Josephson Oscillation and Transition to Self-Trapping for Bose-Einstein-Condensates in a Triple-Well Trap

We investigate the tunnelling dynamics of Bose-Einstein-Condensates(BECs) in a symmetric as well as in a tilted triple-well trap within the framework of mean-field treatment. The eigenenergies as the functions of the zero-point energy difference between the tilted wells show a striking entangled star structure when the atomic interaction is large. We then achieve insight into the oscillation solutions around the corresponding eigenstates and observe several new types of Josephson oscillations. With increasing the atomic interaction, the Josephson-type oscillation is blocked and the self-trapping solution emerges. The condensates are self-trapped either in one well or in two wells but no scaling-law is observed near transition points. In particular, we find that the transition from the Josephson-type oscillation to the self-trapping is accompanied with some irregular regime where tunnelling dynamics is dominated by chaos. The above analysis is facilitated with the help of the Poicar\'{e} section method that visualizes the motions of BECs in a reduced phase plane.Comment: 10 pages, 11 figure

A privacy-preserving, decentralized and functional Bitcoin e-voting protocol

Bitcoin, as a decentralized digital currency, has caused extensive research interest. There are many studies based on related protocols on Bitcoin, Bitcoin-based voting protocols also received attention in related literature. In this paper, we propose a Bitcoin-based decentralized privacy-preserving voting mechanism. It is assumed that there are n voters and m candidates. The candidate who obtains t ballots can get x Bitcoins from each voter, namely nx Bitcoins in total. We use a shuffling mechanism to protect voter's voting privacy, at the same time, decentralized threshold signatures were used to guarantee security and assign voting rights. The protocol can achieve correctness, decentralization and privacy-preservings. By contrast with other schemes, our protocol has a smaller number of transactions and can achieve a more functional voting method.Comment: 5 pages;3 figures;Smartworld 201