A General SU(2) Formulation for Quantum Searching with Certainty

A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching condition relating the phase rotations in the algorithm, (2) a concise formula for evaluating the required number of iterations for the search, and (3) the final state after the search, with a phase angle in its amplitude of unity modulus. Moreover, the optimal choices and modifications of the phase angles in the Grover kernel is also studied.Comment: 8 pages, 2 figure

Anisotropic softening of collective charge modes in the vicinity of critical doping in a doped Mott insulator

Momentum resolved inelastic resonant x-ray scattering is used to map the evolution of charge excitations over a large range of energies, momenta and doping levels in the electron doped Mott insulator class Nd$_{2-x}$Ce$_x$CuO$_4$. As the doping induced AFM-SC (antiferromagnetic-superconducting) transition is approached, we observe an anisotropic softening of collective charge modes over a large energy scale along the Gamma to (\pi,\pi)-direction, whereas the modes exhibit broadening ($\sim$ 1 eV) with relatively little softening along Gamma to (\pi,0) with respect to the parent Mott insulator (x=0). Our study indicates a systematic collapse of the gap consistent with the scenario that the system dopes uniformly with electrons even though the softening of the modes involves an unusually large energy scale.Comment: 5 pages + 5 Figure

Divergence and Shannon information in genomes

Shannon information (SI) and its special case, divergence, are defined for a DNA sequence in terms of probabilities of chemical words in the sequence and are computed for a set of complete genomes highly diverse in length and composition. We find the following: SI (but not divergence) is inversely proportional to sequence length for a random sequence but is length-independent for genomes; the genomic SI is always greater and, for shorter words and longer sequences, hundreds to thousands times greater than the SI in a random sequence whose length and composition match those of the genome; genomic SIs appear to have word-length dependent universal values. The universality is inferred to be an evolution footprint of a universal mode for genome growth.Comment: 4 pages, 3 tables, 2 figure

Evolution of Group Galaxies from the First Red-Sequence Cluster Survey

We study the evolution of the red galaxy fraction (f_red) in 905 galaxy groups with 0.15 < z < 0.52. The galaxy groups are identified by the `probability Friends-of-Friends' algorithm from the first Red-Sequence Cluster Survey (RCS1) photometric-redshift sample. There is a high degree of uniformity in the properties of the red-sequence of the group galaxies, indicating that the luminous red-sequence galaxies in the groups are already in place by z~0.5 and that they have a formation epoch of z>2. In general, groups at lower redshifts exhibit larger f_red than those at higher redshifts, showing a group Butcher-Oemler effect. We investigate the evolution of f_red by examining its dependence on four parameters, which can be classified as one intrinsic and three environmental: galaxy stellar mass (M_*), total group stellar mass(M_{*,grp}, a proxy for group halo mass), normalized group-centric radius (r_grp), and local galaxy density (Sigma_5). We find that M_* is the dominant parameter such that there is a strong correlation between f_red and galaxy stellar mass. Furthermore, the dependence of f_red on the environmental parameters is also a strong function of M_*. Massive galaxies (M_* > 10^11 M_sun) show little dependence of f_red on r_grp, M_{*,grp}, and Sigma_5 over the redshift range. The dependence of f_red on these parameters is primarily seen for galaxies with lower masses, especially for M_* < 10^{10.6} M_{sun}. We observe an apparent `group down-sizing' effect, in that galaxies in lower-mass halos, after controlling for galaxy stellar mass, have lower f_red. We find a dependence of \fred on both \rgrp and \SigmaF after the other parameters are controlled. At a fixed \rgrp, there is a significant dependence of f_red on Sigma_5, while r_grp gradients of f_red are seen for galaxies in similar Sigma_5 regions. This indicates .....Comment: ApJ accepte

A General Phase Matching Condition for Quantum Searching Algorithm

A general consideration on the phase rotations in quantum searching algorithm is taken in this work. As four phase rotations on the initial state, the marked states, and the states orthogonal to them are taken account, we deduce a phase matching condition for a successful search. The optimal options for these phase are obtained consequently.Comment: 3 pages, 3 figure

Geometric and Statistical Properties of the Mean-Field HP Model, the LS Model and Real Protein Sequences

Lattice models, for their coarse-grained nature, are best suited for the study of the ``designability problem'', the phenomenon in which most of the about 16,000 proteins of known structure have their native conformations concentrated in a relatively small number of about 500 topological classes of conformations. Here it is shown that on a lattice the most highly designable simulated protein structures are those that have the largest number of surface-core switchbacks. A combination of physical, mathematical and biological reasons that causes the phenomenon is given. By comparing the most foldable model peptides with protein sequences in the Protein Data Bank, it is shown that whereas different models may yield similar designabilities, predicted foldable peptides will simulate natural proteins only when the model incorporates the correct physics and biology, in this case if the main folding force arises from the differing hydrophobicity of the residues, but does not originate, say, from the steric hindrance effect caused by the differing sizes of the residues.Comment: 12 pages, 10 figure

Mean-Field HP Model, Designability and Alpha-Helices in Protein Structures

Analysis of the geometric properties of a mean-field HP model on a square lattice for protein structure shows that structures with large number of switch backs between surface and core sites are chosen favorably by peptides as unique ground states. Global comparison of model (binary) peptide sequences with concatenated (binary) protein sequences listed in the Protein Data Bank and the Dali Domain Dictionary indicates that the highest correlation occurs between model peptides choosing the favored structures and those portions of protein sequences containing alpha-helices.Comment: 4 pages, 2 figure

The space group classification of topological band insulators

Topological band insulators (TBIs) are bulk insulating materials which feature topologically protected metallic states on their boundary. The existing classification departs from time-reversal symmetry, but the role of the crystal lattice symmetries in the physics of these topological states remained elusive. Here we provide the classification of TBIs protected not only by time-reversal, but also by crystalline symmetries. We find three broad classes of topological states: (a) Gamma-states robust against general time-reversal invariant perturbations; (b) Translationally-active states protected from elastic scattering, but susceptible to topological crystalline disorder; (c) Valley topological insulators sensitive to the effects of non-topological and crystalline disorder. These three classes give rise to 18 different two-dimensional, and, at least 70 three-dimensional TBIs, opening up a route for the systematic search for new types of TBIs.Comment: Accepted in Nature Physic

A coupled optical-thermal-electrical model to predict the performance of hybrid PV/T-CCPC roof-top systems

A crossed compound parabolic concentrator (CCPC) is applied into a photovoltaic/thermal (PV/T) hybrid solar collector, i.e. concentrating PV/T (CPV/T) collector, to develop new hybrid roof-top CPV/T systems. However, to optimise the system configuration and operational parameters as well as to predict their performances, a coupled optical, thermal and electrical model is essential. We establish this model by integrating a number of submodels sourced from literature as well as from our recent work on incidence-dependent optical efficiency, six-parameter electrical model and scaling law for outdoor conditions. With the model, electrical performance and cell temperature are predicted on specific days for the roof-top systems installed in Glasgow, Penryn and Jaen. Results obtained by the proposed model reasonably agree with monitored data and it is also clarified that the systems operate under off-optimal operating condition. Long-term electric performance of the CPV/T systems is estimated as well. In addition, effects of transient terms in heat transfer and diffuse solar irradiance on electric energy are identified and discussed