Modular Schrödinger equation and dynamical duality

Piotr Garbaczewski
Phys. Rev. E 78, 031101 – Published 2 September 2008

Abstract

We discuss quite surprising properties of the one-parameter family of modular nonlinear Schrödinger equations [G. Auberson and P. G. Sabatier, J. Math. Phys. 35, 4028 (1994)]. We develop a unified theoretical framework for this family. Special attention is paid to the emergent dual time evolution scenarios which, albeit running in the real time parameter of the pertinent nonlinear equation, in each considered case may be mapped among each other by means of a suitable analytic continuation-in-time procedure. This dynamical duality is characteristic for nondissipative quantum motions and their dissipative (diffusion-type processes) partners, and naturally extends to classical motions in confining and scattering potentials.

  • Received 12 May 2008

DOI:https://doi.org/10.1103/PhysRevE.78.031101

©2008 American Physical Society

Authors & Affiliations

Piotr Garbaczewski*

  • Institute of Physics, University of Opole, 45-052 Opole, Poland

  • *pgar@uni.opole.pl

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 78, Iss. 3 — September 2008

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×