Analytic extension of the coherent potential approximation to clusters

We put forward the homomorphic cluster coherent potential approximation (HCPA) for substitutionally disordered systems as one possible way of avoiding the breakdown of analyticity in average Green's functions even when effects of clusters are properly taken into account. We assert that a cluster CPA yields an analytic physical solution if a one-particle total Hamiltonian is partitioned into the sum of homomorphic single-cluster Hamiltonians and the CPA condition is applied to one of these homomorphic sub-Hamiltonians.     

Magnetoconductivity of disordered two dimensional tight binding electrons in CPA

The magnetotransport properties of a tight binding model of electrons on a two dimensional square lattice with diagonal disorder and in a perpendicular magnetic field is investigated. The disorder is treated in the coherent potential approximation (CPA) and a quasiclassical solution of the Harper equation is used to calculate the one particle Green's function. Analytical expressions for the CPA vertex corrections to the magnetoconductivity are derived. Numerical results for the density of states and the diagonal magnetoconductivity are discussed. The vertex correction vanishes if the Harper band width is neglected.     

Rigorous proof for analyticity of the homomorphic cluster coherent potential approximation

We rigorously prove that the homomorphic coherent potential approximation (HCPA) is analytic. Along a way analogous to the proof for the analyticity of the molecular coherent potential approximation by Ducastelle, we show the HCPA always provides a physical solution for the average Green's function which satisfies (i) the reality, (ii) definiteness, (iii) analyticity and (iv) boundary conditions.     

Effective-medium theory for goldstone systems with off-diagonal disorder

An effective medium theory for low temperature phonons and other Goldstone excitations with diagonal and off-diagonal disorder is developed which preserves the herglotz property of the self-energy and is correct in both dilute limits c→0 and c→1.     

Electronic theory of surface segregation in the coherent potential approximation: The surface segregation in CoNi, IrPt and RhPt

The surface segregation in CoNi, IrPt and RhPt is calculated within the coherent potential approximation. It is assumed that the metals form substitutional alloys and only diagonal disorder is taken into account. The condition of the local neutrality resulting in the presence of diagonal potentials in the Hamiltonian is also introduced. The alloys are selected in such a way that: (i) the non-diagonal disorder can be neglected with a relatively good approximation, (ii) the d-band filling is not too large to ensure the procedure of determining diagonal potentials from the local neutrality condition to work properly and (iii) the experimental data are available.     

Assessment of the coherent potential approximation for the absorption spectra of a one-dimensional Frenkel exciton system with a Gaussian distribution of fluctuations in the optical transition frequency

We investigate the accuracy of the coherent potential approximation (CPA) for the optical absorption spectra of a one-dimensional Frenkel exciton system with nearest-neighbor interactions and a Gaussian distribution of fluctuations in the optical transition frequency (diagonal Gaussian disorder). Our earlier studies have established that the CPA gives highly accurate results for the integral of the density of states of this system. In this paper we compare the CPA results for the normalized optical absorption with the finite-array calculations of Schreiber and Toyozawa and Schreiber for the same model. It is found that the CPA results for the absorption are in good agreement with their findings. It is pointed out that an expansion of the density of states in terms of the eigenstates of the ideal (no disorder) array contains a term proportional to the normalized absorption. Since the density of states is accurately approximated by the CPA, the presence of this term explains the success of the CPA in reproducing the absorption spectra. Our findings support the use of the Gaussian disorder model to interpret the absorption spectra of one and quasi-one dimensional exciton systems.     

Zero Energy Anomaly in One-Dimensional Anderson Lattice with Exponentially Correlated Weak Diagonal Disorder

We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the correlation of the disorder increases. We found that higher order terms of the correlation must be included into the current perturbation result in order to give the correct localization length, and to connect smoothly the anomaly at zero correlation with the perturbation result for large correlation.     

Zero Energy Anomaly in One-Dimensional Anderson Lattice with Exponentially Correlated Weak Diagonal Disorder

We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the correlation of the disorder increases. We found that higher order terms of the correlation must be included into the current perturbation result in order to give the correct localization length, and to connect smoothly the anomaly at zero correlation with the perturbation result for large correlation.     

Cluster approaches to random alloys: An appraisal

Some of the cluster extensions of the coherent potential approximation (CPA) based on the effective medium theory have been critically studied with respect to the decoupling schemes involved in them. Their computational tractability has been examined and it has been found that theself-consistent calculations in three-dimensional systems are immensely difficult to perform. A self-consistent calculation has been reported for simple cubic lattices with diagonal and off-diagonal disorder using a pair-CPA method. A significant finding of the paper is that it has been shown thatnon-analyticities are a general feature of extensions of CPA within multiple scattering framework. The non-analyticities were reported several times but a general proof of their existence was not noticed. It was also believed that the so-called molecular—CPA is analytic, this has been shown to be wrong here. The density of states results with off-diagonal randomness have been qualitatively understood to yield some information about the influence of off-diagonal randomness on Anderson localisation of an electron.     

无序对金属超晶格电子结构的影响——CPA方法

本文用一种简单的哈密顿模型,在紧束缚近似下,只计及对角矩阵元的无规分布,用CPA方法自洽地计算了无序所引起的金属超晶格电子结构的变化,给出了某些参数下局部态密度和自能曲线。 关键词：     

Numerical results for Anderson localisation in the presence of off-diagonal disorder

Numerical calculations of the inverse participation ratio have been performed for the diamond cubic lattice with nearest neighbour interactions, and both diagonal and off-diagonal disorder. We confirm the prediction of Economou and Antoniou that off-diagonal disorder cannot, per se, produce an Anderson transition, although it reduces the amount of diagonal disorder necessary for the transition. In the presence of off-diagonal disorder alone we do not detect any substantial localisation even in the wings of the band.     

Lorentz violation, two-time physics, and strings

The aim of this paper is to study the generalization of the relativistic particle recently proposed by Kostelecký. An alternative action for this system is presented, and it is shown that this action can be interpreted as a particle in curved space. Furthermore, the following results are established for the model: (i) there exists a limit where the system has more local symmetries than the usual relativistic particle; (ii) in this limit when Lorentz symmetry is restored, a direct relationship with the two-time physics is determined; (iii) if also Poincaré symmetry is recovered, the action of a relativistic bosonic string is obtained.     

Berry phases in the three-level atoms driven by quantized light fields

A theoretical analysis of Berry’s phases is given for the three-level atoms interacting with external one-mode and two-mode quantized light fields. Three main results are obtained: (i) There is a Berry phase which vanishes in the classical limit or this Berry phase is completely induced by the field quantization; (ii) Berry’s phases for the one-mode field and the two-mode field can be equal so long as the photon numbers of the two-mode field are properly chosen; (iii) In the two-mode case, Berry phases of the atom interacting with one mode is affected by the other mode even if the photon number of the other mode is zero.      

On the way towards a nonsingular gravitational collapse-the properties of the Yang-Mills cosmos

Adding gravitational self-interaction to general relativity in an intrinsic way changes drastically the behavior of a physical system under gravitational collapse. In our analysis of this question for homogeneous and isotropic matter distributions we show that (i) theSO(1,3) gauge theory of gravity of the Yang-Mills type has the correct Newtonian limit for the late universe, (ii) it defines intrinsically a dynamical gravitational stressenergy-momentum tensorG T _ab , and (iii) negative self-energy always prevents homogeneous and isotropic matter from forming a big-bang singularity; if the present universe disposes of a positive self-energy, pair creation on the eve of the lepton era generates sufficient gravity to stop the fatal collapse.This essay received an honorable mention (1977) from the Gravity Research Foundation-Ed.Research fellow of Schweizerischer Nationalfonds.     

Nematics with quenched disorder: what is left when long range order Is disrupted?

It is now generally accepted that even low amounts of quenched disorder disrupt long-range order in anisotropic systems with continuous symmetry. However, very little is known on the key item of the nature of the residual order, if any, and particularly if this has quasi-long-range or truly-short-range character. Here we address this problem both experimentally for the nematic 6CB in dilute aerosils and with computer simulations. We find that the residual order is short ranged and scales with disorder density in agreement with the Imry-Ma argument.     

Wetting Transition on a One-Dimensional Disorder

We consider wetting of a one-dimensional random walk on a half-line x≥0 in a short-ranged potential located at the origin x=0. We demonstrate explicitly how the presence of a quenched chemical disorder affects the pinning-depinning transition point. For small disorders we develop a perturbative technique which enables us to compute explicitly the averaged temperature (energy) of the pinning transition. For strong disorder we compute the transition point both numerically and using the renormalization group approach. Our consideration is based on the following idea: the random potential can be viewed as a periodic potential with the period n in the limit n→∞. The advantage of our approach stems from the ability to integrate exactly over all spatial degrees of freedoms in the model and to reduce the initial problem to the analysis of eigenvalues and eigenfunctions of some special non-Hermitian random matrix with disorder-dependent diagonal and constant off-diagonal coefficients. We show that even for strong disorder the shift of the averaged pinning point of the random walk in the ensemble of random realizations of substrate disorder is indistinguishable from the pinning point of the system with preaveraged (i.e. annealed) Boltzmann weight.     

Applications of the CPA to elemental tetrahedrally bonded amorphous semiconductors

It is pointed out that the CPA can easily be coupled with multiband, nearest-neighbor tight-binding Bethe-lattice Hamiltonians to fruitfully study the electronic structure of tetrahedrally bonded elemental amorphous semiconductors. Results are presented which illustrate the effects on the model semiconducting gap of (i) a rectangular distribution of site diagonal terms in the Hamiltonian, and (ii) vacancies distributed randomly over the lattice. The relationship of these results to experiment is briefly explored.     

Glassy synchronization in a population of coupled oscillators

A phase model for a population of oscillators with random excitatory and inhibitory mean-field coupling and subject to external white noise random forces is proposed and studied. In the thermodynamic limit different stable phases for the oscillator population may be found: (i) an incoherent state where all possible values of an oscillator phase are equally probable, (ii) a synchronized state where the population has a nonzero collective phase; (iii) a glassy phase where the global synchronization is zero but the oscillators are in phase with the random disorder; and (iv) a mixed phase where the oscillators are partially synchronized and partially in phase with the disorder. These predictions are based upon bifurcation analysis of the reduced equation valid at the thermodynamic limit and confirmed by Brownian simulation.     

Influence of interstitials and non magnetic impurities on the Kondo effect

The influence of interstitials and non magnetic impurities on the anomalous resistivity, thermopower and Kondo temperature of dilute magnetic alloys was investigated generalizing a model proposed by Bohnen and Fischer. Numerical results are given as a function of the distance between the interstitial (or non magnetic impurity) and the magnetic impurity using their scattering phase shifts as parameters. The Kondo anomalies are altered considerably, if the magnetic impurity is very close to the non magnetic scattering potential, e.g. if it is part of an interstitial dumbbell.This work is part of a doctoral thesis of G.Wehr at the Technische Universität München