Ricci flow, quantum mechanics and gravity

It has been argued that, underlying any given quantum-mechanical model, there exists at least one deterministic system that reproduces, after prequantisation, the given quantum dynamics. For a quantum mechanics with a complex d-dimensional Hilbert space, the Lie group SU(d) represents classical canonical transformations on the projective space CP^{d-1} of quantum states. Let R stand for the Ricci flow of the manifold SU(d-1) down to one point, and let P denote the projection from the Hopf bundle onto its base CP^{d-1}. Then the underlying deterministic model we propose here is the Lie group SU(d), acted on by the operation PR. Finally we comment on some possible consequences that our model may have on a quantum theory of gravity.Comment: 8 page

Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe

Effects of the environment on galaxies in the Catalogue of Isolated Galaxies: physical satellites and large scale structure

We aim to identify and quantify the effects of the satellite distribution around a sample of galaxies in the Catalogue of Isolated Galaxies (CIG), as well as the effects of the Large Scale Structure (LSS) using the SDSS-DR9. To recover the physically bound galaxies we focus on the satellites which are within the escape speed of each CIG galaxy. We also propose a more conservative method using the stacked Gaussian distribution of the velocity difference of the neighbours. The tidal strengths affecting the primary galaxy are estimated to quantify the effects of the local and LSS environments. We also define the projected number density parameter at the 5$^{\rm th}$ nearest neighbour to characterise the LSS around the CIG galaxies. Out of the 386 CIG galaxies considered in this study, at least 340 (88\% of the sample) have no physically linked satellite. Out of the 386 CIG galaxies, 327 (85\% of the sample) have no physical companion within a projected distance of 0.3 Mpc. The CIG galaxies are distributed following the LSS of the local Universe, although presenting a large heterogeneity in their degree of connection with it. A clear segregation appears between early-type CIG galaxies with companions and isolated late-type CIG galaxies. Isolated galaxies are in general bluer, with likely younger stellar populations and rather high star formation with respect to older, redder CIG galaxies with companions. Reciprocally, the satellites are redder and with an older stellar populations around massive early-type CIG galaxies, while they have a younger stellar content around massive late-type CIG galaxies. This suggests that the CIG is composed of a heterogeneous population of galaxies, sampling from old to more recent, dynamical systems of galaxies.Comment: 19 pages, 10 figures, 1 table, accepted for publication in Astronomy & Astrophysic

Model category structures and spectral sequences

Let R be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of R-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a quasi-isomorphism at a certain fixed stage of the associated spectral sequence. For filtered complexes, we relate the different model structures obtained, when we vary the stage of the spectral sequence, using the functors shift and décalage

Pairing in cuprates from high energy electronic states

The in-plane optical conductivity of Bi2Sr2CaCu2O8+d thin films with small carrier density (underdoped) up to large carrier density (overdoped) is analyzed with unprecedented accuracy. Integrating the conductivity up to increasingly higher energies points to the energy scale involved when the superfluid condensate builds up. In the underdoped sample, states extending up to 2 eV contribute to the superfluid. This anomalously large energy scale may be assigned to a change of in-plane kinetic energy at the superconducting transition, and is compatible with an electronic pairing mechanism.Comment: 11 pages, 3 figure