arXiv subjects

Md. Sabir Ali

Publications and source records attributed to Md. Sabir Ali.

3 recordsLinked to original sources

arXiv2022

Patterned Random Matrices: deviations from universality

We investigate the level spacing distribution for three ensembles of real symmetric matrices having additional structural constraint to reduce the number of independent entries to only $ (n+1)/2 $ in contrast to the $ n(n+1)/2 $ for a real symmetric matrix of size $ n \times n $. We derive all the results analytically exactly for the $ 3\times 3 $ matrices and show that spacing distribution display a range of behaviour based on the structural constraint. The spacing distribution of the ensemble of reverse circulant matrices with additional zeros is found to fall slower than exponential for larger spacing while that of symmetric circulant matrices has poisson spacings. The palindromic symmetric toeplitz matrices on the other hand show level repulsion but the distribution is significantly different from Wigner. The behaviour of spacings for all the three ensembles clearly show the departure from universal result of Wigner distribution for real symmetric matrices. The deviation from universality continues in large $ n $ cases as well, which we study numerically.

math-ph↗

arXiv2021

Unruh-DeWitt detector responses for complex scalar fields in de Sitter spacetime

We derive the response function for a comoving, pointlike Unruh-DeWitt particle detector coupled to a complex scalar field $ϕ$, in the $(3+1)$-dimensional cosmological de Sitter spacetime. The field-detector coupling is taken to be proportional to $ϕ^{\dagger} ϕ$. We address both conformally invariant and massless minimally coupled scalar field theories, respectively in the conformal and the Bunch-Davies vacuum. The response function integral for the massless minimal complex scalar, not surprisingly, shows divergences and accordingly we use suitable regularisation scheme to find out well behaved results. The regularised result also contains a de Sitter symmetry breaking logarithm, growing with the cosmological time. Possibility of extension of these results with the so called de Sitter $α$-vacua is discussed. While we find no apparent problem in computing the response function for a real scalar in these vacua, a complex scalar field is shown to contain some possible ambiguities in the detector response. The case of the minimal and nearly massless scalar field theory is also briefly discussed.

hep-th↗

arXiv2020

Joule-Thomson Expansion of Regular Bardeen AdS Black Hole Surrounded by Static Anisotropic Quintessence Field

In the present paper, we investigate the required anisotropy of an exact regular Bardeen black hole characterized by its mass $M$, the nonlinear parameter $g$, the quintessence field parameter $a$ in anti-de sitter spacetime with a static quintessence matter field. We also show that the relative pressure anisotropy, equation of state and the pressure depends on radial coordinate, reflecting the required anisotropy for Bardeen black hole in the quintessence background. Next, we analyze the Joule-Thompson ($JT$) expansion of the black hole spacetime. Treating the cosmological constant as thermodynamic pressure $P$ and its conjugate quantity as thermodynamic volume $V$ we derive the equation of state connecting Hawking temperature and various black hole parameters. We study the $JT$ expansion in the regular Bardeen AdS black holes in the quintessence background through the analysis of inversion temperature and isenthalpic curves. We derive the $JT$ coefficient $μ$, and use them to plot the inversion and isenthalpic curves. We discuss the effect of quintessence parameter $a$ and $ω_q$ on the $JT$ coefficient and inversion temperature, especially with the case of $ω_q=-1$ and $ω_q=-\frac{1}{3}$. Our analysis shows that quintessence dark energy affects the inversion point $(T_i,P_i)$ .

gr-qc↗