Diffusion of a tracer in a dense mixture of soft particles connected to different thermostats

Abstract

We study the dynamics of a tracer in a dense mixture of particles connected to different thermostats. Starting from the overdamped Langevin equations that describe the evolution of the system, we derive the expression of the self-diffusion coefficient of a tagged particle in the suspension, in the limit of soft interactions between the particles. Our derivation, which relies on the linearization of the Dean-Kawasaki equations obeyed by the density fields and on a path-integral representation of the dynamics of the tracer, extends previous derivations that held for tracers in contact with a single bath. Our analytical result is confronted to results from Brownian dynamics simulations. The agreement with numerical simulations is very good even for high densities. We show how the diffusivity of tracers can be affected by the activity of a dense environment of soft particles that may represent polymer coils -- a result that could be of relevance in the interpretation of measurements of diffusivity in biological media. Finally, our analytical result is general and can be applied to the diffusion of tracers coupled to different types of fluctuating environments, provided that their evolution equations are linear and that the coupling between the tracer and the bath is weak.

References in corpus (32)

• Active Particles in Complex and Crowded Environments
• Collective motion
• Motility-Induced Phase Separation
• Langevin Equation for the Density of a System of Interacting Langevin Processes
• Can Polymer Coils be modeled as "Soft Colloids"?
• Mean Field Fluid Behavior of the Gaussian Core Model
• Exact Criterion for Determining Clustering vs. Reentrant Melting Behavior for Bounded Interaction Potentials
• Fluid and solid phases of the Gaussian core model
• Binary Mixtures of Particles with Different Diffusivities Demix
• Small activity differences drive phase separation in active-passive polymer mixtures
• Anomalous structure and dynamics of the Gaussian-core fluid
• Conductivity of Concentrated Electrolytes
• Generalized Langevin equations for a driven tracer in dense soft colloids: construction and applications
• Universal Long Ranged Correlations in Driven Binary Mixtures
• How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure and biased interactions
• A perturbative path integral study of active and passive tracer diffusion in fluctuating fields
• Dissipation controls transport and phase transitions in active fluids: Mobility, diffusion and biased ensembles
• Phase separation and nucleation in mixtures of particles with different temperatures
• Anomalous structural evolution of soft particles: Equibrium liquid state theory
• Extracting maximum power from active colloidal heat engines
• Long-range fluctuation-induced forces in driven electrolytes
• Hot Particles Attract in a Cold Bath
• Driven probe under harmonic confinement in a colloidal bath
• Pair correlation of dilute Active Brownian Particles: from low activity dipolar correction to high activity algebraic depletion wings
• Long-time diffusion and energy transfer in polydisperse mixtures of particles with different temperatures
• Long-time self-diffusion of Brownian Gaussian-core particles
• Transient fluctuation-induced forces in driven electrolytes after an electric field quench
• Mean-field microrheology of a very soft colloidal suspension: inertia induces shear-thickening
• Three-body problem for Langevin dynamics with different temperatures
• Transverse density fluctuations around the ground state distribution of counterions near one charged plate: stochastic density functional view
• Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis
• From predicting to learning dissipation from pair correlations of active liquids

Cited by in corpus (5)

• Irreversible Boltzmann samplers in dense liquids: weak-coupling approximation and mode-coupling theory
• Fluctuating hydrodynamics of active particles interacting via taxis and quorum sensing: static and dynamics
• A Cold Tracer in a Hot Bath: In and Out of Equilibrium
• Statistical mechanics of a cold tracer in a hot bath
• Boundary-Induced Drift and Negative Mobility in Constrained Stochastic Systems