Table of contents

Monodisperse aqueous foams are perfused with fluids of different colour, and their spatial distribution during the drainage process is studied. For uniform perfusion, two side-by-side flows are found to remain segregated for lengths exceeding thousands of bubble diameters. Thus, fluid elements move downwards through the foam network in a coordinated zigzag fashion rather than performing a random walk.

We analyse the equilibrium dynamics of kinetically constrained spin systems which have been proposed as models for strong or fragile glasses and systems undergoing jamming transitions. We develop a novel multi-scale approach which allows us to connect the timescales to the typical size of the regions which have to be rearranged to create/destruct a particle. Thus we obtain exact results for the relaxation time τ as . For most of the models this regime was previously investigated only by numerical simulations. Depending on the choice of constraints, via our technique we obtain or we disprove the previously conjectured scalings. In particular, for the Fredrickson–Andersen and East models at any ρ < 1, we establish that the persistence and the spin–spin time autocorrelation functions decay exponentially. This excludes the stretched exponential relaxation which was derived by numerical simulations. Moreover for the East model we prove log τ = 1/(2 log 2)(log(1–ρ))² as , getting a sharp result for log τ which differs by a factor of 2 from the one conjectured in previous literature. For FA2f in d ≥ 2 and FA3f in d ≥ 3 we obtain the super-Arrhenius bounds exp(1–ρ)^–1 ≤ τ ≤ exp(1–ρ)^–5 and exp exp(1–ρ)^–1 ≤ τ ≤ exp exp(1–ρ)^–2, respectively. For FA1f in d = 1, 2 we rigorously prove the power law scalings recently derived in Jack et al (2006 Preprint cond-mat/0601529). Our techniques are flexible enough to allow a variety of constraints. In particular we can also deal with models displaying an ergodicity-breaking transition at ρ_c < 1, e.g. the North-East model. In this case we prove exponential decay to equilibrium in the whole ergodic regime.

We study the vacuum state of spin chains where each site carries an arbitrary representation. We prove that the string hypothesis usually used to solve the Bethe ansatz equations is valid for representations characterized by rectangular Young tableaux. In these cases, we obtain the density of the centre of the strings for the vacuum. We work through different examples and, in particular, that for spin chains with a periodic array of impurities.

In this paper we present the first theoretical study of the coherent Rayleigh–Brillouin scattering in binary mixtures of monatomic ideal gases. The line shape of the coherent spectrum is determined by solving a kinetic model of the Boltzmann equation that replaces the collision operators by simple relaxation-time terms which are compatible with the two-fluid hydrodynamic theory. Theoretical predictions for the coherent light scattering spectrum in dilute argon–krypton gas mixtures are presented and its dependence on concentration and pressure is analysed.

Starting from a many-body classical system governed by a trace-form entropy we derive, in the stochastic quantization picture, a family of non-linear and non-Hermitian Schrödinger equations describing, in the mean field approximation, a quantum system of interacting particles. The time evolution of the main physical observables is analysed by means of the Ehrenfest equations, showing that, in general, this family of equations takes into account dissipative and damped effects due to the interaction of the system with the background. We explore the presence of steady states by means of solitons, describing conservative solutions. The results are specialized to the case of a system governed by the Boltzmann–Gibbs entropy.

We consider the low temperature T<T_c disorder-dominated phase of the directed polymer in a random potential in dimension 1+1 (where ) and 1+3 (where ). To characterize the localization properties of the polymer of length L, we analyse the statistics of the weights of the last monomer as follows. We numerically compute the probability distributions P₁(w) of the maximal weight , the probability distribution Π(Y₂) of the parameter as well as the average values of the higher-order moments . We find that there exists a temperature T_gap<T_c such that (i) for T<T_gap, the distributions P₁(w) and Π(Y₂) present the characteristic Derrida–Flyvbjerg singularities at w = 1/n and Y₂ = 1/n for n = 1,2... In particular, there exists a temperature-dependent exponent μ(T) that governs the main singularities P₁(w)∼(1−w)^μ(T)−1 and Π(Y₂)∼(1−Y₂)^μ(T)−1 as well as the power-law decay of the moments . The exponent μ(T) grows from the value μ(T = 0) = 0 up to μ(T_gap)∼2. (ii) For T_gap<T<T_c, the distribution P₁(w) vanishes at some value w₀(T)<1, and accordingly the moments decay exponentially as (w₀(T))^k in k. The histograms of spatial correlations also display Derrida–Flyvbjerg singularities for T<T_gap. Both below and above T_gap, the study of typical and averaged correlations is in full agreement with the droplet scaling theory.

We consider the trigonometric Felderhof model of free fermions in an external field, on a finite lattice with domain wall boundary conditions. The vertex weights are functions of rapidities and external fields.

We obtain a determinant expression for the partition function in the special case where the dependence on the rapidities is eliminated, but for general external field variables. This determinant can be evaluated in product form. In the homogeneous limit, it is proportional to a 2-Toda τ function.

Next, we use the algebraic Bethe ansatz factorized basis to obtain a product expression for the partition function in the general case with dependence on all variables.

We study the shock structures in three-states one-dimensional driven-diffusive systems with nearest-neighbour interactions using a matrix product formalism. We consider the cases in which the stationary probability distribution function of the system can be written in terms of the superposition of product shock measures. We show that only three families of three-states systems have this property. In each case the shock performs a random walk provided that some constraints are fulfilled. We calculate the diffusion coefficient and drift velocity of shock for each family.

In this paper we consider the ansatz for multiple Schramm–Loewner evolutions (SLEs) proposed by Bauer, Bernard and Kytölä from a more probabilistic point of view. Here we show their ansatz is a consequence of conformal invariance, reparametrization invariance and a notion of absolute continuity. In so doing we demonstrate that it is only consistent to grow multiple SLEs if their κ parameters are related by κ_i = κ_j or κ_i = 16/κ_j.

This paper gives a pedagogic derivation of the Bethe ansatz solution for 1D interacting anyons. This includes a demonstration of the subtle role of the anyonic phases in the Bethe ansatz arising from the anyonic commutation relations. The thermodynamic Bethe ansatz equations defining the temperature dependent properties of the model are also derived, from which some ground state properties are obtained.

Covering a network with the minimum possible number of boxes can reveal interesting features for the network structure, especially in terms of self-similar or fractal characteristics. Considerable attention has been recently devoted to this problem, with the finding that many real networks are self-similar fractals. Here we present, compare and study in detail a number of algorithms that we have used in previous papers towards this goal. We show that this problem can be mapped to the well-known graph colouring problem and then we simply can apply well-established algorithms. This seems to be the most efficient method, but we also present two other algorithms based on burning which provide a number of other benefits. We argue that the algorithms presented provide a solution close to optimal and that another algorithm that can significantly improve this result in an efficient way does not exist. We offer to anyone that finds such a method to cover his/her expenses for a one-week trip to our lab in New York (details in http://jamlab.org).

Using a high speed camera, we study the peeling dynamics of an adhesive tape under a constant load with a special focus on the so-called stick–slip regime of the peeling. It is the first time that the very fast motion of the peeling point has been imaged. The speed of the camera, up to 16 000 fps, allows us to observe and quantify the details of the peeling point motion during the stick and slip phases: stick and slip velocities, durations and amplitudes. First, in contrast with previous observations, the stick–slip regime appears to be only transient in the force controlled peeling. Additionally, we discover that the stick and slip phases have similar durations and that at high mean peeling velocity, the slip phase actually lasts longer than the stick phase. Depending on the mean peeling velocity, we also observe that the velocity change between stick and slip phases ranges from a rather sudden to a smooth transition. These new observations can help to discriminate between the various assumptions used in theoretical models for describing the complex peeling of an adhesive tape. The present imaging technique opens the door to an extensive study of the velocity controlled stick–slip peeling of an adhesive tape that will allow us to understand the statistical complexity of the stick–slip in a stationary case.

We present an algorithm to evaluate large deviation functions associated to history-dependent observables. Instead of relying on a time discretization procedure to approximate the dynamics, we provide a direct continuous-time algorithm valuable for systems with multiple timescales, thus extending the work of Giardinà, Kurchan and Peliti (2006 Phys. Rev. Lett.96   120603).

The procedure is supplemented with a thermodynamic-integration scheme which improves its efficiency. We also show how the method can be used to probe large deviation functions in systems with a dynamical phase transition—revealed in our context through the appearance of a non-analyticity in the large deviation functions.

We consider the underdamped Brownian dynamics of particles in a symmetric periodic potential by taking into account systematic quantum corrections order by order and show that a very slow asymmetric and periodic modulation with zero temporal average can induce directed quantum transport in the limit , where ω_s, γ and τ are the system frequency, the dissipation constant and the time period of the modulation, respectively.

When a non-conservative system fluctuates around its steady configuration, in general, neither equipartition nor the fluctuation–dissipation theorem are satisfied. Using a path integral approach, we show that in this case the probability distribution is determined in terms of the energy dissipated along the minimum path. The latter is the path of minimum energy dissipation of a fictitious, unit mass particle, moving with constant energy under the influence of an electric and a magnetic field. In addition, the instantaneous speed of this particle equals the mean backward velocity of the Brownian particle. At the end, a Boltzmann-like probability distribution is obtained, which allows us to define an effective temperature kernel. In particular, when the forces applied to the particle are linearly dependent on the distance from the origin, the effective temperature turns out to be the sum between an isotropic and an antisymmetric tensor, which allows us to generalize the fluctuation–dissipation theorem.

A model of knotted polymers in a confined space is studied by considering lattice polygons of fixed knot type in a slab geometry. If p_n(K, w) is the number of lattice polygons of knot type K in a slab of width w, then the generating function of this lattice model is given by , where t is a generating variable conjugate with the length of the polygon. In this paper the scaling of the mean length of polygons in this ensemble is examined. A Metropolis Monte Carlo implementation of the BFACF algorithm is shown to be ergodic in this ensemble, and it is used to estimate the mean lengths of knotted polygons in slabs of various widths. Our numerical results are consistent with the predictions of the scaling arguments. In addition, the metric properties of knotted polygons in this ensemble are examined numerically.