On the relation between E(5)−E(5)-models and the interacting boson model

The connections between the $E(5)-$models (the original E(5) using an infinite square well, $E(5)-\beta^4$, $E(5)-\beta^6$ and $E(5)-\beta^8$), based on particular solutions of the geometrical Bohr Hamiltonian with $\gamma$-unstable potentials, and the interacting boson model (IBM) are explored. For that purpose, the general IBM Hamiltonian for the $U(5)-O(6)$ transition line is used and a numerical fit to the different $E(5)-$models energies is performed, later on the obtained wavefunctions are used to calculate B(E2) transition rates. It is shown that within the IBM one can reproduce very well all these $E(5)-$models. The agreement is the best for $E(5)-\beta^4$ and reduces when passing through $E(5)-\beta^6$, $E(5)-\beta^8$ and E(5), where the worst agreement is obtained (although still very good for a restricted set of lowest lying states). The fitted IBM Hamiltonians correspond to energy surfaces close to those expected for the critical point. A phenomenon similar to the quasidynamical symmetry is observed

Relationship between X(5)-models and the interacting boson model

The connections between the X(5)-models (the original X(5) using an infinite square well, X(5)-$\beta^8$, X(5)-$\beta^6$, X(5)-$\beta^4$, and X(5)-$\beta^2$), based on particular solutions of the geometrical Bohr Hamiltonian with harmonic potential in the $\gamma$ degree of freedom, and the interacting boson model (IBM) are explored. This work is the natural extension of the work presented in [1] for the E(5)-models. For that purpose, a quite general one- and two-body IBM Hamiltonian is used and a numerical fit to the different X(5)-models energies is performed, later on the obtained wave functions are used to calculate B(E2) transition rates. It is shown that within the IBM one can reproduce well the results for energies and B(E2) transition rates obtained with all these X(5)-models, although the agreement is not so impressive as for the E(5)-models. From the fitted IBM parameters the corresponding energy surface can be extracted and it is obtained that, surprisingly, only the X(5) case corresponds in the moderate large N limit to an energy surface very close to the one expected for a critical point, while the rest of models seat a little farther.Comment: Accepted in Physical Review

Total Roman Domination Number of Rooted Product Graphs

[EN] Let G be a graph with no isolated vertex and f:V(G)->{0,1,2} a function. If f satisfies that every vertex in the set {v is an element of V(G):f(v)=0} is adjacent to at least one vertex in the set {v is an element of V(G):f(v)=2}, and if the subgraph induced by the set {v is an element of V(G):f(v)>= 1} has no isolated vertex, then we say that f is a total Roman dominating function on G. The minimum weight omega(f)= n-ary sumation v is an element of V(G)f(v) among all total Roman dominating functions f on G is the total Roman domination number of G. In this article we study this parameter for the rooted product graphs. Specifically, we obtain closed formulas and tight bounds for the total Roman domination number of rooted product graphs in terms of domination invariants of the factor graphs involved in this product.Cabrera Martinez, A.; Cabrera García, S.; Carrión García, A.; Hernandez Mira, FA. (2020). Total Roman Domination Number of Rooted Product Graphs. Mathematics. 8(10):1-13. https://doi.org/10.3390/math8101850S11381

The U(5)-O(6) transition in the Interacting Boson Model and the E(5) critical point symmetry

The relation of the recently proposed E(5) critical point symmetry with the interacting boson model is investigated. The large-N limit of the interacting boson model at the critical point in the transition from U(5) to O(6) is obtained by solving the Richardson equations. It is shown explicitly that this algebraic calculation leads to the same results as the solution of the Bohr differential equation with a $\beta^4$ potential.Comment: Accepted in PR

Foreword by Guest Editors MAA 2018 Volume 18 Issue 4

MAA SPECIAL ISSUE VOL 18 ISSUE 4: Sixty-three (63) Selected (peer reviewed) Papers of the INSAP X – Oxford XI – SEAC 25th Joint Conference ‘ROAD TO THE STARS’, held in Santiago de Compostela, Spain, 18th–22nd September 2017 Mediterranean Archaeology and Archaeometry (MAA) is an Open Access Journal published since 2001 by The University of the Aegean, Department of Mediterranean Studies, Rhodes, Greece. It covers the dual nature of archaeology and cultural heritage with science which includes, amongst others, natural science applied to archaeology (physics, chemistry, biology, geology, geophysics, astronomy), archaeology, ancient history, cultural sustainability, astronomy in culture, physical anthropology, digital heritage, new archaeological finds reports, historical archaeology, architectural archaeology, ethnoarchaeological prospective, critical reviews, from Paleolithic to medieval/Byzantine eras, all pertinent to the Mediterranean including adjacent areas with due interaction and/or parallel comparison to ancient Mediterranean cultures

Shaping point- and mirror-symmetric proto-planetary nebulae by the orbital motion of the central binary system

We present 3D hydrodynamical simulations of a jet launched from the secondary star of a binary system inside a proto-planetary nebula. The secondary star moves around the primary in a close eccentric orbit. From the gasdynamic simulations we compute synthetic [NII] 6583 emission maps. Different jet axis inclinations with respect to the orbital plane, as well as different orientations of the flow with respect to the observer are considered. For some parameter combinations, we obtain structures that show point- or mirror-symmetric morphologies depending on the orientation of the flow with respect to the observer. Furthermore, our models can explain some of the emission distribution asymmetries that are summarized in the classification given by Soker & hadar (2002).Comment: 15 pages, 3 figures, 2 tables, Accepted in Apj Letter

Is keV ion induced pattern formation on Si(001) caused by metal impurities?

We present ion beam erosion experiments performed in ultra high vacuum using a differentially pumped ion source and taking care that the ion beam hits the Si(001) sample only. Under these conditions no ion beam patterns form on Si for angles below 45 degrees with respect to the global surface normal using 2 keV Kr ions and fluences of 2 x 10^22 ions/m^2. In fact, the ion beam induces a smoothening of preformed patterns. Simultaneous sputter deposition of stainless steel in this angular range creates a variety of patterns, similar to those previously ascribed to clean ion beam induced destabilization of the surface profile. Only for grazing incidence with incident angles between 60 degrees and 83 degrees pronounced ion beam patterns form. It appears that the angular dependent stability of Si(001) against pattern formation under clean ion beam erosion conditions is related to the angular dependence of the sputtering yield, and not primarily to a curvature dependent yield as invoked frequently in continuum theory models.Comment: 15 pages, 7 figures. This is an author-created, un-copyedited version of an article published in Nanotechnology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

Partial dynamical symmetry in quantum Hamiltonians with higher-order terms

A generic procedure is proposed to construct many-body quantum Hamiltonians with partial dynamical symmetry. It is based on a tensor decomposition of the Hamiltonian and allows the construction of a hierarchy of interactions that have selected classes of solvable states. The method is illustrated in the SO(6) limit of the interacting boson model of atomic nuclei and applied to the nucleus $^{196}$Pt

Electrically driven photon emission from individual atomic defects in monolayer WS2.

Quantum dot-like single-photon sources in transition metal dichalcogenides (TMDs) exhibit appealing quantum optical properties but lack a well-defined atomic structure and are subject to large spectral variability. Here, we demonstrate electrically stimulated photon emission from individual atomic defects in monolayer WS2 and directly correlate the emission with the local atomic and electronic structure. Radiative transitions are locally excited by sequential inelastic electron tunneling from a metallic tip into selected discrete defect states in the WS2 bandgap. Coupling to the optical far field is mediated by tip plasmons, which transduce the excess energy into a single photon. The applied tip-sample voltage determines the transition energy. Atomically resolved emission maps of individual point defects closely resemble electronic defect orbitals, the final states of the optical transitions. Inelastic charge carrier injection into localized defect states of two-dimensional materials provides a powerful platform for electrically driven, broadly tunable, atomic-scale single-photon sources

Changes in the Papez Circuit in early stages of Alzheimer's Disease

Alzheimer's disease (AD) is the most common cause of demenMa. Neuronal and synapMc losses occur iniMally and predominantly in the medial temporal lobe structures including hippocampus, amygdala and thalamus, structures that belong to the Papez circuit. The integrity of the connecMons amongst them is essenMal for episodic memory, which is specifically impaired in AD. For this reason we have invesMgated the degeneraMon paRern of subcorMcal structures and its relaMon to early stages of AD, i.e. Mild CogniMve Impairment (MCI), both in the amnesic and mulMdomain types using structural magneMc resonance imaging (using a 3T GE scanner) and VBM‐DARTEL