Extended states in 1D lattices: application to quasiperiodic copper-mean chain

The question of the conditions under which 1D systems support extended electronic eigenstates is addressed in a very general context. Using real space renormalisation group arguments we discuss the precise criteria for determining the entire spertrum of extended eigenstates and the corresponding eigenfunctions in disordered as well as quasiperiodic systems. For purposes of illustration we calculate a few selected eigenvalues and the corresponding extended eigenfunctions for the quasiperiodic copper-mean chain. So far, for the infinite copper-mean chain, only a single energy has been numerically shown to support an extended eigenstate [ You et al. (1991)] : we show analytically that there is in fact an infinite number of extended eigenstates in this lattice which form fragmented minibands.Comment: 10 pages + 2 figures available on request; LaTeX version 2.0

Delocalized-localized transition in a semiconductor two-dimensional honeycomb lattice

We report the magneto-transport properties of a two-dimensional electron gas in a modulation-doped AlGaAs/GaAs heterostructure subjected to a lateral potential with honeycomb geometry. Periodic oscillations of the magneto-resistance and a delocalized-localized transition are shown by applying a gate voltage. We argue that electrons in such artificial-graphene lattices offer a promising approach for the simulation of quantum phases dictated by Coulomb interactions

Quantum critical behaviour of the plateau-insulator transition in the quantum Hall regime

High-field magnetotransport experiments provide an excellent tool to investigate the plateau-insulator phase transition in the integral quantum Hall effect. Here we review recent low-temperature high-field magnetotransport studies carried out on several InGaAs/InP heterostructures and an InGaAs/GaAs quantum well. We find that the longitudinal resistivity $\rho_{xx}$ near the critical filling factor $\nu_{c}$ ~ 0.5 follows the universal scaling law $\rho_{xx}(\nu, T) \propto exp[-\Delta \nu/(T/T_{0})^{\kappa}]$, where $\Delta \nu =\nu -\nu_{c}$. The critical exponent $\kappa$ equals $0.56 \pm 0.02$, which indicates that the plateau-insulator transition falls in a non-Fermi liquid universality class.Comment: 8 pages, accepted for publication in Proceedings of the Yamada Conference LX on Research in High Magnetic Fields (August 16-19, 2006, Sendai

An Algorithm for Probabilistic Alternating Simulation

In probabilistic game structures, probabilistic alternating simulation (PA-simulation) relations preserve formulas defined in probabilistic alternating-time temporal logic with respect to the behaviour of a subset of players. We propose a partition based algorithm for computing the largest PA-simulation, which is to our knowledge the first such algorithm that works in polynomial time, by extending the generalised coarsest partition problem (GCPP) in a game-based setting with mixed strategies. The algorithm has higher complexities than those in the literature for non-probabilistic simulation and probabilistic simulation without mixed actions, but slightly improves the existing result for computing probabilistic simulation with respect to mixed actions.Comment: We've fixed a problem in the SOFSEM'12 conference versio

Periodic features in the Dynamic Structure Factor of the Quasiperiodic Period-doubling Lattice

We present an exact real-space renormalization group (RSRG) method for evaluating the dynamic structure factor of an infinite one-dimensional quasiperiodic period-doubling (PD) lattice. We observe that for every normal mode frequency of the chain, the dynamic structure factor $S(q,\omega)$ always exhibits periodicity with respect to the wave vector $q$ and the presence of such periodicity even in absence of translational invariance in the system is quite surprising. Our analysis shows that this periodicity in $S(q,\omega)$ actually indicates the presence of delocalized phonon modes in the PD chain. The Brillouin Zones of the lattice are found to have a hierarchical structure and the dispersion relation gives both the acoustic as well as optical branches. The phonon dispersion curves have a nested structure and we have shown that it is actually the superposition of the dispersion curves of an infinite set of periodic lattices.Comment: 9 pages, 3 postscript figures, REVTeX, To appear in Phys. Rev. B (1 February 1998-I

On the role of a new type of correlated disorder in extended electronic states in the Thue-Morse lattice

A new type of correlated disorder is shown to be responsible for the appearance of extended electronic states in one-dimensional aperiodic systems like the Thue-Morse lattice. Our analysis leads to an understanding of the underlying reason for the extended states in this system, for which only numerical evidence is available in the literature so far. The present work also sheds light on the restrictive conditions under which the extended states are supported by this lattice.Comment: 11 pages, LaTeX V2.09, 1 figure (available on request), to appear in Physical Review Letter

Sandpile model on an optimized scale-free network on Euclidean space

Deterministic sandpile models are studied on a cost optimized Barab\'asi-Albert (BA) scale-free network whose nodes are the sites of a square lattice. For the optimized BA network, the sandpile model has the same critical behaviour as the BTW sandpile, whereas for the un-optimized BA network the critical behaviour is mean-field like.Comment: Five pages, four figure

Instance Space of the Number Partitioning Problem

Within the replica framework we study analytically the instance space of the number partitioning problem. This classic integer programming problem consists of partitioning a sequence of N positive real numbers \{a_1, a_2,..., a_N} (the instance) into two sets such that the absolute value of the difference of the sums of $a_j$ over the two sets is minimized. We show that there is an upper bound $\alpha_c N$ to the number of perfect partitions (i.e. partitions for which that difference is zero) and characterize the statistical properties of the instances for which those partitions exist. In particular, in the case that the two sets have the same cardinality (balanced partitions) we find $\alpha_c=1/2$. Moreover, we show that the disordered model resulting from hte instance space approach can be viewed as a model of replicators where the random interactions are given by the Hebb rule.Comment: 7 page

Enhanced Room Temperature Coefficient of Resistance and Magneto-resistance of Ag-added La0.7Ca0.3-xBaxMnO3 Composites

In this paper we report an enhanced temperature coefficient of resistance (TCR) close to room temperature in La0.7Ca0.3-xBaxMnO3 + Agy (x = 0.10, 0.15 and y = 0.0 to 0.40) (LCBMO+Ag) composite manganites. The observed enhancement of TCR is attributed to the grain growth and opening of new conducting channels in the composites. Ag addition has also been found to enhance intra-granular magneto-resistance. Inter-granular MR, however, is seen to decrease with Ag addition. The enhanced TCR and MR at / near room temperature open up the possibility of the use of such materials as infrared bolometric and magnetic field sensors respectively.Comment: 22 pages of Text + Figs:comments/suggestions([email protected]