Noise-assisted Mound Coarsening in Epitaxial Growth

We propose deposition noise to be an important factor in unstable epitaxial growth of thin films. Our analysis yields a geometrical relation H=(RWL)^2 between the typical mound height W, mound size L, and the film thickness H. Simulations of realistic systems show that the parameter R is a characteristic of the growth conditions, and generally lies in the range 0.2-0.7. The constancy of R in late-stage coarsening yields a scaling relation between the coarsening exponent 1/z and the mound height exponent \beta which, in the case of saturated mound slope, gives \beta = 1/z = 1/4.Comment: 4 pages, RevTex Macros, 3 eps figure

Properties of Resonating-Valence-Bond Spin Liquids and Critical Dimer Models

We use Monte Carlo simulations to study properties of Anderson's resonating-valence-bond (RVB) spin-liquid state on the square lattice (i.e., the equal superposition of all pairing of spins into nearest-neighbor singlet pairs) and compare with the classical dimer model (CDM). The latter system also corresponds to the ground state of the Rokhsar-Kivelson quantum dimer model at its critical point. We find that although spin-spin correlations decay exponentially in the RVB, four-spin valence-bond-solid (VBS) correlations are critical, qualitatively like the well-known dimer-dimer correlations of the CDM, but decaying more slowly (as $1/r^a$ with $a \approx 1.20$, compared with $a=2$ for the CDM). We also compute the distribution of monomer (defect) pair separations, which decay by a larger exponent in the RVB than in the CDM. We further study both models in their different winding number sectors and evaluate the relative weights of different sectors. Like the CDM, all the observed RVB behaviors can be understood in the framework of a mapping to a "height" model characterized by a gradient-squared stiffness constant $K$. Four independent measurements consistently show a value $K_{RVB} \approx 1.6 K_{CDM}$, with the same kinds of numerical evaluations of $K_{CDM}$ give results in agreement with the rigorously known value $K_{CDM}=\pi/16$. The background of a nonzero winding number gradient $W/L$ introduces spatial anisotropies and an increase in the effective K, both of which can be understood as a consequence of anharmonic terms in the height-model free energy, which are of relevance to the recently proposed scenario of "Cantor deconfinement" in extended quantum dimer models. We also study ensembles in which fourth-neighbor (bipartite) bonds are allowed, at a density controlled by a tunable fugacity, resulting (as expected) in a smooth reduction of K.Comment: 26 pages, 21 figures. v3: final versio

The Sample Complexity of Search over Multiple Populations

This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one population corresponding to distribution P1 with as few samples as possible. The main contribution is to quantify the number of samples needed to correctly find one such population. We consider two general approaches: non-adaptive sampling methods, which sample each population a predetermined number of times until a population following P1 is found, and adaptive sampling methods, which employ sequential sampling schemes for each population. We first derive a lower bound on the number of samples required by any sampling scheme. We then consider an adaptive procedure consisting of a series of sequential probability ratio tests, and show it comes within a constant factor of the lower bound. We give explicit expressions for this constant when samples of the populations follow Gaussian and Bernoulli distributions. An alternative adaptive scheme is discussed which does not require full knowledge of P1, and comes within a constant factor of the optimal scheme. For comparison, a lower bound on the sampling requirements of any non-adaptive scheme is presented.Comment: To appear, IEEE Transactions on Information Theor

Magnetotransport properties of strained Ga0.95Mn0.05As epilayers close to the metal-insulator transition: Description using Aronov-Altshuler three-dimensional scaling theory

The magnitude of the anisotropic magnetoresistance (AMR) and the longitudinal resistance in compressively strained Ga0.95Mn0.05As epilayers were measured down to temperatures as low as 30 mK. Below temperatures of 3 K, the conductivity decreases [proportional]T^1/3 over 2 orders of magnitude in temperature. The conductivity can be well described within the framework of a three-dimensional scaling theory of Anderson's transition in the presence of spin scattering in semiconductors. It is shown that the samples are on the metallic side but very close to the metal-insulator transition. At lowest temperatures, a decrease in the AMR effect is observed, which is assigned to changes in the coupling between the remaining itinerant carriers and the local Mn 5/2-spin moments