# Nonlinear Schroedinger Equations within the Nelson Quantization Picture

Source: [Nonlinear Schroedinger Equations within the Nelson Quantization Picture](<https://www.sota2.com/research/paper/68fa261c2c2a3760193b6a6b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T11:09:37.332Z

Authors: G. Kaniadakis, A.M. Scarfone

Published: 2003-03-18T09:47:54.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0303334>)

[PDF](<https://arxiv.org/pdf/cond-mat/0303334.pdf>)