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Rigged Hilbert spaces and time asymmetry: The case of the upside-down simple harmonic oscillator

1997; Springer Science+Business Media; Volume: 36; Issue: 11 Linguagem: Inglês

10.1007/bf02768929

0020-7748

Morio Castagnino, Roberto B. Diener, Luis Lara, Gabriel D. Puccini,

Advanced Thermodynamics and Statistical Mechanics

The upside-down simple harmonic oscillator system is studied in the contexts of quantum mechanics and classical statistical mechanics. It is shown that in order to study in a simple manner the creation and decay of a physical system by way of Gamow vectors we must formulate the theory in a time-asymmetric fashion, namely using two different rigged Hilbert spaces to describe states evolving toward the past and the future. The spaces defined in the contexts of quantum and classical statistical mechanics are shown to be directly related by the Wigner function.