63,776 research outputs found
From Regular to Chaotic States in Atomic Nuclei
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 orderchaos 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
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
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
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
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
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. 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
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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