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

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

Symplectic geometry of entanglement

We present a description of entanglement in composite quantum systems in terms of symplectic geometry. We provide a symplectic characterization of sets of equally entangled states as orbits of group actions in the space of states. In particular, using Kostant-Sternberg theorem, we show that separable states form a unique Kaehler orbit, whereas orbits of entanglement states are characterized by different degrees of degeneracy of the canonical symplectic form on the complex projective space. The degree of degeneracy may be thus used as a new geometric measure of entanglement and we show how to calculate it for various multiparticle systems providing also simple criteria of separability. The presented method is general and can be applied also under different additional symmetry conditions stemming, eg. from the indistinguishability of particles.Comment: LaTex, 31 pages, typos correcte

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

On the generalized Hamiltonian structure of 3D dynamical systems

The Poisson structures for 3D systems possessing one constant of motion can always be constructed from the solution of a linear PDE. When two constants of the motion are available the problem reduces to a quadrature and the structure functions include an arbitrary function of them

Separability and distillability in composite quantum systems -a primer-

Quantum mechanics is already 100 years old, but remains alive and full of challenging open problems. On one hand, the problems encountered at the frontiers of modern theoretical physics like Quantum Gravity, String Theories, etc. concern Quantum Theory, and are at the same time related to open problems of modern mathematics. But even within non-relativistic quantum mechanics itself there are fundamental unresolved problems that can be formulated in elementary terms. These problems are also related to challenging open questions of modern mathematics; linear algebra and functional analysis in particular. Two of these problems will be discussed in this article: a) the separability problem, i.e. the question when the state of a composite quantum system does not contain any quantum correlations or entanglement and b) the distillability problem, i.e. the question when the state of a composite quantum system can be transformed to an entangled pure state using local operations (local refers here to component subsystems of a given system). Although many results concerning the above mentioned problems have been obtained (in particular in the last few years in the framework of Quantum Information Theory), both problems remain until now essentially open. We will present a primer on the current state of knowledge concerning these problems, and discuss the relation of these problems to one of the most challenging questions of linear algebra: the classification and characterization of positive operator maps.Comment: 11 pages latex, 1 eps figure. Final version, to appear in J. Mod. Optics, minor typos corrected, references adde