  Motivated by the recent experimental and theoretical progresses in the
exploration of the effect of disorder in interacting system, we examine the
effect of two types of correlated disorder, the quasi-periodic potential and
speckle disorder potential, on one- and two-particle problem with exact
diagonalization (ED) method. We give the phase diagram for single particle in
the presence of quasi-periodic potential and also analyse the effect of strong
interaction on the phase diagram for ground state in two dimensions. For the
speckle disorder potential case, we examine both the effect of correlation
length and disorder strength on single particle ground state energy and
two-particle binding energy. The transport property for different interaction
strength under speckle disorder potential is also calculated and discussed at
last.
