Self-consistent theory of localization for the Anderson model

The self-consistent theory of electron localization in a random system in the form proposed by Vollhardt and Wölfle is generalized for the analysis of localization in the Anderson model. We derive the general equations appropriate for the system with rather general form of the electronic spectrum. Explicit calculations are restricted to the lattices of cubic symmetry and use the effective mass approximation to obtain the final results. Anderson's critical ratio for the localization of all the electronic states in the tight-binding band is evaluated and found to be in surprisingly good agreement with the results of numerical analysis of localization in the Anderson model.     

Self-consistent treatment of the polaron damping in the Holstein model

Using the Holstein model, the damping of the localized polaron state and the small polaron conductivity are represented by the series of contributions from the multiphonon processes in which the polaron damping is taken into account. The self-consistent treatment of the damping shows the enhancement of the small-polaron relaxation rate by the quantum fluctuations of the lattice corresponding to the energy non-conserving phonon processes. The conditions for the polaron localization as well as the dependence of the d.c. conductivity on the electron transfer integral are discussed.     

Self-consistent treatment of one-gluon exchange in the soliton bag model

In the context of the soliton bag model, the quarks, soliton field and the gluon propagator are calculated self-consistently in the mean-field, one-gluon exchange approximation. The use of a confined propagator, as compared with a free propagator, is primarily to change the effective quark-gluon coupling constant by a factor of approximately two in the case of static, spherical bags. Self-consistency leads to only a small improvement in the fit to physical data, after readjustment of model parameters. Nevertheless, use of a confined propagator is expected to have an important effect on deformed bags and in dynamical calculations.     

Self-consistent quasi-particle model

Here we review the recently developed self-consistent quasi-particle model of QGP and apply it to fit the lattice QCD data on (2+1) flavor QGP.     

A variational treatment of the periodic Anderson model with antiferromagnetic order

We discuss a variational ground state wave function for the symmetric periodic Anderson model with commensurate spin density order. The energy of this ansatz is evaluated in closed form. Our approach generalizes a variational treatment proposed recently by Strack and Vollhardt and results in significantly lower energy. Contrary to the Gutzwiller ansatz the wave function recovers the Schrieffer-Wolff limit for large Coulomb repulsion. We clarify the relation of our approach to unrestricted Hartree-Fock and present a comparison with existing quantum Monte Carlo calculations for one dimension.     

Spectral properties of the Anderson model

An investigation of the one particle spectrum of the (impurity-) Anderson model within the time ordered perturbation approach is presented. The approximation used includes all processes without crossing band electron lines and does not make use of the Brillouin-Wigner scheme. Foregoing treatments are thus generalized in essential points. Local self energies are determined by two coupled integral equations which are solved numerically. Numerical procedures and the validity of the approximation are thoroughly tested for the resonant level model, which deals with only one spin component and is exactly solvable. Calculated spectra for the Anderson model in all regimes of temperature and of local level position are discussed. A remarkable improvement over earlier attempts is found. Connection to the resonant level model is made by analytical continuation in the number of spin components. The approximation is placed into a general context of a conserved skeleton diagram expansion. It is pointed out how it can systematically be improved, and some exact formulas are derived.     

Parabolic problems for the Anderson model

The objective of this paper is a mathematically rigorous investigation of intermittency and related questions intensively studied in different areas of physics, in particular in hydrodynamics. On a qualitative level, intermittent random fields are distinguished by the appearance of sparsely distributed sharp peaks which give the main contribution to the formation of the statistical moments. The paper deals with the Cauchy problem (/t)u(t,x)=Hu(t, x), u(0,x)=t ₀(x) 0, (t, x) ₊ × ^d , for the Anderson HamiltonianH = + (·), (x),x d where is a (generally unbounded) spatially homogeneous random potential. This first part is devoted to some basic problems. Using percolation arguments, a complete answer to the question of existence and uniqueness for the Cauchy problem in the class of all nonnegative solutions is given in the case of i.i.d. random variables. Necessary and sufficient conditions for intermittency of the fieldsu(t,·) ast are found in spectral terms ofH. Rough asymptotic formulas for the statistical moments and the almost sure behavior ofu(t,x) ast are also derived.     

Lifschitz tails for the Anderson model

We present, in an expository way, an elementary rigorous proof (patterned after an argument of Kirsch-Martinelli) that the Anderson model has Lifschitz tails in very great generality.Research partially supported by USNSF Grant No. MCS-81-20833.     

Quasiparticle lifetimes in the Anderson model

Quasiparticles identified with the maxima in the local density of states for the Anderson model are shown to have a relatively long lifetime. This explains why particular configurations of the impurity orbital can be independently detected in the experiment.     

Partition function for the Anderson model

A new approach to the Anderson localized magnetic moment model is given, using the functional integral method. The partition function is explicitely given in an approximation suitable for strong coupling.     

Self-consistent treatment of a phase transition

A self-consistent treatment of a phase transition with a scalar order parameter in the ordered and disordered state is described. The factorization of the correlation functions in the disordered phase leads to a shift of the transition temperature, a linear divergence (=1) for the correlation length, a quadratic divergence (=2) for the susceptibility, and a finite value (=–1) for the specific heat. In the ordered phase the factorization of the correlation functions leads to no divergences in the correlation length and susceptibility. A study of the free energy shows that order persists above the transition temperature found by assuming disorder. The requirement of thermodynamic stability induces a first-order transition at a temperature which lies between the bare transition temperature and the shifted one.Supported in part by NSF grant No-GP-17560.This work is in partial fulfillment of Ph.D. requirements at Brandeis University.     

Self-consistent cluster-Bethe-lattice study of two-band alloy model

The cluster-Bethe-Lattice method is applied to a model two-band alloy. Intra-atomic Coulomb interactions are taken into account within the Hartree-Fock approximation. Charge transfer effects are treated self-consistently. A numerical calculation with parameters appropriate for the AuAg system yields results which are in qualitative agreement with experiments.     

Self-consistent Gaussian model of nonperturbative QCD vacuum

We show that the minimal Gaussian model of nonlocal vacuum quark and quark-gluon condensates in QCD violates the transverse character of the correlator of two vector currents. We suggest the improved Gaussian model of the nonperturbative QCD vacuum, which respects QCD equations of motion and minimizes the revealed gauge-invariance breakdown. We obtain the refined values of pion distribution amplitude (DA) conformal moments 〈ξ^2N 〉_π (N = 1, ..., 5) using the improved QCD vacuum model, including the inverse moment 〈x ^?1〉_π, being inaccessible if one uses the standard QCD SR. We construct the allowed region for Gegenbauer coefficients a ₂ and a ₄ of the pion DA for two values of the QCD vacuum nonlocality parameter, λ _q ² = 0.4 and 0.5 GeV².