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A. Rahmani

Publications and source records attributed to A. Rahmani.

10 recordsLinked to original sources
arXiv2021

Multi-dimensional $ρ$-almost periodic type functions and applications

In this paper, we analyze various classes of multi-dimensional $ρ$-almost periodic type functions $F : I \times X \rightarrow Y$ and multi-dimensional $(ω,ρ)$-almost periodic type functions $F : I \times X \rightarrow Y,$ where $n\in {\mathbb N},$ $\emptyset \neq I \subseteq {\mathbb R}^{n},$ $X$ and $Y$ are complex Banach spaces and $ρ$ is a binary relation on $Y.$ The proposed notion is new even in the one-dimensional setting, for the functions of the form $F : I \rightarrow Y.$ The main structural properties and characterizations for the introduced classes of functions are presented. We provide certain applications of our theoretical results to the abstract Volterra integro-differential equations, as well.

math.FA↗
arXiv2020

Final state of instabilities in Born-Infeld black holes

We study two types of linear instabilities in Einstein-Born-Infeld-scalar field theory and show that small Born-Infeld (BI) black holes suffer from superradiant instability within a particular range of frequencies; the larger the BI coupling parameter, the slower the growth rate of the instability. It is predicted that a small BI black hole decays into a small hairy black hole that has a charged scalar condensate floating near the horizon. We numerically show that there is a phase transition between hairy and BI black holes. The metric solution shows the existence of a hairy black hole for $T T_{c}$. In addition, the BI black hole will suffer from tachyonic mass, resulting in a near horizon scalar condensation instability, which is related to a planar hairy black hole. We show that the BI coupling parameter has a direct relation to the critical temperature in the small hairy black hole framework. This is not true for planar hairy black holes where a larger BI coupling parameter leads to a smaller critical temperature. Finally, it is shown that a small hairy black hole is stable at the critical temperature so it can be considered as the end point of superradiant instability.

gr-qc↗
arXiv2020

Superradiant instability and asymptotically AdS hairy black holes in $F(R)$-charged scalar field theory

We study the phenomena of superradiance for $F(R)$-Maxwell black holes in an AdS space-time. The AdS boundary plays the role of a mirror and provides a natural confining system that makes the superradiant waves bouncing back and forth between the region near the horizon and the reflective boundary, causing a possible superradiant instability. We obtain numerical solutions for static hairy black holes in this scenario and investigate their instability and explicitly address the stability of such solutions for spherical perturbations under specific conditions for the scalar charge and AdS radius. It is shown that for a small scalar charge or AdS radius the static hairy solution is stable under spherical perturbations. We conclude that under such conditions, new hairy black holes emerge as a possible endpoint of superradiant instability of the system.

gr-qc↗
arXiv2020

$c$-Almost periodic type functions and applications

In this paper, we introduce several various classes of $c$-almost periodic type functions and their Stepanov generalizations, where $c\in {\mathbb C}$ and $|c|=1.$ We also consider the corresponding classes of $c$-almost periodic type functions depending on two variables and prove several related composition principles. Plenty of illustrative examples and applications are presented.

math.FA↗
arXiv2020

Thermal phase transition in $F(R)$-charged $AdS_{4}$-scalar theory

We investigate instabilities of $F(R)$-charged $AdS_{4}$ black holes by a massive charged scalar field in a linear perturbation regime. We study tachyonic instabilities as the near horizon scalar condensation in a model of $F(R)$ gravity with planar horizon and investigate properties of possible phase transitions. The results show that such transitions are sensitive to the first derivative of $F(R)$ with respect to $R$ in that the larger its value, the higher the critical temperature, thus resulting in a new generation of high-temperature superconductors. Also, for a certain range of parameters, $F(R)$-charged $AdS_{4}$ black holes suffer from superradiant instability. We consider the effects of the scalar mass and charge on such instabilities and conclude that RN black holes decay into small hairy black holes that have a charged scalar condensate floating near the horizon. It is shown that the existence of phase transition at the critical temperature leading to a hairy black hole solution emerges for $T T_{c}$. The effect of $F(R)$ on the critical temperature is subsequently investigated in the case of superradiant instability, showing that higher critical temperatures would be possible in $F(R)$ gravity. We also check the stability of hairy black holes and show that the resulting hairy solution can be considered as a possible end point of superradiant instability of a small charged black hole.

gr-qc↗
arXiv2016

Polaritonic linear dynamic in Keldysh formalism

We study the dynamic of polaritons in the Keldysh functional formalism. Dissipation is considered through the coupling of the exciton and photon fields to two independent photonic and excitonic baths. As such, this theory allows to describe more intricate decay mechanisms that depend dynamically on the state of the system, such as a direct upper-polariton lifetime, that is motivated from experiments. We show that the dynamical equations in the Keldysh framework otherwise follow the same Josephson--like equations of motions than the standard master equation approach, that is however limited to simple decay channels. We also discuss the stability of the dynamic and reconsider the criterion of strong coupling in the presence of upper polariton decay.

cond-mat.quant-gas↗
arXiv2016

Polaritonic Rabi and Josephson Oscillations

The dynamics of coupled condensates is a wide-encompassing problem with relevance to superconductors, BECs in traps, superfluids, etc. Here, we provide a unified picture of this fundamental problem that includes i) detuning of the free energies, ii) different self-interaction strengths and iii) finite lifetime of the modes. At such, this is particularly relevant for the dynamics of polaritons, both for their internal dynamics between their light and matter constituents, as well as for the more conventional dynamics of two spatially separated condensates. Polaritons are short-lived, interact only through their material fraction and are easily detuned. At such, they bring several variations to their atomic counterpart. We show that the combination of these parameters results in important twists to the phenomenology of the Josephson effect, such as the behaviour of the relative phase (running or oscillating) or the occurrence of self-trapping. We undertake a comprehensive stability analysis of the fixed points on a normalized Bloch sphere, that allows us to provide a generalized criterion to identify the Rabi and Josephson regimes in presence of detuning and decay.

cond-mat.quant-gas↗
arXiv2006

Radio-Detection Signature of High Energy Cosmic Rays by the CODALEMA Experiment

Taking advantage of recent technical progress which has overcome some of the difficulties encountered in the 1960's in the radio detection of extensive air showers induced by ultra high energy cosmic rays (UHECR), a new experimental apparatus (CODALEMA) has been built and operated. We will present the characteristics of this device and the analysis techniques that have been developed for observing electrical transients associated with cosmic rays. We find a collection of events for which both time and arrival direction coincidences between particle and radio signals are observed. The counting rate corresponds to shower energies $\geq 5\times 10^{16}$ eV. The performance level which has been reached considerably enlarges the perspectives for studying UHECR events using radio detection.

astro-ph↗
arXiv2004

Radiodetection of Cosmic Ray Extensive Air Showers

We present the characteristics and performance of a demonstration experiment devoted to the observation of ultra high- energy cosmic ray extensive air showers using a radiodetection technique. In a first step, one antenna narrowed band filtered acting as trigger, with a 4 $σ$ threshold above sky background-level, was used to tag any radio transient in coincidence on the antenna array. Recently, the addition of 4 particle detectors has allowed us to observe cosmic ray events in coincidence with antennas.

astro-ph↗