NONLINEAR QUANTUM-MECHANICAL EFFECTS - REAL OR ARTIFACT OF INACCURATEAPPROXIMATIONS

We critically discuss the reliability of the discrete nonlinear Schrod inger equation (DNSE) approach in the case of a dissipative two-site s ystem. By using the Wigner pseudo-probability formalism we show that t he nonlinear effects predicted by this effective picture are generally incorrect except in the adiabatic limit with the two-site system much faster than its own thermal bath. This is the adiabatic condition opp osite to that usually adopted to derive the DNSE and a simple explanat ion of this result is given by establishing a connection between the H artree approximation and the DNSE. Theoretical arguments are provided to evaluate the error associated to the Hartree approximation, so as t o assess under which physical circumstances this key approximation is reliable.