相关论文: The stochastic acceleration problem in two dimensi…

Einstein's Brownian motion of a quantum particle in a classical environment is studied via virial and equipartition theorems. The effect of continuous measurement in a strongly dissipative environment is accounted for and a quantum…

A constant homogeneous magnetic field is applied to a composite system made of two scalar particles with opposite charges. Motion is described by a pair of coupled Klein-Gordon equations that are written in closed form with help of a…

In this paper we study the homogenization of a stochastic process and its associated evolution equations in which we mix a local part (given by a Brownian motion with a reflection on the boundary) and a nonlocal part (given by a jump…

Quantum gravity has long remained elusive from an observational standpoint. Developing effective cosmological models motivated by the fundamental aspects of quantum gravity is crucial for bridging theory with observations. One key aspect is…

In this paper, we introduce a deterministic approach of quantum mechanics for particles with spin 1 2 moving in one dimension. We present a Lagrangian of a spinning particle ($s ={1 \over 2} $), and deduce the expression of the conjugate…

In this paper we prove a viability result for multidimensional, time dependent, stochastic differential equations driven by fractional Brownian motion with Hurst parameter1/2 < H < 1, using pathwise approach. The sufficient condition is…

The Brownian motion of a test particle interacting with a quantum scalar field in the presence of a perfectly reflecting boundary is studied in (1 + 1)-dimensional flat spacetime. Particularly, the expressions for dispersions in velocity…

The statistics of the diffusive motion of particles often serve as an experimental proxy for their interaction with the environment. However, inferring the physical properties from the observed trajectories is challenging. Inspired by a…

We discuss some Lagrangian and presymplectic models concerning test particles in electromagnetic and gravitational fields, with the aim of describing an upper bound to the acceleration. Some models are based on the relativistic phase space…

We introduce a technique to merge two biased Brownian motions into a single regular process. The outcome follows a stochastic differential equation with a constant diffusion coefficient and a non-linear drift. The emerging stochastic…

We study supercritical branching processes in which all particles evolve according to some general Markovian motion (which may possess absorbing states) and branch independently at a fixed constant rate. Under fairly natural assumptions on…

Motivated by a theorem of Barbour, we revisit some of the classical limit theorems in probability from the viewpoint of the Stein method. We setup the framework to bound Wasserstein distances between some distributions on infinite…

We discuss the two-dimensional motion of a Brownian particle that is confined to a harmonic trap and driven by a shear flow. The surrounding medium induces memory effects modelled by a linear, typically nonreciprocal coupling of the…

The dynamics of fluid particles on cylindrical manifolds is investigated. The velocity field is obtained by generalizing the isotropic Kraichnan ensemble, and is therefore Gaussian and decorrelated in time. The degree of compressibility is…

We study the motion of a solid particle immersed in a Newtonian fluid and confined between two parallel elastic membranes possessing shear and bending rigidity. The hydrodynamic mobility depends on the frequency of the particle motion due…

We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…

Two-boson momentum correlations at fixed particle number constraint are studied in a simple analytically solvable model of a thermal expanding system. We show that the increase of expansion rate, as well as increase of particle…

In this paper we prove the law of large numbers and central limit theorem for trajectories of a particle carried by a two dimensional Eulerian velocity field. The field is given by a solution of a stochastic Navier--Stokes system with a…

We study the one-dimensional ballistic aggregation process in the continuum limit for one-sided Brownian initial velocity (i.e. particles merge when they collide and move freely between collisions, and in the continuum limit the initial…

We study a model for the entanglement of a two-dimensional reflecting Brownian motion in a bounded region divided into two halves by a wall with three or more small windows. We map the Brownian motion into a Markov Chain on the fundamental…