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Physics Letters B

A quantum mechanical analogue for the q-oscillator

Emmanuel G. Floratos, Theodore N. Tomaras

Published Nov 1, 1990• 18 citations
Publisher
DOI
10.1016/0370-2693(90)90247-4

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An aspect of quantum mechanics that has not been fully understood is the energy shift generated by the time operator. In this study, we introduce the use of the eigensurfaces of dynamical variables and commutators in classical mechanics to study the classical analogue of the quantum translation of energy. We determine that there is a conjugate dynamical system that is conjugate to Hamilton's equations of motion, and then we generate the analogue of the time operator and use it in the translation of points along the energy direction, i.e. the classical analogue of the Pauli theorem. The theory is illustrated with a nonlinear oscillator model.
Analogue models for CP\mathrm{CP}CP violation in neutral-meson systems are studied in a general framework. No-go results are obtained for models in classical mechanics that are nondissipative or that involve one-dimensional oscillators. A complete emulation is shown to be possible for a two-dimensional oscillator with rheonomic constraints, and an explicit example with spontaneous T and CPT\mathrm{CPT}CPT violation is presented. The results have implications for analogue models with electrical circuits.