Leaf-to-leaf distances and their moments in finite and infinite m-ary tree graphs

We study the leaf-to-leaf distances on full and complete m-ary graphs using a recursive approach. In our formulation, leaves are ordered along a line. We find explicit analytical formulae for the sum of all paths for arbitrary leaf-to-leaf distance r as well as the average path lengths and the moments thereof. We show that the resulting explicit expressions can be recast in terms of Hurwitz-Lerch transcendants. Results for periodic trees are also given. For incomplete random binary trees, we provide first results by numerical techniques; we find a rapid drop of leaf-to-leaf distances for large r.Comment: 10 pages, 7 figure

High-pressure phases and transitions of the layered alkaline earth nitridosilicates SrSiN2 and BaSiN2

We investigate the high-pressure phase diagram of SrSiN2 and BaSiN2 with density-functional calculation. Searching a manifold of possible candidate structures, we propose new structural modifications of SrSiN2 and BaSiN2 attainable in high-pressure experiments. The monoclinic ground state of SrSiN2 transforms at 3 GPa into an orthorhombic BaSiN2 type. At 14 GPa a CaSiN2-type structure becomes the most stable configuration of SrSiN2. A hitherto unknown Pbcm modification is adopted at 85 GPa and, finally, at 131 GPa a LiFeO2-type structure. The higher homologue BaSiN2 transforms to a CaSiN2 type at 41 GPa and further to a Pbcm modification at 105 GPa. Both systems follow the pressure-coordination rule: the coordination environment of Si increases from tetrahedral through trigonal bipyramidal to octahedral. Some high-pressure phases are related in structure through simple group–subgroup mechanisms, indicating displacive phase transformations with low activation barriers

Interacting particles at a metal-insulator transition

We study the influence of many-particle interaction in a system which, in the single particle case, exhibits a metal-insulator transition induced by a finite amount of onsite pontential fluctuations. Thereby, we consider the problem of interacting particles in the one-dimensional quasiperiodic Aubry-Andre chain. We employ the density-matrix renormalization scheme to investigate the finite particle density situation. In the case of incommensurate densities, the expected transition from the single-particle analysis is reproduced. Generally speaking, interaction does not alter the incommensurate transition. For commensurate densities, we map out the entire phase diagram and find that the transition into a metallic state occurs for attractive interactions and infinite small fluctuations -- in contrast to the case of incommensurate densities. Our results for commensurate densities also show agreement with a recent analytic renormalization group approach.Comment: 8 pages, 8 figures The original paper was splitted and rewritten. This is the published version of the DMRG part of the original pape

Efficient Data Averaging for Spin Noise Spectroscopy in Semiconductors

Spin noise spectroscopy (SNS) is the perfect tool to investigate electron spin dynamics in semiconductors at thermal equilibrium. We simulate SNS measurements and show that ultrafast digitizers with low bit depth enable sensitive, high bandwidth SNS in the presence of strong optical background shot noise. The simulations reveal that optimized input load at the digitizer is crucial for efficient spin noise detection while the bit depth influences the sensitivity rather weakly

Electronic transport in DNA

We study the electronic properties of DNA by way of a tight-binding model applied to four particular DNA sequences. The charge transfer properties are presented in terms of localization lengths (crudely speaking, the length over which electrons travel). Various types of disorder, including random potentials, are employed to account for different real environments. We have performed calculations on poly(dG)-poly(dC), telomeric-DNA, random-ATGC DNA, and l-DNA. We find that random and l-DNA have localization lengths allowing for electron motion among a few dozen basepairs only. A novel enhancement of localization lengths is observed at particular energies for an increasing binary backbone disorder. We comment on the possible biological relevance of sequence-dependent charge transfer in DNA

Electron spin relaxation in bulk GaAs for doping densities close to the metal-to-insulator transition

We have measured the electron spin relaxation rate and the integrated spin noise power in n-doped GaAs for temperatures between 4 K and 80 K and for doping concentrations ranging from 2.7 x 10^{-15} cm^{-3} to 8.8 x 10^{-16} cm^{-3} using spin noise spectroscopy. The temperature dependent measurements show a clear transition from localized to free electrons for the lower doped samples and confirm mainly free electrons at all temperatures for the highest doped sample. While the sample at the metal-insulator-transition shows the longest spin relaxation time at low temperatures, a clear crossing of the spin relaxation rates is observed at 70 K and the highest doped sample reveals the longest spin relaxation time above 70 K.Comment: 6 pages, 4 figure

Rigidity analysis of HIV-1 protease

We present a rigidity analysis on a large number of X-ray crystal structures of the enzyme HIV-1 protease using the 'pebble game' algorithm of the software FIRST. We find that although the rigidity profile remains similar across a comprehensive set of high resolution structures, the profile changes significantly in the presence of an inhibitor. Our study shows that the action of the inhibitors is to restrict the flexibility of the beta-hairpin flaps which allow access to the active site. The results are discussed in the context of full molecular dynamics simulations as well as data from NMR experiments.Comment: 4 pages, 3 figures. Conference proceedings for CMMP conference 2010 which was held at the University of Warwic

General Localization Lengths for Two Interacting Particles in a Disordered Chain

The propagation of an interacting particle pair in a disordered chain is characterized by a set of localization lengths which we define. The localization lengths are computed by a new decimation algorithm and provide a more comprehensive picture of the two-particle propagation. We find that the interaction delocalizes predominantly the center-of-mass motion of the pair and use our approach to propose a consistent interpretation of the discrepancies between previous numerical results.Comment: 4 pages, 2 epsi figure