Scattering of Elastic Waves in a Quasi-One-Dimensional Cavity: Theory and Experiment

• Authors: G. Báez , M. Cobián-Suárez , A. Martínez-Argüello , M. Martínez-Mares , R. Méndez-Sánchez
• Languages of publication: EN

Abstracts

EN

We study the scattering of torsional waves through a quasi-one-dimensional cavity both from the experimental and theoretical points of view. The experiment consists of an elastic rod with square cross-section. In order to form a cavity, a notch at a certain distance of one end of the rod was grooved. To absorb the waves, at the other side of the rod, a wedge, covered by an absorbing foam, was machined. In the theoretical description, the scattering matrix S of the torsional waves was obtained. The distribution of S is given by Poisson's kernel. The theoretical predictions show an excellent agreement with the experimental results. This experiment corresponds, in quantum mechanics, to the scattering by a delta potential, in one dimension, located at a certain distance from an impenetrable wall.

Keywords

EN

46.40.Cd; 62.30.+d; 03.65.Nk; 73.21.Fg

Discipline

• 62.30.+d: Mechanical and elastic waves; vibrations(see also 43.40.+s Structural acoustics and vibration; 46.40.-f Vibrations and mechanical waves in continuum mechanics of solids)
• 46.40.Cd: Mechanical wave propagation (including diffraction, scattering, and dispersion)
• 03.65.Nk: Scattering theory
• 73.21.Fg: Quantum wells

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2013
• Volume: 124
• Issue: 6
• Pages: 1069-1073

Dates

published

2013-12

Contributors

author

G. Báez

• Universidad Autónoma Metropolitana-Azcapotzalco, A.P. 21-267, 04000 México D.F., Mexico

author

M. Cobián-Suárez

• Universidad Autónoma Metropolitana-Azcapotzalco, A.P. 21-267, 04000 México D.F., Mexico

author

A. Martínez-Argüello

• Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, A.P. 55-534, 09340 México D.F., Mexico

author

M. Martínez-Mares

• Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, A.P. 55-534, 09340 México D.F., Mexico

author

R. Méndez-Sánchez

• Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, A.P. 48-3, 62210 Cuernavaca Mor., Mexico

References

• [1] C.W.J. Beenakker, Rev. Mod. Phys. 69, 731 (1997)
• [2] Y. Alhassid, Rev. Mod. Phys. 72, 895 (2000)
• [3] P.A. Mello, N. Kumar, Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations, Oxford University Press, New York 2005
• [4] V.A. Gopar, Ph.D. Thesis, Universidad Nacional Autónoma de México, Distrito Federal 1999
• [5] A.M. Martínez-Argüello, R.A. Méndez-Sánchez, M. Martínez-Mares, Phys. Rev. E 86, 016207 (2012)
• [6] V. Domínguez-Rocha, M. Martínez-Mares, J. Phys. A: Math. Theor. 46, 235101 (2013)
• [7] P.A. Mello, H. Baranger, Interference Phenomena in Electronic Transport through Chaotic Cavities: An Information-Theoretic Approach, AIP Conf. Proc. No. 464, AIP, Melville, New York 2008
• [8] G. Báez, M. Martínez-Mares, R.A. Méndez-Sánchez, Phys. Rev. E 78, 036208 (2008)
• [9] J.A. Méndez-Bermúdez, G.A. Luna-Acosta, F.M. Izrailev, Physica E 22, 881 (2004)
• [10] P.A. Mello, M. Martínez-Mares, Phys. Rev. E 63, 016205 (2000)
• [11] P.A. Mello, V.A. Gopar, J.A. Méndez-Bermúdez, in: Quantum scattering and transport in classically chaotic cavities: An overview of past and new results, in Chaotic Systems: Theory and Applications, -206, Eds. C.H. Skiadas, I. Dimotikalis, World Scientific, Singapore 2010, p. 191
• [12] T. Kottos, U. Smilansky, Phys. Rev. Lett. 79, 4794 (1997)
• [13] C.M. Marcus, A.J. Rimberg, R.M. Westervelt, P.F. Hopkins, A.C. Gossard, Phys. Rev. Lett. 69, 506 (1992)
• [14] M.F. Crommie, C.P. Lutz, D.M. Eigler, Nature 363, 524 (1993)
• [15] E. Doron, U. Smilansky, A. Frenkel, Phys. Rev. Lett. 65, 3072 (1990)
• [16] C.H. Lewenkopf, A. Müller, E. Doron, Phys. Rev. A 45, 2635 (1992)
• [17] R.A. Méndez-Sánchez, U. Kuhl, M. Barth, C.H. Lewenkopf, H.-J. Stöckmann, Phys. Rev. Lett. 91, 174102 (2003)
• [18] H. Schanze, H.J. Stöckmann, M. Martínez-Mares, C.H. Lewenkopf, Phys. Rev. E 71, 016223 (2005)
• [19] U. Kuhl, M. Martínez-Mares, R.A. Méndez-Sánchez, H.-J. Stöckmann, Phys. Rev. Lett. 94, 144101 (2005)
• [20] S. Hemmady, X. Zheng, E. Ott, T.M. Antonsen, Jr., S.M. Anlage, Phys. Rev. Lett. 94, 014102 (2005)
• [21] D. Laurent, O. Legrand, F. Mortessagne, Phys. Rev. E 74, 046219 (2006)
• [22] S. Bittner, B. Dietz, M. Miski-Oglu, P.O. Iriarte, A. Richter, F. Schäfer, Phys. Rev. E 84, 016221 (2011)
• [23] J.U. Nöckel, A.D. Stone, Nature 385, 45 (1997)
• [24] P. Malara, R. Blanchard, T.S. Mansuripur, A.K. Wojcik, A. Belyanin, K. Fujita, T. Edamura, S. Furuta, M. Yamanishi, P. de Natale, F. Capasso, Appl. Phys. Lett. 102, 141105 (2013)
• [25] O. Hul, O. Tymoshchuk, S. Bauch, P.M. Koch, L. Sirko, J. Phys. A, Math. Gen. 38, 10489 (2005)
• [26] S. Catheline, N. Benech, J. Brum, C. Negreira, Phys. Rev. Lett. 100, 064301 (2008)
• [27] A. Morales, A. Díaz-de-Anda, J. Flores, L. Gutiérrez, R.A. Méndez-Sánchez, G. Monsivais, P. Mora, Europhys. Lett. 99, 54002 (2012)
• [28] K.F. Graff, Wave Motion in Elastic Solids, Dover, New York 1991
• [29] P.A. Mello, P. Pereyra, T.H. Seligman, Ann. Phys. (New York) 161, 254 (1985)
• [30] A. Morales, J. Flores, L. Gutiérrez, R.A. Méndez-Sánchez, J. Acoust. Soc. Am. 112, 1961 (2002)
• [31] A. Morales, L. Gutiérrez, J. Flores, Am. J. Phys. 69, 517 (2001)

Identifiers

DOI

10.12693/APhysPolA.124.1069