Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:B1L-C

Session:

Number:324

A Primary Study on Classical Particle Modeling of Electron-Wave Interference Systems

Keisuke Nagata,  Wataru Nakashima,  Hisato Fujisaka,  Takeshi Kamio,  Kazuhisa Haeiwa,  

pp.324-327

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.324

PDF download (335.8KB)

Summary:
Quantum particles such as electrons and photons have wave-particle duality. In this paper, we regard an electron in a simple electron-wave interference system as a classical particle on which random force acts and its behavior as a stochastic process. We applied the Nelson's stochastic quantization theory to the construction of the stochastic process and confirmed by numerical simulation that the stochastic process has the same probability density function with that determined by wave functions of the Schrödinger equation describing the interference system. This primary study will be useful to model quantum effect devices so as to solve difficulty and reduce complexity in the simulation of electronic circuits built of the devices.

References:

[1] C. A. Stafford, D. M. Cardamone and S. Mazumdar, “The Quantum Interference Effect Transistor,” Nanotechnology, Vol. 18, No. 42, 424014(6 pages), 2007.

[2] E. Nelson, “Derivation of the Schrödinger Equation from Newtonian Mechanics,” Physical Review, Vol. 150, No. 4, pp.1079-1085, 1966.

[3] K. Hara and I. Ohba, “Tunneling Time Distribution by means of Nelson's Quantum Mechanics and Wave-Particle Duality,” Physical Revew A, Vol. 67, Issue 5, Pages 052105.6, 2003.

[4] L. Devroye, Non-Uniform Random Variate Generation, Springer-Verlag, 1986.

[5] A. J. Walker, “An Efficient Method for Generating Discrete Random Variables with General Distributions,” ACM Trans. on Mathematical Software (TOMS), Vol. 3, Issue 3, pp.253-256, 1977.

[6] Y. Aharonov and D. Bohm, “Significance of Electromagnetic Potentials in the Quantum Theory,” Physical Review, Vol. 115, Issue 3, pp.485-491, 1959.

[7] A. Tonomura, “Microscopic Distribution of Electromagnetic Fields Observed by Using Electron Waves: Electron Waves Feel Vector Potentials,” Journal of IEICE, Vol. 83, No. 12, pp.906-913, 2000 (in Japanese).