125 research outputs found
On determination of statistical properties of spectra from parametric level dynamics
We analyze an approach aiming at determining statistical properties of
spectra of time-periodic quantum chaotic system based on the parameter dynamics
of their quasienergies. In particular we show that application of the methods
of statistical physics, proposed previously in the literature, taking into
account appropriate integrals of motion of the parametric dynamics is fully
justified, even if the used integrals of motion do not determine the invariant
manifold in a unique way. The indetermination of the manifold is removed by
applying Dirac's theory of constrained Hamiltonian systems and imposing
appropriate primary, first-class constraints and a gauge transformation
generated by them in the standard way. The obtained results close the gap in
the whole reasoning aiming at understanding statistical properties of spectra
in terms of parametric dynamics.Comment: 9 pages without figure
Four-qubit entangled symmetric states with positive partial transpositions
We solve the open question of the existence of four-qubit entangled symmetric
states with positive partial transpositions (PPT states). We reach this goal
with two different approaches. First, we propose a
half-analytical-half-numerical method that allows to construct multipartite PPT
entangled symmetric states (PPTESS) from the qubit-qudit PPT entangled states.
Second, we adapt the algorithm allowing to search for extremal elements in the
convex set of bipartite PPT states [J. M. Leinaas, J. Myrheim, and E. Ovrum,
Phys. Rev. A 76, 034304 (2007)] to the multipartite scenario. With its aid we
search for extremal four-qubit PPTESS and show that generically they have ranks
(5,7,8). Finally, we provide an exhaustive characterization of these states
with respect to their separability properties.Comment: 5+4 pages, improved version, title slightly modifie
Global entangling properties of the coupled kicked tops
We study global entangling properties of the system of coupled kicked tops
testing various hypotheses and predictions concerning entanglement in quantum
chaotic systems. In order to analyze the averaged initial entanglement
production rate and the averaged asymptotic entanglement different ensembles of
initial product states are evolved. Two different ensembles with natural
probability distribution are considered: product states of independent
spin-coherent states and product states of arbitrary states. It appears that
the choice of either of these ensembles results in significantly different
averaged entanglement behavior. We investigate also a relation between the
averaged asymptotic entanglement and the mean entanglement of the eigenvectors
of an evolution operator. Lower bound on the averaged asymptotic entanglement
is derived, expressed in terms of the eigenvector entanglement.Comment: 11 pages, 7 figures, RevTe
Operational load monitoring of a composite panel using artificial neural networks
Operational Load Monitoring consists of the real-time reading and recording of the number and level of strains and stresses during load cycles withstood by a structure in its normal operating environment, in order to make more reliable predictions about its remaining lifetime in service. This is particularly important in aeronautical and aerospace industries, where it is very relevant to extend the components useful life without compromising flight safety. Sensors, like strain gauges, should be mounted on points of the structure where highest strains or stresses are expected. However, if the structure in its normal operating environment is subjected to variable exciting forces acting in different points over time, the number of places where data will have be acquired largely increases. The main idea presented in this paper is that instead of mounting a high number of sensors, an artificial neural network can be trained on the base of finite element simulations in order to estimate the state of the structure in its most stressed points based on data acquired just by a few sensors. The model should also be validated using experimental data to confirm proper predictions of the artificial neural network. An example with an omega-stiffened composite structural panel (a typical part used in aerospace applications) is provided. Artificial neural network was trained using a high-accuracy finite element model of the structure to process data from six strain gauges and return information about the state of the panel during different load cases. The trained neural network was tested in an experimental stand and the measurements confirmed the usefulness of presented approach.The project and publication of this article were financed by the Polish National Agency for
Academic Exchange (project number: PPI/APM/2018/1/00004) in the framework of Academic International
Partnerships program
Extremal spacings between eigenphases of random unitary matrices and their tensor products
Extremal spacings between eigenvalues of random unitary matrices of size N
pertaining to circular ensembles are investigated. Explicit probability
distributions for the minimal spacing for various ensembles are derived for N =
4. We study ensembles of tensor product of k random unitary matrices of size n
which describe independent evolution of a composite quantum system consisting
of k subsystems. In the asymptotic case, as the total dimension N = n^k becomes
large, the nearest neighbor distribution P(s) becomes Poissonian, but
statistics of extreme spacings P(s_min) and P(s_max) reveal certain deviations
from the Poissonian behavior
Information Infrastructure for Cooperative Research in Neuroscience
The paper describes a framework for efficient sharing of knowledge between research groups, which have been working for several years without flaws. The obstacles in cooperation are connected primarily with the lack of platforms for effective exchange of experimental data, models, and algorithms. The solution to these problems is proposed by construction of the platform (EEG.pl) with the semantic aware search scheme between portals. The above approach implanted in the international cooperative projects like NEUROMATH may bring the significant progress in designing efficient methods for neuroscience research
Tunneling and the Band Structure of Chaotic Systems
We compute the dispersion laws of chaotic periodic systems using the
semiclassical periodic orbit theory to approximate the trace of the powers of
the evolution operator. Aside from the usual real trajectories, we also include
complex orbits. These turn out to be fundamental for a proper description of
the band structure since they incorporate conduction processes through
tunneling mechanisms. The results obtained, illustrated with the kicked-Harper
model, are in excellent agreement with numerical simulations, even in the
extreme quantum regime.Comment: 11 pages, Latex, figures on request to the author (to be sent by fax
Review of the methods of determination of directed connectivity from multichannel data
The methods applied for estimation of functional connectivity from multichannel data are described with special emphasis on the estimators of directedness such as directed transfer function (DTF) and partial directed coherence. These estimators based on multivariate autoregressive model are free of pitfalls connected with application of bivariate measures. The examples of applications illustrating the performance of the methods are given. Time-varying estimators of directedness: short-time DTF and adaptive methods are presented
Concurrence classes for general pure multipartite states
We propose concurrence classes for general pure multipartite states based on
an orthogonal complement of a positive operator valued measure on quantum
phase. In particular, we construct class, , and
class concurrences for general pure -partite states. We give explicit
expressions for and class concurrences for general pure
three-partite states and for , , and class
concurrences for general pure four-partite states.Comment: 14 page
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