We extend the classical magnetohydrodynamics formalism to include nonlocal
quantum behavior via the phenomenological Bohm potential. We then solve the
quantum magnetohydrodynamics equations to obtain a new analytical form of the
dynamic structure factor (DSF), a fundamental quantity linking theory and
experiments. Our results show that the three-peak structure -- one central
Rayleigh peak and two Brillouin peaks -- of the DSF arising from quantum
hydrodynamic fluctuations becomes (in general) a five-peak structure -- one
central Rayleigh peak and two pairs of peaks associated with fast and slow
magnetosonic waves. The Bohm contribution influences the positions and
characteristics (height, width, and intensity) of the peaks by introducing
three significant modifications: (a) an increase in effective thermal pressure,
(b) a reduction in the adiabatic index, and (c) an enhancement of effective
thermal diffusivity. The multiple DSF peaks enable concurrent measurements of
diverse plasma properties, transport coefficients, and thermodynamic parameters
in magnetized dense plasmas. The potential for experimental validation of our
theory looms large, particularly through future experiments conducted at
state-of-the-art laser facilities.Comment: 13 pages including 5 figures and 1 table; Comments are welcom