1,608 research outputs found
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 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
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