Weak-coupling expansion for the free energy of the magneto-polaron in two dimensions

Previous weak-coupling expansions of the ground-state energy for a Fröhlich type polaron in two dimensions subject to a perpendicular uniform magnetic field are extended to non-zero temperatures by using the path-integral representation. For every temperature the second-order contribution becomes positive for sufficiently high fields implying that a seemingly natural generalisation of the Jensen-Feynman inequality does not exist.     

Diagrammatic expansion and metastability in the random-field Ising model

Within the perturbation diagrammatic expansion we discuss the origin of differences in determinations of the lower critical dimension of the random-field Ising model and show that below four dimensions metastability and hysteresis occur. We also explain the occurrence of a quasicritical d=2 behavior at weak random fields, which is responsible for local stability of the ordered state above two dimensions.     

Large-N-limit of mixed valence: Diagrammatic expansion and rigorous results

For an intermediate valence model, containing one simply and oneN-fold degeneratef-configuration at a specific lattice site, the large-N-limit is studied within a concise diagrammatic expansion and also rigorously. At zero temperatureT rigorous upper and lower bounds for the ground state energy are found, while at finiteT the large-N-expansion is shown to be equivalent to the principle of classifying the diagrams according the maximum number of spin flips, whereupon various physical quantities can be calculated.On leave of absence from Department of Physics, Beijing University, Beijing, People's Republic of China with support from DAAD     

Diagrammatic non-degenerate RSPT for evaluation of ground-state energy of simple open-shell molecular systems

The diagrammatic non-degenerate Rayleigh-Schrödinger perturbation theory and the coupled cluster approach are applied to the evaluation of the ground state energy of a simple open-shell molecular system described in the zeroth order approximation by a single determinant wavefunction. The corresponding hamiltonian is built up by the creation and annihilation operators introduced over an orthonormal set of restricted Hartree-Fock one-particle functions. The perturbation H₁ is composed of one- and two-particle terms, the one-particle term depending in an explicit way upon the type of restricted Hartree-Fock theory used. The efficiency of the elaborated theory is illustrated for the BeH molecule.     

Diagrammatic expansions for the Yang-Mills ground state

Starting from the finite-time action formulation of the temporal gauge, we derive diagrammatic rules for the perturbative evaluation of the Yang-Mills ground state wave functional and energy to all orders. The perturbative expansions are also easily reorganized into semi-classical expansions. As an application, the ground state wave functional through first non-trivial order is explicitly computed. We also speculate on the use of gauge invariance to improve perturbation theory.     

Diagrammatic method for generalized Pauli operators

A new diagrammatic technique for complicated level many-body systems is presented using generalized Pauli operators. The resulting diagrams are considerably simpler than those constructed by the standard basis operators.     

Diagrammatic perturbation theory: evaluation of fourth-order energy terms involving quadruply-excited states for closed-shell systems

The energy terms involving quadruply-excited states that arise in fourth order in the many-body perturbation series are discussed in detail. Both linked-diagram and unlinked-diagram components are calculated for the nitrogen molecule. The unlinked diagram components, which are required to correct for the unphysical terms included in configuration interaction calculations that are restricted to double excitations, are calculated for some closed-shell diatomic hydrides at their respective equilibrium separations and for the hydrogen fluoride molecule as a function of internuclear distance.     

Pair potential for a weak-coupling,single-crystal superconductor

In the standard treatment of weak-coupling superconductors, the pair potential enters as a nondiagonal but local potential. It is shown that for a pure, weak-coupling, bulk, single-crystal superconductor the quasiparticle wave functions are then Bloch functions and the self-consistent pair potential is periodic in space with the periodicity of the crystal structure. The relation between this periodic character of the pair potential and energy gap structure is discussed, and it is pointed out that energy gap structure of the general character expected appears to have been observed. The validity of a local pair potential is also briefly considered.Supported in part by the National Science FoundationA preliminary account of this work is abstracted in Bull. Am. Phys. Soc.19, 277 (1974)     

Diagrammatic operator formalism for string amplitudes

A diagrammatic operator method based on Fock space formulations of 3-string vertices is developed for computing the integration measure for open or closed string S-matrix to arbitrary loop order. The proposed vertex does not triangulate the moduli space, thus a single diagram incorporates a number of string field theory diagrams. However, the formalism does not naturally lead to a single cover of moduli space, and the restriction to the fundamental domain must be put in by hand, as in the Polyakov functional integral approach.     

Diagrammatic approach for open chaotic systems

A semiclassical diagrammatic approach is constructed for calculating correlation functions of observables in open chaotic systems with time reversal symmetry. The results are expressed in terms of classical correlation functions involving Wigner representations of the observables. The formalism is used to explain a recent microwave experiment on the four-disk problem, and to characterize the two-point function of the photodissociation cross section of complex molecules.     

A self-organizing network in the weak-coupling limit

We prove the existence of spatially localized ground states of the diffusive Haken model. This model describes a self-organizing network whose elements are arranged on a d-dimensional lattice with short-range diffusive coupling. The network evolves according to a competitive gradient dynamics in which the effects of diffusion are counteracted by a localizing potential that incorporates an additional global coupling term. In the absence of diffusive coupling, the ground states of the system are strictly localized, i.e. only one lattice site is excited. For sufficiently small non-zero diffusive coupling , it is shown analytically that localized ground states persist in the network with the excitations exponentially decaying in space. Numerical results establish that localization occurs for arbitrary values of in one dimension but vanishes beyond a critical coupling _c(d), when d> 1. The one-dimensional localized states are interpreted in terms of instanton solutions of a continuum version of the model.     

A perturbative expansion of the Casimir energy

We consider the Casimir energyE _C of a medium with inhomogenous dielectric and diamagnetic constants, with the restriction ε(x)μ(x)=1. We expandE _C with respect to σ(x)=ln ε(x) and discuss the divergences of the second order contribution. We consider especially the transition to dielectrics with sharp boundaries.     

Gradient expansion of the Coulomb exchange energy

With the aid of the gradient expansion technique of Kirzhnits we calculate the lowest order inhomogenity correction to the local approximation of the Coulomb exchange energy density.     

Diagrammatic theory for periodic anderson model

Diagrammatic theory for Periodic Anderson Model has been developed, supposing the Coulomb repulsion of f — localized electrons as a main parameter of the theory. f-Electrons are strongly correlated and c-conduction electrons are uncorrelated. Correlation function for f- and mass operator for c-electrons are determined. The Dyson equation for c- and Dyson-type equation for f-electrons are formulated for their propagators. The skeleton diagrams are defined for correlation function and thermodynamic functional. The stationary property of renormalized thermodynamic potential with respect to, the variation of the mass operator is established. The result is appropriate both for the normal and for the superconducting states of the system.     

Separable interactions and liquid 3He: II. Extrema of Landau expansion and phase diagram in the weak-coupling limit

In a previous paper we derived a Landau expansion starting from an exactly solvable model for a system of fermions with an l = 1 pairing interaction in the presence of a magnetic field. The Landau expansion, which can be used to study the phases of liquid ³He, is a complicated function of 9 complex variables, in which it is not obvious a priori that the field dependence of the coefficients of the fourth-order terms can be neglected. In the present paper the extrema of the Landau expansion are analyzed in some detail with the weak-coupling values of the coefficients. The absolute minimum of the Landau expansion can be found by minimizing a three-parameter function Φ_BW, the minimalization of which leads to three possible phases, the A1-phase, the ABM-phase (or two-dimensional 2D-phase) and the proper generalization of the BW-phase in the presence of a magnetic field. The phase diagram is compared with the one given by Ambegaokar and Mermin.     

Deuteron Photodisintegration in the Diagrammatic Approach

Photodisintegration of the deuteron below the pion-photoproduction threshold is considered in the framework of the diagrammatic approach. The deuteron wave function, the final-state N–N interaction and meson-exchange currents are constructed from the nonrelativistic versions of the Bonn OBE potential. A detailed comparison with the existing data is made. It is shown that the model gives a satisfactory agreement with the experimental data. Possible sources for the remaining disagreements are discussed. Received June 10, 1994; revised September 25, 1994; accepted for publication November 18, 1994     

An asymptotic expansion for energy eigenvalues of anharmonic oscillators

In the present contribution, we derive an asymptotic expansion for the energy eigenvalues of anharmonic oscillators for potentials of the form V(x)=κx^2q+ωx²,q=2,3,…$V\left(x\right)=\kappa x^{2q}+\omega x^2,q=2,3,\dots$ as the energy level n$n$ approaches infinity. The asymptotic expansion is obtained using the WKB theory and series reversion. Furthermore, we construct an algorithm for computing the coefficients of the asymptotic expansion for quartic anharmonic oscillators, leading to an efficient and accurate computation of the energy values for n≥6$n\ge 6$.     

Diagrammatic techniques in the Martin-Schwinger-Puff many-body theory

In an attempt to understand the connection between the Martin-Schwinger-Puff Green's function approach to the many-body problem and the diagrammatic approach of Brueckner and Goldstone, the perturbation expansion of the Green's function theory is studied. This expansion leads naturally to a representation of the theory by two sets of time-dependent diagrams—the kinetic energy diagrams and the potential energy diagrams. Rules are given for writing each time-dependent diagram as a sum of time-independent diagrams. Complications arise in the application of these rules to bubble diagrams. A special simple treatment of these diagrams is then proposed. There exists a simple relation between families of kinetic diagrams and potential diagrams. This relation stems from a rather general thermodynamic identity. Both the relation and its thermodynamic origin are described. As a consequence of these studies, some connections between the Brueckner-Goldstone theory and the Green's function theory are made.