The space of density states in geometrical quantum mechanics

We present a geometrical description of the space of density states of a quantum system of finite dimension. After presenting a brief summary of the geometrical formulation of Quantum Mechanics, we proceed to describe the space of density states \D(\Hil) from a geometrical perspective identifying the stratification associated to the natural GL(\Hil)--action on \D(\Hil) and some of its properties. We apply this construction to the cases of quantum systems of two and three levels.Comment: Amslatex, 18 pages, 4 figure

Tensorial description of quantum mechanics

Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a covariant formulation of quantum mechanics under the full diffeomorphism group.Comment: 8 page

Basics of Quantum Mechanics, Geometrization and some Applications to Quantum Information

In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally, after reviewing the basics of the geometric formulation of quantum mechanics, we apply the methods presented to the most interesting cases of finite dimensional Hilbert spaces: those of two, three and four level systems (one qubit, one qutrit and two qubit systems). As a more practical application, we discuss the advantages that the geometric formulation of quantum mechanics can provide us with in the study of situations as the functional independence of entanglement witnesses.Comment: AmsLaTeX, 37 pages, 8 figures. This paper is an expanded version of some lectures delivered by one of us (G. M.) at the ``Advanced Winter School on the Mathematical Foundation of Quantum Control and Quantum Information'' which took place at Castro Urdiales (Spain), February 11-15, 200

Variation of seed characteristic from natural and artificial selection in the genus Papaver

Papaveraceae is a mediterranean plant family with an important scientific, commercial and ethnobotanical interest. Includes wild species, which are distributed throughout the Spanish territory, as Papaver rhoeas, P. dubium, P. bracteatum, P. hybridum and the wild type of P. somniferum, which are representatives of the natural selection. The species with the greatest commercial interest is P. somniferum, whose management through improvement lines reflects the most profitable plant characteristics obtained by artificial selection: fast and vigorous growth, multiple flowers and big size capsules (1), traits that increase the production of morphine, codeine and thebaine among others opiates derived from the capsule leachate. Occasionally, some breeding lines of P. somniferum shown wild features, such as capsule dehiscence or extended germination time. Papaver becomes, thereby, an interesting plant genus to analyze the differential evolution experienced through natural and artificial selection. In this regard, previous studies reported that seed surface patter can be used in taxonomic classification of Papaveraceae family members (2). The main goal of this project was to characterize several seed traits variation among wild and cultivated samples. Seed size and shape was characterized using images analysis from macro-photography and the software ImageJ. Seed color, defined in the L, a*, b* color space, was recorded with an automatic colorimeter. Electron scanning microscopy (SEM) micrographs were used to study seed surface crosslinked patterns. Finally, confocal scanning microscopy allowed a preliminary approach to the internal seed tissue structure. The results shown that wild species seeds have deeper color than P. somniferum breeding lines but even among those it is possible to distinguish at least four main differentiated groups by color. Likewise, even if all breeded P. somniferum samples had larger seeds than wild species, probably as the results of artificial selection, there were clear variation among them. We discuss if the variations in these seed characteristics was the unintended result of the artificial trait breeding selection with agronomic interest. References * (1) Referencia general aquí * (2) Referencia sobre caracteres de la superficie de la semilla como indicadores taxonómicos Funding Authors thanks funding support from Alcaliber S.A. (OTRI-UMA-8.06/5.03.4280) and the University of Málaga to EMC, and Spanish Ministry of Enconomy and EU grant for AJMA (RYC-2011-08839).Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Introduction to Quantum Mechanics and the Quantum-Classical transition

In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schroedinger and Heisenberg frameworks from this perspective and discuss how the momentum map associated to the action of the unitary group on the Hilbert space allows to relate both approaches. We also study Weyl-Wigner approach to Quantum Mechanics and discuss the implications of bi-Hamiltonian structures at the quantum level.Comment: Survey paper based on the lectures delivered at the XV International Workshop on Geometry and Physics Puerto de la Cruz, Tenerife, Canary Islands, Spain September 11-16, 2006. To appear in Publ. de la RSM

Micro-doppler-based in-home aided and unaided walking recognition with multiple radar and sonar systems

Published in IET Radar, Sonar and Navigation. Online first 21/06/2016.The potential for using micro-Doppler signatures as a basis for distinguishing between aided and unaided gaits is considered in this study for the purpose of characterising normal elderly gait and assessment of patient recovery. In particular, five different classes of mobility are considered: normal unaided walking, walking with a limp, walking using a cane or tripod, walking with a walker, and using a wheelchair. This presents a challenging classification problem as the differences in micro-Doppler for these activities can be quite slight. Within this context, the performance of four different radar and sonar systems – a 40 kHz sonar, a 5.8 GHz wireless pulsed Doppler radar mote, a 10 GHz X-band continuous wave (CW) radar, and a 24 GHz CW radar – is evaluated using a broad range of features. Performance improvements using feature selection is addressed as well as the impact on performance of sensor placement and potential occlusion due to household objects. Results show that nearly 80% correct classification can be achieved with 10 s observations from the 24 GHz CW radar, whereas 86% performance can be achieved with 5 s observations of sonar

Tensorial dynamics on the space of quantum states

A geometric description of the space of states of a finite-dimensional quantum system and of the Markovian evolution associated with the Kossakowski-Lindblad operator is presented. This geometric setting is based on two composition laws on the space of observables defined by a pair of contravariant tensor fields. The first one is a Poisson tensor field that encodes the commutator product and allows us to develop a Hamiltonian mechanics. The other tensor field is symmetric, encodes the Jordan product and provides the variances and covariances of measures associated with the observables. This tensorial formulation of quantum systems is able to describe, in a natural way, the Markovian dynamical evolution as a vector field on the space of states. Therefore, it is possible to consider dynamical effects on non-linear physical quantities, such as entropies, purity and concurrence. In particular, in this work the tensorial formulation is used to consider the dynamical evolution of the symmetric and skew-symmetric tensors and to read off the corresponding limits as giving rise to a contraction of the initial Jordan and Lie products.Comment: 31 pages, 2 figures. Minor correction

Tangent bundle geometry from dynamics: application to the Kepler problem

In this paper we consider a manifold with a dynamical vector field and inquire about the possible tangent bundle structures which would turn the starting vector field into a second order one. The analysis is restricted to manifolds which are diffeomorphic with affine spaces. In particular, we consider the problem in connection with conformal vector fields of second order and apply the procedure to vector fields conformally related with the harmonic oscillator (f-oscillators) . We select one which covers the vector field describing the Kepler problem.Comment: 17 pages, 2 figure

Discrete port-Hamiltonian systems: mixed interconnections

Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling at the discrete level itself. The goal of this paper is to apply a previously developed discrete modeling technique to study the interconnection of continuous systems with discrete ones in such a way that passivity is preserved. Such a theory has potential applications, in the field of haptics, telemanipulation etc. It is shown that our discrete modeling theory can be used to formalize previously developed techniques for obtaining passive interconnections of continuous and discrete systems