Mesoscopic charge relaxation

We consider charge relaxation in the mesoscopic equivalent of an RC circuit. For a single-channel, spin-polarized contact, self-consistent scattering theory predicts a universal charge relaxation resistance equal to half a resistance quantum independent of the transmission properties of the contact. This prediction is in good agreement with recent experimental results. We use a tunneling Hamiltonian formalism and show in Hartree-Fock approximation that at zero temperature the charge relaxation resistance is universal even in the presence of Coulomb blockade effects. We explore departures from universality as a function of temperature and magnetic field.     

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.     

Anomalous diffusion and charge relaxation on comb model: exact solutions

The random walks on the comb structure are considered. It is shown that due to fingers a diffusion has an anomalous character, that is an r.m.s. displacement depends on time by a power way with exponent . The generalized diffusion equation for an anomalous case is deduced. It essentially differs from a usual diffusion equation in the continuity equation form: instead of the first time derivative, the time derivative of fractal order appears. In the second part the charge relaxation on the comb structure is studied. A non-Maxwell character is established. The reason is that the electric field has three components, but a charge may relax only along some conducting lines.     

Metal-insulator transitions in the periodic Anderson model

We solve the periodic Anderson model in the Mott-Hubbard regime, using dynamical mean field theory. Upon electron doping of the Mott insulator, a metal-insulator transition occurs which is qualitatively similar to that of the single band Hubbard model, namely, with a divergent effective mass and a first order character at finite temperatures. Surprisingly, upon hole doping, the metal-insulator transition is not first order and does not show a divergent mass. Thus, the transition scenario of the single band Hubbard model is not generic for the periodic Anderson model, even in the Mott-Hubbard regime.     

Anomalously localized states in the Anderson model

It is demonstrated that anomalously localized states (ALS) in the Anderson model, being lattice specific, are not related to any of the continuous theories. We identify the spatial structure of ALS on a lattice and calculate their likelihood. Analytical results explain peculiarities in previous numerical simulations.     

Valence transition in the periodic Anderson model

A very rich phase diagram has recently been found in CeCu₂Si₂ from high pressure experiments where, in particular, a transition between an intermediate valence configuration and an integral valent heavy fermion state has been observed. We show that such a valence transition can be understood in the framework of the periodic Anderson model. In particular, our results show a breakdown of a mixed-valence state which is accompanied by a drastic change in the f occupation in agreement with experiment. This valence transition can possibly be interpreted as a collapse of the large Fermi surface of the heavy fermion state which incorporates not only the conduction electrons but also the localized f electrons. The theoretical approach used in this paper is based on the novel projector-based renormalization method (PRM). With respect to the periodic Anderson model, the method was before only employed in combination with the basic approximations of the well-known slave-boson mean-field theory. In this paper, the PRM treatment is performed in a more sophisticated manner where both mixed as well as integral valent solutions have been obtained. Furthermore, we argue that the presented PRM approach might be a promising starting point to study the competing interactions in CeCu₂Si₂ and related compounds.     

Moment-conserving decoupling scheme in the Anderson model

The moment-conserving decoupling scheme is applied to the infinite-U Anderson model for dilute magnetic alloys. It is shown that the correct first moment of the spectral density is essential in the occurrence of magnetic solutions.     

Self-consistent treatment of the Anderson model

TheN-fold degenerate Anderson single impurity model in the infiniteU limit is treated by means of the irreducible Green functions method. In this approach a derivation of an exact Dyson equation and an exact self-energy operator is possible. The necessity of introducing auxiliary fields, such as slave-bosons is avoided.     

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.     

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.     

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.     

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.     

Resonance charge relaxation in physical barrier layers

It is shown experimentally that the space charge domain (SCD) of a MIS structure can be described as a layer-macrorelaxer by applying the appropriate formula for the Schottky barrier. The maximal time of the transient t_C (the saturation time t_CH) of the change in MIS-structure capacitance upon imposition of a sufficiently large rectangular depleting voltage pulse is expressed by the formula mentioned. A new method is correspondingly proposed for determining the ionization energy of bulk centers responsible for this relaxation. A comparison with data in the literature is presented and the prospects for developing representations on resonance charge relaxation in barrier layers is indicated.     

Thermopower in the Anderson model of semiconducting glasses

The thermoelectric power in the Anderson model of electrons in localized states in the mobility gap of semiconducting glasses interacting by attractive forces is calculated at low temperatures. Under some conditions, a transition from the activated form ofS to S=const at low temperatures is predicted. In connection with the activated character of the conductivity, it well corresponds to the experiment on some chalcogenide glasses.The author would like to thank ing. V.Cháb for communicating him the experimental data on As₂Te₃TI_x prior to publication.     

Anomalously suppressed localization in the two-channel Anderson model

We study numerically the localization properties of a two-channel quasi-one-dimensional Anderson model with uncorrelated diagonal disorder within the nearest-neighbor tight-binding approximation. We calculate and analyze the disorder-averaged transmittance and the Lyapunov exponent. We find that the localization of the entire system is enhanced by increasing the interchain hopping strength t?. From the numerical investigation of the energy dependence of the Lyapunov exponent for many different interchain hopping strengths, we find that apart from the band center anomaly, which usually occurs in strictly one-dimensional disordered systems, additional anomalies appear at special spectral points. They are found to be associated with the interchain hopping strength and occur at E = ± t?/2 and ± t?. We find that the anomalies at E = ± t? are associated with the π-coupling occurring within one energy band and those at E = ± t?/2 are associated with the π-coupling occurring between two different energy bands. Despite having a similar origin, these two anomalies have distinct characteristics in their dependence on the strength of disorder. We also show that for a suitable range of parameter values, effectively delocalized states are observed in finite-size systems.