Low-energy quasiparticles in high- T c cuprates

The aim of this review is to summarize existing experimental investigations on the nature of the low-energy quasiparticle excitations in high- T c cuprates, and to examine critically recent claims of consistency between the experimentally determined low-temperature thermodynamic and transport properties in certain cuprates and theoretical predictions based on standard perturbation theory for a BCS d-wave superconductor. Measurements of the low-temperature specific heat, thermal conductivity, microwave conductivity, penetration depth and scanning tunnelling microscopy are described, both in the Meissner state and in the mixed state. These results are then compared with the predictions of quasi-classical theory of a d-wave BCS superconductor and the self-consistent T-matrix approximation for both a single impurity and a finite impurity concentration. Detailed inspection reveals that significant discrepancies still exist between experiment and theory, with important implications for the development of a coherent model, perhaps beyond standard perturbation theory. Finally, I discuss how considerations of the possible effects of band structure, anisotropic scattering and low carrier concentration in the underdoped region of the cuprate phase diagram might reconcile some of the discrepancies that have emerged.     

Higher-order radiative perturbation theory

As a computationally effective tool, the first-order term of the radiative perturbation theory has been computed successfully, and has been applied in a number of areas. In this article, we develop the computational expressions for the higher-order terms of the perturbation expansion in a plane parallel atmosphere. These expressions are then implemented, and numerical results for some typical cases are presented. These results indicate that the computation is successful and that the higher-order terms are essential in cases where the first-order term alone cannot predict the perturbation with sufficient accuracy.     

The region of validity of perturbation theory

We present a study of the region of validity of perturbation theory applied to rough surface scattering. We solve numerically the case of a periodic surface or grating varying in one dimension. For a statistical ensemble of gratings with a sufficiently long period one may obtain a good approximation of rough surface scattering. We use this to test the validity of perturbation theory.

Only the perfect conductor case was considered. We find that as the grazing angle becomes small the perturbation result for the TE (E horizontal) polarization remains valid, while for the TM (E vertical) polarization it breaks down. The results show that the perturbation results should be used carefully when being compared with experimental data at grazing angles.     

Percus-Yevick theory and the Chandler-Weeks-Andersen reference fluid

Chandler, Weeks and Andersen have recently developed a successful perturbation theory of liquids. In their theory, the radial distribution function of the reference fluid is calculated from that of the hard-sphere fluid. In their published work, the Percus-Yevick theory is used to calculate the hard-sphere radial distribution function. In this paper, the Percus-Yevick theory is used to calculate directly the thermodynamic properties and radial distribution function of the reference fluid. If the Carnahan and Starling averaging procedure is used, the Percus-Yevick thermodynamic properties are excellent. However, the radial distribution function shows the same discrepancies as that of Chandler, Weeks and Andersen. Finally, recent calculations of Chandler, Weeks and Andersen, using the Monte Carlo estimates of the hardsphere radial distribution function are shown to give good results for the reference fluid distribution function. This indicates that the Percus-Yevick theory, rather than fundamental errors in the Chandler, Weeks and Andersen theory, is responsible for the discrepancies.     

A theory of magneto-optical rotation in diamagnetic molecules of low symmetry

A quantum-mechanical theory for the Faraday effect in polyatomic molecules is developed along the lines of the general theory on natural optical rotation presented by Rosenfeld, Condon, et al.

The stationary perturbation of a magnetic field and the time-dependent perturbation of a light wave are treated simultaneously by means of a second-order time-dependent perturbation theory. The treatment is restricted to molecules having non-degenerate wavefunctions and zero spin. The moment of a single molecule, in the presence of a magnetic field and a light wave, is calculated in Part I. In Part II the average electric and magnetic moments per molecule are used in macroscopic optical equations to determine the Verdet constant, which is shown to be non-vanishing for the molecules under consideration. A discussion of the results will be given subsequently, in Part III of this work.     

The region of validity of perturbation theory

Abstract

We present a study of the region of validity of perturbation theory applied to rough surface scattering. We solve numerically the case of a periodic surface or grating varying in one dimension. For a statistical ensemble of gratings with a sufficiently long period one may obtain a good approximation of rough surface scattering. We use this to test the validity of perturbation theory.

Only the perfect conductor case was considered. We find that as the grazing angle becomes small the perturbation result for the TE (E horizontal) polarization remains valid, while for the TM (E vertical) polarization it breaks down. The results show that the perturbation results should be used carefully when being compared with experimental data at grazing angles.     

Quasiparticle self-consistent GW theory

In past decades the scientific community has been looking for a reliable first-principles method to predict the electronic structure of solids with high accuracy. Here we present an approach which we call the quasiparticle self-consistent approximation. It is based on a kind of self-consistent perturbation theory, where the self-consistency is constructed to minimize the perturbation. We apply it to selections from different classes of materials, including alkali metals, semiconductors, wide band gap insulators, transition metals, transition metal oxides, magnetic insulators, and rare earth compounds. Apart from some mild exceptions, the properties are very well described, particularly in weakly correlated cases. Self-consistency dramatically improves agreement with experiment, and is sometimes essential. Discrepancies with experiment are systematic, and can be explained in terms of approximations made.     

Excited states from range-separated density-functional perturbation theory

We explore the possibility of calculating electronic excited states by using perturbation theory along a range-separated adiabatic connection. Starting from the energies of a partially interacting Hamiltonian, a first-order correction is defined with two variants of perturbation theory: a straightforward perturbation theory and an extension of the Görling–Levy one that has the advantage of keeping the ground-state density constant at each order in the perturbation. Only the first, simpler, variant is tested here on the helium and beryllium atoms and on the hydrogen molecule. The first-order correction within this perturbation theory improves significantly the total ground- and excited-state energies of the different systems. However, the excitation energies mostly deteriorate with respect to the zeroth-order ones, which may be explained by the fact that the ionisation energy is no longer correct for all interaction strengths. The second (Görling–Levy) variant of the perturbation theory should improve these results but has not been tested yet along the range-separated adiabatic connection.     

A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT

A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.     

Generalized wave coupling theory of linear electro-optic effect in absorbent medium

Starting from Maxwell’s equations and considering the linear electro-optic effect as a perturbation, we present a generalized wave coupling theory of linear electro-optic effect in absorbent medium. We give the rigorous solution of the resultant equations for a light wave propagating along any direction with an external dc electric field along an arbitrary direction. As an application, we use the theory to discuss the influence of absorption on the light wave in a KTP crystal. The results demonstrate that the absorption coefficients influence not only the amplitude but also the phase of the light wave.     

Time dependent canonical perturbation theory I: General theory

In this communication, we reanalyze the causes of the singularities of canonical perturbation theory and show that some of these singularities can be removed by using time-dependent canonical perturbation theory. A study of the local and global properties (in terms of the perturbation parameter) is also undertaken.     

Recent progress in the theory of the complex atomic hyperfine structure

The revised analysis of the hyperfine structure of the complex atoms on several selected examples has been performed. The complete set of corrections up to the second order perturbation theory has been taken into account and the accuracy of the wave functions in the intermediate coupling scheme has been carefully checked. The still remaining discrepancies suggest that the commonly used approximate model of the hyperfine structure might require revision. This revised version was published online in August 2006 with corrections to the Cover Date.     

Renormalization group and Fermi liquid theory

We give a Hamiltonian-based interpretation of microscopic Fermi liquid theory within a renormalization group framework. The Fermi liquid fixed-point Hamiltonian with its leading-order corrections is identified and we show that the mean field calculations for this model correspond to the Landau phenomenological approach. This is illustrated first of all for the Kondo and Anderson models of magnetic impurities which display Fermi liquid behaviour at low temperatures. We then show how these results can be deduced by a reorganization of perturbation theory, in close parallel to that for the renormalized φ⁴ field theory. The Fermi liquid results follow from the two lowest order diagrams of the renormalized perturbation expansion. The calculations for the impurity models are simpler than for the general case because the self-energy depends on frequency only. We show, however, that a similar renormalized expansion can be derived also for the case of a translationally invariant system. The parameters specifying the Fermi liquid fixed-point Hamiltonian are related to the renormalized vertices appearing in the perturbation theory. The collective zero sound modes appear in the quasiparticle-quasihole ladder sum of the renormalized perturbation expansion. The renormalized perturbation expansion can in principle be used beyond the Fermi liquid regime to higher temperatures. This approach should be particularly useful for heavy fermions and other strongly correlated electron systems, where the renormalization of the single-particle excitations are particularly large.

We briefly look at the breakdown of Fermi liquid theory from a renormalized perturbation theory point of view. We show how a modified version of the approach can be used in some situations, such as the spinless Luttinger model, where Fermi liquid theory is not applicable. Other examples of systems where the Fermi liquid theory breaks down are also briefly discussed.     

Effects of underwater sound and surface ripples on scattered laser light

The acousto-optic interaction at a water surface perturbed by random waves and by an underwater sound source is studied. The interferometric method is applied to measure the features of the power spectra of the scattered light field. Detection of sound-induced perturbation of the rough surface is performed. The corresponding theory of the scattered light spectra modulation is presented and its results are compared with the data of the experiment. Published in Russian in Akusticheskiĭ Zhurnal, 2008, Vol. 54, No. 2, pp. 244–250. The text was submitted by the authors in English.     

Polar magneto-optic Kerr effect in the near-light field of a small nonmagnetic particle

A theory of elastic light scattering by a small resonantly polarizing particle located near a flat surface of a magnetic medium has been developed. The effective polarizability of the particle was calculated self-consistently taking account of the dynamic “image forces” in all orders of perturbation theory in the interaction of the particle with the demagnetized ferromagnet, and the magneto-optic perturbation was determined to first order in the magnetization. In the case of a ferromagnet magnetized perpendicular to the surface, the light conversion factors and the magneto-optic corrections to the transverse cross sections of all processes in which the scattering of light by a particle and the polar magneto-optic Kerr effect are elementary events, have been calculated. The results, including an analysis of the near-field contribution to light scattering, comprise the physical foundation for constructing a theory of near-field magneto-optic spectroscopy of ferromagnets and magnetic structures. Fiz. Tverd. Tela (St. Petersburg) 39, 560–567 (March 1997)     

A reciprocal phase-perturbation theory for rough-surface scattering

We study the scattering of a scalar plane wave from a two-dimensional, randomly rough surface, on which the Dirichlet boundary condition is satisfied. The scattering amplitude is obtained in the form of the Fourier transform of an exponential, in which the exponent is written as an expansion in powers of the surface profile function. It is shown that the latter expansion can be written in such a way that the corresponding scattering matrix is manifestly reciprocal. Numerical results for the reflectivity, and for the contribution to the mean differential reflection coefficient from the incoherent component of the scattered field, are obtained and compared with the predictions of small-amplitude perturbation theory and the Kirchhoff approximation. As the wavelength of the incident wave is varied continuously the results of the phase-perturbation theory change continuously from those of the small-amplitude perturbation theory to those of the Kirchhoff approximation.     

Extension of the local curvature approximation to third order and improved tilt invariance

The second-order local curvature approximation (LCA2) is a theory of rough surface scattering that reproduces fundamental low and high frequency limits in a tilted frame of reference. Although the existing LCA2 model provides agreement with the first order small perturbation method up to the first order in surface tilt, results reported in this paper produce a new formulation of the model that achieves consistency with perturbation theory to first order in surface height and arbitrary order in surface tilt. In addition, extension of the modified LCA to third order is presented, and allows the theory to match the second-order small perturbation method to arbitrary order in surface tilt. Crucial to the development of the theory are a set of identities involving relationships among the small perturbation method (i.e. low frequency) and Kirchhoff approximation (i.e. high frequency) kernels; a set of new identities obtained in our derivations is also presented. Sample results involving 3D electromagnetic scattering from penetrable rough surfaces, as well as 2D scattering from Dirichlet sinusoidal gratings, are provided to compare the new results with the existing LCA2 model and with other rough surface scattering theories.     

Chemisorption phenomena: Analytic modeling based on perturbation theory and bond-order conservation

Tremendous advances in experimental studies of chemisorption revealed that many phenomena could not be understood and projected by the current theoretical constructs. We discuss some of the experimental puzzles that prompted a development of new analytic approaches to chemisorption based on general principles such as perturbation theory (PT) and bond-order conservation (BOC). The PT results concern the periodic regularities of the heat of chemisorption, the role of the antibonding adsorbate orbitals, and universal patterns of adsorbate-induced surface polarization Some of the PT findings are further corroborated within a much broader BOC approach. The BOC model and its postulates (including the use of a Morse potential) and diverse projections are thoroughly discussed. For atomic A and diatomic AB adsorbates, it is shown how the BOC model explicitly and rigorously interrelates a variety of seemingly disparate phenomena such as preferred adsorbate sites, the activation barriers for surface migration and dissociation, relations between atomic Q_A (Q_B) and molecular Q_AB heats of chemisorption, coverage and coadsorption effects on Q_A, overlayer phase transitions and island formation, the nature of promotion and poisoning. The model also projects possible intermediates and elementary steps of surface reactions. Although some of the findings are counter to commonly held perceptions, the whole picture of chemisorption is coherent and fits experiment well. The new conceptual understanding is stressed and some comments on the theory of chemisorption are made.