Local electric current correlation function in an exponentially decaying magnetic field

The effect of an exponentially decaying magnetic field on the dynamics of Dirac fermions in 3+1 dimensions is explored. The spatially decaying magnetic field is assumed to be aligned in the third direction, and is defined by {\mathbf{B}}(x)=B(x){\mathbf{e}}_{z}, with B(x)=B_{0}e^{-\xi\ x/\ell_{B}}. Here, \xi\ is a dimensionless damping factor and \ell_{B}=(eB_{0})^{-1/2} is the magnetic length. As it turns out, the energy spectrum of fermions in this inhomogeneous magnetic field can be analytically determined using the Ritus method. Assuming the magnetic field to be strong, the chiral condensate and the \textit{local} electric current correlation function are computed in the lowest Landau level (LLL) approximation and the results are compared with those arising from a strong homogeneous magnetic field. Although the constant magnetic field B_{0} can be reproduced by taking the limit of \xi-> 0 and/or x-> 0 from B(x), these limits turn out to be singular once the quantum corrections are taken into account.Comment: V1: 16 pages, 7 figures, 2 tables; V2: Section II improved, references added. Version accepted for publication in PR

Chaos Near to the Critical Point: Butterfly Effect and Pole-Skipping

We study the butterfly effect and pole-skipping phenomenon for the 1RCBH model which enjoys a critical point in its phase diagram. Using the holographic idea, we compute the butterfly velocity and interestingly find that this velocity can probe the critical behavior of this model. We calculate the dynamical exponent of this quantity near the critical point and find a perfect agreement with the value of the other quantity's dynamical exponent near this critical point. We also find that at chaos point, the phenomenon of pole-skipping appears which is a sign of a multivalued retarded correlation function. We briefly address the butterfly velocity and pole-skipping for the AdS-RN black hole solution which on its boundary a strongly coupled charged field theory lives. For both of these models, we find $v_B^2\geq c_s^2$ at each point of parameter space where $c_s$ is the speed of sound wave propagation.Comment: 27 pages, 1 figuer

Chiral phase transition of a dense, magnetized and rotating quark matter

We investigate the chiral symmetry restoration/breaking of a dense, magnetized and rotating quark matter within the Nambu Jona-Lasinio model including $N_f=2$ and $N_c=3$ numbers of flavors and colors, respectively. Imposing the spectral boundary conditions, as well as the positiveness of energy levels, lead to a correlation between the magnetic and rotation fields such that strongly magnetized plasma can not rotate anymore. We solve the gap equation at zero and finite temperature. At finite temperature and baryon chemical potential $\mu_B$, we sketch the phase diagrams $T_c(\mu_B)$ and $T_c(R\Omega)$ in different cases. As a result, we always observe inverse-rotational catalysis mean to decrease $T_c$ by increasing $R\Omega$. But the magnetic field has a more complex structure in the phase diagram. For slowly rotating plasma, we find that $T_c$ decreases by increasing $eB$, while in the fast rotating plasma we see that $T_c$ increases by increasing $eB$. Also, we locate exactly the position of Critical End Point by solving the equations of first and second derivatives of effective action with respect to the order parameters, simultaneously.Comment: 18 pages, 15 figures, 5 tables, comments are welcom