4 research outputs found
A Brownian Motion Model of Parametric Correlations in Ballistic Cavities
A Brownian motion model is proposed to study parametric correlations in the
transmission eigenvalues of open ballistic cavities. We find interesting
universal properties when the eigenvalues are rescaled at the hard edge of the
spectrum. We derive a formula for the power spectrum of the fluctuations of
transport observables as a response to an external adiabatic perturbation. Our
formula correctly recovers the Lorentzian-squared behaviour obtained by
semiclassical approaches for the correlation function of conductance
fluctuations.Comment: 19 pages, written in RevTe
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
Mesoscopic conductance and its fluctuations at non-zero Hall angle
We consider the bilocal conductivity tensor, the two-probe conductance and
its fluctuations for a disordered phase-coherent two-dimensional system of
non-interacting electrons in the presence of a magnetic field, including
correctly the edge effects. Analytical results are obtained by perturbation
theory in the limit . For mesoscopic systems the conduction
process is dominated by diffusion but we show that, due to the lack of
time-reversal symmetry, the boundary condition for diffusion is altered at the
reflecting edges. Instead of the usual condition, that the derivative along the
direction normal to the wall of the diffusing variable vanishes, the derivative
at the Hall angle to the normal vanishes. We demonstrate the origin of this
boundary condition from different starting points, using (i) a simplified
Chalker-Coddington network model, (ii) the standard diagrammatic perturbation
expansion, and (iii) the nonlinear sigma-model with the topological term, thus
establishing connections between the different approaches. Further boundary
effects are found in quantum interference phenomena. We evaluate the mean
bilocal conductivity tensor , and the mean and variance
of the conductance, to leading order in and to order
, and find that the variance of the conductance
increases with the Hall ratio. Thus the conductance fluctuations are no longer
simply described by the unitary universality class of the case,
but instead there is a one-parameter family of probability distributions. In
the quasi-one-dimensional limit, the usual universal result for the conductance
fluctuations of the unitary ensemble is recovered, in contrast to results of
previous authors. Also, a long discussion of current conservation.Comment: Latex, uses RevTex, 58 pages, 5 figures available on request at
[email protected]. Submitted to Phys. Rev.