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

Fermionic coherent states for pseudo-Hermitian two-level systems

We introduce creation and annihilation operators of pseudo-Hermitian fermions for two-level systems described by pseudo-Hermitian Hamiltonian with real eigenvalues. This allows the generalization of the fermionic coherent states approach to such systems. Pseudo-fermionic coherent states are constructed as eigenstates of two pseudo-fermion annihilation operators. These coherent states form a bi-normal and bi-overcomplete system, and their evolution governed by the pseudo-Hermitian Hamiltonian is temporally stable. In terms of the introduced pseudo-fermion operators the two-level system' Hamiltonian takes a factorized form similar to that of a harmonic oscillator.Comment: 13 pages (Latex, article class), no figures; v2: some amendments in section 2, seven new refs adde

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

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

DNA Barcoding Identifies Argentine Fishes from Marine and Brackish Waters

DNA barcoding has been advanced as a promising tool to aid species identification and discovery through the use of short, standardized gene targets. Despite extensive taxonomic studies, for a variety of reasons the identification of fishes can be problematic, even for experts. DNA barcoding is proving to be a useful tool in this context. However, its broad application is impeded by the need to construct a comprehensive reference sequence library for all fish species. Here, we make a regional contribution to this grand challenge by calibrating the species discrimination efficiency of barcoding among 125 Argentine fish species, representing nearly one third of the known fauna, and examine the utility of these data to address several key taxonomic uncertainties pertaining to species in this region..This study constitutes a significant contribution to the global barcode reference sequence library for fishes and demonstrates the utility of barcoding for regional species identification. As an independent assessment of alpha taxonomy, barcodes provide robust support for most morphologically based taxon concepts and also highlight key areas of taxonomic uncertainty worthy of reappraisal