Strong Coupling Case Research Articles

Second order approximation for an optical polaron in the strong coupling case

Here we propose a method of construction of the second order approximation for the ground state energy for a class of model Hamiltonians with a linear type of interaction with respect to Bose operators in the strong coupling case. For an application of the above-mentioned method we have considered the polaron model and proposed a set of nonlinear differential equations for the ground state energy calculation in the strong coupling case. We have considered also the radially symmetric case.

The soft mode behaviour and electron correlation effect in the pseudo Jahn-Teller system

The relationship between electron correlation and lattice instability is discussed in this paper. A exciton Hamiltonian coupled with lattice motion is proposed to include the many body effect of the electron correlation. In strong coupling case we can limit our discussion to an effective Hamiltonian in which only the ground state and the low excited state is included. A pseudo spin representation is introduced, and the Green function technique is used to calculate the frequency of the soft mode. Our result implies that electron correlation will greatly enhance the lattice instability.

Quantum Description of the Magnetic Polaron in Antiferromagnetic Semiconductors

On the basis of exchange interaction of impurity electrons with localized moments, the magnetic polaron Hamiltonian for antiferromagnetic semiconductors is derived. By the method of canonical transformation, the properties of magnetic polarons for the intermediate-coupling case are discussed. Especially in the strong-coupling case, those properties are considered by using the generalized Landau–Pekar method, and the analytical results such as self-energy, effective mass and the space location are given in the long wave-length approximation.

Mixed-valence polyoxometalate clusters. III. Vibronic problem for the 2-electron reduced heteropoly blue with the Keggin structure

Abstract A general approach to the vibronic problem of delocalized electronic pairs in mixed-valence compounds is developed and applied to understand the ways of electron delocalization in dodecanuclear polyoxometalate clusters containing two moving electrons. The interplay between electronic and vibronic interactions is examined. The electronic spectrum is shown to consist of two spin triplets 3 T 1 and 3 T 2 and three spin singlets 1 A 1 , 1 E and 1 T 2 levels determined by the double-transfer processes (parameter P ). Jahn-Teller and pseudo-Jahn-Teller problems ( 3 T 1 + 3 T 2 ) ⊗ ( e + t 2 ) and ( 1 A 1 + 1 E + 1 T 2 ) ⊗ ( e + t 2 ) have been considered in the framework of the Piepho-Krausz-Schatz model dealing with the only vibronic parameter. Several kinds of spatial electronic distribution have been found corresponding to the stable points of the energy surfaces. For spin-triplet states, potential surfaces contain six minima in e space corresponding to partially delocalized electronic pairs over four sides of the T d structure (limiting case of weak coupling), or delocalized over two opposite sides (limiting case of strong coupling). The former situation restricts electron delocalization to two of the three metal octahedra of each M 3 O 12 triad in such a way that each electron moves over a tetrameric unit in which the metal sites are alternatively sharing edges and corners. In the t 2 space the electronic pair can be either delocalized over three sides, giving rise to a trigonal-type distortion of the cluster and a partial electron delocalization over two opposite M 3 O 12 triads (four trigonal minima in the case of strong transfer or relatively weak vibronic interaction), or be completely localized (case of strong vibronic coupling). For spin-singlet states the system possesses a stable point in the high-symmetrical nuclear configuration, corresponding to a full delocalization of the electronic pairs in the Keggin cluster. The influence of vibronic interaction on the nature of the spin of the ground states is considered.

SECOND ORDER APPROXIMATION FOR OPTICAL POLARON IN THE STRONG COUPLING CASE

Here we propose a method of constructing a second order approximation for ground state energy for a class of model Hamiltonian with linear type interaction on bose operators in the strong coupling case. For the application of the above method we have considered polaron model and propose constructing a set of nonlinear differential equations for definition ground state energy in the strong coupling case. We have considered also radial symmetry case.

A calculation of Eliashberg equations for superconducting phase under the ultra-high magnetic field of strong coupling cases in 2 and 3 dimensional systems

The estimation of Tc for the superconducting phase under the ultra-high magnetic field is discussed on the basis of numerical calculation by the use of the expression of Eliashberg equations for strong coupling theory. The essential effect of the retardation of the interaction by phonons on making the gap is pointed out in comparison between 2 and 3 dimensional systems.

Wavefunction of a Cooper pair in crystals ofD 2h 1 andD 4h 17 symmetry

Symmetry description of wavefunctions of Cooper pairs, based on the Pauli exclusion principle and on the Mackey-Bradley theorem, is carried out for the space groupsD2h1 andD4h17. The table of the irreducible representations of Cooper pairs in theL-S and thej-j coupling is presented. The nodal structure of the pairing function in the time-reversal symmetry violation is investigated. It is shown that if the time-reversal symmetry is violated in the strong spin-orbit coupling case, line nodes are possible for the odd superconducting order parameter.

Vibration localization in dual-span, axially moving beams: Part II: Perturbation analysis

An analytical study of the effect of small irregularities on the dynamics of nearly periodic, dual-span, stationary and axially moving beams with cyclic symmetry is presented. Emphasis is placed on utilizing a perturbation approach to extend and interpret the numerical results obtained in the companion paper (Part I). The perturbation approach provides additional insights into the phenomenon of vibration localization, i.e., into the sensitivity of the system dynamics to the tension disorder, the inter-span coupling, as well as the transport speed. Analytical perturbation results are obtained in the limiting cases of weak and strong inter-span coupling. Findings show that the degree of vibration localization depends primarily upon the relative strengths of disorder and inter-span coupling; namely, for strong inter-span coupling (i.e., for small axial band tension) the disordered system behavior is well predicted as a perturbation of that of the corresponding ordered coupled system, in which case a small tension disorder has a minimal effect on the dynamic response. On the other hand, for weak inter-span coupling (i.e., for large axial band tension), the disordered system behavior is well predicted as a perturbation of that of the disordered decoupled system, in which case the natural modes of the coupled system undergo large changes for small tension disorder.

Photoluminescence under selective excitation of thiophene oligomers: relationship to microcrystalline structure

The photoluminescence of thin films of various sexithiophene oligomers has been studied by using excitations near the absorption edge. This emission shows at least two overlapping spectra with very different features. The position of the 0-0 line of the low-energy emission is clearly dependent on the nature and microcrystallinity of the oligomer under study, in contrast with the high-energy one. An identification of the crystalline and molecular levels involved is suggested by using Frenkel exciton theory in the limiting cases of strong and weak intermolecular coupling. Spectral effects due to the reduced size of the grains are discussed.

The local-point interchain delocalization of the polaronic state of a one-dimensional polymer chain

Interchain delocalization of the polaronic state in a quasi-one-dimensional polymer via local hopping at the points of the closest interchain separation has been investigated with a discrete two-chain model, which can be applicable also to the strong electron-phonon coupling and small radius polaron case. We have examined a variational solution of this model and found that the ground state of this model system changes continuously from the localized (one-chain polaron) to the delocalized state above the critical value, γ c , of the relative strength of the local-point transverse transverse integral across the chains. The dependence of γ c ( μ) on the spatial extension of the polaron ( μ −1) has also been studied: for a small polaron ( μ>1) γ c ≃0.5, while for a polaron of intermediate radius γ c changes monotonically with the maximum around μ≃1, in contrast with the simple qualitative expectation.

Matrix decompositions of two-dimensional nuclear magnetic resonance spectra.

Two-dimensional NMR spectra are rectangular arrays of real numbers, which are commonly regarded as digitized images to be analyzed visually. If one treats them instead as mathematical matrices, linear algebra techniques can also be used to extract valuable information from them. This matrix approach is greatly facilitated by means of a physically significant decomposition of these spectra into a product of matrices--namely, S = PAPT. Here, P denotes a matrix whose columns contain the digitized contours of each individual peak or multiple in the one-dimensional spectrum, PT is its transpose, and A is an interaction matrix specific to the experiment in question. The practical applications of this decomposition are considered in detail for two important types of two-dimensional NMR spectra, double quantum-filtered correlated spectroscopy and nuclear Overhauser effect spectroscopy, both in the weak-coupling approximation. The elements of A are the signed intensities of the cross-peaks in a double quantum-filtered correlated spectrum, or the integrated cross-peak intensities in the case of a nuclear Overhauser effect spectrum. This decomposition not only permits these spectra to be efficiently simulated but also permits the corresponding inverse problems to be given an elegant mathematical formulation to which standard numerical methods are applicable. Finally, the extension of this decomposition to the case of strong coupling is given.

Rate expressions for excitation transfer I. Radiationless transition theory perspective

The ideas concerning preparation of an initial state and its subsequent temporal evolution are discussed with reference to interchromophore electronic excitation (energy) transfer (EET), particularly the ‘‘resonance’’ case. The cases of strong and weak coupling, and their consequences, are discussed. It is shown that when the interactions between two identical chromophores lie in the weak coupling regime, then a rate of excitation transfer may be defined on an experimental time scale and is given by a Fermi golden rule expression; the quasicontinuous final state being provided primarily by nonradiative line broadening. In general, such a rate expression applies so long as the donor–acceptor electronic coupling is less than the vibronic band width. The strong coupling limit is shown to result in excimer or exciplex-type emission. A rate equation formalizing donor–acceptor EET in general is determined by consideration of the Green’s function methods of scattering theory. The role of nuclear coordinates, including the possibility of Herzberg–Teller coupling, and the influence of nonradiative processes are examined.

Generalization of the Maxwell-Bloch equations to the case of strong atom-field coupling.

We derive the generalized set of Maxwell-Bloch equations which takes into account the dependence of relaxation coefficients on the amplitude and frequency of the coherent field. This has interesting implications in many problems in quantum optics and laser physics, e.g., the problem of lasing without inversion due to a strong coherent generating field.

Optical measurements of the superconducting gap in single-crystal K3C60 and Rb3C60

THE mechanism of superconductivity in alkali-metal compounds of C6o (refs 1, 2) remains controversial. Electron-pairing mechanisms based on electron-phonon coupling involving both low-frequency (intermolecular) vibrations3 and high-frequency (intramolecular) modes4,5—the strong-coupling and weak-coupling cases respectively—have been proposed. These two mechanisms have different associated energy scales, which is reflected in the magnitude of the superconducting energy gap. Measurements of the gap for these compounds have been reported previously for powder samples6–8, but are somewhat discrepant or ambiguous, perhaps owing to grain-size or grain-junction effects. Here we report measurements on large single-crystal samples of K3C60 and Rb3C60 using optical reflectivity. We obtain values for the reduced gap ratio, 2Δ/k8Tc of 3.44 and 3.45 respectively, consistent with predictions for a mechanism based on standard Bardeen-Cooper-Schrieffer (BCS) electron-phonon coupling to intramolecular modes.

Strong-coupling corrections to the Bardeen-Cooper-Schrieffer ratios for a d-wave superconductor.

We have calculated, for a d-wave superconductor, the strong-coupling corrections to the Bardeen-Cooper-Schrieffer (BCS) ratios: \ensuremath{\Delta}C(${\mathit{T}}_{\mathit{c}}$)/\ensuremath{\gamma}${\mathit{T}}_{\mathit{c}}$,2${\mathrm{\ensuremath{\Delta}}}_{0}$/${\mathit{T}}_{\mathit{c}}$,\ensuremath{\gamma}${\mathit{T}}_{\mathit{c}}^{2}$/${\mathit{H}}_{\mathit{c}}^{2}$(0), ${\mathit{h}}_{\mathit{c}}$(0) as well as the ratios for the normalized slope in the specific-heat jump at ${\mathit{T}}_{\mathit{c}}$ and London penetration depth. We have used a step-function approximation for the gap function and considered an Einstein spectral density for the bosons. We have obtained terms up to O(${\mathit{T}}_{\mathit{c}}^{4}$/${\mathrm{\ensuremath{\omega}}}_{\mathit{E}}^{4}$) (here ${\mathit{T}}_{\mathit{c}}$/${\mathrm{\ensuremath{\omega}}}_{\mathit{E}}$ is the strong-coupling parameter and ${\mathrm{\ensuremath{\omega}}}_{\mathit{E}}$ is the Einstein energy). While our results are approximate for the strong-coupling cases, the weak-coupling results are exact. These weak-coupling ratios are no longer universal and depend on the d-wave considered. Our formulas are also applicable for some extended s-wave superconductors which have a basis function with a zero average over the Fermi surface.

Theory of One-Dimensional Hopping Conductivity

The frequency-dependent conductivity σ(ω) in a one-dimensional hopping-model system, formed of two sublattices with one species of particles, is investigated by means of the three-site approximation of the path probability method (PPM) and the Monte Carlo simulation (MCS). In a strong-coupling case, where the two-site approximation is rather in poor agreement with the MCS, the three-site approximation is satisfactory enough to reproduce the MCS within the present model

Path-integral analysis of the propagator of two coupled graded-index waveguides

The method of path integration is used to study coupled graded-index waveguides in the context of paraxial, scalar-wave optics. The cases of strong and intermediate strength coupling for waveguides of arbitrary and variable spacing are considered, and a variational estimate of the propagator of such waveguide structure is derived in closed form. The complete variational calculation is presented for the case of parallel waveguides only, and the propagator, lowest-order-mode field profile, the first two lowest-order-mode propagation constants, and the beat length of the structure are determined in closed form.

On the sign ambiguity of triplet phases in nonsystematic many-beam effects in CBED patterns

The possibility to determine not only the magnitude but also the sign of three-phase structure invariants from nonsystematic many-beam effects in convergent-beam electron diffraction (CBED) patterns is discussed. From the full dynamical many-beam intensity expression it is clear that it is a principal difference between equivalent three-beam cases of opposite sign of the triplet phases. However, the difference and thus the ability to distinguish between the two cases depends strongly both on the relative magnitude of the structure factors involved and the specimen thickness for which the actual CBED discs are obtained. The largest differences are obtained for a weakly coupled three-beam case where the intensity in the line of the primary reflection, which in this case coincides with the kinematical two-beam position, has a distinct maximum or minimum at the three-beam condition depending on the sign of the triplet phase. In a strong coupling case where the intensity in the primary-reflection line near the three-beam condition is split into two individual segments, the differences are generally less and are not so obvious and quantitative measurements are necessary to distinguish the two cases of opposite sign of the triplet phases. Calculated examples with respect to a nonsystematic three-beam example in the noncentrosymmetric InP are given.

Crosstalk analysis for high-speed pulse propagation in lossy electrical interconnections

The effects of interconnection loss (both DC loss and skin effect loss) on crosstalk noise for a coupled lossy interconnection system, with various termination conditions, coupled lengths, spacings, and interconnection structures (microstrip lines versus strip lines) are investigated. Fourier transform techniques and numerical methods are applied to solve the coupled transmission line equations for the strong coupling case (mutual coupling between the active line and the quiet line). The interconnection is either terminated by its approximated matched load impedance, R/sub o/, or by the equivalent loading capacitance of the receiver, C/sub L/. General design guidelines for controlling the crosstalk noise and reflection noise in lossy interconnections are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Reflection of electromagnetic radiation from a multilayer waveguide structure with an absorbing metal layer

The angular distribution of the reflection coefficient of an asymmetric multilayer planar structure containing a thin metal film and a planar optical waveguide has been found by accurate numerical calculations. There are resonances in the reflection coefficient associated with hybrid modes of the structure. The cases of strong and weak coupling of the surface polariton modes with the waveguide modes are discussed. The results of the numerical analysis agree with solutions of Maxwell's equations for a multilayer planar structure.