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In view of the remarkable progress in micro-rheology to monitor the random motion of Brownian particles with size as small as few nanometers, in association that de Broglie matter waves have been experimentally observed for large molecules…
We construct a theory for the 1+1-dimensional Brownian motion in a viscous medium, which is (i) consistent with Einstein's theory of special relativity, and (ii) reduces to the standard Brownian motion in the Newtonian limit case. In the…
We use the system-plus-reservoir approach to study the quantum dynamics of a bipartite continuous variable system (two generic particles). We present an extension of the traditional model of a bath of oscillators which is capable of…
We investigate the construction of diffusions consisting of infinitely numerous Brownian particles moving in $\mathbb{R}^d$ and interacting via logarithmic functions (two-dimensional Coulomb potentials). These potentials are very strong and…
We study the 2D motion of colloidal dimers by single-particle tracking and compare the experimental observations obtained by bright-field microscopy to theoretical predictions for anisotropic diffusion. The comparison is based on the…
We introduce methods for large scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method at a cost comparable to the…
Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…
We demonstrate how time-integration of stochastic differential equations (i.e. Brownian dynamics simulations) can be combined with continuum numerical bifurcation analysis techniques to analyze the dynamics of liquid crystalline polymers…
We present a diagrammatic formulation of a theory for the time dependence of density fluctuations in equilibrium systems of interacting Brownian particles. To facilitate derivation of the diagrammatic expansion we introduce a basis that…
In this article, results have been presented for the two-time correlation functions for a free and a harmonically confined Brownian particle in a simple shear flow. For a free Brownian particle, the motion along the direction of shear…
In this article we continue the study of couplings of subelliptic Brownian motions on the subRiemannian manifolds SU (2) and SL(2, R). Similar to the case of the Heisenberg group, this subelliptic Brownian motion can be considered as a…
We consider n one-dimensional Brownian motions, such that n/2 Brownian motions start at time t=0 in the starting point a and end at time t=1 in the endpoint b and the other n/2 Brownian motions start at time t=0 at the point -a and end at…
Stimulated by experimental progress in high energy physics and astrophysics, the unification of relativistic and stochastic concepts has re-attracted considerable interest during the past decade. Focusing on the framework of special…
This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the $n$-th Brownian motion is reflected from the Brownian motion with label $n-1$. This model belongs…
Brownian motion of colloidal particles in the quasi-two-dimensional (qTD) confinement displays distinct kinetic characters from that in bulk. Here we experimentally report a dynamic evolution of Brownian particles in the qTD system. The…
Fourier transforms of Lorentz invariant functions in Minkowski space, with support on both the timelike and the spacelike domains are performed by means of direct integration. The cases of 1+1 and 1+2 dimensions are worked out in detail,…
Path integrals developed by Richard Feynman have been an important tool in Physics in studying quantum field theory. In mathematics, it has also been widely used in providing formal proofs in the study of Index theorem and asymptotic…
Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the "active" particle is driven along…
We give a probabilistic representation of a one-dimensional diffusion equation where the solution is discontinuous at $0$ with a jump proportional to its flux. This kind of interface condition is usually seen as a semi-permeable barrier.…
We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location with a generic space-dependent rate of resetting. We present a systematic approach…