Coherence in Disordered Condensed Matter. I: Dissipative Structures in Liquids and Dynamics of Far‐Infrared Absorption

Abstract

AbstractThe Complex Scaling Method (CSM), in connection with Prigogine's Subdynamics predicts the spontaneous emergence of large dissipative (or: coherent) structures in amorphous matter, like liquids. The connection between these structures and the appearance of a large Jordan block (see appendix) with Segré characteristic equal to the dimension or degrees of freedom of the emerged structure, in the CSM‐transformed reduced second order density matrix, is presented and analysed in some detail. The interdependence of the present theoretical considerations with Yang's concept of off‐diagonal long‐range order (ODLRO) is stressed. – The appearance of dissipative structures is accompanied by a quantization condition for the lifetimes of the states contributing to the creation of those structures. The minimum size nmin of a dissipative structure obeys the equation nmin ≅ τrot · (2πkBT/h), where τrot represents the molecular relaxation time that is to be determined by a suitable spectroscopic experiment. – Application to far‐infrared (FIR) absorption spectroscopy is made explicitly. The above formula allows for a surprising interpretation of the well‐known anomalous temperature dependence of the FIR bands from first principles. The “size” of the dissipative structures that contribute to the FIR absorption in liquids is estimated.