Connections between 't Hooft's beables and canonical descriptions of dissipative systems

[摘要] 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.

[发布机构] Institut für Theoretische Physik, J.W. Goethe-Universität Frankfurt Am Main, Max-von-Laue-Str. 1, Frankfurt am Main; D-60438, Germany^1;Dipartimento di Fisica, Università di Salerno, Via Giovanni Paolo II, 132, Fisciano (SA); 84084, Italy^2;Istituto Nazionale di Fisica Nucleare (INFN), Gruppo Collegato di Salerno, Italy^3

[效力级别] 力学 [学科分类] 力学，机械学

[关键词] Canonical transformation;Conventional systems;Coupled oscillators;Dissipative systems;Effective Hamiltonian;Friction force;Information loss