``Bare'' Effective Mass in Finite Sized $\nu = 1/2$ Systems

In this note, we discuss the effective mass of quasiparticles in finite sized $\nu = 1/2$ systems in the lowest Landau level, given a natural notion we have of the Fermi surface in these finite sized systems. The effective mass is related to the difference between instantaneous density-density response functions of the ground state and excited states of the system; we do a finite size calculation for this difference for $\nu = 1/2$ systems with 7, 8 and 9 fermions, and conjecture how the difference must look in the thermodynamic limit.