2013/06/18 by Dieter Schuch, Julio Guerrero, Schuch, Dieter +5 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical Physics (physics.class-ph) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1306.4533
openalex publication_date 2013/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are many approaches for the description of dissipative systems coupled\nto some kind of environment. This environment can be described in different\nways; only effective models will be considered here. In the Bateman model, the\nenvironment is represented by one additional degree of freedom and the\ncorresponding momentum. In two other canonical approaches, no environmental\ndegree of freedom appears explicitly but the canonical variables are connected\nwith the physical ones via non-canonical transformations. The link between the\nBateman approach and those without additional variables is achieved via\ncomparison with a canonical approach using expanding coordinates since, in this\ncase, both Hamiltonians are constants of motion. This leads to constraints that\nallow for the elimination of the additional degree of freedom in the Bateman\napproach. These constraints are not unique. Several choices are studied\nexplicitly and the consequences for the physical interpretation of the\nadditional variable in the Bateman model are discussed.\n