56 research outputs found
Diffusion in Curved Spacetimes
Using simple kinematical arguments, we derive the Fokker-Planck equation for
diffusion processes in curved spacetimes. In the case of Brownian motion, it
coincides with Eckart's relativistic heat equation (albeit in a simpler form),
and therefore provides a microscopic justification for his phenomenological
heat-flux ansatz. Furthermore, we obtain the small-time asymptotic expansion of
the mean square displacement of Brownian motion in static spacetimes. Beyond
general relativity itself, this result has potential applications in analogue
gravitational systems.Comment: 14 pages, substantially revised versio
Holonomy observables in Ponzano-Regge type state sum models
We study observables on group elements in the Ponzano-Regge model. We show
that these observables have a natural interpretation in terms of Feynman
diagrams on a sphere and contrast them to the well studied observables on the
spin labels. We elucidate this interpretation by showing how they arise from
the no-gravity limit of the Turaev-Viro model and Chern-Simons theory.Comment: 15 pages, 2 figure
Critical connectivity in banking networks
The financial crisis of 2007-2009 demonstrated the need to understand the macrodynamics of interconnected financial systems. A fruitful approach to this problem regards financial infrastructures as weighted directed networks, with banks as nodes and loans as links. Using a simple banking model in which banks are linked through interbank lending, with an exogenous shock applied to a single bank, we find a closedform analytical solution for the degree at which failures begin to propagate in the network. This critical degree is expressed as a function of four financial parameters: banking leverage; interbank exposure; return on the investment opportunity; and interbank lending rate. While the transition to failure propagation is sharpest with regular networks, we observe it numerically for random and scale-free networks as well. We find that, if the expected number of failures is not strongly dependent on the network topology and is well captured by the notion of critical degree, the frequency of catastrophic cascades (with a single shock inducing all or most banks in the network to fail) tends to be much larger on scale-free networks than on classical random networks. We interpret this finding as a manifestation of the “robust-yet-fragile” property of scale-free networks
Super-Group Field Cosmology
In this paper we construct a model for group field cosmology. The classical
equations of motion for the non-interactive part of this model generate the
Hamiltonian constraint of loop quantum gravity for a homogeneous isotropic
universe filled with a scalar matter field. The interactions represent topology
changing processes that occurs due to joining and splitting of universes. These
universes in the multiverse are assumed to obey both bosonic and fermionic
statistics, and so a supersymmetric multiverse is constructed using superspace
formalism. We also introduce gauge symmetry in this model. The supersymmetry
and gauge symmetry are introduced at the level of third quantized fields, and
not the second quantized ones. This is the first time that supersymmetry has
been discussed at the level of third quantized fields.Comment: 14 pages, 0 figures, accepted for publication in Class. Quant. Gra
Bubble divergences from cellular cohomology
We consider a class of lattice topological field theories, among which are
the weak-coupling limit of 2d Yang-Mills theory, the Ponzano-Regge model of 3d
quantum gravity and discrete BF theory, whose dynamical variables are flat
discrete connections with compact structure group on a cell 2-complex. In these
models, it is known that the path integral measure is ill-defined in general,
because of a phenomenon called `bubble divergences'. A common expectation is
that the degree of these divergences is given by the number of `bubbles' of the
2-complex. In this note, we show that this expectation, although not realistic
in general, is met in some special cases: when the 2-complex is simply
connected, or when the structure group is Abelian -- in both cases, the
divergence degree is given by the second Betti number of the 2-complex.Comment: 5 page
Cosmological quantum entanglement
We review recent literature on the connection between quantum entanglement
and cosmology, with an emphasis on the context of expanding universes. We
discuss recent theoretical results reporting on the production of entanglement
in quantum fields due to the expansion of the underlying spacetime. We explore
how these results are affected by the statistics of the field (bosonic or
fermionic), the type of expansion (de Sitter or asymptotically stationary), and
the coupling to spacetime curvature (conformal or minimal). We then consider
the extraction of entanglement from a quantum field by coupling to local
detectors and how this procedure can be used to distinguish curvature from
heating by their entanglement signature. We review the role played by quantum
fluctuations in the early universe in nucleating the formation of galaxies and
other cosmic structures through their conversion into classical density
anisotropies during and after inflation. We report on current literature
attempting to account for this transition in a rigorous way and discuss the
importance of entanglement and decoherence in this process. We conclude with
some prospects for further theoretical and experimental research in this area.
These include extensions of current theoretical efforts, possible future
observational pursuits, and experimental analogues that emulate these cosmic
effects in a laboratory setting.Comment: 23 pages, 2 figures. v2 Added journal reference and minor changes to
match the published versio
Degenerate Plebanski Sector and Spin Foam Quantization
We show that the degenerate sector of Spin(4) Plebanski formulation of
four-dimensional gravity is exactly solvable and describes covariantly embedded
SU(2) BF theory. This fact ensures that its spin foam quantization is given by
the SU(2) Crane-Yetter model and allows to test various approaches of imposing
the simplicity constraints. Our analysis strongly suggests that restricting
representations and intertwiners in the state sum for Spin(4) BF theory is not
sufficient to get the correct vertex amplitude. Instead, for a general theory
of Plebanski type, we propose a quantization procedure which is by construction
equivalent to the canonical path integral quantization and, being applied to
our model, reproduces the SU(2) Crane-Yetter state sum. A characteristic
feature of this procedure is the use of secondary second class constraints on
an equal footing with the primary simplicity constraints, which leads to a new
formula for the vertex amplitude.Comment: 34 pages; changes in the abstract and introduction, a few references
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Relational EPR
We study the EPR-type correlations from the perspective of the relational
interpretation of quantum mechanics. We argue that these correlations do not
entail any form of 'non-locality', when viewed in the context of this
interpretation. The abandonment of strict Einstein realism implied by the
relational stance permits to reconcile quantum mechanics, completeness,
(operationally defined) separability, and locality.Comment: Revised, published versio
Non-local Realistic Theories and the Scope of the Bell Theorem
According to a widespread view, the Bell theorem establishes the untenability
of so-called 'local realism'. On the basis of this view, recent proposals by
Leggett, Zeilinger and others have been developed according to which it can be
proved that even some non-local realistic theories have to be ruled out. As a
consequence, within this view the Bell theorem allows one to establish that no
reasonable form of realism, be it local or non-local, can be made compatible
with the (experimentally tested) predictions of quantum mechanics. In the
present paper it is argued that the Bell theorem has demonstrably nothing to do
with the 'realism' as defined by these authors and that, as a consequence,
their conclusions about the foundational significance of the Bell theorem are
unjustified.Comment: Forthcoming in Foundations of Physic
Euclidean three-point function in loop and perturbative gravity
We compute the leading order of the three-point function in loop quantum
gravity, using the vertex expansion of the Euclidean version of the new spin
foam dynamics, in the region of gamma<1. We find results consistent with Regge
calculus in the limit gamma->0 and j->infinity. We also compute the tree-level
three-point function of perturbative quantum general relativity in position
space, and discuss the possibility of directly comparing the two results.Comment: 16 page
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