Brownian oscillators driven by correlated noise in a moving trap

TL;DR

This paper analyzes the dynamics of a Brownian oscillator in a moving trap driven by correlated noise, providing exact solutions for systems with different memory effects, advancing understanding of non-Markovian stochastic processes.

Contribution

It introduces a novel analytical approach to solve the generalized Langevin equation with correlated noise and memory effects in a moving trap scenario.

Findings

Exact solutions for exponentially correlated noise in viscoelastic fluids.

Analytical results for memory effects from Navier-Stokes hydrodynamics.

Enhanced understanding of non-Markovian Brownian motion dynamics.

Abstract

Brownian oscillator, i.e. a micron-sized or smaller particle trapped in a thermally fluctuating environment is studied. The confining harmonic potential can move with a constant velocity. As distinct from the standard Langevin theory, the chaotic force driving the particle is correlated in time. The dynamics of the particle is described by the generalized Langevin equation with the inertial term, a coloured noise force, and a memory integral. We consider two kinds of the memory in the system. The first one corresponds to the exponentially correlated noise in a weakly viscoelastic fluid and in the second case the memory naturally arises within the Navier-Stokes hydrodynamics. Exact analytical solutions are obtained in both the cases using a simple and effective method not applied so far in this kind of problems.