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Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…
We investigate the classical Brownian motion of a particle in a two-dimensional noncommutative (NC) space. Using the standard NC algebra embodied by the sympletic Weyl-Moyal formalism we find that noncommutativity induces a non-vanishing…
We study the influence of the factor of electron-ion collisions on the solution of the Cauchy problem in the one-dimensional relativistic model of cold plasma and show that, depending on their intensity and initial data, two scenarios are…
We consider an infinite system of particles on the positive real line, initiated from a Poisson point process, which move according to Brownian motion up until the hitting time of a barrier. The barrier increases when it is hit, allowing…
We investigate the usage of a recently introduced noise-cancellation algorithm for Brownian simulations to enhance the precision of measuring transport properties such as the mean-square displacement or the velocity-autocorrelation…
We have used two types of thermometry to study thermal fluctuations in a microcantilever-based system below 1 K. We measured the temperature of a cantilever's macroscopic degree-of-freedom (via the Brownian motion of its lowest flexural…
In [arXiv:1806.06668], we have studied the Boltzmann random triangulation of the disk coupled to an Ising model on its faces with Dobrushin boundary condition at its critical temperature. In this paper, we investigate the phase transition…
In this paper, the first microscopic approach to the Brownian motion is developed in the case where the mass density of the suspending bath is of the same order of magnitude as that of the Brownian (B) particle. Starting from an extended…
We address the post-collapse dynamics of a self-gravitating gas of Brownian particles in D dimensions, in both canonical and microcanonical ensembles. In the canonical ensemble, the post-collapse evolution is marked by the formation of a…
We study lower and upper bounds on the parameters for stochastic state vector reduction, focusing on the mass-proportional continuous spontaneous localization (CSL) model. We show that the assumption that the state vector is reduced whan a…
We develop efficient numerical methods for performing many-body Brownian dynamics simulations of a recently-observed fingering instability in an active suspension of colloidal rollers sedimented above a wall [M. Driscoll, B. Delmotte, M.…
We study the convergence of $N-$particle systems described by SDEs driven by Brownian motion and Poisson random measure, where the coefficients depend on the empirical measure of the system. Every particle jumps with a jump rate depending…
The viscosity of glass-forming liquids increases by many orders of magnitude if their temperature is lowered by a mere factor of 2-3 [1,2]. Recent studies suggest that this widespread phenomenon is accompanied by spatially heterogeneous…
Careful monitoring of harmonically bound (or as a limiting case, free) masses is the basis of current and future gravitational wave detectors, and of nanomechanical devices designed to access the quantum regime. We analyze the effects of…
We study the competition between thermal fluctuations and stress enhancement in the failure process of a disordered system by using a local load sharing fiber bundle model. The thermal noise is introduced by defining a failure probability…
I impose the Newtonian criteria of inertial frames on the c.o.m. trajectories of massive objects undergoing spontaneous collapse of their wave function. The corresponding modification of the so far used stochastic Schr\"odinger equation…
Recently, it has been discovered that systems of Active Brownian particles (APB) at high density organise their velocities into coherent domains showing large spatial structures in the velocity field. Such a collective behavior occurs…
A theory for (1+3)-dimensional relativistic Brownian motion under the influence of external force fields is put forward. Starting out from a set of relativistically covariant, but multiplicative Langevin equations we describe the…
We study near-equilibrium thermodynamics of bosonic atoms in a two-dimensional optical lattice by ramping up the lattice depth to convert a superfluid into an inhomogeneous mixture of superfluid and Mott insulator. Detailed study of in situ…
We investigate the properties of localized waves in systems governed by nonlocal nonlinear Schrodinger type equations. We prove rigorously by bounding the Hamiltonian that nonlocality of the nonlinearity prevents collapse in, e.g.,…