4,047 research outputs found
Statistical study of the conductance and shot noise in open quantum-chaotic cavities: Contribution from whispering gallery modes
In the past, a maximum-entropy model was introduced and applied to the study
of statistical scattering by chaotic cavities, when short paths may play an
important role in the scattering process. In particular, the validity of the
model was investigated in relation with the statistical properties of the
conductance in open chaotic cavities. In this article we investigate further
the validity of the maximum-entropy model, by comparing the theoretical
predictions with the results of computer simulations, in which the Schroedinger
equation is solved numerically inside the cavity for one and two open channels
in the leads; we analyze, in addition to the conductance, the zero-frequency
limit of the shot-noise power spectrum. We also obtain theoretical results for
the ensemble average of this last quantity, for the orthogonal and unitary
cases of the circular ensemble and an arbitrary number of channels. Generally
speaking, the agreement between theory and numerics is good. In some of the
cavities that we study, short paths consist of whispering gallery modes, which
were excluded in previous studies. These cavities turn out to be all the more
interesting, as it is in relation with them that we found certain systematic
discrepancies in the comparison with theory. We give evidence that it is the
lack of stationarity inside the energy interval that is analyzed, and hence the
lack of ergodicity that gives rise to the discrepancies. Indeed, the agreement
between theory and numerical simulations is improved when the energy interval
is reduced to a point and the statistics is then collected over an ensemble. It
thus appears that the maximum-entropy model is valid beyond the domain where it
was originally derived. An understanding of this situation is still lacking at
the present moment.Comment: Revised version, minor modifications, 28 pages, 7 figure
Dynamics of Enceladus and Dione inside the 2:1 Mean-Motion Resonance under Tidal Dissipation
In a previous work (Callegari and Yokoyama 2007, Celest. Mech. Dyn. Astr.
vol. 98), the main features of the motion of the pair Enceladus-Dione were
analyzed in the frozen regime, i.e., without considering the tidal evolution.
Here, the results of a great deal of numerical simulations of a pair of
satellites similar to Enceladus and Dione crossing the 2:1 mean-motion
resonance are shown. The resonance crossing is modeled with a linear tidal
theory, considering a two-degrees-of-freedom model written in the framework of
the general three-body planar problem. The main regimes of motion of the system
during the passage through resonance are studied in detail. We discuss our
results comparing them with classical scenarios of tidal evolution of the
system. We show new scenarios of evolution of the Enceladus-Dione system
through resonance not shown in previous approaches of the problem.Comment: 36 pages, 12 figures. Accepted in Celestial Mechanics and Dynamical
Astronom
Nonplanar integrability at two loops
In this article we compute the action of the two loop dilatation operator on
restricted Schur polynomials that belong to the su(2) sector, in the displaced
corners approximation. In this non-planar large N limit, operators that
diagonalize the one loop dilatation operator are not corrected at two loops.
The resulting spectrum of anomalous dimensions is related to a set of decoupled
harmonic oscillators, indicating integrability in this sector of the theory at
two loops. The anomalous dimensions are a non-trivial function of the 't Hooft
coupling, with a spectrum that is continuous and starting at zero at large N,
but discrete at finite N.Comment: version to appear in JHE
Quantum Transparency of Anderson Insulator Junctions: Statistics of Transmission Eigenvalues, Shot Noise, and Proximity Conductance
We investigate quantum transport through strongly disordered barriers, made
of a material with exceptionally high resistivity that behaves as an Anderson
insulator or a ``bad metal'' in the bulk, by analyzing the distribution of
Landauer transmission eigenvalues for a junction where such barrier is attached
to two clean metallic leads. We find that scaling of the transmission
eigenvalue distribution with the junction thickness (starting from the single
interface limit) always predicts a non-zero probability to find high
transmission channels even in relatively thick barriers. Using this
distribution, we compute the zero frequency shot noise power (as well as its
sample-to-sample fluctuations) and demonstrate how it provides a single number
characterization of non-trivial transmission properties of different types of
disordered barriers. The appearance of open conducting channels, whose
transmission eigenvalue is close to one, and corresponding violent mesoscopic
fluctuations of transport quantities explain at least some of the peculiar
zero-bias anomalies in the Anderson-insulator/superconductor junctions observed
in recent experiments [Phys. Rev. B {\bf 61}, 13037 (2000)]. Our findings are
also relevant for the understanding of the role of defects that can undermine
quality of thin tunnel barriers made of conventional band-insulators.Comment: 9 pages, 8 color EPS figures; one additional figure on mesoscopic
fluctuations of Fano facto
Generalized Fokker-Planck Equation For Multichannel Disordered Quantum Conductors
The Dorokhov-Mello-Pereyra-Kumar (DMPK) equation, which describes the
distribution of transmission eigenvalues of multichannel disordered conductors,
has been enormously successful in describing a variety of detailed transport
properties of mesoscopic wires. However, it is limited to the regime of quasi
one dimension only. We derive a one parameter generalization of the DMPK
equation, which should broaden the scope of the equation beyond the limit of
quasi one dimension.Comment: 8 pages, abstract, introduction and summary rewritten for broader
readership. To be published in Phys. Rev. Let
Conductance length autocorrelation in quasi one-dimensional disordered wires
Employing techniques recently developed in the context of the Fokker--Planck
approach to electron transport in disordered systems we calculate the
conductance length correlation function
for quasi 1d wires. Our result is valid for arbitrary lengths L and .
In the metallic limit the correlation function is given by a squared
Lorentzian. In the localized regime it decays exponentially in both L and
. The correlation length is proportional to L in the metallic regime
and saturates at a value approximately given by the localization length
as .Comment: 23 pages, Revtex, two figure
Statistical Scattering of Waves in Disordered Waveguides: from Microscopic Potentials to Limiting Macroscopic Statistics
We study the statistical properties of wave scattering in a disordered
waveguide. The statistical properties of a "building block" of length (delta)L
are derived from a potential model and used to find the evolution with length
of the expectation value of physical quantities. In the potential model the
scattering units consist of thin potential slices, idealized as delta slices,
perpendicular to the longitudinal direction of the waveguide; the variation of
the potential in the transverse direction may be arbitrary. The sets of
parameters defining a given slice are taken to be statistically independent
from those of any other slice and identically distributed. In the
dense-weak-scattering limit, in which the potential slices are very weak and
their linear density is very large, so that the resulting mean free paths are
fixed, the corresponding statistical properties of the full waveguide depend
only on the mean free paths and on no other property of the slice distribution.
The universality that arises demonstrates the existence of a generalized
central-limit theorem.
Our final result is a diffusion equation in the space of transfer matrices of
our system, which describes the evolution with the length L of the disordered
waveguide of the transport properties of interest. In contrast to earlier
publications, in the present analysis the energy of the incident particle is
fully taken into account.Comment: 75 pages, 10 figures, submitted to Phys. Rev
Fokker-Planck description of the transfer matrix limiting distribution in the scattering approach to quantum transport
The scattering approach to quantum transport through a disordered
quasi-one-dimensional conductor in the insulating regime is discussed in terms
of its transfer matrix \bbox{T}. A model of one-dimensional wires which
are coupled by random hopping matrix elements is compared with the transfer
matrix model of Mello and Tomsovic. We derive and discuss the complete
Fokker-Planck equation which describes the evolution of the probability
distribution of \bbox{TT}^{\dagger} with system length in the insulating
regime. It is demonstrated that the eigenvalues of \ln\bbox{TT}^{\dagger}
have a multivariate Gaussian limiting probability distribution. The parameters
of the distribution are expressed in terms of averages over the stationary
distribution of the eigenvectors of \bbox{TT}^{\dagger}. We compare the
general form of the limiting distribution with results of random matrix theory
and the Dorokhov-Mello-Pereyra-Kumar equation.Comment: 25 pages, revtex, no figure
Equivalence of Fokker-Planck approach and non-linear -model for disordered wires in the unitary symmetry class
The exact solution of the Dorokhov-Mello-Pereyra-Kumar-equation for quasi
one-dimensional disordered conductors in the unitary symmetry class is employed
to calculate all -point correlation functions by a generalization of the
method of orthogonal polynomials. We obtain closed expressions for the first
two conductance moments which are valid for the whole range of length scales
from the metallic regime () to the insulating regime () and
for arbitrary channel number. In the limit (with )
our expressions agree exactly with those of the non-linear -model
derived from microscopic Hamiltonians.Comment: 9 pages, Revtex, one postscript figur
Path Integral Approach to the Scattering Theory of Quantum Transport
The scattering theory of quantum transport relates transport properties of
disordered mesoscopic conductors to their transfer matrix \bbox{T}. We
introduce a novel approach to the statistics of transport quantities which
expresses the probability distribution of \bbox{T} as a path integral. The
path integal is derived for a model of conductors with broken time reversal
invariance in arbitrary dimensions. It is applied to the
Dorokhov-Mello-Pereyra-Kumar (DMPK) equation which describes
quasi-one-dimensional wires. We use the equivalent channel model whose
probability distribution for the eigenvalues of \bbox{TT}^{\dagger} is
equivalent to the DMPK equation independent of the values of the forward
scattering mean free paths. We find that infinitely strong forward scattering
corresponds to diffusion on the coset space of the transfer matrix group. It is
shown that the saddle point of the path integral corresponds to ballistic
conductors with large conductances. We solve the saddle point equation and
recover random matrix theory from the saddle point approximation to the path
integral.Comment: REVTEX, 9 pages, no figure
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