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We study the Intermediate Scattering Function (ISF) of the strongly-nonlinear Fermi-Pasta Ulam Model at thermal equilibrium, using both numerical and analytical methods. From the molecular dynamics simulations we distinguish two limit…
In this paper, we investigate the motion of a set of charged particles acted upon by a growing electrostatic wave, in the limit when the initial wave amplitude is vanishingly small and when all the particles have the same initial action,…
We investigate the dynamics of individual colloidal particles in a one-dimensional periodic potential using the intermediate scattering function (ISF) as a key observable. We elaborate a theoretical framework and derive formally exact…
We derive an analytical expression for the intermediate scattering function of a particle on a flat surface obeying the Generalised Langevin Equation, with exponential memory friction. Numerical simulations based on an extended phase space…
We demonstrate differential dynamic microscopy and particle tracking for the characterization of the spatiotemporal behavior of active Janus colloids in terms of the intermediate scattering function (ISF). We provide an analytical solution…
Exact expressions are derived for the intermediate scattering function (ISF) of a quantum particle diffusing in a harmonic potential and linearly coupled to a harmonic bath. The results are valid for arbitrary strength and spectral density…
We study the Langevin dynamics of diffusive particles with regular pairwise interactions under mean-field scaling. By approximating empirical distributions with conditional distributions, we establish coercive and contractive properties for…
We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form $D(x)\sim |x|^c$, at constant temperature. The particle's probability distribution function…
We develop an instanton approach to the non-equilibrium dynamics in one-dimensional random environments. The long time behavior is controlled by rare fluctuations of the disorder potential and, accordingly, by the tail of the distribution…
The generalised Langevin equation with a retarded friction and a double-well potential is solved. The random force is modelled by a multiplicative noise with long jumps. Probability density distributions converge with time to a distribution…
A jumping process, defined in terms of jump size distribution and waiting time distribution, is presented. The jumping rate depends on the process value. The process, which is Markovian and stationary, relaxes to an equilibrium and is…
To address the dynamics of a Brownian particle on a periodic symmetric substrate under high-frequency periodic forcing with a vanishing time average, we construct an effective Langevin dynamics by invoking Kapitza-Landau time window. Our…
The diffusive dynamics of a particle in a medium with space-dependent friction coefficient is studied within the framework of the inertial Langevin equation. In this description, the ambiguous interpretation of the stochastic integral,…
The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…
Langevin equation is used to simulate the fission process of $^{112}$Sn + $^{112}$Sn and $^{116}$Sn + $^{116}$Sn. The mass distribution of the fission fragments are given by assuming the process of symmetric fission or asymmetric fission…
The Langevin dynamics is a diffusion process extensively used, in particular in molecular dynamics simulations, to sample Gibbs measures. Some alternatives based on (piecewise deterministic) kinetic velocity jump processes have gained…
A small tagged particle immersed in a fluid exhibits the Brownian motion and diffuses at the long-time scale. Meanwhile, at the short-time scale, the dynamics of the tagged particle cannot be simply described by the usual generalized…
We employ renewal processes to characterize the spatiotemporal dynamics of an active Brownian particle under stochastic orientational resetting. By computing the experimentally accessible intermediate scattering function (ISF) and…
We present an insightful ``derivation'' of the Langevin equation and the fluctuation dissipation theorem in the specific context of a heavier particle moving through an ideal gas of much lighter particles. The Newton's Law of motion…
The ad-atom dynamic equation, a Langevin type equation is analyzed and solved using some non-linear analytical and numerical tools. We noticeably show that the effect of the surface acoustic wave is to induce an effective potential that…