135 research outputs found
Coulomb gap in one-dimensional disordered electron systems
The density of states of one-dimensional disordered electron systems with
long range Coulomb interaction is studied in the weak pinning limit. The
density of states is found to follow a power law with an exponent determined by
localization length, and this power law behavior is consistent with the
existing numerical results.Comment: RevTeX4 file, 5 pages, no figures To appear in Physical Reviews
Nonlinear spectral calculus and super-expanders
Nonlinear spectral gaps with respect to uniformly convex normed spaces are
shown to satisfy a spectral calculus inequality that establishes their decay
along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to
behave sub-multiplicatively under zigzag products. These results yield a
combinatorial construction of super-expanders, i.e., a sequence of 3-regular
graphs that does not admit a coarse embedding into any uniformly convex normed
space.Comment: Typos fixed based on referee comments. Some of the results of this
paper were announced in arXiv:0910.2041. The corresponding parts of
arXiv:0910.2041 are subsumed by the current pape
Charging effects in quantum wires
We investigate the role of charging effects in a voltage-biased quantum wire.
Both the finite range of the Coulomb interaction and the long-ranged nature of
the Friedel oscillation imply a finite capacitance, leading to a charging
energy. While observable Coulomb blockade effects are absent for a single
impurity, they are crucial if islands are present. For a double barrier, we
give the resonance condition, fully taking into account the charging of the
island.Comment: 6 Pages RevTeX, no figures, Phys. Rev. B (in press
Influence of thermal fluctuations on quantum phase transitions in one-dimensional disordered systems: Charge density waves and Luttinger liquids
The low temperature phase diagram of 1D weakly disordered quantum systems
like charge or spin density waves and Luttinger liquids is studied by a
\emph{full finite temperature} renormalization group (RG) calculation. For
vanishing quantum fluctuations this approach is amended by an \emph{exact}
solution in the case of strong disorder and by a mapping onto the \emph{Burgers
equation with noise} in the case of weak disorder, respectively. At \emph{zero}
temperature we reproduce the quantum phase transition between a pinned
(localized) and an unpinned (delocalized) phase for weak and strong quantum
fluctuations, respectively, as found previously by Fukuyama or Giamarchi and
Schulz.
At \emph{finite} temperatures the localization transition is suppressed: the
random potential is wiped out by thermal fluctuations on length scales larger
than the thermal de Broglie wave length of the phason excitations. The
existence of a zero temperature transition is reflected in a rich cross-over
phase diagram of the correlation functions. In particular we find four
different scaling regions: a \emph{classical disordered}, a \emph{quantum
disordered}, a \emph{quantum critical} and a \emph{thermal} region. The results
can be transferred directly to the discussion of the influence of disorder in
superfluids. Finally we extend the RG calculation to the treatment of a
commensurate lattice potential. Applications to related systems are discussed
as well.Comment: 19 pages, 7 figure
Electronic Spectral Functions for Quantum Hall Edge States
We have evaluated wavevector-dependent electronic spectral functions for
integer and fractional quantum Hall edge states using a chiral Luttinger liquid
model. The spectral functions have a finite width and a complicated line shape
because of the long-range of the Coulomb interaction. We discuss the
possibility of probing these line shapes in vertical tunneling experiments.Comment: 4 pages, RevTex, two figures included, to appear as a Rapid
Communication in PRB; we updated references which have recently appeared in
print and were cited as preprints in our ealier submissio
Variational theory of elastic manifolds with correlated disorder and localization of interacting quantum particles
We apply the gaussian variational method (GVM) to study the equilibrium
statistical mechanics of the two related systems: (i) classical elastic
manifolds, such as flux lattices, in presence of columnar disorder correlated
along the direction (ii) interacting quantum particles in a static
random potential. We find localization by disorder, the localized phase being
described by a replica symmetry broken solution confined to the mode
. For classical systems we compute the correlation function of
relative displacements. In , in the absence of dislocations, the GVM
allows to describes the Bose glass phase. Along the columns the displacements
saturate at a length indicating flux-line localization.
Perpendicularly to the columns long range order is destroyed. We find divergent
tilt modulus and a scaling. Quantum systems
are studied using the analytic continuation from imaginary to real time . We compute the conductivity and find that it behaves at small
frequency as in all dimensions () for
which disorder is relevant. We compute the quantum localization length .
In , where the model also describes interacting fermions in a static
random potential, we find a delocalization transition and obtain analytically
both the low and high frequency behavior of the conductivity for any value of
the interaction. We show that the marginality condition appears as the
condition to obtain the correct physical behavior. Agreement with
renormalization group results is found whenever it can be compared.Comment: 34 pages, REVTeX, no figure
A novel homozygous KCNQ3 loss-of-function variant causes non-syndromic intellectual disability and neonatal-onset pharmacodependent epilepsy
OBJECTIVE:
Heterozygous variants in KCNQ2 or, more rarely, KCNQ3 genes are responsible for early-onset developmental/epileptic disorders characterized by heterogeneous clinical presentation and course, genetic transmission, and prognosis. While familial forms mostly include benign epilepsies with seizures starting in the neonatal or early-infantile period, de novo variants in KCNQ2 or KCNQ3 have been described in sporadic cases of early-onset encephalopathy (EOEE) with pharmacoresistant seizures, various age-related pathological EEG patterns, and moderate/severe developmental impairment. All pathogenic variants in KCNQ2 or KCNQ3 occur in heterozygosity. The aim of this work was to report the clinical, molecular, and functional properties of a new KCNQ3 variant found in homozygous configuration in a 9-year-old girl with pharmacodependent neonatal-onset epilepsy and non-syndromic intellectual disability.
METHODS:
Exome sequencing was used for genetic investigation. KCNQ3 transcript and subunit expression in fibroblasts was analyzed with quantitative real-time PCR and Western blotting or immunofluorescence, respectively. Whole-cell patch-clamp electrophysiology was used for functional characterization of mutant subunits.
RESULTS:
A novel single-base duplication in exon 12 of KCNQ3 (NM_004519.3:c.1599dup) was found in homozygous configuration in the proband born to consanguineous healthy parents; this frameshift variant introduced a premature termination codon (PTC), thus deleting a large part of the C-terminal region. Mutant KCNQ3 transcript and protein abundance was markedly reduced in primary fibroblasts from the proband, consistent with nonsense-mediated mRNA decay. The variant fully abolished the ability of KCNQ3 subunits to assemble into functional homomeric or heteromeric channels with KCNQ2 subunits.
SIGNIFICANCE:
The present results indicate that a homozygous KCNQ3 loss-of-function variant is responsible for a severe phenotype characterized by neonatal-onset pharmacodependent seizures, with developmental delay and intellectual disability. They also reveal difference in genetic and pathogenetic mechanisms between KCNQ2- and KCNQ3-related epilepsies, a crucial observation for patients affected with EOEE and/or developmental disabilities
Dynamical response of a pinned two-dimensional Wigner crystal
We re-examine a long-standing problem of a finite-frequency conductivity of a
weakly pinned two-dimensional classical Wigner crystal. In this system an
inhomogeneously broadened absorption line (pinning mode) centered at disorder
and magnetic field dependent frequency is known to appear. We show
that the relative linewidth of the pinning mode is
of the order of one in weak magnetic fields, exhibits a power-law decrease in
intermediate fields, and eventually saturates at a small value in strong
magnetic fields. The linewidth narrowing is due to a peculiar mechanism of
mixing between the stiffer longitudinal and the softer transverse components of
the collective excitations. The width of the high-field resonance proves to be
related to the density of states in the low-frequency tail of the zero-field
phonon spectrum. We find a qualitative agreement with recent experiments and
point out differences from the previous theoretical work on the subject.Comment: 19 pages, 11 figures. Supersedes cond-mat/990424
Transport of interacting electrons through a double barrier in quantum wires
We generalize the fermionic renormalization group method to describe
analytically transport through a double barrier structure in a one-dimensional
system. Focusing on the case of weakly interacting electrons, we investigate
thoroughly the dependence of the conductance on the strength and the shape of
the double barrier for arbitrary temperature T. Our approach allows us to
systematically analyze the contributions to renormalized scattering amplitudes
from different characteristic scales absent in the case of a single impurity,
without restricting the consideration to the model of a single resonant level.
Both a sequential resonant tunneling for high T and a resonant transmission for
T smaller than the resonance width are studied within the unified treatment of
transport through strong barriers. For weak barriers, we show that two
different regimes are possible. Moderately weak impurities may get strong due
to a renormalization by interacting electrons, so that transport is described
in terms of theory for initially strong barriers. The renormalization of very
weak impurities does not yield any peak in the transmission probability;
however, remarkably, the interaction gives rise to a sharp peak in the
conductance, provided asymmetry is not too high.Comment: 18 pages, 8 figures; figures added, references updated, extended
discussio
Plasmon Modes and Correlation Functions in Quantum Wires and Hall Bars
We present microscopic derivations of the one-dimensional low-energy boson
effective Hamiltonians of quantum wire and quantum Hall bar systems. The
quantum Hall system is distinguished by its spatial separation of oppositely
directed electrons. We discuss qualitative differences in the plasmon
collective mode dispersions and the ground state correlation functions of the
two systems which are consequences of this difference. The slowly-decaying
quasi-solid correlations expected in a quantum wire are strongly suppressed in
quantum Hall bar systems.Comment: 7 pages, RevTex, 3 figures and 1 table included; references updated
and minor typos correcte
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