相关论文: Transition-Event Durations in One Dimensional Acti…
An analytical expression is derived for the transition path time distribution for a one-dimensional particle crossing of a parabolic barrier. Two cases are analyzed: (i) A non-Markovian process described by a generalized Langevin equation…
We study the transition time distribution for a particle moving between two wells of a multidimensional potential in the low-noise limit of overdamped Langevin dynamics. Possible transition paths are restricted to a thin tube surrounding…
Many processes in chemistry, physics, and biology involve rare events in which the system escapes from a metastable state by surmounting an activation barrier. Examples range from chemical reactions, protein folding, and nucleation events…
From a variety of long simulations of all-atom butane using both stochastic and fully-solved molecular dynamics, we have uncovered striking generic behavior which also occurs in one-dimensional systems. We find an apparently universal…
Dependence of the transient process duration on the initial conditions is considered in one- and two-dimensional systems with discrete time, representing a logistic map and the Eno map, respectively.
Metastable transitions in Langevin dynamics can exhibit rich behaviors that are markedly different from its overdamped limit. In addition to local alterations of the transition path geometry, more fundamental global changes may exist. For…
Quantum transitions are described semiclassically as motions of systems along (complex) trajectories. We consider the cases when the semiclassical trajectories are unstable and find that durations of the corresponding transitions are large.…
The general, multidimensional barrier crossing problem for diffusive processes under the action of conservative forces is studied with the goal of developing tractable approximations. Particular attention is given to the effect of different…
For a Markovian dynamics on discrete states, the logarithmic ratio of waiting-time distributions between two successive, instantaneous transitions in forward and backward direction is a measure of time-irreversibility. It thus serves as an…
The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
Biomolecular folding, at least in simple systems, can be described as a two state transition in a free energy landscape with two deep wells separated by a high barrier. Transition paths are the short part of the trajectories that cross the…
Distributions of electron waiting times have been measured in several recent experiments and have been shown to provide complementary information compared to what can be learned from the electric current fluctuations. Existing theories,…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
Chemical reactions subjected to time-varying external forces cannot generally be described through a fixed bottleneck near the transition state barrier or dividing surface. A naive dividing surface attached to the instantaneous, but moving,…
The dynamics of steps on crystal surfaces is considered. In general, the meandering of the steps obeys a subdiffusive behaviour. The characteristic asymptotic time laws depend on the microscopic mechanism for detachment and attachment of…
The phenomenon of phase transitions in one-dimensional systems is discussed. Equilibrium systems are reviewed and some properties of an energy function which may allow phase transitions and phase ordering in one dimension are identified. We…
We present a closed-form, computable expression for the expected number of times any transition event occurs during the transient phase of a reducible Markov chain. Examples of events include time to absorption, number of visits to a state,…
Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of…
The most probable transition path in a one-dimensional overdamped system is rigorously proved to possess less than two turning points. The proof is valid for any potentials, transition times, initial and final transition points.