Phase transition in the assignment problem for random matrices

We report an analytic and numerical study of a phase transition in a P problem (the assignment problem) that separates two phases whose representatives are the simple matching problem (an easy P problem) and the traveling salesman problem (a NP-complete problem). Like other phase transitions found in combinatoric problems (K-satisfiability, number partitioning) this can help to understand the nature of the difficulties in solving NP problems an to find more accurate algorithms for them.Comment: 7 pages, 5 figures; accepted for publication in Europhys. Lett. http://www.edpsciences.org/journal/index.cfm?edpsname=ep

Excited state entanglement in homogeneous fermionic chains

We study the Renyi entanglement entropy of an interval in a periodic fermionic chain for a general eigenstate of a free, translational invariant Hamiltonian. In order to analytically compute the entropy we use two technical tools. The first one is used to reduce logarithmically the complexity of the problem and the second one to compute the R\'enyi entropy of the chosen subsystem. We introduce new strategies to perform the computations, derive new expressions for the entropy of these general states and show the perfect agreement of the analytical computations and the numerical outcome. Finally we discuss the physical interpretation of our results and generalise them to compute the entanglement entropy for a fragment of a fermionic ladder.Comment: 31 pages, 1 table, 8 figures. Final version published in J. Phys. A. References and section added. Typos correcte

Entanglement in fermionic chains with finite range coupling and broken symmetries

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Renyi entropy of a partial observation to a subsystem consisting of $X$ contiguous sites in the limit of large $X$. The present work generalizes similar results due to Its, Jin, Korepin and Its, Mezzadri, Mo. A striking new feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size of $X$. This logarithmic behaviour originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyse the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long range pairing.Comment: 27 pages, 5 figure

Magnetic-field-dependent quasiparticle energy relaxation in mesoscopic wires

In order to find out if magnetic impurities can mediate interactions between quasiparticles in metals, we have measured the effect of a magnetic field B on the energy distribution function f(E) of quasiparticles in two silver wires driven out-of-equilibrium by a bias voltage U. In a sample showing sharp distributions at B=0, no magnetic field effect is found, whereas in the other sample, rounded distributions at low magnetic field get sharper as B is increased, with a characteristic field proportional to U. Comparison is made with recent calculations of the effect of magnetic-impurities-mediated interactions taking into account Kondo physics.Comment: 4 pages, 3 figures, to be published in Physical Review Letter

On the M\"obius transformation in the entanglement entropy of fermionic chains

There is an intimate relation between entanglement entropy and Riemann surfaces. This fact is explicitly noticed for the case of quadratic fermionic Hamiltonians with finite range couplings. After recollecting this fact, we make a comprehensive analysis of the action of the M\"obius transformations on the Riemann surface. We are then able to uncover the origin of some symmetries and dualities of the entanglement entropy already noticed recently in the literature. These results give further support for the use of entanglement entropy to analyse phase transition.Comment: 29 pages, 5 figures. Final version published in JSTAT. Two new figures. Some comments and references added. Typos correcte

Influence of Magnetic Field on Effective Electron-Electron Interactions in a Copper Wire

We have measured in a copper wire the energy exchange rate between quasiparticles as a function of the applied magnetic field. We find that the effective electron-electron interaction is strongly modified by the magnetic field, suggesting that magnetic impurities play a role on the interaction processes.Comment: latex anthore.tex, 8 files, 6 figures, 7 pages in: Proceedings of the XXXVIth Rencontres de Moriond `Electronic Correlations: From Meso- to Nano-physics' Les Arcs, France January 20-27, 2001 [SPEC-S01/027

Ballistic effects in a proximity induced superconducting diffusive metal

Using a Scanning Tunneling Microscope (STM), we investigate the Local Density of States (LDOS) of artificially fabricated normal metal nano-structures in contact with a superconductor. Very low temperature local spectroscopic measurements (100 mK) reveal the presence of well defined subgap peaks at energy |E|<Delta in the LDOS at various positions of the STM tip. Although no clear correlations between the LDOS and the shape of the samples have emerged, some of the peak features suggest they originate from quasi-particle bound states within the normal metal structures (De Gennes St James states). Refocusing of electronic trajectories induced by the granular srtucture of the samples can explain the observation of spatially uncorrelated interference effects in a non-ballistic medium.Comment: 4 pages, 4 figure

Agaricus guachari, sp. nov. (Agaricales), encontrada en Venezuela.

[EN] Agaricus guachari is proposed and described as a new species. It was found growing on dung of a nocturnal bird called "guácharo" (Steatornis caripensis Humboldt), in a cave, showing white basidiomata, which reddenned quickly when cut or robbed. Tbe habitat, presence of a well-developed universal veil and negative Schaeffer's reaction distinguished this species from the rest of taxa included in this genus. Data, including iconography, micro-and ultramicroscopic features, are also added.[ES] Se propone y describe Agaricus guachari como especie nueva para la ciencia. Este hongo se encontró viviendo sobre excrementos de "guácharo" (Steatomis caripensis Humboldt), que es un ave nocturna que habita en cuevas y se alimenta de frotos de plantas tropicales en Suramérica. El hongo presenta basidiomas blancos en fresco, que al rozarlos o cortarlos pasan rápidamente a tomar un color rojizo. Este hábitat tan característico, unido al hecho de presentar velo universal bien desarrollado y reacción negativa frente al reactivo de Schaeffer, confiere a esta especie una identidad propia que la separa y diferencia de los otros táxones de Agaricus conocidos hasta ahora. Además de la descripción completa, se aporta una detallada iconografía con los datos más relevantes sobre sus características micro- y ultramicroscópicas.Peer reviewe