The transport coefficients of the Anderson model are calculated by extending Wilson's numerical renormalization group method to finite temperature Green's functions. Accurate results for the frequency and temperature dependence of the single-particle spectral densities and transport time τ (ω, T ) are obtained and used to extract the temperature dependence of the transport coefficients in the strong correlation limit of the Anderson model. Results are obtained for values of the local level position ranging from the Kondo regime to the mixed valent and empty orbital regimes. The low temperature anomalies in the resistivity, ρ(T ), thermopower, S(T ), thermal conductivity κ(T ) and Hall coefficient, R H (T ), are discussed in terms of the behaviour of the spectral densities. All quantities exhibit the expected Fermi liquid behaviour at low temperature, ρ(T ). Analytic results based on Fermi liquid theory are derived here for the first time for β and the numerical results are shown to be consistent with this coefficient. The range of temperatures over which universal behaviour extends is also discussed. Scattering of conduction electrons in higher, l > 0, angular momentum channels is also considered and an expression is derived for the corresponding transport time and used to discuss the influence of the interference terms between the resonant l = 0 and non-resonant l = 1 channels on the transport properties.The presence of non-resonant scattering is shown to be particularly impor-tant for the thermopower at half-filling, where the sign of the thermopower can depend sensitively on the non-resonant phase shift. Finally the relation of the results to experiment is discussed.Address after 15th October 1993:

The Falicov-Kimball model was introduced in 1969 as a statistical model for metal-insulator transitions; it includes itinerant and localized electrons that mutually interact with a local Coulomb interaction and is the simplest model of electron correlations. It can be solved exactly with dynamical mean-field theory in the limit of large spatial dimensions which provides an interesting benchmark for the physics of locally correlated systems. In this review, we develop the formalism for solving the Falicov-Kimball model from a path-integral perspective, and provide a number of expressions for single and two-particle properties. We examine many important theoretical results that show the absence of fermi-liquid features and provide a detailed description of the static and dynamic correlation functions and of transport properties. The parameter space is rich and one finds a variety of many-body features like metal-insulator transitions, classical valence fluctuating transitions, metamagnetic transitions, charge density wave order-disorder transitions, and phase separation. At the same time, a number of experimental systems have been discovered that show anomalies related to Falicov-Kimball physics [including YbInCu 4 , EuNi 2 (Si 1−x Gex) 2 , NiI 2 and TaxN].

The many-body formalism for dynamical mean-field theory is extended to treat nonequilibrium problems. We illustrate how the formalism works by examining the transient decay of the oscillating current that is driven by a large electric field turned on at time t=0. We show how the Bloch oscillations are quenched by the electron-electron interactions, and how their character changes dramatically for a Mott insulator.

The thermoelectric properties of strongly correlated quantum dots, described by a single-level Anderson model coupled to conduction-electron leads, is investigated using Wilson's numerical renormalization-group method. We calculate the electronic contribution, K e , to the thermal conductance, the thermopower, S, and the electrical conductance, G, of a quantum dot as a function of both temperature, T, and gate voltage, v g , for strong, intermediate, and weak Coulomb correlations, U, on the dot. For strong correlations and in the Kondo regime, we find that the thermopower exhibits two sign changes, at temperatures T 1 ͑v g ͒ and T 2 ͑v g ͒ with T 1 Ͻ T 2 . We find that T 1 Ͼ T p ͑v g ͒ϷT K ͑v g ͒, where T p ͑v g ͒ is the position of the Kondo-induced peak in the thermopower, T K ͑v g ͒ is the Kondo scale, and T 2 = O͑⌫͒, where ⌫ is the level width. The loci of T 1 ͑v g ͒ and T 2 ͑v g ͒ merge at a critical gate voltage, v g = v g c ͑U / ⌫͒ beyond which no sign change occurs at finite gate voltage ͑measured relative to midvalley͒. We determine v g c for different U / ⌫ finding that v g c coincides, in each case, with entry into the mixed-valence regime. No sign change is found outside the Kondo regime, or, for weak correlations U / ⌫Շ1, making such a sign change in S͑T͒ a particularly sensitive signature of strong correlations and Kondo physics. The relevance of this to recent thermopower measurements of Kondo correlated quantum dots is discussed. The results for quantum dots are compared also to the relevant transport coefficients of dilute magnetic impurities in nonmagnetic metals: the electronic contribution, e , to the thermal conductivity, the thermopower, S, and the impurity contribution to the electrical resistivity, . In the mixed-valence and empty-orbital regimes, we find, as a function of temperature, two peaks in K e as compared to a single peak in e , and similarly, G͑T͒ exhibits a finite-temperature peak on entering the mixed-valence regime whereas such a pronounced peak is absent in ͑T͒ even far into the empty-orbital regime. We compare and contrast the figure of merit, power factor, and the extent of violation of the Wiedemann-Franz law in quantum dots and dilute magnetic impurities. The extent of temperature scaling in the thermopower and thermal conductance of quantum dots in the Kondo regime is discussed.