# 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…

## 12 Citations

### On Nonlinear Quantum Mechanics, Brownian Motion, Weyl Geometry and Fisher Information

- Physics
- 2009

A new nonlinear Schrodinger equation is obtained explicitly from the (fractal) Brownian motion of a massive particle with a complex-valued diffusion constant. Real-valued energy plane-wave solutions…

### Torsion Fields, Brownian Motions, Quantum and Hadronic Mechanics

- Mathematics, Physics
- 2008

We review the relation between space-time geometries with torsion fields (the so-called Riemann-Cartan-Weyl (RCW) geometries) and their associated Brownian motions. In this setting, the metric…

### Quantization in Astrophysics, Brownian Motion, and Supersymmetry

- Physics
- 2020

The present book discusses, among other things, various quantization phenomena found in Astrophysics and some related issues including Brownian Motion. With recent discoveries of exoplanets in our…

### Double-slit and Aharonov-Bohm experiments in magnetic field

- Physics
- 2022

We discuss the two-slit experiment and the Aharonov-Bohm (AB) experiment in the magnetic field. In such a case the electron moving in the magnetic field produces so called synchrotron radiation. In…

### Two-Slit and Aharonov-Bohm Experiments in Magnetic Field

- Physics
- 2008

We discuss the two-slit experiment and the Aharonov-Bohm (AB) experiment in the magnetic field. In such a case the electron moving in the magnetic field produces so called synchrotron radiation. In…

### A Journey into Quantization in Astrophysics

- Physics
- 2015

In a number of preceding papers we introduced a new PT-symmetric periodic potential, derived from biquaternion radial Klein-Gordon equation. In the present paper we will review our preceding result,…

### Unfolding the Labyrinth: Open Problems in Mathematics, Physics, Astrophysics, and Other Areas of Science

- Physics, Education
- 2006

Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the…

### The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics Progress in Physics Information for Authors and Subscribers Ultracold Fermi and Bose Gases and Spinless Bose Charged Sound Particles

- Physics
- 2006

2011 Volume 4 " All scientists shall have the right to present their scientific research results, in whole or in part, at relevant scientific conferences, and to publish the same in printed…

### The Trickle up Effect: a Collection of Economic and Scientific Papers

- Economics
- 2013

This book consists of a number of economics, mathematics, and scientific papers, covering different subjects, from global corporate control to cosmology issues. Hopefully the readers will find some…

### QUANTIZATION AND DISCRETIZATION AT LARGE SCALES

- Physics, Geology
- 2012

The ongoing search of extrasolar planets is one of the most attractive fields of research in astrophysics and astronomy nowadays. Up to now, 360 extrasolar planets have been discovered near stars…

## References

SHOWING 1-10 OF 26 REFERENCES

### Dirac Equation in Scale Relativity

- Physics, Mathematics
- 2001

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

- Physics
- 1990

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

- Physics
- 2008

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

- Mathematics
- 2005

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

- Physics
- 1995

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

- Physics
- 2001

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

- Mathematics
- 2005

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