Statistical Properties of Random Environment of 1D Quantum N-Particles System in External Field

摘要

The investigation of 1D quantum N-particle system (PS) with relaxation in the random environment under the influence of external field is conducted within the framework of the stochastic differential equation of the Langevin-Schrodinger (L-Sch) type. Using L-Sch equation, the 2D second-order nonstationary partial differential equation is found, which describes the quantum distribution in the environment, depending on the energy of nonperturbed 1D quantum N-PS and on the external field parameters. It is shown that the average value of the interaction potential between 1D disordered quantum N-PS and the external field, has the ultraviolet divergence. This problem is solved by the renormalization of the equation for the function of quantum distribution. It is shown that it has a sense of dimensional renormalization which is characteristic for the quantum field theory. Critical properties of the environment are investigated in detail. The possibility of the first-order phase transition in the environment distribution depending on amplitude of an external field is been shown.