Description of Compound Physical Systems and Logical Interaction of Physical Systems

Maria Cristina Abbati, Alessandro Manià

Frank Valckenborgh

G. Scolarici, Luigi Solombrino

We analyse some features of alternative Hermitian and quasi-Hermitian quantum descriptions of simple and bipartite compound systems. We show that alternative descriptions of two interacting subsystems are possible if and only if the metric operator of the compound system can be obtained as a tensor product of positive operators on component spaces. Some examples also show that such property could be strictly connected with symmetry properties of the non-Hermitian Hamiltonian.

Krystyna Bugajska, Slawomir Bugajski

Enrico G. Beltrametti, Gianni Cassinelli, Peter Carruthers

Composition of Different and of Identical Systems It is a general tendency of physics to interpret physical systems as composed of simpler, more elementary subsystems. The question “What is it made of?” is a very tempting and popular one. Though this attitude does not reflect a logical necessity, it has proved to be successful in significant circumstances: we think, e.g., of macroscopic matter as composed of atoms and molecules, of molecules as composed of atoms, of atoms as composed of nuclei and electrons, and of nuclei as composed of protons and neutrons. Loosely speaking, one might expect that this attitude will be successful whenever the interaction that packs the constituent subsystems together is not strong enough to make them lose their identity. Here, we are concerned with the problem of constructing the quantum-mechanical formalism of a compound system knowing the formalisms of the constituent subsystems. Thus our first problem is to specify the Hilbert space of the compound system. For the sake of simplicity, let us restrict ourselves to the case of a system composed of only two subsystems. The prescriptions of quantum theory vary according to whether one is faced with the composition of identical or nonidentical subsystems.

Enrico G. Beltrametti, Gianni Cassinelli, Peter Carruthers