Yıl: 2017 Cilt: 7 Sayı: 2 Sayfa Aralığı: 236 - 247 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS

Öz:
In this paper, we study the effects of white-noised potentials on nonlinear quantum tunneling. We use a split-step scheme to numerically solve the nonlinearSchr¨odinger equation (NLSE) with a tunneling potential. We consider three differenttypes of potentials, namely; the single rectangular barrier, double rectangular barrier,and triangular barrier. For all these three cases, we show that white-noise given topotentials do not trigger modulation instability for tunneling of the sech type solitonsolutions of the NLSE. However, white-noised potentials trigger modulation instabilityfor tunneling of the sinusoidal wavefunctions; thus, such a wavefield turns into a chaoticone with many apparent peaks. We argue that peaks of such a field may be in the formof rational rogue wave solutions of the NLSE. Our results can be used to examine theeffects of noise on quantum tunneling. Since a rogue wavefunction means a higher probability of the tunneling particle to be at a given (x,t) coordinate, our results may alsobe used for developing the quantum science and technology with many possible applications including but are not limited to increasing the resolution and efficiency of scanningtunneling microscopes, enhancing proton tunneling for DNA mutation and enhancingsuperconducting properties of junctions
Anahtar Kelime:

Konular: Matematik
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Griffiths,D.J., (2004), An Introduction to Quantum Mechanics, Prentice Hall, USA.
  • [2] Landau,L.D. and Lifschitz,E.M., (1958), Quantum mechanics, Pergamon Press, UK.
  • [3] Fowler,R.H. and Nordheim,L., (1928), Electron emission in intense electric fields, Proc. R. Soc. Lond. A, Vol.119, pp.173.
  • [4] Bayındır,C., (2009), Implementation of a Computational Model for Random Directional Seas and Underwater Acoustics, MS Thesis, University of Delaware.
  • [5] Bayındır,C., (2015), Compressive Split-Step Fourier Method. TWMS: Journal of Applied and Engineering Mathematics, Vol.5, pp.298.
  • [6] Bayındır,C., (2016), Early detection of rogue waves by the wavelet transforms, Physics Letters A, Vol.380, pp.156.
  • [7] Bayındır,C., (2015), Hesaplamalı akı¸skanlar mekani˘gi ¸calı¸smaları i¸cin sıkı¸stırılabilir Fourier tayfı y¨ontemi, 19. Mekanik Kongresi, Trabzon (In Turkish).
  • [8] Bayındır,C., (2015), S¨on¨uml¨u de˘gi¸stirilmi¸s Korteweg de-Vries (KdV) denkleminin analitik ve hesaplamalı ¸c¨oz¨um kar¸sıla¸stırması, 19. Mekanik Kongresi, Trabzon, Turkey. (In Turkish)
  • [9] Bayındır,C., (2015), Okyanus dalgalarının sıkı¸stırılabilir Fourier tayfı y¨ontemiyle hızlı modellenmesi, 19. Mekanik Kongresi, Trabzon (In Turkish).
  • [10] Demiray,H. and Bayındır,C., (2015), A note on the cylindrical solitary waves in an electron-acoustic plasma with vortex electron distribution, Physics of Plasmas, 22, 092105; doi: 10.1063/1.4929863.
  • [11] Karjadi,E.A., Badiey,M., and Kirby,J.T., (2010), Impact of surface gravity waves on high-frequency acoustic propagation in shallow water, The Journal of the Acoustical Society of America, Vol.127, pp.1787-1787.
  • 12] Karjadi,E.A., Badiey,M., Kirby,J.T., and Bayındır,C., (2012), The effects of surface gravity waves on high-frequency acoustic propagation in shallow water, IEEE Journal of Oceanic Engineering, Vol.37, pp.112-121.
  • [13] Bayındır,C., (2016), Early Detection of Rogue Waves Using Compressive Sensing. arXiv Preprint, arXiv:1602.00816.
  • [14] Bayındır,C., (2016), Analytical and numerical aspects of the dissipative nonlinear Schr¨odinger equation, TWMS: Journal of Applied and Engineering Mathematics, Vol.6, No.1, pp.135-142.
  • [15] Bayındır,C., (2016), Compressive spectral method for the simulation of the nonlinear gravity waves, Scientific Reports, 6, 22100; doi: 10.1038/srep22100.
  • [16] Bayındır,C., (2016), Rogue waves of the Kundu-Eckhaus equation in a chaotic wavefield. Physical Review E, 93, 032201.
  • [17] Bayındır,C., (2016), Rogue wave spectra of the Kundu-Eckhaus equation. Physical Review E, 93, 062215.
  • [18] Bayındır,C., (2016), An extended Kundu-Eckhaus equation for modeling dynamics of rogue waves in a chaotic wave-current field. arXiv Preprint, arXiv:1602.05339.
  • [19] Canuto,C., Hussaini,M.Y., Quarteroni,A., and Zang,T.A., (2006), Spectral Methods: Fundamentals in Single Domains, Springer-Verlag, DE.
  • [20] Trefethen,L.N., (2000), Spectral Methods in MATLAB, SIAM, Philadelphia.
  • [21] Akhmediev,N., Ankiewicz,A., and Soto-Crespo,J.M., (2009), Rogue waves and rational solutions of the nonlinear Schrdinger equation, Physical Review E, 80, 026601.
  • [22] Akhmediev,N., Soto-Crespo,J.M., Ankiewicz,A., and Devine,N., (2011), Early detection of rogue waves in a chaotic wave field, Physics Letters A, Vol.375, pp.2999.
  • [23] Akhmediev,N., Soto-Crespo,J.M., and Ankiewicz,A., (2009), Extreme waves that appear from nowhere: On the nature of rogue waves. Physics Letters A, Vol.373, pp.2137.
  • [24] Soto-Crespo,J.M., Devine,N., Hoffmann,N.P., and Akhmediev,N., (2014) Rogue waves of the SasaSatsuma equation in a chaotic wave field. Physical Review E, 90, 032902.
  • [25] Peregrine,H. and Smith,R., (1979), Nonlinear effects upon waves near caustics. Philosophical Transactions of the Royal Society of London A, Vol.292 , pp.341.
  • [26] Kedziora,D., Ankiewicz,A., and Akhmediev,N., (2013) The phase patterns of higher-order rogue waves. Journal of Optics, 15, 6, , 064011.
  • [27] Smith,R., (1976), Giant Waves, Journal of Fluid Mechanics, Vol.77, pp.417.
  • [28] Bayındır,C., (2015), Shapes and statistics of the rogue waves generated by chaotic ocean current. arXiv Preprint, arXiv:1512.03584.
  • [29] Chabchoub,A. and Fink,M., (2014) ,Time-Reversal Generation of Rogue Waves. Physical Review Letters, Vol.112, 124101.
APA BAYINDIR C (2017). ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS. , 236 - 247.
Chicago BAYINDIR C. ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS. (2017): 236 - 247.
MLA BAYINDIR C. ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS. , 2017, ss.236 - 247.
AMA BAYINDIR C ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS. . 2017; 236 - 247.
Vancouver BAYINDIR C ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS. . 2017; 236 - 247.
IEEE BAYINDIR C "ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS." , ss.236 - 247, 2017.
ISNAD BAYINDIR, C.. "ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS". (2017), 236-247.
APA BAYINDIR C (2017). ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, 7(2), 236 - 247.
Chicago BAYINDIR C. ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics 7, no.2 (2017): 236 - 247.
MLA BAYINDIR C. ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, vol.7, no.2, 2017, ss.236 - 247.
AMA BAYINDIR C ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics. 2017; 7(2): 236 - 247.
Vancouver BAYINDIR C ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics. 2017; 7(2): 236 - 247.
IEEE BAYINDIR C "ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS." TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, 7, ss.236 - 247, 2017.
ISNAD BAYINDIR, C.. "ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS". TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics 7/2 (2017), 236-247.