31 research outputs found
A Renormalization-Group approach to the Coulomb Gap
The free energy of the Coulomb Gap problem is expanded as a set of Feynman
diagrams, using the standard diagrammatic methods of perturbation theory. The
gap in the one-particle density of states due to long-ranged interactions
corresponds to a renormalization of the two-point vertex function. By
collecting the leading order logarithmic corrections we have derived the
standard result for the density of states in the critical dimension, d=1. This
method, which is shown to be identical to the approach of Thouless, Anderson
and Palmer to spin glasses, allows us to derive the strong-disorder behaviour
of the density of states. The use of the renormalization group allows this
derivation to be extended to all disorders, and the use of an epsilon-expansion
allows the method to be extended to d=2 and d=3. We speculate that the
renormalization group equations can also be derived diagrammatically, allowing
a simple derivation of the crossover behaviour observed in the case of weak
disorder.Comment: 16 pages, LaTeX. Diagrams available on request from
[email protected]. Changes to figure 4 and second half of section
Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra
Random Matrix Theory (RMT) is a powerful statistical tool to model spectral
fluctuations. This approach has also found fruitful application in Quantum
Chromodynamics (QCD). Importantly, RMT provides very efficient means to
separate different scales in the spectral fluctuations. We try to identify the
equivalent of a Thouless energy in complete spectra of the QCD Dirac operator
for staggered fermions from SU(2) lattice gauge theory for different lattice
size and gauge couplings. In disordered systems, the Thouless energy sets the
universal scale for which RMT applies. This relates to recent theoretical
studies which suggest a strong analogy between QCD and disordered systems. The
wealth of data allows us to analyze several statistical measures in the bulk of
the spectrum with high quality. We find deviations which allows us to give an
estimate for this universal scale. Other deviations than these are seen whose
possible origin is discussed. Moreover, we work out higher order correlators as
well, in particular three--point correlation functions.Comment: 24 pages, 24 figures, all included except one figure, missing eps
file available at http://pluto.mpi-hd.mpg.de/~wilke/diff3.eps.gz, revised
version, to appear in PRD, minor modifications and corrected typos, Fig.4
revise
Phase Relaxation of Electrons in Disordered Conductors
Conduction electrons in disordered metals and heavily doped semiconductors at
low temperatures preserve their phase coherence for a long time: phase
relaxation time can be orders of magnitude longer than the momentum
relaxation time. The large difference in these time scales gives rise to well
known effects of weak localization, such as anomalous magnetoresistance. Among
other interesting characteristics, study of these effects provide quantitative
information on the dephasing rate . This parameter is of
fundamental interest: the relation between and the
temperature (a typical energy scale of an electron) determines how well a
single electron state is defined. We will discuss the basic physical meaning of
in different situations and its difference from the energy
relaxation rate. At low temperatures, the phase relaxation rate is governed by
collisions between electrons. We will review existing theories of dephasing by
these collisions or (which is the same) by electric noise inside the sample. We
also discuss recent experiments on the magnetoresistance of 1D systems: some of
them show saturation of at low temperatures, the other do not. To
resolve this contradiction we discuss dephasing by an external microwave field
and by nonequilibrium electric noise.Comment: Order of figures and references corrected; one reference added; 15
pages, 2 figures, lecture given on 10th International Winterschool on New
Developments in Solid State Physics, Mauterndorf, Salzburg, Austria; 23-27
Feb. 199
Lectures on Chiral Disorder in QCD
I explain the concept that light quarks diffuse in the QCD vacuum following
the spontaneous breakdown of chiral symmetry. I exploit the striking analogy to
disordered electrons in metals, identifying, among others, the universal regime
described by random matrix theory, diffusive regime described by chiral
perturbation theory and the crossover between these two domains.Comment: Lectures given at the Cargese Summer School, August 6-18, 200
Quantum railroads and directed localization at the juncture of quantum Hall systems
The integer quantum Hall effect (QHE) and one-dimensional Anderson
localization (AL) are limiting special cases of a more general phenomenon,
directed localization (DL), predicted to occur in disordered one-dimensional
wave guides called "quantum railroads" (QRR). Here we explain the surprising
results of recent measurements by Kang et al. [Nature 403, 59 (2000)] of
electron transfer between edges of two-dimensional electron systems and
identify experimental evidence of QRR's in the general, but until now entirely
theoretical, DL regime that unifies the QHE and AL. We propose direct
experimental tests of our theory.Comment: 11 pages revtex + 3 jpeg figures, to appear in Phys. Rev.
Two-dimensional SIR epidemics with long range infection
We extend a recent study of susceptible-infected-removed epidemic processes
with long range infection (referred to as I in the following) from
1-dimensional lattices to lattices in two dimensions. As in I we use hashing to
simulate very large lattices for which finite size effects can be neglected, in
spite of the assumed power law for the
probability that a site can infect another site a distance vector
apart. As in I we present detailed results for the critical case, for the
supercritical case with , and for the supercritical case with . For the latter we verify the stretched exponential growth of the
infected cluster with time predicted by M. Biskup. For we find
generic power laws with dependent exponents in the supercritical
phase, but no Kosterlitz-Thouless (KT) like critical point as in 1-d. Instead
of diverging exponentially with the distance from the critical point, the
correlation length increases with an inverse power, as in an ordinary critical
point. Finally we study the dependence of the critical exponents on in
the regime , and compare with field theoretic predictions. In
particular we discuss in detail whether the critical behavior for
slightly less than 2 is in the short range universality class, as conjectured
recently by F. Linder {\it et al.}. As in I we also consider a modified version
of the model where only some of the contacts are long range, the others being
between nearest neighbors. If the number of the latter reaches the percolation
threshold, the critical behavior is changed but the supercritical behavior
stays qualitatively the same.Comment: 14 pages, including 29 figure
Formation and control of electron molecules in artificial atoms: Impurity and magnetic-field effects
Interelectron interactions and correlations in quantum dots can lead to
spontaneous symmetry breaking of the self-consistent mean field resulting in
formation of Wigner molecules. With the use of spin-and-space unrestricted
Hartree-Fock (sS-UHF) calculations, such symmetry breaking is discussed for
field-free conditions, as well as under the influence of an external magnetic
field. Using as paradigms impurity-doped (as well as the limiting case of
clean) two-electron quantum dots (which are analogs to helium-like atoms), it
is shown that the interplay between the interelectron repulsion and the
electronic zero-point kinetic energy leads, for a broad range of impurity
parameters, to formation of a singlet ground-state electron molecule,
reminiscent of the molecular picture of doubly-excited helium. Comparative
analysis of the conditional probability distributions for the sS-UHF and the
exact solutions for the ground state of two interacting electrons in a clean
parabolic quantum dot reveals that both of them describe formation of an
electron molecule with similar characteristics. The self-consistent field
associated with the triplet excited state of the two-electron quantum dot
(clean as well as impurity-doped) exhibits symmetry breaking of the Jahn-Teller
type, similar to that underlying formation of nonspherical open-shell nuclei
and metal clusters. Furthermore, impurity and/or magnetic-field effects can be
used to achieve controlled manipulation of the formation and pinning of the
discrete orientations of the Wigner molecules. Impurity effects are futher
illustrated for the case of a quantum dot with more than two electrons.Comment: Latex/Revtex, 10 pages with 4 gif figures. Small changes to explain
the difference between Wigner and Jahn-Teller electron molecules. A complete
version of the paper with high quality figures inside the text is available
at http://shale.physics.gatech.edu/~costas/qdhelium.html For related papers,
see http://www.prism.gatech.edu/~ph274c
Chern-Simons Theory for Magnetization Plateaus of Frustrated - Heisenberg model
The magnetization curve of the two-dimensional spin-1/2 -
Heisenberg model is investigated by using the Chern-Simons theory under a
uniform mean-field approximation. We find that the magnetization curve is
monotonically increasing for , where the system under zero
external field is in the antiferromagnetic N\'eel phase. For larger ratios of
, various plateaus will appear in the magnetization curve. In
particular, in the disordered phase, our result supports the existence of the
plateau and predicts a new plateau at .
By identifying the onset ratio for the appearance of the 1/2-plateau
with the boundary between the N\'eel and the spin-disordered phases in zero
field, we can determine this phase boundary accurately by this mean-field
calculation. Verification of these interesting results would indicate a strong
connection between the frustrated antiferromagnetic system and the quantum Hall
system.Comment: RevTeX 4, 4 pages, 3 EPS figure
Staggered dimer order in S=1/2 quantum spin ladder system with four spin exchange
We study the S=1/2 quantum spin ladder system with the four-spin exchange,
using density matrix renormalization group method and an exact diagonalization
method. Recently, the phase transition in this system and its universality
class are studied. But there remain controversies whether the phase transition
is second order type or the other type and the nature of order parameter. There
are arguments that the massless phase appears. But this does not agree with our
previous result. Analyzing DMRG data, we try a new approach in order to
determine a phase which appears after the phase transition. We find that the
edge state appears in the open boundary condition, investigating excitation
energies of states with higher magnetizations.Comment: Submitted to Phys. Rev. B, (REVTeX4
Mott Transition in An Anyon Gas
We introduce and analyze a lattice model of anyons in a periodic potential
and an external magnetic field which exhibits a transition from a Mott
insulator to a quantum Hall fluid. The transition is characterized by the anyon
statistics, , which can vary between Fermions, , and Bosons,
. For bosons the transition is in the universality class of the
classical three-dimensional XY model. Near the Fermion limit, the transition is
described by a massless Dirac theory coupled to a Chern-Simons gauge
field. Analytic calculations perturbative in , and also a large
N-expansion, show that due to gauge fluctuations, the critical properties of
the transition are dependent on the anyon statistics. Comparison with previous
calcualations at and near the Boson limit, strongly suggest that our lattice
model exhibits a fixed line of critical points, with universal critical
properties which vary continuosly and monotonically as one passes from Fermions
to Bosons. Possible relevance to experiments on the transitions between
plateaus in the fractional quantum Hall effect and the magnetic field-tuned
superconductor-insulator transition are briefly discussed.Comment: text and figures in Latex, 41 pages, UBCTP-92-28, CTP\#215