We use holography to study N=4 supersymmetric SU(Nc) Yang-Mills theory in the
large-Nc and large-coupling limits coupled to a number Nf << Nc of
(n+1)-dimensional massless supersymmetric hypermultiplets in the Nc
representation of SU(Nc), with n=2,3. We introduce a temperature T, a baryon
number chemical potential mu, and a baryon number magnetic field B, and work in
a regime with mu >> T,\sqrt{B}. We study the collective excitations of these
holographic quantum liquids by computing the poles in the retarded Green's
function of the baryon number charge density operator and the associated peaks
in the spectral function. We focus on the evolution of the collective
excitations as we increase the frequency relative to T, i.e. the
hydrodynamic/collisionless crossover. We find that for all B, at low
frequencies the tallest peak in the spectral function is associated with
hydrodynamic charge diffusion. At high frequencies the tallest peak is
associated with a sound mode similar to the zero sound mode in the
collisionless regime of a Landau Fermi liquid. The sound mode has a gap
proportional to B, and as a result for intermediate frequencies and for B
sufficiently large compared to T the spectral function is strongly suppressed.
We find that the hydrodynamic/collisionless crossover occurs at a frequency
that is approximately B-independent.Comment: 45 pages, 8 png and 47 pdf images in 22 figure