Alessio Squarcini

We study a lattice model describing the nonequilibrium dynamics arising from the pulling of a tracer particle through a disordered medium occupied by randomly placed obstacles. The model is considered in a restricted geometry to investigate confinement-induced effects. We derive exact analytical results for the characteristic function of the displacement moments, valid to first order in the obstacle density. By calculating the velocity autocorrelation function and its long-time tail, we find that even in equilibrium the system exhibits a dimensional crossover. This picture is further confirmed by the approach of the drift velocity to its terminal value attained in the nonequilibrium stationary state. At long times, the diffusion coefficient is affected by both driving and confinement in a way that we quantify analytically. The force-induced diffusion coefficient depends sensitively on confinement, which qualitatively modifies the nonanalytic force dependence observed in the unbounded model. We then examine the fluctuations of the tracer particle along the driving direction. We show that in the intermediate regime superdiffusive behavior persists even in the presence of confinement. We use stochastic simulations to test the validity of the analytical results, exact to first order in the obstacle density and valid for arbitrary force and confinement.

We provide comprehensive details of how a previously overlooked entropic, or low-temperature Casimir contribution, W_{C}, to the total binding potential for three-dimensional short-ranged wetting may be determined from a microscopic Landau-Ginzburg-Wilson Hamiltonian. The entropic contribution comes from the many microscopic configurations corresponding to a given interfacial one, which arise from bulklike fluctuations about the mean-field (MF) constrained profile, and adds to the usual MF contribution W_{MF}. We determine the functional dependence of W_{C} on the interface (and wall) shape using a boundary integral method which can be cast as a diagrammatic expansion with each diagram corresponding to successively higher-order exponentially decaying contributions. The decay of W_{C} is qualitatively different for first-order and critical wetting with the change in form occurring at the MF tricritical point. Including the Casimir contribution to the binding potential preserves the global surface phase diagram but changes, radically, predictions for fluctuation effects at first-order and tricritical wetting, even when capillary-wave fluctuations are not considered.

We employ a procedure that enables us to calculate the excess free energies for a finite Ising cylinder with domain walls analytically. This procedure transparently covers all possible configurations of the domain walls under given boundary conditions and allows for a physical interpretation in terms of coarse-grained quantities such as surface and point tensions. The resulting integrals contain all the information about finite-size effects; we extract them by careful asymptotic analysis using the steepest descent method. To this end, we exactly determine the steepest descent path and analyse its features. For the general class of integrals, which are usually found in the study of systems with inclined domain walls, knowledge of the steepest descent path is necessary to detect possible intersections with poles of the integrand in the complex plane.

We consider a tracer particle performing a random walk on a two-dimensional lattice in the presence of immobile hard obstacles. Starting from equilibrium, a constant force pulling on the particle is switched on, driving the system to a new stationary state. Our study calculates displacement moments in discrete time (number of steps N) for an arbitrarily strong constant driving force, exact to first order in obstacle density. We find that for fixed driving force F, the approach to the terminal discrete velocity scales as ∼N^{-1}exp(-NF^{2}/16) for small F, differing significantly from the exponential decay expected of linear response. Besides a nonanalytic dependence on the force and breakdown of Einstein's linear response, our results show that fluctuations around the mean displacement in direction of the force are enhanced in the presence of obstacles. Notably, the variance grows as ∼N^{3} (superdiffusion) for F→∞ at intermediate steps, reverting to normal diffusion (∼N) at larger steps, a behavior previously observed in continuous time and verified in this work in the discrete domain of the number of steps. Unlike the exponential waiting time case, the superdiffusion regime starts already for N=1. The presented framework allows considering any type of waiting-time distribution between steps and transition to continuous time using subordination methods. Our findings are also validated through computer simulations.

For a long time, the study of thermal effects at three-dimensional (3D) short-ranged wetting transitions considered only the effect of interfacial fluctuations. We show that an entropic Casimir contribution, missed in previous treatments, produces significant effects when it is included; in particular, mean-field predictions are no longer obtained when interfacial fluctuations are ignored. The Casimir term arises from the many different microscopic configurations that correspond to a given interfacial one. By employing a coarse-graining procedure, starting from a microscopic Landau–Ginzburg–Wilson (LGW) Hamiltonian, we identify the interfacial model for 3D wetting and the exact form of the Casimir term. The Casimir contribution does not alter the Nakanishi–Fisher surface phase diagram; it significantly increases the adsorption near a first-order wetting transition and completely changes the predicted critical singularities of tricritical wetting, including the nonuniversality occurring in 3D arising from interfacial fluctuations. We illustrate how the Casimir term leads to a reappraisal of the critical singularities at wetting transitions. Lastly, this paper presents novel results about curvature effects in layers of concentrical spheres and cylinders.

For a long time, the study of thermal effects at three-dimensional (3D) short-ranged wetting transitions considered only the effect of interfacial fluctuations. We show that an entropic Casimir contribution, missed in previous treatments, produces significant effects when it is included; in particular, mean-field predictions are no longer obtained when interfacial fluctuations are ignored. The Casimir term arises from the many different microscopic configurations that correspond to a given interfacial one. By employing a coarse-graining procedure, starting from a microscopic Landau-Ginzburg-Wilson Hamiltonian, we identify the interfacial model for 3D wetting and the exact form of the Casimir term. The Casimir contribution does not alter the Nakanishi-Fisher surface phase diagram; it significantly increases the adsorption near a first-order wetting transition and completely changes the predicted critical singularities of tricritical wetting, including the nonuniversality occurring in 3D arising from interfacial fluctuations. We illustrate how the Casimir term leads to a reappraisal of the critical singularities at wetting transitions.

Critical wetting is of crucial importance for the phase behavior of a simple fluid or Ising magnet confined between walls that exert opposing surface fields so that one wall favors liquid (spin up), while the other favors gas (spin down). We show that arrays of boxes filled with fluid and linked by channels with appropriately chosen opposing walls can exhibit long-range cooperative effects on a length scale far exceeding the bulk correlation length. We give the theoretical foundations of these long-range couplings by using a lattice gas (Ising model) description of a system. Published by the American Physical Society 2024