On the connection between certain properties of the second‐order reduced density matrix and the occurrence of coherent‐dissipative structures in disordered condensed matter

It is demonstrated, from general physical principles, that a new kind of quantum correlations, associated with the appropriate reduced density matrix, Γ, exist in amorphous condensed matter. The treatment starts from general representation properties of the second-order reduced density matrix. The derivations, using general statistical notions in a quantum mechanical framework, lead to a decomposition of the two-matrix into the large-, the small-, and the unpaired components. Since this result can be identified with the extreme case of Coleman, the formulation is automatically ensemble-representable. Introducing the complex scaling method (CSM) into the Bloch–Liouville equation for Γ it is shown how the temperature T in the aforementioned ensemble can be specified. This defines, in the present development, thermalization in a system far from equilibrium. It is further shown that this thermalization leads to the formation of certain irreducible (Jordan) blocks containing some (incomplete) phase information. The connection between these irreducible blocks and the concept of a coherent-dissipative structure is made. The treatment reveals general features of the coherent-dissipative structure and a certain universality of the coherence-breaking mechanism. The main equations relate the relaxation time Trcl and the temperature T with the minimum degrees of freedom Smin and the associated spatial domain dmin of the structure. Relevant examples are, e.g., proton transfer and H+ conductivity in water, conductivity of molten alkali chlorides, quantum correlation effects in high-Tc superconductors, and spin dynamics of Gd far above the Curie point.