19 research outputs found
Reconciling Conductance Fluctuations and the Scaling Theory of Localization
We reconcile the phenomenon of mesoscopic conductance fluctuations with the
single parameter scaling theory of the Anderson transition. We calculate three
averages of the conductance distribution: , and
where is the conductance in units of and is the resistance
and demonstrate that these quantities obey single parameter scaling laws. We
obtain consistent estimates of the critical exponent from the scaling of all
these quantities
Critical conductance of the chiral 2d random flux model
The two-terminal conductance of a random flux model defined on a square
lattice is investigated numerically at the band center using a transfer matrix
method. Due to the chiral symmetry, there exists a critical point where the
ensemble averaged mean conductance is scale independent. We also study the
conductance distribution function which depends on the boundary conditions and
on the number of lattice sites being even or odd. We derive a critical exponent
for square samples of even width using one-parameter scaling
of the conductance. This result could not be obtained previously from the
divergence of the localization length in quasi-one-dimensional systems due to
pronounced finite-size effects.Comment: EP2DS-17, Genua 2007, accepted for publication in Physica
Probability distribution of the conductance at the mobility edge
Distribution of the conductance P(g) at the critical point of the
metal-insulator transition is presented for three and four dimensional
orthogonal systems. The form of the distribution is discussed. Dimension
dependence of P(g) is proven. The limiting cases and are
discussed in detail and relation in the limit is proven.Comment: 4 pages, 3 .eps figure
Low-Dimensional Life of Critical Anderson Electron
We show that critical Anderson electron in 3 dimensions is present in its
spatial effective support, which was recently determined to be a region of
fractal dimension , with probability 1 in infinite volume.
Hence, its physics is fully confined to space of this lower dimension. Stated
differently, effective description of space occupied by critical Anderson
electron becomes a full description in infinite volume. We then show that it is
a general feature of the effective counting dimension underlying these
concepts, that its subnominal value implies an exact description by effective
support.Comment: 4 pages, 2 figures; v2: fixes minor glitches; v3: published versio
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
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
Scaling of the conductance distribution near the Anderson transition
The single parameter scaling hypothesis is the foundation of our
understanding of the Anderson transition. However, the conductance of a
disordered system is a fluctuating quantity which does not obey a one parameter
scaling law. It is essential to investigate the scaling of the full conductance
distribution to establish the scaling hypothesis. We present a clear cut
numerical demonstration that the conductance distribution indeed obeys one
parameter scaling near the Anderson transition
Conductance fluctuations and boundary conditions
The conductance fluctuations for various types for two-- and
three--dimensional disordered systems with hard wall and periodic boundary
conditions are studied, all the way from the ballistic (metallic) regime to the
localized regime. It is shown that the universal conductance fluctuations (UCF)
depend on the boundary conditions. The same holds for the metal to insulator
transition. The conditions for observing the UCF are also given.Comment: 4 pages RevTeX, 5 figures include
Slovanský literární svět: kontexty a konfrontace IV
Title in English: Slavonic Literary World: Contexts and Confrontations IV The collection of papers called Slavonic Literary World: Contexts and Confrontations IV presents results of research of young slavists working at Slavonic departures in the Czech Republic (Brno, Hradec Králové) and abroad (Slovakia, Poland)
Non-Linear Thermoelectric Devices with Surface-Disordered Nanowires
We reviewed some recent ideas to improve the efficiency and power output of thermoelectric nano-devices. We focused on two essentially independent aspects: (i) increasing the charge current by taking advantage of an interplay between the material and the thermodynamic parameters, which is only available in the non-linear regime; and (ii) decreasing the heat current by using nanowires with surface disorder, which helps excite localized phonons at random positions that can strongly scatter the propagating phonons carrying the thermal current