Schwarzian Derivative of Third Chaotic Transition in Mercury Based Superconductors

Yıl 2019, Cilt: 2 Sayı: 3, 17 - 21, 31.12.2019

Özden Aslan Çataltepe

Öz

The superconductivity displays some nonlinear quantum properties such as quantum chaotic transitions, effective mass of quasi-particles. The calculation of the effective mass equation of the mercury based superconductor has a crucial step in order to determine chaotic behavior of the sample. The sample has three quantum chaotic points; the critical transition (Tc), paramagnetic Meissner transition (TPME) and the quantum gravitational transition temperatures (TQG). Tc and TPME were already investigated by means of Schwarzian derivative and it was found that the Schwarzian derivatives are both negative at two chaotic points. In the study, the third quantum chaotic point of the system, TQG is investigated by the Schwarzian derivative of the effective mass of the sample. As is known, the object’s mass varies in a gravitational field. Hence, it is determined that the Schwarzian derivative of the effective mass, which has the negative value, shows the quantum chaotic transition in the system. At the vicinity of TQG where the first derivative of the net effective mass has a maximum value, the plasma frequency shifts from microwave to infrared. As a result, it is proposed that the Schwarzian derivative is a convenient mathematical method for precise prediction of chaotic points and transitions in superconducting systems.

Anahtar Kelimeler

Mercury based superconductor, Nonlinear behavior of the superconducting system, Schwarzian Derivative, Quantum chaotic transition.

Kaynakça

• [1] Z. Güven Özdemir, Schwarzian derivative as a proof of the chaotic behavior. Pramana-J Phys, vol.77(6), pp.1159-1169, 2011.
• [2] Ü. Onbaşlı, Z. Güven Özdemir and Ö. Aslan, Symmetry Breaking and Double Helix Quantum Structure in d-Wave Superconductivity. Chaos Soliton Fract, vol.42(4), pp.1980-1989, 2009.
• [3] M. Cirillo and NF. Pedersen, On bifurcations and transition to chaos in a Josephson junction, Phys Lett A, vol. 90(3), pp.150–152. 1982.
• [4] WJ. Yeh, OG. Symko and DJ. Zheng, Chaos in long Josephson junctions without external rf driving force, Phys Rev B, vol. 42/7, pp. 4080-4087, 1990.
• [5] KN. Yugay, NV. Blinov and IV Shirokov, Effect of memory and dynamical chaos in long Josephson junctions. Phys Rev B, vol.51/18, pp.12737, 1995.
• [6] A. Mourachkine, High-temperature superconductivity: The nonlinear mechanism and tunneling measurements. New York: Kluwer Academic Publishers, 2002.
• [7] Ö. Aslan Çataltepe, Some Chaotic Points in Cuprate Superconductors. in Superconductor, AM Luiz ed. India: Sciyo Company Press, 2010, pp. 273-290.
• [8] Ö. Aslan, Z. Güven Özdemir and SS. Keskin and Ü. Onbaslı, The chaotic points and XRD analysis of Hg-based superconductors. J Phys Conf Ser, vol.153/012002: pp.1-9. 2009.
• [9] Ö. Aslan Investigation of the Symmetries and the Breakages in Relativistic and Non-Relativistic Regions in High Temperature Superconductors. PhD Thesis, Marmara University, İstanbul, Turkey, 2007.
• [10] Z. Güven Özdemir, Ö. Aslan Çataltepe and Ü. Onbaslı, The Correlation between the Double Helix Quantum Wave in d-Wave Superconductors and Human DNA, Acta Phys Pol A, vol.121/1, pp.13-15, 2012.
• [11] Ü. Onbaslı and Z. Güven Özdemir Superconductors and Quantum Gravity. in Superconductor, AM Luiz ed. India: Sciyo Company Press, 2010, pp. 291-310.
• [12] Z. Likui and S. Yining, Discussion on Mass in a Gravitational Field. International Journal of Physics, vol.1/5; pp.110-114, 2013.
• [13] ZG. Özdemir, Ö. Aslan and Ü. Onbaşlı, Calculation of Microwave Plasma Oscillations In High Temperature Superconductors, in Vibration Problems-ICOVP 2005, E, İnan, E. Kırıs, eds. Dordrecht, The Netherlands: Springer, 2007, pp.377-382.
• [14] Z. Güven Özdemir, Ö. Aslan and Ü. Onbaslı, Terahertz Oscillations in Mercury Cuprates Superconductors, Pramana-J Phys, vol.73/4, pp.755-763, 2009.
• [15] Ö. Aslan Çataltepe, Z, Güven Özdemir and Ü. Onbaslı, Role of oxygen content on micro-whiskers in mercury based superconductors, J Magn Magn Mater, vol.373, pp. 23–26, 2015.
• [16] ZG. Özdemir, Ö. Aslan and Ü. Onbaşlı, Determination of c-axis Electrodynamics Parameters of Mercury Cuprates, J Phys Chem Solids, vol.67(1-3), pp.453-456, 2006.
• [17] Ö. Aslan Çataltepe, Z. Güven Özdemir and Ü. Onbaslı An Investigation of the Effect of Grain Size on Some Properties of Intrinsic Josepson Junction, Physica C,; vol.491(15), pp.59-61, 2013.
• [18] O. Aslan, ZG. Ozdemir and U. Onbasli, Correlation Between The Anisotropy and The Effective Mass of The Quasi‐Particles in Oxide Superconductors, AIP Conf. Proc. 89, American Institute of Physics, Melville, NY, pp. 271-272, 2007.
• [19] Z. Güven Özdemir, Determination of the electrical and magnetic properties of the mercury based copper oxide layered high temperature superconductors, PhD Thesis, Marmara University, İstanbul, Turkey, 2007.
• [20] M.S. El Naschie, From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold. Chaos Soliton Fract, Vol. 25 No. 5, 969-977, 2005.
• [21] P. Collet and JP. Eckmann, Iterated maps on the interval as dynamical systems, Birkhäuser, Boston, USA, Springer,1980.
• [22] J. Guckenheimer, Sensitive dependence to initial conditions for one dimensional maps, Communications in Mathematical Physics, vol.70(2), pp.133-160. 1979;
• [23] G. Hacıbekiroğlu, M. Çağlar and Y. Polatoğlu, The higher-order Schwarzian derivative: its applications for chaotic behavior and new invariant sufficient condition of chaos. Nonlinear Anal-Real, vol.10(3), pp.1270-1275, 2009.
• [24] L. Katz, Note on the Schwarzian derivative, Chaos Soliton Fract vol.7(9), pp.1495-1496, 1996.