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 $\hbar$. 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, $\nu_x$ and $\nu_y$, 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