Positivity Preserving non-Markovian Master Equation for Open Quantum System Dynamics: Stochastic Schr\"{o}dinger Equation Approach

Positivity preservation is naturally guaranteed in exact non-Markovian master equations for open quantum system dynamics. However, in many approximated non-Markovian master equations, the positivity of the reduced density matrix is not guaranteed. In this paper, we provide a general class of time-local, perturbative and positivity-preserving non-Markovian master equations generated from stochastic Schrodinger equations, particularly quantum-state-diffusion equations. Our method has an expanded range of applicability for accommodating a variety of non-Markovian environments. We show the positivity-preserving master equation for a three-level system coupled to a dissipative bosonic environment as a particular example to exemplify our general approach. We illustrate the numerical simulations with an analysis explaining why the previous approximated non-Markovian master equations cannot guarantee positivity. Our work provides a consistent master equation for studying the non-Markovian dynamics in ultrafast quantum processes and strong-coupling systems.Comment: 9 pages, 4 figure

Effect of Micro-Scale Er on the Microstructure and Fluidity of ZL205A Alloy

The effect of Er addition on the fluidity and microstructure transformation of the as-cast and T5 heat-treated ZL205A alloys was investigated by optical microscope (OM), scanning electron microscopy (SEM), X-ray diffraction (XRD) and energy dispersive spectrometer (EDS). The fluidity of the liquid metal after adding Er was tested and the fracture characteristics of the material were analyzed. The results indicated that Er was mainly dissolved into an α–Al matrix near the grain boundaries (GBs). It is easily segregated and enriched in the intersection of the GBs or the interface between the α and θ phase, which caused the intermetallic compounds to be distributed along the GBs to the neck and to fuse. Er could also inhibit the diffusion of Cu atoms in the process of solid solution, so that increased the residual eutectic structures in the crystal, while accelerating the precipitation progress of the Guinier–Preston (GP) zone and θ’ phase and increasing precipitation of the θ phase. A small amount of precipitation of θ phase and micro-scale Er (0.1–0.5 wt %) can significantly increase the fluidity and reduce the casting defects, which can effectively improve the castability of the ZL205A alloy. The interface between the (Al8Cu4Er) phase and matrix is the main area of microcracks, through analyzing the fracture morphology