  Long-range spatial correlations in the velocity and energy fields of a
granular fluid are discussed in the framework of a 1d lattice model. The
dynamics of the velocity field occurs through nearest-neighbour inelastic
collisions that conserve momentum but dissipate energy. A set of equations for
the fluctuating hydrodynamics of the velocity and energy mesoscopic fields give
a first approximation for (i) the velocity structure factor and (ii) the
finite-size correction to the Haff law, both in the homogeneous cooling regime.
At a more refined level, we have derived the equations for the two-site
velocity correlations and the total energy fluctuations. First, we seek a
perturbative solution thereof, in powers of the inverse of system size. On the
one hand, when scaled with the granular temperature, the velocity correlations
tend to a stationary value in the long time limit. On the other hand, the
scaled standard deviation of the total energy diverges, that is, the system
shows multiscaling. Second, we find an exact solution for the velocity
correlations in terms of the spectrum of eigenvalues of a certain matrix. The
results of numerical simulations of the microscopic model confirm our
theoretical results, including the above described multiscaling phenomenon.
