Tracer particle in a confined correlated medium: an adiabatic elimination method

Abstract

We present a simple and systematic procedure to determine the effective dynamics of a Brownian particle coupled to a rapidly fluctuating correlated medium, modeled as a scalar Gaussian field, under spatial confinement. The method allows us, in particular, to address the case in which the fluctuations of the medium are suppressed in the vicinity of the particle, as described by a quadratic coupling in the underlying Hamiltonian. As a consequence of the confinement of the correlated medium, the resulting effective Fokker-Planck equation features spatially dependent drift and diffusion coefficients. We apply our method to simplified fluid models of binary mixtures and microemulsions near criticality containing a colloidal particle, and we analyze the corrections to the stationary distribution of the particle position and the diffusion coefficient.

arXiv comment29 pages, 4 figures

References in corpus (36)

• The `Friction' of Vacuum, and other Fluctuation-Induced Forces
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study
• Critical Casimir effect in classical binary liquid mixtures
• The Casimir effect: from quantum to critical fluctuations
• Spinodal decomposition to a lamellar phase: effects of hydrodynamic flow
• Collective behavior of colloids due to critical Casimir interactions
• Lateral diffusion of a protein on a fluctuating membrane
• Hybrid Elastic/Discrete-Particle Approach to Biomembrane Dynamics with Application to the Mobility of Curved Integral Membrane Proteins
• Diffusion on Ruffled Membrane Surfaces
• Nonequilibrium critical Casimir interactions in binary fluids
• Critical dynamics in thin films
• Diffusing proteins on a fluctuating membrane: Analytical theory and simulations
• Lattice Boltzmann simulations of lamellar and droplet phases
• A perturbative path integral study of active and passive tracer diffusion in fluctuating fields
• Projection operators in statistical mechanics: a pedagogical approach
• The out of equilibrium behavior of Casimir type fluctuation induced forces for free classical fields
• Many-body effects for critical Casimir forces
• Drag forces on inclusions in classical fields with dissipative dynamics
• Energy transfer between colloids via critical interactions
• Transient Casimir forces from quenches in thermal and active matter
• Many-body critical Casimir interactions in colloidal suspensions
• Thermal Casimir drag in fluctuating classical fields
• Diffusion of active tracers in fluctuating fields
• Dynamics of a colloidal particle coupled to a Gaussian field: from a confinement-dependent to a non-linear memory
• Fluctuation Amplitude of a Trapped Rigid Sphere Immersed in a Near-Critical Binary Fluid Mixture within the Regime of the Gaussian Model
• Diffusion of a particle quadratically coupled to a thermally fluctuating field
• Critical Casimir interaction between colloidal Janus-type particles in two spatial dimensions
• Surface-induced non-equilibrium dynamics and critical Casimir forces for model B in film geometry
• Dynamics and steady states of a tracer particle in a confined critical fluid
• Inducing oscillations of trapped particles in a near-critical Gaussian field
• Spatial Organization of Active Particles with Field Mediated Interactions
• First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect
• Dynamics of the critical Casimir force for a conserved order parameter after a critical quench
• Soft inclusion in a confined fluctuating active gel
• Fluctuations of the critical Casimir force

Cited by in corpus (8)

• Memory-induced oscillations of a driven particle in a dissipative correlated medium
• Stochastic thermodynamics of a probe in a fluctuating correlated field
• Inducing oscillations of trapped particles in a near-critical Gaussian field
• Non-Gaussian fluctuations of a probe coupled to a Gaussian field
• Structure and dynamics of a Rouse polymer in a fluctuating correlated medium
• Weight fluctuations in (deep) linear neural networks and a derivation of the inverse-variance flatness relation
• Universal scale-free decay of tracer-bath correlations in $d$-dimensional interacting particle systems
• Recoil of a driven tracer in a correlated medium