Nonequilibrium Fluctuation-Induced Interactions


red ball Are there long-ranged fluctuation-induced interactions in active matter?

yellow ball "Fluctuation-Induced Casimir Forces in Granular Fluids,"

C. Cattuto, R. Brito, U.M.B. Marconi, F. Nori, and R. Soto, Phys. Rev. Lett. 96, 178001 (2006)

yellow ball "Nonadditivity of Fluctuation-Induced Forces in Fluidized Granular Media,"

M.R. Shaebani1, J. Sarabadani, and D.E. Wolf, Phys. Rev. Lett. 108, 198001 (2012)

yellow ball "Casimir effect in actice mtter systems,"

D. Ray, C. Reichhardt, and C.J. Olson Reichhardt, Phys. Rev. E 90, 013019 (2014)

yellow ballThe answer is negative: no long-ranged correlations and no long-ranged interactions.


red ball Agitating active matter from rest:

yellow ball C.M. Rohwer, M. Kardar and Matthias Krüger, PRL 188, 015702 (2017)

Self-propelled colloidal particles                                                                     Shaken Grains                             

red ballFluctuations of the conserved density field satisfy (model B):

Resulting in the trivial (uncorrelated) steady state

red ballWhat happens when the level of activity/noise is suddently changed (quench) with confining plates?

yellow ballThe assumption of local equilibrium suggests a time-varying pressure on each plate:

yellow ball The density fluctuations on the two sides of plates in a parallel plate geometry are different.

In a Gaussian model, the second term leads to transient universal long-range fluctuation-induced force:


red ball Simulations of Active Brownian Particles agitated (from rest) between walls separated by L:

yellow ballActive particles condense on a repulsive surface!

yellow ballThe evolution of the mean density profile leads to an additonal (calculable) contribution from the first term.

yellow ballSimulations results for an interacting gas (initial condition corresponding to infinite temperature):

yellow ballThe transient force due to relaxation of the mean density profile decays with time exponentially

yellow ballThe long time decay of the force is due to the (repulsive) contribution of transient density fluctuations.


red ball  Long-range (and universal) Casimir forces arise from long-range correlated (quantum or thermal) fluctuations.

yellow ballNon-equilibrium fluctuations of conserved quantities can be long-ranged.

Fluctuating hydrodynamics predicts long-range correlated temperature/density fluctuations.

H. Wada, and S.-i. Sasa,  Phys. Rev. E 67, 065302 (2003) (Fluctuating shear flow)

T. R. Kirkpatrick, J. M. Ortiz de Zárate, and J. V. Sengers, Phys. Rev. Lett. 110, 235902 (2013)


red ball Steady state fluctuation force: Consider diffusion between reservoirs at different densities; i.e. a steady state with a uniform current.

 "Fluctuation-induced forces in Non-equilibrium (difusive) dynamics," Aminov, Kafri, & M.K., PRL 114, 230602 (2015)

ρl    ρr

yellow ballThe presence of a current leads to correlated, position dependent, fluctuations in density.

yellow ballDensity fluctuations are different on the 2 sides of each plate, leading to a position-dependent pressure

For the Symmetric Simple Exclusion Process (SSEP) in two dimensions

yellow ballWe tested this prediction numerically:

yellow ballMore generally, for small density gradients:

 The amplitude is non-universal, and dependent on dynamics.

 The force can be attractive (SSEP) or repulsive.

 The same (non-extensive) form is obtained in higher dimensions


Conserved density leads to long-ranged correlations and interactions out of equilibrium.


 

 

 

 

 

 

 

 

 

red ballTransient fluctuation-induced force between two inclusions: