Open AccessModes and Noise Propagation in Phase Space
Author(s) -
J. Ben-Benjamin,
Leon Cohen
Publication year - 2015
Publication title -
coherent optical phenomena
Language(s) - English
Resource type - Journals
ISSN - 2299-3983
DOI - 10.1515/coph-2015-0003
Subject(s) - hamiltonian (control theory) , phase space , operator (biology) , hermitian matrix , physics , wigner distribution function , dispersion relation , wavenumber , quantum mechanics , attenuation , mathematical physics , mathematical analysis , mathematics , statistical physics , quantum , mathematical optimization , biochemistry , chemistry , repressor , transcription factor , gene
We show that phase space methods developedfor quantum mechanics, such as the Wigner distribution,can be effectively used to study the evolution of nonstationarynoise in dispersive media. We formulate the issuein terms of modes and show how modes evolve andhow they are effected by sources.We show that each modesatisfies a Schrödinger type equation where the “Hamiltonian”may not be Hermitian. The Hamiltonian operatorcorresponds to dispersion relationwhere thewavenumberis replaced by the wavenumber operator. A complex dispersionrelation corresponds to a non Hermitian operatorand indicates that we have attenuation. A number of examplesare given