V. E. Kravtsov

Notes on crystal optics of superlattices

Abstract Dielectric permeability of superlattices has been calculated with regard to effects of spatial dispersion and two-dimensional nature of excitons. Dispersion of polaritons in the region of exciton resonance is discussed. The expressions have been obtained for the dispersion of surface waves with the inclusion or retardation effects and for different orientations of the surface with respect to the superlattice axis. In the simplest case the expressions have been obtained for the nonlinear (microscopic) polarizability tensor of the superlattice and the gyrotropy constant.

Eigenfunction fractality and pseudogap state near the superconductor-insulator transition.

We develop a theory of a pseudogap state appearing near the superconductor-insulator (SI) transition in strongly disordered metals with an attractive interaction. We show that such an interaction combined with the fractal nature of the single-particle wave functions near the mobility edge leads to an anomalously large single-particle gap in the superconducting state near SI transition that persists and even increases in the insulating state long after the superconductivity is destroyed. We give analytic expressions for the value of the pseudogap in terms of the inverse participation ratio of the corresponding localization problem.

Universal spectral correlations at the mobility edge

We demonstrate the level statistics in the vicinity of the Anderson transition in dg2 dimensions to be universal and drastically different from both Wigner-Dyson in the metallic regime and Poisson in the insulator regime. The variance of the number of levels N in a given energy interval with 〈N〉\ensuremath{\gg}1 is proved to behave as 〈N

Dynamic localization in quantum dots: analytical theory.

{\mathrm{〉}}^{\ensuremath{\gamma}}

New Class of Random Matrix Ensembles with Multifractal Eigenvectors

where \ensuremath{\gamma}=1-(\ensuremath{\nu}d

Anomalous dimensions of high gradient operators in the extended nonlinear σ model and distribution of mesoscopic fluctuations

{)}^{\mathrm{\ensuremath{-}}1}

Applicability of scaling description to the distribution of mesoscopic fluctuations

and \ensuremath{\nu} is the correlation length exponent. The inequality \ensuremath{\gamma}1, shown to be required by an exact sum rule, results from nontrivial cancellations (due to the causality and scaling requirements) in calculating the two-level correlation function.

Jumps in current-voltage characteristics in disordered films.

We analyze the response of a complex quantum-mechanical system (e.g., a quantum dot) to a time-dependent perturbation phi(t). Assuming the dot to be described by random-matrix theory for the Gaussian orthogonal ensemble, we find the quantum correction to the energy absorption rate as a function of the dephasing time t(phi). If phi(t) is a sum of d harmonics with incommensurate frequencies, the correction behaves similarly to that for the conductivity deltasigma(d)(t(phi)) in the d-dimensional Anderson model of the orthogonal symmetry class. For a generic periodic perturbation, the leading quantum correction is absent as in the systems of the unitary symmetry class, unless phi(-t+tau)=phi(t+tau) for some tau, which falls into the quasi-1D orthogonal universality class.

Spectral rigidity and eigenfunction correlations at the Anderson transition

Three recently suggested random matrix ensembles (RME) are linked together by an exact mapping and plausible conjections. Since it is known that in one of these ensembles the eigenvector statistics is multifractal, we argue that all three ensembles belong to a new class of critical RME with multifractal eigenfunction statistics and a universal critical spectral statitics. The generic form of the two-level correlation function for weak and extremely strong multifractality is suggested. Applications to the spectral statistics at the Anderson transition and for certain systems on the border of chaos and integrability is discussed.

Random walks in media with constrained disorder

Abstract Some problems of the theory of quantum disordered conductors required using the extended nonlinear σ model which includes high gradient vertices. Here we present a derivation of such a model starting from the usual model of free electrons in a random potential. We perform a renormalization group analysis of the extended σ model and show the anomalous dimensions of the charges attached to the high gradient vertices to be proportional to n2−n. As a result, these vertices turn out to be relevant, in particular, for the asymptotics of distributions of mesoscopic fluctuations of the conductance and density of states.