Geodesic
Weak Signals Amplification Through Controlled Bifurcations in Quasi-Two-Dimensional Electron Gas
Russian journal of nonlinear dynamics, Tome 14 (2018) no. 4, pp. 453-472.

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In this paper, we consider the activation processes in a nonlinear bistable system based on a lateral (quasi-two-dimensional) superlattice and study the dynamics of such a system externally driven by a harmonic force. The internal control parameters are the longitudinal applied electric field and the sample temperature. The spontaneous transverse electric field is considered as an order parameter. The forced violations of the order parameter are considered as a response of a system to periodic driving. We investigate the cooperative effects of self-organization and harmonic forcing from the viewpoint of catastrophe theory. Complex nonlinear behaviors including the energetic activation barrier or, more generally, a form of threshold leading to forced bifurcations of dc components of output response accompanied by enhancement of its odd harmonic components were discovered in limited narrow ranges of the control parameters space through numerical simulations. We observed the resonant behaviors of spectral amplification coefficient which is maximized when control parameters are tuned near the critical values of synergetic potential.
Keywords: lateral superlattices, applied electric field, spontaneous transverse electric field, nonequilibrium phase transitions, synergetic potential, forced bifurcations, resonant enhancement. 
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I. I. Maglevanny; V. A. Smolar; T. I. Karyakina. Weak Signals Amplification Through Controlled Bifurcations in Quasi-Two-Dimensional Electron Gas. Russian journal of nonlinear dynamics, Tome 14 (2018) no. 4, pp. 453-472. http://geodesic.mathdoc.fr/item/ND_2018_14_4_a2/

[1] Gammaitoni, L., Hänggi, P., Jung, P., and Marchesoni, F., “Stochastic Resonance”, Rev. Mod. Phys., 70:1 (1998), 223–287 | DOI

[2] Landa, P. S. and McClintock, P. V. E., “Vibrational Resonance”, J. Phys. A, 33:45 (2000), L433–L438 | DOI | MR | Zbl

[3] Karabalin, R. B., Lifshitz, R., Cross, M. C., Matheny, M. H., Masmanidis, S. C., and Roukes, M. L., “Signal Amplification by Sensitive Control of Bifurcation Topology”, Phys. Rev. Lett., 106:9 (2011), 094102, 4 pp. | DOI

[4] Vijay, R., Devoret, M. H., and Siddiqi, I., “Invited Review Article: The Josephson Bifurcation Amplifier”, Rev. Sci. Instrum., 80:11 (2009), 111101, 17 pp. | DOI

[5] Guckenheimer, J. and Holmes, Ph., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Appl. Math. Sci., 42, 5th ed., Springer, New York, 1997, 459 pp. | MR

[6] Jafrate, G. J., Ferry, D., and Reich, R., “Lateral (Two-Dimensional) Superlattices: Quantum-Well Confinement and Charge Instabilities”, Surf. Sci., 113:1–3 (1982), 485–488 | DOI

[7] Reich, R. K., Crondin, R. O., and Ferry, D. K., “Transport in Lateral Surface Superlattices”, Phys. Rev. B, 27:6 (1983), 3483–3493 | DOI

[8] Shmelev, G. M. and Maglevanny, I. I., “Transverse EMF in Lateral Superlattices”, Physics of Low-Dimensional Structures, 9–10 (1996), 81–88

[9] Maglevanny, I. I., Smolar, V. A., and Karyakina, T. I., “Thermally and Electrically Controllable Multiple High Harmonics Generation by Harmonically Driven Quasi-Two-Dimensional Electron Gas”, Superlattices Microstruct., 118 (2018), 29–44 | DOI

[10] Epshtein, E. M., Shmelev, G. M., and Maglevanny, I. I., “Ferromagnetic and Ferroelectric Properties of Nonequilibrium Electron Gas”, Phys. Lett. A, 254:1–2 (1999), 107–111 | DOI

[11] Maglevanny, I. I., “Highly Nonlinear Phenomena of Self-Organization of Quasi-Two-Dimensional Electron Gas in High Magnetic and Electric Fields”, Phys. Status Solidi B, 246:6 (2009), 1297–1305 | DOI

[12] Grahn, H. T., von Klitzing, K., Ploog, K., and Döhler, G. H., “Electrical Transport in Narrow-Miniband Semiconductor Superlattices”, Phys. Rev. B, 43:14 (1991), 12094–12097 | DOI

[13] Bass, F. G. and Tetervov, A. P., “High-Frequency Phenomena in Semiconductor Superlattices”, Phys. Rep., 140:5 (1986), 237–322 | DOI

[14] Jung, P. and Talkner, P., “Suppression of Higher Harmonics at Noise Induced Resonances”, Phys. Rev. E, 51:3 (1995), 2640–2643 | DOI

[15] Contemporary Problems in Statistical Physics, ed. G. H. Weiss, SIAM, Philadelphia, 1994, xviii + 251 pp. | Zbl

[16] Gilmore, R., Catastrophe Theory for Scientists and Engineers, Dover, New York, 1993, 666 pp. | MR

[17] Poston, T. and Stewart, I., Catastrophe Theory and Its Application, Pitman, London, 1978, xviii+491 pp. | MR

[18] Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., Numerical Recipes: The Art of Scientific Computing, 3rd ed., Cambridge University Press, New York, 2007, 1256 pp. | MR | Zbl

[19] Hairer, E., Nørsett, S. P., and Wanner, G., Solving Ordinary Differential Equations: 1. Nonstiff Problems, Springer Series in Computational Mathematics, 8, 2nd ed., rev., Springer, Berlin, 1993, XV, 528 pp. | MR

[20] Bendat, J. S. and Piersol, A. G., Random Data: Analysis and Measurement Procedures, 4th ed., Wiley, New York, 2010, 640 pp. | MR | Zbl