No abstract

We study the connection between magnetization transport and magnetization profiles in zero-temperature XX chains. The time evolution of the transverse magnetization m(x,t) is calculated using an inhomogeneous initial state that is the ground state at fixed magnetization but with m reversed from -m(0) for x<0 to m(0) for x>0. In the long-time limit, the magnetization evolves into a scaling form m(x,t)=Phi(x/t) and the profile develops a flat part (m=Phi=0) in the (x/t)1/2 while it expands with the maximum velocity c(0)=1 for m(0)-->0. The states emerging in the scaling limit are compared to those of a homogeneous system where the same magnetization current is driven by a bulk field, and we find that the expectation values of various quantities (energy, occupation number in the fermionic representation) agree in the two systems.

One-dimensional free fermions are studied with emphasis on propagating fronts emerging from a step initial condition. The probability distribution of the number of particles at the edge of the front is determined exactly. It is found that the full counting statistics coincide with the eigenvalue statistics of the edge spectrum of matrices from the Gaussian unitary ensemble. The correspondence established between the random matrix eigenvalues and the particle positions yields the order statistics of the rightmost particles in the front and, furthermore, it implies their subdiffusive spreading.

No abstract

Theoretical models of the Liesegang phenomena are studied and simple expressions for the spacing coefficients characterizing the patterns are derived. The emphasis is on displaying the explicite dependences on the concentrations of the inner-and the outer-electrolytes. Competing theories (ionproduct supersaturation, nucleation and droplet growth, induced sol-coagulation) are treated with the aim of finding the distinguishing features of the theories. The predictions are compared with experiments and the results suggest that the induced sol-coagulation theory is the best candidate for describing the experimental observations embodied in the Matalon-Packter law.

The steady-state particle density n and the relaxation time r of homogeneous density fluctuations are calculated for one-dimensional systems in which particles move diffusively and annihilate irreversibly, and steady sources of either single particles (model I) or pairs of neighboring particles (model II) are also present. For small particle-production rates h, we find n ~h l/b and r~/z _A with 8 = 3, A = y for model I and 8=2, A= 1 for model II. If we interpret particles as solitons, model II is used to account for some aspects of the experimental data on the photoinduced absorption of trans-(CH) x .PACS numbers: 05.40. + j, 05.50. + q, 05.70.LnThe principles of equilibrium statistical mechanics are well established and progress in describing nearequilibrium relaxational processes has also been remarkable. 1 ' 2 Little is known, however, about the properties of systems which are either in or relaxing towards a farfrom-equilibrium steady state. Given the importance and the difficulty of these nonequilibrium problems, one often tries to develop and study simple model systems which are mathematically transparent but at the same time show some resemblance to actual processes occurring in nature. In this paper, two such model systems will be considered and the exact calculation of the relevant steady-state and relaxational properties will be outlined.The basic process is the same in both models. Particles execute a random walk (with hopping rate T per unit time) along a one-dimensional lattice and annihilate if they land on the same site simultaneously. This system would evolve into a trivial, completely empty state in the long-time limit (t -> oo ) and therefore to make the steady state more interesting we assume that particle sources are also present. The two models we consider are distinct in the mode of production of the particles. Single particles are created at a rate of Th per lattice site in model I. In model II, on the other hand, the particles are produced in pairs at nearest-neighbor lattice sites and the rate of production is Th per adjacent pair of lattice sites.Model I may be regarded as a first approximation to the kinetics of the reaction A -\-A->0 in a onedimensional chemical reactor with steady inflow and outflow of particles. It may also be viewed as a reference model for a class of aggregation processes which display common scaling properties. For example, one-dimensional models of aerosol formation 3 describing circumstances when the aggregation centers are generated by photo-oxidation and sedimentation processes make the larger clusters disappear from the system are expected 4 to be in one universality class with model I.Model II is more closely related to a real system. In frans-polyacetylene, soliton-antisoliton pairs can be generated by photoexcitation. 5 The solitons and the antisolitons are quite free to move along one-dimensional chains and at elevated temperatures they execute a random walk under the influence of thermal fluctuations. Furthermore, since solitons alternate with antisoliton...

No abstract

Simulations of restricted solid-on-solid growth models are used to build the width distributions of d=2-5 dimensional Kardar-Parisi-Zhang (KPZ) interfaces. We find that the universal scaling function associated with the steady-state width distribution changes smoothly as d is increased, thus strongly suggesting that d=4 is not an upper critical dimension for the KPZ equation. The dimensional trends observed in the scaling functions indicate that the upper critical dimension is at infinity.