619 research outputs found
A mean-field theory of Anderson localization
Anderson model of noninteracting disordered electrons is studied in high
spatial dimensions. We find that off-diagonal one- and two-particle propagators
behave as gaussian random variables w.r.t. momentum summations. With this
simplification and with the electron-hole symmetry we reduce the parquet
equations for two-particle irreducible vertices to a single algebraic equation
for a local vertex. We find a disorder-driven bifurcation point in this
equation signalling vanishing of diffusion and onset of Anderson localization.
There is no bifurcation in where all states are localized. A natural
order parameter for Anderson localization pops up in the construction.Comment: REVTeX4, 4 pages, 2 EPS figure
Charge accumulation at the boundaries of a graphene strip induced by a gate voltage: Electrostatic approach
Distribution of charge induced by a gate voltage in a graphene strip is
investigated. We calculate analytically the charge profile and demonstrate a
strong(macroscopic) charge accumulation along the boundaries of a
micrometers-wide strip. This charge inhomogeneity is especially important in
the quantum Hall regime where we predict the doubling of the number of edge
states and coexistence of two different types of such states. Applications to
graphene-based nanoelectronics are discussed.Comment: 5 pages, 6 figures, Title changed due to Edito
Role of the impurity-potential range in disordered d-wave superconductors
We analyze how the range of disorder affects the localization properties of
quasiparticles in a two-dimensional d-wave superconductor within the standard
non-linear sigma-model approach to disordered systems. We show that for purely
long-range disorder, which only induces intra-node scattering processes, the
approach is free from the ambiguities which often beset the disordered
Dirac-fermion theories, and gives rise to a Wess-Zumino-Novikov-Witten action
leading to vanishing density of states and finite conductivities. We also study
the crossover induced by internode scattering due to a short range component of
the disorder, thus providing a coherent non-linear sigma-model description in
agreement with all the various findings of different approaches.Comment: 38 pages, 1 figur
Phase Transition in a Model with Non-Compact Symmetry on Bethe Lattice and the Replica Limit
We solve nonlinear vector model on Bethe lattice and show that it
exhibits a transition from ordered to disordered state for . If
the replica limit is taken carefully, the model is shown to reduce to
the corresponding supersymmetric model. The latter was introduced by Zirnbauer
as a toy model for the Anderson localization transition. We argue thus that the
non-compact replica models describe correctly the Anderson transition features.
This should be contrasted to their failure in the case of the level correlation
problem.Comment: 21 pages, REVTEX, 2 Postscript figures, uses epsf styl
A nearly closed ballistic billiard with random boundary transmission
A variety of mesoscopic systems can be represented as a billiard with a
random coupling to the exterior at the boundary. Examples include quantum dots
with multiple leads, quantum corrals with different kinds of atoms forming the
boundary, and optical cavities with random surface refractive index. The
specific example we study is a circular (integrable) billiard with no internal
impurities weakly coupled to the exterior by a large number of leads with one
channel open in each lead. We construct a supersymmetric nonlinear
-model by averaging over the random coupling strengths between bound
states and channels. The resulting theory can be used to evaluate the
statistical properties of any physically measurable quantity in a billiard. As
an illustration, we present results for the local density of states.Comment: 5 pages, 1 figur
Nonperturbative interaction effects in the thermodynamics of disordered wires
We study nonperturbative interaction corrections to the thermodynamic
quantities of multichannel disordered wires in the presence of the Coulomb
interactions. Within the replica nonlinear -model (NLM)
formalism, they arise from nonperturbative soliton saddle points of the
NLM action. The problem is reduced to evaluating the partition function
of a replicated classical one dimensional Coulomb gas. The state of the latter
depends on two parameters: the number of transverse channels in the wire,
N_{ch}, and the dimensionless conductance, G(L_T), of a wire segment of length
equal to the thermal diffusion length, L_T. At relatively high temperatures,
, the gas is dimerized, i.e. consists of bound
neutral pairs. At lower temperatures, ,
the pairs overlap and form a Coulomb plasma. The crossover between the two
regimes occurs at a parametrically large conductance ,
and may be studied independently from the perturbative effects. Specializing to
the high temperature regime, we obtain the leading nonperturbative correction
to the wire heat capacity. Its ratio to the heat capacity for noninteracting
electrons, C_0, is .Comment: 18 page
Dynamics of weakly localized waves
We develop a transport theory to describe the dynamics of (weakly) localized
waves in a quasi-1D tube geometry both in reflection and in transmission. We
compare our results to recent experiments with microwaves, and to other
theories such as random matrix theory and supersymmetric theory.Comment: RevTeX, 4 pages, 2 figure
Dynamics of excitations in a one-dimensional Bose liquid
We show that the dynamic structure factor of a one-dimensional Bose liquid
has a power-law singularity defining the main mode of collective excitations.
Using the Lieb-Liniger model, we evaluate the corresponding exponent as a
function of the wave vector and the interaction strength
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