Effect of particle-hole symmetry on the behavior of tracer and jump diffusion coefficients.

This paper analyzes the effect of particle-hole symmetry on the behavior of the tracer diffusion coefficient as well as the jump diffusion coefficient. The coefficients are obtained by performing a random walk of individual atoms in a two-dimensional square lattice at monolayer, using the n-fold way Monte Carlo simulation. Different hopping mechanisms have been introduced to study the effect of particle-hole symmetry. For hopping kinetics where the initial-state interactions are involved, the diffusion coefficient at high coverage falls several orders of magnitude due to the effect of particle-hole symmetry. For hopping kinetics where the final-state interactions are present, the effect is the opposite. For those involving both initial- and final-state interactions, like the so-called interaction kinetics, the effect of particle-hole symmetry is also discussed. This effect seems to be critical for repulsive lateral interactions, for which the behavior of the diffusion coefficients is modified by introducing the particle-hole symmetry condition.

Single-file diffusion in a box: effect of the initial configuration.

This paper studies the single-file diffusion process on a linear chain of identical pointlike particles with multiple-site occupation confined in a one-dimensional box. The particles are noninteracting, except that double occupancy is forbidden. When particles are confined in a finite box, the final stage is saturation. By means of combinatorial analysis, an exact numerical evaluation of the saturation values for both the mean-square displacement (MSD) of a tracer particle and the center of mass of the system are obtained. Different initial distributions of particles are introduced. The time dependence of the MSD is obtained by means of Monte Carlo simulations. The values of the MSD for the tracer particles as well as the center of mass of the system depend on the size of the particle, the size of the box, and the initial distribution. Moreover, the transient regime depends on the initial distribution. In fact, the crossover from normal to subdiffusive regime is observed for random and alternate initial distributions, while superdiffusive diffusion appears for any stacked initial distributions. In all cases, it is shown that the collisions between particles do not determine the time exponent of the MSD. A simple expression for the transient regime is also obtained for the especial case of random initial distribution.

One-dimensional diffusion: discrepancy between exact results and Monte Carlo calculations.

The exact expression for the collective diffusion coefficient in one dimension, obtained by Payne and Kreuzer [Phys. Rev. B. 75, 115403 (2007)], is compared with Monte Carlo simulation. Different hopping kinetics are analyzed. For initial- and final-state interaction kinetics no anomalies are observed. However, for the so-called interaction kinetics where both initial- and final-state interactions are involved, it is shown that even when the transition rates satisfy the principle of detail balance, additional constraints are necessary to guarantee the diffusion of particles. These restrictions give rise to a phase diagram that determines the regions where the exact solution of the diffusion coefficient seem to be not physically sound. The Monte Carlo simulation allows us to analyze the mechanism of diffusion in these regions, where in some cases the simulation does not match the exact solution. A possible explanation is presented.

Additional constraints in adsorption-desorption kinetics.

In this work, the adsorption-desorption kinetic in the framework of the lattice gas model is analyzed. The transition probabilities are written as an expansion of the occupation configurations. Due to that, the detail balance principle determine half of the adsorption A{i} and desorption D{i} coefficients, consequently, different functional relations between them are proposed. Introducing additional constrains, it is demonstrated that when those coefficients are linearly related through a parameter gamma , there are values of lateral interaction V , that lead to anomalous behavior in the adsorption isotherms, the sticking coefficient and the thermal programmed desorption spectra. Diagrams for the allowed values of V and gamma are also shown. Alternatively, a more reliable formulation for the adsorption desorption kinetic based on the transition state theory is introduced. In such way the equilibrium and non equilibrium observables do not present anomalous or inconsistent behavior.

Hard versus soft dynamics for adsorption-desorption kinetics: Exact results in one-dimension.

The adsorption-desorption kinetics is discussed in the framework of the kinetic lattice-gas model. The master equation formalism has been introduced to describe the evolution of the system, where the transition probabilities are written as an expansion of the occupation configurations of all neighboring sites. Since the detailed balance principle determines half of the coefficients that arise from the expansion, it is necessary to introduce ad hoc, a dynamic scheme to get the rest of them. Three schemes of the so-called hard dynamics, in which the probability of transition from single site cannot be factored into a part which depends only on the interaction energy and one that only depends on the field energy, and five schemes of the so-called soft dynamics, in which this factorization is possible, were introduced for this purpose. It is observed that for the hard dynamic schemes, the equilibrium and nonequilibrium observables, such as adsorption isotherms, sticking coefficients, and thermal desorption spectra, have a normal or physical sustainable behavior. While for the soft dynamics schemes, with the exception of the transition state theory, the equilibrium and nonequilibrium observables have several problems. Some of them can be regarded as abnormal behavior.

One-dimensional diffusion: validity of various expressions for jump rates.

The coverage dependence of the one-dimensional collective diffusion coefficient is analyzed by using the gradient expansion of the local density. The transition probabilities are written as an expansion of the probabilities of the occupation configurations. Since the detail balance principle determines only a part of the diffusion terms in the expansion, different functional relations are proposed for these terms. The diffusion coefficient is obtained for various choices of these relations. However, some of them seem to be not physically sound and the diffusion coefficient does not behave properly. The range of validity of various expressions for the jump rates is determined and phase diagrams are shown. Besides that, it is shown that the transition state theory guarantees physically suitable behavior of the coefficient of one-dimensional diffusion.

Analysis of the convergence of the 1t and Wang-Landau algorithms in the calculation of multidimensional integrals.

In this Brief Report, the convergence of the 1t and Wang-Landau algorithms in the calculation of multidimensional numerical integrals is analyzed. Both simulation methods are applied to a wide variety of integrals without restrictions in one, two, and higher dimensions. The efficiency and accuracy of both algorithms are determined by the dynamical behavior of the errors between the exact and the calculated values of the integral. It is observed that the time dependence of the error calculated with the 1t algorithm varies as N;{-12} [with N the number of Monte Carlo (MC) trials], in quantitative agreement with the simple sampling Monte Carlo method. In contrast, the error calculated with the Wang-Landau algorithm saturates in time, evidencing the nonconvergence of this method. The sources of error for both methods are also determined.

Adsorption of a multicomponent mixture of gases with multisite occupancy.

In this paper, we present a study of the adsorption of multicomponent mixtures with multisite occupancy. The transfer-matrix technique is used to analyze the one-dimensional binary mixtures for interacting systems. A general expression for the characteristic polynomial is derived. Extension of the treatment to a higher dimension is also presented by using the mean-field Bragg-Williams approximation, transfer-matrix calculations, and Monte Carlo simulation. Partial and total isotherms are obtained for the dimer-trimer mixture where a different order appears.

Random deposition of two annihilating species in the (1+1) dimension.

We present simulation results for the one-dimensional random deposition of two annihilating species A and B, falling with probabilities p and q (p+q=1), which then react to produce an inert product, i.e., A+B-->0. Two different annihilation rules are defined: top annihilation and nearest-neighbor annihilation (NNA), leading to distinct scaling behaviors. In particular, the values of the scaling exponents for NNA are found to be dependent on probability p, suggesting different universality classes.