Relation between the thermodynamic Casimir effect in Bose-gas slabs and critical Casimir forces

In a recent letter, Martin and Zagrebnov [Europhys. Lett., 73 (2006) 1] discussed the thermodynamic Casimir effect for the ideal Bose gas confined in a thin film. We point out that their findings can be expressed in terms of previous general results for the Casimir effect induced by confined critical fluctuations. This highlights the links between the Casimir effect in the contexts of critical phenomena and Bose-Einstein condensation.Comment: Comment on cond-mat/050726

Critical Casimir effect for colloids close to chemically patterned substrates

Colloids immersed in a critical or near-critical binary liquid mixture and close to a chemically patterned substrate are subject to normal and lateral critical Casimir forces of dominating strength. For a single colloid we calculate these attractive or repulsive forces and the corresponding critical Casimir potentials within mean-field theory. Within this approach we also discuss the quality of the Derjaguin approximation and apply it to Monte Carlo simulation data available for the system under study. We find that the range of validity of the Derjaguin approximation is rather large and that it fails only for surface structures which are very small compared to the geometric mean of the size of the colloid and its distance from the substrate. For certain chemical structures of the substrate the critical Casimir force acting on the colloid can change sign as a function of the distance between the particle and the substrate; this provides a mechanism for stable levitation at a certain distance which can be strongly tuned by temperature, i.e., with a sensitivity of more than 200nm/K.Comment: 27 pages, 14 figure

Normal and lateral critical Casimir forces between colloids and patterned substrates

We study the normal and lateral effective critical Casimir forces acting on a spherical colloid immersed in a critical binary solvent and close to a chemically structured substrate with alternating adsorption preference. We calculate the universal scaling function for the corresponding potential and compare our results with recent experimental data [Soyka F., Zvyagolskaya O., Hertlein C., Helden L., and Bechinger C., Phys. Rev. Lett., 101, 208301 (2008)]. The experimental potentials are properly captured by our predictions only by accounting for geometrical details of the substrate pattern for which, according to our theory, critical Casimir forces turn out to be a sensitive probe.Comment: 6 pages, 3 figure

The Casimir effect: from quantum to critical fluctuations

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

Tunability of Critical Casimir Interactions by Boundary Conditions

We experimentally demonstrate that critical Casimir forces in colloidal systems can be continuously tuned by the choice of boundary conditions. The interaction potential of a colloidal particle in a mixture of water and 2,6-lutidine has been measured above a substrate with a gradient in its preferential adsorption properties for the mixture's components. We find that the interaction potentials at constant temperature but different positions relative to the gradient continuously change from attraction to repulsion. This demonstrates that critical Casimir forces respond not only to minute temperature changes but also to small changes in the surface properties.Comment: 4 figures; http://www.iop.org/EJ/article/0295-5075/88/2/26001/epl_88_2_26001.htm

Dynamic crossover in the global persistence at criticality

We investigate the global persistence properties of critical systems relaxing from an initial state with non-vanishing value of the order parameter (e.g., the magnetization in the Ising model). The persistence probability of the global order parameter displays two consecutive regimes in which it decays algebraically in time with two distinct universal exponents. The associated crossover is controlled by the initial value m_0 of the order parameter and the typical time at which it occurs diverges as m_0 vanishes. Monte-Carlo simulations of the two-dimensional Ising model with Glauber dynamics display clearly this crossover. The measured exponent of the ultimate algebraic decay is in rather good agreement with our theoretical predictions for the Ising universality class.Comment: 5 pages, 2 figure

Monte Carlo simulation results for critical Casimir forces

The confinement of critical fluctuations in soft media induces critical Casimir forces acting on the confining surfaces. The temperature and geometry dependences of such forces are characterized by universal scaling functions. A novel approach is presented to determine them for films via Monte Carlo simulations of lattice models. The method is based on an integration scheme of free energy differences. Our results for the Ising and the XY universality class compare favourably with corresponding experimental results for wetting layers of classical binary liquid mixtures and of 4He, respectively.Comment: 14 pages, 5 figure

Effective temperatures in a simple model of non-equilibrium, non-Markovian dynamics

The concept of effective temperatures in nonequilibrium systems is studied within an exactly solvable model of non-Markovian diffusion. The system is coupled to two heat baths which are kept at different temperatures: one ('fast') bath associated with an uncorrelated Gaussian noise and a second ('slow') bath with an exponential memory kernel. Various definitions of effective temperatures proposed in the literature are evaluated and compared. The range of validity of these definitions is discussed. It is shown in particular, that the effective temperature defined from the fluctuation-dissipation relation mirrors the temperature of the slow bath in parameter regions corresponding to a separation of time scales. On the contrary, quasi-static and thermodynamic definitions of an effective temperature are found to display the temperature of the fast bath in most parameter regions

Spreading in narrow channels

We study a lattice model for the spreading of fluid films, which are a few molecular layers thick, in narrow channels with inert lateral walls. We focus on systems connected to two particle reservoirs at different chemical potentials, considering an attractive substrate potential at the bottom, confining side walls, and hard-core repulsive fluid-fluid interactions. Using kinetic Monte Carlo simulations we find a diffusive behavior. The corresponding diffusion coefficient depends on the density and is bounded from below by the free one-dimensional diffusion coefficient, valid for an inert bottom wall. These numerical results are rationalized within the corresponding continuum limit.Comment: 16 pages, 10 figure

Critical Langevin dynamics of the O(N)-Ginzburg-Landau model with correlated noise

We use the perturbative renormalization group to study classical stochastic processes with memory. We focus on the generalized Langevin dynamics of the \phi^4 Ginzburg-Landau model with additive noise, the correlations of which are local in space but decay as a power-law with exponent \alpha in time. These correlations are assumed to be due to the coupling to an equilibrium thermal bath. We study both the equilibrium dynamics at the critical point and quenches towards it, deriving the corresponding scaling forms and the associated equilibrium and non-equilibrium critical exponents \eta, \nu, z and \theta. We show that, while the first two retain their equilibrium values independently of \alpha, the non-Markovian character of the dynamics affects the dynamic exponents (z and \theta) for \alpha < \alpha_c(D, N) where D is the spatial dimensionality, N the number of components of the order parameter, and \alpha_c(x,y) a function which we determine at second order in 4-D. We analyze the dependence of the asymptotic fluctuation-dissipation ratio on various parameters, including \alpha. We discuss the implications of our results for several physical situations