Mathematical Models for Unstable Quantum Systems and Gamow States.

We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces.

Coherence resource power of isocoherent states.

We address the problem of comparing quantum states with the same amount of coherence in terms of their coherence resource power given by the preorder of incoherent operations. For any coherence measure, two states with null or maximum value of coherence are equivalent with respect to that preorder. This is no longer true for intermediate values of coherence when pure states of quantum systems with dimension greater than two are considered.

Transformations of superpositions by means of incoherent operations.

In this paper we study how the coherence of a superposition of pure states is related with the coherence of its components. We consider two pure initial states and two pure final coherent states, such that the former ones cannot be transformed into the latter ones by means of incoherent transformations. In this situation, we analyze conditions for the existence of superpositions of the initial states that can be transformed into superpositions of the final states.