Particle escapes in an open quantum network via multiple leads

Quantum escape of a particle from an end of a one-dimensional finite region to N semi-infinite leads is discussed from a scattering theory approach. Depending on the 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 at long times; one is proportional to N2/t3 and another is proportional to 1/(N2t). In addition, the velocity V(t) for a particle to leave the finite region, defined from a probability current of the particle position, decays asymptotically as a power of time ∼1/t, independent of the number of leads and the initial wave function. For a finite time, the probability P(t) decays exponentially in time with a smaller decay rate for a greater number of leads, and the velocity V(t) shows a time oscillation whose amplitude is larger for a greater number of leads. Particle escapes from the both ends of a finite region to multiple leads are also discussed using a different boundary condition.