2,573 research outputs found
On the waiting time distribution for continuous stochastic systems
The waiting time distribution (WTD) is a common tool for analysing discrete
stochastic processes in classical and quantum systems. However, there are many
physical examples where the dynamics is continuous and only approximately
discrete, or where it is favourable to discuss the dynamics on a discretized
and a continuous level in parallel. An example is the hindered motion of
particles through potential landscapes with barriers. In the present paper we
propose a consistent generalisation of the WTD from the discrete case to
situations where the particles perform continuous barrier-crossing
characterised by a finite duration. To this end, we introduce a recipe to
calculate the WTD from the Fokker-Planck/Smoluchowski equation. In contrast to
the closely related first passage time distribution (FPTD), which is frequently
used to describe continuous processes, the WTD contains information about the
direction of motion. As an application, we consider the paradigmatic example of
an overdamped particle diffusing through a washboard potential. To verify the
approach and to elucidate its numerical implications, we compare the WTD
defined via the Smoluchowski equation with data from direct simulation of the
underlying Langevin equation and find full consistency provided that the jumps
in the Langevin approach are defined properly. Moreover, for sufficiently large
energy barriers, the WTD defined via the Smoluchowski equation becomes
consistent with that resulting from the analytical solution of a (two-state)
master equation model for the short-time dynamics developed previous by us [PRE
86, 061135 (2012)]. Thus, our approach "interpolates" between these two types
of stochastic motion. We illustrate our approach for both symmetric systems and
systems under constant force.Comment: 12 pages, 10 figure
Fractional calculus and continuous-time finance II: the waiting-time distribution
We complement the theory of tick-by-tick dynamics of financial markets based
on a Continuous-Time Random Walk (CTRW) model recently proposed by Scalas et
al., and we point out its consistency with the behaviour observed in the
waiting-time distribution for BUND future prices traded at LIFFE, London.Comment: Revised version, 17 pages, 4 figures. Physica A, Vol. 287, No 3-4,
468--481 (2000). Proceedings of the International Workshop on "Economic
Dynamics from the Physics Point of View", Bad-Honnef (Germany), 27-30 March
200
Waiting time distribution for electron transport in a molecular junction with electron-vibration interaction
On the elementary level, electronic current consists of individual electron
tunnelling events that are separated by random time intervals. The waiting time
distribution is a probability to observe the electron transfer in the detector
electrode at time given that an electron was detected in the same
electrode at earlier time . We study waiting time distribution for quantum
transport in a vibrating molecular junction. By treating the electron-vibration
interaction exactly and molecule-electrode coupling perturbatively, we obtain
master equation and compute the distribution of waiting times for electron
transport. The details of waiting time distributions are used to elucidate
microscopic mechanism of electron transport and the role of electron-vibration
interactions. We find that as nonequilibrium develops in molecular junction,
the skewness and dispersion of the waiting time distribution experience
stepwise drops with the increase of the electric current. These steps are
associated with the excitations of vibrational states by tunnelling electrons.
In the strong electron-vibration coupling regime, the dispersion decrease
dominates over all other changes in the waiting time distribution as the
molecular junction departs far away from the equilibrium
Single Molecule Michaelis-Menten Equation beyond Quasi-Static Disorder
The classic Michaelis-Menten equation describes the catalytic activities for
ensembles of enzyme molecules very well. But recent single-molecule experiment
showed that the waiting time distribution and other properties of single enzyme
molecule are not consistent with the prediction based on the viewpoint of
ensemble. It has been contributed to the slow inner conformational changes of
single enzyme in the catalytic processes. In this work we study the general
dynamics of single enzyme in the presence of dynamic disorder. We find that at
two limiting cases, the slow reaction and nondiffusion limits, Michaelis-Menten
equation exactly holds although the waiting time distribution has a
multiexponential decay behaviors in the nondiffusion limit.Particularly, the
classic Michaelis-Menten equation still is an excellent approximation other
than the two limits.Comment: 10 pages, 1 figur
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