Evolution of quantum observables: from non-commutativity to commutativity

SEBASTIAN FORTIN; MANUEL GADELLA; FEDERICO HOLIK; MARCELO LOSADA

SOFT COMPUTING - (Print)

SPRINGER

Lugar: Berlin; Año: 2019

1472-7643

A fundamental aspect of the quantum-to-classical limit is the transition from a noncommutative algebra of observables to commutative one.However, this transition is not possible if we only consider unitary evolutions. One way to describe this transition is to consider the Gamow vectors, which introduce exponential decays in the evolution. In this paper, we give two mathematical models in which this transition happens in the infinite time limit.In the first one, we consider operators acting on the space of the Gamow vectors,which represent quantum resonances. In the second one, we use an algebraicformalism from scattering theory. We construct a non-commuting algebra whichcommutes in the infinite time limit.