Related papers: A Geometric Renormalisation Group in Discrete Quan…
Noncommutative spacetimes are widely believed to model some properties of the quantum structure of spacetime at the Planck regime. In this contribution the construction of (anti-)de Sitter noncommutative spacetimes obtained through quantum…
Time-dependent renormalization was employed to derive a nonlinear quantum master equation (QME), in which the dynamics of a non-equilibrium fluctuation in an irrelevant system are fed back into that of a relevant one. In terms of…
We analyze two models of random geometries~: planar hyper-cubic random surfaces and four dimensional simplicial quantum gravity. We show for the hyper-cubic random surface model that a geometrical constraint does not change the critical…
In this paper, we consider a renormalization group perspective on the quantum dynamics of a particle moving in the Euclidean $\mathbb{R}^N$ space through the complex landscape provided by a disordered Hamiltonian of type $2+p$. We focus on…
This is an introduction for nonspecialists to the noncommutative geometric approach to Planck scale physics coming out of quantum groups. The canonical role of the `Planck scale quantum group' $C[x]\bicross C[p]$ and its observable-state…
We have analysed here the role of the geometric phase in dynamical mechanism of quantum phase transition in the transverse Ising model. We have investigated the system when it is driven at a fixed rate characterized by a quench time…
Lattice regularization is a standard technique for the nonperturbative definition of a quantum theory of fields. Several approaches to the construction of a quantum theory of gravity adopt this technique either explicitly or implicitly. A…
After a brief review of spin networks and their interpretation as wave functions for the (space) geometry, we discuss the renormalisation of the area operator in loop quantum gravity. In such a background independent framework, we propose…
Results that illuminate the physical interpretation of states of nonperturbative quantum gravity are obtained using the recently introduced loop variables. It is shown that: i) While local operators such as the metric at a point may not be…
We assume that space-time at the Planck scale is discrete, quantised in Planck units and "qubitsed" (each pixel of Planck area encodes one qubit), that is, quantum space-time can be viewed as a quantum computer. Within this model, one finds…
Quantum renormalization group scheme provides a microscopic understanding of holography through a general mapping between the beta functions of underlying quantum field theories and the holographic actions in the bulk. We show that the…
While renormalization groups are fundamental in physics, renormalization of complex networks remains vague in its conceptual definition and methodology. Here, we propose a novel strategy to renormalize complex networks. Rather than…
The functional renormalisation group is employed to study the non-linear regime of late-time cosmic structure formation. This framework naturally allows for non-perturbative approximation schemes, usually guided by underlying symmetries or…
We extend the Hertz-Millis theory of quantum phase transitions in itinerant electron systems to phases with broken discrete symmetry. Using a set of coupled flow equations derived within the functional renormalization group framework, we…
Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…
We investigate the effects of Quantum Gravity on the Planck era of the universe. In particular, using different versions of the Generalized Uncertainty Principle and under specific conditions we find that the main Planck quantities such as…
The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the…
We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…
Diverse theories of Quantum Gravity expect modification of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle.It was shown by some authors that the Generalized uncertainty principle…
Quantum graphs model processes in complex systems represented as spatial networks in various fields of natural science and technology. An example is the oscillations of elastic string networks, the nodes of which, besides the continuity…