Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state. Our results are relevant to the entanglement properties of eigenvectors of the orthogonal and unitary ensembles of random matrix theory and quantum chaotic systems. They also provide a rare exactly solvable case for the distribution of the minimum of a set of N {\em strongly correlated} random variables for all values of N (and not just for large N).Comment: 13 pages, 2 figures included; typos corrected; to appear in J. Stat. Phy

The relativistic Sagnac Effect: two derivations

The phase shift due to the Sagnac Effect, for relativistic matter and electromagnetic beams, counter-propagating in a rotating interferometer, is deduced using two different approaches. From one hand, we show that the relativistic law of velocity addition leads to the well known Sagnac time difference, which is the same independently of the physical nature of the interfering beams, evidencing in this way the universality of the effect. Another derivation is based on a formal analogy with the phase shift induced by the magnetic potential for charged particles travelling in a region where a constant vector potential is present: this is the so called Aharonov-Bohm effect. Both derivations are carried out in a fully relativistic context, using a suitable 1+3 splitting that allows us to recognize and define the space where electromagnetic and matter waves propagate: this is an extended 3-space, which we call "relative space". It is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the 'physical space of the rotating platform': the geometry of this space turns out to be non Euclidean, according to Einstein's early intuition.Comment: 49 pages, LaTeX, 3 EPS figures. Revised (final) version, minor corrections; to appear in "Relativity in Rotating Frames", ed. G. Rizzi and M.L. Ruggiero, Kluwer Academic Publishers, Dordrecht, (2003). See also http://digilander.libero.it/solciclo

Faraday rotation in graphene

We study magneto--optical properties of monolayer graphene by means of quantum field theory methods in the framework of the Dirac model. We reveal a good agreement between the Dirac model and a recent experiment on giant Faraday rotation in cyclotron resonance. We also predict other regimes when the effects are well pronounced. The general dependence of the Faraday rotation and absorption on various parameters of samples is revealed both for suspended and epitaxial graphene.Comment: 10 pp; v2: typos corrected and references added, v3, v4: small changes and more reference

Time Evolution of Unstable Particle Decay Seen with Finite Resolution

Time evolution of the decay process of unstable particles is investigated in field theory models. We first formulate how to renormalize the non-decay amplitude beyond perturbation theory and then discuss short-time behavior of very long-lived particles. Two different formalisms, one that does and one that does not, assume existence of the asymptotic field of unstable particles are considered. The non-decay amplitude is then calculated by introducing a finite time resolution of measurement, which makes it possible to discuss both renormalizable and non-renormalizable decay interaction including the nucleon decay. In ordinary circumstances the onset of the exponential decay law starts at times as early as at roughly the resolution time, but with an enhanced amplitude which may be measurable. It is confirmed that the short-time formula $1 - \Gamma t$ of the exponential decay law may be used to set limits on the nucleon decay rate in underground experiments. On the other hand, an exceptional example of S-wave decay of very small Q-value is found, which does not have the exponential period at all.Comment: 26 pages, LATEX file with 8 PS figure

Shell occupation by the hermit crab Dardanus insignis (Decapoda, Diogenidae) from the north Coast of São Paulo state, Brazil

Abstract The pattern of shell occupation by the hermit crab Dardanus insignis (Saussure, 1858) from the subtropical region of southeastern coast of Brazil was investigated in the present study. The percentage of shell types that were occupied and the morphometric relationships between hermit crabs and occupied shells were analyzed from monthly collections conducted during two years (from January 1998 to December 1999). Individuals were categorized according to sex and gonadal maturation, weighed and measured with respect to their cephalothoracic shield length (CSL) and wet weight (CWW). Shells were measured regarding their aperture width (SAW), dry weight (SDW) and internal volume (SIV). A total of 1086 hermit crabs was collected, occupying shells of 11 gastropod species. Olivancillaria urceus (Roding, 1798) was most commonly used by the hermit crab D. insignis, followed by Buccinanops cochlidium (Dillwyn, 1817), and Stramonita haemastoma (Linnaeus, 1767). The highest determination coefficients (r2 > 0.50, p < 0.01) were recorded particularly in the morphometric relationships between CSL vs. CWW and SAW vs. SIV, which are important indication that in this D. insignis population the great majority the animals occupied adequate shells during the two years analysed. The high number of used shell species and relative plasticity in pattern of shell utilization by smaller individuals of D. insignis indicated that occupation is influenced by the shell availability, while larger individuals demonstrated more specialized occupation in Tonna galea (Linnaeus, 1758) shell

Desenvolvimento inicial de clones IAC de seringueira em São José do Rio Preto, SP

In this study the development of four clones (IAC 35; 40; 300 e 301) of rubber tree [Hevea brasiliensis (Willd. ex A. Juss.) Müell. Arg.] selected by Instituto Agronômico de Campinas were evaluated during the first 24 months of cultivation. The experiment was laid out in randomized block design with three replications and four plants for parcel following the 1.5mx1.0m spacing at São José do Rio Preto, SP. The clone RRIM 600 was used as check. The variables analyzed were the trunk girth, the number of matured whorl, the photosynthesis rate and the concentrations of chlorophyll a, b, total and carotenoids. At the end of the experiment the values of trunk girth at 0.5m above the budgrafting union varied from 5.85 cm (IAC 301) to 10.53 cm (IAC 300) and the mean number of matured whorl varied from 2.58 (IAC 301) to 3.91 (RRIM 600). During the dry season, when the plants were 22 month old, the mean value of photosynthesis rate of IAC 40 and IAC 301 (12mol m-2 s-1) were lower compared to the other clones (15mol m-2 s-1). The chlorophyll a, b and total carotenoids concentrations were equal or superior to the check, never lower. Considering the variables analyzed, excluding the IAC 301, the other clones show performance comparable to RRIM 600.Neste estudo, acompanhou-se o desenvolvimento de quatro clones de seringueira [Hevea brasiliensis (Willd. ex A. Juss.) Müell. Arg.] selecionados pelo Instituto Agronômico de Campinas (IAC 35; 40; 300 e 301) com relação à testemunha RRIM 600, durante os primeiros 24 meses de cultivo. O experimento foi instalado com espaçamento 1,5x1,0m, em delineamento em blocos casualizados, com três repetições e quatro plantas por parcela, em São José do Rio Preto, SP. Foram avaliados o perímetro do caule e o número de lançamentos maduros; a taxa fotossintética e o conteúdo de pigmentos fotossintéticos. Ao final do acompanhamento, o perímetro médio do tronco, a 50cm do calo de enxertia, variou entre 5,85cm (IAC 301) e 10,53cm (IAC 300) e o número médio de lançamentos maduros, de 2,58 (IAC 301) a 3,91 (RRIM 600). No período seco, em idade de 22 meses após o plantio, os valores médios de taxa fotossintética de IAC 40 e IAC 301 (12mol m-2 s-1) foram inferiores aos dos demais clones (15mol m-2 s-1). Os teores de clorofila a, clorofila b e carotenoides totais foram iguais ou superiores aos da testemunha, mas nunca inferiores. Considerando as variáveis analisadas, com exceção do 301, os clones IAC mostram desempenho comparável ao do clone RRIM 600.Universidade Estadual Paulista Departamento de Zoologia e BotânicaUNESP Programa de Pós-graduação em Produção VegetalUniversidade Estadual Paulista Departamento de Zoologia e BotânicaUNESP Programa de Pós-graduação em Produção Vegeta

Rhodophyta de ambientes lóticos de Unidades de Conservação da região Sul do Brasil

Species of Rhodophyta from 10 Conservation Units from the south region of Brazil were surveyed. The samplings were carried out in 105 stream reaches, consisting of 10 m length transects. The floristic survey involved 80 populations, representing three genera, Batrachospermum, Kumanoa and Hildenbrandia plus the 'Chantransia' stages. Batrachospermum was represented by five species (B. arcuatum Kylin, B. atrum (Hudson) Harvey, B. helminthosum Bory, B. keratophytum Bory and B. puiggarianum Grunow in Wittrock & Nordstedt). The genus Kumanoa was represented by K. abilii (Reis) Necchi Junior & Vis and K. ambigua (Montagne) Entwisle et al., while Hildenbrandia only by H. angolensis W.West & G.S.West. Our results confirm Batachospermum as the best represented genus, in terms of species number, among freshwater Rhdophyta. B. arcuatum was a new record for the south region of Brazil, thus extending its austral distribution range.Espécies de Rhodophyta de 10 Unidades de Conservação da região Sul do Brasil foram investigadas. As amostragens foram conduzidas em 105 segmentos de riachos consistindo em transeções de 10 m de comprimento. O levantamento florístico resultou em 80 populações representando três gêneros, Batrachospermum, Kumanoa e Hildenbrandia, além do estágios ‘Chantransia’. Batrachospermum foi representado por cinco espécies (B. arcuatum Kylin, B. atrum (Hudson) Harvey, B. helminthosum Bory, B. keratophytum Bory, B. puiggarianum Grunow in Wittrock & Nordstedt). O gênero Kumanoa foi representado por K. abilii (Reis) Necchi Júnior & Vis e K. ambigua (Montagne) Entwisle et al., enquanto Hildenbrandia exclusivamente por H. angolensis W. West & G.S. West. Nossos resultados confirmam Batachospermum como o gênero melhor representado, em termos de número de espécies, entre as Rhdophyta de água doce. Batrachospermum arcuatum foi registrado pela primeira vez na região Sul do Brasil, ampliando assim, o limite austral de sua distribuição.Univ Estadual Paulista UNESP, FCL, BR-19806900 Assis, SP, BrazilUniv Fed Integracao Latino Amer UNILA, Foz do Iguacu, PR, BrazilUniv Estadual Paulista UNESP, Dept Zool & Bot, BR-15054000 Sao Jose do Rio Preto, SP, BrazilUniv Estadual Paulista UNESP, FCL, BR-19806900 Assis, SP, BrazilUniv Estadual Paulista UNESP, Dept Zool & Bot, BR-15054000 Sao Jose do Rio Preto, SP, Brazi