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Exact calculations of collective excitations and charge/spin (pseudo)gaps inan ensemble of bipartite and nonbipartite clusters yield level crossingdegeneracies, spin-charge separation, condensation and recombination ofelectron charge and spin, driven by interaction strength, inter-site couplingsand temperature. Near crossing degeneracies, the electron configurations of thelowest energies control the physics of electronic pairing, phase separation andmagnetic transitions. Rigorous conditions are found for the smooth and dramaticphase transitions with competing stable and unstable inhomogeneities.Condensation of electron charge and spin degrees at various temperatures offersa new mechanism of pairing and a possible route to superconductivity ininhomogeneous systems, different from the BCS scenario. Small bipartite andfrustrated clusters exhibit charge and spin inhomogeneities in many respectstypical for nano and heterostructured materials. The calculated phase diagramsin various geometries may be linked to atomic scale experiments in high T$_c$cuprates, manganites and other concentrated transition metal oxides.

Electron coherent and incoherent pairing instabilities in inhomogeneous bipartite and nonbipartite nanoclusters