Related papers: Augmented Transition Path Theory for Sequences of …
In real-world scenario, many phenomena produce a collection of events that occur in continuous time. Point Processes provide a natural mathematical framework for modeling these sequences of events. In this survey, we investigate…
A scarcity of known chemical kinetic parameters leads to the use of many reaction rate estimates, which are not always sufficiently accurate, in the construction of detailed kinetic models. To reduce the reliance on these estimates and…
Relativistic quantum transport theory has begun to play an important role in the space-time description of matter under extreme conditions of high energy density in out-of-equilibrium situations. The following introductory lectures on some…
A general semiclassical theory for the calculation of reaction rate constants is developed. The theory can be understood as a formal framework that encompasses existing semiclassical methods: instanton theory and semiclassical transition…
Quantum tunneling is considered from the point of view of local realism. It is concluded that a quantum object tunneling through a potential barrier cannot be interpreted as a point-like particle because such an interpretation generates a…
We formulate the generalized master equation for a class of continuous time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
Discrete temporal transitions occur in a variety of domains, but this work is mainly motivated by applications in molecular biology: explaining and analyzing observed transcriptome and proteome time series by literature and database…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
Reaction-diffusion equations deliver a versatile tool for the description of reactions in inhomogeneous systems under the assumption that the characteristic reaction scales and the scales of the inhomogeneities in the reactant…
This Report discusses a recently developed concept of Limiting Phase Trajectories (LPTs) providing a unified description of resonant energy transport in a wide range of classical and quantum dynamical systems with constant and time-varying…
This paper is concerned with transition fronts for reaction-diffusion equations of the Fisher-KPP type. Basic examples of transition fronts connecting the unstable steady state to the stable one are the standard traveling fronts, but the…
It is proved that in non-relativistic quantum mechanics (without spin) the transition probability may be described in terms of particle paths, every path having a (positive) probability. This leads to a stochastic hidden variables theory…
We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked to the theory of phase transitions. We also provide examples of new kinds of transient behaviour.
The classical theory of chemical reactions can be understood in terms of diffusive barrier crossing, where the rate of a reaction is determined by the inverse of the mean first passage time (FPT) to cross a free energy barrier. Whenever a…
An extension of the classical action principle obtained in the framework of the gauge transformations, is used to describe the motion of a particle. This extension assigns many, but not all, paths to a particle. Properties of the particle…
We present the statistical method as a direct extension of the mean first-passage time concept to the analysis of molecular dynamics simulation data of a phase transformation. According to the method, the mean first-passage time…
The reaction-coordinate mapping is a useful technique to study complex quantum dissipative dynamics into structured environments. In essence, it aims to mimic the original problem by means of an 'augmented system', which includes a suitably…
The relaxation time approximation (RTA) is a well known method of describing the time evolution of a statistical ensemble by linking distributions of the variables of interest at different stages of their temporal evolution. We show that if…
To capture the dynamic behaviors of reaction-subdiffusion in flow fields, in the present paper we analyze a simple monomolecular conversion A $\rightarrow$ B. We derive the corresponding master equations for the distribution of A and B…