Open AccessConnections between ’t Hooft’s beables and canonical descriptions of dissipative systems
Author(s) -
Dieter Schuch,
Massimo Blasone
Publication year - 2017
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/880/1/012050
Subject(s) - dissipative system , canonical transformation , quantization (signal processing) , canonical quantization , hamiltonian (control theory) , canonical coordinates , canonical form , hamiltonian system , classical mechanics , physics , transformation (genetics) , mathematics , theoretical physics , pure mathematics , quantum mechanics , quantum , algorithm , mathematical optimization , biochemistry , chemistry , quantum gravity , phase space , gene
According to a proposal by 't Hooft, information loss introduced by constraints in certain classical dissipative systems may lead to quantization. This scheme can be realized within the Bateman model of two coupled oscillators, one damped and one accelerated. In this paper we analyze the links of this approach to effective Hamiltonians where the environmental degrees of freedom do not appear explicitly but their effect leads to the same friction force appearing in the Bateman model. In particular, it is shown that by imposing constraints, the Bateman Hamiltonian can be transformed into an effective one expressed in expanding coordinates. This one can be transformed via a canonical transformation into Caldirola and Kanai's effective Hamiltonian that can be linked to the conventional system-plus-reservoir approach, for example, in a form used by Caldeira and Leggett