37,542 research outputs found
An alternative theoretical approach to describe planetary systems through a Schrodinger-type diffusion equation
In the present work we show that planetary mean distances can be calculated
with the help of a Schrodinger-type diffusion equation. The obtained results
are shown to agree with the observed orbits of all the planets and of the
asteroid belt in the solar system, with only three empty states. Furthermore,
the equation solutions predict a fundamental orbit at 0.05 AU from solar-type
stars, a result confirmed by recent discoveries. In contrast to other similar
approaches previously presented in the literature, we take into account the
flatness of the solar system, by considering the flat solutions of the
Schrodinger-type equation. The model has just one input parameter, given by the
mean distance of Mercury.Comment: 6 pages. Version accepted for publication in Chaos, Solitons &
Fractal
Optimization of hierarchical structures of information flow
The efficiency of a large hierarchical organisation is simulated on
Barabasi-Albert networks, when each needed link leads to a loss of information.
The optimum is found at a finite network size, corresponding to about five
hierarchical layers, provided a cost for building the network is included in
our optimization.Comment: Draft of 6 pages including all figure
Physical properties of the Schur complement of local covariance matrices
General properties of global covariance matrices representing bipartite
Gaussian states can be decomposed into properties of local covariance matrices
and their Schur complements. We demonstrate that given a bipartite Gaussian
state described by a covariance matrix \textbf{V}, the
Schur complement of a local covariance submatrix of it can be
interpreted as a new covariance matrix representing a Gaussian operator of
party 1 conditioned to local parity measurements on party 2. The connection
with a partial parity measurement over a bipartite quantum state and the
determination of the reduced Wigner function is given and an operational
process of parity measurement is developed. Generalization of this procedure to
a -partite Gaussian state is given and it is demonstrated that the
system state conditioned to a partial parity projection is given by a
covariance matrix such as its block elements are Schur complements
of special local matrices.Comment: 10 pages. Replaced with final published versio
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