Quantum-dynamical semigroup generators for proton-spin relaxation in water.

Abstract

Various aspects of a rather general treatment of proton-spin relaxation in water are discussed within the framework of quantum-dynamical semigroup theory for a four-level system coupled to a reservoir in equilibrium. In particular, the specifications of the infinitesimal generator of time evolution, either in Kossakowski or in Davies form, are worked out in detail. With the help of the Lie algebra of SU(4), the results are used to derive, under suitable simplifications, generalized Bloch equations for the static and alternating-field case. The relevant correlation functions are calculated using conventional approaches but supplemented by taking into account explicitly results from a stochastic model for formation and breaking of hydrogen bridges. A further approximate reduction of the coupled general equations to simpler ordinary Bloch equations leads to an identification of the relevant relaxation times. This approach provides a somewhat different interpretation of rotational correlation times whose numerical values are estimated over a wide temperature range.