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 di...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2011-12, Vol.84 (6), Article 062707
Main Authors: Taniguchi, Tooru, Sawada, Shin-ichi
Format: Article
Language:English
Subjects:
AMPLITUDES
ATOMIC AND MOLECULAR PHYSICS
BOUNDARY CONDITIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DECAY
ONE-DIMENSIONAL CALCULATIONS
OSCILLATIONS
POTENTIALS
PROBABILITY
SCATTERING
VELOCITY
WAVE FUNCTIONS
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Summary: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 N{sup 2}/t{sup 3} and another is proportional to 1/(N{sup 2}t). 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 {approx}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.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.84.062707