arXiv subjects

Abdellah Touati

Publications and source records attributed to Abdellah Touati.

13 recordsLinked to original sources

arXiv2026

Interacting Tomonaga-Lüttinger liquid with impurity for interaction constant $K = 1/2$: Thermopower investigation, entropy variation and heat capacity densities associated with thermoelectric particle transport

We investigate thermoelectric and thermodynamic properties of a Tomonaga-Luttinger liquid with interaction parameter $K=1/2$ in the presence of a localized impurity. Using bosonization and refermionization, we derive an exact expression for the thermopower in the nonlinear regime and obtain the corresponding Seebeck coefficient in linear response. At low temperature, the Seebeck coefficient follows a Mott-like relation governed by the energy dependence of the transmission coefficient and is found to be closely related to the entropy per particle. This connection allows us to derive using Kelvin formula the thermopower contribution to the entropy density variation and the charge-carriers contribution to the heat capacity density. Both quantities exhibit Mott-like behavior in the low-temperature regime. We apply our results to a fractional quantum Hall quantum point contact and to a one-channel quantum conductor coupled to an Ohmic environment. Our results demonstrate the close connection between thermoelectric transport and thermodynamic properties in interacting one-dimensional quantum systems.

cond-mat.mes-hall↗

arXiv2026

Bound state solutions with a linear combination of Yukawa plus four-parameter diatomic potentials using path integral approach: Thermodynamic properties

In this paper, we investigate the approximate analytical bound states with a linear combination of two diatomic molecule potentials, Yukawa and four parameters potentials, within the framework of the path integral formalism. With the help of an appropriate approximation to evaluate the centrifugal term, the energy spectrum and the normalized wave functions of the bound states are derived from the poles of Green's function and its residues. The partition function and other thermodynamic properties were obtained using the compact form of the energy equation.

quant-ph↗

arXiv2026

Black Hole Radiation Sparsity and Bekenstein Entropy Loss in Non-Commutative Schwarzschild Spacetime

In this paper, we investigate the sparsity of black hole radiation, the Bekenstein entropy loss, and the total particle emission of a Schwarzschild black hole (SBH) within the framework of non-commutative (NC) gauge theory of gravity. First, we provide a brief review of black hole (BH) thermodynamics, computing both the deformed Hawking temperature and entropy. In this geometry, the divergent behavior of the temperature is removed, and a logarithmic correction to the entropy emerges. We then present the NC corrections to the Bekenstein entropy loss of the SBH alongside the total number of emitted particles. Our results show that the total number of emitted particles is proportional to the entropy behavior of the NC SBH, which is consistent with non-thermal radiation. Finally, we analyze the sparsity of Hawking radiation in this geometry, finding that the NC SBH exhibits extremely sparse radiation ($\hatη \gg 1$), which diverges at the final stage of evaporation as the black hole ceases to radiate.

gr-qc↗

arXiv2026

New Construction of Black Hole Solution in Non-Commutative Geometry and Their Thermodynamic Properties

In this work, we present a new construction of black hole solutions in non-commutative gauge theory by applying the Seiberg-Witten map directly to interaction potentials before solving Einstein's equations. This approach provides a dynamical effect of spacetime non-commutativity that preserves gauge covariance. We obtain both NC Schwarzschild and charged Reissner-Nordstrom-like black hole solutions, showing that the charged sector exhibits a novel branch dependence between attractive and repulsive electric interactions absent in the commutative limit. We analyze the geometrical properties, energy conditions, and thermodynamic properties of these spacetimes. Our results reveal that non-commutativity eliminates the temperature divergence at the final evaporation stage, inducing a second-order phase transition, or a Hawking-Page-like phase transition in the presence of pressure. Additionally, linear response analysis indicates high sensitivity to the NC parameter for small black holes. Finally, quantum tunneling investigations for both thermal and non-thermal radiation demonstrate that the NC deformation suppresses the particle-number density and weakens correlations between successive emissions, acting as a barrier to particle escape and supports the formation of a cold finite remnant. From a cosmological standpoint, since these stable remnant possess a fixed Planck-scale mass ($M^{\text{min}}\simeq2.73 M_{P}$), they provide a dynamically generated, purely gravitational cold dark matter candidate that aligns with dark universe phenomenology while simultaneously resolving the black hole information loss paradox.

hep-th↗

arXiv2025

Quark confinement in presence of both chromoelectric and chromomagnetic fields and the structure of spacetime

The strong interaction between quarks inside hadrons in curved spacetime is investigated in the presence of a new non-abelian gauge potential based on the $SU(3)$ group. This potential presented both chromo-electric and chromo-magnetic fields, including a magnetic monopole-like term, together with a radial non-Abelian Coulomb-like component. A spacetime metric induced by the presence of a Yang-Mills field is derived by solving Einstein's equations in the specific limit where the $SU(3)$ gauge symmetry is reduced to an embedded $SU(2)$ subgroup, accompanied by a dynamical $U(1)$ monopole sector. It is explicitly shown that the Schwarzschild radius of the strong interaction between quarks within hadrons corresponds approximately to the size of these latter and that the corresponding, for both quarks and gluons, wave function presents a discontinuity at Schwarzschild surface. The obtained results allow us to interpret the confinement of quarks as a geometric property of spacetime, emerging naturally from its structure without introducing any confinement potential. Moreover, the energy spectra of quarks in presence of chromo-electric and chromo-magnetic fields reproduce the mass of hadrons with a very good accuracy compared to the experimental data, and the presence of the residual non-abelian term correction enhance our numerical results.

hep-ph↗

arXiv2025

Lyapunov exponents and geodesic stability of Schwarzschild black hole in the non-commutative gauge theory of gravity

In this paper, we study the stability of geodesic motion for both massive and massless particles using Lyapunov exponents in the non-commutative (NC) Schwarzschild black hole (BH) via the gauge theory of gravity. As a first step, we investigate the both time-like and null radial motion of particles, the mean result in NC geometry shows that the particles take infinity proper time to reach the NC singularity (infinite time affine parameter framework for photons). The proper/coordinate time of Lyapunov exponents and their ratio of time-like geodesic for the circular motion of this black hole shows a new behavior, which describes a new range of stable circular orbits between unstable ones. Then we analyze the circular motion of photons, where the result shows a new photon sphere near the event horizon which is not allowed in the commutative case, and the Lyapunov exponent is expressed in this geometry, where this confirms the instability of the outer photon sphere and the stability of the inner one. Moreover, we studied the effect of noncommutativity on the black hole shadow radius, We found a similarity between the non-commutativity and the mass of a black hole. Then we using experimental data from the event horizon telescope, we show that a noncommutativity parameter of the order of $Θ^{\text{Phy}}\sim 10^{-32}m$.

hep-th↗

arXiv2024

Geodesic motion of a test particle around a noncommutative Schwarzchild Anti-de Sitter black hole

In this work, we derive non-commutative corrections to the Schwarzschild-Anti-de Sitter solution up to the first and second orders of the non-commutative parameter $Θ$. Additionally, we obtain the corresponding deformed effective potentials and the non-commutative geodesic equations for massive particles. Through the analysis of time-like non-commutative geodesics for various values of $Θ$, we demonstrate that the circular geodesic orbits of the non-commutative Schwarzschild-Anti-de Sitter black hole exhibit greater stability compared to those of the commutative one. Furthermore, we derive corrections to the perihelion deviation angle per revolution as a function of $Θ$. By applying this result to the perihelion precession of Mercury and utilizing experimental data, we establish a new upper bound on the non-commutative parameter, estimated to be on the order of $10^{-66}\,\mathrm{m}^2$.

gr-qc↗

arXiv2024

Elastic scattering of electron by a Yukawa potential in non-commutative spacetime

In this paper, we investigate the elastic scattering of an electron by a Yukawa potential within the framework of non-commutative (NC) geometry. We first derive the NC correction to the Yukawa potential at leading order in the NC parameter, resulting in a modified potential resembling a screened Kratzer potential. This potential reduces to the standard Kratzer form when considering the NC correction to the Coulomb potential. Subsequently, we calculate the NC correction to the electron scattering amplitude using the first-order Born approximation. We then analyze the effects of NC geometry on both the differential and total cross sections for elastic scattering. Our results indicate that non-commutativity enhances the differential cross section at small scattering angles and naturally gives rise to a Kratzer-like potential, reflecting the quantum nature of spacetime. Additionally, we establish a direct relationship between the system's energy level and the bound on the NC parameter. Specifically, for an ultra-relativistic incident electron scattering by a heavy molecule, we derive a new lower bound on $Θ$ of the order of $10^{-28}\,\text{m}$.

quant-ph↗

arXiv2023

Quantum tunneling from Schwarzschild black hole in non-commutative gauge theory of gravity

In this letter, we present the first study of Hawking radiation as a tunneling process within the framework of non-commutative (NC) gauge theory of gravity. First, we reconstruct the non-commutative Schwarzschild black hole (NC SBH) within the gauge theory of gravity, employing the Seiberg-Witten (SW) map and the star product. Then, we compute the emission spectrum of outgoing massless particles using the quantum tunneling mechanism. In the first scenario, we calculate the tunneling rate of massless particles crossing the event horizon of the NC SBH with lower frequencies. Our results reveal pure thermal radiation. Notably, we find that the Hawking temperature remains consistent in both the classical thermodynamics and the quantum tunneling approach, suggesting equivalence between these two approaches in NC spacetime. However, in the case of massless particle emission with higher frequencies, we account for energy conservation resulting in the tunneling rate to deviate from pure thermal radiation. This tunneling rate remains consistent with an underlying unitary quantum theory. We establish a relationship between this deviation and the change in the black hole entropy, revealing a logarithmic correction to the entropy within this geometry. Furthermore, we demonstrate that non-commutativity enhances the correlations between two successively emitted particles. Additionally, we determine the NC density number of particle emission and conclude by discussing the implications of our findings.

gr-qc↗

arXiv2023

Schwarzschild black hole surrounded by a cavity and phase transition in the non-commutative gauge theory of gravity

In this work, we investigate the phase transition of the Schwarzschild black hole (SBH) inside an isothermal spherical cavity in the context of the non-commutative (NC) gauge theory of gravity, by using the Seiberg-Witten (SW) map and the star product. Firstly, we compute the NC correction to the Hawking temperature and derive the logarithmic correction to the entropy, then we derive the local temperature and local energy of NC SBH in isothermal cavity. Our results show that the non-commutativity removes the commutative divergence behavior of temperature, and prevents the SBH from the complete evaporation, which leads to a remnant black hole, and this geometry has predicted a minimal length in the order of Planck scale $Θ\sim l_{planck}$. Therefore, the thermodynamic stability and phase transition is studied by analyzing the behavior of the local heat capacity and the Helmholtz free energy in the NC spacetime, where the results show that, the NC SBH has a two second-order phase transition and one first-order phase transition, with two Hawking-Page phase transition in the NC gauge theory.

gr-qc↗

arXiv2023

Thermodynamic Properties of Schwarzschild Black Hole in Non-Commutative Gauge Theory of Gravity

In this paper, we used the non-commutative (NC) gauge theory of gravity to investigate the thermodynamic properties of a deformed Schwarzschild black hole (SBH). Our results present a new scenario of black hole evaporation. As a first step, we described the Arnowitt-Deser-Misner (ADM) mass, the Hawking temperature, and the entropy of NC SBH. The non-commutativity removes the divergence behavior of temperature, and the result shows a difference in the pole-equator temperature. These corrections also reveal a new fundamental length at the Planck scale order, $Θ\approx 2.257 \times 10^{-35}\,m$. In the last stage of evaporation, the NC correction exposes a remnant entropy $\hat{S}_0$ of the NC SBH. Then, the description of the heat capacity and the Gibbs free energy of the deformed black hole shows the effect of the NC gauge theory on the thermodynamic stability and the phase transitions. Finally, we investigate the influence of the black hole pressure on the stability and the phase transition of SBH in NC spacetime. In this study, we found that the NC parameter plays a similar role to the thermodynamic variables. The results show a second-order phase transition of NC SBH.

gr-qc↗

arXiv2022

On Modified First Law of Black hole Thermodynamics in The Non-Commutative Gauge Theory

In this paper, we investigated the thermodynamic properties of Schwarzschild black hole (SBH) in the non-commutative (NC) gauge theory of gravity. According to our previous work, we modify the first law of the black hole (BH) thermodynamics by the physical quantity (NC potential) $\mathcal{A}$ which is the conjugate to the NC parameter $Θ$, which leads to this expression $d\hat{M}=\hat{T}d\hat{S}+\mathcal{A}dΘ$. Our result shows that the NC SBH has a phase transition, and the non-commutativity affected this transition. And the NC potential $\mathcal{A}$ is effective only in the final stage of the BH evaporation, where it increases the Gibbs free energy at this stage, and the NC parameter in this study can represent the tension of the spacetime. Then the study of the pressure of the SBH in the modified first law of the BH thermodynamic shows a second-order phase transition, and the critical value of the thermodynamical variables are related to each value of $Θ$, and that leads to this parameter to play the same role as a thermodynamical variable.

gr-qc↗

arXiv2021

Geodesic equation in non-commutative gauge theory of gravity

In this work, we construct a non-commutative (NC) gauge theory of gravity for any metric with spherical symmetries, where we use a non-diagonal tetrad field. The deformed gauge potentials (tetrad fields) and the components of deformed metric are computed to the second order in the NC parameter $Θ^{μν}$, as the application to the Schwarzschild black hole we show that the NC geometry removes the singularity at the origin of the black hole, and increase the event horizon. The non-commutativity correction to the effective potential of the Schwarzschild metric is also computed and we show how this geometry affects the stability condition which it found the NC parameter plays the same role as the mass that can be used to explain the dark matter and we show that the NC Schwarzschild space-time has new stable circular orbits appear near the event horizon that is not allowed by Schwarzschild space-time. The geodesic equations in the NC space and the corrections to the periastron advance in terms of $Θ$ are obtained. We have also specified the problem of Mercury's perihelion and used the experimental data to estimate the NC parameter $Θ$, then we show that $Θ$ of the order $10^{-25}s.kg^{-1}$ gives observable corrections to the movement at a large scale. We show that the NC propriety of the spacetime appears at the High Energy.

gr-qc↗