Influence of rotation and FLR corrections on self-gravitational Jeans instability in quantum plasma

In the present work, the self-gravitational instability of quantum plasma is investigated including the effects of finite Larmor radius corrections (FLR) and rotation. The formulation is done employing quantum magnetohydrodynamic (QMHD) model. The plane wave solutions are employed on the linearized perturbed QMHD set of equations to obtain the general dispersion relation. The rotation is assumed only along the z-direction. The general dispersion relation is further reduced for transverse and longitudinal directions of propagation. It is found that in transverse direction of propagation the Jeans criterion is modified due to the rotation, FLR and quantum corrections while in longitudinal direction of propagation it is observed that the Jeans criterion is modified by quantum corrections only. The growth rate of perturbation is discussed numerically including the considered parameters FLR and quantum corrections. The growth rate is observed to be modified significantly due to the quantum correction and FLR effects.