Related papers: A Brownian Model for Crystal Nucleation
An angular time-dependent probability density function describing Brownian or anomalous rotational dynamics of fixed-length atom-to-atom vectors is presented. The probability density function, which fully incorporates angular boundary…
We propose to introduce a new stochastic process in molecular dynamics in order to improve the description of the nucleon emission process from a hot nucleus. We give momentum fluctuations originating from the momentum width of the nucleon…
Stochastic thermodynamics is the field of study relating fluctuations in stochastic systems to thermodynamic quantities. The total entropy production (EP), is central to the thermodynamic classification of systems. Non-equilibrium systems…
The nucleation rate derived in the classical theory contains at least one undetermined parameter, which may be expressed in terms of the Langer first-principles theory. But the uncertainties in the accounting for fluctuation modes, which…
While statistical mechanics provides a comprehensive framework for the understanding of equilibrium phase behavior, predicting the kinetics of phase transformations remains a challenge. Classical nucleation theory (CNT) provides a…
It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct…
Statistical aspects of the dynamics of chaotic scattering in the classical model of $\alpha$-cluster nuclei are studied. It is found that the dynamics governed by hyperbolic instabilities which results in an exponential decay of the…
Aim of this note is to analyse branching Brownian motion within the class of models introduced in the recent paper [4] and called chemical diffusion master equations. These models provide a description for the probabilistic evolution of…
Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it…
The Smoluchowsky equation for a system of interacting Brownian particles in a temperature gradient is derived from the Kramers equation by means of a multiple time-scale method. The interparticle interactions are assumed to be represented…
In the last ten years, a number of ``Conventional Fluctuation Theorems'' have been derived for systems with deterministic or stochastic dynamics, in a transient or in a non-equilibrium stationary state. These theorems gave explicit…
We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to…
A thermal analogue of the classical brachistochrone problem, which minimizes the connection time between two equilibrium states of harmonically confined Brownian particles, has recently been solved theoretically. Here we report its…
Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific…
The circular Dyson Brownian motion model refers to the stochastic dynamics of the log-gas on a circle. It also specifies the eigenvalues of certain parameter-dependent ensembles of unitary random matrices. This model is considered with the…
Bubble chambers and droplet detectors used in dosimetry and dark matter particle search experiments use a superheated metastable liquid in which nuclear recoils trigger bubble nucleation. This process is described by the classical heat…
We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…
Induction time, a measure of how long one will wait for nucleation to occur, is an important parameter in quantifying nucleation kinetics and its underlying mechanisms. Due to the stochastic nature of nucleation, efficient methods for…
We perform an analytic study on the stochastic thermodynamics of a small classical particle trapped in a time dependent single-well potential in the highly underdamped limit. It is shown that the nonequilibrium probability density function…
This article present a continuous cascade model of volatility formulated as a stochastic differential equation. Two independent Brownian motions are introduced as random sources triggering the volatility cascade. One multiplicatively…