Coarsening and persistence in a one-dimensional system of orienting arrowheads: Domain-wall kinetics with A+B→0.

We demonstrate the large-scale effects of the interplay between shape and hard-core interactions in a system with left- and right-pointing arrowheads <> on a line, with reorientation dynamics. This interplay leads to the formation of two types of domain walls, >< (A) and <> (B). The correlation length in the equilibrium state diverges exponentially with increasing arrowhead density, with an ordered state of like orientations arising in the limit.

Bond percolation in higher dimensions.

We collect results for bond percolation on various lattices from two to fourteen dimensions that, in the limit of large dimension d or number of neighbors z, smoothly approach a randomly diluted Erdős-Rényi graph. We include results on bond-diluted hypersphere packs in up to nine dimensions, which show the mean coordination, excess kurtosis, and skewness evolving smoothly with dimension towards the Erdős-Rényi limit.

Nonuniversal disordered Glauber dynamics.

We consider the one-dimensional Glauber dynamics with coupling disorder in terms of bilinear fermion Hamiltonians. Dynamic exponents embodied in the spectrum gap of these latter are evaluated numerically by averaging over both binary and Gaussian disorder realizations. In the first case, these exponents are found to follow the nonuniversal values of those of plain dimerized chains.

Quantum annealing in a kinetically constrained system.

Classical and quantum annealing is discussed in the case of a generalized kinetically constrained model, where the relaxation dynamics of a system with trivial ground state is retarded by the appearance of energy barriers in the relaxation path, following a local kinetic rule. Effectiveness of thermal and quantum fluctuations in overcoming these kinetic barriers to reach the ground state are studied. It has been shown that for certain barrier characteristics, quantum annealing might by far surpass its thermal counter part in reaching the ground state faster.

Master equation for a kinetic model of a trading market and its analytic solution.

We analyze an ideal-gas-like model of a trading market with quenched random saving factors for its agents and show that the steady state income (m) distribution P(m) in the model has a power law tail with Pareto index nu exactly equal to unity, confirming the earlier numerical studies on this model. The analysis starts with the development of a master equation for the time development of P(m) . Precise solutions are then obtained in some special cases.

Spatially heterogeneous dynamics in a model for granular compaction.

We suggest the emergence of spatially correlated dynamics in slowly compacting dense granular media by analyzing analytically and numerically multipoint correlation functions in a simple particle model characterized by slow nonequilibrium dynamics. We show that the logarithmically slow dynamics at large times is accompanied by spatially extended dynamic structures that resemble the ones observed in glass-forming liquids and dense colloidal suspensions. This suggests that dynamic heterogeneity is another key common feature present in very different jamming materials.

Fluctuation-dissipation relation and the Edwards entropy for a glassy granular compaction model.

We analytically study a one-dimensional compaction model in the glassy regime. Both correlation and response functions are calculated exactly in the evolving dense and low tapping strength limit, where the density relaxes in a 1/ln t fashion. The response and correlation functions turn out to be connected through a nonequilibrium generalization of the fluctuation-dissipation theorem.

Exact probability function for bulk density and current in the asymmetric exclusion process.

We examine the asymmetric simple exclusion process with open boundaries, a paradigm of driven diffusive systems, having a nonequilibrium steady-state transition. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Depken and R.

Exact joint density-current probability function for the asymmetric exclusion process.

We study the asymmetric simple exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach and by the introduction of new operators satisfying a modified version of the original algebra.

Marginal scaling scenario and analytic results for a glassy compaction model.

A diffusion-deposition model for glassy dynamics in compacting granular systems is treated by time scaling and by a method that provides the exact asymptotic (long-time) behavior. The results include Vogel-Fulcher dependence of rates on density, inverse logarithmic time decay of densities, exponential distribution of decay times, and broadening of noise spectrum. These are all in broad agreement with experiments.