IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v32y2007i2p312-345.html
   My bibliography  Save this article

Complex tunneling dynamics

Author

Listed:
  • Yang, Ciann-Dong

Abstract

Tunneling dynamics and tunneling trajectories are modeled exactly by complex-extended Hamilton–Jacobi formulation in this paper. It is found that the wave-like properties of tunneling particles, such as reflection, refraction, and transmission resonance, can be identified and explained in terms of particle’s motion in complex space with the tunneling time defined as the usual sense of classical time. Following the complex trajectories determined by the complex Hamilton equations of motion, we can connect classical trajectories smoothly with tunneling trajectories using position and velocity continuity at the interface of the media, locate the particle’s position at any instant, and find the time spent by a particle within the potential. A microscopic tunneling model is also developed to explain the probabilistic nature why a particle with the same incident conditions sometimes transmits the potential and sometimes is reflected from the potential.

Suggested Citation

  • Yang, Ciann-Dong, 2007. "Complex tunneling dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 312-345.
  • Handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:312-345
    DOI: 10.1016/j.chaos.2006.04.060
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906004243
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2006.04.060?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. El Naschie, M.S., 2006. "Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 39-42.
    2. El Naschie, M.S., 2005. "A new solution for the two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 935-939.
    3. Yang, Ciann-Dong, 2006. "Modeling quantum harmonic oscillator in complex domain," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 342-362.
    4. Yang, Ciann-Dong, 2006. "On modeling and visualizing single-electron spin motion," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 41-50.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yang, Ciann-Dong, 2009. "Complex spin and anti-spin dynamics: A generalization of de Broglie–Bohm theory to complex space," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 317-333.
    2. Yang, Ciann-Dong & Weng, Hung-Jen, 2012. "Nonlinear quantum dynamics in diatomic molecules: Vibration, rotation and spin," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 402-415.
    3. Yang, Ciann-Dong, 2009. "Stability and quantization of complex-valued nonlinear quantum systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 711-723.
    4. Yang, Ciann-Dong, 2008. "On the existence of complex spacetime in relativistic quantum mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 316-331.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yang, Ciann-Dong, 2009. "Complex spin and anti-spin dynamics: A generalization of de Broglie–Bohm theory to complex space," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 317-333.
    2. Yang, Ciann-Dong, 2007. "The origin and proof of quantization axiom p→pˆ=-iℏ∇ in complex spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 274-283.
    3. Agop, M. & Murgulet, C., 2007. "Ball lightning as a self-organizing process of a plasma–plasma interface and El Naschie’s ε(∞) space–time," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 754-769.
    4. Yang, Ciann-Dong & Wei, Chia-Hung, 2007. "Parameterization of all path integral trajectories," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 118-134.
    5. Agop, M. & Craciun, P., 2006. "El Naschie’s Cantorian gravity and Einstein’s quantum gravity," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 30-40.
    6. Agop, M. & Craciun, P., 2006. "El Naschie’s ε(∞) space–time and the two slit experiment in the Weyl–Dirac theory," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 441-452.
    7. Yang, Ciann-Dong & Weng, Hung- Jen, 2008. "Complex dynamics in diatomic molecules. Part II: Quantum trajectories," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 16-35.
    8. Iovane, G., 2006. "Cantorian spacetime and Hilbert space: Part I—Foundations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 857-878.
    9. Agop, M. & Chicos, Liliana & Nica, P., 2009. "Transport phenomena in nanostructures and non-differentiable space–time," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 803-814.
    10. Agop, M. & Vasilica, M., 2006. "El Naschie’s supergravity by means of the gravitational instantons synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 318-323.
    11. Agop, M. & Nica, P. & Ioannou, P.D. & Malandraki, Olga & Gavanas-Pahomi, I., 2007. "El Naschie’s ε(∞) space–time, hydrodynamic model of scale relativity theory and some applications," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1704-1723.
    12. Agop, M. & Abacioaie, D., 2007. "El Naschie’s ε(∞) space–time, interface between Weyl–Dirac bubbles and Cantorian fractal superstring," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 235-243.
    13. Buzea, C. Gh. & Agop, M. & Galusca, G. & Vizureanu, P. & Ionita, I., 2007. "El Naschie’s superconductivity in the time dependent Ginzburg–Landau model," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1060-1074.
    14. Sun, Lei & Cheng, Zhengxing & Huang, Yongdong, 2007. "Construction of trivariate biorthogonal compactly supported wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1412-1420.
    15. Sun, Lei & Zhang, Xiaozhong, 2009. "A note on biorthogonality of the scaling functions with arbitrary matrix dilation factor," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 711-715.
    16. Iovane, Gerardo, 2009. "The set of prime numbers: Multiscale analysis and numeric accelerators," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1953-1965.
    17. Chen, Qing-Jiang & Qu, Xiao-Gang, 2009. "Characteristics of a class of vector-valued non-separable higher-dimensional wavelet packet bases," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1676-1683.
    18. Liu, Zhanwei & Hu, Guoen & Lu, Zhibo, 2009. "Parseval frame scaling sets and MSF Parseval frame wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1966-1974.
    19. EL-Nabulsi, Ahmad Rami, 2009. "Fractional action-like variational problems in holonomic, non-holonomic and semi-holonomic constrained and dissipative dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 52-61.
    20. El Naschie, M.S., 2007. "The Fibonacci code behind super strings and P-Branes. An answer to M. Kaku’s fundamental question," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 537-547.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:312-345. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.