Jensen-Shannon Divergence and Non-linear Quantum Dynamics

Using the statistical inference method, a non-relativistic, spinless, non-linear quantum dynamical equation is derived with the Fisher information metric substituted by the Jensen-Shannon distance information. Among all possible implications, it is shown that the non-linear Schr\"odinger equati...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Molladavoudi, Saeid, Zainuddin, Hishamuddin, Chan, Kar Tim
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.10.2012
Subjects
Divergence
Hilbert space
Mathematics - Mathematical Physics
Nonlinear dynamics
Physics - Mathematical Physics
Statistical inference
Online AccessGet full text

Cover

More Information
Summary:Using the statistical inference method, a non-relativistic, spinless, non-linear quantum dynamical equation is derived with the Fisher information metric substituted by the Jensen-Shannon distance information. Among all possible implications, it is shown that the non-linear Schr\"odinger equation preserves the symplectic structure of the complex Hilbert space, hence a Hamiltonian dynamics. The canonically projected dynamics is obtained on the corresponding projective Hilbert space of pure state density operators.
ISSN:2331-8422
DOI:10.48550/arxiv.1210.3879