三角势垒下的隧穿时间
The Tunnel Time in a Triangular Potential
DOI: 10.12677/AAM.2021.104130, PDF,  被引量   
作者: 郑 爽, 肖 智：华北电力大学数理学院，北京
关键词: 量子隧穿；相位时间；驻留时间；Tunneling； Phase Time； Dwell Time
摘要: 量子隧穿作为没有经典对应的纯粹量子力学现象，其发生是否是瞬时的，即是否需要有限的时间，自量子力学建立到现在一直是人们悬而未决饱受争论的研究课题。本文通过计算粒子经过三角势垒的Wigner相位时间以及驻留时间可发现：随着波数k的变化，透射相位与反射相位呈两种相反变化趋势，而驻留时间则与透射相位时间变化相同；但相位时间和驻留时间均会出现峰值，且有振荡行为。
Abstract: Quantum tunneling is a pure quantum phenomenon without any classical analogy. Whether it is instantaneous process or a process with finite time is an intensively debated issue since the early days of quantum mechanics. In this paper, we calculate the Wigner phase time and dwell time for a particle tunneling through a triangle barrier. We find that with the change of wave number k, the transmission phase time and the reflection phase show two opposite trends, while the dwell time changes the same as the transmission phase time. However, the phase time and dwell time both appear peak and oscillate.
文章引用：郑爽, 肖智. 三角势垒下的隧穿时间[J]. 应用数学进展, 2021, 10(4): 1197-1206. https://doi.org/10.12677/AAM.2021.104130

参考文献

[1] Trixler, F. (2013) Quantum Tunnelling to the Origin and Evolution of Life. Current Organic Chemistry, 17, 1758-1770. [Google Scholar] [CrossRef] [PubMed]
[2] Griffiths, D.J. (2016) Introduction to Quantum Mechanics. Cambridge University Press, Cambridge.
[3] Condon, M. (1931) Quantum Mechanics of Collision Processes I. Scattering of Particles in a Definite Force Field. Review of Modern Physics, 3, 43-88. [Google Scholar] [CrossRef] 
[4] MacColl, L.A. (1932) Note on the Transmission and Reflection of Wave Packets by Potential Barriers. Physical Review, 40, 621-626. [Google Scholar] [CrossRef] 
[5] Donoso, A. and Martens, C.C. (2001) Quantum Tunneling Using Entangled Classical Trajectories. Physical Review Letters, 87, Article ID: 223202. [Google Scholar] [CrossRef] 
[6] Pauli, W. (1933) Die allgemeinen Prinzipien der Wellenmechanik. In: Quantentheorie, Springer, Berlin, Handbuch der Physik, Vol. 24, 83-272. [Google Scholar] [CrossRef] 
[7] Hartman, T.E. (1962) Tunneling of a Wave Packet. Journal of Applied Physics, 33, 3427-3433. [Google Scholar] [CrossRef] 
[8] Wigner, E.P. (1955) Lower Limit for the Energy Derivative of the Scattering Phase Shift. Physical Review, 98, 145-147. [Google Scholar] [CrossRef] 
[9] Smith, F.T. (1960) Lifetime Matrix in Collision Theory. Physical Review, 119, 2098-2098. [Google Scholar] [CrossRef] 
[10] Buttiker, M. (1983) Larmor Precession and the Traversal Time for Tunneling. Physical Review B, 27, 6178-6188. [Google Scholar] [CrossRef] 
[11] Keller, U., Gallmann, L., et al. (2014) Ultrafast Resolution of Tunneling Delay Time. Optica, 1, 343. [Google Scholar] [CrossRef] 
[12] Litvinyuk, I.V., Sang, R.T., et al. (2019) Attosecond Angular Streaking and Tunnelling Time in Atomic Hydrogen. Nature, 568, 75-77. [Google Scholar] [CrossRef] [PubMed]
[13] Ramos, R., Spierings, D., Racicot, L. and Steinberg, A.M. (2020) Measurement of the Time Spent by a Tunneling Atom within the Barrier Region. Nature, 583, 529-532. [Google Scholar] [CrossRef] [PubMed]
[14] Landauer, R. and Martin, Th. (1994) Barrier Interaction Time in Tunneling. Reviews of Modern Physics, 66, 217. [Google Scholar] [CrossRef] 
[15] Peres, A. (1980) Measurement of Time by Quantum Clocks. American Journal of Physics, 48, 552. [Google Scholar] [CrossRef] 
[16] Büttikerm, M. and Landauer, R. (1982) Traversal Time for Tunneling. Physical Review Letters, 49, 1739-1742. [Google Scholar] [CrossRef] 

为你推荐