Diffusion-Limited Reaction in One Dimension: Paired and Unpaired Nucleation

We consider the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation (creation of particles) with constant probability per unit time and length. The cases of nucleation of single particles and nucleation in pairs are considered. A new method of analysis permits exact calculation of the steady state density and its time evolution in terms of the three parameters describing the microscopic dynamics: the nucleation rate, the initial separation of nucleated pairs and the diffusivity of a particle. For paired nucleation at sufficiently small initial separation the nucleation rate is proportional to the square of the steady state density. For unpaired nucleation, and for paired nucleation at sufficiently large initial separation, the nucleation rate is proportional to the cube of the steady state density

Multiplicative Noise: Applications in Cosmology and Field Theory

Physical situations involving multiplicative noise arise generically in cosmology and field theory. In this paper, the focus is first on exact nonlinear Langevin equations, appropriate in a cosmologica setting, for a system with one degree of freedom. The Langevin equations are derived using an appropriate time-dependent generalization of a model due to Zwanzig. These models are then extended to field theories and the generation of multiplicative noise in such a context is discussed. Important issues in both the cosmological and field theoretic cases are the fluctuation-dissipation relations and the relaxation time scale. Of some importance in cosmology is the fact that multiplicative noise can substantially reduce the relaxation time. In the field theoretic context such a noise can lead to a significant enhancement in the nucleation rate of topological defects.Comment: 21 pages, LaTex, LA-UR-93-210

Escape of a Uniform Random Walk from an Interval

We study the first-passage properties of a random walk in the unit interval in which the length of a single step is uniformly distributed over the finite range [-a,a]. For a of the order of one, the exit probabilities to each edge of the interval and the exit time from the interval exhibit anomalous properties stemming from the change in the minimum number of steps to escape the interval as a function of the starting point. As a decreases, first-passage properties approach those of continuum diffusion, but non-diffusive effects remain because of residual discreteness effectsComment: 8 pages, 8 figures, 2 column revtex4 forma

Light-Induced Currents at Domain Walls in Multiferroic BiFeO3.

Multiferroic BiFeO3 (BFO) films with spontaneously formed periodic stripe domains can generate above-gap open circuit voltages under visible light illumination; nevertheless the underlying mechanism behind this intriguing optoelectronic response has not been understood to date. Here, we make contact-free measurements of light-induced currents in epitaxial BFO films via detecting terahertz radiation emanated by these currents, enabling a direct probe of the intrinsic charge separation mechanisms along with quantitative measurements of the current amplitudes and their directions. In the periodic stripe samples, we find that the net photocurrent is dominated by the charge separation across the domain walls, whereas in the monodomain samples the photovoltaic response arises from a bulk shift current associated with the non-centrosymmetry of the crystal. The peak current amplitude driven by the charge separation at the domain walls is found to be 2 orders of magnitude higher than the bulk shift current response, indicating the prominent role of domain walls acting as nanoscale junctions to efficiently separate photogenerated charges in the stripe domain BFO films. These findings show that domain-wall-engineered BFO thin films offer exciting prospects for ferroelectric-based optoelectronics, as well as bias-free strong terahertz emitters

Diffusion on a solid surface: Anomalous is normal

We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic or a random two dimensional potential. The model leads to a rich variety of different transport regimes, some of which correspond to anomalous diffusion such as has recently been observed in experiments and Monte Carlo simulations. We show that this anomalous behavior is controlled by the friction coefficient, and stress that it emerges naturally in a system described by ordinary canonical Maxwell-Boltzmann statistics

The target problem with evanescent subdiffusive traps

We calculate the survival probability of a stationary target in one dimension surrounded by diffusive or subdiffusive traps of time-dependent density. The survival probability of a target in the presence of traps of constant density is known to go to zero as a stretched exponential whose specific power is determined by the exponent that characterizes the motion of the traps. A density of traps that grows in time always leads to an asymptotically vanishing survival probability. Trap evanescence leads to a survival probability of the target that may be go to zero or to a finite value indicating a probability of eternal survival, depending on the way in which the traps disappear with time

Generalization of escape rate from a metastable state driven by external cross-correlated noise processes

We propose generalization of escape rate from a metastable state for externally driven correlated noise processes in one dimension. In addition to the internal non-Markovian thermal fluctuations, the external correlated noise processes we consider are Gaussian, stationary in nature and are of Ornstein-Uhlenbeck type. Based on a Fokker-Planck description of the effective noise processes with finite memory we derive the generalized escape rate from a metastable state in the moderate to large damping limit and investigate the effect of degree of correlation on the resulting rate. Comparison of the theoretical expression with numerical simulation gives a satisfactory agreement and shows that by increasing the degree of external noise correlation one can enhance the escape rate through the dressed effective noise strength.Comment: 9 pages, 1 figur

Dynamics of a metastable state nonlinearly coupled to a heat bath driven by an external noise

Based on a system-reservoir model, where the system is nonlinearly coupled to a heat bath and the heat bath is modulated by an external stationary Gaussian noise, we derive the generalized Langevin equation with space dependent friction and multiplicative noise and construct the corresponding Fokker-Planck equation, valid for short correlation time, with space dependent diffusion coefficient to study the escape rate from a metastable state in the moderate to large damping regime. By considering the dynamics in a model cubic potential we analyze the result numerically which are in good agreement with the theoretical prediction. It has been shown numerically that the enhancement of rate is possible by properly tuning the correlation time of the external noise.Comment: 13 pages, 5 figures, Revtex4. To appear in Physical Review