Symbol correspondences for spin systems

The present monograph explores the correspondence between quantum and classical mechanics in the particular context of spin systems, that is, SU(2)-symmetric mechanical systems. Here, a detailed presentation of quantum spin-j systems, with emphasis on the SO(3)-invariant decomposition of their operator algebras, is followed by an introduction to the Poisson algebra of the classical spin system and a similarly detailed presentation of its SO(3)-invariant decomposition. Subsequently, this monograph proceeds with a detailed and systematic study of general quantum-classical symbol correspondences for spin-j systems and their induced twisted products of functions on the 2-sphere. This original systematic presentation culminates with the study of twisted products in the asymptotic limit of high spin numbers. In the context of spin systems, it shows how classical mechanics may or may not emerge as an asymptotic limit of quantum mechanics.Comment: Research Monograph, 171 pages (book format, preliminary version

Endohedrally confined hydrogen atom with a moving nucleus

We studied the hydrogen atom as a system of two quantum particles in different confinement conditions; a spherical-impenetrable-wall cavity and a fullerene molecule cage. The motion is referred to the center of spherical cavities, and the Schr\"{o}dinger equation solved by means of a Generalized Sturmian Function expansion in spherical coordinates. The solutions present different properties from the ones described by the many models in the literature, where the proton is fixed in space and only the electron is considered as a quantum particle. Our results show that the position of the proton (i.e. the center of mas of the H atom) is very sensitive to the confinement condition, and could vary substantially from one state to another, from being sharply centered to being localized outside the fullerene molecule. Interchange of the localization characteristics between the states when varying the strength of the fullerene cage and mass occurred through crossing phenomena

Clearance of apoptotic cells by macrophages induces regulatory phenotype and involves stimulation of cd36 and platelet-activating factor receptor

Phagocytosis of apoptotic cells (efferocytosis) induces macrophage differentiation towards a regulatory phenotype (IL-10high/IL-12p40low). CD36 is involved in the recognition of apoptotic cells (AC), and we have shown that the platelet-activating factor receptor (PAFR) is also involved. Here, we investigated the contribution of PAFR and CD36 to efferocytosis and to the establishment of a regulatory macrophage phenotype. Mice bone marrow-derived macrophages were cocultured with apoptotic thymocytes, and the phagocytic index was determined. Blockage of PAFR with antagonists or CD36 with specific antibodies inhibited the phagocytosis of AC (~70–80%). Using immunoprecipitation and confocal microscopy, we showed that efferocytosis increased the CD36 and PAFR colocalisation in the macrophage plasma membrane; PAFR and CD36 coimmunoprecipitated with flotillin-1, a constitutive lipid raft protein, and disruption of these membrane microdomains by methyl-β-cyclodextrin reduced AC phagocytosis. Efferocytosis induced a pattern of cytokine production, IL-10high/IL-12p40low, that is, characteristic of a regulatory phenotype. LPS potentiated the efferocytosis-induced production of IL-10, and this was prevented by blocking PAFR or CD36. It can be concluded that phagocytosis of apoptotic cells engages CD36 and PAFR, possibly in lipid rafts, and this is required for optimal efferocytosis and the establishment of the macrophage regulatory phenotype

Correlations within the Non-Equilibrium Green's Function Method

Non-equilibrium Green's Function (NGF) method is a powerful tool for studying the evolution of quantum many-body systems. Different types of correlations can be systematically incorporated within the formalism. The time evolution of the single-particle Green's functions is described in terms of the Kadanoff-Baym equations. The current work initially focuses on introducing the correlations within infinite nuclear matter in one dimension and then in a finite system in the NGF approach. Starting from the harmonic oscillator Hamiltonian, by switching on adiabatically the mean-field and correlations simultaneously, a correlated state with ground-state characteristics is arrived at within the NGF method. Furthermore the use of cooling to for improving the adiabatic switching is explored.Comment: Contribution to Proc. 5th Conference on Nuclei and Mesoscopic Physics, E Lansing, 6-10 March 2017; 9 pages, 8 figure

Moving frames for cotangent bundles

Cartan's moving frames method is a standard tool in riemannian geometry. We set up the machinery for applying moving frames to cotangent bundles and its sub-bundles defined by non-holonomic constraints.Comment: 13 pages, to appear in Rep. Math. Phy

Shapes and Dynamics from the Time-Dependent Mean Field

Explaining observed properties in terms of underlying shape degrees of freedom is a well--established prism with which to understand atomic nuclei. Self--consistent mean--field models provide one tool to understand nuclear shapes, and their link to other nuclear properties and observables. We present examples of how the time--dependent extension of the mean--field approach can be used in particular to shed light on nuclear shape properties, particularly looking at the giant resonances built on deformed nuclear ground states, and at dynamics in highly-deformed fission isomers. Example calculations are shown of $^{28}$Si in the first case, and $^{240}$Pu in the latter case.Comment: 9 pages, 5 figures, to appear in proceedings of International Workshop "Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects" (SDANCA-15), 8-10 October 2015, Sofia, Bulgari