Fluctuations of the critical Casimir force
arXiv:2011.12212 · doi:10.1103/PhysRevE.103.062118
Abstract
The critical Casimir force (CCF) arises from confining fluctuations in a critical fluid and thus it is a fluctuating quantity itself. While the mean CCF is universal, its (static) variance has previously been found to depend on the microscopic details of the system which effectively set a large-momentum cutoff in the underlying field theory, rendering it potentially large. This raises the question how the properties of the force variance are reflected in experimentally observable quantities, such as the thickness of a wetting film or the position of a suspended colloidal particle. Here, based on a rigorous definition of the instantaneous force, we analyze static and dynamic correlations of the CCF for a conserved fluid in film geometry for various boundary conditions within the Gaussian approximation. We find that the dynamic correlation function of the CCF is independent of the momentum cutoff and decays algebraically in time. Within the Gaussian approximation, the associated exponent depends only on the dynamic universality class but not on the boundary conditions. We furthermore consider a fluid film, the thickness of which can fluctuate under the influence of the time-dependent CCF. The latter gives rise to an effective non-Markovian noise in the equation of motion of the film boundary and induces a distinct contribution to the position variance. Within the approximations used here, at short times, this contribution grows algebraically in time whereas, at long times, it saturates and contributes to the steady-state variance of the film thickness.
arXiv comment31 pages, 3 figures
References in corpus (29)
- Critical Casimir effect in classical binary liquid mixtures
- The Casimir effect: from quantum to critical fluctuations
- Critical Casimir force in He films: confirmation of finite-size scaling
- Collective behavior of colloids due to critical Casimir interactions
- Nonadditivity of Critical Casimir Forces
- The critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results
- Nonequilibrium critical Casimir interactions in binary fluids
- Critical dynamics in thin films
- A perturbative path integral study of active and passive tracer diffusion in fluctuating fields
- Fluctuations of Fluctuation-Induced "Casimir" Forces
- Interplay of critical Casimir and dispersion forces
- Brownian colloidal particles: Ito, Stratonovich or a different stochastic interpretation
- Relaxation phenomena at criticality
- The out of equilibrium behavior of Casimir type fluctuation induced forces for free classical fields
- Universality of the thermodynamic Casimir effect
- Fluctuations of the Casimir-like force between two membrane inclusions
- Stresses in non-equilibrium fluids: Exact formulation and coarse grained theory
- Drag forces on inclusions in classical fields with dissipative dynamics
- Diffusion of active tracers in fluctuating fields
- Thermal Casimir drag in fluctuating classical fields
- Statistical field theory with constraints: application to critical Casimir forces in the canonical ensemble
- Drag Coefficient of a Rigid Spherical Particle in a Near-Critical Binary Fluid Mixture beyond the Regime of the Gaussian Model
- 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
- Surface-induced non-equilibrium dynamics and critical Casimir forces for model B in film geometry
- On the fluctuation of thermal van der Waals forces due to dipole fluctuations
- Dynamics of the critical Casimir force for a conserved order parameter after a critical quench
- Sign change in the net force in sphere-plate and sphere-sphere systems immersed in nonpolar critical fluid due to the interplay between the critical Casimir and dispersion van der Waals forces
- Correlations and forces in sheared fluids with or without quenching