Abstract
As the size of electronic devices is narrowed down to the nanoscale, quantum effects become so prominent that the conventional Newton mechanics is no longer able to provide an accurate description for the electrons moving in nanostructures. On the other hand, the probabilistic description provided by quantum mechanics requires a large enough ensemble of electrons to yield the representative mean motion consistent with probability prediction. However, in some nanoelectronic devices, moving electrons may be so few that they do not averagely exhibit the mean motion predicted from quantum mechanics. Under such a circumstance, we need a new method that can describe not only the particle behavior of an individual electron, but also the wave behavior of an ensemble of electrons. In this paper, the complex-valued Newton mechanics is shown to possess the desired ability of manifesting the wave-particle duality of electrons moving in nanostructures. The first part of this paper establishes the nonlinear quantum dynamics characterizing the motion of individual electrons and finds their quantum trajectories in the presence of channelized quantum potential. The second part is devoted to showing how the collective motion of electrons yields the phenomenon of conductance quantization and the various wave behaviors such as tunneling, transmission and reflection within narrow-channel nanostructures.
| Original language | English |
|---|---|
| Pages (from-to) | 297-318 |
| Number of pages | 22 |
| Journal | International Journal of Nonlinear Sciences and Numerical Simulation |
| Volume | 11 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2010 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Computational Mechanics
- Modelling and Simulation
- Engineering (miscellaneous)
- Mechanics of Materials
- Physics and Astronomy(all)
- Applied Mathematics
Cite this
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Nonlinear quantum motions in 2D nano-channels part I : Complex potential and quantum trajectories. / Yang, Ciann-Dong; Lee, Chen Bin.
In: International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 11, No. 5, 01.01.2010, p. 297-318.Research output: Contribution to journal › Article
TY - JOUR
T1 - Nonlinear quantum motions in 2D nano-channels part I
T2 - Complex potential and quantum trajectories
AU - Yang, Ciann-Dong
AU - Lee, Chen Bin
PY - 2010/1/1
Y1 - 2010/1/1
N2 - As the size of electronic devices is narrowed down to the nanoscale, quantum effects become so prominent that the conventional Newton mechanics is no longer able to provide an accurate description for the electrons moving in nanostructures. On the other hand, the probabilistic description provided by quantum mechanics requires a large enough ensemble of electrons to yield the representative mean motion consistent with probability prediction. However, in some nanoelectronic devices, moving electrons may be so few that they do not averagely exhibit the mean motion predicted from quantum mechanics. Under such a circumstance, we need a new method that can describe not only the particle behavior of an individual electron, but also the wave behavior of an ensemble of electrons. In this paper, the complex-valued Newton mechanics is shown to possess the desired ability of manifesting the wave-particle duality of electrons moving in nanostructures. The first part of this paper establishes the nonlinear quantum dynamics characterizing the motion of individual electrons and finds their quantum trajectories in the presence of channelized quantum potential. The second part is devoted to showing how the collective motion of electrons yields the phenomenon of conductance quantization and the various wave behaviors such as tunneling, transmission and reflection within narrow-channel nanostructures.
AB - As the size of electronic devices is narrowed down to the nanoscale, quantum effects become so prominent that the conventional Newton mechanics is no longer able to provide an accurate description for the electrons moving in nanostructures. On the other hand, the probabilistic description provided by quantum mechanics requires a large enough ensemble of electrons to yield the representative mean motion consistent with probability prediction. However, in some nanoelectronic devices, moving electrons may be so few that they do not averagely exhibit the mean motion predicted from quantum mechanics. Under such a circumstance, we need a new method that can describe not only the particle behavior of an individual electron, but also the wave behavior of an ensemble of electrons. In this paper, the complex-valued Newton mechanics is shown to possess the desired ability of manifesting the wave-particle duality of electrons moving in nanostructures. The first part of this paper establishes the nonlinear quantum dynamics characterizing the motion of individual electrons and finds their quantum trajectories in the presence of channelized quantum potential. The second part is devoted to showing how the collective motion of electrons yields the phenomenon of conductance quantization and the various wave behaviors such as tunneling, transmission and reflection within narrow-channel nanostructures.
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U2 - 10.1515/IJNSNS.2010.11.5.297
DO - 10.1515/IJNSNS.2010.11.5.297
M3 - Article
VL - 11
SP - 297
EP - 318
JO - International Journal of Nonlinear Sciences and Numerical Simulation
JF - International Journal of Nonlinear Sciences and Numerical Simulation
SN - 1565-1339
IS - 5
ER -