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

Tensorial characterization and quantum estimation of weakly entangled qubits

In the case of two qubits, standard entanglement monotones like the linear entropy fail to provide an efficient quantum estimation in the regime of weak entanglement. In this paper, a more efficient entanglement estimation, by means of a novel class of entanglement monotones, is proposed. Following an approach based on the geometric formulation of quantum mechanics, these entanglement monotones are defined by inner products on invariant tensor fields on bipartite qubit orbits of the group SU(2)xSU(2).Comment: 23 pages, 3 figure

Homeobox genes in normal and abnormal vasculogenesis

Homeobox containing genes are a family of transcription factors regulating normal development and controlling primary cellular processes (cell identity, cell division and differentiation) recently enriched by the discovery of their interaction with miRNAs and ncRNAs. Class I human homeobox genes (HOX genes) are characterized by a unique genomic network organization: four compact chromosomal loci where 39 sequence corresponding genes can be aligned with each other in 13 antero-posterior paralogous groups. The cardiovascular system is the first mesoderm organ-system to be generated during embryonic development; subsequently it generates the blood and lymphatic vascular systems. Cardiovascular remodelling is involved through homeobox gene regulation and deregulation in adult physiology (menstrual cycle and wound healing) and pathology (atherosclerosis, arterial restenosis, tumour angiogenesis and lymphangiogenesis). Understanding the role played by homeobox genes in endothelial and smooth muscle cell phenotype determination will be crucial in identifying the molecular processes involved in vascular cell differentiation, as well as to support future therapeutic strategies. We report here on the current knowledge of the role played by homeobox genes in normal and abnormal vasculogenesis and postulate a common molecular mechanism accounting for the involvement of homeobox genes in the regulation of the nuclear export of specific transcripts potentially capable of generating endothelial phenotype modification involved in new vessel formation

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

Classical Tensors and Quantum Entanglement I: Pure States

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.Comment: 16 pages, 1 figure, to appear in Int. J. Geom. Meth. Mod. Phy

Teachers’ Agreement and Manifestation of Educational Philosophies

This study sets forth the philosophical frameworks of teachers in the teaching-learning process. The descriptive-correlational research design was utilized in determining the teachers’ extent of agreement and extent of manifestation of educational philosophies. It is revealed in this study that the respondents have very strong agreement and manifestation of the philosophy of idealism; with no significant difference in their agreement and manifestation of the idealism and existentialism, while with significant difference in realism and pragmatism as regards sex, while no significant difference in all the four philosophies with reference to age, civil status, and along seminar, trainings, and workshops. On the other hand, there is a significant relationship between the teacher’s extent of agreement and extent of their pedagogical manifestation in all the four philosophies of education along teacher’s role, teaching strategies, classroom management, and curriculu