Inverse magneto-rotational catalysis and the phase diagram of a rotating hot and magnetized quark matter

TL;DR

This paper investigates how rotation and magnetic fields influence quark matter, revealing an inverse magneto-rotational catalysis effect where increasing magnetic field and rotation suppress chiral symmetry breaking, affecting phase transition temperatures.

Contribution

It introduces a detailed analysis of rotating, magnetized quark matter using the Ritus eigenfunction method, demonstrating the inverse magneto-rotational catalysis effect and its impact on phase diagrams.

Findings

Inverse magneto-rotational catalysis observed, with decreasing critical temperature and frequency.

Magnetic field and rotation suppress the dynamical mass and phase transition temperatures.

Finite size effects and boundary conditions significantly influence fermion energy modes.

Abstract

We study the properties of a hot and magnetized quark matter in a rotating cylinder in the presence of a constant magnetic field. To do this, we solve the corresponding Dirac equation using the Ritus eigenfunction method. This leads to the energy dispersion relation, Ritus eigenfunctions, and the quantization relation for magnetized fermions. To avoid causality-violating effects, we impose a certain global boundary condition, and study its effect, in particular, on the energy eigenmodes and the quantization relations of fermions. Using the fermion propagator arising from this method, we then solve the gap equation at zero and nonzero temperatures. At zero temperature, the dynamical mass $\bar{m}$ does not depend on the angular frequency, as expected. We thus study its dependence on the distance $r$ relative to the axis of rotation and the magnetic field $B$, and explore the corresponding finite size effect for various couplings $G$. We then consider the finite temperature case. The dependence of $\bar{m}$ on the temperature $T$, magnetic field $B$, angular frequency $\Omega$, and distance $r$ for various $G$ is studied. We show that $\bar{m}$ decreases, in general, with $B$ and $\Omega$. This is the ''inverse magneto-rotational catalysis (IMRC)'' or the ''rotational magnetic inhibition'', previously discussed in the literature. To explore the evidence of this effect in the phase diagrams of our model, we examine the phase portraits of the critical temperature $T_c$ as well as the critical angular frequency $\Omega_c$ with respect to $G, B,\Omega$, and $r$ as well as $G, B, T$, and $r$, respectively. We show that $T_{c}$ and $\Omega_c$ decrease, in particular, with $B$. This is interpreted as clear evidence for IMRC.