• Corpus ID: 16084497

Nonlinear QM as a fractal Brownian motion with complex diffusion constant

@article{Castro2002NonlinearQA,
  title={Nonlinear QM as a fractal Brownian motion with complex diffusion constant},
  author={Carlos Castro and Jorge Mahecha and Boris A. Rodr{\'i}guez},
  journal={arXiv: Quantum Physics},
  year={2002}
}

• C. Castro, J. Mahecha, B. Rodríguez
• Published 5 February 2002
• Physics, Mathematics
• arXiv: Quantum Physics

A new nonlinear Schrodinger equation is obtained explicitly from the fractal Brownian motion of a massive particle with a complex-valued dif- fusion constant. Real-valued energy (momentum) plane wave and soliton solutions are found in the free particle case. The hydro-dynamical model analog yields another (new) nonlinear QM wave equation with physically meaningful soliton solutions. One remarkable feature of this nonlinear Schrodinger equation based on a fractal Brownian motion model, over all the other nonlinear QM models, is that the quantum-mechanical energy functional coincides with the field theory one.