1,964 research outputs found
Residual mean first-passage time for jump processes: theory and applications to L\'evy flights and fractional Brownian motion
We derive a functional equation for the mean first-passage time (MFPT) of a
generic self-similar Markovian continuous process to a target in a
one-dimensional domain and obtain its exact solution. We show that the obtained
expression of the MFPT for continuous processes is actually different from the
large system size limit of the MFPT for discrete jump processes allowing
leapovers. In the case considered here, the asymptotic MFPT admits
non-vanishing corrections, which we call residual MFPT. The case of L/'evy
flights with diverging variance of jump lengths is investigated in detail, in
particular, with respect to the associated leapover behaviour. We also show
numerically that our results apply with good accuracy to fractional Brownian
motion, despite its non-Markovian nature.Comment: 13 pages, 8 figure
Mean first-passage time of quantum transition processes
In this paper, we consider the problem of mean first-passage time (MFPT) in
quantum mechanics; the MFPT is the average time of the transition from a given
initial state, passing through some intermediate states, to a given final state
for the first time. We apply the method developed in statistical mechanics for
calculating the MFPT of random walks to calculate the MFPT of a transition
process. As applications, we (1) calculate the MFPT for multiple-state systems,
(2) discuss transition processes occurring in an environment background, (3)
consider a roundabout transition in a hydrogen atom, and (4) apply the approach
to laser theory.Comment: 11 pages, no figur
Activation process driven by strongly non-Gaussian noises
The constructive role of non-Gaussian random fluctuations is studied in the
context of the passage over the dichotomously switching potential barrier. Our
attention focuses on the interplay of the effects of independent sources of
fluctuations: an additive stable noise representing non-equilibrium external
random force acting on the system and a fluctuating barrier. In particular, the
influence of the structure of stable noises on the mean escape time and on the
phenomenon of resonant activation (RA) is investigated. By use of the numerical
Monte Carlo method it is documented that the suitable choice of the barrier
switching rate and random external fields may produce resonant phenomenon
leading to the enhancement of the kinetics and the shortest, most efficient
reaction time.Comment: 11 pages, 8 figure
Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response
We investigate a stochastic version of a simple enzymatic reaction which
follows the generic Michaelis-Menten kinetics. At sufficiently high
concentrations of reacting species, the molecular fluctuations can be
approximated as a realization of a Brownian dynamics for which the model
reaction kinetics takes on the form of a stochastic differential equation.
After eliminating a fast kinetics, the model can be rephrased into a form of a
one-dimensional overdamped Langevin equation. We discuss physical aspects of
environmental noises acting in such a reduced system, pointing out the
possibility of coexistence of dynamical regimes where noise-enhanced stability
and resonant activation phenomena can be observed together.Comment: 18 pages, 11 figures, published in Physical Review E 74, 041904
(2006
Anomalous biased diffusion in networks
We study diffusion with a bias towards a target node in networks. This
problem is relevant to efficient routing strategies in emerging communication
networks like optical networks. Bias is represented by a probability of the
packet/particle to travel at every hop towards a site which is along the
shortest path to the target node. We investigate the scaling of the mean first
passage time (MFPT) with the size of the network. We find by using theoretical
analysis and computer simulations that for Random Regular (RR) and
Erd\H{o}s-R\'{e}nyi (ER) networks, there exists a threshold probability,
, such that for the MFPT scales anomalously as ,
where is the number of nodes, and depends on . For
the MFPT scales logarithmically with . The threshold value of the
bias parameter for which the regime transition occurs is found to depend only
on the mean degree of the nodes. An exact solution for every value of is
given for the scaling of the MFPT in RR networks. The regime transition is also
observed for the second moment of the probability distribution function, the
standard deviation.Comment: 13 Pages, To appear in PR
- …