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

Stochastic Model and Equivalent Ferromagnetic Spin Chain with Alternation

We investigate a non-equilibrium reaction-diffusion model and equivalent ferromagnetic spin 1/2 XY spin chain with alternating coupling constant. The exact energy spectrum and the n-point hole correlations are considered with the help of the Jordan-Wigner fermionization and the inter-particle distribution function method. Although the Hamiltonian has no explicit translational symmetry, the translational invariance is recovered after long time due to the diffusion. We see the scaling relations for the concentration and the two-point function in finite size analysis.Comment: 7 pages, LaTeX file, to appear in J. Phys. A: Math. and Ge

Two-Species Annihilation with Drift: A Model with Continuous Concentration-Decay Exponents

We propose a model for diffusion-limited annihilation of two species, $A+B\to A$ or $B$, where the motion of the particles is subject to a drift. For equal initial concentrations of the two species, the density follows a power-law decay for large times. However, the decay exponent varies continuously as a function of the probability of which particle, the hopping one or the target, survives in the reaction. These results suggest that diffusion-limited reactions subject to drift do not fall into a limited number of universality classes.Comment: 10 pages, tex, 3 figures, also available upon reques

Time evolution of the reaction front in a subdiffusive system

Using the quasistatic approximation, we show that in a subdiffusion--reaction system the reaction front $x_{f}$ evolves in time according to the formula $x_{f} \sim t^{\alpha/2}$, with $\alpha$ being the subdiffusion parameter. The result is derived for the system where the subdiffusion coefficients of reactants differ from each other. It includes the case of one static reactant. As an application of our results, we compare the time evolution of reaction front extracted from experimental data with the theoretical formula and we find that the transport process of organic acid particles in the tooth enamel is subdiffusive.Comment: 18 pages, 3 figure

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

Exactly solvable models through the empty interval method, for more-than-two-site interactions

Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for $E_n(t)$'s, the probability that $n$ consecutive sites are empty at time $t$. The general method of solving the time evolution equation is discussed. As an example, a system with next-nearest-neighbor interaction is studied.Comment: 19 pages, LaTeX2

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 $m$ at time $t$, $c(m,t)~m^{-1/2}(log(t)/t)^{3/4}$, for $1 << m << \sqrt{t/log(t)}$. The total concentration of clusters, $c(t)$, decays as $c(t)~\sqrt{log(t)/t}$ at $t --> \infty$. We also investigate the problem with a localized steady source of monomers and find that the steady-state concentration $c(r)$ scales as $r^{-1}(log(r))^{1/2}$, $r^{-1}$, and $r^{-1}(log(r))^{-1/2}$, respectively, for the spatial dimension $d$ equal to 1, 2, and 3. The total number of clusters, $N(t)$, grows with time as $(log(t))^{3/2}$, $t^{1/2}$, and $t(log(t))^{-1/2}$ for $d$ = 1, 2, and 3. Furthermore, in three dimensions we obtain an asymptotic solution for the steady state cluster-mass distribution: $c(m,r) \sim r^{-1}(log(r))^{-1}\Phi(z)$, with the scaling function $\Phi(z)=z^{-1/2}\exp(-z)$ and the scaling variable $z ~ m/\sqrt{log(r)}$.Comment: 12 pages, plain Te

Non-equilibrium Magnetization Dynamics in the Fe_8 Single-Molecule Magnet Induced by High-Intensity Microwave Radiation

Resonant microwave radiation applied to a single crystal of the molecular magnet Fe_8 induces dramatic changes in the sample's magnetization. Transitions between excited states are found even though at the nominal system temperature these levels have negligible population. We find evidence that the sample heats significantly when the resonance condition is met. In addition, heating is observed after a short pulse of intense radiation has been turned off, indicating that the spin system is out of equilibrium with the lattice.Comment: Version to appear in Europhysics Letters. Minor changes and updated reference

Determining mean first-passage time on a class of treelike regular fractals

Relatively general techniques for computing mean first-passage time (MFPT) of random walks on networks with a specific property are very useful, since a universal method for calculating MFPT on general graphs is not available because of their complexity and diversity. In this paper, we present techniques for explicitly determining the partial mean first-passage time (PMFPT), i.e., the average of MFPTs to a given target averaged over all possible starting positions, and the entire mean first-passage time (EMFPT), which is the average of MFPTs over all pairs of nodes on regular treelike fractals. We describe the processes with a family of regular fractals with treelike structure. The proposed fractals include the $T$ fractal and the Peano basin fractal as their special cases. We provide a formula for MFPT between two directly connected nodes in general trees on the basis of which we derive an exact expression for PMFPT to the central node in the fractals. Moreover, we give a technique for calculating EMFPT, which is based on the relationship between characteristic polynomials of the fractals at different generations and avoids the computation of eigenvalues of the characteristic polynomials. Making use of the proposed methods, we obtain analytically the closed-form solutions to PMFPT and EMFPT on the fractals and show how they scale with the number of nodes. In addition, to exhibit the generality of our methods, we also apply them to the Vicsek fractals and the iterative scale-free fractal tree and recover the results previously obtained.Comment: Definitive version published in Physical Review

Experimental Upper Bound on Superradiance Emission from Mn12 Acetate

We used a Josephson junction as a radiation detector to look for evidence of the emission of electromagnetic radiation during magnetization avalanches in a crystal assembly of Mn_12-Acetate. The crystal assembly exhibits avalanches at several magnetic fields in the temperature range from 1.8 to 2.6 K with durations of the order of 1 ms. Although a recent study shows evidence of electromagnetic radiation bursts during these avalanches [J. Tejada, et al., Appl. Phys. Lett. {\bf 84}, 2373 (2004)], we were unable to detect any significant radiation at well-defined frequencies. A control experiment with external radiation pulses allows us to determine that the energy released as radiation during an avalanche is less than 1 part in 10^4 of the total energy released. In addition, our avalanche data indicates that the magnetization reversal process does not occur uniformly throughout the sample.Comment: 4 RevTeX pages, 3 eps figure