86 research outputs found
Weak Chaos in a Quantum Kepler Problem
Transition from regular to chaotic dynamics in a crystal made of singular
scatterers 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 with small off-diagonal elements: . 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 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 on
is found in both regimes for values of q \alt 4g^{-1}, where is the
coupling constant of the model.Comment: RevTex4, 5 two-column pages, 5 .eps figures, to be published in Phys.
Rev.
- …