Inverse magnetorotational catalysis and the phase diagram of a rotating hot and magnetized quark matter

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 m over bar 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 m over bar on the temperature T, magnetic field B, angular frequency omega, and distance r for various G is studied. We show that m over bar decreases, in general, with B and omega. This is the "inverse magnetorotational 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 Tc 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 Tc and omega c decrease, in particular, with B. This is interpreted as clear evidence for IMRC.