Localization phase diagram of two-dimensional quantum percolation

We examine quantum percolation on a square lattice with random dilution up to $q=38$ and energy $0.001 \le E \le 1.6$ (measured in units of the hopping matrix element), using numerical calculations of the transmission coefficient at a much larger scale than previously. Our results confirm the previous finding that the two dimensional quantum percolation model exhibits localization-delocalization transitions, where the localized region splits into an exponentially localized region and a power-law localization region. We determine a fuller phase diagram confirming all three regions for energies as low as $E=0.1$, and the delocalized and exponentially localized regions for energies down to $E=0.001$. We also examine the scaling behavior of the residual transmission coefficient in the delocalized region, the power law exponent in the power-law localized region, and the localization length in the exponentially localized region. Our results suggest that the residual transmission at the delocalized to power-law localized phase boundary may be discontinuous, and that the localization length is likely not to diverge with a power-law at the exponentially localized to power-law localized phase boundary. However, further work is needed to definitively assess the characters of the two phase transitions as well as the nature of the intermediate power-law regime

Fractal Properties of the Distribution of Earthquake Hypocenters

We investigate a recent suggestion that the spatial distribution of earthquake hypocenters makes a fractal set with a structure and fractal dimensionality close to those of the backbone of critical percolation clusters, by analyzing four different sets of data for the hypocenter distributions and calculating the dynamical properties of the geometrical distribution such as the spectral dimension $d_s$. We find that the value of $d_s$ is consistent with that of the backbone, thus supporting further the identification of the hypocenter distribution as having the structure of the percolation backbone.Comment: 11 pages, LaTeX, HLRZ 68/9

Effect of Loops on the Vibrational Spectrum of Percolation Network

We study the effects of adding loops to a critical percolation cluster on the diffusional, and equivalently, (scalar) elastic properties of the fractal network. From the numerical calculations of the eigenspectrum of the transition probability matrix, we find that the spectral dimension $d_s$ and the walk dimension $d_w$ change suddenly as soon as the floppy ends of a critical percolation cluster are connected together to form relatively large loops, and that the additional inclusion of successively smaller loops only change these exponents little if at all. This suggests that there is a new universality class associated with the loop-enhanced percolation problem.Comment: 12 pages, LaTeX, HLRZ 107/9

Markov chain analysis of random walks on disordered medium

We study the dynamical exponents $d_{w}$ and $d_{s}$ for a particle diffusing in a disordered medium (modeled by a percolation cluster), from the regime of extreme disorder (i.e., when the percolation cluster is a fractal at $p=p_{c}$) to the Lorentz gas regime when the cluster has weak disorder at $p>p_{c}$ and the leading behavior is standard diffusion. A new technique of relating the velocity autocorrelation function and the return to the starting point probability to the asymptotic spectral properties of the hopping transition probability matrix of the diffusing particle is used, and the latter is numerically analyzed using the Arnoldi-Saad algorithm. We also present evidence for a new scaling relation for the second largest eigenvalue in terms of the size of the cluster, $|\ln{\lambda}_{max}|\sim S^{-d_w/d_f}$, which provides a very efficient and accurate method of extracting the spectral dimension $d_s$ where $d_s=2d_f/d_w$.Comment: 34 pages, REVTEX 3.

Incorporation rate measurements of 10Be, 230Th, 231Pa, and 239,240Pu radionuclides in manganese crust in the Pacific Ocean: A search for extraterrestrial material

高エネルギー加速器研究機構　共通基盤研究施設・放射線科学センター金沢大学大学院自然科学研究科物質情報解析金沢大学理学部In order to estimate the deposition rate of extraterrestrial material onto a manganese crust in a search for supernova debris, we analyzed the contents of 10Be, 230Th, 231Pa, and 239,240Pu in a sample of manganese crust collected from the North Pacific Ocean. On the basis of the depth profile of 10Be, the growth rate of the manganese crust was determined to be 2.3 mm Myr-1. The uptake rates of 10Be, 230Th, and 231Pa onto the manganese crust were estimated to be 0.22-0.44%, 0.11-0.73%, and 1.4-4.5%, respectively, as compared to the deposition rates onto the deep-sea sediments near the sampling station, while that for 239,240Pu was 0.14% as compared to the total inventory of seawater and sediment column. Assuming that sinking particles represent 0.11-4.5% of the uptake rates, the deposition rate of extraterrestrial material onto the manganese crust was estimated to be 2-800 μ g cm-2Myr-1 according to the uptake of 10Be onto the manganese crust. Further, our estimate is similar to the value of 9-90 μ g cm-2Myr-1 obtained using the integrated global production rate of 10Be and the deposition rate of 10Be onto the manganese crust. © The Oceanographic Society of Japan/TERRAPUB/Springer 2007