标题： 粒子通过多个引线在开放量子网络中的逃逸 显示英文标题

标题： Particle escapes in an open quantum network via multiple leads

摘要： 粒子从一维有限区域的一端逃逸到$N$个半无限引线的量子逃逸问题通过散射理论方法进行讨论。 根据连接处势垒的幅度，粒子在时间$t$时仍留在有限区域的概率$P(t)$在长时间后表现出两种不同的衰减行为；一种与$N^{2}/t^{3}$成正比，另一种与$1/(N^{2}t)$成正比。 此外，粒子从有限区域离开的速度$V(t)$，由粒子位置的概率流定义，在时间上渐近地以幂次$\sim 1/t$衰减，与引出的数目$N$和初始波函数等无关。 对于有限时间，概率$P(t)$随时间呈指数衰减，引出数目$N$越多，衰减速率越小，而速度$V(t)$表现出时间振荡，其振幅随着引出数目$N$的增加而增大。 还通过使用不同的边界条件讨论了粒子从有限区域的两端逃逸到多个引出的情况。 显示英文摘要

摘要： Quantum escapes of a particle from an end of a one-dimensional finite region to $N$ number of semi-infinite leads are discussed by a scattering theoretical approach. Depending on a potential barrier amplitude at the junction, the probability $P(t)$ for a particle to remain in the finite region at time $t$ shows two different decay behaviors after a long time; one is proportional to $N^{2}/t^{3}$ and another is proportional to $1/(N^{2}t)$. In addition, the velocity $V(t)$ for a particle to leave from the finite region, defined from a probability current of the particle position, decays in power $\sim 1/t$ asymptotically in time, independently of the number $N$ of leads and the initial wave function, etc. For a finite time, the probability $P(t)$ decays exponentially in time with a smaller decay rate for more number $N$ of leads, and the velocity $V(t)$ shows a time-oscillation whose amplitude is larger for more number $N$ of leads. Particle escapes from the both ends of a finite region to multiple leads are also discussed by using a different boundary condition.