- Complex Systems researcheredit
In this paper we construct a methodology for separating the divergencies due to different topological manifolds dual to Feynman graphs in colored group field theory. After having introduced the amplitude bounds using propagator cuts, we... more
In this paper we construct a methodology for separating the divergencies due to different topological manifolds dual to Feynman graphs in colored group field theory. After having introduced the amplitude bounds using propagator cuts, we show how Graph-Encoded-Manifolds (GEM) techniques can be used in order to factorize divergencies related to different parts of the dual topologies of the Feynman graphs in the general case. We show the potential of the formalism in the case of 3-dimensional solid torii in the colored Boulatov model.
In this short note we use results from the theory of crystallizations to prove that color in group field theories garantees orientability of the piecewise linear pseudo-manifolds associated to each graph generated perturbatively. The... more
In this short note we use results from the theory of crystallizations to prove that color in group field theories garantees orientability of the piecewise linear pseudo-manifolds associated to each graph generated perturbatively. The origin of orientability is the presence of two interaction vertices.
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We show that after a quantum quench of the parameter controlling the number of particles in a Fermi-Hubbard model on scale free graphs, the distribution of energy modes follows a power law dependent on the quenched parameter and the... more
We show that after a quantum quench of the parameter controlling the number of particles in a Fermi-Hubbard model on scale free graphs, the distribution of energy modes follows a power law dependent on the quenched parameter and the connectivity of the graph.
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We present a mapping of dynamical graphs and, in particular, the graphs used in the Quantum Graphity models for emergent geometry, into an Ising hamiltonian on the line graph of a complete graph with a fixed number of vertices. We use... more
We present a mapping of dynamical graphs and, in particular, the graphs used in the Quantum Graphity models for emergent geometry, into an Ising hamiltonian on the line graph of a complete graph with a fixed number of vertices. We use this method to study the properties of Quantum Graphity models at low temperature in the limit in which the valence coupling constant of the model is much greater than the coupling constants of the loop terms. Using mean field theory we find that an order parameter for the model is the average valence of the graph. We calculate the equilibrium distribution for the valence as an implicit function of the temperature. In the approximation in which the temperature is low, we find the first two Taylor coefficients of the valence in the temperature expansion. A discussion of the susceptibility function and a generalization of the model are given in the end.
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In this paper we perform the calculation of the spectral dimension of the space-time in 3d quantum gravity using the dynamics of the Ponzano-Regge vertex (PR) and its quantum group generalization (Turaev-Viro model (TV)). We realize this... more
In this paper we perform the calculation of the spectral dimension of the space-time in 3d quantum gravity using the dynamics of the Ponzano-Regge vertex (PR) and its quantum group generalization (Turaev-Viro model (TV)). We realize this considering a very simple decomposition of the 3d space-time and introducing a boundary state which selects a classical geometry on the boundary. We obtain that the spectral dimension of the space-time runs from 2 to 3, across a 1.5 phase, when the energy of a probe scalar field decreases from high to low energy. For the TV model the spectral dimension at hight energy increase with the value of the cosmological constant. At low energy the presence of the cosmological constant does not change the spectral dimension.
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Recently, two of us have argued that non-Kerr black holes in gravity theories different from General Relativity may have a topologically non-trivial event horizon. More precisely, the spatial topology of the horizon of non-rotating and... more
Recently, two of us have argued that non-Kerr black holes in gravity theories different from General Relativity may have a topologically non-trivial event horizon. More precisely, the spatial topology of the horizon of non-rotating and slow-rotating objects would be a 2-sphere, like in Kerr space-time, while it would change above a critical value of the spin parameter. When the topology of the horizon changes, the black hole central singularity shows up. The accretion process from a thin disk can potentially overspin these black holes and induce the topology transition, violating the Weak Cosmic Censorship Conjecture. If the astrophysical black hole candidates are not the black holes predicted by General Relativity, we might have the quite unique opportunity to see their central region, where classical physics breaks down and quantum gravity effects should appear. Even if the quantum gravity region turned out to be extremely small, at the level of the Planck scale, the size of its apparent image would be finite and potentially observable with future facilities.
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Many realistic networks are scale-free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes... more
Many realistic networks are scale-free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes place. However, this mechanism is non-local, in the sense that it requires knowledge of the whole graph in order for the graph to be updated. Instead, if preferential attachment and realistic networks occur in physical systems, these features need to emerge from a local model. In this paper, we propose a local model and show that a possible ingredient (which is often underrated) for obtaining scale-free networks with local rules is memory. Such a model can be realised in solid-state circuits, using non-linear passive elements with memory such as memristors, and thus can be tested experimentally.
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We present a toy model for interacting matter and geometry that explores quantum dynamics in a spin system as a precursor to a quantum theory of gravity. The model has no a priori geometric properties; instead, locality is inferred from... more
We present a toy model for interacting matter and geometry that explores quantum dynamics in a spin system as a precursor to a quantum theory of gravity. The model has no a priori geometric properties; instead, locality is inferred from the more fundamental notion of interaction between the matter degrees of freedom. The interaction terms are themselves quantum degrees of freedom so that the structure of interactions and hence the resulting local and causal structures are dynamical. The system is a Hubbard model where the graph of the interactions is a set of quantum evolving variables. We show entanglement between spatial and matter degrees of freedom. We study numerically the quantum system and analyze its entanglement dynamics. We analyze the asymptotic behavior of the classical model. Finally, we discuss analogues of trapped surfaces and gravitational attraction in this simple model.
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In this paper we construct four Kerr-like spacetimes starting from the loop black hole Schwarzschild solutions (LBH) and applying the Newman-Janis transformation. In previous papers the Schwarzschild LBH was obtained replacing the... more
In this paper we construct four Kerr-like spacetimes starting from the loop black hole Schwarzschild solutions (LBH) and applying the Newman-Janis transformation. In previous papers the Schwarzschild LBH was obtained replacing the Ashtekar connection with holonomies on a particular graph in a minisuperspace approximation which describes the black hole interior. Starting from this solution, we use a Newman-Janis transformation and we specialize to two different and natural complexifications inspired from the complexifications of the Schwarzschild and Reissner-Nordstrom metrics. We show explicitly that the space-times obtained in this way are singularity free and thus there are no naked singularities. We show that the transformation move, if any, the causality violating regions of the Kerr metric far from r=0. We study the space-time structure with particular attention to the horizons shape. We conclude the paper with a discussion on a regular Reissner-Nordstrom black hole derived from the Schwarzschild LBH and then applying again the Newmann-Janis transformation.
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Using the Wald's relation between the Noether charge of diffeomorphisms and the entropy for a generic spacetime possessing a bifurcation surface, we introduce a method to obtain a family of higher order derivatives effective actions from... more
Using the Wald's relation between the Noether charge of diffeomorphisms and the entropy for a generic spacetime possessing a bifurcation surface, we introduce a method to obtain a family of higher order derivatives effective actions from the entropy of black holes. Our point of view is to consider fundamental the black hole entropy and the action an emerged object. We then specialize to a particular class of effective theories: the f(R) theories. We apply the idea, using a simple mind ansatz, to loop quantum gravity and to a general class of log-corrected entropy formulas.