Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDynamical Scaling Implications of Ferrari, Pr{a}hofer, and Spohns Remarkable Spatial Scaling Results for Facet-Edge Fluctuations
99
0
0.0
(
0
)
Added by
Theodore L. Einstein
Publication date
2013
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Spurred by theoretical predictions from Spohn and coworkers [Phys. Rev. E {bf 69}, 035102(R) (2004)], we rederived and extended their result heuristically as well as investigated the scaling properties of the associated Langevin equation in curved geometry with an asymmetric potential. With experimental colleagues we used STM line scans to corroborate their prediction that the fluctuations of the step bounding a facet exhibit scaling properties distinct from those of isolated steps or steps on vicinal surfaces. The correlation functions was shown to go as $t^{0.15(3)}$ decidedly different from the $t^{0.26(2)}$ behavior for fluctuations of isolated steps. From the exponents, we were able to categorize the universality, confirming the prediction that the non-linear term of the KPZ equation, long known to play a central role in non-equilibrium phenomena, can also arise from the curvature or potential-asymmetry contribution to the step free energy. We also considered, with modest Monte Carlo simulations, a toy model to show that confinement of a step by another nearby step can modify as predicted the scaling exponents of the steps fluctuations. This paper is an expansion of a celebratory talk at the 95$^{rm th}$ Rutgers Statistical Mechanics Conference, May 2006.
rate research
Read More
The typical values and fluctuations of time-integrated observables of nonequilibrium processes driven in steady states are known to be characterized by large deviation functions, generalizing the entropy and free energy to nonequilibrium systems. The definition of these functions involves a scaling limit, similar to the thermodynamic limit, in which the integration time $tau$ appears linearly, unless the process considered has long-range correlations, in which case $tau$ is generally replaced by $tau^xi$ with $xi eq 1$. Here we show that such an anomalous power-law scaling in time of large deviations can also arise without long-range correlations in Markovian processes as simple as the Langevin equation. We describe the mechanism underlying this scaling using path integrals and discuss its physical consequences for more general processes.
In a recent paper [Ferrari et al., Phys. Rev. E 69, 035102(R) (2004)], the scaling law of the fluctuations of the step limiting a crystal facet has been computed as a function of the facet size. Ferrari et al. use rigorous, but physically rather obscure, arguments. Approaching the problem from a different perspective, we rederive more transparently the scaling behavior of facet edge fluctuations as a function of time. Such behavior can be scrutinized with STM experiments and with numerical simulations.
The Boltzmann factor comes from the linear change in entropy of an infinite heat bath during a local fluctuation; small systems have significant nonlinear terms. We present theoretical arguments, experimental data, and Monte-Carlo simulations indicating that nonlinear terms may also occur when a particle interacts directly with a finite number of neighboring particles, forming a local region that fluctuates independent of the infinite bath. A possible mechanism comes from the net force necessary to change the state of a particle while conserving local momentum. These finite-sized local regions yield nonlinear fluctuation constraints, beyond the Boltzmann factor. One such fluctuation constraint applied to simulations of the Ising model lowers the energy, makes the entropy extensive, and greatly improves agreement with the corrections to scaling measured in ferromagnetic materials and critical fluids.
The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the finite-size scaling away from criticality and find a scaling function, which discriminates between phases with different topological indexes. This function appears to be universal for all five Altland-Zirnbauer symmetry classes with non-trivial topology in one spatial dimension. We obtain an analytic form of the scaling function and compare it with numerical results.
Large scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor $S_4(q,t)$. Both cases, elastic ($varepsilon=1$) as well as inelastic ($varepsilon < 1$) collisions, are studied. As the fluid approaches structural arrest, i.e. for packing fractions in the range $0.6 le phi le 0.805$, scaling is shown to hold: $S_4(q,t)/chi_4(t)=s(qxi(t))$. Both the dynamic susceptibility, $chi_4(tau_{alpha})$, as well as the dynamic correlation length, $xi(tau_{alpha})$, evaluated at the $alpha$ relaxation time, $tau_{alpha}$, can be fitted to a power law divergence at a critical packing fraction. The measured $xi(tau_{alpha})$ widely exceeds the largest one previously observed for hard sphere 3d fluids. The number of particles in a slow cluster and the correlation length are related by a robust power law, $chi_4(tau_{alpha}) approxxi^{d-p}(tau_{alpha})$, with an exponent $d-papprox 1.6$. This scaling is remarkably independent of $varepsilon$, even though the strength of the dynamical heterogeneity increases dramatically as $varepsilon$ grows.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
