Semi-Groups and Time Operators for Quantum Unstable Systems



We use spectral projections of time operator in the Liouville space for simple quantum scattering systems in order to define a space of unstable particle states evolving under a contractive semi-group. This space includes purely exponentially decaying states that correspond to complex eigenvalues of this semi-group. The construction provides a probabilistic interpretation of the resonant states characterized in terms of the Hardy class.


quantum ustable system time operator semigroup time evolution Hardy spaces Liouville spaces 


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique de la Matière CondenséeUniversité Paris 7 – Denis DiderotParis Cedex 05France

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