Modular Schr\"{o}dinger equation and dynamical duality
Quantum Physics
2009-11-13 v2 Statistical Mechanics
High Energy Physics - Theory
Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We discuss quite surprising properties of the one-parameter family of modular (Auberson and Sabatier (1994)) nonlinear Schr\"{o}dinger equations. We develop a unified theoretical framework for this family. Special attention is paid to the emergent \it dual \rm time evolution scenarios which, albeit running in the \it real time \rm parameter of the pertinent nonlinear equation, in each considered case, may be mapped among each other by means of an "imaginary time" transformation (more seriously, an analytic continuation in time procedure).
Cite
@article{arxiv.0805.1536,
title = {Modular Schr\"{o}dinger equation and dynamical duality},
author = {Piotr Garbaczewski},
journal= {arXiv preprint arXiv:0805.1536},
year = {2009}
}
Comments
To appear in Phys. Rev. E (2008)