NONLINEAR QUANTUM-MECHANICAL EFFECTS - REAL OR ARTIFACT OF INACCURATE APPROXIMATIONS

We critically discuss the reliability of the discrete nonlinear Schrodinger equation (DNSE) approach in the case of a dissipative two-site system. By using the Wigner pseudo-probability formalism we show that the 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 opposite to that usually adopted to derive the DNSE and a simple explanation of this result is given by establishing a connection between the Hartree approximation and the DNSE. Theoretical arguments are provided to evaluate the error associated to the Hartree approximation, so as to assess under which physical circumstances this key approximation is reliable.