General properties between the canonical correlation and the independent-oscillator model on a partial *-algebra. (English) Zbl 0896.46050
Summary: We consider a quantum particle in thermal equilibrium with any quantum system in a finite volume under some conditions. For the Heisenberg operator of the momentum operator of the quantum particle, we show that, on a partial \(^*\)-algebra, the Heisenberg operator satisfies a quantum Langevin equation, which is similar to the work of [G. W. Ford, J. T. Lewis and R. F. O’Connell, Phys. Rev. A 37, 4419 (1988)]. Through the Langevin equation, we show general and mathematical properties between the canonical correlation and the independent-oscillator model.
MSC:
| 46N50 | Applications of functional analysis in quantum physics |
| 47L60 | Algebras of unbounded operators; partial algebras of operators |
| 46L60 | Applications of selfadjoint operator algebras to physics |
| 81T10 | Model quantum field theories |
Keywords:
quantum particle in thermal equilibrium; Heisenberg operator; momentum operator; partial \(^*\)-algebra; quantum Langevin equationReferences:
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