6,138 research outputs found
Residence time statistics for blinking quantum dots and other stochastic processes
We present a study of residence time statistics for blinking quantum
dots. With numerical simulations and exact calculations we show sharp
transitions for a critical number of dots. In contrast to expectation the
fluctuations in the limit of are non-trivial. Besides quantum
dots our work describes residence time statistics in several other many
particle systems for example Brownian particles. Our work provides a
natural framework to detect non-ergodic kinetics from measurements of many
blinking chromophores, without the need to reach the single molecule limit
The longest excursion of stochastic processes in nonequilibrium systems
We consider the excursions, i.e. the intervals between consecutive zeros, of
stochastic processes that arise in a variety of nonequilibrium systems and
study the temporal growth of the longest one l_{\max}(t) up to time t. For
smooth processes, we find a universal linear growth \simeq
Q_{\infty} t with a model dependent amplitude Q_\infty. In contrast, for
non-smooth processes with a persistence exponent \theta, we show that <
l_{\max}(t) > has a linear growth if \theta
\sim t^{1-\psi} if \theta > \theta_c. The amplitude Q_{\infty} and the exponent
\psi are novel quantities associated to nonequilibrium dynamics. These
behaviors are obtained by exact analytical calculations for renewal and
multiplicative processes and numerical simulations for other systems such as
the coarsening dynamics in Ising model as well as the diffusion equation with
random initial conditions.Comment: 4 pages,2 figure
Exact Persistence Exponent for One-dimensional Potts Models with Parallel Dynamics
We obtain \theta_p(q) = 2\theta_s(q) for one-dimensional q-state
ferromagnetic Potts models evolving under parallel dynamics at zero temperature
from an initially disordered state, where \theta_p(q) is the persistence
exponent for parallel dynamics and \theta_s(q) = -{1/8}+
\frac{2}{\pi^2}[cos^{-1}{(2-q)/q\sqrt{2}}]^2 [PRL, {\bf 75}, 751, (1995)], the
persistence exponent under serial dynamics. This result is a consequence of an
exact, albeit non-trivial, mapping of the evolution of configurations of Potts
spins under parallel dynamics to the dynamics of two decoupled reaction
diffusion systems.Comment: 13 pages Latex file, 5 postscript figure
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