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We establish the limiting dynamics of a class of inhomogeneous bipolaronic models for superconductivity which incorporate deviations from the homogeneous models strong enough to require disjoint representations. The models are of the Hubbard type and the thermodynamics of their homogeneous part has been already elaborated by the authors. Now the dynamics of the systems is evaluated in terms of a generalized perturbation theory and leads to a C*-dynamical system over a classically extended algebra of observables. The classical part of the dynamical system, expressed by a set of 15 nonlinear differential equations, is observed to be independent from the perturbations. The KMS states of the C*-dynamical system are determined on the state space of the extended algebra of observables. The subsimplices of KMS states with unbroken symmetries are investigated and used to define the “type” of a phase. The KMS phase diagrams are worked out explicitly and compared with the thermodynamic phase structures obtained in the preceding works.

We continue the discussion of a bipolaronic superconductor (resp. an anisotropic antiferromagnet in quasispin formulation) as formulated in a previous work, based on a quantum-statistical, microscopic mean-field model. The grand-canonical thermodynamic limit is compared with the canonical thermodynamic limit in terms of a net of perturbations, becoming singular in the infinite lattice limit. A generalized thermostatistical framework is elaborated which covers model potentials with infinite parts. The function of the limiting free energy density in selecting the (stable) phases with broken symmetry is graphically illustrated. The phase diagrams for the two types of ensembles are shown to differ in the region where both the gauge symmetry and the invariance under sublattice exchange are broken. In particular, the type of the phase transitions, the order of the critical points, and the shape of some phase boundaries are found to depend on the ensemble, which clarifies certain controversial topics for these models. The uniqueness of the limiting Gibbs states with free boundary conditions in all thermodynamic phase regions is proved, and their decomposition into pure phase states in terms of a symmetric measure is evaluated. The field operators of the condensed particles are determined in the representations over the limiting Gibbs states.

In the frame of operator-algebraic quantum statistical mechanics we calculate the grand canonical equilibrium states of a bipartite, microscopic mean-field model for bipolaronic superconductors (or anisotropic antiferromagnetic materials in the quasispin formulation). Depending on temperature and chemical potential, the sets of statistical equilibrium states exhibit four qualitatively different regions, describing the normal, superconducting (spin-flopped), charge ordered (antiferromagnetic), and coexistence phases. Besides phase transitions of the second kind, the model also shows phase transitions of the first kind between the superconducting and the charge ordered phases. A unique limiting Gibbs state is found in its central decomposition for all temperatures, even in the coexistence region, if the thermodynamic limit is performed at fixed particle density (magnetization).