63,776 research outputs found

    From Regular to Chaotic States in Atomic Nuclei

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    An interesting aspect of nuclear dynamics is the co--existence, in atomic nuclei, of regular and chaotic states. In the first part of the present work, we review the state of the art of nuclear dynamics and use a schematic shell model to show how a very simple and schematic nucleon--nucleon interaction can produce an order→\tochaos transition. The second part is devoted to a discussion of the wave function behaviour and decay of chaotic states using some simple models (to be published in Rivista Nuovo Cimento).Comment: 65 pages, LaTex (the figures are not included), Preprint DFPD/94/TH/26, University of Padov

    Galois-stability for Tame Abstract Elementary Classes

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    We introduce tame abstract elementary classes as a generalization of all cases of abstract elementary classes that are known to permit development of stability-like theory. In this paper we explore stability results in this context. We assume that \K is a tame abstract elementary class satisfying the amalgamation property with no maximal model. The main results include: (1) Galois-stability above the Hanf number implies that \kappa(K) is less than the Hanf number. Where \kappa(K) is the parallel of \kapppa(T) for f.o. T. (2) We use (1) to construct Morley sequences (for non-splitting) improving previous results of Shelah (from Sh394) and Grossberg & Lessmann. (3) We obtain a partial stability-spectrum theorem for classes categorical above the Hanf number.Comment: 23 page

    (p,q)-Deformations and (p,q)-Vector Coherent States of the Jaynes-Cummings Model in the Rotating Wave Approximation

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    Classes of (p,q)-deformations of the Jaynes-Cummings model in the rotating wave approximation are considered. Diagonalization of the Hamiltonian is performed exactly, leading to useful spectral decompositions of a series of relevant operators. The latter include ladder operators acting between adjacent energy eigenstates within two separate infinite discrete towers, except for a singleton state. These ladder operators allow for the construction of (p,q)-deformed vector coherent states. Using (p,q)-arithmetics, explicit and exact solutions to the associated moment problem are displayed, providing new classes of coherent states for such models. Finally, in the limit of decoupled spin sectors, our analysis translates into (p,q)-deformations of the supersymmetric harmonic oscillator, such that the two supersymmetric sectors get intertwined through the action of the ladder operators as well as in the associated coherent states.Comment: 1+25 pages, no figure

    Atomic and Molecular Data for Stellar Physics: Former Successes and Future Challenges

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    This review highlights current (and future) hot topics in astrophysics where atomic or molecular input data are (or will be) essential, with special emphasis on topics relating to nucleosynthesis and cosmochemistry. We first discuss issues (like the abundances of oxygen and iron in the Sun, and that of lithium in post-AGB stars) where the use of poor-quality atomic or molecular data have led to spurious astrophysical puzzles which sparked fancy astrophysical models or theories. We then address issues where the advent of new instruments (like the ultraviolet high-resolution spectrographs--GHRS onboard HST, Keck-HRS or VLT-UVES--or future infrared satellites) calls for new and accurate atomic or molecular data.Comment: 20 pages, 12 figures, to appear in Physica Scripta, Topical Issue (Proceedings of the 35th EGAS conference -- European Group for Atomic Spectroscopy

    Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice

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    In this work, we examine the topological phases that can arise in triangular lattices with disconnected elementary band representations. We show that, although these phases may be "fragile" with respect to the addition of extra bands, their topological properties are manifest in certain nontrivial holonomies (Wilson loops) in the space of nontrivial bands. We introduce an eigenvalue index for fragile topology, and we show how a nontrivial value of this index manifests as the winding of a hexagonal Wilson loop; this remains true even in the absence of time-reversal or sixfold rotational symmetry. Additionally, when time-reversal and twofold rotational symmetry are present, we show directly that there is a protected nontrivial winding in more conventional Wilson loops. Crucially, we emphasize that these Wilson loops cannot change without closing a gap to the nontrivial bands. By studying the entanglement spectrum for the fragile bands, we comment on the relationship between fragile topology and the "obstructed atomic limit" of B. Bradlyn et al., Nature 547, 298--305 (2017). We conclude with some perspectives on topological matter beyond the K-theory classification.Comment: 13 pages, 10 figures v2. accepted versio

    Shift insulators: rotation-protected two-dimensional topological crystalline insulators

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    We study a two-dimensional (2D) tight-binding model of a topological crystalline insulator (TCI) protected by rotation symmetry. The model is built by stacking two Chern insulators with opposite Chern numbers which transform under conjugate representations of the rotation group, e.g. p±p_\pm orbitals. Despite its apparent similarity to the Kane-Mele model, it does not host stable gapless surface states. Nevertheless the model exhibits topological responses including the appearance of quantized fractional charge bound to rotational defects (disclinations) and the pumping of angular momentum in response to threading an elementary magnetic flux, which are described by a mutual Chern-Simons coupling between the electromagnetic gauge field and an effective gauge field corresponding to the rotation symmetry. In addition, we show that although the filled bands of the model do not admit a symmetric Wannier representation, this obstruction is removed upon the addition of appropriate atomic orbitals, which implies `fragile' topology. As a result, the response of the model can be derived by representing it as a superposition of atomic orbitals with positive and negative integer coefficients. Following the analysis of the model, which serves as a prototypical example of 2D TCIs protected by rotation, we show that all TCIs protected by point group symmetries which do not have protected surface states are either atomic insulators or fragile phases. Remarkably, this implies that gapless surface states exist in free electron systems if and only if there is a stable Wannier obstruction. We then use dimensional reduction to map the problem of classifying 2D TCIs protected by rotation to a zero-dimensional (0D) problem which is then used to obtain the complete non-interacting classification of such TCIs as well as the reduction of this classification in the presence of interactions.Comment: 33 pages, 16 figure

    The new physics of non-equilibrium condensates: insights from classical dynamics

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    We discuss the dynamics of classical Dicke-type models, aiming to clarify the mechanisms by which coherent states could develop in potentially non-equilibrium systems such as semiconductor microcavities. We present simulations of an undamped model which show spontaneous coherent states with persistent oscillations in the magnitude of the order parameter. These states are generalisations of superradiant ringing to the case of inhomogeneous broadening. They correspond to the persistent gap oscillations proposed in fermionic atomic condensates, and arise from a variety of initial conditions. We show that introducing randomness into the couplings can suppress the oscillations, leading to a limiting dynamics with a time-independent order parameter. This demonstrates that non-equilibrium generalisations of polariton condensates can be created even without dissipation. We explain the dynamical origins of the coherence in terms of instabilities of the normal state, and consider how it can additionally develop through scattering and dissipation.Comment: 10 pages, 4 figures, submitted for a special issue of J. Phys.: Condensed Matter on "Optical coherence and collective phenomena in nanostructures". v2: added discussion of links to exact solution
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