The so-called Lindblad equation, a typical master equation describing the dissipative quantum dynamics, is shown to be solvable for finite-level systems in a compact form without resort to writing it down as a set of equations among matrix elements. The solution is then naturally given in an operator form, known as the Kraus representation. Following a few simple examples, the general applicability of the method is clarified.

A qubit (a spin-1/2 particle) prepared in the up state is scattered by local spin-flipping potentials produced by the two target qubits (two fixed spins), both prepared in the down state, to generate an entangled state in the latter when the former is found in the down state after scattering. The scattering process is analyzed in three dimensions, both to lowest order and in full order in perturbation, with an appropriate renormalization for the latter. The entanglement is evaluated in terms of the concurrence as a function of the incident and scattering angles, the size of the incident wave packet, and the detector resolution, to clarify the key elements for obtaining an entanglement with high quality. The characteristics of the results are also discussed in the context of (in)distinguishability of alternative paths for a quantum particle.

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As population decline advances in the mountain areas that cover the major part of Japan's land area, nurturing human resources for local revitalization has become a crucial issue.In the mountain areas of the Chugoku region, almost all residents have had the experience of migrating to cities for education or employment during the early part of their life course. Using the concept of "outsiders grown up inside their hometown," this study considers how family business successors form hybrid identities that combine the natures of a local resident and a city resident and how nurturing "outsiders grown up inside their hometown" may serve as the driving force behind local revitalization.The study approaches the construction of identity from temporal and spatial aspects. To clarify the process by which the two identities integrate while experiencing internal conflict, the life story method was employed to conduct empirical surveys with family business successors. The analysis reveals the fact that family business successors, with their hybrid identities, face structural changes related to population decline in the local community. In the narratives of the family business successors, when changes in the local community turned into problems that impacted the family business, the nature of "outsiders who grew up inside their hometown" functioned as an agency of business reform.Arguments concerning local revitalization have thus far often emphasized the opposing aspects of endogenous development through nurturing and harnessing the unique characteristics and spontaneity of local residents and exogenous development that incorporates a new sense of values from outsiders. In contrast, the findings of this study point to the importance of research into the hybrid identity of human resources for local revitalization in mountain areas, where the issue of family business succession is simultaneously endogenous and exogenous.