Coexistence of observables

PEKKA J. LAHTI, Sylvia Pulmannová

PEKKA J. LAHTI, Sylvia Pulmannová, Kari Ylinen

We characterize functionally coexistent observables in terms of biobservables and joint observables. Coexistent sets of effects are characterized in terms of projective systems of simple observables.

Olivia Nicoletti

Yasushi Yoneta, Akira Shimizu

Coexisting phases in a phase coexistence state cannot be distinguished by thermodynamic forces, such as temperature and chemical potential, because the forces take the same values over all coexisting phases. Therefore, to investigate a phase coexistence state, it is necessary to employ an ensemble in which all additive observables that distinguish the coexisting phases have macroscopically definite values. Although the microcanonical ensemble is conventionally employed as such an ensemble, it becomes ill-defined when some of the additive observables do not commute with each other, and a new ensemble has been craved. We propose a novel class of ensembles such that the additive observables, which are generally noncommutative, always have macroscopically definite values even in a first-order phase transition region. Using these ensembles, we propose a concrete method to construct phase coexistence states of general quantum systems. Furthermore, these ensembles are convenient for practical calculations because of good analytic properties. To demonstrate that our formulation successfully gives phase coexistence states of quantum systems, we apply it to a two-dimensional system whose coexisting phases are distinguished by an additive observable (order parameter) that does not commute with the Hamiltonian. To the author's best knowledge, this is the first work that obtains phase coexistence states separated by phase interfaces at finite temperature in such a quantum system.