Nonlinear Schroedinger Equations within the Nelson Quantization Picture
arXiv:cond-mat/0303334 · doi:10.1016/S0034-4877(03)80016-2
Abstract
We present a class of nonlinear Schroedinger equations (NLSEs) describing, in the mean field approximation, systems of interacting particles. This class of NLSEs is obtained generalizing expediently the approach proposed in Ref. [G.K. Phys. Rev. A 55, 941 (1997)], where a classical system obeying to an exclusion-inclusion principle is quantized using the Nelson stochastic quantization. The new class of NLSEs is obtained starting from the most general nonlinear classical kinetics compatible with a constant diffusion coefficient D=\hbar/2m. Finally, in the case of s-stationary states, we propose a transformation which linearizes the NLSEs here proposed.
5 pages, (RevTeX4), to appear in Rep. Math. Phys. 51 (2003)