The bulk correlation length and the range of thermodynamic Casimir forces at Bose-Einstein condensation

The relation between the bulk correlation length and the decay length of thermodynamic Casimir forces is investigated microscopically in two three-dimensional systems undergoing Bose-Einstein condensation: the perfect Bose gas and the imperfect mean-field Bose gas. For each of these systems, both lengths diverge upon approaching the corresponding condensation point from the one-phase side, and are proportional to each other. We determine the proportionality factors and discuss their dependence on the boundary conditions. The values of the corresponding critical exponents for the decay length and the correlation length are the same, equal to 1/2 for the perfect gas, and 1 for the imperfect gas

The Casimir effect for the Bose-Gas in Slabs

We study the Casimir effect for the perfect Bose-gase in the slab geometry for various boundary conditions. We show that the grand canonical potential per unit area at the bulk critical chemical potential $\mu=0$ has the standard asymptotic form with universal Casimir terms.Comment: 6 pages, submitted to Europhysics LettersWe study the Casimir effect for the perfect Bose-gase in the slab geometry for various boundary conditions. We show that the grand canonical potential per unit area at the bulk critical chemical potential $\mu=0$ has the standard asymptotic form with universal Casimir term

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

Thermodynamic Casimir effect for films in the 3D Ising universality class: Symmetry breaking boundary conditions

We study the thermodynamic Casimir force for films in the three-dimensional Ising universality class with symmetry breaking boundary conditions. To this end we simulate the improved Blume-Capel model on the simple cubic lattice. We study the two cases ++, where all spins at the boundary are fixed to +1 and +-, where the spins at one boundary are fixed to +1 while those at the other boundary are fixed to -1. An important issue in analyzing Monte Carlo and experimental data are corrections to scaling. Since we simulate an improved model, leading corrections to scaling, which are proportional to L_0^-omega, where L_0 is the thickness of the film and omega approx 0.8, can be ignored. This allows us to focus on corrections to scaling that are caused by the boundary conditions. We confirm the theoretical expectation that these corrections can be accounted for by an effective thickness L_0,eff = L_0 + L_s. Studying the correlation length of the films, the energy per area, the magnetization profile and the thermodynamic Casimir force at the bulk critical point we find L_s=1.9(1) for our model and the boundary conditions discussed here. Using this result for L_s we find a nice collapse of the finite size scaling curves obtained for the thicknesses L_0=8.5, 16.5 and 32.5 for the full range of temperatures that we consider. We compare our results for the finite size scaling functions theta_++ and theta_+- of the thermodynamic Casimir force with those obtained in a previous Monte Carlo study, by the de Gennes-Fisher local-functional method, field theoretic methods and an experiment with a binary mixture.Comment: 30 pages 10 figures, discussion on the transfermatrix extended, section on the magnetisation profile added, references adde

Short-time scaling behavior of growing interfaces

The short-time evolution of a growing interface is studied within the framework of the dynamic renormalization group approach for the Kadar-Parisi-Zhang (KPZ) equation and for an idealized continuum model of molecular beam epitaxy (MBE). The scaling behavior of response and correlation functions is reminiscent of the ``initial slip'' behavior found in purely dissipative critical relaxation (model A) and critical relaxation with conserved order parameter (model B), respectively. Unlike model A the initial slip exponent for the KPZ equation can be expressed by the dynamical exponent z. In 1+1 dimensions, for which z is known exactly, the analytical theory for the KPZ equation is confirmed by a Monte-Carlo simulation of a simple ballistic deposition model. In 2+1 dimensions z is estimated from the short-time evolution of the correlation function.Comment: 27 pages LaTeX with epsf style, 4 figures in eps format, submitted to Phys. Rev.

Critical Casimir forces and adsorption profiles in the presence of a chemically structured substrate

Motivated by recent experiments with confined binary liquid mixtures near demixing, we study the universal critical properties of a system, which belongs to the Ising universality class, in the film geometry. We employ periodic boundary conditions in the two lateral directions and fixed boundary conditions on the two confining surfaces, such that one of them has a spatially homogeneous adsorption preference while the other one exhibits a laterally alternating adsorption preference, resembling locally a single chemical step. By means of Monte Carlo simulations of an improved Hamiltonian, so that the leading scaling corrections are suppressed, numerical integration, and finite-size scaling analysis we determine the critical Casimir force and its universal scaling function for various values of the aspect ratio of the film. In the limit of a vanishing aspect ratio the critical Casimir force of this system reduces to the mean value of the critical Casimir force for laterally homogeneous ++ and +- boundary conditions, corresponding to the surface spins on the two surfaces being fixed to equal and opposite values, respectively. We show that the universal scaling function of the critical Casimir force for small but finite aspect ratios displays a linear dependence on the aspect ratio which is solely due to the presence of the lateral inhomogeneity. We also analyze the order-parameter profiles at criticality and their universal scaling function which allows us to probe theoretical predictions and to compare with experimental data.Comment: revised version, section 5.2 expanded; 53 pages, 12 figures, iopart clas

Shot Noise in Mesoscopic Conductors

Theoretical and experimental work concerned with dynamic fluctuations has developed into a very active and fascinating subfield of mesoscopic physics. We present a review of this development focusing on shot noise in small electric conductors. Shot noise is a consequence of the quantization of charge. It can be used to obtain information on a system which is not available through conductance measurements. In particular, shot noise experiments can determine the charge and statistics of the quasiparticles relevant for transport, and reveal information on the potential profile and internal energy scales of mesoscopic systems. Shot noise is generally more sensitive to the effects of electron-electron interactions than the average conductance. We present a discussion based on the conceptually transparent scattering approach and on the classical Langevin and Boltzmann-Langevin methods; in addition a discussion of results which cannot be obtained by these methods is provided. We conclude the review by pointing out a number of unsolved problems and an outlook on the likely future development of the field.Comment: 99 two-column pages; 38 .eps figures included. Submitted to Physics Reports. Many minor improvements; typos corrected; references added and update

Shot noise in mesoscopic systems

This is a review of shot noise, the time-dependent fluctuations in the electrical current due to the discreteness of the electron charge, in small conductors. The shot-noise power can be smaller than that of a Poisson process as a result of correlations in the electron transmission imposed by the Pauli principle. This suppression takes on simple universal values in a symmetric double-barrier junction (suppression factor 1/2), a disordered metal (factor 1/3), and a chaotic cavity (factor 1/4). Loss of phase coherence has no effect on this shot-noise suppression, while thermalization of the electrons due to electron-electron scattering increases the shot noise slightly. Sub-Poissonian shot noise has been observed experimentally. So far unobserved phenomena involve the interplay of shot noise with the Aharonov-Bohm effect, Andreev reflection, and the fractional quantum Hall effect.Comment: 37 pages, Latex, 10 figures (eps). To be published in "Mesoscopic Electron Transport," edited by L. P. Kouwenhoven, G. Schoen, and L. L. Sohn, NATO ASI Series E (Kluwer Academic Publishing, Dordrecht

Critical behavior of the three-dimensional XY universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class. We find alpha=-0.0146(8), gamma=1.3177(5), nu=0.67155(27), eta=0.0380(4), beta=0.3485(2), and delta=4.780(2). We observe a discrepancy with the most recent experimental estimate of alpha; this discrepancy calls for further theoretical and experimental investigations. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods, and high-temperature expansions. Two improved models (with suppressed leading scaling corrections) are selected by Monte Carlo computation. The critical exponents are computed from high-temperature expansions specialized to these improved models. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine the specific-heat amplitude ratio.Comment: 61 pages, 3 figures, RevTe