Related papers: Generalized Elastic Model: Fractional Langevin Des…
We discuss the well known Einstein and the Kubo Fluctuation Dissipation Relations (FDRs) in the wider framework of a generalized FDR for systems with a stationary probability distribution. A multi-variate linear Langevin model, which…
We present a new time-dependent Density Functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of…
The Generalized Langevin Equation, in history, arises as a natural fix for the rather traditional Langevin equation when the random force is no longer memoryless. It has been proved that with fractional Gaussian noise (fGn) mostly…
The phenomena of subdiffusion are widely observed in physical and biological systems. To investigate the effects of external potentials, say, harmonic potential, linear potential, and time dependent force, we study the subdiffusion…
Normal human heart rate shows complex fluctuations in time, which is natural, since heart rate is controlled by a large number of different feedback control loops. These unpredictable fluctuations have been shown to display fractal…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
We show how a general formulation of the Fluctuation-Response Relation is able to describe in detail the connection between response properties to external perturbations and spontaneous fluctuations in systems with fast and slow variables.…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
We consider the asymptotic behaviour of the fluctuation process for large stochastic systems of interacting particles driven by both idiosyncratic and common noise with an interaction kernel \(k \in L^2(\R^d) \cap L^\infty(\R^d)\). Our…
In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of…
Fractional generalized Langevin equation with external force is used to model single-file diffusion. It is found that for external force that varies with power law the solution for such a fractional Langevin equation gives the correct short…
Fluctuations of the instantaneous local Lagrangian strain $\epsilon_{ij}(\bf{r},t)$, measured with respect to a static ``reference'' lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic…
The Macroscopic Fluctuating Theory is presented from a practical and self consistent point of view. We take as starting point the assumption that a system at a mesoscopic scale is described by a field $\phi(x,t)$ that evolves by a Langevin…
We study the fluctuations of a stochastic Maxwell-Lorentz particle model driven by an external field to determine the extent to which fluctuation relations are related to large deviations. Focusing on the total entropy production of this…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many…
Finding the dynamical law of observable quantities lies at the core of physics. Within the particular field of statistical mechanics, the generalized Langevin equation (GLE) comprises a general model for the evolution of observables…
We study a gas of hard rods on a ring, driven by an external thermostat, with either elastic or inelastic collisions, which exhibits sub-diffusive behavior $<x^2 > \sim t^{1/2}$. We show the validity of the usual Fluctuation-Dissipation…
We present an exact functional formalism to deal with linear Langevin equations with arbitrary memory kernels and driven by any noise structure characterized through its characteristic functional. No others hypothesis are assumed over the…