Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics

The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.     

Resonant-interaction-induced Rydberg antiblockade and its applications

Different from the conventional Rydberg antiblockade (RAB) regime that either requires weak Rydberg-Rydberg interaction (RRI), or compensates the RRI-induced energy shift by introducing off-resonant interactions, we show that RAB regime can be achieved by resonantly driving the transitions between ground state and Rydberg state under strong RRI. The Rabi frequencies are of small amplitude and time-dependent harmonic oscillation, which plays a critical role for the presented RAB. The proposed unconventional RAB regime is used to construct high-fidelity controlled-Z (CZ) gate and controlled-not (CNOT) gate in one step. Each atom requires single external driving. And the atomic addressability is not required for the presented unconventional RAB, which would simplify experimental complexity and reduce resource consumption.     

DNA‐Based Adaptive Plasmonic Logic Gates

Self‐assembled plasmonic logic gates that read DNA molecules as input and return plasmonic chiroptical signals as outputs are reported. Such logic gates are achieved on a DNA‐based platform that logically regulate the conformation of a chiral plasmonic nanostructure, upon specific input DNA strands and internal computing units. With systematical designs, a complete set of Boolean logical gates are realized. Intriguingly, the logic gates could be endowed with adaptiveness, so they can autonomously alter their logics when the environment changes. As a demonstration, a logic gate that performs AND function at body temperature while OR function at cold storage temperature is constructed. In addition, the plasmonic chiroptical output has three distinctive states, which makes a three‐state molecular logic gate readily achievable on this platform. Such DNA‐based plasmonic logic gates are envisioned to execute more complex tasks giving these unique characteristics.     

Controlled Logic Gates—Switch Gate and Fredkin Gate Based on Enzyme‐Biocatalyzed Reactions Realized in Flow Cells

Controlled logic gates, where the logic operations on the Data inputs are performed in the way determined by the Control signal, were designed in a chemical fashion. Specifically, the systems where the Data output signals directed to various output channels depending on the logic value of the Control input signal have been designed based on enzyme biocatalyzed reactions performed in a multi‐cell flow system. In the Switch gate one Data signal was directed to one of two possible output channels depending on the logic value of the Control input signal. In the reversible Fredkin gate the routing of two Data signals between two output channels is controlled by the third Control signal. The flow devices were created using a network of flow cells, each modified with one enzyme that biocatalyzed one chemical reaction. The enzymatic cascade was realized by moving the solution from one reacting cell to another which were organized in a specific network. The modular design of the enzyme‐based systems realized in the flow device allowed easy reconfiguration of the logic system, thus allowing simple extension of the logic operation from the 2‐input/3‐output channels in the Switch gate to the 3‐input/3‐output channels in the Fredkin gate. Further increase of the system complexity for realization of various logic processes is feasible with the use of the flow cell modular design.     

分子逻辑器件研究进展

分子器件具有尺寸小、设计合成可控、存储量大、反应速度快、人工智能等诸多优点,是当今化学、物理和材料等领域研究最为重要的一个交叉领域.综述了近些年来分子逻辑器件领域的研究进展.介绍了各种类型的分子逻辑门、半(加)减法器、分子逻辑线路以及DNA分子和固态分子计算.最后提出了分子器件存在的问题并展望了其应用前景.     

局部对称的黎曼流形中的极小子流形

主要研究了局部对称的黎曼流形中的定向紧致无边极小子流形的内蕴刚性问题,利用一个矩阵不等式,得到了这类子流形的一个刚性定理．所得结果部分改进了已有的一个结论．     

剩余格与正则剩余格的特征定理

本文进一步研究了具有广泛应用的一类模糊逻辑代数系统——剩余格，并引入了正则剩余格的概念，对剩余格与正则剩余格的定义进行了讨论，给出了剩余格与正则剩余格的特征定理，其中包含剩余格与正则剩余格的等式特征，从而这两个格类都构成簇．本文还讨论了剩余格与正则剩余格公理系统的独立性，以及它们与相近代数结构的关系．     

二阶积分微分方程周期边值问题的解的存在性

通过对比结果,用单调迭代方法证明了Banach空间中二阶积分微分方程的周期边值问题的最大最小解的存在性定理。     

集值向量优化的二阶最优性必要条件

在赋范空间中给出了集值映射的二阶切集的概念,利用二阶切集,定义了集值映射的二阶切导数。然后,获得了集值向量优化问题弱极小元的两个二阶最优性必要条件。