Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation

The paper presents a new theory of unfolding of eigenvalue surfaces of real symmetric and Hermitian matrices due to an arbitrary complex perturbation near a diabolic point. General asymptotic formulae describing deformations of a conical surface for different kinds of perturbing matrices are derived. As a physical application, singularities of the surfaces of refractive indices in crystal optics are studied.Comment: 23 pages, 7 figure

Spectral Singularities of a General Point Interaction

We study the problem of locating spectral singularities of a general complex point interaction with a support at a single point. We also determine the bound states, examine the special cases where the point interaction is P-, T-, and PT-symmetric, and explore the issue of the coalescence of spectral singularities and bound states.Comment: 11 page

Complex magnetic monopoles, geometric phases and quantum evolution in vicinity of diabolic and exceptional points

We consider the geometric phase and quantum tunneling in vicinity of diabolic and exceptional points. We show that the geometric phase associated with the degeneracy points is defined by the flux of complex magnetic monopole. In weak-coupling limit the leading contribution to the real part of geometric phase is given by the flux of the Dirac monopole plus quadrupole term, and the expansion for its imaginary part starts with the dipolelike field. For a two-level system governed by the generic non-Hermitian Hamiltonian, we derive a formula to compute the non-adiabatic complex geometric phase by integral over the complex Bloch sphere. We apply our results to to study a two-level dissipative system driven by periodic electromagnetic field and show that in the vicinity of the exceptional point the complex geometric phase behaves as step-like function. Studying tunneling process near and at exceptional point, we find two different regimes: coherent and incoherent. The coherent regime is characterized by the Rabi oscillations and one-sheeted hyperbolic monopole emerges in this region of the parameters. In turn with the incoherent regime the two-sheeted hyperbolic monopole is associated. The exceptional point is the critical point of the system where the topological transition occurs and both of the regimes yield the quadratic dependence on time. We show that the dissipation brings into existence of pulses in the complex geometric phase and the pulses are disappeared when dissipation dies out. Such a strong coupling effect of the environment is beyond of the conventional adiabatic treatment of the Berry phase.Comment: 29 pages, 21 figure

Stochastic pump effect and geometric phases in dissipative and stochastic systems

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).Comment: Review. 35 pages. J. Phys. A: Math, Theor. (in press

Morphological analysis and description of the ovaries of female silky sharks, Carcharhinus falciformis (Müller & Henle, 1839)

This work aims to study the female reproductive tract of silky sharks, Carcharhinus falciformis, captured in the South and Equatorial Atlantic Ocean. Samples were collected between January 2008 and March 2010 through oceanic commercial vessels that targeted tuna and swordfish, with a total of 17 females collected. The methodologies followed for analyzing the ovaries of those females included both macroscopic and histological analysis. Macroscopically, it was possible to determine that the ovaries on these sharks is suspended by mesenteries in the anterior section of the body cavity, heavily irrigated by blood vessels, and contains a wide range of oocytes. Ovaries were found in three distinct maturational stages: Stage I (Immature), Stage II (Maturing) and Stage III (Mature). Immature ovaries were small, with widths ranging from 1.0 to 3.1 cm, and had a gelatinous or granulose internal structure; maturing ovaries were slightly larger, ranging in width between 5.2 and 6.0 cm; mature ovaries ranged in width between 6.5 and 7.8 cm, and had a more rounded shape and the presence of large and well developed oocytes. Under microscopic examination, it was observed that the ovaries were covered with simple epithelial tissue during the early development stages and a simple cubic epithelium in the final stages of maturation. During the initial maturation stages the epigonal organ was not differentiated from the ovary. In mature specimens, the ovary showed a simple cubic epithelium and just below this epithelium there was a layer of dense connective tissue and muscle with the presence of vitellogenic oocytes and fat cells. A thin yolk membrane enclosing the oocytes was also evident. Finally, it was possible to distinguish a zona pellucida, separating the oocytes from the follicle wall and a basal lamina between the granular layers and the teak layer.info:eu-repo/semantics/publishedVersio

Resolving taxonomic uncertainty in vulnerable elasmobranchs : are the Madeira skate (Raja maderensis) and the thornback ray (Raja clavata) distinct species?

Skates and rays constitute the most speciose group of chondrichthyan fishes, yet are characterised by remarkable levels of morphological and ecological conservatism. They can be challenging to identify, which makes monitoring species compositions for fisheries management purposes problematic. Owing to their slow growth and low fecundity, skates are vulnerable to exploitation and species exhibiting endemism or limited ranges are considered to be the most at risk. The Madeira skate Raja maderensis is endemic and classified as ‘Data Deficient’ by the IUCN, yet its taxonomic distinctiveness from the morphologically similar and more wide-ranging thornback ray Raja clavate is unresolved. This study evaluated the sequence divergence of both the variable control region and cytochrome oxidase I ‘DNA barcode’ gene of the mitochondrial genome to elucidate the genetic differentiation of specimens identified as R. maderensis and R. clavate collected across much of their geographic ranges. Genetic evidence was insufficient to support the different species designations. However regardless of putative species identification, individuals occupying waters around the Azores and North African Seamounts represent an evolutionarily significant unit worthy of special consideration for conservation management