arXiv subjects

Djamel Dou

Publications and source records attributed to Djamel Dou.

8 recordsLinked to original sources

arXiv2023

On Horizon Molecules and Entropy in Causal Sets

We review the different proposals and attempts to identify the ``horizon molecules" that would give a kinematical estimation for the black hole entropy in causal set theory. The proposals are presented according to their chronological appearance in scientific literature. The review is neither very technical nor merely descriptive; it is aimed to provide the reader with a lucid introduction to the necessary concepts and mathematical background, and give him or her a broad view on the subject, by focusing on the main technical and conceptual issues that summarize the progress made in the last two decades.

gr-qc↗

arXiv2020

Green's Function Approach to Entanglement Entropy on Lattices and Fuzzy Spaces

We develop a Green's function approach to compute Rényi entanglement entropy on lattices and fuzzy spaces. The Rényi entropy resulting from tracing out an arbitrary collection of subsets of coupled harmonic oscillators is written as zero temperature partition function generated by an Euclidean action with $n$-fold step potential. The associated Green's function is explicitly constructed and an alternative new formula for the Rényi entropy is obtained. Finally it is outlined how this approach can be used to go beyond the gaussian state and include interaction by writing a perturbative expansion for the entanglement entropy .

hep-th↗

arXiv2017

Comment on "Quantum Raychaudhuri equation"

We address the validity of the formalism and results presented in [ S. Das, Phys. Rev. {\bf D89} 084068 (2014)] with regard to quantum Raychaudhuri equation. The author obtained the so called quantum Raychaudhuri equation by replacing classical geodesics with quantal trajectories arising from Bhommian mechanics. The resulting modified equation was used to draw some conclusions about the inevitability of focussing and the formation of conjugate points and therefore singularity. We show that the whole procedure is full of problematic points, on both physical relevancy and mathematical correctness. In particular, we illustrate the problems associated with the technical derivation of the so called quantum Raychaudhuri equation, as well as its invalid physical implications.

gr-qc↗

arXiv2009

Comments on the Entanglement Entropy on Fuzzy Spaces

We locate the relevant degrees of freedom for the entanglement entropy on some 2+1 fuzzy models. It is found that the entropy is stored in the near boundary degrees of freedom. We give a simple analytical derivation for the area law using $1/N$ like expansion when only the near boundary degrees of freedom are incorporated. Numerical and qualitative evidences for the validity of near boundary approximation are finally given .

gr-qc↗

arXiv2009

The Running Gravitational Couplings

We compute the running of the cosmological constant and Newton's constant taking into account the effect of quantum fields with any spin between 0 and 2. We find that Newton's constant does not vary appreciably but the cosmological constant can change by many orders of magnitude when one goes from cosmological scales to typical elementary particle scales. In the extreme infrared, zero modes drive the cosmological constant to zero.

hep-th↗

arXiv2007

Topology Change From Quantum Instability of Gauge Theory on Fuzzy CP^2

Many gauge theory models on fuzzy complex projective spaces will contain a strong instability in the quantum field theory leading to topology change. This can be thought of as due to the interaction between spacetime via its noncommutativity and the fields (matrices) and it is related to the perturbative UV-IR mixing. We work out in detail the example of fuzzy CP^2 and discuss at the level of the phase diagram the quantum transitions between the 3 spaces (spacetimes) CP^2, S^2 and the 0-dimensional space consisting of a single point {0}.

hep-th↗

arXiv2006

Entanglement Entropy on Fuzzy Spaces

We study the entanglement entropy of a scalar filed in 2+1 spacetime where space is modeled by a fuzzy sphere and a fuzzy disc. In both models we evaluate numerically the resulting entropies and find that they are proportional to the number of boundary degrees of freedom. In the Moyal plan limit of the fuzzy disc the entanglement entropy per unit area (length) diverges if the ignored region is of infinite size. The divergence is (interpreted) of IR-UV mixing origin. In general we expect the entanglement entropy per unit area to be finite on a non-commutative space if the ignored region is of finite size.

gr-qc↗

arXiv2003

Black Hole Entropy as Causal Links

We model a black hole spacetime as a causal set and count, with a certain definition, the number of causal links crossing the horizon in proximity to a spacelike or null hypersurface $\Sigma$. We find that this number is proportional to the horizon's area on $\Sigma $, thus supporting the interpretation of the links as the ``horizon atoms'' that account for its entropy. The cases studied include not only equilibrium black holes but ones far from equilibrium.

gr-qc↗