A simple green function approach to the Dicke model with external fields

Using the technique of double-time temperature-dependent Green functions, the lack of phase transition in the Dicke model with external fields is proved.     

Electronic states in superlattices: A new theoretical approach within the memory function formalism

A new approach is proposed for studying the electronic structure of superlattices. The novelty consists in our efficiently combining standard k-space and memory function methods for describing the electron motion perpendicular and parallel to the superlattice axis, respectively. Our approach is computationally manageable and can account for charge transfer at the layer interfaces.     

Memory function approach to the Ziman formula for the electrical conductivity in liquid metals

The Ziman formula for the electrical conductivity and its generalization including dynamical correlations are discussed from the memory function approach.     

A simple approach to evaluation of lattice sums

It is shown that starting from a Fourier transform relation one can derive, in a surprisingly simple manner, all the well-known results of lattice summation, that have been obtained so far by a complicated use of the Ewald theta transformation. We show that the Ewald transformation follows directly from the Fourier transform relation.     

A green function approach to shear viscosity coefficient

Modified transport equations are derived from Kadanoff and Baym kinetic equations, suitable for the study of thermal transport coefficients. These equations include the Hartree average energy term which has been ignored in the previous studies of thermal transport coefficients. They are linearised and the successive perturbation method is employed to solve them. The solutions are applied to shear viscosity coefficient of gases and the results are compared with the recent experimental measurements for several complex and simple gases. The potential assumed is a hard core one with a perturbation tail. The agreements are particularly good for gases with low molecular weight and in the high temperature range. For complex molecules even in the low temperature range, the agreement is better than the previous calculations. The formula derived yields the explicit temperature dependence of the viscosity coefficient.     

Self-consistent green function approach for calculation of electronic structure in transition metals

We present an approach for self-consistent calculations of the many-body Green function in transition metals. The distinguishing feature of our approach is the use of one-site approximation and the self-consistent quasiparticle wave function basis set obtained from the solution of the Schr?dinger equation with a nonlocal potential. We analyze several sets of skeleton diagrams as generating functionals for the Green function self-energy, including GW and fluctuating exchange sets. Calculations for Fe and Ni revealed stronger energy dependence of the effective interaction and self-energy of the d electrons near the Fermi level compared to s and p electron states.     

Memory function parametrization in the GLE-Ghost atom formalism: A microscopic approach

The memory function used in the GLE approach to solid atom motion is modeled as a generalization of the position autocorrelation function for a multidimensional Brownian oscillator. The exact microscopic memory function and the assumed form are required to agree in two limits: at short times and for the low frequency density of states. This suffices to specify all the parameters, including those which control the memory of correlated motion between primary zone atoms as mediated by the rest of the solid. Determination of these parameters utilizes as the fundamental input the frequency matrix for the solid. An example is presented for various fcc solid surfaces assuming Lennard-Jones (12, 6) forces between the solid atoms. The approach is capable, in principle, of treating such interesting structures as high Miller index surfaces, molecular solids and adsorbed species while retaining only a small number of primary zone atoms.     

A simple formalism for the BPS monopole

A simple formalism for the BPS monopole is obtained by generalizing the ADHM construction of multi-instantons to a Hilbert space. Both the potential itself and the Green's functions for different isospin can be obtained with very little effort from the instanton formulae.     

A green function approach to the relaxation time of phonon assisted tunneling

Although many elegant formulations of the phonon assisted tunneling problem have been given, the calculation of the relaxation time itself always has been based on the “golden rule”, which requires the artifice of a fictitious static field. In this communication the relaxation time is given by means of linear response theory, unitary transformations and an application of the Bogoliubov inequality. The artifice of a static field is no longer required.     

A green function approach to the paramagnetic phase of a Heisenberg ferromagnet

A higher-order decoupling similar to the first-order Bogolyubov-Tyablikov decoupling is used to find various correlation functions in the paramagnetic region for a Heisenberg ferromagnet. Expressions are given for the susceptibility, the nearest-neighbor correlation, and autocorrelation at the critical point as well as at high temperatures.This paper is based on the first author's Oxford University D. Phil, thesis. A preliminary account has been published elsewhere. (¹)     

A field theoretical approach to the anomalous hall effect in semiconductors

The anomalous Hall effect for polarized electrons in semiconductors is calculated by a field theoretical method. The results obtained are essentially equivalent to those of Luttinger except for minor generalizations (the treatment of collisions is not limited to the first term in a Born expansion and the conductivity is calculated at finite frequency). The main purpose is to set a very simple formulation that can be used to treat more complicated problems, e.g. anomalous Hall effect in the presence of a magnetic field or with a resonant precessing spin magnetization. The existence of two distinct contributions to the anomalous Hall effect is clearly shown, one of which is missed in the transport equation formulation. The order of magnitude of each contribution is discussed for two different experimental situations.     

High frequency conductivity in the quantum hall regime

We have measured the complex conductivity sigma(xx) of a two-dimensional electron system in the quantum Hall regime up to frequencies of 6 GHz at electron temperatures below 100 mK. Using both its imaginary and real part we show that sigma(xx) can be scaled to a single function for different frequencies and several transitions between plateaus in the quantum Hall effect. Additionally, the conductivity in the variable-range hopping regime is used for a direct evaluation of the localization length xi. Even for large filling factor distances deltanu from the critical point we find xi approximately equals deltanu(-gamma) with a scaling exponent gamma = 2.3.     

On the theory of hall conductivity in disordered systems

A general formula for the Hall conductivity, which is exact in the one-particle approximation, has been obtained. Making use of this formula, the Hall coefficient for small polarons has been calculated.     

A new mechanism for the anomalous hall coefficient with application to liquid metals

The effect of spin-orbit coupling of conduction electrons on the Hall coefficient of liquid metals is studied and a new mechanism for the anomalous Hall coefficient is suggested. S.O. coupling causes asymmetric scattering and a current, perpendicular to the magnetic field and to the electric field, is set up. This leads to an additional Hall coefficient , as was first calculated by Luttinger. But S.O. coupling also causes a dipole to appear near each ion, leading to an electrical polarization and an additional Hall coefficient,R _so.R _so is calculated for liquid normal metals and transition metals to first order in S.O. coupling. In normal metals,R _so and are proportional to the Pauli susceptibility. Both are positive for electron-like charge carriers. S.O. coupling leads to a maximum deviation from nearly free electron value in the Hall coefficient of a heavy, four or five-valent liquid metal with short mean free path. In transition metals, different expressions are obtained forR _so depending whether localized moments are present (magnetic model) or not (non-magnetic model). The sign ofR _so is determined by the value of thed-phase shift alone.R _so is proportional to the susceptibility ofd-electrons and can be large, leading to a positive Hall coefficient in the liquid transition metal.     

Lifetimes of long wavelength longitudinal phonons in impure metals

The standard Green function theory of electron-phonon interaction in metals is extended to include the effect of impurities moving with the lattice. The importance of various diagrams in the perturbation expansion of the phonon Green function is discussed in the light of the accepted theories of ultrasonic absorption in impure metals. The screened impurity potential is treated as arbitrary function of the scattering angle.     

Pseudoclassical approach to electron and ion density correlations in simple liquid metals

Il Nuovo Cimento D - Electron-electron and electron-ion structural correlations in simple liquid metals are treated by using effective pair potentials to incorporate quantal effects into a...     

A general approach to polarisation conductivity

A general modelisation of the polarisation conductivity is envisaged. This approach is justified by the nature of this property which is the manifestation of dissipation processes accompanying the propagation of an electrical field inside a solid. The evocation of the fluctuation phenomenon constitutes an interesting possibility to describe this reorganisation at a microscopic scale of the studied system.