• 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}
}
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… 

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References

SHOWING 1-10 OF 26 REFERENCES

Dirac Equation in Scale Relativity

The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows to recover quantum mechanics as mechanics on a

Chaos in classical and quantum mechanics

Contents: Introduction.- The Mechanics of Lagrange.- The Mechanics of Hamilton and Jacobi.- Integrable Systems.- The Three-Body Problem: Moon-Earth-Sun.- Three Methods of Section.- Periodic Orbits.-

On the Staruszkiewicz Modification of the Schrödinger Equation

We discuss Staruszkiewicz’s nonlinear modification of the Schrödinger equation. It is pointed out that the expression for the energy functional for this modification is not unique as the

Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions

Number theory and fractal geometry are combined in this study of the vibrations of fractal strings. The book centres around a notion of complex dimension, originally developed for the proof of the

Quaternionic quantum mechanics and quantum fields

PART I: INTRODUCTION AND GENERAL FORMALISM 1: Introduction 2: General Framework of Quaternionic Quantum Mechanics 3: Further General Results in Quaternionic Quantum Mechanics PART II:

Noncommutative Sp(2,R) gauge theories: A field theory approach to two-time physics

Phase space and its relativistic extension is a natural space for realizing $\mathrm{Sp}(2,R)$ symmetry through canonical transformations. On a $(D\ifmmode\times\else\texttimes\fi{}2)$-dimensional

Random Matrices

The elementary properties of random matrices are reviewed and widely used mathematical methods for both hermitian and nonhermitian random matrix ensembles are discussed.

Stochatic processes applied to physics and other related fields

  • World Scientific
  • 1983

To the nonlinear QM. quant-ph/0111105

  • To the nonlinear QM. quant-ph/0111105

Journal of Chaos, Solitons and Fractals

  • 1994