Static and Dynamic Properties of Type-II Composite Fermion Wigner Crystals

The Wigner crystal of composite fermions is a strongly correlated state of complex emergent particles, and therefore its unambiguous detection would be of significant importance. Recent observation of optical resonances in the vicinity of filling factor {\nu} = 1/3 has been interpreted as evidence for a pinned Wigner crystal of composite fermions [Zhu et al., Phys. Rev. Lett. 105, 126803 (2010)]. We evaluate in a microscopic theory the shear modulus and the magnetophonon and magnetoplasmon dispersions of the composite fermion Wigner crystal in the vicinity of filling factors 1/3, 2/5, and 3/7. We determine the region of stability of the crystal phase, and also relate the frequency of its pinning mode to that of the corresponding electron crystal near integer fillings. These results are in good semiquantitative agreement with experiment, and therefore support the identification of the optical resonance as the pinning mode of the composite fermions Wigner crystal. Our calculations also bring out certain puzzling features, such as a relatively small melting temperature for the composite fermion Wigner crystal, and also suggest a higher asymmetry between Wigner crystals of composite fermion particles and holes than that observed experimentally.Comment: Composite Fermion Wigner Crystal; 14 pages, 9 figure

Extreme value distributions for weakly correlated fitnesses in block model

We study the limit distribution of the largest fitness for two models of weakly correlated and identically distributed random fitnesses. The correlated fitness is given by a linear combination of a fixed number of independent random variables drawn from a common parent distribution. We find that for certain class of parent distributions, the extreme value distribution for correlated random variables can be related either to one of the known limit laws for independent variables or the parent distribution itself. For other cases, new limiting distributions appear. The conditions under which these results hold are identified.Comment: Expanded, added reference

p-Chloro Substituted Cinnamohydroxamic Acids as Analytical Reagent for Cerium. Spectrophotometric Determination with N-Phenyl-p-Chlorocinnamohydroxamic Acid

A selective and sensitive method for the solvent extraction and spectrophotometric determination of cerium(IV) with N-phenyl- p-chlorocinnamohydroxamic acid (N-p-p-Cl-CHA) has been described. It forms a red colored complex with cerium and the complex can be extracted with chloroform at pH 9 to 10. The effect of the pH, reagent concentration, extraction time, stability of color, diverse ions and stoichiometry of the complex is discussed

Application of p-Substituted Cinnamohydroxamic Acids to the Spectrophotometric Determination of Molybdenum(VI)

The formation of greenish yellow coloured complex o.E molybdenum( VI) with nine new p-substituted cinnamohydroxamic acids have been studied. This study shows that the molybdenum complex of nine new hydroxamic acids have molar absorptivities between 3.5 x 104 and 1.1 x 105 1 moi-1 cm-1• This value is considerably large as compared to value obtained by benzohydroxamic acid, N-phenylbenzohydroxamic acid and N-p-chlorophenylbenzo- hydroxamic acidi.2• A rapid extraction and spectrophotometric method for the determination of molybdenum is described, employing the most promising of these reagents, N-p-tolyl-p-methoxycinnamohydroxamic acid

Composite-fermion crystallites in quantum dots

The correlations in the ground state of interacting electrons in a two-dimensional quantum dot in a high magnetic field are known to undergo a qualitative change from liquid-like to crystal-like as the total angular momentum becomes large. We show that the composite-fermion theory provides an excellent account of the states in both regimes. The quantum mechanical formation of composite fermions with a large number of attached vortices automatically generates omposite fermion crystallites in finite quantum dots.Comment: 5 pages, 3 figure

A Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market

We present the first combinatorial polynomial time algorithm for computing the equilibrium of the Arrow-Debreu market model with linear utilities.Comment: Preliminary version in ICALP 201

Budget-restricted utility games with ordered strategic decisions

We introduce the concept of budget games. Players choose a set of tasks and each task has a certain demand on every resource in the game. Each resource has a budget. If the budget is not enough to satisfy the sum of all demands, it has to be shared between the tasks. We study strategic budget games, where the budget is shared proportionally. We also consider a variant in which the order of the strategic decisions influences the distribution of the budgets. The complexity of the optimal solution as well as existence, complexity and quality of equilibria are analyzed. Finally, we show that the time an ordered budget game needs to convergence towards an equilibrium may be exponential

Half-Integral Spin-Singlet Quantum Hall Effect

We provide numerical evidence that the ground state of a short range interaction model at $\nu=1/2$ is incompressible and spin-singlet for a wide range of repulsive interactions. Furthermore it is accurately described by a trial wave function studied earlier. For the Coulomb interaction we find that this wave function provides a good description of the lowest lying spin-singlet state, and propose that fractional quantum Hall effect would occur at $\nu=1/2$ if this state became the global ground state.Comment: Latex 13 pages, 3 figures upon reques