low dimensional system
method of quantum hydrodynamic
P.A. Andreev, L.S. Kuz’menkov, M.I. Trukhanova
The derivation of a general system of the quantum hydrodynamics equations was obtained for the purpose of research of the non-equilibrium processes in the system of the charged particles with the dipole electrical moment. As a result, the system of the balance momentum equation, the polarization equation and the flux density of polarization equation were found, based on the many-particle Schrödinger equation. The problem of definition of the inherent wave disturbance spectrum was steed and solved in such systems. The wave dispersion in the 2D gas of the charged particles with the dipole electrical moment was researched. The contribution of the dipole electrical moment to the dispersion of the Langmuir waves was determined and the existence of the new mode of wave propagation, provided by the existence of the dipole electrical moment at the particles, was predicted. The version of the 2D gas of the neutral particles with the dipole electrical moment was contemplated separately. Was revealed, that, in the such systems of the dipoles, the waves can be excited without excitation of the collective motions of the particles. The proper waves in the 2D conductor, situated in the external field, were researched. The dispersion law of such waves was calculated. In this case the existence of the new mode of wave propagation, specified of the ions polarization was predicted. The result of the calculations reveals that the perturbations in the one-dimensional system of dipoles are not stable. The appropriate instability increment was established.