Weak Coupling Approximation Research Articles

Acoustic Soliton in One-Dimensional Ferromagnetic Systems

The local nonlinear excitation caused by the magnon-phonon interactions as an anisotropic source of nonlinearity is studied. The nonlinear equation for the Schrödinger probability amplitude of spin motion is given, and its soliton solutions are obtained in a weak coupling approximation. The existence conditions are discussed. It is shown that the soliton excitation energy can be less than a one-magnon state and a gap appears in the energy spectrum. The effect of the magnon-magnon interactions on the local acoustic soliton excitation is also discussed.

Kink Casimir energy in a lattice sine-Gordon model.

The Casimir energy of quantum fluctuations about the classical kink configuration is computed numerically in the weak coupling approximation for a recently proposed lattice sine-Gordon model. This energy depends periodically on the kink position and is found to be approximately sinusoidal.

Electron impact excitation of atomic systems

Starting from the usual partial wave method, we present a theoretically exact formulation for the calculation of differential and total cross sections corresponding to electron impact excitation in atomic systems. For transitions involving an s state the derived formulae are very simple, free of Racah or Clebsch-Gordan coefficients, so that for computational purposes they are more convenient than the usual expressions. In particular, we have considered monopole, dipole and quadrupole transitions from (or to) an s state. In comparison with the usual formulation, the present one also has the advantage that it allows us to separate out the scattering amplitudes corresponding to excitation of individual magnetic substates: electron-photon coincidence parameters for dipole and quadrupole transitions from an s state can be obtained directly. For the total differential cross section an alternative formulation is derived and compared with the previous one. Both formulations given here are very general because they can be employed using any non-relativistic T-matrix, and are valid for both neutral and charged targets. In the weak coupling approximation and for alkali-like systems, the resulting formulae are compared with others of the literature; as an illustration the Coulomb Bethe approach is described. Finally, expressions for the integrated cross sections corresponding to excitation of individual magnetic substates are also given and it is shown how, for charged targets, the Coulomb phase must be included in all calculations except in those which give the total integrated cross section.

Derivation of Master Equation for Totally Quadratic System in Quantum Brownian Motion

We consider Quantum Brownian motion of a toy model, which is a harmonic oscillator that interacts with environment consisting of harmonic oscillators through both qQ and pP types of coupling. At first, we formally derive exact master equation following Unruh and Zurek's method. Subsequently we estimate the behavior of the coefficients in the master equation at initial stage and at late time stage under weak coupling approximation. We find that, as the model with qQ coupling only, the system in supraohmic environment is less dissipative and less diffusive beyond the cutoff time scale than the system in ohmic environment. The cause is due to the weakness of spectral densities of environment in infrared sector

Radiative opacities for carbon- and oxygen-rich mixtures

Recent OPAL calculations have obtained significant differences in the Rosseland mean opacities compared with earlier Los Alamos work. These new opacities have had a favorable impact on several astrophysical problems, but the efforts have concentrated on hydrogen main-sequence stars or stellar envelopes. The present calculations consider carbon- and oxygen-rich mixtures. It is shown that for such mixtures the Coulomb corrections beyond the weak-coupling approximation are not negligible in the ionization-balance calculations when Rosseland mean opacities are computed. As for hydrogen-rich compositions, the hydrogen-depleted mixtures can show factors of 2-3 enhancements in the opacity compared with the Los Alamos results at temperatures of a few hundred thousand degrees

Scaling theory of the Mott-Hubbard metal-insulator transition in one dimension.

We use the Bethe ansatz equations to calculate the charge stiffness ${\mathit{D}}_{\mathit{c}}$=(L/2)${\mathit{d}}^{2}$${\mathit{E}}_{0}$/d${\mathrm{\ensuremath{\Phi}}}_{\mathit{c}}^{2}$${\mathrm{\ensuremath{\Vert}}}_{\mathrm{\ensuremath{\Phi}}\mathit{c}}$=0 of the one-dimensional repulsive-interaction Hubbard model for electron densities close to the Mott insulating value of one electron per site (n=1), where ${\mathit{E}}_{0}$ is the ground-state energy, L is the circumference of the system (assumed to have periodic boundary conditions), and (\ensuremath{\Elzxh}c/e)${\mathrm{\ensuremath{\Phi}}}_{\mathit{c}}$ is the magnetic flux enclosed. We obtain an exact result for the asymptotic form of ${\mathit{D}}_{\mathit{c}}$(L) as L\ensuremath{\rightarrow}\ensuremath{\infty} at n=1, which defines and yields an analytic expression for the correlation length \ensuremath{\xi} in the Mott insulating phase of the model as a function of the on-site repulsion U. In the vicinity of the zero-temperature critical point U=0, n=1, we show that the charge stiffness has the hyperscaling form ${\mathit{D}}_{\mathit{c}}$(n,L,U)=${\mathit{Y}}_{+}$(\ensuremath{\xi}\ensuremath{\delta},\ensuremath{\xi}/L), where \ensuremath{\delta}=\ensuremath{\Vert}1-n\ensuremath{\Vert} and ${\mathit{Y}}_{+}$ is a universal scaling function which we calculate. The physical significance of \ensuremath{\xi} in the metallic phase of the model is that it defines the characteristic size of the charge-carrying solitons, or holons. We construct an explicit mapping for arbitrary U and \ensuremath{\xi}\ensuremath{\delta}\ensuremath{\ll}1 of the holons onto weakly interacting spinless fermions, and use this mapping to obtain an asymptotically exact expression for the low-temperature thermopower near the metal-insulator transition, which is a generalization to arbitrary U of a result previously obtained using a weak-coupling approximation, and implies holelike transport for 01-n\ensuremath{\ll}${\ensuremath{\xi}}^{\mathrm{\ensuremath{-}}1}$.

Liouville models of black hole evaporation

A renormalizable two-dimensional quantum field theory, containing a metric, a dilaton and N massless scalar matter fields, has been proposed as a model for black hole evaporation reflecting the conformal anomaly. Previous work on this model has been done in the large- N (weak coupling) approximation and clear evidence for Hawking radiation and its back-reaction on the metric has been seen. There are, however, quantum consistency questions since the original model was only designed to be a c = 26 conformal field theory in the weak coupling limit. In this paper we construct new theories, differing from the old only in the dilaton dependence of the cosmological constant and reducing to it in the weak coupling limit. They are exact c = 26 conformal field theories and presumably consistent frameworks for discussing this problem. We also study the new theories with a change in the Polyakov action proposed by Strominger with a view to eliminating unphysical ghost Hawking radiation. The classical equations of motion of the new theories are explicitly soluble, thus permitting an exact analysis of both static solutions and dynamic scenarios. While the static solutions are, by and large, physically reasonable, the dynamical solutions include puzzling examples where wrong-sign Hawking radiation is stimulated by allowing matter to fall into a static solution. We indicate how the latter problem may be resolved in the full quantum theory.

SUPERCONDUCTIVITY: GAUGE FIELD THEORY FORMULATION

The nonrelativistic BCS theory of superconductivity is studied in the framework which allows an application of field-theoretic methods. The gauge technique of relativistic quantum electrodynamics is shown to be a suitable basis which makes it feasible to extend BCS theory beyond the original weak coupling approximation. We derive a relation between the superconducting transition temperature, the Debye temperature, the effective coupling constant and the effective electron mass. In addition to the BCS type solution, we establish an interesting new solution which corresponds to a high transition temperature.

Anyon spectra and the third virial coefficient

The third virial coefficient of a gas of anyons in a harmonic potential is studied using two different approximations to obtain the three-anyon spectrum. A semiclassical (weak-coupling) approximation which provides us with the overall behavior of the spectrum leads to a divergent third virial coefficient. As a second approximation the low-lying three-anyon spectrum at the fermion point is constructed up to second order in the statistical parameter. The analogue spectrum at the boson point follows by symmetry. In this case the results are consistent with a finite third virial coefficient. The semiclassical approximation is also applied to the four-anyon spectrum and can be readily generalized to many anyons. Within their range of validity, both types of approximate spectra are in complete agreement with previously obtained exact numerical spectra.

Homogeneous spin precession in rotating vortex-freeHe3-B: Measurement of the superfluid density anisotropy

In transverse NMR at high rf excitation, it is possible to separate a $^{3}\mathit{B}$ sample into two magnetic domains. In one domain the spins are precessing coherently with a large tilting angle in relation to the polarizing magnetic field while in the other they are stationary and oriented parallel to the field. We have studied the two-domain system during vortex-free rotation and found that the boundary region between the precessing and static domains is sensitive to superfluid counterflow, flowing parallel to the boundary. The volume of the precessing domain decreases and the NMR absorption, associated with spin diffusion across the boundary, increases. The shift of the domain boundary is analyzed in terms of the competition between the kinetic energy of counterflow and the gradient in the Zeeman energy. From the shift we obtain the superfluid density anisotropy, induced by the magnetic field. A calculation in the weak-coupling approximation explains only half of the measured ansiotropy at low pressures. At high pressures the discrepancy is smaller.

Polarisation in the Temperature Equilibration of Anisotropic Plasmas

Abstract The polarisation effect on the isotropisation of a magnetized bi-Maxwellian plasma is investigated in the weak coupling approximation. Based on the Rostoker collision operator, which reduces in the magnetic field free limit to the Balescu-Lenard operator, the equipartition frequency v is evaluated numerically for B→0 and analytically for B→∞, respectively. This frequency, depending nonlinearly on ε and B, describes the approach to thermodynamic equilibrium of the anisotropy parameter ε = T⊥/T‖ via dε/dt - (1 - ε) ν(ε, B). It is found that in both limits dynamical screening makes a negligible contribution to the relaxation process. For finite B a simplified, yet unexploited expression for ν(ε, B) is presented, which invokes three new functions

Spin-fluctuation-induced superconductivity in the copper oxides: A strong coupling calculation.

We have carried out a strong coupling calculation of spin-fluctuation-induced superconductivity for ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ using the experimentally determined spin excitation spectrum. We find that it is extremely important to take full account of the momentum and frequency dependence of the interaction and that while lifetime effects substantially reduce ${\mathit{T}}_{\mathit{c}}$ from its value calculated in a weak coupling approximation, it is still possible for spin fluctuations to give rise to high-temperature superconductivity.

Test-particle motion in a relativistic plasma III. Collective effects

We give a covariant description of the behaviour of a test-particle in a dense relativistic plasma. We show how the collective effects modify the results obtained in the weak-coupling or Landau approximation.

Delta expansion applied to quantum electrodynamics.

A recently proposed technique known as the \ensuremath{\delta} expansion provides a nonperturbative treatment of a quantum field theory. The \ensuremath{\delta}-expansion approach can be applied to electrodynamics in such a way that local gauge invariance is preserved. In this paper it is shown that for electrodynamic processes involving only external photon lines and no external electron lines the \ensuremath{\delta} expansion is equivalent to a fermion loop expansion. That is, the coefficient of ${\mathrm{\ensuremath{\delta}}}^{\mathit{n}}$ in the \ensuremath{\delta} expansion is precisely the sum of all n-electron-loop Feynman diagrams in a conventional weak-coupling approximation. This equivalence does not extend to processes having external electron lines. When external electron lines are present, the \ensuremath{\delta} expansion is truly nonperturbative and does not have a simple interpretation as a resummation of conventional Feynman diagrams. To illustrate the nonperturbative character of the \ensuremath{\delta} expansion we perform a speculative calculation of the fermion condensate in the massive Schwinger model in the limit of large coupling constant.

Charge transfer instability and superconductivity

Superconductivity in the system near charge transfer instability is investigated for CuO 2 layer structure. By treating the transfer between Cu and O perturbatively, the effective interaction of O holes is derived and the possible symmetries of superconductivity is studied. The critical temperatures of superconductivity are estimated as a function of the doping rate, σ, based on weak-coupling approximation and are found to have characteristic σ-dependences depending on symmetry. We also examined the possible ground states with n = 1,2,3, or 4 holes for a wide range of the Coulomb repulsions on Cu sites and O sites.

Kinetic theory in the weak-coupling approximation: III. Classical systems: extension of the theory and further applications

The kinetic theory of open classical systems in the weak-coupling approximation presented in a previous paper (paper I), is extended here to a wider class of systems so that it is applicable when the Liouville operator of the open system has a continuous spectrum. It is applied (i) to an anharmonic-oscillator and (ii) to a free test-particle model, thus leading to a generalization of the conventionally used linearized Landau equation. Problems related to the divergences that appear when the kinetic equations, obtained by the formalism of paper I, are considered in the limit of a continuous spectrum of the open system's Liouville operator are also discussed.

Resonant magnetohydrodynamic modes with toroidal coupling. Part I: Tearing modes

In a cylindrical plasma, tearing modes can be calculated by asymptotic matching of ideal magnetohydrodynamic (MHD) solutions across a critical layer. This requires a quantity Δ′ that represents the ‘‘discontinuity’’ in the ideal solution across the layer. In a torus, poloidal harmonics are coupled and there are many critical surfaces for each toroidal mode number, and correspondingly many discontinuities Δ′m. The ideal MHD solutions do not then determine the Δm but only a relation between them—described by an ‘‘E matrix.’’ The calculation of the E matrix for a large-aspect-ratio tokamak is discussed. In a weak-coupling approximation, it is tridiagonal and can be computed from integrals over the uncoupled eigenfunctions or from simple ‘‘basis functions’’ comprising triplets of coupled poloidal harmonics. This weak-coupling approximation fails if Δ′m is already small for an uncoupled harmonic. An alternative strong-coupling approximation is developed for this case.

Collective excitations in the A phase of 3He.

A microscopic theory of the collective excitations (CE) in the A phase of $^{3}\mathrm{He}$ is constructed with the use of a path-integration method. The whole CE spectrum, taking damping into account, is calculated. The cause of additional Goldstone modes in the weak-coupling approximation and their analogy to W bosons in the weak-interaction theory are discussed. The whole set of equations, which describe the CE in arbitrary magnetic fields, is obtained. They are solved for small magnetic fields and the linear Zeeman effect for clapping and pair-breaking modes is obtained.

Superconductivity near Charge Transfer Instability in CuO2Structure

The possible symmetries of superconductivity is studied on a system near charge transfer instability in CuO 2 layer structure for a case where the Cu sites do not have magnetic moment. This case corresponds either to ignore the existence of magnetic moments in actual high T c Cu-oxides by focusing only on charge fluctuations or to consider the ground state configurations of d 8 or d 10 at the Cu-sites. By deriving effective interaction processes, which become important near the charge transfer instability, the critical temperatures have been estimated as a function of the doping rate, δ, based on weak-coupling approximation. It is seen that they have characteristic δ-dependence depending on symmetry.

Correction for the extinction efficiency factors given in the Jones solution for the electromagnetic scattering by agglomerates of small spheres

Formulas for the extinction efficiency factor in the Jones solution for electromagnetic scattering and absorption by agglomerates of small spheres have been corrected by adding an exp(-ikzi) term. For most cases, this correction makes a substantial difference to the numerical results. A closed-form solution for the extinction efficiency factor under the second-order Born (i.e. weak-coupling) approximation has also been corrected. Weak-coupling solutions for straight chain agglomerates in various orientations are then derived. A way of establishing the single scattering criterion for the extinction of individual particles is discussed. The difference caused by Jones' error in the representation of complex refractive index is found to be significant only for the extinction of densely packed agglomerates. As a consequence of not including the higher order multiple scattering terms, values given by Jones' solution for the extinction efficiency factor are actually closer to the absorption.