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Register a new userContrasts between coarsening and relaxational dynamics of surfaces
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We discuss static and dynamic fluctuations of domain walls separating areas of constant but different slopes in steady-state configurations of crystalline surfaces both by an analytic treatment of the appropriate Langevin equation and by numerical simulations. In contrast to other situations that describe the dynamics in Ising-like systems such as models A and B, we find that the dynamic exponent z=2 that governs the domain wall relaxation function is not equal to the inverse of the exponent n=1/4 that describes the coarsening process that leads to the steady state.
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The newly discovered iron pnictide superconductors apparently present an unusual case of interband-channel pairing superconductivity. Here we show that, in the limit where the pairing occurs within the interband channel, several surprising effects occur quite naturally and generally: different density-of-states on the two bands lead to several unusual properties, including a gap ratio which behaves inversely to the ratio of density-of-states; the weak-coupling limit of the Eliashberg and the BCS theory, commonly taken as equivalent, in fact predict qualitatively different dependence of the $Delta_{1}/Delta_{2}$ and $Delta/T_{c}$ ratios on coupling constants. We show analytically that these effects follow directly from the interband character of superconductivity. Our results show that in the interband-only pairing model the maximal gap ratio is $sqrt{N_{2}/N_{1}}$ as strong-coupling effects act only to reduce this ratio. This suggests that if the large experimentally reported gap ratios (up to a factor 2) are correct, the pairing mechanism must include more intraband interaction than is usually assumed.
We argue that a strict relation exists between two in principle unrelated quantities: The size of the growing domains in a coarsening system, and the kinetic roughening of an interface. This relation is confirmed by extensive simulations of the Ising model with different forms of quenched disorder, such as random bonds, random fields and stochastic dilution.
We study the purely relaxational dynamics (model A) at criticality in three-dimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and bond-diluted Ising models, and the +- J Ising model along the paramagnetic-ferromagnetic transition line. We perform Monte Carlo simulations at the critical point using the Metropolis algorithm and study the dynamic behaviour in equilibrium at various values of the disorder parameter. The results provide a robust evidence of the existence of a unique model-A dynamic universality class which describes the relaxational critical dynamics in all considered models. In particular, the analysis of the size-dependence of suitably defined autocorrelation times at the critical point provides the estimate z=2.35(2) for the universal dynamic critical exponent. We also study the off-equilibrium relaxational dynamics following a quench from T=infty to T=T_c. In agreement with the field-theory scenario, the analysis of the off-equilibrium dynamic critical behavior gives an estimate of z that is perfectly consistent with the equilibrium estimate z=2.35(2).
We investigate the nonequilibrium coarsening dynamics in two-dimensional overdamped superconducting arrays under zero external current, where ohmic dissipation occurs on junctions between superconducting islands through uniform resistance. The nonequilibrium relaxation of the unfrustrated array and also of the fully frustrated array, quenched to low temperature ordered states or quasi-ordered ones, is dominated by characteristic features of coarsening processes via decay of point and line defects, respectively. In the case of unfrustrated arrays, it is argued that due to finiteness of the friction constant for a vortex (in the limit of large spatial extent of the vortex), the typical length scale grows as $ell_s sim t^{1/2}$ accompanied by the number of point vortices decaying as $N_v sim 1/t $. This is in contrast with the case that dominant dissipation occurs between each island and the substrate, where the friction constant diverges logarithmically and the length scale exhibits diffusive growth with a logarithmic correction term. We perform extensive numerical simulations, to obtain results in reasonable agreement. In the case of fully frustrated arrays, the domain growth of Ising-like chiral order exhibits the low-temperature behavior $ell_q sim t^{1/z_q}$, with the growth exponent $1/z_q$ apparently showing a strong temperature dependence in the low-temperature limit.
A mean-field theory is developed for the scale-invariant length distributions observed during the coarsening of one-dimensional faceted surfaces. This theory closely follows the Lifshitz-Slyozov-Wagner theory of Ostwald ripening in two-phase systems [1-3], but the mechanism of coarsening in faceted surfaces requires the addition of convolution terms recalling the work of Smoluchowski [4] and Schumann [5] on coalescence. The model is solved by the exponential distribution, but agreement with experiment is limited by the assumption that neighboring facet lengths are uncorrelated. However, the method concisely describes the essential processes operating in the scaling state, illuminates a clear path for future refinement, and offers a framework for the investigation of faceted surfaces evolving under arbitrary dynamics. [1] I. Lifshitz, V. Slezov, Soviet Physics JETP 38 (1959) 331-339. [2] I. Lifshitz, V. Slyozov, J. Phys. Chem. Solids 19 (1961) 35-50. [3] C. Wagner, Elektrochemie 65 (1961) 581-591. [4] M. von Smoluchowski, Physikalische Zeitschrift 17 (1916) 557-571. [5] T. Schumann, J. Roy. Met. Soc. 66 (1940) 195-207.
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