Spin tunneling in magnetic molecules: Quantitative estimates for Fe8 clusters

Spin tunneling in the particular case of the magnetic molecular cluster octanuclear iron(III), Fe8, is treated by an effective Hamiltonian that allows for an angle-based description of the process. The presence of an external magnetic field along the easy axis is also taken into account in this description. Analytic expressions for the energy levels and barriers are obtained from a harmonic approximation of the potential function which give results in good agreement with the experimental results. The energy splittings due to spin tunneling is treated in an adapted WKB approach and it is shown that the present description can give results to a reliable degree of accuracy.Comment: 17 pages, 2 figures, preprint submitted to Physica

Entanglement universality of two-qubit X-states

We demonstrate that for every two-qubit state there is a X-counterpart, i.e., a corresponding two-qubit X-state of same spectrum and entanglement, as measured by concurrence, negativity or relative entropy of entanglement. By parametrizing the set of two-qubit X-states and a family of unitary transformations that preserve the sparse structure of a two-qubit X-state density matrix, we obtain the parametric form of a unitary transformation that converts arbitrary two-qubit states into their X-counterparts. Moreover, we provide a semi-analytic prescription on how to set the parameters of this unitary transformation in order to preserve concurrence or negativity. We also explicitly construct a set of X-state density matrices, parametrized by their purity and concurrence, whose elements are in one-to-one correspondence with the points of the concurrence versus purity (CP) diagram for generic two-qubit states.Comment: 24 pages, 6 figures. v2 includes new references and minor changes (accepted version

The Wigner function associated to the Rogers-Szego polynomials

We show here that besides the well known Hermite polynomials, the q-deformed harmonic oscillator algebra admits another function space associated to a particular family of q-polynomials, namely the Rogers-Szego polynomials. Their main properties are presented, the associated Wigner function is calculated and its properties are discussed. It is shown that the angle probability density obtained from the Wigner function is a well-behaved function defined in the interval [-Pi,Pi), while the action probability only assumes integer values greater or equal than zero. It is emphasized the fact that the width of the angle probability density is governed by the free parameter q characterizing the polynomial.Comment: 12 pages, 2 (mathemathica) figure

New insights into North Sea deep crustal structure and extension from transdimensional ambient noise tomography

SUMMARY The deep crustal structure beneath the North Sea is poorly understood since it is constrained by only a few seismic reflection and refraction profiles. However, it is widely acknowledged that the mid to lower crust plays important roles in rift initiation and evolution, particularly when large-scale sutures and/or terrane boundaries are present, since these inherited features can focus strain or act as inhibitors to extensional deformation. Ancient tectonic features are known to exist beneath the iconic failed rift system of the North Sea, making it an ideal location to investigate the complex interplay between pre-existing regional heterogeneity and rifting. To this end, we produce a 3-D shear wave velocity model from transdimensional ambient seismic noise tomography to constrain crustal properties to ∼30 km depth beneath the North Sea and its surrounding landmasses. Major North Sea sedimentary basins appear as low shear wave velocity zones that are a good match to published sediment thickness maps. We constrain relatively thin crust (13–18 km) beneath the Central Graben depocentres that contrasts with crust elsewhere at least 25–30 km thick. Significant variations in crustal structure and rift symmetry are identified along the failed rift system that appears to be related to the locations of Laurentia–Avalonia–Baltica palaeoplate boundaries. We constrain first-order differences in structure between palaeoplates; with strong lateral gradients in crustal velocity related to Laurentia–Avalonia–Baltica plate juxtaposition and reduced lower crustal velocities in the vicinity of the Thor suture, possibly representing the remnants of a Caledonian accretionary complex. Our results provide fresh insight into the pivotal roles that ancient terranes can play in the formation and failure of continental rifts and may help explain the characteristics of other similar continental rifts globally.</jats:p

Quasiprobability distribution functions for periodic phase-spaces: I. Theoretical Aspects

An approach featuring $s$-parametrized quasiprobability distribution functions is developed for situations where a circular topology is observed. For such an approach, a suitable set of angle-angular momentum coherent states must be constructed in appropriate fashion.Comment: 13 pages, 3 figure

Schwinger, Pegg and Barnett approaches and a relationship between angular and Cartesian quantum descriptions II: Phase Spaces

Following the discussion -- in state space language -- presented in a preceding paper, we work on the passage from the phase space description of a degree of freedom described by a finite number of states (without classical counterpart) to one described by an infinite (and continuously labeled) number of states. With that it is possible to relate an original Schwinger idea to the Pegg and Barnett approach to the phase problem. In phase space language, this discussion shows that one can obtain the Weyl-Wigner formalism, for both Cartesian {\em and} angular coordinates, as limiting elements of the discrete phase space formalism.Comment: Subm. to J. Phys A: Math and Gen. 7 pages, sequel of quant-ph/0108031 (which is to appear on J.Phys A: Math and Gen

Genetic pattern and demographic history of Salminus brasiliensis: population expansion in the Pantanal Region during the Pleistocene

Pleistocene climate changes were major historical events that impacted South American biodiversity. Although the effects of such changes are well-documented for several biomes, it is poorly known how these climate shifts affected the biodiversity of the Pantanal floodplain. Fish are one of the most diverse groups in the Pantanal floodplains and can be taken as a suitable biological model for reconstructing paleoenvironmental scenarios. To identify the effects of Pleistocene climate changes on Pantanal?s ichthyofauna, we used genetic data from multiple populations of a top-predator longdistance migratory fish, Salminus brasiliensis. We specifically investigated whether Pleistocene climate changes affected the demography of this species. If this was the case, we expected to find changes in population size over time. Thus, we assessed the genetic diversity of S. brasiliensis to trace the demographic history of nine populations from the Upper Paraguay basin, which includes the Pantanal floodplain, that form a single genetic group, employing approximate Bayesian computation (ABC) to test five scenarios: constant population, old expansion, old decline, old bottleneck following by recent expansion, and old expansion following by recent decline. Based on two mitochondrial DNA markers, our inferences from ABC analysis, the results of Bayesian skyline plot, the implications of star-like networks, and the patterns of genetic diversity (high haplotype diversity and low-to-moderate nucleotide diversity) indicated a sudden population expansion. ABC allowed us to make strong quantitative inferences about the demographic history of S. brasiliensis. We estimated a small ancestral population size that underwent a drastic fivefold expansion, probably associated with the colonization of newly formed habitats. The estimated time of this expansion was consistent with a humid and warm phase as inferred by speleothem growth phases and travertine records during Pleistocene interglacial periods. The strong concordance between our genetic inferences and this historical data could represent the first genetic record of a humid and warm phase in the Pantanal in the period since the Last Interglacial to 40 ka

Finite-dimensional Schwinger basis, deformed symmetries, Wigner function, and an algebraic approach to quantum phase

Schwinger's finite (D) dimensional periodic Hilbert space representations are studied on the toroidal lattice {\ee Z}_{D} \times {\ee Z}_{D} with specific emphasis on the deformed oscillator subalgebras and the generalized representations of the Wigner function. These subalgebras are shown to be admissible endowed with the non-negative norm of Hilbert space vectors. Hence, they provide the desired canonical basis for the algebraic formulation of the quantum phase problem. Certain equivalence classes in the space of labels are identified within each subalgebra, and connections with area-preserving canonical transformations are examined. The generalized representations of the Wigner function are examined in the finite-dimensional cyclic Schwinger basis. These representations are shown to conform to all fundamental conditions of the generalized phase space Wigner distribution. As a specific application of the Schwinger basis, the number-phase unitary operator pair in {\ee Z}_{D} \times {\ee Z}_{D} is studied and, based on the admissibility of the underlying q-oscillator subalgebra, an {\it algebraic} approach to the unitary quantum phase operator is established. This being the focus of this work, connections with the Susskind-Glogower- Carruthers-Nieto phase operator formalism as well as standard action-angle Wigner function formalisms are examined in the infinite-period limit. The concept of continuously shifted Fock basis is introduced to facilitate the Fock space representations of the Wigner function.Comment: 19 pages, no figure

Green's Function for Nonlocal Potentials

The single-particle nuclear potential is intrinsically nonlocal. In this paper, we consider nonlocalities which arise from the many-body and fermionic nature of the nucleus. We investigate the effects of nonlocality in the nuclear potential by developing the Green's function for nonlocal potentials. The formal Green's function integral is solved analytically in two different limits of the wavelength as compared to the scale of nonlocality. Both results are studied in a quasi-free limit. The results illuminate some of the basic effects of nonlocality in the nuclear medium.Comment: Accepted for publication in J. Phys.