Weak Chaos in a Quantum Kepler Problem

Transition from regular to chaotic dynamics in a crystal made of singular scatterers $U(r)=\lambda |r|^{-\sigma}$ can be reached by varying either sigma or lambda. We map the problem to a localization problem, and find that in all space dimensions the transition occurs at sigma=1, i.e., Coulomb potential has marginal singularity. We study the critical line sigma=1 by means of a renormalization group technique, and describe universality classes of this new transition. An RG equation is written in the basis of states localized in momentum space. The RG flow evolves the distribution of coupling parameters to a universal stationary distribution. Analytic properties of the RG equation are similar to that of Boltzmann kinetic equation: the RG dynamics has integrals of motion and obeys an H-theorem. The RG results for sigma=1 are used to derive scaling laws for transport and to calculate critical exponents.Comment: 28 pages, ReVTeX, 4 EPS figures, to appear in the I. M. Lifshitz memorial volume of Physics Report

Spatial structure of an incompressible Quantum Hall strip

The incompressible Quantum Hall strip is sensitive to charging of localized states in the cyclotron gap. We study the effect of localized states by a density functional approach and find electron density and the strip width as a function of the density of states in the gap. Another important effect is electron exchange. By using a model density functional which accounts for negative compressibility of the QH state, we find electron density around the strip. At large exchange, the density profile becomes nonmonotonic, indicating formation of a 1D Wigner crystal at the strip edge. Both effects, localized states and exchange, lead to a substantial increase of the strip width.Comment: 6 LaTeX pages, 2 postscript figures, to be published in EP2DS proceeding

Time ordering and counting statistics

The basic quantum mechanical relation between fluctuations of transported charge and current correlators is discussed. It is found that, as a rule, the correlators are to be time-ordered in an unusual way. Instances where the difference with the conventional ordering matters are illustrated by means of a simple scattering model. We apply the results to resolve a discrepancy concerning the third cumulant of charge transport across a quantum point contact.Comment: 19 pages, 1 figure; inconsequential mistake and typos correcte

Shot noise of spin polarized electrons

The shot noise of spin polarized electrons is shown to be generically dependent upon spin-flip processes. Such a situation represents perhaps the simplest instance where the two-particle character of current fluctuations out of equilibrium is explicit, leading to trinomial statistics of charge transfer in a single channel model. We calculate the effect of spin-orbit coupling, magnetic impurities, and precession in an external magnetic field on the noise in the experimentally relevant cases of diffusive wires and lateral semiconductor dots, finding dramatic enhancements of the Fano factor. The possibility of using the shot noise to measure the spin-relaxation time in an open mesoscopic system is raised.Comment: Published version. Minor clarifications and correction

Electromechanical noise in a diffusive conductor

Theoretical Physic

Electromechanical noise in a diffusive conductor

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Density of states for almost diagonal random matrices

We study the density of states (DOS) for disordered systems whose spectral statistics can be described by a Gaussian ensemble of almost diagonal Hermitian random matrices. The matrices have independent random entries $H_{i \geq j}$ with small off-diagonal elements: $\ll <|H_{ii}|^{2} > \sim 1$. Using the recently suggested method of a {\it virial expansion in the number of interacting energy levels} (Journ.Phys.A {\bf 36}, 8265), we calculate the leading correction to the Poissonian DOS in the cases of the Gaussian Orthogonal and Unitary Ensembles. We apply the general formula to the critical power-law banded random matrices and the unitary Moshe-Neuberger-Shapiro model and compare DOS of these models.Comment: submitted to Phys. Rev.

Fredholm determinants and the statistics of charge transport

Using operator algebraic methods we show that the moment generating function of charge transport in a system with infinitely many non-interacting Fermions is given by a determinant of a certain operator in the one-particle Hilbert space. The formula is equivalent to a formula of Levitov and Lesovik in the finite dimensional case and may be viewed as its regularized form in general. Our result embodies two tenets often realized in mesoscopic physics, namely, that the transport properties are essentially independent of the length of the leads and of the depth of the Fermi sea.Comment: 30 pages, 2 figures, reference added, credit amende

Multifractality of Hamiltonians with power-law transfer terms

Finite-size effects in the generalized fractal dimensions $d_q$ are investigated numerically. We concentrate on a one-dimensional disordered model with long-range random hopping amplitudes in both the strong- and the weak-coupling regime. At the macroscopic limit, a linear dependence of $d_q$ on $q$ is found in both regimes for values of q \alt 4g^{-1}, where $g$ is the coupling constant of the model.Comment: RevTex4, 5 two-column pages, 5 .eps figures, to be published in Phys. Rev.