Majorana zero modes and their bosonization

The simplest continuum model of a one-dimensional non-interacting superconducting fermionic symmetry-protected topological (SPT) phase is studied in great detail using analytical methods. In a first step, we present a full exact diagonalization of the fermionic Bogoliubov-de Gennes Hamiltonian for a system of finite length and with open boundaries. In particular, we derive exact analytical expressions for the Majorana zero modes emerging in the topologically non-trivial phase, revealing their spatial localization, their transformation properties under symmetry operations, and the exact finite-size energy splitting of the associated quasi-degenerate ground states. We then proceed to analyze the model via exact operator bosonization in both open and closed geometries. In the closed wire geometry, we demonstrate fermion parity switching from twisting boundary conditions in the topologically non-trivial phase. For the open wire, on the other hand, we first take a semiclassical approach employing the Mathieu equation to study the two quasi-degenerate ground states as well as their energy splitting at finite system sizes. We then finally derive the exact forms of the Majorana zero modes in the bosonic language using vertex-algebra techniques. These modes are verified to be in exact agreement with the results obtained from the fermionic description. The complementary viewpoints provided by the fermionic and bosonic formulations of the superconducting SPT phase are reconciled, allowing us to provide a complete and exact account of how Majorana zero modes manifest in a bosonized description of an SPT phase

Setting up Pharmaceutical Laboratory Business in China: An Exploratory Study

This project is trying to explore the possibility of Pharmaceutical Division, Applied Sciences Group (ASG), a division in Health Sciences Authority (HSA), Ministry of Health in setting up a pharmaceutical laboratory with office in People’s Republic of China. There are several objectives in doing so but the main objective is to generate revenues in a new booming economy in Asia - China. The author is a certified foreign expert appointed by the Mayors of Shaoxing city (2003) and Xian city (2006). I had worked in China for four years as a Head of Department and Administrator. This project seeks to affirm the critical success factors (CSFs) that HSA and other pharmaceutical/ healthcare-related organisations should be aware of when venturing into China Two centuries ago, Napoleon warned all in that China was a ‘sleeping giant’ that ‘once awake would astonish the world’. That prediction looks like it is about to be fulfilled – look at its amazing economic growth and market size. This project was carried out to evaluate whether HSA should venture into China. Through HSA is a statutory board but there are discussions whether to privatise ASG. China is an emerging market that many cannot ignore it. This project seeks to analyse the economic figures, trends and statistics. Interviews were carried out to collect valuable opinions by experts connected closely to China and science fields – scientists, China Embassy in Singapore, Singapore-China Business Association and Chinese lawyers located in Shanghai etc. Conversation analysis was carried out from interviewees’ comments. At the end of this project, recommendations using country specific advantages (CSAs), firm specific advantages (FSAs) and critical success factors (CSFs) were proposed how HSA could venture into China