26 research outputs found
Disordered quantum wires: microscopic origins of the DMPK theory and Ohm's law
We study the electronic transport properties of the Anderson model on a
strip, modeling a quasi one-dimensional disordered quantum wire. In the
literature, the standard description of such wires is via random matrix theory
(RMT). Our objective is to firmly relate this theory to a microscopic model. We
correct and extend previous work (arXiv:0912.1574) on the same topic. In
particular, we obtain through a physically motivated scaling limit an ensemble
of random matrices that is close to, but not identical to the standard transfer
matrix ensembles (sometimes called TOE, TUE), corresponding to the Dyson
symmetry classes \beta=1,2. In the \beta=2 class, the resulting conductance is
the same as the one from the ideal ensemble, i.e.\ from TUE. In the \beta=1
class, we find a deviation from TOE. It remains to be seen whether or not this
deviation vanishes in a thick-wire limit, which is the experimentally relevant
regime. For the ideal ensembles, we also prove Ohm's law for all symmetry
classes, making mathematically precise a moment expansion by Mello and Stone.
This proof bypasses the explicit but intricate solution methods that underlie
most previous results.Comment: Corrects and extends arXiv:0912.157
The random phase property and the Lyapunov Spectrum for disordered multi-channel systems
A random phase property establishing in the weak coupling limit a link between quasi-one-dimensional random Schrödinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system of coordinates act on the isotropic frames and lead to a Markov process with a unique invariant measure which is of geometric nature. On the elliptic part of the transfer matrices, this measure is invariant under the unitaries in the hermitian symplectic group of the universality class under study. While the random phase property can up to now only be proved in special models or in a restricted sense, we provide strong numerical evidence that it holds in the Anderson model of localization. A main outcome of the random phase property is a perturbative calculation of the Lyapunov exponents which shows that the Lyapunov spectrum is equidistant and that the localization lengths for large systems in the unitary, orthogonal and symplectic ensemble differ by a factor 2 each. In an Anderson-Ando model on a tubular geometry with magnetic field and spin-orbit coupling, the normal system of coordinates is calculated and this is used to derive explicit energy dependent formulas for the Lyapunov spectrum
Decay Rate Distributions of Disordered Slabs and Application to Random Lasers
We compute the distribution of the decay rates (also referred to as residues)
of the eigenstates of a disordered slab from a numerical model. From the
results of the numerical simulations, we are able to find simple analytical
formulae that describe those results well. This is possible for samples both in
the diffusive and in the localised regime. As example of a possible
application, we investigate the lasing threshold of random lasers.Comment: 11 pages, 11 figure
Electronic transport in strongly anisotropic disordered systems: model for the random matrix theory with non-integer beta
We study numerically an electronic transport in strongly anisotropic weakly
disorderd two-dimensional systems. We find that the conductance distribution is
gaussian but the conductance fluctuations increase when anisotropy becomes
stronger. We interpret this result by random matrix theory with non-integer
symmetry parameter beta, in accordance with recent theoretical work of
K.A.Muttalib and J.R.Klauder [Phys.Rev.Lett. 82 (1999) 4272]. Analysis of the
statistics of transport paramateres supports this hypothesis.Comment: 8 pages, 7 *.eps figure
Impurity band in clean superconducting weak links
Weak impurity scattering produces a narrow band with a finite density of
states near the phase difference in the mid-gap energy spectrum of
a macroscopic superconducting weak link. The equivalent distribution of
transmission coefficients of various cunducting quantum channels is found.Comment: 4 pages, 4 figures, changed conten
Strong Effects of Weak Localization in Charge Density Wave/Normal Metal Hybrids
Collective transport through a multichannel disordered conductor in contact
with charge-density-wave electrodes is theoretically investigated. The
statistical distribution function of the threshold potential for charge-density
wave sliding is calculated by random matrix theory. In the diffusive regime
weak localization has a strong effect on the sliding motion.Comment: To be published in Physical Review
Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar
The 2-- to 1--dimensional crossover of the localisation length of electrons
confined to a disordered quantum wire of finite width is studied in a
model of electrons moving in the potential of uncorrelated impurities. An
analytical formula for the localisation length is derived, describing the
dimensional crossover as function of width , conductance and
perpendicular magnetic field . On the basis of these results, the scaling
analysis of the quantum Hall effect in high Landau levels, and the
delocalisation transition in a quantum Hall wire are reconsidered.Comment: 12 pages, 7 figure
Conductance distribution in disordered quantum wires: Crossover between the metallic and insulating regimes
We calculate the distribution of the conductance P(g) for a
quasi-one-dimensional system in the metal to insulator crossover regime, based
on a recent analytical method valid for all strengths of disorder. We show the
evolution of P(g) as a function of the disorder parameter from a insulator to a
metal. Our results agree with numerical studies reported on this problem, and
with analytical results for the average and variance of g.Comment: 8 pages, 5 figures. Final version (minor changes
Symmetry, dimension and the distribution of the conductance at the mobility edge
The probability distribution of the conductance at the mobility edge,
, in different universality classes and dimensions is investigated
numerically for a variety of random systems. It is shown that is
universal for systems of given symmetry, dimensionality, and boundary
conditions. An analytical form of for small values of is discussed
and agreement with numerical data is observed. For , is
proportional to rather than .Comment: 4 pages REVTeX, 5 figures and 2 tables include
Shot Noise at High Temperatures
We consider the possibility of measuring non-equilibrium properties of the
current correlation functions at high temperatures (and small bias). Through
the example of the third cumulant of the current () we demonstrate
that odd order correlation functions represent non-equilibrium physics even at
small external bias and high temperatures. We calculate for a quasi-one-dimensional diffusive constriction. We calculate the
scaling function in two regimes: when the scattering processes are purely
elastic and when the inelastic electron-electron scattering is strong. In both
cases we find that interpolates between two constants. In the low (high)
temperature limit is strongly (weakly) enhanced (suppressed) by the
electron-electron scattering.Comment: 11 pages 4 fig. submitted to Phys. Rev.