101 research outputs found
Dimensionality dependence of the wave function statistics at the Anderson transition
The statistics of critical wave functions at the Anderson transition in three
and four dimensions are studied numerically. The distribution of the inverse
participation ratios (IPR) is shown to acquire a scale-invariant form in
the limit of large system size. Multifractality spectra governing the scaling
of the ensemble-averaged IPRs are determined. Conjectures concerning the IPR
statistics and the multifractality at the Anderson transition in a high spatial
dimensionality are formulated.Comment: 4 pages, 4 figure
Distribution of local density of states in disordered metallic samples: logarithmically normal asymptotics
Asymptotical behavior of the distribution function of local density of states
(LDOS) in disordered metallic samples is studied with making use of the
supersymmetric --model approach, in combination with the saddle--point
method. The LDOS distribution is found to have the logarithmically normal
asymptotics for quasi--1D and 2D sample geometry. In the case of a quasi--1D
sample, the result is confirmed by the exact solution. In 2D case a perfect
agreement with an earlier renormalization group calculation is found. In 3D the
found asymptotics is of somewhat different type: P(\rho)\sim
\exp(-\mbox{const}\,|\ln^3\rho|).Comment: REVTEX, 14 pages, no figure
Fluctuation of the Correlation Dimension and the Inverse Participation Number at the Anderson Transition
The distribution of the correlation dimension in a power law band random
matrix model having critical, i.e. multifractal, eigenstates is numerically
investigated. It is shown that their probability distribution function has a
fixed point as the system size is varied exactly at a value obtained from the
scaling properties of the typical value of the inverse participation number.
Therefore the state-to-state fluctuation of the correlation dimension is
tightly linked to the scaling properties of the joint probability distribution
of the eigenstates.Comment: 4 pages, 5 figure
Localization and fluctuations of local spectral density on tree-like structures with large connectivity: Application to the quasiparticle line shape in quantum dots
We study fluctuations of the local density of states (LDOS) on a tree-like
lattice with large branching number . The average form of the local spectral
function (at given value of the random potential in the observation point)
shows a crossover from the Lorentzian to semicircular form at ,
where , is the typical value of the hopping matrix
element, and is the width of the distribution of random site energies. For
the LDOS fluctuations (with respect to this average form) are
weak. In the opposite case, , the fluctuations get strong and the
average LDOS ceases to be representative, which is related to the existence of
the Anderson transition at . On the localized side
of the transition the spectrum is discrete, and LDOS is given by a set of
-like peaks. The effective number of components in this regime is given
by , with being the inverse participation ratio. It is shown that
has in the transition point a limiting value close to unity, , so that the system undergoes a transition directly from the deeply
localized to extended phase. On the side of delocalized states, the peaks in
LDOS get broadened, with a width being exponentially small near the
transition point. We discuss application of our results to the problem of the
quasiparticle line shape in a finite Fermi system, as suggested recently by
Altshuler, Gefen, Kamenev, and Levitov.Comment: 12 pages, 1 figure. Misprints in eqs.(21) and (28) corrected, section
VII added. Accepted for publication in Phys. Rev.
Quasiclassical magnetotransport in a random array of antidots
We study theoretically the magnetoresistance of a
two-dimensional electron gas scattered by a random ensemble of impenetrable
discs in the presence of a long-range correlated random potential. We believe
that this model describes a high-mobility semiconductor heterostructure with a
random array of antidots. We show that the interplay of scattering by the two
types of disorder generates new behavior of which is absent for
only one kind of disorder. We demonstrate that even a weak long-range disorder
becomes important with increasing . In particular, although
vanishes in the limit of large when only one type of disorder is present,
we show that it keeps growing with increasing in the antidot array in the
presence of smooth disorder. The reversal of the behavior of is
due to a mutual destruction of the quasiclassical localization induced by a
strong magnetic field: specifically, the adiabatic localization in the
long-range Gaussian disorder is washed out by the scattering on hard discs,
whereas the adiabatic drift and related percolation of cyclotron orbits
destroys the localization in the dilute system of hard discs. For intermediate
magnetic fields in a dilute antidot array, we show the existence of a strong
negative magnetoresistance, which leads to a nonmonotonic dependence of
.Comment: 21 pages, 13 figure
Current correlations and quantum localization in 2D disordered systems with broken time-reversal invariance
We study long-range correlations of equilibrium current densities in a
two-dimensional mesoscopic system with the time reversal invariance broken by a
random or homogeneous magnetic field. Our result is universal, i.e. it does not
depend on the type (random potential or random magnetic field) or correlation
length of disorder. This contradicts recent sigma-model calculations of
Taras-Semchuk and Efetov (TS&E) for the current correlation function, as well
as for the renormalization of the conductivity. We show explicitly that the new
term in the sigma-model derived by TS&E and claimed to lead to delocalization
does not exist. The error in the derivation of TS&E is traced to an incorrect
ultraviolet regularization procedure violating current conservation and gauge
invariance.Comment: 8 pages, 3 figure
Frequency Dependence of Magnetopolarizability of Mesoscopic Grains
We calculate average magnetopolarizability of an isolated metallic sample at
frequency comparable to the mean level spacing . The frequency
dependence of the magnetopolarizability is described by a universal function of
.Comment: 3 pages, 1 figur
Fractional microwave-induced resistance oscillations
We develop a systematic theory of microwave-induced oscillations in
magnetoresistivity of a 2D electron gas in the vicinity of fractional harmonics
of the cyclotron resonance, observed in recent experiments. We show that in the
limit of well-separated Landau levels the effect is dominated by the
multiphoton inelastic mechanism. At moderate magnetic field, two single-photon
mechanisms become important. One of them is due to resonant series of multiple
single-photon transitions, while the other originates from microwave-induced
sidebands in the density of states of disorder-broadened Landau levels.Comment: 3 pages, 2 figures; Proceedings of EP2DS17 to be published in Physica
E; less technical version of arXiv:0707.099
Critical generalized inverse participation ratio distributions
The system size dependence of the fluctuations in generalized inverse
participation ratios (IPR's) at criticality is investigated
numerically. The variances of the IPR logarithms are found to be
scale-invariant at the macroscopic limit. The finite size corrections to the
variances decay algebraically with nontrivial exponents, which depend on the
Hamiltonian symmetry and the dimensionality. The large- dependence of the
asymptotic values of the variances behaves as according to theoretical
estimates. These results ensure the self-averaging of the corresponding
generalized dimensions.Comment: RevTex4, 5 pages, 4 .eps figures, to be published in Phys. Rev.
- …