N+3 =-2N(6N+5)/(2N+3) perturbed by the φ (1,3) operator, leads us to conjecture the identification of these perturbed CFTs with the S-matrix theories we found. The case N=1 was treated by Cardy and Mussardo. We also present the S-matrix of an E 7 -related unitary model. (orig.)
Nucleon and delta masses in twisted mass chiral perturbation theory
International Nuclear Information System (INIS)
Walker-Loud, Andre; Wu, Jackson M.S.
2005-01-01
We calculate the masses of the nucleons and deltas in twisted mass heavy baryon chiral perturbation theory. We work to quadratic order in a power counting scheme in which we treat the lattice spacing, a, and the quark masses, m q , to be of the same order. We give expressions for the mass and the mass splitting of the nucleons and deltas both in and away from the isospin limit. We give an argument using the chiral Lagrangian treatment that, in the strong isospin limit, the nucleons remain degenerate and the delta multiplet breaks into two degenerate pairs to all orders in chiral perturbation theory. We show that the mass splitting between the degenerate pairs of the deltas first appears at quadratic order in the lattice spacing. We discuss the subtleties in the effective chiral theory that arise from the inclusion of isospin breaking
Introduction to non-perturbative heavy quark effective theory
International Nuclear Information System (INIS)
Sommer, R.
2010-08-01
My lectures on the effective field theory for heavy quarks, an expansion around the static limit, concentrate on the motivation and formulation of HQET, its renormalization and discretization. This provides the basis for understanding that and how this effective theory can be formulated fully non-perturbatively in the QCD coupling, while by the very nature of an effective field theory, it is perturbative in the expansion parameter 1/m. After the couplings in the effective theory have been determined, the result at a certain order in 1/m is unique up to higher order terms in 1/m. In particular the continuum limit of the lattice regularized theory exists and leaves no trace of how it was regularized. In other words, the theory yields an asymptotic expansion of the QCD observables in 1/m - as usual in a quantum field theory modified by powers of logarithms. None of these properties has been shown rigorously (e.g. to all orders in perturbation theory) but perturbative computations and recently also non-perturbative lattice results give strong support to this ''standard wisdom''. A subtle issue is that a theoretically consistent formulation of the theory is only possible through a non-perturbative matching of its parameters with QCD at finite values of 1/m. As a consequence one finds immediately that the splitting of a result for a certain observable into, for example, lowest order and first order is ambiguous. Depending on how the matching between effective theory and QCD is done, a first order contribution may vanish and appear instead in the lowest order. For example, the often cited phenomenological HQET parameters anti Λ and λ 1 lack a unique non-perturbative definition. But this does not affect the precision of the asymptotic expansion in 1/m. The final result for an observable is correct up to order (1/m) n+1 if the theory was treated including (1/m) n terms. Clearly, the weakest point of HQET is that it intrinsically is an expansion. In practise, carrying it
Introduction to non-perturbative heavy quark effective theory
Energy Technology Data Exchange (ETDEWEB)
Sommer, R. [DESY, Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2010-08-15
My lectures on the effective field theory for heavy quarks, an expansion around the static limit, concentrate on the motivation and formulation of HQET, its renormalization and discretization. This provides the basis for understanding that and how this effective theory can be formulated fully non-perturbatively in the QCD coupling, while by the very nature of an effective field theory, it is perturbative in the expansion parameter 1/m. After the couplings in the effective theory have been determined, the result at a certain order in 1/m is unique up to higher order terms in 1/m. In particular the continuum limit of the lattice regularized theory exists and leaves no trace of how it was regularized. In other words, the theory yields an asymptotic expansion of the QCD observables in 1/m - as usual in a quantum field theory modified by powers of logarithms. None of these properties has been shown rigorously (e.g. to all orders in perturbation theory) but perturbative computations and recently also non-perturbative lattice results give strong support to this ''standard wisdom''. A subtle issue is that a theoretically consistent formulation of the theory is only possible through a non-perturbative matching of its parameters with QCD at finite values of 1/m. As a consequence one finds immediately that the splitting of a result for a certain observable into, for example, lowest order and first order is ambiguous. Depending on how the matching between effective theory and QCD is done, a first order contribution may vanish and appear instead in the lowest order. For example, the often cited phenomenological HQET parameters anti {lambda} and {lambda}{sub 1} lack a unique non-perturbative definition. But this does not affect the precision of the asymptotic expansion in 1/m. The final result for an observable is correct up to order (1/m){sup n+1} if the theory was treated including (1/m){sup n} terms. Clearly, the weakest point of HQET is that it
Probing non-perturbative effects in M-theory
International Nuclear Information System (INIS)
Hatsuda, Yasuyuki; Okuyama, Kazumi
2014-07-01
The AdS/CFT correspondence enables us to probe M-theory on various backgrounds from the corresponding dual gauge theories. Here we investigate in detail a three-dimensional U(N) N=4 super Yang-Mills theory coupled to one adjoint hypermultiplet and N f fundamental hypermultiplets, which is large N dual to M-theory on AdS 4 x S 7 /Z N f . Using the localization and the Fermi-gas formulation, we explore non-perturbative corrections to the partition function. As in the ABJM theory, we find that there exists a non-trivial pole cancellation mechanism, which guarantees the theory to be well-defined, between worldsheet instantons and membrane instantons for all rational (in particular, physical or integral) values of N f .
Modified potentials in many-body perturbation theory
International Nuclear Information System (INIS)
Silver, D.M.; Bartlett, R.J.
1976-01-01
Many-body perturbation-theory calculations of the pair-correlation energy within the regime of various finite expansions in two-center Slater-type basis sets are performed using a wide variety of modified potentials for the determination of unoccupied orbitals. To achieve meaningful convergence, it appears that the perturbation series must be carried through third order, using shifted denominators to include contributions from various higher-order diagrams. Moreover, certain denominator shifts are found necessary to ensure that a negative-definite resolvent accompanies the perturbation scheme when an arbitrary modified potential is employed. Through third order with denominator shifts, well-behaved modified potentials are found to give results that are equivalent, within 1 kcal/mole, to those obtained for pair-correlation energies with the standard self-consistent-field-V/sup N/ potential
A Theory of the Perturbed Consumer with General Budgets
DEFF Research Database (Denmark)
McFadden, Daniel L; Fosgerau, Mogens
We consider demand systems for utility-maximizing consumers facing general budget constraints whose utilities are perturbed by additive linear shifts in marginal utilities. Budgets are required to be compact but are not required to be convex. We define demand generating functions (DGF) whose...... subgradients with respect to these perturbations are convex hulls of the utility-maximizing demands. We give necessary as well as sufficient conditions for DGF to be consistent with utility maximization, and establish under quite general conditions that utility-maximizing demands are almost everywhere single......-valued and smooth in their arguments. We also give sufficient conditions for integrability of perturbed demand. Our analysis provides a foundation for applications of consumer theory to problems with nonlinear budget constraints....
Dimensional perturbation theory for the two-electron atom
International Nuclear Information System (INIS)
Goodson, D.Z.
1987-01-01
Perturbation theory in δ = 1/D, where D is the dimensionality of space, is applied to the two-electron atom. In Chapter 1 an efficient procedure for calculating the coefficients of the perturbation series for the ground-state energy is developed using recursion relations between the moments of the coordinate operators. Results through tenth order are presented. The series is divergent, but Pade summation gives results comparable in accuracy to the best configuration-interaction calculations. The singularity structure of the Pade approximants confirms the hypothesis that the energy as a function of δ has an infinite sequence of poles on the negative real axis that approaches an essential singularity at δ = O. The essential singularity causes the divergence of the perturbation series. There are also two poles at δ = 1 that slow the asymptotic convergence of the low-order terms. In Chapter 2, various techniques are demonstrated for removing the effect of these poles, and accurate results are thereby obtained, even at very low order. In Chapter 3, the large D limit of the correlation energy (CE) is investigated. In the limit D → infinity it is only 35% smaller than at D = 3. It can be made to vanish in the limit by modifying the Hartree-Fock (HF) wavefunction. In Chapter 4, perturbation theory is applied to the Hooke's-law model of the atom. Prospects for treating more-complicated systems are briefly discussed
Estimation of high orders of the perturbation theory in quantum mechanics
International Nuclear Information System (INIS)
Seznec, Reynald.
1978-01-01
First of all the simple case of an integral of one variable (zero-dimensional model) is examined to illustrate the methods and concepts used. A system n quantum oscillators 0(n) (spherical model) is then studied. A theory of perturbations around the saddle point dominating the functional integral is developed (theory of perturbations around the instanton). The fluctuation propagator is calculated explicitly. Some properties of the corresponding Feynman diagrams are also investigated. Methods are proposed to generalize the calculations to more complicated potentials. As an example of application the calculations of the first correction to the Lipatovian term are given for the spherical model [fr
Perturbative algebraic quantum field theory an introduction for mathematicians
Rejzner, Kasia
2016-01-01
Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities. We discuss in detail the examples of scalar fields and gauge theories and generalize them to QFT on curved spacetimes. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses QFT on curved spacetimes and effective quantum gravity. The book aims to be accessible researchers and graduate students interested in the mathematical foundations of pQFT are th...
Regular perturbation theory for two-electron atoms
International Nuclear Information System (INIS)
Feranchuk, I.D.; Triguk, V.V.
2011-01-01
Regular perturbation theory (RPT) for the ground and excited states of two-electron atoms or ions is developed. It is shown for the first time that summation of the matrix elements from the electron-electron interaction operator over all intermediate states can be calculated in a closed form by means of the two-particle Coulomb Green's function constructed in the Letter. It is shown that the second order approximation of RPT includes the main part of the correlation energy both for the ground and excited states. This approach can be also useful for description of two-electron atoms in external fields. -- Highlights: → We develop regular perturbation theory for the two-electron atoms or ions. → We calculate the sum of the matrix elements over all intermediate states. → We construct the two-particle Coulomb Green's function.
Algebraic perturbation theory for dense liquids with discrete potentials
Adib, Artur B.
2007-06-01
A simple theory for the leading-order correction g1(r) to the structure of a hard-sphere liquid with discrete (e.g., square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively eliminates four-particle correlations from g1(r) with good accuracy at high densities. For the particular case of discrete perturbations, the remaining three-particle correlations can be modeled with a simple volume-exclusion argument, resulting in an algebraic and surprisingly accurate expression for g1(r) . The structure of a discrete “core-softened” model for liquids with anomalous thermodynamic properties is reproduced as an application.
Perturbation theory and nonperturbative effects: a happy marriage?
International Nuclear Information System (INIS)
Chyla, J.
1992-01-01
Perturbation expansions in renormalized quantum theories are reformulated in a way that permits a straightforward handling of situations when in the conventional approach, i.e. in fixed renormalization scheme, these expansions are factorially divergent and even of asymptotically constant sign. The result takes the form of convergent (under certain circumstances) expansions in a set of functions Z k (a,χ) of the couplant and the free parameter χ specifies the procedure involved. The value of χ is shown to be correlated to the basic properties of nonperturbative effects as embodied in power corrections. A close connection of this procedure to the Borel summation technique is demonstrated and its relation to conventional perturbation theory in fixed renormalization schemes elucidated. (author) 3 figs., 17 refs
Non-perturbative Green functions in quantum gauge theories
International Nuclear Information System (INIS)
Shabanov, S.V.
1991-01-01
Non-perturbative Green functions for gauge invariant variables are considered. The Green functions are found to be modified as compared with the usual ones in a definite gauge because of a physical configuration space (PCS) reduction. In the Yang-Mills theory with fermions this phenomenon follows from the Singer theorem about the absence of a global gauge condition for the fields tensing to zero at spatial infinity. 20 refs
Hyperon decay form factors in chiral perturbation theory
International Nuclear Information System (INIS)
Lacour, Andre; Kubis, Bastian; Meissner, Ulf-G.
2007-01-01
We present a complete calculation of the SU(3)-breaking corrections to the hyperon vector form factors up to O(p 4 ) in covariant baryon chiral perturbation theory. Partial higher-order contributions are obtained, and we discuss chiral extrapolations of the vector form factor at zero momentum transfer. In addition we derive low-energy theorems for the subleading moments in hyperon decays, the weak Dirac radii and the weak anomalous magnetic moments, up to O(p 4 )
Calibrated geometries and non perturbative superpotentials in M-theory
International Nuclear Information System (INIS)
Hernandez, R.
1999-12-01
We consider non perturbative effects in M-theory compactifications on a seven-manifold of G 2 holonomy arising from membranes wrapped on supersymmetric three-cycles. When membranes are wrapped on associative submanifolds they induce a superpotential that can be calculated using calibrated geometry. This superpotential is also derived from compactification on a seven-manifold, to four dimensional Anti-de Sitter spacetime, of eleven dimensional supergravity with non vanishing expectation value of the four-form field strength. (author)
Modified perturbation theory for strongly correlated electron systems
International Nuclear Information System (INIS)
Takagi, Osamu; Saso, Tetsuro
1999-01-01
We propose a modified scheme for calculating the single-particle excitation spectrum of the impurity Anderson model. It is based on the second order perturbation theory, but modifies the self-energy so as to reproduce the correct atomic limit and to fulfill the Friedel sum rule. Therefore, it offers a simple scheme valid over wide range of excitation energy and parameters, and would be useful also for potential application to the lattice problems. (author)
International Nuclear Information System (INIS)
Lyubovitskij, V.E.; Gutsche, Th.; Faessler, Amand; Mau, R. Vinh
2002-01-01
We apply the perturbative chiral quark model to the study of the low-energy πN interaction. Using an effective chiral Lagrangian we reproduce the Weinberg-Tomozawa result for the S-wave πN scattering lengths. After inclusion of the photon field we give predictions for the electromagnetic O(p 2 ) low-energy couplings of the chiral perturbation theory effective Lagrangian that define the electromagnetic mass shifts of nucleons and first-order (e 2 ) radiative corrections to the πN scattering amplitude. Finally, we estimate the leading isospin-breaking correction to the strong energy shift of the π - p atom in the 1s state, which is relevant for the experiment 'pionic hydrogen' at PSI
Three-nucleon scattering by using chiral perturbation theory potential
International Nuclear Information System (INIS)
Kamata, Hiroyuki
2003-01-01
Three-nucleon scattering problems are studied by using two-nucleon and three-nucleon potentials derived from chiral perturbation theory. The three-nucleon term is shown to appear in the effective potential of the rank of next-to-next-to-leading order (NNLO). New three-nucleon forces are taken into consideration in addition to the conventional Fujita-Miyazawa (FM) type three-nucleon potential. Two-nucleon potential of the chiral perturbation theory is as precise as the conventional ones in low energy region. The FM type three-nucleon force which explains Sagara discrepancy in high energy region is introduced automatically. Concerning the Ay puzzle, the results seems to behave as if the puzzle has been solved at the level of NLO, but at the NNLO (without three-nucleon force) level the result is similar to the cases of conventional potential indicating the need of three-nucleon force. In contrast to the FM type three-nucleon force, five free parameters exist in the new D and E type three-nucleon forces introduced by the NNLO, but they are reduced to two independent parameters by antisymmetrization, which are found to be sensitive to the coupling energy of tritons and to the nd scattering length (spin doublet state). Parameters determined from them cannot give satisfactory answer to the A y puzzle. It seems, however, too hasty to conclude that A y puzzle cannot be solved by the chiral perturbation theory. (S. Funahashi)
An intermolecular perturbation theory for the region of moderate overlap
International Nuclear Information System (INIS)
Hayes, I.C.; Stone, A.J.
1984-01-01
A perturbational method is described for calculating the interaction energy of two molecules in the region where the overlap between their wave-functions is significant. By working directly with a basis of determinants constructed from the SCF orbitals of the separated molecules, without orthogonalization, it is possible to avoid many of the disadvantages of other methods. (author)
Systems of evolution equations and the singular perturbation method
International Nuclear Information System (INIS)
Mika, J.
Several fundamental theorems are presented important for the solution of linear evolution equations in the Banach space. The algorithm is deduced extending the solution of the system of singularly perturbed evolution equations into an asymptotic series with respect to a small positive parameter. The asymptotic convergence is shown of an approximate solution to the accurate solution. Singularly perturbed evolution equations of the resonance type were analysed. The special role is considered of the asymptotic equivalence of P1 equations obtained as the first order approximation if the spherical harmonics method is applied to the linear Boltzmann equation, and the diffusion equations of the linear transport theory where the small parameter approaches zero. (J.B.)
Including the Δ(1232) resonance in baryon chiral perturbation theory
International Nuclear Information System (INIS)
Hacker, C.; Wies, N.; Scherer, S.; Gegelia, J.
2005-01-01
Baryon chiral perturbation theory with explicit Δ(1232) degrees of freedom is considered. The most general interactions of pions, nucleons, and Δ consistent with all underlying symmetries as well as with the constraint structure of higher-spin fields are constructed. By use of the extended on-mass-shell renormalization scheme, a manifestly Lorentz-invariant effective-field theory with a systematic power counting is obtained. As applications, we discuss the mass of the nucleon, the pion-nucleon σ term, and the pole of the Δ propagator
Analytic perturbation theory in analyzing some QCD observables
International Nuclear Information System (INIS)
Shirkov, D.V.
2001-01-01
The paper is devoted to application of recently devised ghost-free Analytic Perturbation Theory (APT) for analysis of some QCD observables. We start with the discussion of the main problem of the perturbative QCD - ghost singularities and with the resume of this trouble solution within the APT. By a few examples in the various energy and momentum transfer regions (with the flavor number f = 3, 4 and 5) we demonstrate the effect of improved convergence of the APT modified perturbative QCD expansion. Our first observation is that in the APT analysis the three-loop contribution (of an order of α s 3 ) is as a rule numerically inessential. This raises hope for practical solving the well-known problem of asymptotic nature of common QFT perturbation series. The second conclusion is that a common perturbative analysis of time-like events with the big π 2 term in the π 2 coefficient is not adequate at s ≤ 2 GeV 2 . In particular, this relates to τ decay. Then, for the 'high' (f = 5) region it is shown that the common two-loop (NLO, NLLA) perturbation approximation widely used there (at 10 GeV ≤ √s ≤ 170 GeV) for analysis of shape/events data contains a systematic negative error of a 1 - 2 per cent level for the extracted α bar s (2) values. Our physical conclusion is that the α bar s (M Z 2 ) value averaged over the f = 5 data s (M Z 2 )> APT; f= 5 ≅ 0.124 appreciably differs from the currently accepted 'world average' (= 0.118)
Application of Classical and Lie Transform Methods to Zonal Perturbation in the Artificial Satellite
San-Juan, J. F.; San-Martin, M.; Perez, I.; Lopez-Ochoa, L. M.
2013-08-01
A scalable second-order analytical orbit propagator program is being carried out. This analytical orbit propagator combines modern perturbation methods, based on the canonical frame of the Lie transform, and classical perturbation methods in function of orbit types or the requirements needed for a space mission, such as catalog maintenance operations, long period evolution, and so on. As a first step on the validation of part of our orbit propagator, in this work we only consider the perturbation produced by zonal harmonic coefficients in the Earth's gravity potential, so that it is possible to analyze the behaviour of the perturbation methods involved in the corresponding analytical theories.
Superconvergent perturbation theory for euclidean scalar field theories
International Nuclear Information System (INIS)
Ushveridze, A.G.
1984-01-01
It is shown that the bare (unrenormalized) correlation functions in the euclidean scalar field theories can be expanded in a series whose terms, being computable in a relatively simple way, are free from ultraviolet and infrared divergencies. This series is convergent (divergent) for finite (infinite) values of the correlation functions. (orig.)
The Hill-determinant perturbation theory with triangular propagators
International Nuclear Information System (INIS)
Znojil, M.
1996-01-01
A new version of the Rayleigh-Schroedinger perturbation prescription is proposed. Its main formal feature lies in an unusual choice of the model space and unperturbed H 0 and in a resulting lower-triangular matrix structure of its propagators. Within the framework of the so-called Hill-determinant method, an admissibility of any incompletely solvable zero-order Hamiltonian is achieved in this way. As a consequence, the range of practical applicability of our new perturbative formalism may be expected to incorporate many new phenomenological interactions with a strongly anharmonic character. 18 refs
A non-perturbative analysis in finite volume gauge theory
International Nuclear Information System (INIS)
Koller, J.; State Univ. of New York, Stony Brook; Van Baal, P.; State Univ. of New York, Stony Brook
1988-01-01
We discuss SU(2) gauge theory on a three-torus using a finite volume expansion. Our discovery of natural coordinates allows us to obtain continuum results in a region where Monte Carlo data are also available. The obtained results agree well with the perturbative and semiclassical analysis for small volumes, and there is fair agreement with the Monte Carlo results in intermediate volumes. The simple picture which emerges for the approximate low energy dynamics is that of three interacting particles enclosed in a sphere, with zero total 'angular momentum'. The validity of an adiabatic approximation is investigated. The fundamentally new understanding gained, is that non-perturbative dynamics can be incorporated by imposing boundary conditions which arise through the nontrivial topology of configuration space. (orig.)
Interacting fermions in two dimensions: Beyond the perturbation theory
International Nuclear Information System (INIS)
Gangadharaiah, S.; Maslov, D.L.; Chubukov, A.V.; Glazman, L.I.
2005-05-01
We consider a system of 2D fermions with short-range interaction. A straightforward perturbation theory is shown to be ill-defined even for an infinitesimally weak interaction, as the perturbative series for the self-energy diverges near the mass shell. We show that the divergences result from the interaction of fermions with the zero-sound collective mode. By re-summing the most divergent diagrams, we obtain a closed form of the self-energy near the mass shell. The spectral function exhibits a threshold feature at the onset of the emission of the zero-sound waves. We also show that the interaction with the zero sound does not affect a non- analytic, T 2 -part of the specific heat. (author)
Nonperturbative calculations in the framework of variational perturbation theory in QCD
Solovtsova, O. P.
2017-07-01
We discuss applications of the method based on the variational perturbation theory to perform calculations down to the lowest energy scale. The variational series is different from the conventional perturbative expansion and can be used to go beyond the weak-coupling regime. We apply this method to investigate the Borel representation of the light Adler function constructed from the τ data and to determine the residual condensates. It is shown that within the method suggested the optimal values of these lower dimension condensates are close to zero.
Extended Møller-Plesset perturbation theory for dynamical and static correlations
International Nuclear Information System (INIS)
Tsuchimochi, Takashi; Van Voorhis, Troy
2014-01-01
We present a novel method that appropriately handles both dynamical and static electron correlations in a balanced manner, using a perturbation theory on a spin-extended Hartree-Fock (EHF) wave function reference. While EHF is a suitable candidate for degenerate systems where static correlation is ubiquitous, it is known that most of dynamical correlation is neglected in EHF. In this work, we derive a perturbative correction to a fully spin-projected self-consistent wave function based on second-order Møller-Plesset perturbation theory (MP2). The proposed method efficiently captures the ability of EHF to describe static correlation in degeneracy, combined with MP2's ability to treat dynamical correlation effects. We demonstrate drastic improvements on molecular ground state and excited state potential energy curves and singlet-triplet splitting energies over both EHF and MP2 with similar computational effort to the latter
Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
Romano, Antonio Enea; Mooij, Sander; Sasaki, Misao
2016-04-01
We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid δPnad, another is for a general matter field δPc,nad, and the last one is valid only on superhorizon scales. The first two definitions coincide if cs2 = cw2 where cs is the propagation speed of the perturbation, while cw2 = P ˙ / ρ ˙ . Assuming the adiabaticity in the general sense, δPc,nad = 0, we derive a relation between the lapse function in the comoving slicing Ac and δPnad valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as cs ≠cw, the uniform density, comoving and the proper-time slicings coincide approximately for any gravity theory and for any matter field if δPnad = 0 approximately. In the case of general relativity this gives the equivalence between the comoving curvature perturbation Rc and the uniform density curvature perturbation ζ on superhorizon scales, and their conservation. This is realized on superhorizon scales in standard slow-roll inflation. We then consider an example in which cw =cs, where δPnad = δPc,nad = 0 exactly, but the equivalence between Rc and ζ no longer holds. Namely we consider the so-called ultra slow-roll inflation. In this case both Rc and ζ are not conserved. In particular, as for ζ, we find that it is crucial to take into account the next-to-leading order term in ζ's spatial gradient expansion to show its non-conservation, even on superhorizon scales. This is an example of the fact that adiabaticity (in the thermodynamic sense) is not always enough to ensure the conservation of Rc or ζ.
Perturbation theory of the quark-gluon plasma at finite temperature and baryon number density
International Nuclear Information System (INIS)
Anon.
1984-01-01
At very high energy densities, hadronic matter becomes an almost ideal gas of quarks and gluons. In these circumstances, the effects of particle interactions are small, and to some order in perturbation theory are computable by methods involving weak coupling expansions. To illustrate the perturbative methods which may be used to compute the thermodynamic potential, the results and methods which are employed to compute to first order in α/sub s/ are reviewed. The problem of the plasmon effect, and the necessity of using non-perturbative methods when going beyond first order in α/sub s/ in evaluating the thermodynamic potential are discussed. The results at zero temperature and finite baryon number density to second order in α/sub s/ are also reviewed. The method of renormalization group improving the weak coupling expansions by replacing the expansion by an expansion in a temperature and baryon number density dependent coupling which approaches zero at high energy densities is discussed. Non-perturbative effects such as instantons are briefly mentioned and the breakdown of perturbation theory for the thermodynamical at order α/sub s/ 3 for finite temperature is presented
A non-perturbative study of massive gauge theories
DEFF Research Database (Denmark)
Della Morte, Michele; Hernandez, Pilar
2013-01-01
and the lightest degrees of freedom are spin one vector particles with the same quantum numbers as the conserved current, we argue that the most general effective theory describing their low-energy dynamics must be a massive gauge theory. We present results of a exploratory numerical simulation of the model......We consider a non-perturbative formulation of an SU(2) massive gauge theory on a space-time lattice, which is also a discretised gauged non-linear chiral model. The lattice model is shown to have an exactly conserved global SU(2) symmetry. If a scaling region for the lattice model exists...... and find indications for the presence of a scaling region where both a triplet vector and a scalar remain light....
Perturbations and quasi-normal modes of black holes in Einstein-Aether theory
International Nuclear Information System (INIS)
Konoplya, R.A.; Zhidenko, A.
2007-01-01
We develop a new method for calculation of quasi-normal modes of black holes, when the effective potential, which governs black hole perturbations, is known only numerically in some region near the black hole. This method can be applied to perturbations of a wide class of numerical black hole solutions. We apply it to the black holes in the Einstein-Aether theory, a theory where general relativity is coupled to a unit time-like vector field, in order to observe local Lorentz symmetry violation. We found that in the non-reduced Einstein-Aether theory, real oscillation frequency and damping rate of quasi-normal modes are larger than those of Schwarzschild black holes in the Einstein theory
Energy Technology Data Exchange (ETDEWEB)
Rossi, Lubianka Ferrari Russo
2014-07-01
The main target of this study is to introduce a new method for calculating the coefficients of sensibility through the union of differential method and generalized perturbation theory, which are the two methods generally used in reactor physics to obtain such variables. These two methods, separated, have some issues turning the sensibility coefficients calculation slower or computationally exhaustive. However, putting them together, it is possible to repair these issues and build a new equation for the coefficient of sensibility. The method introduced in this study was applied in a PWR reactor, where it was performed the sensibility analysis for the production and {sup 239}Pu conversion rate during 120 days (1 cycle) of burnup. The computational code used for both burnup and sensibility analysis, the CINEW, was developed in this study and all the results were compared with codes widely used in reactor physics, such as CINDER and SERPENT. The new mathematical method for calculating the sensibility coefficients and the code CINEW provide good numerical agility and also good efficiency and security, once the new method, when compared with traditional ones, provide satisfactory results, even when the other methods use different mathematical approaches. The burnup analysis, performed using the code CINEW, was compared with the code CINDER, showing an acceptable variation, though CINDER presents some computational issues due to the period it was built. The originality of this study is the application of such method in problems involving temporal dependence and, not least, the elaboration of the first national code for burnup and sensitivity analysis. (author)
International Nuclear Information System (INIS)
Kropaczek, D.J.; Turinsky, P.J.
1990-01-01
Perturbation techniques utilized in reactor analysis have recently been applied in the solution of the in-core nuclear fuel management optimization problem. The use of such methods is motivated by the need to evaluate many times over, the core physics characteristics of loading pattern solutions obtained through an optimization process, which is typically iterative. Perturbation theory provides an efficient alternative to the prohibitively expensive, repetitive solutions of the system few-group neutron diffusion equations required in solving the fuel placement problem. A primary concern in the use of such methods is the control of perturbation errors arising during the fuel shuffling process. First-order accurate models inevitably resort to undue restriction of fuel movement during the optimization process to control these errors. Higher order perturbation theory models have the potential to overcome such limitations, which may result in the identification of local versus global optima. An accurate, computationally efficient reactor physics model based on higher order perturbation theory and geared toward the needs of large-scale in-core fuel management optimization is presented in this paper
Bozkaya, Uǧur; Turney, Justin M.; Yamaguchi, Yukio; Schaefer, Henry F.; Sherrill, C. David
2011-09-01
Using a Lagrangian-based approach, we present a more elegant derivation of the equations necessary for the variational optimization of the molecular orbitals (MOs) for the coupled-cluster doubles (CCD) method and second-order Møller-Plesset perturbation theory (MP2). These orbital-optimized theories are referred to as OO-CCD and OO-MP2 (or simply "OD" and "OMP2" for short), respectively. We also present an improved algorithm for orbital optimization in these methods. Explicit equations for response density matrices, the MO gradient, and the MO Hessian are reported both in spin-orbital and closed-shell spin-adapted forms. The Newton-Raphson algorithm is used for the optimization procedure using the MO gradient and Hessian. Further, orbital stability analyses are also carried out at correlated levels. The OD and OMP2 approaches are compared with the standard MP2, CCD, CCSD, and CCSD(T) methods. All these methods are applied to H2O, three diatomics, and the O_4^+ molecule. Results demonstrate that the CCSD and OD methods give nearly identical results for H2O and diatomics; however, in symmetry-breaking problems as exemplified by O_4^+, the OD method provides better results for vibrational frequencies. The OD method has further advantages over CCSD: its analytic gradients are easier to compute since there is no need to solve the coupled-perturbed equations for the orbital response, the computation of one-electron properties are easier because there is no response contribution to the particle density matrices, the variational optimized orbitals can be readily extended to allow inactive orbitals, it avoids spurious second-order poles in its response function, and its transition dipole moments are gauge invariant. The OMP2 has these same advantages over canonical MP2, making it promising for excited state properties via linear response theory. The quadratically convergent orbital-optimization procedure converges quickly for OMP2, and provides molecular properties that
Xu, Enhua; Zhao, Dongbo; Li, Shuhua
2015-10-13
A multireference second order perturbation theory based on a complete active space configuration interaction (CASCI) function or density matrix renormalized group (DMRG) function has been proposed. This method may be considered as an approximation to the CAS/A approach with the same reference, in which the dynamical correlation is simplified with blocked correlated second order perturbation theory based on the generalized valence bond (GVB) reference (GVB-BCPT2). This method, denoted as CASCI-BCPT2/GVB or DMRG-BCPT2/GVB, is size consistent and has a similar computational cost as the conventional second order perturbation theory (MP2). We have applied it to investigate a number of problems of chemical interest. These problems include bond-breaking potential energy surfaces in four molecules, the spectroscopic constants of six diatomic molecules, the reaction barrier for the automerization of cyclobutadiene, and the energy difference between the monocyclic and bicyclic forms of 2,6-pyridyne. Our test applications demonstrate that CASCI-BCPT2/GVB can provide comparable results with CASPT2 (second order perturbation theory based on the complete active space self-consistent-field wave function) for systems under study. Furthermore, the DMRG-BCPT2/GVB method is applicable to treat strongly correlated systems with large active spaces, which are beyond the capability of CASPT2.
S-duality invariant perturbation theory improved by holography
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, Abhishek [Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India); Honda, Masazumi [Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 7610001 (Israel); Thakur, Somyadip [Tata Institute of Fundamental Research,Mumbai 400005 (India)
2017-04-26
We study anomalous dimensions of unprotected low twist operators in the four-dimensional SU (N)N=4 supersymmetric Yang-Mills theory. We construct a class of interpolating functions to approximate the dimensions of the leading twist operators for arbitrary gauge coupling τ. The interpolating functions are consistent with previous results on the perturbation theory, holographic computation and full S-duality. We use our interpolating functions to test a recent conjecture by the N=4 superconformal bootstrap that upper bounds on the dimensions are saturated at one of the duality-invariant points τ=i and τ=e{sup iπ/3}. It turns out that our interpolating functions have maximum at τ=e{sup iπ/3}, which are close to the conjectural values by the conformal bootstrap. In terms of the interpolating functions, we draw the image of conformal manifold in the space of the dimensions. We find that the image is almost a line despite the conformal manifold is two-dimensional. We also construct interpolating functions for the subleading twist operator and study level crossing phenomenon between the leading and subleading twist operators. Finally we study the dimension of the Konishi operator in the planar limit. We find that our interpolating functions match with numerical result obtained by Thermodynamic Bethe Ansatz very well. It turns out that analytic properties of the interpolating functions reflect an expectation on a radius of convergence of the perturbation theory.
Semiclassical perturbation theory for diffraction in heavy atom surface scattering.
Miret-Artés, Salvador; Daon, Shauli; Pollak, Eli
2012-05-28
The semiclassical perturbation theory formalism of Hubbard and Miller [J. Chem. Phys. 78, 1801 (1983)] for atom surface scattering is used to explore the possibility of observation of heavy atom diffractive scattering. In the limit of vanishing ℏ the semiclassical theory is shown to reduce to the classical perturbation theory. The quantum diffraction pattern is sensitive to the characteristics of the beam of incoming particles. Necessary conditions for observation of quantum diffraction are derived for the angular width of the incoming beam. An analytic expression for the angular distribution as a function of the angular and momentum variance of the incoming beam is obtained. We show both analytically and through some numerical results that increasing the angular width of the incident beam leads to decoherence of the quantum diffraction peaks and one approaches the classical limit. However, the incoherence of the beam in the parallel direction does not destroy the diffraction pattern. We consider the specific example of Ar atoms scattered from a rigid LiF(100) surface.
In-core fuel management via perturbation theory
International Nuclear Information System (INIS)
Mingle, J.O.
1975-01-01
A two-step procedure is developed for the optimization of in-core nuclear fuel management using perturbation theory to predict the effects of various core configurations. The first procedure is a cycle cost minimization using linear programming with a zoned core and discrete burnup groups. The second program utilizes an individual fuel assembly shuffling sequence to minimize the maldistribution of power generation. This latter quantity is represented by a figure of merit or by an assembly power peaking factor. A pressurized water reactor example calculation is utilized. 24 references
Applications of perturbation theory to the study of CANDU reactors
International Nuclear Information System (INIS)
Rozon, D.; Beaudet, M.
1990-01-01
The use of Generalized Perturbation Theory (GPT) in the computer code OPTEX-4 is described. This code can be used to simultaneously optimize the fuel management and the control absorber distribution in a CANDU reactor at equilibrium refueling. The gradient of the characteristic functionals are obtained using two independent approaches, requiring the solution of a fixed source eigenvalue problem (direct for the explicit approach. adjoint for the implicit approach). These solutions, as well as the solution of the diffusion problem is obtained in 3D by calling the diffusion module TRIVAC-2. The equivalence of the two approaches is demonstrated [fr
Is there a signal of quark confinement from perturbation theory
International Nuclear Information System (INIS)
Poggio, E.C.
1977-01-01
The question of whether the presence of the large infrared logarithms affects in any sense the determination of physical amplitudes involving quarks and gluons is considered in a report of results from previous investigations. Global impressions of their nature and of what they mean as far as the confinement issue is concerned. A comparison is made with analogous quantum electrodynamic processes, where the corresponding infrared aspects are completely understood. Quark form factor behavior, quark-antiquark scattering, the weak and the strong KLN theorems, and perturbation theory and confinement are treated. 26 references
Nonlinear PI control of chaotic systems using singular perturbation theory
International Nuclear Information System (INIS)
Wang Jiang; Wang Jing; Li Huiyan
2005-01-01
In this paper, we develop the nonlinear PI controllers for a class of chaotic systems based on singular perturbation theory. The original system is decomposed into two reduced order systems, to which the nonlinear uncertain terms belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and combined to construct the composite controller for the full order system. The effectiveness and feasibility of the proposed control scheme is demonstrated through numerical simulations on the chaotic Chua's circuit
Wavefunction of the Universe and Chern-Simons perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Soo Chopin [Department of Physics, National Cheng Kung University Tainan 70101, Taiwan (China)
2002-03-21
The Chern-Simons exact solution of four-dimensional quantum gravity with nonvanishing cosmological constant is presented in metric variables as the partition function of Chern-Simons theory with nontrivial source. The perturbative expansion is given, and the wavefunction is computed to the lowest order of approximation for the Cauchy surface which is topologically a 3-sphere. The state is well-defined even at degenerate and vanishing values of the dreibein. Reality conditions for the Ashtekar variables are also taken into account, and remarkable features of the Chern-Simons state and their relevance to cosmology are pointed out.
Zeeman effect: new outlook on old perturbation theory
International Nuclear Information System (INIS)
Turbiner, A.V.
1980-01-01
The problem of hydrogen atom placed in constant external magnetic field is studied. The properties of ordinary perturbation theory (in powers of the field) in the framework of a new approach proposed earlier are investigated. The ground state are considered in detailed while the excited states are discussed only in brief. It is shown that the ''wave function corrections'' with in this approach are simpler than within ordinary one and contain a finite number of harmonics with polynomial coefficients. Some coefficients of these polynomials are found explicitly
An integral for second-order multiple scattering perturbation theory
International Nuclear Information System (INIS)
Hoffman, G.G.
1997-01-01
This paper presents the closed form evaluation of a six-dimensional integral. The integral arises in the application to many-electron systems of a multiple scattering perturbation expansion at second order when formulated in fourier space. The resulting function can be used for the calculation of both the electron density and the effective one-electron potential in an SCF calculations. The closed form expression derived here greatly facilitates these calculations. In addition, the evaluated integral can be used for the computation of second-order corrections to the open-quotes optimized Thomas-Fermi theory.close quotes 10 refs., 2 figs
Bound-state perturbation theory and annihilation effects in positronium
International Nuclear Information System (INIS)
Abbasabadi, A.; Repko, W.W.
1987-01-01
Working in Coulomb gauge and using the lowest-order equation proposed by Barbieri and Remiddi it is calculated, in the one-loop order of perturbation theory, the decay rate and the energy shift of the ground states of parapositronium and orthopositronium, respectively. Our result for the decay rate agrees with that of Harris and Brown. For contribution of one-photon-annihilation channel to the energy shift, it is confirmed the result of Karplus and Klein. These results are derived completely within the bound-state formalism and avoid the necessity of performing on-mass-shell wave function and vertex renormalization subtractions
Nf=2 Lattice QCD and Chiral Perturbation Theory
International Nuclear Information System (INIS)
Scorzato, L.; Farchioni, F.; Hofmann, P.; Jansen, K.; Montvay, I.; Muenster, G.; Papinutto, M.; Scholz, E.E.; Shindler, A.; Ukita, N.; Urbach, C.; Wenger, U.; Wetzorke, I.
2006-01-01
By employing a twisted mass term, we compare recent results from lattice calculations of N f =2 dynamical Wilson fermions with Wilson Chiral Perturbation Theory (WChPT). The final goal is to determine some com- binations of Gasser-Leutwyler Low Energy Constants (LECs). A wide set of data with different lattice spacings (a ∼ 0.2 - 0.12 fm), different gauge actions (Wilson plaquette, DBW2) and different quark masses (down to the lowest pion mass allowed by lattice artifacts and including negative quark masses) provide a strong check of the applicability of WChPT in this regime and the scaling behaviours in the continuum limit
Gluon cascades and amplitudes in light-front perturbation theory
International Nuclear Information System (INIS)
Cruz-Santiago, C.A.; Staśto, A.M.
2013-01-01
We construct the gluon wave functions, fragmentation functions and scattering amplitudes within the light-front perturbation theory. Recursion relations on the light-front are constructed for the wave functions and fragmentation functions, which in the latter case are the light-front analogs of the Berends–Giele recursion relations. Using general relations between wave functions and scattering amplitudes it is demonstrated how to obtain the maximally-helicity violating amplitudes, and explicit verification of the results is based on simple examples.
Approximate solution fuzzy pantograph equation by using homotopy perturbation method
Jameel, A. F.; Saaban, A.; Ahadkulov, H.; Alipiah, F. M.
2017-09-01
In this paper, Homotopy Perturbation Method (HPM) is modified and formulated to find the approximate solution for its employment to solve (FDDEs) involving a fuzzy pantograph equation. The solution that can be obtained by using HPM is in the form of infinite series that converge to the actual solution of the FDDE and this is one of the benefits of this method In addition, it can be used for solving high order fuzzy delay differential equations directly without reduction to a first order system. Moreover, the accuracy of HPM can be detected without needing the exact solution. The HPM is studied for fuzzy initial value problems involving pantograph equation. Using the properties of fuzzy set theory, we reformulate the standard approximate method of HPM and obtain the approximate solutions. The effectiveness of the proposed method is demonstrated for third order fuzzy pantograph equation.
Energy Technology Data Exchange (ETDEWEB)
Guo, Yang; Sivalingam, Kantharuban; Neese, Frank, E-mail: Frank.Neese@cec.mpg.de [Max Planck Institut für Chemische Energiekonversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr (Germany); Valeev, Edward F. [Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24014 (United States)
2016-03-07
Multi-reference (MR) electronic structure methods, such as MR configuration interaction or MR perturbation theory, can provide reliable energies and properties for many molecular phenomena like bond breaking, excited states, transition states or magnetic properties of transition metal complexes and clusters. However, owing to their inherent complexity, most MR methods are still too computationally expensive for large systems. Therefore the development of more computationally attractive MR approaches is necessary to enable routine application for large-scale chemical systems. Among the state-of-the-art MR methods, second-order N-electron valence state perturbation theory (NEVPT2) is an efficient, size-consistent, and intruder-state-free method. However, there are still two important bottlenecks in practical applications of NEVPT2 to large systems: (a) the high computational cost of NEVPT2 for large molecules, even with moderate active spaces and (b) the prohibitive cost for treating large active spaces. In this work, we address problem (a) by developing a linear scaling “partially contracted” NEVPT2 method. This development uses the idea of domain-based local pair natural orbitals (DLPNOs) to form a highly efficient algorithm. As shown previously in the framework of single-reference methods, the DLPNO concept leads to an enormous reduction in computational effort while at the same time providing high accuracy (approaching 99.9% of the correlation energy), robustness, and black-box character. In the DLPNO approach, the virtual space is spanned by pair natural orbitals that are expanded in terms of projected atomic orbitals in large orbital domains, while the inactive space is spanned by localized orbitals. The active orbitals are left untouched. Our implementation features a highly efficient “electron pair prescreening” that skips the negligible inactive pairs. The surviving pairs are treated using the partially contracted NEVPT2 formalism. A detailed
Exact-to-precision generalized perturbation theory for source-driven systems
International Nuclear Information System (INIS)
Wang Congjian; Abdel-Khalik, Hany S.
2011-01-01
Highlights: ► We present a new development in higher order generalized perturbation theory. ► The method addresses the explosion in the flux phase space, input parameters, and responses. ► The method hybridizes first-order GPT and proper orthogonal decomposition snapshots method. ► A simplified 1D and realistic 2D assembly models demonstrate applicability of the method. ► The accuracy of the method is compared to exact direct perturbations and first-order GPT. - Abstract: Presented in this manuscript are new developments to perturbation theory which are intended to extend its applicability to estimate, with quantifiable accuracy, the exact variations in all responses calculated by the model with respect to all possible perturbations in the model's input parameters. The new developments place high premium on reducing the associated computational overhead in order to enable the use of perturbation theory in routine reactor design calculations. By way of examples, these developments could be employed in core simulation to accurately estimate the few-group cross-sections variations resulting from perturbations in neutronics and thermal-hydraulics core conditions. These variations are currently being described using a look-up table approach, where thousands of assembly calculations are performed to capture few-group cross-sections variations for the downstream core calculations. Other applications include the efficient evaluation of surrogates for applications that require repeated model runs such as design optimization, inverse studies, uncertainty quantification, and online core monitoring. The theoretical background of these developments applied to source-driven systems and supporting numerical experiments are presented in this manuscript. Extension to eigenvalue problems will be presented in a future article.
Time-Sliced Perturbation Theory for Large Scale Structure I: General Formalism
Blas, Diego; Ivanov, Mikhail M.; Sibiryakov, Sergey
2016-01-01
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein--de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This pave...
Exponential time-dependent perturbation theory in rotationally inelastic scattering
International Nuclear Information System (INIS)
Cross, R.J.
1983-01-01
An exponential form of time-dependent perturbation theory (the Magnus approximation) is developed for rotationally inelastic scattering. A phase-shift matrix is calculated as an integral in time over the anisotropic part of the potential. The trajectory used for this integral is specified by the diagonal part of the potential matrix and the arithmetic average of the initial and final velocities and the average orbital angular momentum. The exponential of the phase-shift matrix gives the scattering matrix and the various cross sections. A special representation is used where the orbital angular momentum is either treated classically or may be frozen out to yield the orbital sudden approximation. Calculations on Ar+N 2 and Ar+TIF show that the theory generally gives very good agreement with accurate calculations, even where the orbital sudden approximation (coupled-states) results are seriously in error
Basics of thermal field theory a tutorial on perturbative computations
Laine, Mikko
2016-01-01
This book presents thermal field theory techniques, which can be applied in both cosmology and the theoretical description of the QCD plasma generated in heavy-ion collision experiments. It focuses on gauge interactions (whether weak or strong), which are essential in both contexts. As well as the many differences in the physics questions posed and in the microscopic forces playing a central role, the authors also explain the similarities and the techniques, such as the resummations, that are needed for developing a formally consistent perturbative expansion. The formalism is developed step by step, starting from quantum mechanics; introducing scalar, fermionic and gauge fields; describing the issues of infrared divergences; resummations and effective field theories; and incorporating systems with finite chemical potentials. With this machinery in place, the important class of real-time (dynamic) observables is treated in some detail. This is followed by an overview of a number of applications, ranging from t...
Stringy horizons and generalized FZZ duality in perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Giribet, Gaston [Martin Fisher School of Physics, Brandeis University,Waltham, Massachusetts 02453 (United States); Departamento de Física, Universidad de Buenos Aires FCEN-UBA and IFIBA-CONICET,Ciudad Universitaria, Pabellón I, 1428, Buenos Aires (Argentina)
2017-02-14
We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We start with a simple derivation of the Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation functions of the sine-Liouville integrable model on the Riemann sphere to tree-level string amplitudes on the Euclidean two-dimensional black hole. This derivation of FZZ duality is based on perturbation theory, and it relies on a trick originally due to Fateev, which involves duality relations between different Selberg type integrals. This enables us to rewrite the correlation functions of sine-Liouville theory in terms of a special set of correlators in the gauged Wess-Zumino-Witten (WZW) theory, and use this to perform further consistency checks of the recently conjectured Generalized FZZ (GFZZ) duality. In particular, we prove that n-point correlation functions in sine-Liouville theory involving n−2 winding modes actually coincide with the correlation functions in the SL(2,ℝ)/U(1) gauged WZW model that include n−2 oscillator operators of the type described by Giveon, Itzhaki and Kutasov in reference https://www.doi.org/10.1007/JHEP10(2016)157. This proves the GFZZ duality for the case of tree level maximally winding violating n-point amplitudes with arbitrary n. We also comment on the connection between GFZZ and other marginal deformations previously considered in the literature.
Technical fine-tuning problem in renormalized perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Foda, O.E.
1983-01-01
The technical - as opposed to physical - fine tuning problem, i.e. the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a number of different models is studied. These include softly-broken supersymmetric models, and non-supersymmetric ones with a hierarchy of spontaneously-broken gauge symmetries. The models are renormalized using the BPHZ prescription, with momentum subtractions. Explicit calculations indicate that the tree-level hierarchy is not upset by the radiative corrections, and consequently no further fine-tuning is required to maintain it. Furthermore, this result is shown to run counter to that obtained via Dimensional Renormalization, (the only scheme used in previous literature on the subject). The discrepancy originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Within fully-renormalized perturbation theory the answer to the technical fine-tuning question (in the sense of whether the radiative corrections will ''readily'' respect the tree level gauge hierarchy or not) is contingent on the renormalization scheme used to define the model at the quantum level, rather than on the model itself. In other words, the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.
Enforcing conservation laws in nonequilibrium cluster perturbation theory
Gramsch, Christian; Potthoff, Michael
2017-05-01
Using the recently introduced time-local formulation of the nonequilibrium cluster perturbation theory (CPT), we construct a generalization of the approach such that macroscopic conservation laws are respected. This is achieved by exploiting the freedom for the choice of the starting point of the all-order perturbation theory in the intercluster hopping. The proposed conserving CPT is a self-consistent propagation scheme which respects the conservation of energy, particle number, and spin, which treats short-range correlations exactly up to the linear scale of the cluster, and which represents a mean-field-like approach on length scales beyond the cluster size. Using Green's functions, conservation laws are formulated as local constraints on the local spin-dependent particle and the doublon density. We consider them as conditional equations to self-consistently fix the time-dependent intracluster one-particle parameters. Thanks to the intrinsic causality of the CPT, this can be set up as a step-by-step time propagation scheme with a computational effort scaling linearly with the maximum propagation time and exponentially in the cluster size. As a proof of concept, we consider the dynamics of the two-dimensional, particle-hole-symmetric Hubbard model following a weak interaction quench by simply employing two-site clusters only. Conservation laws are satisfied by construction. We demonstrate that enforcing them has strong impact on the dynamics. While the doublon density is strongly oscillating within plain CPT, a monotonic relaxation is observed within the conserving CPT.
Technical fine-tuning problem in renormalized perturbation theory
International Nuclear Information System (INIS)
Foda, O.E.
1983-01-01
The technical - as opposed to physical - fine tuning problem, i.e. the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a number of different models is studied. These include softly-broken supersymmetric models, and non-supersymmetric ones with a hierarchy of spontaneously-broken gauge symmetries. The models are renormalized using the BPHZ prescription, with momentum subtractions. Explicit calculations indicate that the tree-level hierarchy is not upset by the radiative corrections, and consequently no further fine-tuning is required to maintain it. Furthermore, this result is shown to run counter to that obtained via Dimensional Renormalization, (the only scheme used in previous literature on the subject). The discrepancy originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Within fully-renormalized perturbation theory the answer to the technical fine-tuning question (in the sense of whether the radiative corrections will ''readily'' respect the tree level gauge hierarchy or not) is contingent on the renormalization scheme used to define the model at the quantum level, rather than on the model itself. In other words, the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes
Heavy-light semileptonic decays in staggered chiral perturbation theory
Aubin, C.; Bernard, C.
2007-07-01
We calculate the form factors for the semileptonic decays of heavy-light pseudoscalar mesons in partially quenched staggered chiral perturbation theory (SχPT), working to leading order in 1/mQ, where mQ is the heavy-quark mass. We take the light meson in the final state to be a pseudoscalar corresponding to the exact chiral symmetry of staggered quarks. The treatment assumes the validity of the standard prescription for representing the staggered “fourth-root trick” within SχPT by insertions of factors of 1/4 for each sea-quark loop. Our calculation is based on an existing partially quenched continuum chiral perturbation theory calculation with degenerate sea quarks by Bećirević, Prelovsek, and Zupan, which we generalize to the staggered (and nondegenerate) case. As a byproduct, we obtain the continuum partially quenched results with nondegenerate sea quarks. We analyze the effects of nonleading chiral terms, and find a relation among the coefficients governing the analytic valence mass dependence at this order. Our results are useful in analyzing lattice computations of form factors B→π and D→K, when the light quarks are simulated with the staggered action.
Methods of thermal field theory
Energy Technology Data Exchange (ETDEWEB)
Mallik, S [Saha Institute of Nuclear Physics, Calcutta (India)
1998-11-01
We introduce the basic ideas of thermal field theory and review its path integral formulation. We then discuss the problems of QCD theory at high and at low temperatures. At high temperature the naive perturbation expansion breaks down and is cured by resummation. We illustrate this improved perturbation expansion with the g{sup 2}{phi}{sup 4} theory and then sketch its application to find the gluon damping rate in QCD theory. At low temperature the hadronic phase is described systematically by the chiral perturbation theory. The results obtained from this theory for the quark and the gluon condensates are discussed. (author) 22 refs., 6 figs.
Perturbative methods applied for sensitive coefficients calculations in thermal-hydraulic systems
International Nuclear Information System (INIS)
Andrade Lima, F.R. de
1993-01-01
The differential formalism and the Generalized Perturbation Theory (GPT) are applied to sensitivity analysis of thermal-hydraulics problems related to pressurized water reactor cores. The equations describing the thermal-hydraulic behavior of these reactors cores, used in COBRA-IV-I code, are conveniently written. The importance function related to the response of interest and the sensitivity coefficient of this response with respect to various selected parameters are obtained by using Differential and Generalized Perturbation Theory. The comparison among the results obtained with the application of these perturbative methods and those obtained directly with the model developed in COBRA-IV-I code shows a very good agreement. (author)
Sensitivity theory for reactor burnup analysis based on depletion perturbation theory
International Nuclear Information System (INIS)
Yang, Wonsik.
1989-01-01
The large computational effort involved in the design and analysis of advanced reactor configurations motivated the development of Depletion Perturbation Theory (DPT) for general fuel cycle analysis. The work here focused on two important advances in the current methods. First, the adjoint equations were developed for using the efficient linear flux approximation to decouple the neutron/nuclide field equations. And second, DPT was extended to the constrained equilibrium cycle which is important for the consistent comparison and evaluation of alternative reactor designs. Practical strategies were formulated for solving the resulting adjoint equations and a computer code was developed for practical applications. In all cases analyzed, the sensitivity coefficients generated by DPT were in excellent agreement with the results of exact calculations. The work here indicates that for a given core response, the sensitivity coefficients to all input parameters can be computed by DPT with a computational effort similar to a single forward depletion calculation
The sine-Gordon model and the small κ+ region of light- cone perturbation theory
International Nuclear Information System (INIS)
Griffin, P.A.
1992-01-01
The non-perturbative ultraviolet divergence of the sine-Gordon model is used to study the k + = 0 region of light-cone perturbation theory. The light-cone vacuum is shown to be unstable at the non- perturbative β 2 = 8π critical point by a light-cone version of Coleman's variational method. Vacuum bubbles, which are k + = 0 diagram in light-cone field theory and are individually finite and non-vanishing for all β, conspire to generate ultraviolet divergences of the light-cone energy density. The k + = 0 region of momentum also contributed to connected Green's functions: the connected two point function will not diverge, as it should, at the critical point unless diagrams which contribute only at k + = 0 are properly included. This analysis shows in a simple way how the k + = 0 region cannot be ignored even for connected diagrams. This phenomenon is expected to occur in higher dimensional gauge theories starting at two loop order in light-cone perturbation theory
Pion parameters in nuclear medium from chiral perturbation theory and virial expansion
International Nuclear Information System (INIS)
Mallik, S.; Sarkar, Sourav
2004-01-01
We consider two methods to find the effective parameters of the pion traversing a nuclear medium. One is the first order chiral perturbation theoretic evaluation of the pion pole contribution to the two-point function of the axial-vector current. The other is the exact, first order virial expansion of the pion self-energy. We find that, although the results of chiral perturbation theory are not valid at normal nuclear density, those from the virial expansion may be reliable at such density. The latter predicts both the mass shift and the in-medium decay width of the pion to be small, of about a few MeV
Topological string theory, modularity and non-perturbative physics
Energy Technology Data Exchange (ETDEWEB)
Rauch, Marco
2011-09-15
In this thesis the holomorphic anomaly of correlators in topological string theory, matrix models and supersymmetric gauge theories is investigated. In the first part it is shown how the techniques of direct integration known from topological string theory can be used to solve the closed amplitudes of Hermitian multi-cut matrix models with polynomial potentials. In the case of the cubic matrix model, explicit expressions for the ring of non-holomorphic modular forms that are needed to express all closed matrix model amplitudes are given. This allows to integrate the holomorphic anomaly equation up to holomorphic modular terms that are fixed by the gap condition up to genus four. There is an one-dimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg-Witten curve and the ring reduces to the non-holomorphic modular ring of the group {gamma}(2). On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. Using these results it is possible to make precision tests of the connection between the large order behavior of the 1/N expansion and non-perturbative effects due to instantons. Finally, it is argued that a full understanding of the large genus asymptotics in the multi-cut case requires a new class of non-perturbative sectors in the matrix model. In the second part a holomorphic anomaly equation for the modified elliptic genus of two M5-branes wrapping a rigid divisor inside a Calabi-Yau manifold is derived using wall-crossing formulae and the theory of mock modular forms. The anomaly originates from restoring modularity of an indefinite theta-function capturing the wall-crossing of BPS invariants associated to D4- D2-D0 brane systems. The compatibility of this equation with anomaly equations previously observed in the context of N=4 topological Yang-Mills theory on P{sup 2} and E-strings obtained from wrapping M5-branes on a del Pezzo surface which in
Topological string theory, modularity and non-perturbative physics
International Nuclear Information System (INIS)
Rauch, Marco
2011-09-01
In this thesis the holomorphic anomaly of correlators in topological string theory, matrix models and supersymmetric gauge theories is investigated. In the first part it is shown how the techniques of direct integration known from topological string theory can be used to solve the closed amplitudes of Hermitian multi-cut matrix models with polynomial potentials. In the case of the cubic matrix model, explicit expressions for the ring of non-holomorphic modular forms that are needed to express all closed matrix model amplitudes are given. This allows to integrate the holomorphic anomaly equation up to holomorphic modular terms that are fixed by the gap condition up to genus four. There is an one-dimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg-Witten curve and the ring reduces to the non-holomorphic modular ring of the group Γ(2). On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. Using these results it is possible to make precision tests of the connection between the large order behavior of the 1/N expansion and non-perturbative effects due to instantons. Finally, it is argued that a full understanding of the large genus asymptotics in the multi-cut case requires a new class of non-perturbative sectors in the matrix model. In the second part a holomorphic anomaly equation for the modified elliptic genus of two M5-branes wrapping a rigid divisor inside a Calabi-Yau manifold is derived using wall-crossing formulae and the theory of mock modular forms. The anomaly originates from restoring modularity of an indefinite theta-function capturing the wall-crossing of BPS invariants associated to D4- D2-D0 brane systems. The compatibility of this equation with anomaly equations previously observed in the context of N=4 topological Yang-Mills theory on P 2 and E-strings obtained from wrapping M5-branes on a del Pezzo surface which in turn is
Existence of localizing solutions in plasticity via the geometric singular perturbation theory
Lee, Min-Gi; Tzavaras, Athanasios
2017-01-01
system has fast and slow time scales, forming a singularly perturbed problem. Geometric singular perturbation theory is applied to this problem to achieve an invariant surface. The flow on the invariant surface is analyzed via the Poincaré
International Nuclear Information System (INIS)
Van de Wetering, J.F.W.H.
1992-01-01
Using perturbative Chern-Simons theory in the almost axial gauge on the euclidean manifold S 1 xR 2 , we give a prescription for the computation of knot invariants. The method gives the correct expectation value of the unknot to all orders in perturbation theory and gives the correct answer for the spectral-parameter-dependent universal R-matrix to second order. All results are derived for a general semi-simple Lie algebra. (orig.)
On the acceleration of convergence of many-body perturbation theory. Pt. 2
International Nuclear Information System (INIS)
Dietz, K.; Schmidt, C.; Warken, M.; Hess, B.A.
1992-07-01
We employ the method developed in a previous paper to small systems-Be, LiH, H 2 -where full CI-calculations are available for monitoring convergence of many-body perturbation theory. It is shown that divergent series, in particular for excited states, can be transformed into fast converging ones. In essence our method consists in performing infinite subsummations of perturbation series in order to improve convergence: coupling constants are redefined such that singularities are incorporated in a non-perturbative manner and remaining correlations can be expanded in a larger domain of the complex coupling constant plane. It is in this way that the notion of 'improved convergence' has a well defined meaning. (orig.)
Small-sample-worth perturbation methods
International Nuclear Information System (INIS)
1985-01-01
It has been assumed that the perturbed region, R/sub p/, is large enough so that: (1) even without a great deal of biasing there is a substantial probability that an average source-neutron will enter it; and (2) once having entered, the neutron is likely to make several collisions in R/sub p/ during its lifetime. Unfortunately neither assumption is valid for the typical configurations one encounters in small-sample-worth experiments. In such experiments one measures the reactivity change which is induced when a very small void in a critical assembly is filled with a sample of some test-material. Only a minute fraction of the fission-source neutrons ever gets into the sample and, of those neutrons that do, most emerge uncollided. Monte Carlo small-sample perturbations computations are described
Perturbation theory in Lagrangian hydrodynamics for a cosmological fluid with velocity dispersion
International Nuclear Information System (INIS)
Tatekawa, Takayuki; Suda, Momoko; Maeda, Kei-ichi; Morita, Masaaki; Anzai, Hiroki
2002-01-01
We extensively develop a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. We solve the hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic equation of state, using a perturbation method up to second order. This perturbative approach is an extension of the usual Lagrangian perturbation theory for a pressureless fluid, in view of the inclusion of the pressure effect, which should be taken into account on the occurrence of velocity dispersion. We obtain the first-order solutions in generic background universes and the second-order solutions in a wider range of a polytropic index, whereas our previous work gives the first-order solutions only in the Einstein-de Sitter background and the second-order solutions for the polytropic index 4/3. Using the perturbation solutions, we present illustrative examples of our formulation in one- and two-dimensional systems, and discuss how the evolution of inhomogeneities changes for the variation of the polytropic index
Energy Technology Data Exchange (ETDEWEB)
White, J.R.
1980-08-01
A generalized depletion perturbation formulation based on the quasi-static method for solving realistic multicycle reactor depletion problems is developed and implemented within the VENTURE/BURNER modular code system. The present development extends the original formulation derived by M.L. Williams to include nuclide discontinuities such as fuel shuffling and discharge. This theory is first described in detail with particular emphasis given to the similarity of the forward and adjoint quasi-static burnup equations. The specific algorithm and computational methods utilized to solve the adjoint problem within the newly developed DEPTH (Depletion Perturbation Theory) module are then briefly discussed. Finally, the main features and computational accuracy of this new method are illustrated through its application to several representative reactor depletion problems.
One-Group Perturbation Theory Applied to Measurements with Void
International Nuclear Information System (INIS)
Persson, Rolf
1966-09-01
Formulas suitable for evaluating progressive as well as single rod substitution measurements are derived by means of one-group perturbation theory. The diffusion coefficient may depend on direction and position. By using the buckling concept one can derive expressions which are quite simple and the perturbed flux can be taken into account in a comparatively simple way. By using an unconventional definition of cells a transition region is introduced quite logically. Experiments with voids around metal rods, diam. 3.05 cm, have been analysed. The agreement between extrapolated and directly measured buckling values is excellent, the buckling difference between lattices with water-filled and voided shrouds being 0. 263 ± 0.015/m 2 and 0.267 ± 0.005/m 2 resp. From single-rod experiments differences between diffusion coefficients are determined to δD r /D = 0.083 ± 0.004 and δD z /D = 0.120 ± 0.018. With air-filled shrouds there is consequently anisotropy in the neutron diffusion and we have (D z /D r ) air = 1.034 ± 0.020
One-Group Perturbation Theory Applied to Measurements with Void
Energy Technology Data Exchange (ETDEWEB)
Persson, Rolf
1966-09-15
Formulas suitable for evaluating progressive as well as single rod substitution measurements are derived by means of one-group perturbation theory. The diffusion coefficient may depend on direction and position. By using the buckling concept one can derive expressions which are quite simple and the perturbed flux can be taken into account in a comparatively simple way. By using an unconventional definition of cells a transition region is introduced quite logically. Experiments with voids around metal rods, diam. 3.05 cm, have been analysed. The agreement between extrapolated and directly measured buckling values is excellent, the buckling difference between lattices with water-filled and voided shrouds being 0. 263 {+-} 0.015/m{sup 2} and 0.267 {+-} 0.005/m{sup 2} resp. From single-rod experiments differences between diffusion coefficients are determined to {delta}D{sub r}/D = 0.083 {+-} 0.004 and {delta}D{sub z}/D = 0.120 {+-} 0.018. With air-filled shrouds there is consequently anisotropy in the neutron diffusion and we have (D{sub z}/D{sub r}){sub air} = 1.034 {+-} 0.020.
A Parameter Robust Method for Singularly Perturbed Delay Differential Equations
Directory of Open Access Journals (Sweden)
Erdogan Fevzi
2010-01-01
Full Text Available Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to be uniformly convergent with respect to the perturbation parameter. A numerical example is solved using the presented method, and the computed result is compared with exact solution of the problem.
High orders of perturbation theory. Are renormalons significant?
International Nuclear Information System (INIS)
Suslov, I.M.
1999-01-01
According to Lipatov [Sov. Phys. JETP 45, 216 (1977)], the high orders of perturbation theory are determined by saddle-point configurations, i.e., instantons, which correspond to functional integrals. According to another opinion, the contributions of individual large diagrams, i.e., renormalons, which, according to t'Hooft [The Whys of Subnuclear Physics: Proceedings of the 1977 International School of Subnuclear Physics (Erice, Trapani, Sicily, 1977), A. Zichichi (Ed.), Plenum Press, New York (1979)], are not contained in the Lipatov contribution, are also significant. The history of the conception of renormalons is presented, and the arguments in favor of and against their existence are discussed. The analytic properties of the Borel transforms of functional integrals, Green's functions, vertex parts, and scaling functions are investigated in the case of φ 4 theory. Their analyticity in a complex plane with a cut from the first instanton singularity to infinity (the Le Guillou-Zinn-Justin hypothesis [Phys. Rev. Lett. 39, 95 (1977); Phys. Rev. B 21, 3976 (1980)] is proved. It rules out the existence of the renormalon singularities pointed out by t'Hooft and demonstrates the nonconstructiveness of the conception of renormalons as a whole. The results can be interpreted as an indication of the internal consistency of φ 4 theory
SIMP model at NNLO in chiral perturbation theory
Hansen, Martin; Langæble, Kasper; Sannino, Francesco
2015-10-01
We investigate the phenomenological viability of a recently proposed class of composite dark matter models where the relic density is determined by 3 →2 number-changing processes in the dark sector. Here the pions of the strongly interacting field theory constitute the dark matter particles. By performing a consistent next-to-leading- and next-to-next-to-leading-order chiral perturbative investigation we demonstrate that the leading-order analysis cannot be used to draw conclusions about the viability of the model. We further show that higher-order corrections substantially increase the tension with phenomenological constraints challenging the viability of the simplest realization of the strongly interacting massive particle paradigm.
The role of resonances in chiral perturbation theory
International Nuclear Information System (INIS)
Ecker, G.; Rafael, E. de
1988-09-01
The strong interactions of low-lying meson resonances (spin ≤ 1) with the octet of pseudoscalar mesons (π,Κ,η) are considered to lowest order in the derivative expansion of chiral SU(3). The resonance contributions to the coupling constants of the O(p 4 ) effective chiral lagrangian involving pseudoscalar fields only are determined. These low-energy coupling constants are found to be dominated by the resonance contributions. Although we do not treat the vector and axial-vector mesons as gauge bosons of local chiral symmetry, vector meson dominance emerges as a prominent result of our analysis. As a further application of chiral resonance couplings, we calculate the electromagnetic pion mass difference to lowest order in chiral perturbation theory with explicit resonance fields. 29 refs., 2 figs., 5 tabs. (Author)
Universality of fast quenches from the conformal perturbation theory
Dymarsky, Anatoly; Smolkin, Michael
2018-01-01
We consider global quantum quenches, a protocol when a continuous field theoretic system in the ground state is driven by a homogeneous time-dependent external interaction. When the typical inverse time scale of the interaction is much larger than all relevant scales except for the UV-cutoff the system's response exhibits universal scaling behavior. We provide both qualitative and quantitative explanations of this universality and argue that physics of the response during and shortly after the quench is governed by the conformal perturbation theory around the UV fixed point. We proceed to calculate the response of one and two-point correlation functions confirming and generalizing universal scalings found previously. Finally, we discuss late time behavior after the quench and argue that all local quantities will equilibrate to their thermal values specified by an excess energy acquired by the system during the quench.
On the non-linear scale of cosmological perturbation theory
Blas, Diego; Konstandin, Thomas
2013-01-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
On the non-linear scale of cosmological perturbation theory
International Nuclear Information System (INIS)
Blas, Diego; Garny, Mathias; Konstandin, Thomas
2013-04-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Exploring perturbative conformal field theory in Mellin space
Energy Technology Data Exchange (ETDEWEB)
Nizami, Amin A. [International Centre for Theoretical Sciences, TIFR,Hesaraghatta, Hubli, Bengaluru-560089 (India); Rudra, Arnab [Center for Quantum Mathematics and Physics (QMAP), Department of Physics,University of California, Davis, 1 Shields Ave, Davis, CA 95616 (United States); Sarkar, Sourav [Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, IRIS-Adlershof,Zum Großen Windkanal 6, 12489 Berlin (Germany); Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,Am Mühlenberg 1, 14476 Potsdam (Germany); Verma, Mritunjay [International Centre for Theoretical Sciences, TIFR,Hesaraghatta, Hubli, Bengaluru-560089 (India); Harish-Chandra Research Institute,Chhatnag Road, Jhunsi, Allahabad-211019 (India)
2017-01-24
We explore the Mellin representation of correlation functions in conformal field theories in the weak coupling regime. We provide a complete proof for a set of Feynman rules to write the Mellin amplitude for a general tree level Feynman diagram involving only scalar operators. We find a factorised form involving beta functions associated to the propagators, similar to tree level Feynman rules in momentum space for ordinary QFTs. We also briefly consider the case where a generic scalar perturbation of the free CFT breaks conformal invariance. Mellin space still has some utility and one can consider non-conformal Mellin representations. In this context, we find that the beta function corresponding to conformal propagator uplifts to a hypergeometric function.
Meson-baryon interactions in unitarized chiral perturbation theory
International Nuclear Information System (INIS)
Garcia Recio, G.; Nieves, J.; Ruiz Arriola, E.; Vicente Vacas, M.
2003-01-01
Meson-Baryon Interactions can be successfully described using both Chiral Symmetry and Unitarity. The s-wave meson-baryon scattering amplitude is analyzed in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry in the potential. Two body coupled channel unitarity is exactly preserved. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. Off-shell behavior is parameterized in terms of low energy constants. The relation to the heavy baryon limit is discussed. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths baryonic resonances of the N(1535), N(1670), Λ(1405) and Λ(1670) resonances which compare well with accepted numbers
International Nuclear Information System (INIS)
Franca Walter, F.L.; Alvim, A.C.M.; Silva, F.C. da; Melo e Frutuoso, P.F.
1995-01-01
The application of the GPT methodology to a reliability engineering problem of great practical interest is discussed: that of the analysis of the influence of the demand rate on the accident rate of a process plant equipped with a single protective channel. This problem has been solved in the literature by traditional methods, that is, for each demand rate value the system of differential equations that governs the system behavior (derived from a Markovian reliability model) is solved and the resulting points are employed to generate the desired curve. This sensitivity analysis has been performed by means of a GPT approach in order to show how it could simplify the calculations. Although an analytical solution is available for the above equations, the application of the GPT approach needed the solution of the system for a few points (reference solutions) and the results agree very well with those published. (author). 9 refs, 4 figs
Nonrelativistic hyperfine splitting in muonic helium by adiabatic perturbation theory
International Nuclear Information System (INIS)
Drachman, R.J.
1980-01-01
Huang and Hughes have recently discussed the hyperfine splitting Δν of muonic helium (α ++ μ - e - ) using a variational approach. In this paper, the Born-Oppenheimer approximation is used to simplify the evaluation of Δν in the nonrelativistic limit. The first-order perturbed wave function of the electron is obtained in closed form by slightly modifying the method used by Dalgarno and Lynn. The result Δν=4450 MHz, is quite close to the published result of Huang and Hughes 4455.2 +- 1 MHz, which required a very large Hylleraas expansion as well as considerable extrapolation
An algebraic description of perturbation theory in quantum electrodynamics
International Nuclear Information System (INIS)
Wright, J.D.
1982-01-01
An algebraic formulation of the electromagnetic field, in which various quantization procedures can be described, is used to discuss perturbation calculations. The Feynman rules and the second order calculation of the self-energy of the electron can be developed on the basis of the Fermi method of quantization. The algebraic approach clarifies the problems in defining the vacuum and other states, which are associated with calculations in terms of field algebra operators. The vacuum state defined on the field algebra by Schwinger leads to incorrect results in the self-energy calculation
Constrained Perturbation Regularization Approach for Signal Estimation Using Random Matrix Theory
Suliman, Mohamed Abdalla Elhag
2016-10-06
In this work, we propose a new regularization approach for linear least-squares problems with random matrices. In the proposed constrained perturbation regularization approach, an artificial perturbation matrix with a bounded norm is forced into the system model matrix. This perturbation is introduced to improve the singular-value structure of the model matrix and, hence, the solution of the estimation problem. Relying on the randomness of the model matrix, a number of deterministic equivalents from random matrix theory are applied to derive the near-optimum regularizer that minimizes the mean-squared error of the estimator. Simulation results demonstrate that the proposed approach outperforms a set of benchmark regularization methods for various estimated signal characteristics. In addition, simulations show that our approach is robust in the presence of model uncertainty.
Magnetic exchange couplings from noncollinear perturbation theory: dinuclear CuII complexes.
Phillips, Jordan J; Peralta, Juan E
2014-08-07
To benchmark the performance of a new method based on noncollinear coupled-perturbed density functional theory [J. Chem. Phys. 138, 174115 (2013)], we calculate the magnetic exchange couplings in a series of triply bridged ferromagnetic dinuclear Cu(II) complexes that have been recently synthesized [Phys. Chem. Chem. Phys. 15, 1966 (2013)]. We find that for any basis-set the couplings from our noncollinear coupled-perturbed methodology are practically identical to those of spin-projected energy-differences when a hybrid density functional approximation is employed. This demonstrates that our methodology properly recovers a Heisenberg description for these systems, and is robust in its predictive power of magnetic couplings. Furthermore, this indicates that the failure of density functional theory to capture the subtle variation of the exchange couplings in these complexes is not simply an artifact of broken-symmetry methods, but rather a fundamental weakness of current approximate density functionals for the description of magnetic couplings.
Zhumagulov, Yaroslav V.; Krasavin, Andrey V.; Kashurnikov, Vladimir A.
2018-05-01
The method is developed for calculation of electronic properties of an ensemble of metal nanoclusters with the use of cluster perturbation theory. This method is applied to the system of gold nanoclusters. The Greens function of single nanocluster is obtained by ab initio calculations within the framework of the density functional theory, and then is used in Dyson equation to group nanoclusters together and to compute the Greens function as well as the electron density of states of the whole ensemble. The transition from insulator state of a single nanocluster to metallic state of bulk gold is observed.
GAPER-1D, 1-D Multigroup 1. Order Perturbation Transport Theory for Reactivity Coefficient
International Nuclear Information System (INIS)
Koch, P.K.
1976-01-01
1 - Description of problem or function: Reactivity coefficients are computed using first-order transport perturbation theory for one- dimensional multi-region reactor assemblies. The number of spatial mesh-points and energy groups is arbitrary. An elementary synthesis scheme is employed for treatment of two- and three-dimensional problems. The contributions to the change in inverse multiplication factor, delta(1/k), from perturbations in the individual capture, net fission, total scattering, (n,2n), inelastic scattering, and leakage cross sections are computed. A multi-dimensional prompt neutron lifetime calculation is also available. 2 - Method of solution: Broad group cross sections for the core and perturbing or sample materials are required as input. Scalar neutron fluxes and currents, as computed by SN transport calculations, are then utilized to solve the first-order transport perturbation theory equations. A synthesis scheme is used, along with independent SN calculations in two or three dimensions, to treat a multi- dimensional assembly. Spherical harmonics expansions of the angular fluxes and scattering source terms are used with leakage and anisotropic scattering treated in a P1 approximation. The angular integrations in the perturbation theory equations are performed analytically. Various reactivity coefficients and material worths are then easily computed at specified positions in the assembly. 3 - Restrictions on the complexity of the problem: The formulation of the synthesis scheme used for two- and three-dimensional problems assumes that the fluxes and currents were computed by the DTF4 code (NESC Abstract 209). Therefore, fluxes and currents from two- or three-dimensional transport or diffusion theory codes cannot be used
International Nuclear Information System (INIS)
Andrade Lima, F.R. de
1986-01-01
The sensitivity of non linear responses associated with physical quantities governed by non linear differential systems can be studied using perturbation theory. The equivalence and formal differences between the differential and GPT formalisms are shown and both are used for sensitivity calculations of transient problems in a typical PWR coolant channel. The results obtained are encouraging with respect to the potential of the method for thermalhydraulics calculations normally performed for reactor design and safety analysis. (Author) [pt
Development of a VVER-1000 core loading pattern optimization program based on perturbation theory
International Nuclear Information System (INIS)
Hosseini, Mohammad; Vosoughi, Naser
2012-01-01
Highlights: ► We use perturbation theory to find an optimum fuel loading pattern in a VVER-1000. ► We provide a software for in-core fuel management optimization. ► We consider two objectives for our method (perturbation theory). ► We show that perturbation theory method is very fast and accurate for optimization. - Abstract: In-core nuclear fuel management is one of the most important concerns in the design of nuclear reactors. Two main goals in core fuel loading pattern design optimization are maximizing the core effective multiplication factor in order to extract the maximum energy, and keeping the local power peaking factor lower than a predetermined value to maintain the fuel integrity. Because of the numerous possible patterns of fuel assemblies in the reactor core, finding the best configuration is so important and challenging. Different techniques for optimization of fuel loading pattern in the reactor core have been introduced by now. In this study, a software is programmed in C language to find an order of the fuel loading pattern of a VVER-1000 reactor core using the perturbation theory. Our optimization method is based on minimizing the radial power peaking factor. The optimization process launches by considering an initial loading pattern and the specifications of the fuel assemblies which are given as the input of the software. The results on a typical VVER-1000 reactor reveal that the method could reach to a pattern with an allowed radial power peaking factor and increases the cycle length 1.1 days, as well.
Generalized perturbation theory error control within PWR core-loading pattern optimization
International Nuclear Information System (INIS)
Imbriani, J.S.; Turinsky, P.J.; Kropaczek, D.J.
1995-01-01
The fuel management optimization code FORMOSA-P has been developed to determine the family of near-optimum loading patterns for PWR reactors. The code couples the optimization technique of simulated annealing (SA) with a generalized perturbation theory (GPT) model for evaluating core physics characteristics. To ensure the accuracy of the GPT predictions, as well as to maximize the efficient of the SA search, a GPT error control method has been developed
Perturbation methods and closure approximations in nonlinear systems
International Nuclear Information System (INIS)
Dubin, D.H.E.
1984-01-01
In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak is considered. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase-space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. In the second section, statistical closure theories are applied to simple dynamical systems. The logistic map is used as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the direct interaction approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodically constraint on a Langevin form of the DIA a new stable closure is developed
Analysis of Diffusion Problems using Homotopy Perturbation and Variational Iteration Methods
DEFF Research Database (Denmark)
Barari, Amin; Poor, A. Tahmasebi; Jorjani, A.
2010-01-01
In this paper, variational iteration method and homotopy perturbation method are applied to different forms of diffusion equation. The diffusion equations have found wide applications in heat transfer problems, theory of consolidation and many other problems in engineering. The methods proposed...
International Nuclear Information System (INIS)
Fisch, J.M.L.
1990-01-01
The algebraic structure of the antifield-antibracket formalism for both reducible and irreducible gauge theories is clarified. This is done by using the methods of Homological Perturbation Theory (HPT). A crucial ingredient of the construction is the Koszul-Tate complex associated with the stationary surface of the classical extremals. The Koszul-Tate differential acts on the antifields and is graded by the antighost number. It provides a resolution of the algebra A of functions defined on the stationary surface, namely, it is acyclic except at degree zero where its homology group reduces to A. Acyclicity only holds because of the introduction of the ghosts of ghosts and provides an alternative criterion for what is meant by a proper solution of the master equation. The existence of the BRST symmetry follows from the techniques of HPT. The classical Lagrangian BRST cohomology is completely worked out and shown to be isomorphic with the cohomology of the exterior derivative along the gauge orbits on the stationary surface. The algebraic structure of the formalism is identical with the structure of the Hamiltonian BRST construction. The role played there by the constraint surface is played here by the stationary surface. Only elementary quantum questions (general properties of the measure) are addressed. (orig.)
Finite density two color chiral perturbation theory revisited
Adhikari, Prabal; Beleznay, Soma B.; Mannarelli, Massimo
2018-06-01
We revisit two-color, two-flavor chiral perturbation theory at finite isospin and baryon density. We investigate the phase diagram obtained varying the isospin and the baryon chemical potentials, focusing on the phase transition occurring when the two chemical potentials are equal and exceed the pion mass (which is degenerate with the diquark mass). In this case, there is a change in the order parameter of the theory that does not lend itself to the standard picture of first order transitions. We explore this phase transition both within a Ginzburg-Landau framework valid in a limited parameter space and then by inspecting the full chiral Lagrangian in all the accessible parameter space. Across the phase transition between the two broken phases the order parameter becomes an SU(2) doublet, with the ground state fixing the expectation value of the sum of the magnitude squared of the pion and the diquark fields. Furthermore, we find that the Lagrangian at equal chemical potentials is invariant under global SU(2) transformations and construct the effective Lagrangian of the three Goldstone degrees of freedom by integrating out the radial fluctuations.
Suliman, Mohamed Abdalla Elhag; Ballal, Tarig; Kammoun, Abla; Alnaffouri, Tareq Y.
2016-01-01
In this supplementary appendix we provide proofs and additional simulation results that complement the paper (constrained perturbation regularization approach for signal estimation using random matrix theory).
International Nuclear Information System (INIS)
Garcia, Juan Matias
2005-01-01
Perturbation Methods represent a powerful tool to do sensitivity analysis, and they found many aplications in nuclear engineering.As an introduction to this kind of analysis, we develope a program that apply the Generalized Perturbation Theory or GPT Method to bidimensional system of rectangular geometry.We first consider an homogeneous system of non-multiplying material and then an heterogeneous system with region of multiplying material, with the intention of make concret aplications of perturbation method to nuclear engineering problems.The program, that we called Pert, determines neutron fluxes and importance functions applying the Multigroup Diffusion Theory; and also solves the integrals required to calculate sensitivity coefficients.Using this perturbation methods we could verify the low computational cost required to make this kind of analysis and the simplicity of the equations systems involved, allowing us to make elaborates sensitivity analysis for the responses of our interest
A stochastic perturbation theory for non-autonomous systems
Energy Technology Data Exchange (ETDEWEB)
Moon, W., E-mail: wm275@damtp.cam.ac.uk [Yale University, New Haven, Connecticut 06520-8109 (United States); Wettlaufer, J. S., E-mail: wettlaufer@maths.ox.ac.uk [Yale University, New Haven, Connecticut 06520-8109 (United States); Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom)
2013-12-15
We develop a perturbation theory for a class of first order nonlinear non-autonomous stochastic ordinary differential equations that arise in climate physics. The perturbative procedure produces moments in terms of integral delay equations, whose order by order decay is characterized in a Floquet-like sense. Both additive and multiplicative sources of noise are discussed and the question of how the nature of the noise influences the results is addressed theoretically and numerically. By invoking the Martingale property, we rationalize the transformation of the underlying Stratonovich form of the model to an Ito form, independent of whether the noise is additive or multiplicative. The generality of the analysis is demonstrated by developing it both for a Brownian particle moving in a periodically forced quartic potential, which acts as a simple model of stochastic resonance, as well as for our more complex climate physics model. The validity of the approach is shown by comparison with numerical solutions. The particular climate dynamics problem upon which we focus involves a low-order model for the evolution of Arctic sea ice under the influence of increasing greenhouse gas forcing ΔF{sub 0}. The deterministic model, developed by Eisenman and Wettlaufer [“Nonlinear threshold behavior during the loss of Arctic sea ice,” Proc. Natl. Acad. Sci. U.S.A. 106(1), 28–32 (2009)] exhibits several transitions as ΔF{sub 0} increases and the stochastic analysis is used to understand the manner in which noise influences these transitions and the stability of the system.
Rebolini, Elisa; Teale, Andrew M.; Helgaker, Trygve; Savin, Andreas; Toulouse, Julien
2018-06-01
A Görling-Levy (GL)-based perturbation theory along the range-separated adiabatic connection is assessed for the calculation of electronic excitation energies. In comparison with the Rayleigh-Schrödinger (RS)-based perturbation theory this GL-based perturbation theory keeps the ground-state density constant at each order and thus gives the correct ionisation energy at each order. Excitation energies up to first order in the perturbation have been calculated numerically for the helium and beryllium atoms and the hydrogen molecule without introducing any density-functional approximations. In comparison with the RS-based perturbation theory, the present GL-based perturbation theory gives much more accurate excitation energies for Rydberg states but similar excitation energies for valence states.
The cosmological perturbation theory in loop cosmology with holonomy corrections
International Nuclear Information System (INIS)
Wu, Jian-Pin; Ling, Yi
2010-01-01
In this paper we investigate the scalar mode of first-order metric perturbations over spatially flat FRW spacetime when the holonomy correction is taken into account in the semi-classical framework of loop quantum cosmology. By means of the Hamiltonian derivation, the cosmological perturbation equations is obtained in longitudinal gauge. It turns out that in the presence of metric perturbation the holonomy effects influence both background and perturbations, and contribute the non-trivial terms S h1 and S h2 in the cosmological perturbation equations
Keldysh meets Lindblad: Correlated Gain and Loss in Higher Order Perturbation Theory
Stace, Tom; Mueller, Clemens
Motivated by correlated decay processes driving gain, loss and lasing in driven artificial quantum systems, we develop a theoretical technique using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been proposed to describe similar systems. All of the additional terms contribute to the system behaviour at the same order of perturbation theory. We then apply these results to analyse the phonon-assisted steady-state gain of a microwave field driving a double quantum-dot in a resonator. We show that resonator gain and loss are substantially affected by dephasing- assisted dissipative processes in the quantum-dot system. These additional processes, which go beyond recently proposed polaronic theories, are in good quantitative agreement with experimental observations.
Multidimensional periodic Schrödinger operator perturbation theory and applications
Veliev, Oktay
2015-01-01
The book describes the direct problems and the inverse problem of the multidimensional Schrödinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral invariants and finding the periodic potential from the given Bloch eigenvalues. The unique method of this book derives the asymptotic formulas for Bloch eigenvalues and Bloch functions for arbitrary dimension. Moreover, the measure of the iso-energetic surfaces in the high energy region is construct and estimated. It implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed in this book, the spectral invariants of the multidimensional operator from the given Bloch eigenvalues are determined. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential. This way the possibility to determine the potential constructively by using Bloch eigenvalues as input data is given. In the ...
Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.
Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura
2016-07-12
A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.
International Nuclear Information System (INIS)
Kang, Kai; Qin, Shaojing; Wang, Chuilin
2011-01-01
We calculated numerically the localization length of one-dimensional Anderson model with diagonal disorder. For weak disorder, we showed that the localization length changes continuously as the energy changes from the band center to the boundary of the anomalous region near the band edge. We found that all the localization lengths for different disorder strengths and different energies collapse onto a single curve, which can be fitted by a simple equation. Thus the description of the perturbation theory and the band center anomaly were unified into this equation. -- Highlights: → We study the band center anomaly of one-dimensional Anderson localization. → We study numerically the Lyapunov exponent through a parametrization method of the transfer matrix. → We give a unified equation to describe the band center anomaly and perturbation theory.
International Nuclear Information System (INIS)
Zavaljevski, N.
1985-01-01
Proposed optimization procedure is fast due to application of linear programming. Non-linear constraints which demand iterative application of linear programming are slowing down the calculation. Linearization can be done by different procedures starting from simple empirical rules for fuel in-core management to complicated general perturbation theory with higher order of corrections. A mathematical model was formulated for optimization of improved fuel cycle. A detailed algorithm for determining minimum of fresh fuel at the beginning of each fuel cycle is shown and the problem is linearized by first order perturbation theory and it is optimized by linear programming. Numerical illustration of the proposed method was done for the experimental reactor mostly for saving computer time
Solution to the Diffusion equation for multi groups in X Y geometry using Linear Perturbation theory
International Nuclear Information System (INIS)
Mugica R, C.A.
2004-01-01
Diverse methods exist to solve numerically the neutron diffusion equation for several energy groups in stationary state among those that highlight those of finite elements. In this work the numerical solution of this equation is presented using Raviart-Thomas nodal methods type finite element, the RT0 and RT1, in combination with iterative techniques that allow to obtain the approached solution in a quick form. Nevertheless the above mentioned, the precision of a method is intimately bound to the dimension of the approach space by cell, 5 for the case RT0 and 12 for the RT1, and/or to the mesh refinement, that makes the order of the problem of own value to solve to grow considerably. By this way if it wants to know an acceptable approach to the value of the effective multiplication factor of the system when this it has experimented a small perturbation it was appeal to the Linear perturbation theory with which is possible to determine it starting from the neutron flow and of the effective multiplication factor of the not perturbed case. Results are presented for a reference problem in which a perturbation is introduced in an assemble that simulates changes in the control bar. (Author)
Neutral pion electroproduction off light nuclei in chiral perturbation theory
International Nuclear Information System (INIS)
Lenkewitz, Mark
2013-01-01
Threshold pion electroproduction on tri-nucleon systems is investigated in the framework of baryon Chiral Perturbation Theory (ChPT) at next-to-leading one-loop order O(q 4 ) in the chiral expansion. To this order in small momenta, the production operator is a sum of one- and two-nucleon terms. While the one-nucleon terms resemble the impulse approximation, the two-nucleon contributions represent corrections due to the relevant nuclear interactions, e.g. pion-exchange interactions, which prove to be dominant, and due to recoil effects of the participating nucleons, which appear to be negligible. We calculate the expectation value of the production operator using chiral wave functions in a three-dimensional approach without partial wave expansion. The resulting integrals are evaluated using adaptive Monte Carlo integration, the VEGAS algorithm of Lepage. We obtain results for the threshold production multipoles E 0+ and L 0+ on 3 He and 3 H and comment on the sensitivity to the fundamental neutron amplitude E 0+ π 0 n . 3 He appears to be a particularly promising target to extract information about the neutron amplitude. This idea is usually invoked for spin-dependent quantities since the 3 He wave function is strongly dominated by the principal S-state component which suggests that its spin is largely driven by the one of the neutron.
Generalized polarizabilities of the nucleon in baryon chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Lensky, Vadim [Johannes Gutenberg Universitaet Mainz, Institut fuer Kernphysik, Cluster of Excellence PRISMA, Mainz (Germany); Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation); Pascalutsa, Vladimir; Vanderhaeghen, Marc [Johannes Gutenberg Universitaet Mainz, Institut fuer Kernphysik, Cluster of Excellence PRISMA, Mainz (Germany)
2017-02-15
The nucleon generalized polarizabilities (GPs), probed in virtual Compton scattering (VCS), describe the spatial distribution of the polarization density in a nucleon. They are accessed experimentally via the process of electron-proton bremsstrahlung (ep → epγ) at electron-beam facilities, such as MIT-Bates, CEBAF (Jefferson Lab), and MAMI (Mainz). We present the calculation of the nucleon GPs and VCS observables at next-to-leading order in baryon chiral perturbation theory (BχPT), and confront the results with the empirical information. At this order our results are predictions, in the sense that all the parameters are well known from elsewhere. Within the relatively large uncertainties of our calculation we find good agreement with the experimental observations of VCS and the empirical extractions of the GPs. We find large discrepancies with previous chiral calculations - all done in heavy-baryon χPT (HBχPT) - and discuss the differences between BχPT and HBχPT responsible for these discrepancies. (orig.)
Generalised perturbation theory and source of information through chemical measurements
International Nuclear Information System (INIS)
Lelek, V.; Marek, T.
2001-01-01
It is important to make all analyses and collect all information from the work of the new facility (which the transmutation demonstration unit will surely be) to be sure that the operation corresponds to the forecast or to correct the equations of the facility. The behaviour of the molten salt reactor and in particular the system of measurement are very different from that of the solid fuel reactor. Key information from the long time kinetics could be the nearly on line knowledge of the fuel composition. In this work it is shown how to include it into the control and use such data for the correction of neutron cross-sections for the high actinides or other characteristics. Also the problem of safety - change of the boundary problem to the initial problem - is mentioned. The problem is transformed into the generalised perturbation theory in which the adjoint function is obtained through the solution of the equations with right hand side having the form of source. Such an approach should be a theoretical base for the calculation of the sensitivity coefficients. (authors)
Extended Krenciglowa-Kuo method and perturbation expansion of Q-box
International Nuclear Information System (INIS)
Shimizu, Genki; Otsuka, Takaharu; Takayanagi, Kazuo
2015-01-01
The Extended Krenciglowa-Kuo (EKK) method is a microscopic method to construct the energy-independent effective Hamiltonian H eff ; provided with an exact Q-box of the system, we can show which eigenstates are described by H eff given by the EKK method. In actual calculations, however, we can calculate the Q-box only up to a finite order in the perturbation theory. In this work, we examine the EKK method with the approximate Q-box, and show that the perturbative calculation of the Q-box does not harm the convergence properties of the EKK iterative method. (author)
Screening of Coulomb interaction and many-body perturbation theory in atoms
International Nuclear Information System (INIS)
Dzyuba, V.A.; Flambaum, V.V.; Sil'vestrov, P.G.; Sushkov, O.P.
1988-01-01
Taking into account the electron Coulomb interaction screening considerably improves the convergence of perturbation theory in residual interaction. The developed technique allows to take into account screening diagrams in all orders of perturbation theory. Calculation of the correlation corrections to the thallium energy levels is carried out as an example
Theory of Perturbed Equilibria for Solving the Grad-Shafranov Equation
International Nuclear Information System (INIS)
Pletzer, A.; Zakharov, L.E.
1999-01-01
The theory of perturbed magnetohydrodynamic equilibria is presented for different formulations of the tokamak equilibrium problem. For numerical codes, it gives an explicit Newton scheme for solving the Grad-Shafranov equation subject to different constraints. The problem of stability of axisymmetric modes is shown to be a particular case of the equilibrium perturbation theory
Teruo, KISHIMOTO; Tetsuo, KAMMURI; Institute of Physics, University of Tsukuba; Department of Physics, Osaka University
1990-01-01
With the Dynamical Nuclear Field Theory (DNFT) in the Tamm-Dancoff representation we examine higher order corrections in the vibrational mode of a spherical nuclear system. Due to the effects of bubble diagrams, the perturbation expansion in terms of the unrenormalized coupling strength and boson energy fails at full self-consistency. On the other hand, it becomes applicable in the form of linked-cluster expansion when we use thses constants renormalized by the effect of bubble diagrams, in t...
Time-sliced perturbation theory for large scale structure I: general formalism
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego; Garny, Mathias; Sibiryakov, Sergey [Theory Division, CERN, CH-1211 Genève 23 (Switzerland); Ivanov, Mikhail M., E-mail: diego.blas@cern.ch, E-mail: mathias.garny@cern.ch, E-mail: mikhail.ivanov@cern.ch, E-mail: sergey.sibiryakov@cern.ch [FSB/ITP/LPPC, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne (Switzerland)
2016-07-01
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.
International Nuclear Information System (INIS)
Bender, C.M.; Cooper, F.
1985-01-01
An apparent difference between formulating mean field perturbation theory for lambdaphi 4 field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)lambdaphi 4 field theory. A simply method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action GAMMA(phi,chi) is obtained by directly integrating the functional differential equations for the fields phi and chi (equivalent1/2lambda/Nphi/sub α/phi/sup α/-μ 2 ) in the presence of two external sources j = -deltaGAMMA/deltaphi, S = -deltaGAMMA/deltachi
DEFF Research Database (Denmark)
Fromager, Emmanuel; Jensen, Hans Jørgen Aagaard
2011-01-01
Range-separated density-functional theory combines wave function theory for the long-range part of the two-electron interaction with density-functional theory for the short-range part. When describing the long-range interaction with non-variational methods, such as perturbation or coupled......-cluster theories, self-consistency effects are introduced in the density functional part, which for an exact solution requires iterations. They are generally assumed to be small but no detailed study has been performed so far. Here, the authors analyze self-consistency when using Møller-Plesset-type (MP......) perturbation theory for the long range interaction. The lowest-order self-consistency corrections to the wave function and the energy, that enter the perturbation expansions at the second and fourth order, respectively, are both expressed in terms of the one-electron reduced density matrix. The computational...
Quantum field theory with a momentum space of constant curvature (perturbation theory)
International Nuclear Information System (INIS)
Mir-Kasimov, R.M.
1978-01-01
In the framework of the field-theoretical approach in which the off-the-mass shell extension proceeds in the p-space of constant curvature, the perburbation theory is developed. The configurational representation of the de Sitter space is introduced with the help of the Fourier transformation of the group of motions. On the basis of a natural generalization of the Bogolyubov causality condition to the case of the new configurational representation a perturbation theory is constructed with the local in xi space Lagrangian density fucntion. The obtained S matrix obeys the reguirement of translation invariance. The S matrix elements are given by convergent expressions
Energy Technology Data Exchange (ETDEWEB)
Bozkaya, Uğur, E-mail: ugur.bozkaya@atauni.edu.tr [Department of Chemistry, Atatürk University, Erzurum 25240, Turkey and Department of Chemistry, Middle East Technical University, Ankara 06800 (Turkey)
2014-09-28
General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele, Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.
Adiabatic perturbation theory for atoms and molecules in the low-frequency regime.
Martiskainen, Hanna; Moiseyev, Nimrod
2017-12-14
There is an increasing interest in the photoinduced dynamics in the low frequency, ω, regime. The multiphoton absorptions by molecules in strong laser fields depend on the polarization of the laser and on the molecular structure. The unique properties of the interaction of atoms and molecules with lasers in the low-frequency regime imply new concepts and directions in strong-field light-matter interactions. Here we represent a perturbational approach for the calculations of the quasi-energy spectrum in the low-frequency regime, which avoids the construction of the Floquet operator with extremely large number of Floquet channels. The zero-order Hamiltonian in our perturbational approach is the adiabatic Hamiltonian where the atoms/molecules are exposed to a dc electric field rather than to ac-field. This is in the spirit of the first step in the Corkum three-step model. The second-order perturbation correction terms are obtained when iℏω∂∂τ serves as a perturbation and τ is a dimensionless variable. The second-order adiabatic perturbation scheme is found to be an excellent approach for calculating the ac-field Floquet solutions in our test case studies of a simple one-dimensional time-periodic model Hamiltonian. It is straightforward to implement the perturbation approach presented here for calculating atomic and molecular energy shifts (positions) due to the interaction with low-frequency ac-fields using high-level electronic structure methods. This is enabled since standard quantum chemistry packages allow the calculations of atomic and molecular energy shifts due to the interaction with dc-fields. In addition to the shift of the energy positions, the energy widths (inverse lifetimes) can be obtained at the same level of theory. These energy shifts are functions of the laser parameters (low frequency, intensity, and polarization).
International Nuclear Information System (INIS)
Kovtun, Pave; Uensal, Mithat; Yaffe, Laurence G.
2005-01-01
Large N coherent state methods are used to study the relation between U(N c ) gauge theories containing adjoint representation matter fields and their orbifold projections. The classical dynamical systems which reproduce the large N c limits of the quantum dynamics in parent and daughter orbifold theories are compared. We demonstrate that the large N c dynamics of the parent theory, restricted to the subspace invariant under the orbifold projection symmetry, and the large N c dynamics of the daughter theory, restricted to the untwisted sector invariant under 'theory space' permutations, coincide. This implies equality, in the large N c limit, between appropriately identified connected correlation functions in parent and daughter theories, provided the orbifold projection symmetry is not spontaneously broken in the parent theory and the theory space permutation symmetry is not spontaneously broken in the daughter. The necessity of these symmetry realization conditions for the validity of the large N c equivalence is unsurprising, but demonstrating the sufficiency of these conditions is new. This work extends an earlier proof of non-perturbative large N c equivalence which was only valid in the phase of the (lattice regularized) theories continuously connected to large mass and strong coupling
Higher order alchemical derivatives from coupled perturbed self-consistent field theory.
Lesiuk, Michał; Balawender, Robert; Zachara, Janusz
2012-01-21
We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals. © 2012 American Institute of Physics
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
International Nuclear Information System (INIS)
Lima, Fernando R.A.; Lira, Carlos A.B.O.; Gandini, Augusto
1995-01-01
During the last two decades perturbative methods became an efficient tool to perform sensitivity analysis in nuclear reactor safety problems. In this paper, a comparative study taking into account perturbation formalisms (Diferential and Matricial Mthods and generalized Perturbation Theory - GPT) is considered. Then a few number of applications are described to analyze the sensitivity of some functions relavant to thermal hydraulics designs or safety analysis of nuclear reactor cores and steam generators. The behaviours of the nuclear reactor cores and steam generators are simulated, respectively, by the COBRA-IV-I and GEVAP codes. Results of sensitivity calculations have shown a good agreement when compared to those obtained directly by using the mentioned codes. So, a significative computational time safe can be obtained with perturbative methods performing sensitivity analysis in nuclear power plants. (author). 25 refs., 5 tabs
Perturbation method for periodic solutions of nonlinear jerk equations
International Nuclear Information System (INIS)
Hu, H.
2008-01-01
A Lindstedt-Poincare type perturbation method with bookkeeping parameters is presented for determining accurate analytical approximate periodic solutions of some third-order (jerk) differential equations with cubic nonlinearities. In the process of the solution, higher-order approximate angular frequencies are obtained by Newton's method. A typical example is given to illustrate the effectiveness and simplicity of the proposed method
International Nuclear Information System (INIS)
Dominguez, Fabio; Marquet, C.; Mueller, A.H.; Wu Bin; Xiao, Bo-Wen
2008-01-01
We compare medium induced energy loss and p perpendicular -broadening in perturbative QCD with that of the trailing string picture of SYM theory. We consider finite and infinite extent matter as well as relativistic heavy quarks which correspond to those being produced in the medium or external to it. When expressed in terms of the appropriate saturation momentum, we find identical parametric forms for energy loss in perturbative QCD and SYM theory. We find simple correspondences between p perpendicular -broadening in QCD and in SYM theory although p perpendicular -broadening is radiation dominated in SYM theory and multiple scattering dominated in perturbative QCD
A semi perturbative method for QED
Jora, Renata; Schechter, Joseph
2014-01-01
We compute the QED beta function using a new method of functional integration. It turns out that in this procedure the beta function contains only the first two orders coefficients and thus corresponds to a new renormalization scheme, long time supposed to exist.
Two-dimensional sigma models: modelling non-perturbative effects of gauge theories
International Nuclear Information System (INIS)
Novikov, V.A.; Shifman, M.A.; Vainshtein, A.I.; Zakharov, V.I.
1984-01-01
The review is devoted to a discussion of non-perturbative effects in gauge theories and two-dimensional sigma models. The main emphasis is put on supersymmetric 0(3) sigma model. The instanton-based method for calculating the exact Gell-Mann-Low function and bifermionic condensate is considered in detail. All aspects of the method in simplifying conditions are discussed. The basic points are: the instanton measure from purely classical analysis; a non-renormalization theorem in self-dual external fields; existence of vacuum condensates and their compatibility with supersymmetry
Do we need Feynman diagrams for higher order perturbation theory?
International Nuclear Information System (INIS)
Jora, Renata
2012-01-01
We compute the two loop and three loop corrections to the beta function for Yang-Mills theories in the background gauge field method and using the background gauge field as the only source. The calculations are based on the separation of the one loop effective potential into zero and positive modes contributions and are entirely analytical. No two or three loop Feynman diagrams are considered in the process.
Equation-of-motion coupled cluster perturbation theory revisited
DEFF Research Database (Denmark)
Eriksen, Janus Juul; Jørgensen, Poul; Olsen, Jeppe
2014-01-01
The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally con- verges towards the full configuration interaction energy limit. The series is based on a Møller-Ples......-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby rem- edying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873138]...
Utilization of the perturbation method for determination of the buckling heterogenous reactors
International Nuclear Information System (INIS)
Gheorghe, R.
1975-01-01
Evaluation of material buckling for heterogenous nulcear reactors is a key-problem for reactor people. In this direction several methods have been elaborated: bi-group method, heterogenous method and perturbation methods. Out of them, mostly employed is the perturbation method which is also presented in this paper and is applied in some parameter calculations of a new cell type for which fuel is positioned in the marginal area and the moderator is in the centre. It is based on the technique of progressive substitution. Advantages of the method: buckling comes out clearly, high level defects due to differences between O perturbated fluxes and the unperturbated flux Osub(o) can be corrected by an iterative procedure; using a modified bi-group theory, one can clearly describe effects of other parameters
Non-standard perturbative methods for the effective potential in λφ4 QFT
International Nuclear Information System (INIS)
Okopinska, A.
1986-07-01
The effective potential in scalar QFT is calculated in the non-standard perturbative methods and compared with the conventional loop expansion. In the space time dimensions 0 and 1 the results are compared with the ''exact'' effective potential obtained numerically. In 4 dimensions we show that λφ 4 theory is non-interacting. (author)
Born approximation to a perturbative numerical method for the solution of the Schroedinger equation
International Nuclear Information System (INIS)
Adam, Gh.
1978-01-01
A step function perturbative numerical method (SF-PN method) is developed for the solution of the Cauchy problem for the second order liniar differential equation in normal form. An important point stressed in the present paper, which seems to have been previously ignored in the literature devoted to the PN methods, is the close connection between the first order perturbation theory of the PN approach and the wellknown Born approximation, and, in general, the connection between the varjous orders of the PN corrections and the Neumann series. (author)
Born approximation to a perturbative numerical method for the solution of the Schrodinger equation
International Nuclear Information System (INIS)
Adam, Gh.
1978-05-01
A perturbative numerical (PN) method is given for the solution of a regular one-dimensional Cauchy problem arising from the Schroedinger equation. The present method uses a step function approximation for the potential. Global, free of scaling difficulty, forward and backward PN algorithms are derived within first order perturbation theory (Born approximation). A rigorous analysis of the local truncation errors is performed. This shows that the order of accuracy of the method is equal to four. In between the mesh points, the global formula for the wavefunction is accurate within O(h 4 ), while that for the first order derivative is accurate within O(h 3 ). (author)
Finding a nonlinear lattice with improved integrability using Lie transform perturbation theory
International Nuclear Information System (INIS)
Sonnad, Kiran G.; Cary, John R.
2004-01-01
A condition for improved dynamic aperture for nonlinear, alternating gradient transport systems is derived using Lie transform perturbation theory. The Lie transform perturbation method is used here to perform averaging over fast oscillations by canonically transforming to slowly oscillating variables. This is first demonstrated for a linear sinusoidal focusing system. This method is then employed to average the dynamics over a lattice period for a nonlinear focusing system, provided by the use of higher order poles such as sextupoles and octupoles along with alternate gradient quadrupoles. Unlike the traditional approach, the higher order focusing is not treated as a perturbation. The Lie transform method is particularly advantageous for such a system where the form of the Hamiltonian is complex. This is because the method exploits the property of canonical invariance of Poisson brackets so that the change of variables is accomplished by just replacing the old ones with the new. The analysis shows the existence of a condition in which the system is azimuthally symmetric in the transformed, slowly oscillating frame. Such a symmetry in the time averaged frame renders the system nearly integrable in the laboratory frame. This condition leads to reduced chaos and improved confinement when compared to a system that is not close to integrability. Numerical calculations of single-particle trajectories and phase space projections of the dynamic aperture performed for a lattice with quadrupoles and sextupoles confirm that this is indeed the case
Electrodynamics as a problem of eigenvalues. III. Maxwell operator and perturbation theory
International Nuclear Information System (INIS)
Yudin, L.A.; Kapchinsky, M.I.; Korenev, I.L.; Efimov, S.P.
1996-01-01
This part of the work deals with perturbation theory. The standard technique permits us to solve problems of volume disturbances in free space, waveguides, and cavities, of disturbances of boundary conditions caused by finite conductivity of walls, and of disturbances of the boundary shape. Expressions for frequency and wave number shifts caused by the perturbation are obtained by the unified method. Several examples are presented: wave amplification in the waveguide filled with a resonant medium like an electron beam in a longitudinal magnetic field, the frequency shift (and increment/decrement) of a cavity loaded by an electron beam, and the field disturbance in the waveguide caused by finite conductivity of the walls. copyright 1996 American Institute of Physics
An Operator Perturbation Method of Polarized Line Transfer V ...
Indian Academy of Sciences (India)
tribpo
imate Lambda Iteration) method to the resonance scattering in spectral lines formed in the presence of weak magnetic fields. The method is based on an operator perturbation approach, and can efficiently give solutions for oriented vector magnetic fields in the solar atmosphere. Key words. ... 1999 for observational.
expansion method and travelling wave solutions for the perturbed ...
Indian Academy of Sciences (India)
Abstract. In this paper, we construct the travelling wave solutions to the perturbed nonlinear. Schrödinger's equation (NLSE) with Kerr law non-linearity by the extended (G /G)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with. Kerr law nonlinearity with arbitrary ...
Perturbation Method of Analysis Applied to Substitution Measurements of Buckling
Energy Technology Data Exchange (ETDEWEB)
Persson, Rolf
1966-11-15
Calculations with two-group perturbation theory on substitution experiments with homogenized regions show that a condensation of the results into a one-group formula is possible, provided that a transition region is introduced in a proper way. In heterogeneous cores the transition region comes in as a consequence of a new cell concept. By making use of progressive substitutions the properties of the transition region can be regarded as fitting parameters in the evaluation procedure. The thickness of the region is approximately equal to the sum of 1/(1/{tau} + 1/L{sup 2}){sup 1/2} for the test and reference regions. Consequently a region where L{sup 2} >> {tau}, e.g. D{sub 2}O, contributes with {radical}{tau} to the thickness. In cores where {tau} >> L{sup 2} , e.g. H{sub 2}O assemblies, the thickness of the transition region is determined by L. Experiments on rod lattices in D{sub 2}O and on test regions of D{sub 2}O alone (where B{sup 2} = - 1/L{sup 2} ) are analysed. The lattice measurements, where the pitches differed by a factor of {radical}2, gave excellent results, whereas the determination of the diffusion length in D{sub 2}O by this method was not quite successful. Even regions containing only one test element can be used in a meaningful way in the analysis.
Dense fluid self-diffusion coefficient calculations using perturbation theory and molecular dynamics
Directory of Open Access Journals (Sweden)
COELHO L. A. F.
1999-01-01
Full Text Available A procedure to correlate self-diffusion coefficients in dense fluids by using the perturbation theory (WCA coupled with the smooth-hard-sphere theory is presented and tested against molecular simulations and experimental data. This simple algebraic expression correlates well the self-diffusion coefficients of carbon dioxide, ethane, propane, ethylene, and sulfur hexafluoride. We have also performed canonical ensemble molecular dynamics simulations by using the Hoover-Nosé thermostat and the mean-square displacement formula to compute self-diffusion coefficients for the reference WCA intermolecular potential. The good agreement obtained from both methods, when compared with experimental data, suggests that the smooth-effective-sphere theory is a useful procedure to correlate diffusivity of pure substances.
Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals
Simonović, Marko; Baldauf, Tobias; Zaldarriaga, Matias; Carrasco, John Joseph; Kollmeier, Juna A.
2018-04-01
We present a new method for calculating loops in cosmological perturbation theory. This method is based on approximating a ΛCDM-like cosmology as a finite sum of complex power-law universes. The decomposition is naturally achieved using an FFTLog algorithm. For power-law cosmologies, all loop integrals are formally equivalent to loop integrals of massless quantum field theory. These integrals have analytic solutions in terms of generalized hypergeometric functions. We provide explicit formulae for the one-loop and the two-loop power spectrum and the one-loop bispectrum. A chief advantage of our approach is that the difficult part of the calculation is cosmology independent, need be done only once, and can be recycled for any relevant predictions. Evaluation of standard loop diagrams then boils down to a simple matrix multiplication. We demonstrate the promise of this method for applications to higher multiplicity/loop correlation functions.
Non-perturbative methods applied to multiphoton ionization
International Nuclear Information System (INIS)
Brandi, H.S.; Davidovich, L.; Zagury, N.
1982-09-01
The use of non-perturbative methods in the treatment of atomic ionization is discussed. Particular attention is given to schemes of the type proposed by Keldysh where multiphoton ionization and tunnel auto-ionization occur for high intensity fields. These methods are shown to correspond to a certain type of expansion of the T-matrix in the intra-atomic potential; in this manner a criterium concerning the range of application of these non-perturbative schemes is suggested. A brief comparison between the ionization rate of atoms in the presence of linearly and circularly polarized light is presented. (Author) [pt
Domain walls and perturbation theory in high-temperature gauge theory: SU(2) in 2+1 dimensions
International Nuclear Information System (INIS)
Korthals Altes, C.; Michels, A.; Teper, M.; Stephanov, M.
1997-01-01
We study the detailed properties of Z 2 domain walls in the deconfined high-temperature phase of the d=2+1 SU(2) gauge theory. These walls are studied both by computer simulations of the lattice theory and by one-loop perturbative calculations. The latter are carried out both in the continuum and on the lattice. We find that leading order perturbation theory reproduces the detailed properties of these domain walls remarkably accurately even at temperatures where the effective dimensionless expansion parameter g 2 /T is close to unity. The quantities studied include the surface tension, the action density profiles, roughening, and the electric screening mass. It is only for the last quantity that we find an exception to the precocious success of perturbation theory. All this shows that, despite the presence of infrared divergences at higher orders, high-T perturbation theory can be an accurate calculational tool. copyright 1997 The American Physical Society
Directory of Open Access Journals (Sweden)
Pasquale Imperatore
2017-12-01
Full Text Available A general, approximate perturbation method, able to provide closed-form expressions of scattering from a layered structure with an arbitrary number of rough interfaces, has been recently developed. Such a method provides a unique tool for the characterization of radar response patterns of natural rough multilayers. In order to show that, here, for the first time in a journal paper, we describe the application of the developed perturbation theory to fractal interfaces; we then employ the perturbative method solution to analyze the scattering from real-world layered structures of practical interest in remote sensing applications. We focus on the dependence of normalized radar cross section on geometrical and physical properties of the considered scenarios, and we choose two classes of natural stratifications: wet paleosoil covered by a low-loss dry sand layer and a sea-ice layer above water with dry snow cover. Results are in accordance with the experimental evidence available in the literature for the low-loss dry sand layer, and they may provide useful indications about the actual ability of remote sensing instruments to perform sub-surface sensing for different sensor and scene parameters.
Imperatore, Pasquale; Iodice, Antonio; Riccio, Daniele
2017-12-27
A general, approximate perturbation method, able to provide closed-form expressions of scattering from a layered structure with an arbitrary number of rough interfaces, has been recently developed. Such a method provides a unique tool for the characterization of radar response patterns of natural rough multilayers. In order to show that, here, for the first time in a journal paper, we describe the application of the developed perturbation theory to fractal interfaces; we then employ the perturbative method solution to analyze the scattering from real-world layered structures of practical interest in remote sensing applications. We focus on the dependence of normalized radar cross section on geometrical and physical properties of the considered scenarios, and we choose two classes of natural stratifications: wet paleosoil covered by a low-loss dry sand layer and a sea-ice layer above water with dry snow cover. Results are in accordance with the experimental evidence available in the literature for the low-loss dry sand layer, and they may provide useful indications about the actual ability of remote sensing instruments to perform sub-surface sensing for different sensor and scene parameters.
International Nuclear Information System (INIS)
Moore, B.R.; Turinsky, P.J.
1998-01-01
Boiling water reactor (BWR) loading pattern assessment requires solving the two-group, nodal form of the neutron diffusion equation and drift-flux form of the fluid equations simultaneously because these equation sets are strongly coupled via nonlinear feedback. To reduce the computational burden associated with the calculation of the core attributes (that is, core eigenvalue and thermal margins) of a perturbed BWR loading pattern, the analytical and numerical aspects of a higher order generalized perturbation theory (GPT) method, which correctly addresses the strong nonlinear feedbacks of two-phase flow, have been established. Inclusion of Jacobian information in the definition of the generalized flux adjoints provides for a rapidly convergent iterative method for solution of the power distribution and eigenvalue of a loading pattern perturbed from a reference state. Results show that the computational speedup of GPT compared with conventional forward solution methods demanding consistent accuracy is highly dependent on the number of spatial nodes utilized by the core simulator, varying from superior to inferior performance as the number of nodes increases
In what sense the canonical perturbation theory is gauge-invariant
International Nuclear Information System (INIS)
Chen, C.Y.
1992-07-01
It is shown that the time-dependent canonical perturbation theory in classical mechanics has unsatisfactory features when dealing with electromagnetic perturbed fields (the perturbed vector potential A-tilde ≠ 0). As a numerical apparatus, the theory relates to gauge-dependent vectors larger than expected. As an analytic apparatus, the theory is involved in unphysical concepts and yields inherently non-gauge-invariant formalisms. By defining the root cause of the problem, an alternative approach is accordingly introduced. (author). 8 refs, 2 figs
Contribution of higher order terms in the reductive perturbation theory, 2
International Nuclear Information System (INIS)
Ichikawa, Y.H.; Mitsuhashi, Teruo; Konno, Kimiaki.
1977-01-01
Contribution of higher order terms in the reductive perturbation theory has been investigated for nonlinear propagation of strongly dispersive ion plasma wave. The basic set of fluid equation is reduced to a coupled set of the nonlinear Schroedinger equation for the first order perturbed potential and a linear inhomogeneous equation for the second order perturbed potential. A steady state solution of the coupled set of equations has been solved analytically in the asymptotic limit of small wave number. (auth.)
On the treatment of nonlinear local feedbacks within advanced nodal generalized perturbation theory
International Nuclear Information System (INIS)
Maldonado, G.I.; Turinsky, P.J.; Kropaczek, D.J.
1993-01-01
Recent efforts to upgrade the underlying neutronics formulations within the in-core nuclear fuel management optimization code FORMOSA (Ref. 1) have produced two important developments; first, a computationally efficient and second-order-accurate advanced nodal generalized perturbation theory (GPT) model [derived from the nonlinear iterative nodal expansion method (NEM)] for evaluating core attributes (i.e., k eff and power distribution versus cycle burnup), and second, an equally efficient and accurate treatment of local thermal-hydraulic and fission product feedbacks embedded within NEM GPT. The latter development is the focus of this paper
Theoretical approaches to many-body perturbation theory and the challenges
International Nuclear Information System (INIS)
Barrett, Bruce R
2005-01-01
A brief review of the history of many-body perturbation theory (MBPT) and its applications in nuclear physics is given. Problems regarding its application to nuclear-structure calculations are discussed and analysed. It is concluded that the usefulness of nuclear MBPT in terms of an expansion in the nuclear reaction matrix G for the calculation of effective interactions in shell-model investigations is severely challenged and restricted by the problems and uncertainties connected with this approach. New methods based on unitary transformation approaches have proven to be more accurate and reliable, particularly for light nuclei
Low energy pion-pion phase shifts from chiral perturbation theory
International Nuclear Information System (INIS)
Borges, J. Sa; Barbosa, J. Soares; Oguri, V.
1997-01-01
The low energy pion-pion S- and P- experimental phase-shifts are fitted with chiral perturbation theory (Ch PT) amplitude. The low energy pion-pion S- and P- experimental phase-shifts. The parameters l 1 and l 2 of the one loop corrected amplitude are fixed and the corresponding values of the scattering lengths are calculated. We propose that the present method is the best way to fix Ch P T parameters. The unitarization program of current algebra is also discussed. (author)
Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions
Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)
1994-01-01
Moller-Plesset perturbation theory is developed to second order for a selection of Kramers restricted Dirac-Hartree-Fock closed and open-shell reference wave functions. The open-shell wave functions considered are limited to those with no more than two electrons in open shells, but include the case of a two-configuration SCF reference. Denominator shifts are included in the style of Davidson's OPT2 method. An implementation which uses unordered integrals with labels is presented, and results are given for a few test cases.
Generalized perturbation theory for LWR depletion analysis and core design applications
International Nuclear Information System (INIS)
White, J.R.; Frank, B.R.
1986-01-01
A comprehensive time-dependent perturbation theory formulation that includes macroscopic depletion, thermal-hydraulic and poison feedback effects, and a criticality reset mechanism is developed. The methodology is compatible with most current LWR design codes. This new development allows GTP/DTP methods to be used quantitatively in a variety of realistic LWR physics applications that were not possible prior to this work. A GTP-based optimization technique for incore fuel management analyses is addressed as a promising application of the new formulation
Shiozaki, Toru; Győrffy, Werner; Celani, Paolo; Werner, Hans-Joachim
2011-08-01
The extended multireference quasi-degenerate perturbation theory, proposed by Granovsky [J. Chem. Phys. 134, 214113 (2011)], is combined with internally contracted multi-state complete active space second-order perturbation theory (XMS-CASPT2). The first-order wavefunction is expanded in terms of the union of internally contracted basis functions generated from all the reference functions, which guarantees invariance of the theory with respect to unitary rotations of the reference functions. The method yields improved potentials in the vicinity of avoided crossings and conical intersections. The theory for computing nuclear energy gradients for MS-CASPT2 and XMS-CASPT2 is also presented and the first implementation of these gradient methods is reported. A number of illustrative applications of the new methods are presented.
The 1/ N Expansion of Tensor Models Beyond Perturbation Theory
Gurau, Razvan
2014-09-01
We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/ N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/ N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges. As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N→ ∞ limit, in the universality class of Gaussian tensor models.
Perturbative quantization of superstring theory in Anti de-Sitter spaces
Energy Technology Data Exchange (ETDEWEB)
Sundin, Per
2010-07-12
In this thesis we study superstring theory on AdS{sub 5} x S{sup 5}, AdS{sub 3} x S{sup 3} and AdS{sub 4} x CP{sub 3}. A shared feature of each theory is that their corresponding symmetry algebras allows for a decomposition under a Z{sub 4} grading. The grading can be realized through an automorphism which allows for a convenient construction of the string Lagrangians directly in terms of graded components. We adopt a uniform light-cone gauge and expand in a near plane wave limit, or equivalently, an expansion in transverse string coordinates. With a main focus on the two critical string theories, we perform a perturbative quantization up to quartic order in the number of fields. Each string theory is, through holographic descriptions, conjectured to be dual to lower dimensional gauge theories. The conjectures imply that the conformal dimensions of single trace operators in gauge theory should be equal to the energy of string states. What is more, through the use of integrable methods, one can write down a set of Bethe equations whose solutions encode the full spectral problem. One main theme of this thesis is to match the predictions of these equations, written in a language suitable for the light-cone gauge we employ, against explicit string theory calculations. We do this for a large class of string states and the perfect agreement we find lends strong support for the validity of the conjectures. (orig.)
Perturbative quantization of superstring theory in Anti de-Sitter spaces
International Nuclear Information System (INIS)
Sundin, Per
2010-01-01
In this thesis we study superstring theory on AdS 5 x S 5 , AdS 3 x S 3 and AdS 4 x CP 3 . A shared feature of each theory is that their corresponding symmetry algebras allows for a decomposition under a Z 4 grading. The grading can be realized through an automorphism which allows for a convenient construction of the string Lagrangians directly in terms of graded components. We adopt a uniform light-cone gauge and expand in a near plane wave limit, or equivalently, an expansion in transverse string coordinates. With a main focus on the two critical string theories, we perform a perturbative quantization up to quartic order in the number of fields. Each string theory is, through holographic descriptions, conjectured to be dual to lower dimensional gauge theories. The conjectures imply that the conformal dimensions of single trace operators in gauge theory should be equal to the energy of string states. What is more, through the use of integrable methods, one can write down a set of Bethe equations whose solutions encode the full spectral problem. One main theme of this thesis is to match the predictions of these equations, written in a language suitable for the light-cone gauge we employ, against explicit string theory calculations. We do this for a large class of string states and the perfect agreement we find lends strong support for the validity of the conjectures. (orig.)
International Nuclear Information System (INIS)
Somogyi, Gabor; Smith, Robert E.
2010-01-01
We generalize the renormalized perturbation theory (RPT) formalism of Crocce and Scoccimarro [M. Crocce and R. Scoccimarro, Phys. Rev. D 73, 063519 (2006)] to deal with multiple fluids in the Universe and here we present the complete calculations up to the one-loop level in the RPT. We apply this approach to the problem of following the nonlinear evolution of baryon and cold dark matter (CDM) perturbations, evolving from the distinct sets of initial conditions, from the high redshift post-recombination Universe right through to the present day. In current theoretical and numerical models of structure formation, it is standard practice to treat baryons and CDM as an effective single matter fluid--the so-called dark matter only modeling. In this approximation, one uses a weighed sum of late-time baryon and CDM transfer functions to set initial mass fluctuations. In this paper we explore whether this approach can be employed for high precision modeling of structure formation. We show that, even if we only follow the linear evolution, there is a large-scale scale-dependent bias between baryons and CDM for the currently favored WMAP5 ΛCDM model. This time evolving bias is significant (>1%) until the present day, when it is driven towards unity through gravitational relaxation processes. Using the RPT formalism we test this approximation in the nonlinear regime. We show that the nonlinear CDM power spectrum in the two-component fluid differs from that obtained from an effective mean-mass one-component fluid by ∼3% on scales of order k∼0.05h Mpc -1 at z=10, and by ∼0.5% at z=0. However, for the case of the nonlinear evolution of the baryons the situation is worse and we find that the power spectrum is suppressed, relative to the total matter, by ∼15% on scales k∼0.05h Mpc -1 at z=10, and by ∼3%-5% at z=0. Importantly, besides the suppression of the spectrum, the baryonic acoustic oscillation (BAO) features are amplified for baryon and slightly damped for CDM
Somogyi, Gábor; Smith, Robert E.
2010-01-01
We generalize the renormalized perturbation theory (RPT) formalism of Crocce and Scoccimarro [M. Crocce and R. Scoccimarro, Phys. Rev. DPRVDAQ1550-7998 73, 063519 (2006)10.1103/PhysRevD.73.063519] to deal with multiple fluids in the Universe and here we present the complete calculations up to the one-loop level in the RPT. We apply this approach to the problem of following the nonlinear evolution of baryon and cold dark matter (CDM) perturbations, evolving from the distinct sets of initial conditions, from the high redshift post-recombination Universe right through to the present day. In current theoretical and numerical models of structure formation, it is standard practice to treat baryons and CDM as an effective single matter fluid—the so-called dark matter only modeling. In this approximation, one uses a weighed sum of late-time baryon and CDM transfer functions to set initial mass fluctuations. In this paper we explore whether this approach can be employed for high precision modeling of structure formation. We show that, even if we only follow the linear evolution, there is a large-scale scale-dependent bias between baryons and CDM for the currently favored WMAP5 ΛCDM model. This time evolving bias is significant (>1%) until the present day, when it is driven towards unity through gravitational relaxation processes. Using the RPT formalism we test this approximation in the nonlinear regime. We show that the nonlinear CDM power spectrum in the two-component fluid differs from that obtained from an effective mean-mass one-component fluid by ˜3% on scales of order k˜0.05hMpc-1 at z=10, and by ˜0.5% at z=0. However, for the case of the nonlinear evolution of the baryons the situation is worse and we find that the power spectrum is suppressed, relative to the total matter, by ˜15% on scales k˜0.05hMpc-1 at z=10, and by ˜3%-5% at z=0. Importantly, besides the suppression of the spectrum, the baryonic acoustic oscillation (BAO) features are amplified for
Perturbation method for calculating impurity binding energy in an ...
Indian Academy of Sciences (India)
Nilanjan Sil
2017-12-18
Dec 18, 2017 ... Abstract. In the present paper, we have studied the binding energy of the shallow donor hydrogenic impurity, which is confined in an inhomogeneous cylindrical quantum dot (CQD) of GaAs-AlxGa1−xAs. Perturbation method is used to calculate the binding energy within the framework of effective mass ...
Application of New Variational Homotopy Perturbation Method For ...
African Journals Online (AJOL)
This paper discusses the application of the New Variational Homotopy Perturbation Method (NVHPM) for solving integro-differential equations. The advantage of the new Scheme is that it does not require discretization, linearization or any restrictive assumption of any form be fore it is applied. Several test problems are ...
Diagrammatic perturbation methods in networks and sports ranking combinatorics
International Nuclear Information System (INIS)
Park, Juyong
2010-01-01
Analytic and computational tools developed in statistical physics are being increasingly applied to the study of complex networks. Here we present recent developments in the diagrammatic perturbation methods for the exponential random graph models, and apply them to the combinatoric problem of determining the ranking of nodes in directed networks that represent pairwise competitions
Singular perturbations introduction to system order reduction methods with applications
Shchepakina, Elena; Mortell, Michael P
2014-01-01
These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate stude...
Lee, Timothy J.; Langhoff, Stephen R. (Technical Monitor)
1997-01-01
Recent work on the development of single-reference perturbation theories for the study of excited electronic states will be discussed. The utility of these methods will be demonstrated by comparison to linear-response coupled-cluster excitation energies. Results for some halogen molecules of interest in stratospheric chemistry will be presented.
Uncertainty Analysis of Few Group Cross Sections Based on Generalized Perturbation Theory
International Nuclear Information System (INIS)
Han, Tae Young; Lee, Hyun Chul; Noh, Jae Man
2014-01-01
In this paper, the methodology of the sensitivity and uncertainty analysis code based on GPT was described and the preliminary verification calculations on the PMR200 pin cell problem were carried out. As a result, they are in a good agreement when compared with the results by TSUNAMI. From this study, it is expected that MUSAD code based on GPT can produce the uncertainty of the homogenized few group microscopic cross sections for a core simulator. For sensitivity and uncertainty analyses for general core responses, a two-step method is available and it utilizes the generalized perturbation theory (GPT) for homogenized few group cross sections in the first step and stochastic sampling method for general core responses in the second step. The uncertainty analysis procedure based on GPT in the first step needs the generalized adjoint solution from a cell or lattice code. For this, the generalized adjoint solver has been integrated into DeCART in our previous work. In this paper, MUSAD (Modues of Uncertainty and Sensitivity Analysis for DeCART) code based on the classical perturbation theory was expanded to the function of the sensitivity and uncertainty analysis for few group cross sections based on GPT. First, the uncertainty analysis method based on GPT was described and, in the next section, the preliminary results of the verification calculation on a VHTR pin cell problem were compared with the results by TSUNAMI of SCALE 6.1
Perturbative quantum field theory in the framework of the fermionic projector
International Nuclear Information System (INIS)
Finster, Felix
2014-01-01
We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur
Perturbative Quantum Field Theory in the Framework of the Fermionic Projector
Finster, Felix
2013-01-01
We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.
Perturbative quantum field theory in the framework of the fermionic projector
Energy Technology Data Exchange (ETDEWEB)
Finster, Felix, E-mail: finster@ur.de [Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg (Germany)
2014-04-15
We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.
Perturbative quantum field theory in the framework of the fermionic projector
Finster, Felix
2014-04-01
We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.
Effective Lagrangians for SUSY QCD with properties seen in perturbation theory
International Nuclear Information System (INIS)
Sharatchandra, H.S.
1984-06-01
We construct effective Lagrangians for supersymmetric QCD which properly incorporate the relevant Ward identities and possess features encountered in perturbation theory. This shows that the unusual scenarios, proposed for SUSY QCD, are not necessary. (author)
Renormalized perturbation theory: Vlasov-Poisson System, weak turbulence limit and gyrokinetics
International Nuclear Information System (INIS)
Zhang, Y.Z.; Mahajan, S.M.
1987-10-01
The Self-consistency of the renormalized perturbation theory is demonstrated by applying it to the Vlasov-Poisson System and showing that the theory has the correct weak turbulence limit. Energy conservation is proved to arbitrary high order for the electrostatic drift waves. The theory is applied to derive renormalized equations for a low-β gyrokinetic system. Comparison of our theory with other current theories is presented. 22 refs
Singular perturbation methods for nonlinear dynamic systems with time delays
International Nuclear Information System (INIS)
Hu, H.Y.; Wang, Z.H.
2009-01-01
This review article surveys the recent advances in the dynamics and control of time-delay systems, with emphasis on the singular perturbation methods, such as the method of multiple scales, the method of averaging, and two newly developed methods, the energy analysis and the pseudo-oscillator analysis. Some examples are given to demonstrate the advantages of the methods. The comparisons with other methods show that these methods lead to easier computations and higher accurate prediction on the local dynamics of time-delay systems near a Hopf bifurcation.
Energy Technology Data Exchange (ETDEWEB)
Dosch, H G [Heidelberg Univ. (F.R. Germany). Inst. fuer Theoretische Physik; Mueller, V F [Trier-Kaiserslautern Univ., Kaiserslautern (F.R. Germany). Fachbereich Physik
1975-01-01
Extending the inductive renormalization procedure of Epstein and Glaser which is essentially based on locality, we show that quantum electrodynamics in an external time independent electromagnetic field has a renormalizable formal perturbation expansion. The interaction involving the quantized radiation field but not the action of the external field is treated by perturbation theory. It turns out that vacuum polarization is undetermined in the framework of such a theory.
Mihálka, Zsuzsanna É.; Surján, Péter R.
2017-12-01
The method of analytic continuation is applied to estimate eigenvalues of linear operators from finite order results of perturbation theory even in cases when the latter is divergent. Given a finite number of terms E(k ),k =1 ,2 ,⋯M resulting from a Rayleigh-Schrödinger perturbation calculation, scaling these numbers by μk (μ being the perturbation parameter) we form the sum E (μ ) =∑kμkE(k ) for small μ values for which the finite series is convergent to a certain numerical accuracy. Extrapolating the function E (μ ) to μ =1 yields an estimation of the exact solution of the problem. For divergent series, this procedure may serve as resummation tool provided the perturbation problem has a nonzero radius of convergence. As illustrations, we treat the anharmonic (quartic) oscillator and an example from the many-electron correlation problem.
Intermolecular symmetry-adapted perturbation theory study of large organic complexes
International Nuclear Information System (INIS)
Heßelmann, Andreas; Korona, Tatiana
2014-01-01
Binding energies for the complexes of the S12L database by Grimme [Chem. Eur. J. 18, 9955 (2012)] were calculated using intermolecular symmetry-adapted perturbation theory combined with a density-functional theory description of the interacting molecules. The individual interaction energy decompositions revealed no particular change in the stabilisation pattern as compared to smaller dimer systems at equilibrium structures. This demonstrates that, to some extent, the qualitative description of the interaction of small dimer systems may be extrapolated to larger systems, a method that is widely used in force-fields in which the total interaction energy is decomposed into atom-atom contributions. A comparison of the binding energies with accurate experimental reference values from Grimme, the latter including thermodynamic corrections from semiempirical calculations, has shown a fairly good agreement to within the error range of the reference binding energies
Green's functions in quantum chemistry - I. The Σ perturbation method
International Nuclear Information System (INIS)
Sebastian, K.L.
1978-01-01
As an improvement over the Hartree-Fock approximation, a Green's Function method - the Σ perturbation method - is investigated for molecular calculations. The method is applied to the hydrogen molecule and to the π-electron system of ethylene under PPP approximation. It is found that when the algebraic approximation is used, the energy obtained is better than that of the HF approach, but is not as good as that of the configuration-interaction method. The main advantage of this procedure is that it is devoid of the most serious defect of HF method, viz. incorrect dissociation limits. (K.B.)
Variational, projection methods and Pade approximants in scattering theory
International Nuclear Information System (INIS)
Turchetti, G.
1980-12-01
Several aspects on the scattering theory are discussed in a perturbative scheme. The Pade approximant method plays an important role in such a scheme. Solitons solutions are also discussed in this same scheme. (L.C.) [pt
Second-order generalized perturbation theory for source-driven systems
International Nuclear Information System (INIS)
Greenspan, E.; Gilai, D.; Oblow, E.M.
1978-01-01
A second-order generalized perturbation theory (GPT) for the effect of multiple system variations on a general flux functional in source-driven systems is derived. The derivation is based on a functional Taylor series in which second-order derivatives are retained. The resulting formulation accounts for the nonlinear effect of a given variation accurate to third order in the flux and adjoint perturbations. It also accounts for the effect of interaction between any number of variations. The new formulation is compared with exact perturbation theory as well as with perturbation theory for altered systems. The usefulnes of the second-order GPT formulation is illustrated by applying it to optimization problems. Its applicability to areas of cross-section sensitivity analysis and system design and evaluation is also discussed
Perturbation theory of the periodic Anderson lattice and superconductivity
International Nuclear Information System (INIS)
Geertsuma, W.
1988-01-01
In this paper the author develops a perturbation calculation of the second and fourth order interparticle interaction in band states, based on the Periodic Anderson Lattice. The author shows that 4th order interparticle interactions giving rise to the well known Kondo effect vanish in the superconducting ground state. This term survives in the presence of a magnetic field. Pair excitations can only give rise to an appreciable attractive contribution when the d states are less than half filled and the pair energy is near the Fermi level. The only important attractive interaction comes from the normal fourth order terms
Short-time perturbation theory and nonrelativistic duality
International Nuclear Information System (INIS)
Whitenton, J.B.; Durand, B.; Durand, L.
1983-01-01
We give a simple proof of the nonrelativistic duality relation 2 sigma/sub bound/>roughly-equal 2 sigma/sub free/> for appropriate energy averages of the cross sections for e + e - →(qq-bar bound states) and e + e - →(free qq-bar pair), and calculate the corrections to the relation by relating W 2 sigma to the Fourier transform of the Feynman propagation function and developing a short-time perturbation series for that function. We illustrate our results in detail for simple power-law potentials and potentials which involve combinations of powers
Perturbative quantum gravity as a double copy of gauge theory.
Bern, Zvi; Carrasco, John Joseph M; Johansson, Henrik
2010-08-06
In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.
Short-distance perturbation theory for the leading logarithm models
International Nuclear Information System (INIS)
Adler, S.L.
1983-01-01
I derive a short-distance perturbation expansion for the static potential of quasi-abelian quark and antiquark source charges, in the models in which renormalization group radiative corrections are retained in the gauge gluon effective dielectric functional. A natural running coupling parameter zeta for the models is identified, and the scale mass #betta#sub(p) appearing in zeta is computed by requiring the vanishing of the O(zeta 2 ) term in the perturbation expansions. The models are shown to give unsatisfactory results beyond one-loop order in the short-distance expansion, as a result of the breakdown in the ultraviolet of the assumption that the effective action is a local functional of the field strength. The same argument indicates that the assumption of a local effective action becomes self-consistent in the large-distance limit. The coupling parameter zeta is identified as a running coupling which evolves in field strength, rather than momentum, and which becomes infinite in the large-distance limit. (orig.)
Sound Attenuation in Elliptic Mufflers Using a Regular Perturbation Method
Banerjee, Subhabrata; Jacobi, Anthony M.
2012-01-01
The study of sound attenuation in an elliptical chamber involves the solution of the Helmholtz equation in elliptic coordinate systems. The Eigen solutions for such problems involve the Mathieu and the modified Mathieu functions. The computation of such functions poses considerable challenge. An alternative method to solve such problems had been proposed in this paper. The elliptical cross-section of the muffler has been treated as a perturbed circle, enabling the use of a regular perturbatio...
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
International Nuclear Information System (INIS)
Caswell, W.E.
1979-01-01
We introduce a generalization of Wick-ordering which maps the anharmonic oscillator (AO) Hamiltonian for mass m and coupling lambda exactly into a ''Wick-ordered'' Hamiltonian with an effective mass M which is a simple analytic function of lambda and m. The effective coupling Λ=lambda/M 3 is bounded. We transform the AO perturbation series in lambda into one in Λ. This series may then be summed using Borel summation methods. We also introduce a new summation method for the AO series (which is a practical necessity to obtain accurate energy levels of the excited states). We obtain a numerical accuracy for (E/sub P/T--E/sub e/xact)/ E/sub e/xact of at least 10 -7 (using 20 orders of perturbation theory) and 10 -3 (using only 2 orders of perturbation theory) for all couplings and all energy levels of the anharmonic oscillator. The methods are applicable also to the double-well potential (DWP, the AO with a negative mass-squared). The only change is that now the effective coupling is unbounded as lambda→0. The series in Λ is, however, still summable. The relative accuracy in the energy levels for 20 orders of perturbation theory varies from 10 -7 for large coupling to 1% at lambda=0.1 and to 10% at lambda=.05. We also present results for the sextic oscillator
International Nuclear Information System (INIS)
Keski-Vakkuri, E.; Kraus, P.
1998-01-01
Polchinski and Pouliot have shown that M-momentum transfer between membranes in supergravity can be understood as a non-perturbative instanton effect in gauge theory. Here we consider a dual process: electric flux transmission between D-branes. We show that this process can be described in perturbation theory as virtual string pair creation, and is closely related to Schwinger's treatment of the pair creation of charged particles in a uniform electric field. Through the application of dualities, our perturbative calculation gives results for various non-perturbative amplitudes, including M-momentum transfer between gravitons, membranes and longitudinal fivebranes. Thus perturbation theory plus dualities are sufficient to demonstrate agreement between supergravity and gauge theory for a number of M-momentum transferring processes. A variety of other processes where branes are transmitted between branes, e.g. (p,q)-string transmission in IIB theory, can also be studied. We discuss the implications of our results for proving the eleven-dimensional Lorentz invariance of matrix theory. (orig.)
International Nuclear Information System (INIS)
Zinn-Justin, J.; Freie Univ. Berlin
1981-01-01
In this review I present a method to estimate the large order behavior of perturbation theory in quantum mechanics and field theory. The basic idea, due to Lipatov, is to relate the large order behavior to (in general complex) instanton contributions to the path integral representation of Green's functions. I explain the method first in the case of a simple integral and of the anharmonic oscillator and recover the results of Bender and Wu. I apply it then to the PHI 4 field theory. I study general potentials and boson field theories. I show, following Parisi, how the method can be generalized to theories with fermions. Finally I outline the implications of these results for the summability of the series. In particular I explain a method to sum divergent series based on a Borel transformation. In a last section I compare the larger order behavior predictions to actual series calculation. I present also some numerical examples of series summation. (orig.)
International Nuclear Information System (INIS)
Bovier, A.; Felder, G.
1984-01-01
We use the polymer representation of PHI 4 -quantum field theories to prove an infinite family of correlation inequalities, called ''skeleton inequalities'', for the 2n-point Green's functions. As an application, we show that they imply that Feynman perturbation theory is asymptotic in less than four dimensions. (orig.)
Block correlated second order perturbation theory with a generalized valence bond reference function
International Nuclear Information System (INIS)
Xu, Enhua; Li, Shuhua
2013-01-01
The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a “multi-orbital” block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Møller–Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods
Xu, Enhua; Li, Shuhua
2013-11-07
The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a "multi-orbital" block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Mo̸ller-Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods.
On the all-order perturbative finiteness of the deformed N=4 SYM theory
International Nuclear Information System (INIS)
Rossi, G.C.; Sokatchev, E.; Stanev, Ya.S.
2006-01-01
We prove that the chiral propagator of the deformed N=4 SYM theory can be made finite to all orders in perturbation theory for any complex value of the deformation parameter. For any such value the set of finite deformed theories can be parametrized by a whole complex function of the coupling constant g. We reveal a new protection mechanism for chiral operators of dimension three. These are obtained by differentiating the Lagrangian with respect to the independent coupling constants. A particular combination of them is a CPO involving only chiral matter. Its all-order form is derived directly from the finiteness condition. The procedure is confirmed perturbatively through order g 6
Radiation perturbation theory in gravity and quantum universe as a hydrogen atom
International Nuclear Information System (INIS)
Pervushin, V.N.
1992-01-01
In quantum theory of gravity of the (n+1)-dimensional space-time the Faddeev-Popov functional integral is constructed for radiation perturbation theory. In this version the Universe expansion looks as the collective superfluid motion of quantum space, and the vacuum energy density plays the role of the hidden mass. 6 refs
International Nuclear Information System (INIS)
Schlichting, H.
1985-01-01
We do a linearised mean field calculation in axial gauge for the four dimensional mixed fundamental adjoint SU(2) lattice gauge theory and extract the gluon condensate parameter from the expectation values of the plaquette and the action by subtracting mean field perturbation theory from Monte Carlo data. (orig.)
Stochastic Recursive Algorithms for Optimization Simultaneous Perturbation Methods
Bhatnagar, S; Prashanth, L A
2013-01-01
Stochastic Recursive Algorithms for Optimization presents algorithms for constrained and unconstrained optimization and for reinforcement learning. Efficient perturbation approaches form a thread unifying all the algorithms considered. Simultaneous perturbation stochastic approximation and smooth fractional estimators for gradient- and Hessian-based methods are presented. These algorithms: • are easily implemented; • do not require an explicit system model; and • work with real or simulated data. Chapters on their application in service systems, vehicular traffic control and communications networks illustrate this point. The book is self-contained with necessary mathematical results placed in an appendix. The text provides easy-to-use, off-the-shelf algorithms that are given detailed mathematical treatment so the material presented will be of significant interest to practitioners, academic researchers and graduate students alike. The breadth of applications makes the book appropriate for reader from sim...
Perturbation method utilization in the analysis of the Convertible Spectral Shift Reactor (RCVS)
International Nuclear Information System (INIS)
Bruna, G.B; Legendre, J.F.; Porta, J.; Doriath, J.Y.
1988-01-01
In the framework of the preliminary faisability studies on a new core concept, techniques derived from perturbation theory show-up very useful in the calculation and physical analysis of project parameters. We show, in the present work, some applications of these methods to the RCVS (Reacteur Convertible a Variation de Spectre - Convertible Spectral Shift Reactor) Concept studies. Actually, we present here the search of a few group project type energy structure and the splitting of reactivity effects into individual components [fr
International Nuclear Information System (INIS)
Gurjao, Emir Candeia
1996-02-01
The differential and GPT (Generalized Perturbation Theory) formalisms of the Perturbation Theory were applied in this work to a simplified U-tubes steam generator model to perform sensitivity analysis. The adjoint and importance equations, with the corresponding expressions for the sensitivity coefficients, were derived for this steam generator model. The system was numerically was numerically solved in a Fortran program, called GEVADJ, in order to calculate the sensitivity coefficients. A transient loss of forced primary coolant in the nuclear power plant Angra-1 was used as example case. The average and final values of functionals: secondary pressure and enthalpy were studied in relation to changes in the secondary feedwater flow, enthalpy and total volume in secondary circuit. Absolute variations in the above functionals were calculated using the perturbative methods, considering the variations in the feedwater flow and total secondary volume. Comparison with the same variations obtained via direct model showed in general good agreement, demonstrating the potentiality of perturbative methods for sensitivity analysis of nuclear systems. (author)
Improved Monte Carlo-perturbation method for estimation of control rod worths in a research reactor
International Nuclear Information System (INIS)
Kalcheva, Silva; Koonen, Edgar
2009-01-01
A hybrid method dedicated to improve the experimental technique for estimation of control rod worths in a research reactor is presented. The method uses a combination of Monte Carlo technique and perturbation theory. Perturbation method is used to obtain the equation for the relative efficiency of control rod insertion. A series of coefficients, describing the axial absorption profile are used to correct the equation for a composite rod, having a complicated burn-up irradiation history. These coefficients have to be determined - by experiment or by using some theoretical/numerical method. In the present paper they are derived from the macroscopic absorption cross-sections, obtained from detailed Monte Carlo calculations by MCNPX 2.6.F of the axial burn-up profile during control rod life. The method is validated on measurements of control rod worths at the BR2 reactor. Comparison with direct MCNPX evaluations of control rod worths is also presented
International Nuclear Information System (INIS)
Oliveira, A.C.J.G. de.
1988-12-01
Sensitivity calculations are very important in design and safety of nuclear reactor cores. Large codes with a great number of physical considerations have been used to perform sensitivity studies. However, these codes need long computation time involving high costs. The perturbation theory has constituted an efficient and economical method to perform sensitivity analysis. The present work is an application of the perturbation theory (matricial formalism) to a simplified model of DNB (Departure from Nucleate Boiling) analysis to perform sensitivity calculations in PWR cores. Expressions to calculate the sensitivity coefficients of enthalpy and coolant velocity with respect to coolant density and hot channel area were developed from the proposed model. The CASNUR.FOR code to evaluate these sensitivity coefficients was written in Fortran. The comparison between results obtained from the matricial formalism of perturbation theory with those obtained directly from the proposed model makes evident the efficiency and potentiality of this perturbation method for nuclear reactor cores sensitivity calculations (author). 23 refs, 4 figs, 7 tabs
International Nuclear Information System (INIS)
Geroyannis, V.S.
1988-01-01
In this paper, a numerical method is developed for determining the structure distortion of a polytropic star which rotates either uniformly or differentially. This method carries out the required numerical integrations in the complex plane. The method is implemented to compute indicative quantities, such as the critical perturbation parameter which represents an upper limit in the rotational behavior of the star. From such indicative results, it is inferred that this method achieves impressive improvement against other relevant methods; most important, it is comparable to some of the most elaborate and accurate techniques on the subject. It is also shown that the use of this method with Chandrasekhar's first-order perturbation theory yields an immediate drastic improvement of the results. Thus, there is no neeed - for most applications concerning rotating polytropic models - to proceed to the further use of the method with higher order techniques, unless the maximum accuracy of the method is required. 31 references
Perturbation theory of intermolecular interactions: What is the problem, are there solutions?
International Nuclear Information System (INIS)
Adams, W.H.
1990-01-01
We review the nature of the problem in the framework of Rayleigh-Schroedinger perturbation theory (the polarization approximation) considering explicitly two examples: the interaction of two hydrogen atoms and the interaction of Li with H. We show, in agreement with the work of Claverie and of Morgan and Simon, that the LiH problem is dramatically different from the H 2 problem. In particular, the physical states of LiH are higher in energy than an infinite number of discrete, unphysical states and they are buried in a continuum of unbound, unphysical states, which starts well below the lowest physical state. Clavrie has shown that the perturbation expansion, under these circumstances, is likely to converge to an unphysical state of lower energy than the physical ground state, if it converges at all. We review, also, the application of two classes of exchange perturbation theory to LiH and larger systems. We show that the spectra of three Eisenschitz-London (EL) class, exchange perturbation theories have no continuum of unphysical states overlaying the physical states and no discrete, unphysical states below the lowest physical state. In contrast, the spectra of two Hirschfelder-Silbey class theories differ hardly at all from that found with the polarization approximation. Not one of the EL class of perturbation theories, however, eliminates all of the discrete unphysical states
Use of the Halbach perturbation theory for the multipole design of the ALS storage ring sextupole
Energy Technology Data Exchange (ETDEWEB)
Marks, S. [Lawrence Berkeley Lab., CA (United States)
1995-02-01
The Advanced Light Source (ALS) storage ring sextupole is a unique multi-purpose magnet. It is designed to operate in the primary or sextupole mode and in three auxiliary trim modes: horizontal steering, vertical steering, and skew quadrupole. Klaus Halbach developed a perturbation theory for iron-dominated magnets which provides the basis for this design. Many magnet designers, certainly those who have been exposed to Klaus, are familiar with this theory and have used it for such things as evaluating the effect of assembly alignment errors. The ALS sextupole design process was somewhat novel in its use of the perturbation theory to design essential features of the magnet. In particular, the steering and skew quadrupole functions are produced by violating sextupole symmetry and are thus perturbations of the normal sextupole excitation. The magnet was designed such that all four modes are decoupled and can be excited independently. This paper discusses the use of Halbach`s perturbation theory to design the trim functions and to evaluate the primary asymmetry in the sextupole mode, namely, a gap in the return yoke to accommodate the vacuum chamber. Prototype testing verified all operating modes of the magnet and confirmed the expected performance from calculations based upon the Halbach perturbation theory. A total of 48 sextupole magnets of this design are now installed and operating successfully in the ALS storage ring.
International Nuclear Information System (INIS)
Budgor, A.B.; West, B.J.
1978-01-01
We employ the equivalence between Zwanzig's projection-operator formalism and perturbation theory to demonstrate that the approximate-solution technique of statistical linearization for nonlinear stochastic differential equations corresponds to the lowest-order β truncation in both the consolidated perturbation expansions and in the ''mass operator'' of a renormalized Green's function equation. Other consolidated equations can be obtained by selectively modifying this mass operator. We particularize the results of this paper to the Duffing anharmonic oscillator equation
Absorption line profiles in a moving atmosphere - A single scattering linear perturbation theory
Hays, P. B.; Abreu, V. J.
1989-01-01
An integral equation is derived which linearly relates Doppler perturbations in the spectrum of atmospheric absorption features to the wind system which creates them. The perturbation theory is developed using a single scattering model, which is validated against a multiple scattering calculation. The nature and basic properties of the kernels in the integral equation are examined. It is concluded that the kernels are well behaved and that wind velocity profiles can be recovered using standard inversion techniques.
Mikulecky, Peter J; Feig, Andrew L
2004-01-01
In proteins, empirical correlations have shown that changes in heat capacity (DeltaC(P)) scale linearly with the hydrophobic surface area buried upon folding. The influence of DeltaC(P) on RNA folding has been widely overlooked and is poorly understood. In addition to considerations of solvent reorganization, electrostatic effects might contribute to DeltaC(P)s of folding in polyanionic species such as RNAs. Here, we employ a perturbation method based on electrostatic theory to probe the hot and cold denaturation behavior of the hammerhead ribozyme. This treatment avoids much of the error associated with imposing two-state folding models on non-two-state systems. Ribozyme stability is perturbed across a matrix of solvent conditions by varying the concentration of NaCl and methanol co-solvent. Temperature-dependent unfolding is then monitored by circular dichroism spectroscopy. The resulting array of unfolding transitions can be used to calculate a DeltaC(P) of folding that accurately predicts the observed cold denaturation temperature. We confirm the accuracy of the calculated DeltaC(P) by using isothermal titration calorimetry, and also demonstrate a methanol-dependence of the DeltaC(P). We weigh the strengths and limitations of this method for determining DeltaC(P) values. Finally, we discuss the data in light of the physical origins of the DeltaC(P)s for RNA folding and consider their impact on biological function.
Tautomerism methods and theories
Antonov, Liudmil
2013-01-01
Covering the gap between basic textbooks and over-specialized scientific publications, this is the first reference available to describe this interdisciplinary topic for PhD students and scientists starting in the field. The result is an introductory description providing suitable practical examples of the basic methods used to study tautomeric processes, as well as the theories describing the tautomerism and proton transfer phenomena. It also includes different spectroscopic methods for examining tautomerism, such as UV-VIs, time-resolved fluorescence spectroscopy, and NMR spectrosc
Spherical perturbations of hairy black holes in designer gravity theories
International Nuclear Information System (INIS)
Battarra, Lorenzo
2012-01-01
We study the spectrum of the scalar l = 0 quasi-normal frequencies of anti-de Sitter hairy black holes in four- and five-dimensional designer gravity theories of the Einstein-scalar type, arising as consistent truncations of N= 8 gauged supergravity. In the dual field theory, such hairy black holes represent thermal states in which the operator corresponding to the bulk scalar field is condensed, due to the multi-trace deformation associated with non-standard boundary conditions. We show that, in a particular class of models, the effective potential describing the vacua of the deformed dual theory can be identified, at large values of the condensate, with the deformation plus the conformal coupling of the condensate to the curvature of the boundary geometry. In this limit, we show that the least damped quasi-normal frequency of the corresponding hairy black holes can be accurately predicted by the curvature of the effective potential describing the field theory at finite entropy. (paper)
Non-perturbative string theories and singular surfaces
International Nuclear Information System (INIS)
Bochicchio, M.
1990-01-01
Singular surfaces are shown to be dense in the Teichmueller space of all Riemann surfaces and in the grasmannian. This happens because a regular surface of genus h, obtained identifying 2h disks in pairs, can be approximated by a very large genus singular surface with punctures dense in the 2h disks. A scale ε is introduced and the approximate genus is defined as half the number of connected regions covered by punctures of radius ε. The non-perturbative partition function is proposed to be a scaling limit of the partition function on such infinite genus singular surfaces with a weight which is the coupling constant g raised to the approximate genus. For a gaussian model in any space-time dimension the regularized partition function on singular surfaces of infinite genus is the partition function of a two-dimensional lattice gas of charges and monopoles. It is shown that modular invariance of the partition function implies a version of the Dirac quantization condition for the values of the e/m charges. Before the scaling limit the phases of the lattice gas may be classified according to the 't Hooft criteria for the condensation of e/m operators. (orig.)
Chiral perturbation theory approach to hadronic weak amplitudes
International Nuclear Information System (INIS)
Rafael, E. de
1989-01-01
We are concerned with applications to the non-leptonic weak interactions in the sector of light quark flavors: u, d and s. Both strangeness changing ΔS=1 and ΔS=2 non-leptonic transitions can be described as weak perturbations to the strong effective chiral Lagrangian; the chiral structure of the weak effective Lagrangian being dictated by the transformation properties of the weak non-leptonic Hamiltonian of the Standard Model under global SU(3) Left xSU(3) Right rotations of the quark-fields. These lectures are organized as follows. Section 2 gives a review of the basic properties of chiral symmetry. Section 3 explains the effective chiral realization of the non-leptonic weak Hamiltonian of the Standard Model to lowest order in derivatives and masses. Section 4 deals with non-leptonic weak transitions in the presence of electromagnetism. Some recent applications to radiative kaon decays are reviewed and the effect of the so called electromagnetic penguin like diagrams is also discussed. Section 5 explains the basic ideas of the QCD-hadronic duality approach to the evaluation of coupling constants of the non-leptonic chiral weak Lagrangian. (orig./HSI)
Simple perturbative renormalization scheme for supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)
1983-06-30
We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of ((p+q)/..delta..)/sup -/delta in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, ..lambda.. is a renormalization mass, and delta is a suitable non-integer: the analog of epsilon in dimensional schemes. All Dirac algebra and integration are four-dimensional, and renormalization is achieved by subtracting poles in delta, followed by setting delta->O. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is bypassed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously.
A simple perturbative renormalization scheme for supersymmetric gauge theories
International Nuclear Information System (INIS)
Foda, O.E.
1983-01-01
We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of [(p+q)/δ] - delta in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, #betta# is a renormalization mass, and delta is a suitable non-integer: the analog of epsilon in dimensional schemes. All Dirac algebra and integration are four-dimensional, and renormalization is achieved by subtracting poles in delta, followed by setting delta->O. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is bypassed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously. (orig.)
Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave functions
International Nuclear Information System (INIS)
Ishikawa, Y.; Quiney, H.M.
1993-01-01
A relativistic many-body perturbation theory based on the Dirac-Fock-Breit wave functions has been developed and implemented by employing analytic basis sets of Gaussian-type functions. The instantaneous Coulomb and low-frequency Breit interactions are treated using a unified formalism in both the construction of the Dirac-Fock-Breit self-consistent-field atomic potential and in the evaluation of many-body perturbation-theory diagrams. The relativistic many-body perturbation-theory calculations have been performed on the helium atom and ions of the helium isoelectronic sequence up to Z=50. The contribution of the low-frequency Breit interaction to the relativistic correlation energy is examined for the helium isoelectronic sequence
Perturbation theory of a symmetric center within Liénard equations
Françoise, Jean-Pierre; Xiao, Dongmei
2015-09-01
In this article, we introduce the use of Lambert function to develop further the global perturbation theory of an integrable Liénard equation which displays a symmetric center. We prove a global Morse lemma for the first integral and deduce the existence of an associated Picard-Fuchs system. We revisit previous contributions to first-order perturbation theory with the help of these new analytic techniques and in particular, we check that the fundamental integrals are linearly independent. The Lambert function allows to find an expansion formula for these integrals. We also study the possibility to develop a higher-order perturbation theory. The algorithm of the successive derivatives works in general in the class of analytic functions on the domain D where the level sets of the first integral are ovals. We end the article with some results on the first integral of a symmetric Liénard equation deduced from the algorithm of successive derivatives.
SIMP model at NNLO in chiral perturbation theory
DEFF Research Database (Denmark)
Hansen, Martin Rasmus Lundquist; Langaeble, K.; Sannino, F.
2015-01-01
We investigate the phenomenological viability of a recently proposed class of composite dark matter models where the relic density is determined by 3 to 2 number-changing processes in the dark sector. Here the pions of the strongly interacting field theory constitute the dark matter particles...... with phenomenological constraints challenging the viability of the simplest realisation of the strongly interacting massive particle (SIMP) paradigm....
Determination of the QCD Λ-parameter and the accuracy of perturbation theory at high energies
International Nuclear Information System (INIS)
Dalla Brida, Mattia; Fritzsch, Patrick; Korzec, Tomasz; Ramos, Alberto; Sint, Stefan; Sommer, Rainer; Humboldt-Universitaet, Berlin
2016-04-01
We discuss the determination of the strong coupling α_M_S(m_Z) or equivalently the QCD Λ-parameter. Its determination requires the use of perturbation theory in α_s(μ) in some scheme, s, and at some energy scale μ. The higher the scale μ the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the Λ-parameter in three-flavor QCD, we perform lattice computations in a scheme which allows us to non-perturbatively reach very high energies, corresponding to α_s=0.1 and below. We find that (continuum) perturbation theory is very accurate there, yielding a three percent error in the Λ-parameter, while data around α_s∼0.2 is clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.
Determination of the QCD Λ-parameter and the accuracy of perturbation theory at high energies
Energy Technology Data Exchange (ETDEWEB)
Dalla Brida, Mattia [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Fritzsch, Patrick [Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM/CSIC; Korzec, Tomasz [Wuppertal Univ. (Germany). Dept. of Physics; Ramos, Alberto [CERN - European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Collaboration: ALPHA Collaboration
2016-04-15
We discuss the determination of the strong coupling α{sub MS}(m{sub Z}) or equivalently the QCD Λ-parameter. Its determination requires the use of perturbation theory in α{sub s}(μ) in some scheme, s, and at some energy scale μ. The higher the scale μ the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the Λ-parameter in three-flavor QCD, we perform lattice computations in a scheme which allows us to non-perturbatively reach very high energies, corresponding to α{sub s}=0.1 and below. We find that (continuum) perturbation theory is very accurate there, yielding a three percent error in the Λ-parameter, while data around α{sub s}∼0.2 is clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.
One-loop divergences in chiral perturbation theory and right-invariant metrics on SU(3)
International Nuclear Information System (INIS)
Esposito-Farese, G.
1991-01-01
In the framework of chiral perturbation theory, we compute the one-loop divergences of the effective Lagrangian describing strong and non-leptonic weak interactions of pseudoscalar mesons. We use the background field method and the heat-kernel expansion, and underline the geometrical meaning of the different terms, showing how the right-invariance of the metrics on SU(3) allows to clarify and simplify the calculations. Our results are given in terms of a minimal set of independent counterterms, and shorten previous ones of the literature, in the particular case where the electromagnetic field is the only external source which is considered. We also show that a geometrical construction of the effective Lagrangian at order O(p 4 ) allows to derive some relations between the finite parts of the coupling constants. These relations do not depend on the scale μ used to renormalize. (orig.)
On the use of the autonomous Birkhoff equations in Lie series perturbation theory
Boronenko, T. S.
2017-02-01
In this article, we present the Lie transformation algorithm for autonomous Birkhoff systems. Here, we are referring to Hamiltonian systems that obey a symplectic structure of the general form. The Birkhoff equations are derived from the linear first-order Pfaff-Birkhoff variational principle, which is more general than the Hamilton principle. The use of 1-form in formulating the equations of motion in dynamics makes the Birkhoff method more universal and flexible. Birkhoff's equations have a tensorial character, so their form is independent of the coordinate system used. Two examples of normalization in the restricted three-body problem are given to illustrate the application of the algorithm in perturbation theory. The efficiency of this algorithm for problems of asymptotic integration in dynamics is discussed for the case where there is a need to use non-canonical variables in phase space.
Symmetry-adapted perturbation theory interaction energy decomposition for some noble gas complexes
Cukras, Janusz; Sadlej, Joanna
2008-06-01
This Letter contains a study of the interaction energy in HArF⋯N 2 and HArF⋯P 2 complexes. Symmetry-adapted perturbation theory (SAPT) has been applied to analyze the electrostatic, induction, dispersion and exchange contributions to the total interaction energy. The interaction energy has also been obtained by supermolecular method at the MP2, MP4, CCSD, CCSD(T) levels. The interaction energy for the studied complexes results from a partial cancelation of large attractive electrostatic, induction, dispersion terms by a strong repulsive exchange contribution. The induction and dispersion effects proved to be crucial in establishing the preference for the colinear HArF⋯N 2 and HArF⋯P 2 structures and shift direction of νHAr stretching vibrations.
International Nuclear Information System (INIS)
Chowdhury, A.R.; Roy, T.
1980-01-01
We have considered the problem of evaluating the large order estimates of perturbation theory in a quantum field theory with more than one coupling constant. The theory considered is four dimensional and possesses instanton-type solutions. It contains a Boson field coupled with a Fermion through the usual g anti psi psi phi type interaction, along with the self-interaction of the Boson lambda phi 4 . Our analysis reveals a phenomenon not observed in a theory with only one coupling constant. One gets different kinds of behavior in different regions of the (lambda, g) plane. The results are quite encouraging for the application to more realistic field theories
International Nuclear Information System (INIS)
Ibral, Asmaa; Zouitine, Asmaa; Assaid, El Mahdi
2015-01-01
Poisson equation is solved analytically in the case of a point charge placed anywhere in a spherical core/shell nanostructure, immersed in aqueous or organic solution or embedded in semiconducting or insulating matrix. Conduction and valence band-edge alignments between core and shell are described by finite height barriers. Influence of polarization charges induced at the surfaces where two adjacent materials meet is taken into account. Original expressions of electrostatic potential created everywhere in the space by a source point charge are derived. Expressions of self-polarization potential describing the interaction of a point charge with its own image–charge are deduced. Contributions of double dielectric constant mismatch to electron and hole ground state energies as well as nanostructure effective gap are calculated via first order perturbation theory and also by finite difference approach. Dependencies of electron, hole and gap energies against core to shell radii ratio are determined in the case of ZnS/CdSe core/shell nanostructure immersed in water or in toluene. It appears that finite difference approach is more efficient than first order perturbation method and that the effect of polarization charge may in no case be neglected as its contribution can reach a significant proportion of the value of nanostructure gap
Energy Technology Data Exchange (ETDEWEB)
Ibral, Asmaa [Equipe d' Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Laboratoire d' Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Zouitine, Asmaa [Département de Physique, Ecole Nationale Supérieure d' Enseignement Technique, Université Mohammed V Souissi, B. P. 6207 Rabat-Instituts, Rabat, Royaume du Maroc (Morocco); Assaid, El Mahdi, E-mail: eassaid@yahoo.fr [Equipe d' Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Laboratoire d' Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); and others
2015-02-01
Poisson equation is solved analytically in the case of a point charge placed anywhere in a spherical core/shell nanostructure, immersed in aqueous or organic solution or embedded in semiconducting or insulating matrix. Conduction and valence band-edge alignments between core and shell are described by finite height barriers. Influence of polarization charges induced at the surfaces where two adjacent materials meet is taken into account. Original expressions of electrostatic potential created everywhere in the space by a source point charge are derived. Expressions of self-polarization potential describing the interaction of a point charge with its own image–charge are deduced. Contributions of double dielectric constant mismatch to electron and hole ground state energies as well as nanostructure effective gap are calculated via first order perturbation theory and also by finite difference approach. Dependencies of electron, hole and gap energies against core to shell radii ratio are determined in the case of ZnS/CdSe core/shell nanostructure immersed in water or in toluene. It appears that finite difference approach is more efficient than first order perturbation method and that the effect of polarization charge may in no case be neglected as its contribution can reach a significant proportion of the value of nanostructure gap.
International Nuclear Information System (INIS)
Fink, Reinhold F.
2009-01-01
The retaining the excitation degree (RE) partitioning [R.F. Fink, Chem. Phys. Lett. 428 (2006) 461(20 September)] is reformulated and applied to multi-reference cases with complete active space (CAS) reference wave functions. The generalised van Vleck perturbation theory is employed to set up the perturbation equations. It is demonstrated that this leads to a consistent and well defined theory which fulfils all important criteria of a generally applicable ab initio method: The theory is proven numerically and analytically to be size-consistent and invariant with respect to unitary orbital transformations within the inactive, active and virtual orbital spaces. In contrast to most previously proposed multi-reference perturbation theories the necessary condition for a proper perturbation theory to fulfil the zeroth order perturbation equation is exactly satisfied with the RE partitioning itself without additional projectors on configurational spaces. The theory is applied to several excited states of the benchmark systems CH 2 , SiH 2 , and NH 2 , as well as to the lowest states of the carbon, nitrogen and oxygen atoms. In all cases comparisons are made with full configuration interaction results. The multi-reference (MR)-RE method is shown to provide very rapidly converging perturbation series. Energy differences between states of similar configurations converge even faster
International Nuclear Information System (INIS)
Kim, Do Heon; Choi, Hang Bok
2001-03-01
A user's guide for GENOVA, a GENeralized perturbation theory (GPT)-based Optimization and uncertainty analysis program for Canada deuterium uranium (CANDU) physics VAriables, was prepared. The program was developed under the framework of CANDU physics design and analysis code RFSP. The generalized perturbation method was implemented in GENOVA to estimate the zone controller unit (ZCU) level upon refueling operation and calculate various sensitivity coefficients for fuel management study and uncertainty analyses, respectively. This documentation contains descriptions and directions of four major modules of GENOVA such as ADJOINT, GADJINT, PERTURB, and PERTXS so that it can be used as a practical guide for GENOVA users. This documentation includes sample inputs for the ZCU level estimation and sensitivity coefficient calculation, which are the main application of GENOVA. The GENOVA can be used as a supplementary tool of the current CANDU physics design code for advanced CANDU core analysis and fuel development
Dynamical generation of non-abelian gauge group via the improved perturbation theory
International Nuclear Information System (INIS)
Kuroki, Tsunehide
2008-01-01
It was suggested that the massive Yang-Mills-Chern-Simons matrix model has three phases and that in one of them a non-Abelian gauge symmetry is dynamically generated. The analysis was at the one-loop level around a classical solution of fuzzy sphere type. We obtain evidences that three phases are indeed realized as nonperturbative vacua by using the improved perturbation theory. It gives a good example that even if we start from a trivial vacuum, the improved perturbation theory around it enables us to observe nontrivial vacua. (author)
The calculation of isotopic partition function ratios by a perturbation theory technique
International Nuclear Information System (INIS)
Singh, G.; Wolfsberg, M.
1975-01-01
The vibrational Hamiltonian of a molecule in the harmonic approximation, H = (1/2) Σ (g/subi/jp/subi/p/subj/ + f/subi/jq/subi/q/subj/), has been divided into a diagonal part (terms with i=j) and an off-diagonal part (inot-equalj), which is regarded as the perturbation. The vibrational partition function of the molecule is then calculated by Schwinger perturbation theory as the partition function of the unperturbed problem, corresponding to a collection of oscillators with frequencies 2πν/subi/' = (f/subi/ig/subi/i)/sup 1 / 2 /, plus perturbation correction terms which are calculated to second order. With the usual assumptions of isotope effect calculations that the molecular translations and rotations are classical and separable from the vibrations, the perturbation formulation of the vibrational partition function is easily transformed into a perturbation theory formulation of (reduced) isotopic partition function ratios. If, for example, the molecular potential function is expressed in terms of the displacements of bond stretches and bond angle bends from their respective equilibrium values, the unperturbed partition function ratio corresponds to the isotope effect expected for noninteracting bond-stretch and bond-angle-bend oscillators. Detailed comparison is made for a number of molecular systems of perturbation theory calculations of partition functions and isotopic partition function ratios with exact calculations carried out by actually obtaining the normal mode vibrational frequencies of the vibrational Hamiltonian. Good agreement is found. The utility of the perturbation theory formulation resides in the fact that it permits one to look at isotope effects in a very simple manner; some demonstrations are given
Duality in a Supersymmetric Gauge Theory From a Perturbative Viewpoint
DEFF Research Database (Denmark)
Ryttov, Thomas A.; Shrock, Robert
2018-01-01
points of the renormalization group emerge in scheme-independent series expansions in the electric and magnetic theories. We further demonstrate that truncations of these series expansions to modest order yield very accurate approximations to these quantities and suggest possible implications......We study duality in N ¼ 1 supersymmetric QCD in the non-Abelian Coulomb phase, order-by-order in scheme-independent series expansions. Using exact results, we show how the dimensions of various fundamental and composite chiral superfields, and the quantities a, c, a=c, and b at superconformal fixed...
The Rise and Fall of the Cosmic String Theory for Cosmological Perturbations
International Nuclear Information System (INIS)
Perivolaropoulos, L.
2005-01-01
The cosmic string theory for cosmological fluctuations is a good example of healthy scientific progress in cosmology. It is a well defined physically motivated model that has been tested by cosmological observations and has been ruled out as a primary source of primordial fluctuations. Until about fifteen years ago, the cosmic string theory of cosmological perturbations provided one of the two physically motivated candidate theories for the generation of primordial perturbations. The cosmological data that appeared during the last decade have been compared with the well defined predictions of the theory and have ruled out cosmic strings as a primary source of primordial cosmological perturbations. Since cosmic strings are predicted to form after inflation in a wide range of microphysical theories (including supersymmetric and fundamental string theories) their observational bounds may serve a source of serious constraints for these theories. This is a pedagogical review of the historical development, the main predictions of the cosmic string theory and the constraints that have been imposed on it by cosmological observations. Recent lensing events that could be attributed to lighter cosmic strings are also discussed
Non-perturbative selection rules in F-theory
Energy Technology Data Exchange (ETDEWEB)
Martucci, Luca [Dipartimento di Fisica e Astronomia ‘Galileo Galilei’, Università di Padova, and I.N.F.N. Sezione di Padova, via Marzolo 8, Padova, I-35131 (Italy); Weigand, Timo [Institut für Theoretische Physik, Ruprecht-Karls-Universität, Philosophenweg 19, Heidelberg, 69120 (Germany)
2015-09-29
We discuss the structure of charged matter couplings in 4-dimensional F-theory compactifications. Charged matter is known to arise from M2-branes wrapping fibral curves on an elliptic or genus-one fibration Y. If a set of fibral curves satisfies a homological relation in the fibre homology, a coupling involving the states can arise without exponential volume suppression due to a splitting and joining of the M2-branes. If the fibral curves only sum to zero in the integral homology of the full fibration, no such coupling is possible. In this case an M2-instanton wrapping a 3-chain bounded by the fibral matter curves can induce a D-term which is volume suppressed. We elucidate the consequences of this pattern for the appearance of massive U(1) symmetries in F-theory and analyse the structure of discrete selection rules in the coupling sector. The weakly coupled analogue of said M2-instantons is worked out to be given by D1-F1 instantons. The generation of an exponentially suppressed F-term requires the formation of half-BPS bound states of M2 and M5-instantons. This effect and its description in terms of fluxed M5-instantons is discussed in a companion paper.
Martin, Alexandre; Torrent, Marc; Caracas, Razvan
2015-03-01
A formulation of the response of a system to strain and electric field perturbations in the pseudopotential-based density functional perturbation theory (DFPT) has been proposed by D.R Hamman and co-workers. It uses an elegant formalism based on the expression of DFT total energy in reduced coordinates, the key quantity being the metric tensor and its first and second derivatives. We propose to extend this formulation to the Projector Augmented-Wave approach (PAW). In this context, we express the full elastic tensor including the clamped-atom tensor, the atomic-relaxation contributions (internal stresses) and the response to electric field change (piezoelectric tensor and effective charges). With this we are able to compute the elastic tensor for all materials (metals and insulators) within a fully analytical formulation. The comparison with finite differences calculations on simple systems shows an excellent agreement. This formalism has been implemented in the plane-wave based DFT ABINIT code. We apply it to the computation of elastic properties and seismic-wave velocities of iron with impurity elements. By analogy with the materials contained in meteorites, tested impurities are light elements (H, O, C, S, Si).
International Nuclear Information System (INIS)
Neese, Frank; Schwabe, Tobias; Grimme, Stefan
2007-01-01
A recently proposed new family of density functionals [S. Grimme, J. Chem. Phys. 124, 34108 (2006)] adds a fraction of nonlocal correlation as a new ingredient to density functional theory (DFT). This fractional correlation energy is calculated at the level of second-order many-body perturbation theory (PT2) and replaces some of the semilocal DFT correlation of standard hybrid DFT methods. The new ''double hybrid'' functionals (termed, e.g., B2-PLYP) contain only two empirical parameters that have been adjusted in thermochemical calculations on parts of the G2/3 benchmark set. The methods have provided the lowest errors ever obtained by any DFT method for the full G3 set of molecules. In this work, the applicability of the new functionals is extended to the exploration of potential energy surfaces with analytic gradients. The theory of the analytic gradient largely follows the standard theory of PT2 gradients with some additional subtleties due to the presence of the exchange-correlation terms in the self-consistent field operator. An implementation is reported for closed-shell as well as spin-unrestricted reference determinants. Furthermore, the implementation includes external point charge fields and also accommodates continuum solvation models at the level of the conductor like screening model. The density fitting resolution of the identity (RI) approximation can be applied to the evaluation of the PT2 part with large gains in computational efficiency. For systems with ∼500-600 basis functions the evaluation of the double hybrid gradient is approximately four times more expensive than the calculation of the standard hybrid DFT gradient. Extensive test calculations are provided for main group elements and transition metal containing species. The results reveal that the B2-PLYP functional provides excellent molecular geometries that are superior compared to those from standard DFT and MP2
Makarewicz, Emilia; Gordon, Agnieszka J; Mierzwicki, Krzysztof; Latajka, Zdzislaw; Berski, Slawomir
2014-06-05
Quantum chemistry methods have been applied to study the influence of the Xe atom inserted into the hydrogen-bromine bond (HBr → HXeBr), particularly on the nature of atomic interactions in the HBr···CO2 and HXeBr···CO2 complexes. Detailed analysis of the nature of chemical bonds has been carried out using topological analysis of the electron localization function, while topological analysis of electron density was used to gain insight into the nature of weak nonbonding interactions. Symmetry-adapted perturbation theory within the orbital approach was applied for greater understanding of the physical contributions to the total interaction energy.
Energy Technology Data Exchange (ETDEWEB)
Takac, S M [Institute of Nuclear Sciences Boris Kidric, Vinca, Beograd (Yugoslavia)
1972-07-01
The method is based on perturbation of the reactor cell from a few up to few tens of percent. Measurements were performed for square lattice calls of zero power reactors ANNA, NORA and RB, with metal uranium and uranium oxide fuel elements, water, heavy water and graphite moderators. Character and functional dependence of perturbations were obtained from the experimental results. Zero perturbation was determined by extrapolation thus obtaining the real physical neutron flux distribution in the reactor cell. Simple diffusion theory for partial plate cell perturbation was developed for verification of the perturbation method. The results of these calculation proved that introducing the perturbation sample in the fuel results in flattening the thermal neutron density dependent on the amplitude of the applied perturbation. Extrapolation applied for perturbed distributions was found to be justified.
Revisiting the pion's scalar form factor in chiral perturbation theory
Juttner, Andreas
2012-01-01
The quark-connected and the quark-disconnected Wick contractions contributing to the pion's scalar form factor are computed in the two and in the three flavour chiral effective theory at next-to-leading order. While the quark-disconnected contribution to the form factor itself turns out to be power-counting suppressed its contribution to the scalar radius is of the same order of magnitude as the one of the quark-connected contribution. This result underlines that neglecting quark-disconnected contributions in simulations of lattice QCD can cause significant systematic effects. The technique used to derive these predictions can be applied to a large class of observables relevant for QCD-phenomenology.
Higher order perturbation theory applied to radiative transfer in non-plane-parallel media
International Nuclear Information System (INIS)
Box, M.A.; Polonsky, I.N.; Davis, A.B.
2003-01-01
Radiative transfer in non-plane-parallel media is a very challenging problem, which is currently the subject of concerted efforts to develop computational techniques which may be used to tackle different tasks. In this paper we develop the full formalism for another technique, based on radiative perturbation theory. With this approach, one starts with a plane-parallel 'base model', for which many solution techniques exist, and treat the horizontal variability as a perturbation. We show that under the most logical assumption as to the base model, the first-order perturbation term is zero for domain-average radiation quantities, so that it is necessary to go to higher order terms. This requires the computation of the Green's function. While this task is by no means simple, once the various pieces have been assembled they may be re-used for any number of perturbations--that is, any horizontal variations
Performance prediction of electrohydrodynamic thrusters by the perturbation method
International Nuclear Information System (INIS)
Shibata, H.; Watanabe, Y.; Suzuki, K.
2016-01-01
In this paper, we present a novel method for analyzing electrohydrodynamic (EHD) thrusters. The method is based on a perturbation technique applied to a set of drift-diffusion equations, similar to the one introduced in our previous study on estimating breakdown voltage. The thrust-to-current ratio is generalized to represent the performance of EHD thrusters. We have compared the thrust-to-current ratio obtained theoretically with that obtained from the proposed method under atmospheric air conditions, and we have obtained good quantitative agreement. Also, we have conducted a numerical simulation in more complex thruster geometries, such as the dual-stage thruster developed by Masuyama and Barrett [Proc. R. Soc. A 469, 20120623 (2013)]. We quantitatively clarify the fact that if the magnitude of a third electrode voltage is low, the effective gap distance shortens, whereas if the magnitude of the third electrode voltage is sufficiently high, the effective gap distance lengthens.
Perturbation theory for the effective diffusion constant in a medium of random scatterers
International Nuclear Information System (INIS)
Dean, D S; Drummond, I T; Horgan, R R; Lefevre, A
2004-01-01
We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random medium. The random medium contains point scatterers of density ρ uniformly distributed throughout the material. The tracer is a Langevin particle subjected to the quenched random force generated by the scatterers. Via our perturbative analysis, we determine when the random potential can be approximated by a Gaussian random potential. We also develop a self-similar renormalization group approach based on thinning out the scatterers; this scheme is similar to that used with success for diffusion in Gaussian random potentials and agrees with known exact results. To assess the accuracy of this approximation scheme, its predictions are confronted with results obtained by numerical simulation
Self-consistent many-body perturbation theory in range-separated density-functional theory
DEFF Research Database (Denmark)
Fromager, Emmanuel; Jensen, Hans Jørgen Aagaard
2008-01-01
effects adequately which, on the other hand, can be described by many-body perturbation theory MBPT. It is therefore of interest to develop a hybrid model which combines the best of both the MBPT and DFT approaches. This can be achieved by splitting the two-electron interaction into long-range and short...