The role of the Berry Phase in Dynamical Jahn-Teller Systems

The presence/absence of a Berry phase depends on the topology of the manifold of dynamical Jahn-Teller potential minima. We describe in detail the relation between these topological properties and the way the lowest two adiabatic potential surfaces get locally degenerate. We illustrate our arguments through spherical generalizations of the linear T x h and H x h cases, relevant for the physics of fullerene ions. Our analysis allows us to classify all the spherical Jahn-Teller systems with respect to the Berry phase. Its absence can, but does not necessarily, lead to a nondegenerate ground state.Comment: revtex 7 pages, 2 eps figures include

Dirac fermions in a power-law-correlated random vector potential

We study localization properties of two-dimensional Dirac fermions subject to a power-law-correlated random vector potential describing, e.g., the effect of "ripples" in graphene. By using a variety of techniques (low-order perturbation theory, self-consistent Born approximation, replicas, and supersymmetry) we make a case for a possible complete localization of all the electronic states and compute the density of states.Comment: Latex, 4+ page

Atomistic simulations of structural and thermodynamic properties of bilayer graphene

We study the structural and thermodynamic properties of bilayer graphene, a prototype two-layer membrane, by means of Monte Carlo simulations based on the empirical bond order potential LCBOPII. We present the temperature dependence of lattice parameter, bending rigidity and high temperature heat capacity as well as the correlation function of out-of-plane atomic displacements. The thermal expansion coefficient changes sign from negative to positive above $\approx 400$ K, which is lower than previously found for single layer graphene and close to the experimental value of bulk graphite. The bending rigidity is twice as large than for single layer graphene, making the out-of-plane fluctuations smaller. The crossover from correlated to uncorrelated out-of-plane fluctuations of the two carbon planes occurs for wavevectors shorter than $\approx 3$ nm$^{-1}$Comment: 6 pages, 7 figures

High power impulse magnetron sputtering discharges: Instabilities and plasma self-organization

We report on instabilities in high power impulse magnetron sputtering plasmas which are likely to be of the generalized drift wave type. They are characterized by well defined regions of high and low plasma emissivity along the racetrack of the magnetron and cause periodic shifts in floating potential. The azimuthal mode number m depends on plasma current, plasma density, and gas pressure. The structures rotate in × direction at velocities of ∼10 km s−1 and frequencies up to 200 kHz. Collisions with residual gas atoms slow down the rotating wave, whereas increasing ionization degree of the gas and plasma conductivity speeds it up

Formation of van der Waals molecules in buffer gas cooled magnetic traps

We show that a large class of helium-containing cold polar molecules form readily in a cryogenic buffer gas, achieving densities as high as 10^12 cm^-3. We explore the spin relaxation of these molecules in buffer gas loaded magnetic traps, and identify a loss mechanism based on Landau-Zener transitions arising from the anisotropic hyperfine interaction. Our results show that the recently observed strong T^6 thermal dependence of spin change in buffer gas trapped silver (Ag) is accounted for by the formation and spin change of AgHe, thus providing evidence for molecular formation in a buffer gas trap.Comment: 4 pages, 4 figure

Finding instabilities in the community structure of complex networks

The problem of finding clusters in complex networks has been extensively studied by mathematicians, computer scientists and, more recently, by physicists. Many of the existing algorithms partition a network into clear clusters, without overlap. We here introduce a method to identify the nodes lying ``between clusters'' and that allows for a general measure of the stability of the clusters. This is done by adding noise over the weights of the edges of the network. Our method can in principle be applied with any clustering algorithm, provided that it works on weighted networks. We present several applications on real-world networks using the Markov Clustering Algorithm (MCL).Comment: 4 pages, 5 figure

On the structure of non-full-rank perfect codes

The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-error-correcting binary code can be constructed by this combining construction is generalized to the $q$-ary case. Simply, every non-full-rank perfect code $C$ is the union of a well-defined family of $\mu$-components $K_\mu$, where $\mu$ belongs to an "outer" perfect code $C^*$, and these components are at distance three from each other. Components from distinct codes can thus freely be combined to obtain new perfect codes. The Phelps general product construction of perfect binary code from 1984 is generalized to obtain $\mu$-components, and new lower bounds on the number of perfect 1-error-correcting $q$-ary codes are presented.Comment: 8 page

Analyzing connectivity in collective transportation line networks by means of hypergraphs

In this paper we will show how hypergraphs and some measures related to them can help in extracting information about Collective Transportation Line Networks. We will also prove that these measures satisfy certain properties that validate their use to compare the connectivity of different networks. © 2013 EDP Sciences and Springer.This work was partially supported by Ministerio de Educacion, Ciencia e Innovacion (Spain)/FEDER under project MTM2009-14243 and by Junta de Andalucia (Spain)/FEDER under excellence proyects P09-TEP-5022 and FQM-5849. Special thanks are due to two anonymous referees for their valuable comments and advice.Barrena, E.; De-Los-Santos, A.; Mesa López-Colmenar, JA.; Perea Rojas Marcos, F. (2013). Analyzing connectivity in collective transportation line networks by means of hypergraphs. European Physical Journal - Special Topics. 215(1):93-108. https://doi.org/10.1140/epjst/e2013-01717-3S931082151D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)V. Latora, M. Marchiori, Phys. Rev. Lett. 87, 198701 (2001)V. Latora, M. Marchiori, Physica A 314, 109 (2002)R. Criado, B. Hernández-Bermejo, M. Romance, Int. J. Bifurcation Chaos 17, 2289 (2007)A. De-Los-Santos, G. Laporte, J.A. Mesa, F. Perea, Transp. Res. Part C: Emerging Technol. 20, 34 (2012)E. Barrena, A. De-Los-Santos, J.A. Mesa, F. Perea, Technical proofs of paper “Analyzing Connectivity in Collective Transportation Line Networks by means of Hypergraphs”, http://grupo.us.es/transfers/ (2012)C. Berge, Graphs and Hypergraphs (Elsevier Science Ltd., 1985)C. Berge, Hypergraphs: combinatorics of finite sets (North Holland)D.J. Watts, Small Worlds: The Dynamics of Networks between Order and Randomness (Princeton University Press, Princeton, 1999), p. 262M.E.J. Newman, Technical report, Santa Fe Institute (2001)M.E.J. Newman, Phys. Rev. E 64, 016131 (2001)M.E.J. Newman, Phys. Rev. E 64, 016132 (2001)E. Estrada, J.A. Rodríguez-Velázquez, Phys. A: Statist. Mech. Appl. 364, 581 (2006)R. Dechter, Constraint Processing (Morgan Kaufmann, 2003), p. 450P. Sen, S. Dasgupta, A. Chatterjee, P.A. Sreeram, G. Mukherjee, S.S. Manna, Phys. Rev. E 67 (2003)P. Crucitti, V. Latora, M. Marchiori, A. Rapisarda, Physica A 320, 642 (2002) [cond-mat/0205601]V. Latora, M. Marchiori, Chaos Solitons Fract. 20, 69 (2004)V. Latora, M. Marchiori, Eur. Phys. J. B 32, 249 (2002

A Computational Approach to Multistationarity of Power-Law Kinetic Systems

This paper presents a computational solution to determine if a chemical reaction network endowed with power-law kinetics (PLK system) has the capacity for multistationarity, i.e., whether there exist positive rate constants such that the corresponding differential equations admit multiple positive steady states within a stoichiometric class. The approach, which is called the "Multistationarity Algorithm for PLK systems" (MSA), combines (i) the extension of the "higher deficiency algorithm" of Ji and Feinberg for mass action to PLK systems with reactant-determined interactions, and (ii) a method that transforms any PLK system to a dynamically equivalent one with reactant-determined interactions. Using this algorithm, we obtain two new results: the monostationarity of a popular model of anaerobic yeast fermentation pathway, and the multistationarity of a global carbon cycle model with climate engineering, both in the generalized mass action format of biochemical systems theory. We also provide examples of the broader scope of our approach for deficiency one PLK systems in comparison to the extension of Feinberg's "deficiency one algorithm" to such systems