110 research outputs found
Localization of Charged Quantum Particles in a Static Random Magnetic Field
We consider a charged quantum particle in a random magnetic field with
Gaussian, delta-correlated statistics. We show that although the single
particle properties are peculiar, two particle quantities such as the diffusion
constant can be calculated in perturbation theory. We map the problem onto a
non-linear sigma-model for Q-matrices of unitary symmetry with renormalized
diffusion coefficient for which all states are known to be localized in
dimensions. Our results compare well with recent numerical data.Comment: REVTEX, 12 pages, 1 figure attached as a postscript file. To appear
in Phys.Rev.
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
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.
Statistics of pre-localized states in disordered conductors
The distribution function of local amplitudes of single-particle states in
disordered conductors is calculated on the basis of the supersymmetric
-model approach using a saddle-point solution of its reduced version.
Although the distribution of relatively small amplitudes can be approximated by
the universal Porter-Thomas formulae known from the random matrix theory, the
statistics of large amplitudes is strongly modified by localization effects. In
particular, we find a multifractal behavior of eigenstates in 2D conductors
which follows from the non-integer power-law scaling for the inverse
participation numbers (IPN) with the size of the system. This result is valid
for all fundamental symmetry classes (unitary, orthogonal and symplectic). The
multifractality is due to the existence of pre-localized states which are
characterized by power-law envelopes of wave functions, , . The pre-localized states in short quasi-1D wires have the
power-law tails , too, although their IPN's
indicate no fractal behavior. The distribution function of the
largest-amplitude fluctuations of wave functions in 2D and 3D conductors has
logarithmically-normal asymptotics.Comment: RevTex, 17 twocolumn pages; revised version (several misprint
corrected
Magnetoresistance of Granular Superconducting Metals in a Strong Magnetic Field
The magnetoresistance of a granular superconductor in a strong magnetic field
is considered. It is assumed that this field destroys the superconducting gap
in each grain, such that all interesting effects considered in the paper are
due to superconducting fluctuations. The conductance of the system is assumed
to be large, which allows us to neglect all localization effects as well as the
Coulomb interaction. It is shown that at low temperatures the superconducting
fluctuations reduce the one-particle density of states but do not contribute to
transport. As a result, the resistivity of the normal state exceeds the
classical resistivity approaching the latter only in the limit of extremely
strong magnetic fields, and this leads to a negative magnetoresistance. We
present detailed calculations of physical quatities relevant for describing the
effect and make a comparison with existing experiments.Comment: 24 pages, 10 figure
Coulomb effects in granular materials at not very low temperatures
We consider effects of Coulomb interaction in a granular normal metal at not
very low temperatures suppressing weak localization effects. In this limit
calculations with the initial electron Hamiltonian are reduced to integrations
over a phase variable with an effective action, which can be considered as a
bosonization for the granular metal. Conditions of the applicability of the
effective action are considered in detail and importance of winding numbers for
the phase variables is emphasized. Explicit calculations are carried out for
the conductivity and the tunneling density of states in the limits of large
and small tunnelling conductances. It is demonstrated for any
dimension of the array of the grains that at small the conductivity and the
tunnelling density of states decay with temperature exponentially. At large
the conductivity also decays with decreasing the temparature and its
temperature dependence is logarithmic independent of dimensionality and
presence of a magnetic field. The tunnelling density of states for is
anomalous in any dimension but the anomaly is stronger than logarithmic in low
dimensions and is similar to that for disordered systems. The formulae derived
are compared with existing experiments. The logarithmic behavior of the
conductivity at large obtained in our model can explain numerous
experiments on systems with a granular structure including some high
materials.Comment: 30 page
Constructive Matrix Theory
We extend the technique of constructive expansions to compute the connected
functions of matrix models in a uniform way as the size of the matrix
increases. This provides the main missing ingredient for a non-perturbative
construction of the field theory on the Moyal four
dimensional space.Comment: 12 pages, 3 figure
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
Parity Effects in Stacked Nanoscopic Quantum Rings
The ground state and the dielectric response of stacked quantum rings are
investigated in the presence of an applied magnetic field along the ring axis.
For odd number of rings and an electric field perpendicular to the axis, a
linear Stark effect occurs at distinct values of the magnetic field. At those
fields energy levels cross in the absence of electric field. For even values of
a quadratic Stark effect is expected in all cases, but the induced electric
polarization is discontinuous at those special magnetic fields. Experimental
consequences for related nanostructures are discussed.Comment: typos corrected, to appear Phys. Rev. B (Rapid Communication) 15 Au
Gap Fluctuations in Inhomogeneous Superconductors
Spatial fluctuations of the effective pairing interaction between electrons
in a superconductor induce variations of the order parameter which in turn lead
to significant changes in the density of states. In addition to an overall
reduction of the quasi-particle energy gap, theory suggests that mesoscopic
fluctuations of the impurity potential induce localised tail states below the
mean-field gap edge. Using a field theoretic approach, we elucidate the nature
of the states in the `sub-gap' region. Specifically, we show that these states
are associated with replica symmetry broken instanton solutions of the
mean-field equations.Comment: 11 pages, 3 figures included. To be published in PRB (Sept. 2001
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