Initial correlations effects on decoherence at zero temperature

The decoherence evolution in momentum space of a non relativistic particle linearly interacting with a bath at zero temperature, starting from an initial state that contains correlations between the momenta of the particle wave packet and the bath, is studied. The reduced density matrix of the particle is obtained using the Hamiltonian in the dipole approximation. Some results are then explicitly derived for a charge-electromagnetic field form of interaction. When correlations are initially present between the momenta and all the oscillators of the bath, decoherence in momentum space is time independent and complete. When initial correlations occur only with the bath oscillators at frequency larger than a lower cut off $\varpi$, the initial partial decoherence evolves in time and shows a dependence on $\varpi$