Finite-size particles, advection, and chaos: A collective phenomenon of intermittent bursting

We consider finite-size particles colliding elastically, advected by a chaotic flow. The collisionless dynamics has a quasiperiodic attractor and particles are advected towards this attractor. We show in this work that the collisions have dramatic effects in the system's dynamics, giving rise to collective phenomena not found in the one-particle dynamics. In particular, the collisions induce a kind of instability, in which particles abruptly spread out from the vicinity of the attractor, reaching the neighborhood of a coexisting chaotic saddle, in an autoexcitable regime. This saddle, not present in the dynamics of a single particle, emerges due to the collective particle interaction. We argue that this phenomenon is general for advected, interacting particles in chaotic flows.

Effective actions at finite temperature

This is a more detailed version of our recent paper where we proposed, from first principles, a direct method for evaluating the exact fermion propagator in the presence of a general background field at finite temperature. This can, in turn, be used to determine the finite temperature effective action for the system. As applications, we discuss the complete one loop finite temperature effective actions for 0+1 dimensional QED as well as for the Schwinger model in detail. These effective actions, which are derived in the real time (closed time path) formalism, generate systematically all the Feynman amplitudes calculated in thermal perturbation theory and also show that the retarded (advanced) amplitudes vanish in these theories. Various other aspects of the problem are also discussed in detail.

Finite-temperature Casimir effect for graphene

We adopt the Dirac model for quasiparticles in graphene and calculate the finite-temperature Casimir interaction between a suspended graphene layer and a parallel conducting surface. We find that at high temperature, the Casimir interaction in such system is just one-half of that for two ideal conductors separated by the same distance. In this limit, a single graphene layer behaves exactly as a Drude metal. In particular, the contribution of the TE mode is suppressed, while the contribution of the TM mode saturates at the ideal-metal value. The behavior of the Casimir interaction for intermediate temperatures and separations accessible in experiments is studied in some detail. We also find an interesting interplay between two fundamental constants of graphene physics: the fine-structure constant and the Fermi velocity.

Cooperative scattering and radiation pressure force in dense atomic clouds

Atomic clouds prepared in ""timed Dicke"" states, i.e. states where the phase of the oscillating atomic dipole moments linearly varies along one direction of space, are efficient sources of superradiant light emission [Scully et al., Phys. Rev. Lett. 96, 010501 (2006)]. Here, we show that, in contrast to previous assertions, timed Dicke states are not the states automatically generated by incident laser light. In reality, the atoms act back on the driving field because of the finite refraction of the cloud. This leads to nonuniform phase shifts, which, at higher optical densities, dramatically alter the cooperative scattering properties, as we show by explicit calculation of macroscopic observables, such as the radiation pressure force.

Protecting a quantum state from environmental noise by an incompatible finite-time measurement

We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analytical predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.

Finite-size corrections to entanglement in quantum critical systems

We analyze the finite-size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite-size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system L -> infinity) exhibit a unique pattern of entanglement, which differ only at leading order (1/L)(2). In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary length L for both periodic and twisted boundary conditions.

Universal and nonuniversal contributions to block-block entanglement in many-fermion systems

We calculate the entanglement entropy of blocks of size x embedded in a larger system of size L, by means of a combination of analytical and numerical techniques. The complete entanglement entropy in this case is a sum of three terms. One is a universal x- and L-dependent term, first predicted by Calabrese and Cardy, the second is a nonuniversal term arising from the thermodynamic limit, and the third is a finite size correction. We give an explicit expression for the second, nonuniversal, term for the one-dimensional Hubbard model, and numerically assess the importance of all three contributions by comparing to the entropy obtained from fully numerical diagonalization of the many-body Hamiltonian. We find that finite-size corrections are very small. The universal Calabrese-Cardy term is equally small for small blocks, but becomes larger for x > 1. In all investigated situations, however, the by far dominating contribution is the nonuniversal term stemming from the thermodynamic limit.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.

k(0)-INAA for determining chemical elements in bird feathers

The k(0)-method instrumental neutron activation analysis (k(0)-INAA) was employed for determining chemical elements in bird feathers. A collection was obtained taking into account several bird species from wet ecosystems in diverse regions of Brazil. For comparison reason, feathers were actively sampled in a riparian forest from the Marins Stream, Piracicaba, Sao Paulo State, using mist nets specific for capturing birds. Biological certified reference materials were used for assessing the quality of analytical procedure. Quantification of chemical elements was performed using the k(0)-INAA Quantu Software. Sixteen chemical elements, including macro and micronutrients, and trace elements, have been quantified in feathers, in which analytical uncertainties varied from 2% to 40% depending on the chemical element mass fraction. Results indicated high mass fractions of Br (max=7.9 mgkg(-1)), Co (max= 0.47 mg kg(-1)), Cr (max =68 mg kg(-1)), Hg (max =2.79 mg kg(-1)), Sb (max= 0.20 mg kg(-1)), Se (max=1.3 mg kg(-1)) and Zn (max =192 mg kg(-1)) in bird feathers, probably associated with the degree of pollution of the areas evaluated. In order to corroborate the use of k(0)-INAA results in biomonitoring studies using avian community, different factor analysis methods were used to check chemical element source apportionment and locality clustering based on feather chemical composition. (C) 2010 Elsevier B.V. All rights reserved.

Variation in the Distribution of Trace Elements in Renal Cell Carcinoma

The development of cancer is a complex, multistage process during which a normal cell undergoes genetic changes that result in phenotypic alterations and in the acquisition of the ability to invade other sites. Inductively coupled plasma optical emission spectroscopy was used to estimate the contents of Al, Ca, Cd, Cr, Cu, Fe, K, Mg, Mn, Na, P, Pb, and Zn in healthy kidney and renal cell carcinoma (RCC), and significant differences were found for all elements. Along with the progression of the malignant disease, a progressive decrease of Cd and K was observed. In fact, for Cd, the concentration in stage T4 was 263.9 times lower than in stage T1, and for K, the concentration in stage T4 was 1.73 times lower than in stage T1. Progressive accumulation was detected for P, Pb, and Zn in stage T4. For P, the concentration in stage T4 was 11.1 times higher than in stage T1; for Pb, the concentration in stage T4 was 232.7 times higher than in T1; and for Zn, the concentration in T4 was 8.452 times higher than in T1. This study highlights the marked differences in the concentrations of selected trace metals in different malignant tumor stages. These findings indicate that some trace metals may play important roles in the pathogenesis of RCC.

Collimated scanning LS-INAA for testing trace elements homogeneity in Brazilian coffee beans

The degree of homogeneity is normally assessed by the variability of the results of independent analyses of several (e.g., 15) normal-scale replicates. Large sample instrumental neutron activation analysis (LS-INAA) with a collimated Ge detector allows inspecting the degree of homogeneity of the initial batch material, using a kilogram-size sample. The test is based on the spatial distributions of induced radioactivity. Such test was applied to samples of Brazilian whole (green) coffee beans (Coffea arabica and Coffea canephora) of approximately I kg in the frame of development of a coffee reference material. Results indicated that the material do not contain significant element composition inhomogeneities between batches of approximately 30-50 g, masses typically forming the starting base of a reference material.

Native bromeliads as biomonitors of airborne chemical elements in a Brazilian restinga forest

Epiphytic bromeliads have been used as biomonitors of air pollution since they have specialized structures in leaves for absorbing humidity and nutrients available in the atmosphere. Leaves of five bromeliad species were collected in the conservation unit Parque Estadual Ilha do Cardoso, Sao Paulo State, Brazil, and analyzed by INAA. Vriesea carinata was the species showing most accumulation, with the highest mass fractions of K, Na, Rb and Zn. Similar results were previously found for the same species collected in the dense ombrophilous forest. Chemical composition of bromeliads provided an indication of the atmosphere status in the conservation unit.

Status of chemical elements in Atlantic Forest tree species near an industrial complex

Environmental quality assessment studies have been conducted with tree species largely distributed in the Atlantic Forest. Leaf and soil samples were collected in the conservation unit Parque Estadual da Serra do Mar (PESM) nearby the industrial complex of Cubatao, Sao Paulo State, Brazil, and analyzed for chemical elements by instrumental neutron activation analysis. Results were compared to background values obtained in the Parque Estadual Carlos Botelho (PECB). The higher As, Fe, Hg and Zn mass fractions in the tree leaves of PESM indicated anthropogenic influence on this conservation unit.

Atlantic forest: A natural reservoir of chemical elements

The accumulation of chemical elements in biological compartments is one of the strategies of tropical species to adapt to a low-nutrient soil. This study focuses on the Atlantic Forest because of its eco-environmental importance as a natural reservoir of chemical elements. About 20 elements were determined by INAA in leaf, soil, litter and epiphyte compartments. There was no seasonality for chemical element concentrations in leaves, which probably indicated the maintainance of chemical elements in this compartment. Considering the estimated quantities, past deforestation events could have released large amounts of chemical elements to the environment.