  In this paper we present a new model for modeling the diffusion and relative
dispersion of particles in homogeneous isotropic turbulence. We use an
Heisenberg-like Hamiltonian to incorporate spatial correlations between fluid
particles, which are modeled by stochastic processes correlated in time. We are
able to reproduce the ballistic regime in the mean squared displacement of
single particles and the transition to a normal diffusion regime for long
times. For the dispersion of particle pairs we find a $t^{2}$-dependence of the
mean squared separation at short times and a $t$-dependence for long ones. For
intermediate times indications for a Richardson $t^{3}$ law are observed in
certain situations. Finally the influence of inertia of real particles on the
dispersion is investigated.
