1,170 research outputs found
Correlation Functions in Disordered Systems
{Recently, we found that the correlation between the eigenvalues of random
hermitean matrices exhibits universal behavior. Here we study this universal
behavior and develop a diagrammatic approach which enables us to extend our
previous work to the case in which the random matrix evolves in time or varies
as some external parameters vary. We compute the current-current correlation
function, discuss various generalizations, and compare our work with the work
of other authors. We study the distribution of eigenvalues of Hamiltonians
consisting of a sum of a deterministic term and a random term. The correlation
between the eigenvalues when the deterministic term is varied is calculated.}Comment: 19 pages, figures not included (available on request), Tex,
NSF-ITP-93-12
Anomalously large conductance fluctuations in weakly disordered graphene
We have studied numerically the mesoscopic fluctuations of the conductance of
a graphene strip (width W large compared to length L), in an ensemble of
samples with different realizations of the random electrostatic potential
landscape. For strong disorder (potential fluctuations comparable to the
hopping energy), the variance of the conductance approaches the value predicted
by the Altshuler-Lee-Stone theory of universal conductance fluctuations. For
weaker disorder the variance is greatly enhanced if the potential is smooth on
the scale of the atomic separation. There is no enhancement if the potential
varies on the atomic scale, indicating that the absence of backscattering on
the honeycomb lattice is at the origin of the anomalously large fluctuations.Comment: 5 pages, 8 figure
Statistical translation invariance protects a topological insulator from interactions
We investigate the effect of interactions on the stability of a disordered,
two-dimensional topological insulator realized as an array of nanowires or
chains of magnetic atoms on a superconducting substrate. The Majorana
zero-energy modes present at the ends of the wires overlap, forming a
dispersive edge mode with thermal conductance determined by the central charge
of the low-energy effective field theory of the edge. We show numerically
that, in the presence of disorder, the Majorana edge mode remains
delocalized up to extremely strong attractive interactions, while repulsive
interactions drive a transition to a edge phase localized by disorder.
The absence of localization for strong attractive interactions is explained by
a self-duality symmetry of the statistical ensemble of disorder configurations
and of the edge interactions, originating from translation invariance on the
length scale of the underlying mesoscopic array.Comment: 5+2 pages, 8 figure
Manipulation of photon statistics of highly degenerate chaotic radiation
Highly degenerate chaotic radiation has a Gaussian density matrix and a large
occupation number of modes . If it is passed through a weakly transmitting
barrier, its counting statistics is close to Poissonian. We show that a second
identical barrier, in series with the first, drastically modifies the
statistics. The variance of the photocount is increased above the mean by a
factor times a numerical coefficient. The photocount distribution reaches a
limiting form with a Gaussian body and highly asymmetric tails. These are
general consequences of the combination of weak transmission and multiple
scattering.Comment: 4 pages, 2 figure
Medium/high field magnetoconductance in chaotic quantum dots
The magnetoconductance G in chaotic quantum dots at medium/high magnetic
fluxes Phi is calculated by means of a tight binding Hamiltonian on a square
lattice. Chaotic dots are simulated by introducing diagonal disorder on surface
sites of L x L clusters. It is shown that when the ratio W/L is sufficiently
large, W being the leads width, G increases steadily showing a maximum at a
flux Phi_max ~ W. Bulk disordered ballistic cavities (with an amount of
impurities proportional to L) does not show this effect. On the other hand, for
magnetic fluxes larger than that for which the cyclotron radius is of the order
of L/2, the average magnetoconductance inceases almost linearly with the flux
with a slope proportional to W^2, shows a maximum and then decreases stepwise.
These results closely follow a theory proposed by Beenakker and van Houten to
explain the magnetoconductance of two point contacts in series.Comment: RevTeX including six postscript figure
Classical limit of transport in quantum kicked maps
We investigate the behavior of weak localization, conductance fluctuations,
and shot noise of a chaotic scatterer in the semiclassical limit. Time resolved
numerical results, obtained by truncating the time-evolution of a kicked
quantum map after a certain number of iterations, are compared to semiclassical
theory. Considering how the appearance of quantum effects is delayed as a
function of the Ehrenfest time gives a new method to compare theory and
numerical simulations. We find that both weak localization and shot noise agree
with semiclassical theory, which predicts exponential suppression with
increasing Ehrenfest time. However, conductance fluctuations exhibit different
behavior, with only a slight dependence on the Ehrenfest time.Comment: 17 pages, 13 figures. Final versio
Metallic phase of the quantum Hall effect in four-dimensional space
We study the phase diagram of the quantum Hall effect in four-dimensional
(4D) space. Unlike in 2D, in 4D there exists a metallic as well as an
insulating phase, depending on the disorder strength. The critical exponent
of the diverging localization length at the quantum Hall
insulator-to-metal transition differs from the semiclassical value of
4D Anderson transitions in the presence of time-reversal symmetry. Our
numerical analysis is based on a mapping of the 4D Hamiltonian onto a 1D
dynamical system, providing a route towards the experimental realization of the
4D quantum Hall effect.Comment: 4+epsilon pages, 3 figure
Universal correlations for deterministic plus random Hamiltonians
We consider the (smoothed) average correlation between the density of energy
levels of a disordered system, in which the Hamiltonian is equal to the sum of
a deterministic H0 and of a random potential . Remarkably, this
correlation function may be explicitly determined in the limit of large
matrices, for any unperturbed H0 and for a class of probability distribution
P of the random potential. We find a compact representation of the
correlation function. From this representation one obtains readily the short
distance behavior, which has been conjectured in various contexts to be
universal. Indeed we find that it is totally independent of both H0 and
P().Comment: 26P, (+5 figures not included
Correlations between eigenvalues of large random matrices with independent entries
We derive the connected correlation functions for eigenvalues of large
Hermitian random matrices with independently distributed elements using both a
diagrammatic and a renormalization group (RG) inspired approach. With the
diagrammatic method we obtain a general form for the one, two and three-point
connected Green function for this class of ensembles when matrix elements are
identically distributed, and then discuss the derivation of higher order
functions by the same approach. Using the RG approach we re-derive the one and
two-point Green functions and show they are unchanged by choosing certain
ensembles with non-identically distributed elements. Throughout, we compare the
Green functions we obtain to those from the class of ensembles with unitary
invariant distributions and discuss universality in both ensemble classes.Comment: 23 pages, RevTex, hard figures available from [email protected]
Conductance Fluctuations in a Disordered Double-Barrier Junction
We consider the effect of disorder on coherent tunneling through two barriers
in series, in the regime of overlapping transmission resonances. We present
analytical calculations (using random-matrix theory) and numerical simulations
(on a lattice) to show that strong mode-mixing in the inter-barrier region
induces mesoscopic fluctuations in the conductance of universal magnitude
for a symmetric junction. For an asymmetric junction, the
root-mean-square fluctuations depend on the ratio of the two tunnel
resistances according to ,
where in the presence (absence) of time-reversal symmetry.Comment: 12 pages, REVTeX-3.0, 2 figures, submitted to Physical Review
- âŠ