50,013 research outputs found
Diffusive propagation of wave packets in a fluctuating periodic potential
We consider the evolution of a tight binding wave packet propagating in a
fluctuating periodic potential. If the fluctuations stem from a stationary
Markov process satisfying certain technical criteria, we show that the square
amplitude of the wave packet after diffusive rescaling converges to a
superposition of solutions of a heat equation.Comment: 13 pages (v2: added a paragraph on the history of the problem, added
some references, correct a few typos; v3 minor corrections, added keywords
and subject classes
Mesoscopic Kondo Effect in an Aharonov-Bohm Ring
An interacting quantum dot inserted in a mesoscopic ring is investigated. A
variational ansatz is employed to describe the ground state of the system in
the presence of the Aharonov-Bohm flux. It is shown that, for even number of
electrons with the energy level spacing smaller than the Kondo temperature, the
persistent current has a value similar to that of a perfect ring with the same
radius. On the other hand, for a ring with odd number electrons, the persistent
current is found to be strongly suppressed compared to that of an ideal ring,
which implies the suppression of the Kondo-resonant transmission. Various
aspects of the Kondo-assisted persistent current are discussed.Comment: 4 pages Revtex, 4 Postscript figures, final version to appear in
Phys. Rev. Lett. 85, No.26 (Dec. 25, 2000
Diffusion of wave packets in a Markov random potential
We consider the evolution of a tight binding wave packet propagating in a
time dependent potential. If the potential evolves according to a stationary
Markov process, we show that the square amplitude of the wave packet converges,
after diffusive rescaling, to a solution of a heat equation.Comment: 19 pages, acknowledgments added and typos correcte
Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case
In proving the Fermionic formulae, combinatorial bijection called the
Kerov--Kirillov--Reshetikhin (KKR) bijection plays the central role. It is a
bijection between the set of highest paths and the set of rigged
configurations. In this paper, we give a proof of crystal theoretic
reformulation of the KKR bijection. It is the main claim of Part I
(math.QA/0601630) written by A. Kuniba, M. Okado, T. Takagi, Y. Yamada, and the
author. The proof is given by introducing a structure of affine combinatorial
matrices on rigged configurations.Comment: 45 pages, version for publication. Introduction revised, more
explanations added to the main tex
Granular gases under extreme driving
We study inelastic gases in two dimensions using event-driven molecular
dynamics simulations. Our focus is the nature of the stationary state attained
by rare injection of large amounts of energy to balance the dissipation due to
collisions. We find that under such extreme driving, with the injection rate
much smaller than the collision rate, the velocity distribution has a power-law
high energy tail. The numerically measured exponent characterizing this tail is
in excellent agreement with predictions of kinetic theory over a wide range of
system parameters. We conclude that driving by rare but powerful energy
injection leads to a well-mixed gas and constitutes an alternative mechanism
for agitating granular matter. In this distinct nonequilibrium steady-state,
energy cascades from large to small scales. Our simulations also show that when
the injection rate is comparable with the collision rate, the velocity
distribution has a stretched exponential tail.Comment: 6 pages, 7 figures; new version contains 2 new figures and text
describing cascade
Kondo-resonance, Coulomb blockade, and Andreev transport through a quantum dot
We study resonant tunneling through an interacting quantum dot coupled to
normal metallic and superconducting leads. We show that large Coulomb
interaction gives rise to novel effects in Andreev transport. Adopting an exact
relation for the Green's function, we find that at zero temperature, the linear
response conductance is enhanced due to Kondo-Andreev resonance in the Kondo
limit, while it is suppressed in the empty site limit. In the Coulomb blockaded
region, on the other hand, the conductance is reduced more than the
corresponding conductance with normal leads because large charging energy
suppresses Andreev reflection.Comment: 3 pages Revtex, 4 Postscript figures, accepted for publication in
Phys. Rev.
A new perturbation treatment applied to the transport through a quantum dot
Resonant tunnelling through an Anderson impurity is investigated by employing
a new perturbation scheme at nonequilibrium. This new approach gives the
correct weak and strong coupling limit in by introducing adjustable
parameters in the self-energy and imposing self-consistency of the occupation
number of the impurity. We have found that the zero-temperature linear response
conductance agrees well with that obtained from the exact sum rule. At finite
temperature the conductance shows a nonzero minimum at the Kondo valley, as
shown in recent experiments. The effects of an applied bias voltage on the
single-particle density of states and on the differential conductances are
discussed for Kondo and non-Kondo systems.Comment: 4 pages, 4 figures, submitted to PRB-Rapid Comm. Email addresses
[email protected], [email protected]
Diffusion-Limited Aggregation Processes with 3-Particle Elementary Reactions
A diffusion-limited aggregation process, in which clusters coalesce by means
of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a
heuristic argument that predicts logarithmic corrections to the mean-field
asymptotic behavior for the concentration of clusters of mass at time ,
, for . The total
concentration of clusters, , decays as at . We also investigate the problem with a localized steady source of
monomers and find that the steady-state concentration scales as
, , and , respectively,
for the spatial dimension equal to 1, 2, and 3. The total number of
clusters, , grows with time as , , and
for = 1, 2, and 3. Furthermore, in three dimensions we
obtain an asymptotic solution for the steady state cluster-mass distribution:
, with the scaling function
and the scaling variable .Comment: 12 pages, plain Te
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