Roberto Laura

Functional approach to quantum decoherence and the classical final limit

A quantum system with discrete and continuos evolution spectrum is studied. A final pointer basis is found, that can be defined in a presised mathematical way. This result is use to explain the quantum measurement in the system.

Functional Approach to Quantum Decoherence and the Classical Final Limit: The Mott and Cosmological Problems

Decoherence and the approach to the classical final limit are studied in twosimilar cases: the Mott and the cosmological problems.

A general theoretical framework for decoherence in open and closed systems

A general theoretical framework for decoherence is proposed, which encompasses formalisms originally devised to deal just with open or closed systems. The conditions for decoherence are clearly stated and the relaxation and decoherence times are compared. Finally, the spin-bath model is developed in detail from the new perspective.

Gamow functionals on operator algebras

We obtain the precise form of two Gamow functionals representing the exponentially decaying part of a quantum resonance and its mirror image that grows exponentially, as a linear, positive and continuous functional on an algebra containing observables. These functionals do not admit normalization and, with an appropriate choice of the algebra, are time reversal of each other.

Quantum decay processes and Gamov states

By extending the notion of states to functionals acting on the space of observables we obtain a well-defined complex spectral decomposition for the time evolution of quantum-decaying systems, where Gamov states play a fundamental role. It is shown that Gamov vectors are well-defined state functionals and, therefore, they stand on the same footing as plane waves.

A General Conceptual Framework for Decoherence in Closed and Open Systems

In this paper we argue that the formalisms for decoherence originally devised to deal just with closed or open systems can be subsumed under a general conceptual framework, in such a way that they cooperate in the understanding of the same physical phenomenon. This new perspective dissolves certain conceptual difficulties of the einselection program but, at the same time, shows that the openness of the quantum system is not the essential ingredient for decoherence.

The Gamow Functional.

We present a formalism that represents pure states, mixtures and generalized states as functionals on an algebra containing the observables of the system. Along these states, there are other functionals that decay exponentially at all times and therefore can be used to describe resonance phenomena.

Perturbative method for generalized spectral decompositions

Imposing analytic properties to states and observables we construct a perturbative method to obtain a generalized biorthogonal system of eigenvalues and eigenvectors for quantum unstable systems. A decay process can be described using this generalized spectral decomposition, and the final generalized state is obtained.

Gamow Vectors and Time Asymmetry

We prove that Gamow vectors are important toolsin the quantum theory of irreversibility. We use themathematical formalism of rigged Hilbert spaces. Wediscuss some spectral formulas that include Gamow vectors as well as some results concerningGamow vectors. The role of the time-reversal operator isstudied. The formalism can be applied to formulate asense of irreversibility in cosmology.

Quantum histories without contrary inferences

Abstract In the consistent histories formulation of quantum theory it was shown that it is possible to retrodict contrary properties. We show that this problem do not appear in our formalism of generalized contexts for quantum histories.