Superscattering operators, lie- admissible generalizations of quantum mechanics and dynamical semigroups

Abstract

We analyse the notion of superscattering operators (operators which can describe transitions from an initial to a final density operator via an irreversible process) within the frameworks provided by Lie-admissible generalizations of quantum mechanics and by the theory of dynamical semigroups. Mignani has shown that the non-factorizability of the superscattering operator is a straightforward consequence of the non-potential scattering theory in the framework of the Lie-admissible formalism. A very naive reading of this formalism leads us to the somewhat dual statement that superscattering operators always factorize, though in general not in terms of unitary operators. It is furthermore found that superscattering operators can be hosted in the theory of semigroups at the cost of a serious restriction of the notion and a suitable enlargement of the definition of semigroup.