Self-Consistent Theory of Anderson Localization: General Formalism and Applications

The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered solids, the regimes of weak and strong localization are discussed. Then the scaling theory of the Anderson localization transition is reviewed. The renormalization group theory is introduced and results and consequences are presented. It is shown how scale-dependent terms in the renormalized perturbation theory of the inverse diffusion coefficient lead in a natural way to a self-consistent equation for the diffusion coefficient. The latter accounts quantitatively for the static and dynamic transport properties except for a region near the critical point. Several recent applications and extensions of the self-consistent theory, in particular for classical waves, are discussed.Comment: 25 pages, 2 figures; published version including correction

Transport through asymmetric two-lead junctions of Luttinger liquid wires

We calculate the conductance of a system of two spinless Luttinger liquid wires with different interaction strengths g_1, g_2, connected through a short junction, within the scattering state formalism. Following earlier work we formulate the problem in current algebra language, and calculate the scale dependent contribution to the conductance in perturbation theory keeping the leading universal contributions to all orders in the interaction strength. From that we derive a renormalization group (RG) equation for the conductance. The analytical solution of the RG-equation is discussed in dependence on g_1, g_2. The regions of stability of the two fixed points corresponding to conductance G=0 and G=1, respectively, are determined.Comment: 6 pages, 3 figures, REVTE

Transport of interacting electrons through a potential barrier: nonperturbative RG approach

We calculate the linear response conductance of electrons in a Luttinger liquid with arbitrary interaction g_2, and subject to a potential barrier of arbitrary strength, as a function of temperature. We first map the Hamiltonian in the basis of scattering states into an effective low energy Hamiltonian in current algebra form. Analyzing the perturbation theory in the fermionic representation the diagrams contributing to the renormalization group (RG) \beta-function are identified. A universal part of the \beta-function is given by a ladder series and summed to all orders in g_2. First non-universal corrections beyond the ladder series are discussed. The RG-equation for the temperature dependent conductance is solved analytically. Our result agrees with known limiting cases.Comment: 6 pages, 5 figure

Nonequilibrium Transport through a Kondo Dot: Decoherence Effects

We investigate the effects of voltage induced spin-relaxation in a quantum dot in the Kondo regime. Using nonequilibrium perturbation theory, we determine the joint effect of self-energy and vertex corrections to the conduction electron T-matrix in the limit of transport voltage much larger than temperature. The logarithmic divergences, developing near the different chemical potentials of the leads, are found to be cut off by spin-relaxation rates, implying that the nonequilibrium Kondo-problem remains at weak coupling as long as voltage is much larger than the Kondo temperature.Comment: 16 pages, 4 figure

Diagrammatic theory of the Anderson impurity model with finite Coulomb interaction

We have developed a self-consistent conserving pseudo particle approximation for the Anderson impurity model with finite Coulomb interaction, derivable from a Luttinger Ward functional. It contains an infinite series of skeleton diagrams built out of fully renormalized Green's functions. The choice of diagrams is motivated by the Schrieffer Wolff transformation which shows that singly and doubly occupied states should appear in all bare diagrams symmetrically. Our numerical results for $T_K$ are in excellent agreement with the exact values known from the Bethe ansatz solution. The low energy physics of non-Fermi liquid Anderson impurity systems is correctly described while the present approximation fails to describe Fermi liquid systems, since some important coherent spin flip and charge transfer processes are not yet included. It is believed that CTMA (Conserving T-matrix approximation) diagrams will recover also Fermi liquid behavior for Anderson models with finite Coulomb interaction as they do for infinite Coulomb interaction.Comment: 4 pages, 2 figures, presented at the NATO Advanced Research Workshop on "Size Dependent MAgnetic Scattering", Pecs, Hungary, May 28 - June 1, 200