The Casimir effect: from quantum to critical fluctuations

Abstract

The Casimir effect in quantum electrodynamics (QED) is perhaps the best-known example of fluctuation-induced long-ranged force acting on objects (conducting plates) immersed in a fluctuating medium (quantum electromagnetic field in vacuum). A similar effect emerges in statistical physics, where the force acting, e.g., on colloidal particles immersed in a binary liquid mixture is affected by the classical thermal fluctuations occurring in the surrounding medium. The resulting Casimir-like force acquires universal features upon approaching a critical point of the medium and becomes long-ranged at criticality. In turn, this universality allows one to investigate theoretically the temperature dependence of the force via representative models and to stringently test the corresponding predictions in experiments. In contrast to QED, the Casimir force resulting from critical fluctuations can be easily tuned with respect to strength and sign by surface treatments and temperature control. We present some recent advances in the theoretical study of the universal properties of the critical Casimir force arising in thin films. The corresponding predictions compare very well with the experimental results obtained for wetting layers of various fluids. We discuss how the Casimir force between a colloidal particle and a planar wall immersed in a binary liquid mixture has been measured with femto-Newton accuracy, comparing these experimental results with the corresponding theoretical predictions.

Talk delivered at the International Workshop "60 Years of Casimir Effect", Brasilia, 23-27 June 2008 (17 pages, 7 figures)

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Cited by in corpus (142)

• Critical Casimir effect in classical binary liquid mixtures
• Large deviations and universality in quantum quenches
• Casimir Effect in Active Matter Systems
• Collective behavior of colloids due to critical Casimir interactions
• Nonadditivity of Critical Casimir Forces
• Statistics of the work done by splitting a one-dimensional quasi-condensate
• Boundary critical behavior of the three-dimensional Heisenberg universality class
• Nonequilibrium critical Casimir interactions in binary fluids
• The thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class
• Thermodynamic Casimir effect for films in the 3D Ising universality class: Symmetry breaking boundary conditions
• Casimir interactions in Ising strips with boundary fields: exact results
• Thermodynamic Casimir effect: Universality and Corrections to Scaling
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• Critical Casimir effect for colloids close to chemically patterned substrates
• Crossover of Critical Casimir forces between different surface universality classes
• Aspect-ratio dependence of thermodynamic Casimir forces
• Thermodynamic Casimir Forces between a Sphere and a Plate: Monte Carlo Simulation of a Spin Model
• Critical Casimir forces for Ising films with variable boundary fields
• Failure of local thermal equilibrium in quantum friction
• Trapping colloids near chemical stripes via critical Casimir forces
• Normal and lateral critical Casimir forces between colloids and patterned substrates
• Critical Casimir Effect: Exact Results
• Critical Casimir forces and adsorption profiles in the presence of a chemically structured substrate
• The specific heat, the energy density and the thermodynamic Casimir force in the neighbourhood of the lambda-transition
• The out of equilibrium behavior of Casimir type fluctuation induced forces for free classical fields
• Local theory for ions in binary liquid mixtures
• Phase behavior of colloidal suspensions with critical solvents in terms of effective interactions
• Fluctuations of the Casimir-like force between two membrane inclusions
• The thermodynamic Casimir effect in the neighbourhood of the lambda-transition: A Monte Carlo study of an improved three dimensional lattice model
• Many-body effects for critical Casimir forces
• Physical origin of nonequilibrium fluctuation-induced forces in fluids
• Casimir force induced by imperfect Bose gas
• Long-range fluctuation-induced forces in driven electrolytes
• Tunable critical Casimir forces counteract Casimir-Lifshitz attraction
• Critical Casimir torques and forces acting on needles in two spatial dimensions
• Critical Casimir Forces for Films with Bulk Ordering Fields
• Critical Casimir forces between homogeneous and chemically striped surfaces
• Critical adsorption and critical Casimir forces in the canonical ensemble
• Effective field theory approach to Casimir interactions on soft matter surfaces
• Exact thermodynamic Casimir forces for an interacting three-dimensional model system in film geometry with free surfaces
• Fluctuation-induced forces in strongly anisotropic critical systems
• Critical Casimir Interactions Between Spherical Particles in the Presence of the Bulk Ordering Fields
• Structure and aggregation of colloids immersed in critical solvents
• The imperfect Bose gas in d dimensions: critical behavior and Casimir forces
• Effective field theory approach to fluctuation-induced forces between colloids at an interface
• Statistical field theory with constraints: application to critical Casimir forces in the canonical ensemble
• Autonomous quantum rotator
• Yet another method to compute the thermodynamic Casimir force in lattice models
• Critical Casimir effect in films for generic non-symmetry-breaking boundary conditions
• Forces exerted by a correlated fluid on embedded inclusions
• Casimir force in the O(n -> infinity) model with free boundary conditions
• Crossover from Goldstone to critical fluctuations: Casimir forces in confined O$(\mathbf{n})$ symmetric systems
• Fluctuation-induced forces in confined ideal and imperfect Bose gases
• Critical free energy and Casimir forces in rectangular geometries
• The square lattice Ising model on the rectangle II: Finite-size scaling limit
• Critical Casimir force in the presence of random local adsorption preference
• Memory-induced oscillations of a driven particle in a dissipative correlated medium
• Three-body critical Casimir forces
• Transient fluctuation-induced forces in driven electrolytes after an electric field quench
• Scattering Approach for Fluctuation--Induced Interactions at Fluid Interfaces
• Thermal Casimir effect for the scalar field in flat spacetime under a helix boundary condition
• Critical Casimir forces along the iso-fields
• Critical fluctuations in a confined driven-dissipative quantum condensate
• Critical Casimir forces from the equation of state of quantum critical systems
• Crossover from low-temperature to high-temperature fluctuations. I. Thermodynamic Casimir forces of isotropic systems
• Direct calculation of the critical Casimir force in a binary fluid
• Crossover from low-temperature to high-temperature fluctuations. II. Nonuniversal thermodynamic Casimir forces of anisotropic systems
• Tracer particle in a confined correlated medium: an adiabatic elimination method
• Repulsive Casimir force in Bose-Einstein Condensate
• Surface-induced non-equilibrium dynamics and critical Casimir forces for model B in film geometry
• Exact results for the behavior of the thermodynamic Casimir force in a model with a strong adsorption
• Critical Casimir forces between defects in the 2D Ising model
• Critical Casimir forces for O(N) models from functional renormalization
• Exact Critical Casimir Amplitude of Anisotropic Systems from Conformal Field Theory and Self-Similarity of Finite-Size Scaling Functions in $d\ge 2$ Dimensions
• Exact pre-transition effects in kinetically constrained circuits: dynamical fluctuations in the Floquet-East model
• Classical Casimir force from a quasi-condensate of light
• Line contribution to the critical Casimir force between a homogeneous and a chemically stepped surface
• Casimir force in the rotor model with twisted boundary conditions
• Dynamics and steady states of a tracer particle in a confined critical fluid
• Pronounced minimum of the thermodynamic Casimir forces of O($\mathbf{n}$) symmetric film systems: Analytic theory
• Inducing oscillations of trapped particles in a near-critical Gaussian field
• Casimir force in dense confined electrolytes
• Cluster expansion for ground states of local Hamiltonians
• Critical Casimir Force between Inhomogeneous Boundaries
• The O(n) ${\varphi }^4$ model with free surfaces in the large-$n$ limit: Some exact results for boundary critical behaviour, fluctuation-induced forces and distant-wall corrections
• Critical and near critical phase behaviour and interplay between the thermodynamic Casimir and van der Waals forces in confined non-polar fluid medium with competing surface and substrate potentials
• Universal amplitudes of the Casimir-like interactions between four types of rods in fluid membranes
• Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theories
• Lateral critical Casimir force in 2D Ising strip with inhomogeneous walls
• The bulk correlation length and the range of thermodynamic Casimir forces at Bose-Einstein condensation
• The role of quantum work statistics in many-body physics
• The Casimir Effect from a Condensed Matter Perspective
• Critical Casimir forces in a magnetic system: An experimental protocol
• Fluctuation-induced forces between rings threaded around a polymer chain under tension
• Classification of the sign of the critical Casimir force in two dimensional systems at asymptotically large separations
• Universal anisotropic finite-size critical behavior of the two-dimensional Ising model on a strip and of d-dimensional models on films
• 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
• Repulsive to Attractive Fluctuation-Induced Forces in Disordered Landau-Ginzburg Model
• Conformal field theory of critical Casimir forces between surfaces with alternating boundary conditions in two dimensions
• The ordinary surface universality class of the three-dimensional O($N$) model
• Work, work fluctuations, and the work distribution in a thermal non-equilibrium steady state
• Casimir interaction of rod-like particles in a two-dimensional critical system
• Effective interaction between a colloid and a soft interface near criticality
• Inverse scattering-theory approach to the exact large-$n$ solutions of $O(n)$ ${\varphi }^4$ models on films and semi-infinite systems bounded by free surfaces
• Universal Casimir interactions in the sphere-sphere geometry
• Thermodynamic Casimir forces in strongly anisotropic systems within the $N\to \infty$ class
• Bridging transitions and capillary forces for colloids in a slit
• Casimir Force in a Model with Strongly Adsorbing Competing Walls: Analytical Results
• Critical Casimir effects in 2D Ising model with curved defect lines
• Casimir effect of an ideal Bose gas trapped in a generic power-law potential
• Restoration of a Spontaneously Broken Symmetry in an Euclidean Quantum $\lambda {\phi }_{d+1}^4$ model with Quenched Disorder
• Viscosity of a sheared correlated (near-critical) model fluid in confinement
• Membrane-mediated interactions
• Role of topology on the work distribution function of a quenched Haldane model of graphene
• Critical Casimir forces between planar and crenellated surfaces
• Universal work statistics in long-range interacting quantum systems
• The square lattice Ising model on the rectangle III: Hankel and Toeplitz determinants
• Fluctuations of the critical Casimir force
• Non-universal Casimir forces at Bose-Einstein condensation of an ideal gas: effect of Dirichlet boundary conditions
• Manipulation and amplification of the Casimir force through surface fields using helicity
• Finite-size scaling of the magnetization probability density for the critical Ising model in slab geometry
• On the dynamics of the interaction between triggered active inclusions
• Lattice Boltzmann Simulations of Non-Equilibrium Fluctuations in a Non-Ideal Binary Mixture
• Exact results for the Casimir force of a three-dimensional model of relativistic Bose gas in a film geometry
• Playing with Casimir in the vacuum sandbox
• Casimir forces for the ideal Bose gas in anisotropic optical lattices: the effect of alternating sign upon varying dimensionality
• Spin models in three dimensions: Adaptive lattice spacing
• Boundary operator product expansion coefficients of the three-dimensional Ising universality class
• Critical Casimir Interactions and Percolation: the quantitative description of critical fluctuations
• Recoil of a driven tracer in a correlated medium
• Robust orbital diamagnetism of correlated Dirac fermions in chiral Ising universality class
• One-Loop Correction to the Casimir Energy in Lorentz-Violating ${\varphi }^4$ Theory with Rough Membrane Boundaries
• Casimir effect in critical $\mathrm{O}(N)$ models from non-equilibrium Monte Carlo simulations
• Casimir effect for a Bose-Einstein condensate inside a cylindrical tube
• The three-dimensional $O(n)$ ${\varphi }^4$ model on a strip with free boundary conditions: exact results for a nontrivial dimensional crossover in the limit $n\to \infty$
• Tricritical Casimir forces and order parameter profiles in wetting films of ${}^3\text{He}$ -${}^4\text{He}$ mixtures
• Thermal Casimir effect for a Dirac field on flat space with a nontrivial circular boundary condition
• Nonequilibrium relaxation of a trapped particle in a near-critical Gaussian field
• Thermal Casimir effect in the spin-orbit coupled Bose gas
• Casimir Energy for Lorentz-Violating Scalar Field with Helical Boundary Condition in d Spatial Dimensions
• Æther Coupling Effects on Casimir Energy for Self-Interacting Scalar Field within Extra Dimension
• Critical fluctuations of a confined binary mixture