A disordered 1D quantum N-particle system in an environment under the influence of an external field

We consider a 1D quantum disordered N-particle system (N-PS) in an external field with relaxation in media. Mathematically, the problem is formulated within the limits of the stochastic differential equation of type Langevin-Schroedinger. Using the Langevin-Schroedinger equation, we found the 2D Fokker-Plank equation that describes the quantum distribution (QD) depending on the energy of nonperturbed 1D N-PS and from the parameters of the external field. The properties of QD are investigated in detail. It is shown that the average value of interaction potentials between the 1D disordered N-PS and the external field has an ultraviolet divergence that is solved by dimensional renormalization.