Interrelations between different canonical descriptions of dissipative systems

DOI: 
10.1088/0031-8949/90/4/045209
Publication date: 
01/04/2015
Main author: 
Schuch D.
IAA authors: 
Aldaya V.
Authors: 
Schuch D., Guerrero J., López-Ruiz F.F., Aldaya V.
Journal: 
Physica Scripta
Publication type: 
Article
Volume: 
90
Pages: 
Number: 
045209
Abstract: 
There are many approaches for the description of dissipative systems coupled to some kind of environment. This environment can be described in different ways; only effective models are being considered here. In the Bateman model, the environment is represented by one additional degree of freedom and the corresponding momentum. In two other canonical approaches, no environmental degree of freedom appears explicitly, but the canonical variables are connected with the physical ones via non-canonical transformations. The link between the Bateman approach and those without additional variables is achieved via comparison with a canonical approach using expanding coordinates, as, in this case, both Hamiltonians are constants of motion. This leads to constraints that allow for the elimination of the additional degree of freedom in the Bateman approach. These constraints are not unique. Several choices are studied explicitly, and the consequences for the physical interpretation of the additional variable in the Bateman model are discussed. © 2015 The Royal Swedish Academy of Sciences.
Database: 
WOK
SCOPUS
ADS
SCOPUS
URL: 
https://ui.adsabs.harvard.edu/#abs/2015PhyS...90d5209S/abstract
ADS Bibcode: 
2015PhyS...90d5209S
Keywords: 
Bateman; Caldirola Kanai; classical mechanics; constraints; dissipation; expanding coordinate