78 research outputs found
Single parameter scaling in 1-D localized absorbing systems
Numerical study of the scaling of transmission fluctuations in the 1-D
localization problem in the presence of absorption is carried out. Violations
of single parameter scaling for lossy systems are found and explained on the
basis of a new criterion for different types of scaling behavior derived by
Deych et al [Phys. Rev. Lett., {\bf 84}, 2678 (2000)].Comment: 7 pages, 6 figures, RevTex, submitted to Phys. Rev.
Ground state properties of the 2D disordered Hubbard model
We study the ground state of the two-dimensional (2D) disordered Hubbard
model by means of the projector quantum Monte Carlo (PQMC) method. This
approach allows us to investigate the ground state properties of this model for
lattice sizes up to , at quarter filling, for a broad range of
interaction and disorder strengths. Our results show that the ground state of
this system of spin-1/2 fermions remains localised in the presence of the
short-ranged Hubbard interaction.Comment: 7 pages, 9 figure
Wave function multifractality and dephasing at metal-insulator and quantum Hall transitions
We analyze the critical behavior of the dephasing rate induced by short-range
electron-electron interaction near an Anderson transition of metal-insulator or
quantum Hall type. The corresponding exponent characterizes the scaling of the
transition width with temperature. Assuming no spin degeneracy, the critical
behavior can be studied by performing the scaling analysis in the vicinity of
the non-interacting fixed point, since the latter is stable with respect to the
interaction. We combine an analytical treatment (that includes the
identification of operators responsible for dephasing in the formalism of the
non-linear sigma-model and the corresponding renormalization-group analysis in
dimensions) with numerical simulations on the Chalker-Coddington
network model of the quantum Hall transition. Finally, we discuss the current
understanding of the Coulomb interaction case and the available experimental
data.Comment: 33 pages, 7 figures, elsart styl
Metal-insulator transition in two-dimensional disordered systems with power-law transfer terms
We investigate a disordered two-dimensional lattice model for noninteracting
electrons with long-range power-law transfer terms and apply the method of
level statistics for the calculation of the critical properties. The
eigenvalues used are obtained numerically by direct diagonalization. We find a
metal-insulator transition for a system with orthogonal symmetry. The exponent
governing the divergence of the correlation length at the transition is
extracted from a finite size scaling analysis and found to be . The critical eigenstates are also analyzed and the distribution of the
generalized multifractal dimensions is extrapolated.Comment: 4 pages with 4 figures, printed version: PRB, Rapid Communication
Statistical properties of phases and delay times of the one-dimensional Anderson model with one open channel
We study the distribution of phases and of Wigner delay times for a
one-dimensional Anderson model with one open channel. Our approach, based on
classical Hamiltonian maps, allows us an analytical treatment. We find that the
distribution of phases depends drastically on the parameter where is the variance of the disorder distribution and
the wavevector. It undergoes a transition from uniformity to singular
behaviour as increases. The distribution of delay times shows
universal power law tails , while the short time behaviour is
- dependent.Comment: 4 pages, 2 figures, Submitted to PR
Delocalization and Diffusion Profile for Random Band Matrices
We consider Hermitian and symmetric random band matrices in dimensions. The matrix entries , indexed by x,y \in
(\bZ/L\bZ)^d, are independent, centred random variables with variances s_{xy}
= \E |h_{xy}|^2. We assume that is negligible if exceeds the
band width . In one dimension we prove that the eigenvectors of are
delocalized if . We also show that the magnitude of the matrix
entries \abs{G_{xy}}^2 of the resolvent is self-averaging
and we compute \E \abs{G_{xy}}^2. We show that, as and , the behaviour of \E |G_{xy}|^2 is governed by a diffusion operator
whose diffusion constant we compute. Similar results are obtained in higher
dimensions
Inelastic Scattering Time for Conductance Fluctuations
We revisit the problem of inelastic times governing the temperature behavior
of the weak localization correction and mesoscopic fluctuations in one- and
two-dimensional systems. It is shown that, for dephasing by the electron
electron interaction, not only are those times identical but the scaling
functions are also the same.Comment: 10 pages Revtex; 5 eps files include
Magnetotunneling spectroscopy of mesoscopic correlations in two-dimensional electron systems
An approach to experimentally exploring electronic correlation functions in
mesoscopic regimes is proposed. The idea is to monitor the mesoscopic
fluctuations of a tunneling current flowing between the two layers of a
semiconductor double-quantum-well structure. From the dependence of these
fluctuations on external parameters, such as in-plane or perpendicular magnetic
fields, external bias voltages, etc., the temporal and spatial dependence of
various prominent correlation functions of mesoscopic physics can be
determined. Due to the absence of spatially localized external probes, the
method provides a way to explore the interplay of interaction and localization
effects in two-dimensional systems within a relatively unperturbed environment.
We describe the theoretical background of the approach and quantitatively
discuss the behavior of the current fluctuations in diffusive and ergodic
regimes. The influence of both various interaction mechanisms and localization
effects on the current is discussed. Finally a proposal is made on how, at
least in principle, the method may be used to experimentally determine the
relevant critical exponents of localization-delocalization transitions.Comment: 15 pages, 3 figures include
Hidden degree of freedom and critical states in a two-dimensional electron gas in the presence of a random magnetic field
We establish the existence of a hidden degree of freedom and the critical
states of a spinless electron system in a spatially-correlated random magnetic
field with vanishing mean. Whereas the critical states are carried by the
zero-field contours of the field landscape, the hidden degree of freedom is
recognized as being associated with the formation of vortices in these special
contours. It is argued that, as opposed to the coherent backscattering
mechanism of weak localization, a new type of scattering processes in the
contours controls the underlying physics of localization in the random magnetic
field system. In addition, we investigate the role of vortices in governing the
metal-insulator transition and propose a renormalization-group diagram for the
system under study.Comment: 17 pages, 16 figures; Figs. 1, 7, 9, and 10 have been reduced in
quality for e-submissio
Which Kubo formula gives the exact conductance of a mesoscopic disordered system?
In both research and textbook literature one often finds two ``different''
Kubo formulas for the zero-temperature conductance of a non-interacting Fermi
system. They contain a trace of the product of velocity operators and
single-particle (retarded and advanced) Green operators: or . The study investigates the relationship between
these expressions, as well as the requirements of current conservation, through
exact evaluation of such quantum-mechanical traces for a nanoscale (containing
1000 atoms) mesoscopic disordered conductor. The traces are computed in the
semiclassical regime (where disorder is weak) and, more importantly, in the
nonperturbative transport regime (including the region around
localization-delocalization transition) where concept of mean free path ceases
to exist. Since quantum interference effects for such strong disorder are not
amenable to diagrammatic or nonlinear -model techniques, the evolution
of different Green function terms with disorder strength provides novel insight
into the development of an Anderson localized phase.Comment: 7 pages, 5 embedded EPS figures, final published version (note: PRB
article has different title due to editorial censorship
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