1,895 research outputs found
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
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
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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
On the occurrence of oscillatory modulations in the power-law behavior of dynamic and kinetic processes in fractals
The dynamic and kinetic behavior of processes occurring in fractals with
spatial discrete scale invariance (DSI) is considered. Spatial DSI implies the
existence of a fundamental scaling ratio (b_1). We address time-dependent
physical processes, which as a consequence of the time evolution develop a
characteristic length of the form , where z is the dynamic
exponent. So, we conjecture that the interplay between the physical process and
the symmetry properties of the fractal leads to the occurrence of time DSI
evidenced by soft log-periodic modulations of physical observables, with a
fundamental time scaling ratio given by . The conjecture is
tested numerically for random walks, and representative systems of broad
universality classes in the fields of irreversible and equilibrium critical
phenomena.Comment: 6 pages, 3 figures. Submitted to EP
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
Intermittent random walks for an optimal search strategy: One-dimensional case
We study the search kinetics of an immobile target by a concentration of
randomly moving searchers. The object of the study is to optimize the
probability of detection within the constraints of our model. The target is
hidden on a one-dimensional lattice in the sense that searchers have no a
priori information about where it is, and may detect it only upon encounter.
The searchers perform random walks in discrete time n=0,1,2, ..., N, where N is
the maximal time the search process is allowed to run. With probability \alpha
the searchers step on a nearest-neighbour, and with probability (1-\alpha) they
leave the lattice and stay off until they land back on the lattice at a fixed
distance L away from the departure point. The random walk is thus intermittent.
We calculate the probability P_N that the target remains undetected up to the
maximal search time N, and seek to minimize this probability. We find that P_N
is a non-monotonic function of \alpha, and show that there is an optimal choice
\alpha_{opt}(N) of \alpha well within the intermittent regime, 0 <
\alpha_{opt}(N) < 1, whereby P_N can be orders of magnitude smaller compared to
the "pure" random walk cases \alpha =0 and \alpha = 1.Comment: 19 pages, 5 figures; submitted to Journal of Physics: Condensed
Matter; special issue on Chemical Kinetics Beyond the Textbook: Fluctuations,
Many-Particle Effects and Anomalous Dynamics, eds. K.Lindenberg, G.Oshanin
and M.Tachiy
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