Particle escapes in an open quantum network via multiple leads

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.

16 pages, 7 figures

References in corpus (5)

• Long-time behavior of many-particle quantum decay
• Poincare recurrences and transient chaos in systems with leaks
• Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates
• Poincare recurrences from the perspective of transient chaos
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Cited by in corpus (3)

• Influence of boundary conditions on quantum escape
• Escape Dynamics of Many Hard Disks
• Quantum particle escape from a time-dependent confining potential