12,957 research outputs found
Short periodic orbits theory for partially open quantum maps
We extend the semiclassical theory of short periodic orbits [Phys. Rev. E
{\bf 80}, 035202(R) (2009)] to partially open quantum maps. They correspond to
classical maps where the trajectories are partially bounced back due to a
finite reflectivity . These maps are representative of a class that has many
experimental applications. The open scar functions are conveniently redefined,
providing a suitable tool for the investigation of these kind of systems. Our
theory is applied to the paradigmatic partially open tribaker map. We find that
the set of periodic orbits that belong to the classical repeller of the open
map () are able to support the set of long-lived resonances of the
partially open quantum map in a perturbative regime. By including the most
relevant trajectories outside of this set, the validity of the approximation is
extended to a broad range of values. Finally, we identify the details of
the transition from qualitatively open to qualitatively closed behaviour,
providing an explanation in terms of short periodic orbits.Comment: 6 pages, 4 figure
OTOC, complexity and entropy in bi-partite systems
There is a remarkable interest in the study of Out-of-time ordered
correlators (OTOCs) that goes from many body theory and high energy physics to
quantum chaos. In this latter case there is a special focus on the comparison
with the traditional measures of quantum complexity such as the spectral
statistics, for example. The exponential growth has been verified for many
paradigmatic maps and systems. But less is known for multi-partite cases. On
the other hand the recently introduced Wigner separability entropy (WSE) and
its classical counterpart (CSE) provide with a complexity measure that treats
equally quantum and classical distributions in phase space. We have compared
the behavior of these measures in a system consisting of two coupled and
perturbed cat maps with different dynamics: double hyperbolic (HH), double
elliptic (EE) and mixed (HE). In all cases, we have found that the OTOCs and
the WSE have essentially the same behavior, providing with a complete
characterization in generic bi-partite systems and at the same time revealing
them as very good measures of quantum complexity for phase space distributions.
Moreover, we establish a relation between both quantities by means of a
recently proven theorem linking the second Renyi entropy and OTOCs.Comment: 6 pages, 5 figure
Classical to quantum correspondence in dissipative directed transport
We compare the quantum and classical properties of the (Quantum) Isoperiodic
Stable Structures -- (Q)ISSs -- which organize the parameter space of a
paradigmatic dissipative ratchet model, i.e. the dissipative modified kicked
rotator. We study the spectral behavior of the corresponding classical
Perron-Frobenius operators with thermal noise and the quantum superoperators
without it for small values. We find a remarkable similarity
between the classical and quantum spectra. This finding significantly extends
previous results -- obtained for the mean currents and asymptotic distributions
only -- and on the other hand unveils a classical to quantum correspondence
mechanism where the classical noise is qualitatively different from the quantum
one. This is crucial not only for simple attractors but also for chaotic ones,
where just analyzing the asymptotic distribution reveals insufficient.
Moreover, we provide with a detailed characterization of relevant eigenvectors
by means of the corresponding Weyl-Wigner distributions, in order to better
identify similarities and differences. Finally, this model being generic, it
allows us to conjecture that this classical to quantum correspondence mechanism
is a universal feature of dissipative systems.Comment: 7 pages, 6 figure
The role of short periodic orbits in quantum maps with continuous openings
We apply a recently developed semiclassical theory of short periodic orbits
to the continuously open quantum tribaker map. In this paradigmatic system the
trajectories are partially bounced back according to continuous reflectivity
functions. This is relevant in many situations that include optical
microresonators and more complicated boundary conditions. In a perturbative
regime, the shortest periodic orbits belonging to the classical repeller of the
open map - a cantor set given by a region of exactly zero reflectivity - prove
to be extremely robust in supporting a set of long-lived resonances of the
continuously open quantum maps. Moreover, for step like functions a significant
reduction in the number needed is obtained, similarly to the completely open
situation. This happens despite a strong change in the spectral properties when
compared to the discontinuous reflectivity case.Comment: 6 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1604.0181
Lagrangian descriptors for open maps
We adapt the concept of Lagrangian descriptors, which have been recently
introduced as efficient indicators of phase space structures in chaotic
systems, to unveil the key features of open maps. We apply them to the open
tribaker map, a paradigmatic example not only in classical but also in quantum
chaos. Our definition allows to identify in a very simple way the inner
structure of the chaotic repeller, which is the fundamental invariant set that
governs the dynamics of this system. The homoclinic tangles of periodic orbits
(POs) that belong to this set are clearly found. This could also have important
consequences for chaotic scattering and in the development of the semiclassical
theory of short POs for open systems.Comment: 7 pages, 10 figure
Scattering solutions of the spinless Salpeter equation
A method to compute the scattering solutions of a spinless Salpeter equation
(or a Schrodinger equation) with a central interaction is presented. This
method relies on the 3-dimensional Fourier grid Hamiltonian method used to
compute bound states. It requires only the evaluation of the potential at
equally spaced grid points and yields the radial part of the scattering
solution at the same grid points. It can be easily extended to the case of
coupled channel equations and to the case of non-local interactions.Comment: 7 page
Integration Readiness levels Evaluation and Systems Architecture: A Literature Review
The success of complex systems projects is strongly influenced by their architecture. A key role of a system architect is to decide whether and how to integrate new technologies in a system architecture. Technology readiness levels (TRL) scale has been used for decades to support decision making regarding the technology infusion in complex systems, but it still faces challenges related to the integration of technologies to a system architecture. Integration Readiness Levels (IRL) scale has been elaborated in the last decade to face these challenges, representing the integration maturity between the technological elements of a system. The aim of this theoretical article is to perform a literature review on IRL scale evaluation and on systems architecture, through bibliographic research. Results show the review organized in five topics that surrounds the research objective, presenting the IRL and TRL scales evolution, comparing their evaluation practices, and exploring the architecture complexity of systems. Suggestions for future research are proposed based on these results
On the environmental stability of quantum chaotic ratchets
The transitory and stationary behavior of a quantum chaotic ratchet
consisting of a biharmonic potential under the effect of different drivings in
contact with a thermal environment is studied. For weak forcing and finite
, we identify a strong dependence of the current on the structure of the
chaotic region. Moreover, we have determined the robustness of the current
against thermal fluctuations in the very weak coupling regime. In the case of
strong forcing, the current is determined by the shape of a chaotic attractor.
In both cases the temperature quickly stabilizes the ratchet, but in the latter
it also destroys the asymmetry responsible for the current generation. Finally,
applications to isomerization reactions are discussed.Comment: 6 pages, 5 figure
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