Particle escapes in an open quantum network via multiple leads

TL;DR

This paper investigates how particles escape from a finite quantum region into multiple leads, revealing different long-term decay behaviors and the influence of the number of leads on escape dynamics using scattering theory.

Contribution

It introduces a scattering theoretical analysis of quantum escape dynamics in multi-lead networks, identifying distinct power-law decay behaviors and effects of lead number.

Findings

Probability decay follows N^2/t^3 or 1/(N^2 t) depending on conditions.

Escape velocity decays as 1/t regardless of number of leads.

Number of leads affects decay rate and causes oscillations in escape velocity.

Abstract

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.