Vol. 2
Latest Volume
All Volumes
PIERL 123 [2025] PIERL 122 [2024] PIERL 121 [2024] PIERL 120 [2024] PIERL 119 [2024] PIERL 118 [2024] PIERL 117 [2024] PIERL 116 [2024] PIERL 115 [2024] PIERL 114 [2023] PIERL 113 [2023] PIERL 112 [2023] PIERL 111 [2023] PIERL 110 [2023] PIERL 109 [2023] PIERL 108 [2023] PIERL 107 [2022] PIERL 106 [2022] PIERL 105 [2022] PIERL 104 [2022] PIERL 103 [2022] PIERL 102 [2022] PIERL 101 [2021] PIERL 100 [2021] PIERL 99 [2021] PIERL 98 [2021] PIERL 97 [2021] PIERL 96 [2021] PIERL 95 [2021] PIERL 94 [2020] PIERL 93 [2020] PIERL 92 [2020] PIERL 91 [2020] PIERL 90 [2020] PIERL 89 [2020] PIERL 88 [2020] PIERL 87 [2019] PIERL 86 [2019] PIERL 85 [2019] PIERL 84 [2019] PIERL 83 [2019] PIERL 82 [2019] PIERL 81 [2019] PIERL 80 [2018] PIERL 79 [2018] PIERL 78 [2018] PIERL 77 [2018] PIERL 76 [2018] PIERL 75 [2018] PIERL 74 [2018] PIERL 73 [2018] PIERL 72 [2018] PIERL 71 [2017] PIERL 70 [2017] PIERL 69 [2017] PIERL 68 [2017] PIERL 67 [2017] PIERL 66 [2017] PIERL 65 [2017] PIERL 64 [2016] PIERL 63 [2016] PIERL 62 [2016] PIERL 61 [2016] PIERL 60 [2016] PIERL 59 [2016] PIERL 58 [2016] PIERL 57 [2015] PIERL 56 [2015] PIERL 55 [2015] PIERL 54 [2015] PIERL 53 [2015] PIERL 52 [2015] PIERL 51 [2015] PIERL 50 [2014] PIERL 49 [2014] PIERL 48 [2014] PIERL 47 [2014] PIERL 46 [2014] PIERL 45 [2014] PIERL 44 [2014] PIERL 43 [2013] PIERL 42 [2013] PIERL 41 [2013] PIERL 40 [2013] PIERL 39 [2013] PIERL 38 [2013] PIERL 37 [2013] PIERL 36 [2013] PIERL 35 [2012] PIERL 34 [2012] PIERL 33 [2012] PIERL 32 [2012] PIERL 31 [2012] PIERL 30 [2012] PIERL 29 [2012] PIERL 28 [2012] PIERL 27 [2011] PIERL 26 [2011] PIERL 25 [2011] PIERL 24 [2011] PIERL 23 [2011] PIERL 22 [2011] PIERL 21 [2011] PIERL 20 [2011] PIERL 19 [2010] PIERL 18 [2010] PIERL 17 [2010] PIERL 16 [2010] PIERL 15 [2010] PIERL 14 [2010] PIERL 13 [2010] PIERL 12 [2009] PIERL 11 [2009] PIERL 10 [2009] PIERL 9 [2009] PIERL 8 [2009] PIERL 7 [2009] PIERL 6 [2009] PIERL 5 [2008] PIERL 4 [2008] PIERL 3 [2008] PIERL 2 [2008] PIERL 1 [2008]
2008-01-19
Transmittance and Fractality in a Cantor-Like Multibarrier System
By
, Vol. 2, 149-155, 2008
Abstract
The transmittance is studied for a Cantor-like multibarrier system. The calculation are made in the framework of effective mass theory. Some typical values of effective masses and potentials are used in order to have an experimental reference. The techniques of Transfer Matrix are used to calculate the transmittance of the entire structure having some dozens of layers. The results display a complex structure of peaks and valleys. The set of maxima is studied with the tool of the q-dependent dimension D(q). The set of transmittance maxima exhibits a fractal structure, or more exactly, a multifractal structure, i.e., a q-dependent dimension, characterized as usually with limit one when q parameter tends to -∞ but witha limit between 0 and 1 when tends to +∞. This numerical experiment demonstrate that spatially bounded potential may exhibit spectrum with fractal character.
Citation
Dan Diaz-Guerrero, Fernando Montoya, Luis Manuel Gaggero-Sager, and Rolando Perez-Alvarez, "Transmittance and Fractality in a Cantor-Like Multibarrier System," , Vol. 2, 149-155, 2008.
doi:10.2528/PIERL07122804
References

1. Gaggero-Sager, L. M., E. R. Pujals, and O. Sotolongo-Costa, "Self-similarity in a Cantor-like semiconductor quantum well," Phys. Stat. Sol. (B), Vol. 220, 167-169, 2000.
doi:10.1002/1521-3951(200007)220:1<167::AID-PSSB167>3.0.CO;2-L

2. Lavrinenko, A. V., S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, "Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor filter," Phys. Rev. E, Vol. 65, 036621, 2002.
doi:10.1103/PhysRevE.65.036621

3. Zhukovsky, S. V., A. V. Lavrinenko, and S. V. Gaponenko, "Spectral scalability as a result of geometrical self-similarity in fractal multilayers," Europhys. Lett., Vol. 66, No. 3, 455-461, 2004.
doi:10.1209/epl/i2003-10226-8

4. Moretti, L., I. Rea, L. de Stefano, and I. Rendina, "Periodic versus aperiodic: Enhancing the sensitivity of porous silicon based optical sensors," Applied Physics Letters, Vol. 90, 191112, 2007.
doi:10.1063/1.2737391

5. Perez-Alvarez, R. and F. Garcıa-Moliner, Transfer Matrix, Green Function and Related Techniques: Tools for the Study of Multilayer Heterostructures , 2004.

6. Mora, M., R. Perez- Alvarez, and C. Sommers, "Transfer matrix in one dimensional problems," J. Physique, Vol. 46, No. 7, 1021-1026, 1985.
doi:10.1051/jphys:019850046070102100

7. Griffiths, D. J. and C. A. Steinke, "Waves in locally periodic media," Am. J. Phys., Vol. 69, No. 2, 137-154, 2001.
doi:10.1119/1.1308266

8. Rasband, S. N., Chaos Dynamics of Nonlinear Systems, Wiley Professional Paperback Series, 1997.

9. Perez-Alvarez, R., F. Garcıa-Moliner, C. Trallero-Giner, and V. R. Velasco, "Polar optical modes in Fibonacci heterostructures," J. Raman Spectroscopy, Vol. 31, No. 5, 421-425, 2000.
doi:10.1002/1097-4555(200005)31:5<421::AID-JRS532>3.0.CO;2-7

10. Perez-Alvarez, R. and F. Garcıa-Moliner, The spectrum of quasiregular heterostructures, invited chapter in Contemporary Problems of the Condensed Matter Physics, S. Vlaev and L. M. Gaggero-Sager (eds.), Editorial Nov, 2001.

11. Velasco, V. R., R. Perez-Alvarez, and F. Garcıa-Moliner, "Some properties of the elastic waves in quasiregular heterostructures," J. Phys.: Cond. Matt., Vol. 14, 5933-5957, 2002.
doi:10.1088/0953-8984/14/24/305

12. Perez- Alvarez, R., F. Garcıa-Moliner, and V. R. Velasco, "Some elementary questions in the theory of quasiperiodic heterostructures," J. of Phys.: Condens. Matter, Vol. 13, 3689-3698, 2001.
doi:10.1088/0953-8984/13/15/312

13. Bovier, A. and J. M. Ghez, "Spectral properties of one-dimensional Schrodinger operators withp otentials generated by substitutions," Commun. Math. Phys., Vol. 158, No. 1, 45-66, 1993.
doi:10.1007/BF02097231

14. Bovier, A. and J. M. Ghez, "Remarks on the spectral properties of tight-binding and Kronig-Penney models with substitution sequences ," J. Phys. A:Math. Gen., Vol. 28, No. 8, 2313-2324, 1995.
doi:10.1088/0305-4470/28/8/022