120 research outputs found

### Where do bosons actually belong?

We explore a variety of reasons for considering su(1,1) instead of the
customary h(1) as the natural unifying frame for characterizing boson systems.
Resorting to the Lie-Hopf structure of these algebras, that shows how the
Bose-Einstein statistics for identical bosons is correctly given in the su(1,1)
framework, we prove that quantization of Maxwell's equations leads to su(1,1),
relativistic covariance being naturally recognized as an internal symmetry of
this dynamical algebra. Moreover su(1,1) rather than h(1) coordinates are
associated to circularly polarized electromagnetic waves. As for interacting
bosons, the su(1,1) formulation of the Jaynes-Cummings model is discussed,
showing its advantages over h(1).Comment: 9 pages, to appear in J. Phys. A: Math. Theo

### Spin network setting of topological quantum computation

The spin network simulator model represents a bridge between (generalised)
circuit schemes for standard quantum computation and approaches based on
notions from Topological Quantum Field Theories (TQFTs). The key tool is
provided by the fiber space structure underlying the model which exhibits
combinatorial properties closely related to SU(2) state sum models, widely
employed in discretizing TQFTs and quantum gravity in low spacetime dimensions.Comment: Proc. "Foundations of Quantum Information", Camerino (Italy), 16-19
April 2004, to be published in Int. J. of Quantum Informatio

### Entropy estimates for Simplicial Quantum Gravity

Through techniques of controlled topology we determine the entropy function characterizing the distribution of combinatorially inequivalent metric ball coverings of n-dimensional manifolds of bounded geometry for every n â‰Ą 2. Such functions control the asymptotic distribution of dynamical triangulations of the corresponding n-dimensional (pseudo)manifolds M of bounded geometry. They have an exponential leading behavior determined by the Reidemeister-Franz torsion associated with orthogonal representations of the fundamental group of the manifold. The subleading terms are instead controlled by the Euler characteristic of M. Such results are either consistent with the known asymptotics of dynamically triangulated two-dimensional surfaces, or with the numerical evidence supporting an exponential leading behavior for the number of inequivalent dynamical triangulations on three- and four-dimensional manifolds

### Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials

Eigenvalues and eigenfunctions of the volume operator, associated with the
symmetric coupling of three SU(2) angular momentum operators, can be analyzed
on the basis of a discrete Schroedinger-like equation which provides a
semiclassical Hamiltonian picture of the evolution of a `quantum of space', as
shown by the authors in a recent paper. Emphasis is given here to the
formalization in terms of a quadratic symmetry algebra and its automorphism
group. This view is related to the Askey scheme, the hierarchical structure
which includes all hypergeometric polynomials of one (discrete or continuous)
variable. Key tool for this comparative analysis is the duality operation
defined on the generators of the quadratic algebra and suitably extended to the
various families of overlap functions (generalized recoupling coefficients).
These families, recognized as lying at the top level of the Askey scheme, are
classified and a few limiting cases are addressed.Comment: 10 pages, talk given at "Physics and Mathematics of Nonlinear
Phenomena" (PMNP2013), to appear in J. Phys. Conf. Serie

### The geometry of dynamical triangulations

We discuss the geometry of dynamical triangulations associated with
3-dimensional and 4-dimensional simplicial quantum gravity. We provide
analytical expressions for the canonical partition function in both cases, and
study its large volume behavior. In the space of the coupling constants of the
theory, we characterize the infinite volume line and the associated critical
points. The results of this analysis are found to be in excellent agreement
with the MonteCarlo simulations of simplicial quantum gravity. In particular,
we provide an analytical proof that simply-connected dynamically triangulated
4-manifolds undergo a higher order phase transition at a value of the inverse
gravitational coupling given by 1.387, and that the nature of this transition
can be concealed by a bystable behavior. A similar analysis in the
3-dimensional case characterizes a value of the critical coupling (3.845) at
which hysteresis effects are present.Comment: 166 pages, Revtex (latex) fil

### Combinatorial and topological phase structure of non-perturbative n-dimensional quantum gravity

We provide a non-perturbative geometrical characterization of the partition
function of $n$-dimensional quantum gravity based on a coarse classification of
riemannian geometries. We show that, under natural geometrical constraints, the
theory admits a continuum limit with a non-trivial phase structure parametrized
by the homotopy types of the class of manifolds considered. The results
obtained qualitatively coincide, when specialized to dimension two, with those
of two-dimensional quantum gravity models based on random triangulations of
surfaces.Comment: 13 page

### Using Ground Transportation for Aviation System Disruption Alleviation

An investigation was made into whether passenger delays and airline costs due to disruptive events affecting European airports could be reduced by a coordinated strategy of using alternative flights and ground transportation to help stranded passengers reach their final destination using airport collaborative decision-making concepts. Optimizing for airline cost for hypothetical disruptive events suggests that, for airport closures of up to 10 h, airlines could benefit from up to a 20% reduction in passenger delay-related costs. The mean passenger delay could be reduced by up to 70%, mainly via a reduction in very long delays

### Implementing holographic projections in Ponzano--Regge gravity

We consider the path-sum of Ponzano-Regge with additional boundary
contributions in the context of the holographic principle of Quantum Gravity.
We calculate an holographic projection in which the bulk partition function
goes to a semi-classical limit while the boundary state functional remains
quantum-mechanical. The properties of the resulting boundary theory are
discussed.Comment: 20 pages, late

- â€¦