Quantum Kinetic Evolution of Marginal Observables

We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics of a solution of the initial-value problem of the dual quantum BBGKY hierarchy is constructed. Moreover, links of the evolution of marginal observables and the evolution of quantum states described in terms of a one-particle marginal density operator are established. Such approach gives the alternative description of the kinetic evolution of quantum many-particle systems to generally accepted approach on basis of kinetic equations.Comment: 18 page

Effectiveness and Compatibility of a Novel Sustainable Method for Stone Consolidation Based on Di-Ammonium Phosphate and Calcium-Based Nanomaterials

External surfaces of stones used in historic buildings often carry high artistic value and need to be preserved from the damages of time, especially from the detrimental effects of the weathering. This study aimed to test the effectiveness and compatibility of some new environmentally-friendly materials for stone consolidation, as the use thereof has been so far poorly investigated. The treatments were based on combinations of an aqueous solution of di-ammonium phosphate (DAP) and two calcium-based nanomaterials, namely a commercial nanosuspension of Ca(OH)2 and a novel nanosuspension of calcite. The treatments were applied to samples of two porous stones: a limestone and a sandstone. The effectiveness of the treatments was assessed using scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy, Fourier-transform infrared spectroscopy, ultrasound pulse velocity test, colour measurements, and capillary water absorption test. The results suggest that the combined use of DAP and Ca-based nanosuspensions can be advantageous over other commonly used consolidants in terms of retreatability and physical-chemical compatibility with the stone. Some limitations are also highlighted, such as the uneven distribution and low penetration of the consolidants