Related papers: Combinatorial dynamics in quantum gravity
Quantum gravity may shed light on the prehistory of the universe. Quantum corrections to gravity affect the dynamics of the expansion of the universe. Their influence is studied on the example of the exactly solvable quantum model. The…
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…
Recently Gambini and Pullin proposed a new consistent discrete approach to quantum gravity and applied it to cosmological models. One remarkable result of this approach is that the cosmological singularity can be avoided in a general…
We describe the construction of quantum gravity, i.e. of a theory of self-interacting massless spin-2 quantum gauge fields, the gravitons, on flat space-time, in the framework of causal perturbation theory.
In quantum systems with many degrees of freedom the replica method is a useful tool to study the entanglement of arbitrary spatial regions. We apply it in a way which allows them to back-react. As a consequence, they become dynamical…
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…
Previous work has shown that the macroscopic structure of the theory of quantum gravity defined by causal dynamical triangulations (CDT) is compatible with that of a de Sitter universe. After emphasizing the strictly nonperturbative nature…
It is argued that some approaches to non-perturbative quantum general relativity lack a sensible continuum limit that reproduces general relativity. The basic problem is that generic physical states lack long ranged correlations, because…
The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years,…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
In this short article we introduce the mathematical framework of the principle of the fermionic projector and set up a variational principle in discrete space-time. The underlying physical principles are discussed. We outline the connection…
I briefly review the current status of quantum gravity. After giving some general motivations for the need of such a theory, I discuss the main approaches in quantizing general relativity: Covariant approaches (perturbation theory,…
We review and extend the recently proposed model of combinatorial quantum gravity. Contrary to previous discrete approaches, this model is defined on (regular) random graphs and is driven by a purely combinatorial version of Ricci…
Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear…
In this review, we study some aspects of the non-equilibrium dynamics of quantum systems. In particular, we consider the effect of varying a parameter in the Hamiltonian of a quantum system which takes it across a quantum critical point or…
Within the framework of loop quantum cosmology, there exists a semi-classical regime where spacetime may be approximated in terms of a continuous manifold, but where the standard Friedmann equations of classical Einstein gravity receive…
We have computed the low energy quantum states and low frequency dynamical susceptibility of complex quantum spin systems in the limit of strong interactions, obtaining exact results for system sizes enormously larger than accessible…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…
The construction of a continuum limit for the dynamics of loop quantum gravity is unavoidable to complete the theory. We explain that such a construction is equivalent to obtaining the continuum physical Hilbert space, which encodes the…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…