3,410 research outputs found
On the scattering length of the K^- d system
Multiple-scattering approximations to Faddeev calculations of the K^- d
scattering length are reviewed and compared with published Kbar-N-N pi-Y-N
fully reactive Faddeev calculations. A new multiple-scattering approximation
which goes beyond the `fixed-center' assumption for the nucleons is proposed,
aiming at accuracies of 5-10%. A precise value of the K^- d scattering length
from the measurement of the K^- d 1s atomic level shift and width, planned by
the DEAR/SIDDHARTA collaboration, plus a precise value for the K^- p scattering
length by improving the K^- p atom measurements, are essential for extracting
the K^- n scattering length, for resolving persistent puzzles in low-energy
Kbar-N phenomenology and for extrapolating into Kbar-nuclear systems.Comment: Invited talk at MESON 2006, Krakow, June 2006. To be published in
International Journal of Modern Physics A. Requires use of ws-ijmpa.cl
Diffusion-Limited One-Species Reactions in the Bethe Lattice
We study the kinetics of diffusion-limited coalescence, A+A-->A, and
annihilation, A+A-->0, in the Bethe lattice of coordination number z.
Correlations build up over time so that the probability to find a particle next
to another varies from \rho^2 (\rho is the particle density), initially, when
the particles are uncorrelated, to [(z-2)/z]\rho^2, in the long-time asymptotic
limit. As a result, the particle density decays inversely proportional to time,
\rho ~ 1/kt, but at a rate k that slowly decreases to an asymptotic constant
value.Comment: To be published in JPCM, special issue on Kinetics of Chemical
Reaction
Adiabatic pumping through a quantum dot in the Kondo regime: Exact results at the Toulouse limit
Transport properties of ultrasmall quantum dots with a single unpaired
electron are commonly modeled by the nonequilibrium Kondo model, describing the
exchange interaction of a spin-1/2 local moment with two leads of
noninteracting electrons. Remarkably, the model possesses an exact solution
when tuned to a special manifold in its parameter space known as the Toulouse
limit. We use the Toulouse limit to exactly calculate the adiabatically pumped
spin current in the Kondo regime. In the absence of both potential scattering
and a voltage bias, the instantaneous charge current is strictly zero for a
generic Kondo model. However, a nonzero spin current can be pumped through the
system in the presence of a finite magnetic field, provided the spin couples
asymmetrically to the two leads. Tunneling through a Kondo impurity thus offers
a natural mechanism for generating a pure spin current. We show, in particular,
that one can devise pumping cycles along which the average spin pumped per
cycle is closely equal to . By analogy with Brouwer's formula for
noninteracting systems with two driven parameters, the pumped spin current is
expressed as a geometrical property of a scattering matrix. However, the
relevant %Alex: I replaced topological with geometrical in the sentence above
scattering matrix that enters the formulation pertains to the Majorana fermions
that appear at the Toulouse limit rather than the physical electrons that carry
the current. These results are obtained by combining the nonequilibrium Keldysh
Green function technique with a systematic gradient expansion, explicitly
exposing the small parameter controlling the adiabatic limit.Comment: 14 pages, 3 figures, revised versio
Anomalous diffusion with log-periodic modulation in a selected time interval
On certain self-similar substrates the time behavior of a random walk is
modulated by logarithmic periodic oscillations on all time scales. We show that
if disorder is introduced in a way that self-similarity holds only in average,
the modulating oscillations are washed out but subdiffusion remains as in the
perfect self-similar case. Also, if disorder distribution is appropriately
chosen the oscillations are localized in a selected time interval. Both the
overall random walk exponent and the period of the oscillations are
analytically obtained and confirmed by Monte Carlo simulations.Comment: 4 pages, 5 figure
Complete Exact Solution of Diffusion-Limited Coalescence, A + A -> A
Some models of diffusion-limited reaction processes in one dimension lend
themselves to exact analysis. The known approaches yield exact expressions for
a limited number of quantities of interest, such as the particle concentration,
or the distribution of distances between nearest particles. However, a full
characterization of a particle system is only provided by the infinite
hierarchy of multiple-point density correlation functions. We derive an exact
description of the full hierarchy of correlation functions for the
diffusion-limited irreversible coalescence process A + A -> A.Comment: 4 pages, 2 figures (postscript). Typeset with Revte
A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0
We introduce a method of intervals for the analysis of diffusion-limited
annihilation, A+A -> 0, on the line. The method leads to manageable diffusion
equations whose interpretation is intuitively clear. As an example, we treat
the following cases: (a) annihilation in the infinite line and in infinite
(discrete) chains; (b) annihilation with input of single particles, adjacent
particle pairs, and particle pairs separated by a given distance; (c)
annihilation, A+A -> 0, along with the birth reaction A -> 3A, on finite rings,
with and without diffusion.Comment: RevTeX, 13 pages, 4 figures, 1 table. References Added, and some
other minor changes, to conform with final for
Anisotropic anomalous diffusion modulated by log-periodic oscillations
We introduce finite ramified self-affine substrates in two dimensions with a
set of appropriate hopping rates between nearest-neighbor sites, where the
diffusion of a single random walk presents an anomalous {\it anisotropic}
behavior modulated by log-periodic oscillations. The anisotropy is revealed by
two different random walk exponents, and , in the {\it x} and
{\it y} direction, respectively. The values of these exponents, as well as the
period of the oscillation, are analytically obtained and confirmed by Monte
Carlo simulations.Comment: 7 pages, 7 figure
A Random Walk to a Non-Ergodic Equilibrium Concept
Random walk models, such as the trap model, continuous time random walks, and
comb models exhibit weak ergodicity breaking, when the average waiting time is
infinite. The open question is: what statistical mechanical theory replaces the
canonical Boltzmann-Gibbs theory for such systems? In this manuscript a
non-ergodic equilibrium concept is investigated, for a continuous time random
walk model in a potential field. In particular we show that in the non-ergodic
phase the distribution of the occupation time of the particle on a given
lattice point, approaches U or W shaped distributions related to the arcsin
law. We show that when conditions of detailed balance are applied, these
distributions depend on the partition function of the problem, thus
establishing a relation between the non-ergodic dynamics and canonical
statistical mechanics. In the ergodic phase the distribution function of the
occupation times approaches a delta function centered on the value predicted
based on standard Boltzmann-Gibbs statistics. Relation of our work with single
molecule experiments is briefly discussed.Comment: 14 pages, 6 figure
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