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Micron-sized self-propelled (active) particles can be considered as model systems for characterizing more complex biological organisms like swimming bacteria or motile cells. We produce asymmetric microswimmers by soft lithography and study…
Numerical algorithms are proposed for simulating the Brownian dynamics of charged particles in an external magnetic field, taking into account the Brownian motion of charged particles, damping effect and the effect of magnetic field…
The goal of these expository notes is to give an introduction to random matrices for non-specialist of this topic focusing on the link between random matrices and systems of particles in interaction. We first recall some general results…
We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
Dyson's Brownian motion model with the parameter $\beta=2$, which we simply call the Dyson model in the present paper, is realized as an $h$-transform of the absorbing Brownian motion in a Weyl chamber of type A. Depending on initial…
This paper is the second of a series devoted to the study of the dynamics of the spectrum of large random matrices. We study general extensions of the partial differential equation arising to characterize the limit spectral measure of the…
The dynamics of two Brownian particles trapped by two neighboring harmonic potentials in a linear shear flow is investigated. The positional correlation functions in this system are calculated analytically and analyzed as a function of the…
Applications of active particles require a method for controlling their dynamics. While this is typically achieved via direct interventions, indirect interventions based, e.g., on an orientation-dependent self-propulsion speed of the…
Putting dynamics into random matrix models leads to finitely many nonintersecting Brownian motions on the real line for the eigenvalues, as was discovered by Dyson. Applying scaling limits to the random matrix models, combined with Dyson's…
We consider finite systems of interacting Brownian particles including active friction in the framework of nonlinear dynamics and statistical/stochastic theory. First we study the statistical properties for $1-d$ systems of masses connected…
Standard approach to dynamical random matrix models relies on the description of trajectories of eigenvalues. Using the analogy from optics, based on the duality between the Fermat principle(trajectories) and the Huygens principle…
We establish a correspondence between the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random Gaussian perturbing matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we prove the…
We study the time evolution of Ginibre matrices whose elements undergo Brownian motion. The non-Hermitian character of the Ginibre ensemble binds the dynamics of eigenvalues to the evolution of eigenvectors in a non-trivial way, leading to…
We study the dynamic properties of a thermal autonomous machine made up of two quantum Brownian particles, each of which is in contact with an environment at different temperature and moves on a periodic sinusoidal track. When such tracks…
The complicated interactions in presence of disorder lead to a correlated randomization of states. The Hamiltonian as a result behaves like a multi-parametric random matrix with correlated elements. We show that the eigenvalue correlations…
In active Brownian motion, an internal propulsion mechanism interacts with translational and rotational thermal noise and other internal fluctuations to produce directed motion. We derive the distribution of its extreme fluctuations and…
Motions of fluctuating Brownian particles in an incompressible viscous fluid have been studied by coupled simulations of Brownian particles and host fluid. We calculated the velocity autocorrelation functions of Brownian particles and…
In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with symmetric external input signals, deterministic or random, alike, can assist directed motion of particles at the submicron scales. In such cases,…
The model of Brownian Percolation has been introduced as an approximation of discrete last-passage percolation models close to the axis. It allowed to compute some explicit limits and prove fluctuation theorems for these, based on the…