Golden Ratio Discovered in Nonlinear Superconductor

Abstract

Mercury based high temperature superconductor as a nonlinear dynamical system constitutes a natural laboratory for searching quantum chaotic transitions. In our previous works, these chaotic transitions had been expressed in details and mathematically proved by determination of negative Schwarzian derivative. In this work, we have focused on the net effective mass of the quasi particles, m* at the vicinity of absolute zero temperature and the mass of the double helix quantum wave i.e. topological Segâh solitons. The net effective mass of the quasi particles as the function of the phase of the superconducting system had already been determined in our previous works by using an advanced differential method that is based on the magnetic data obtained by SQUID (Superconducting Quantum Interference Device) measurements. The mass of the double helix quantum wave, whose wave length coincides with ultraviolet region of the electromagnetic spectrum, muv, has also been calculated with the wave length of the solitons in relativistic manner. Since we have already proved the three dimensional resonance at low temperatures for the mercury cuprates, the determination of the ratio of these masses at the vicinity of absolute zero would be a promising method for searching the properties of resonance. Hence, we have determined the resonance state which appears as the golden ratio in muv/m* values for the distances x=0.23m and x=2,361m at absolute zero temperature for the optimally and over oxygen doped mercury cuprate superconducting nonlinear condensed matter system, respectively

Keywords

• Golden ratio, net effective mass, solitons’ mass, mercury cuprate, nonlinear condensed matter system

References

1. www.goldennumber.net.
2. R Coldea, D A Tennant, E M Wheeler, E Wawrzynska, D Prabhakaran, M Telling, K Habicht, P Smeibidl, K Kiefer, “Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry”, Science, 327, 177, 2010.
3. X F Pang, Y PFeng, Quantum Mechanics in Nonlinear Systems World Scientific Publishing, Singapore, 2005.
4. Physics Survey Committee, Physics Through the 1990’s Condensed Matter Physics, National Academy Press, Washington DC, 1986.
5. Ü. Onbaşlı, Z. Güven Özdemir, and Ö. Aslan, “Symmetry breakings and topological solitons in mercury based d-wave Superconductors”, Chaos Solitons Fractals, vol. 42, pp. 1980-1989, 2009.
6. Ö Aslan, Z Güven Özdemir, S S Keskin, Ü Onbaşlı, “The chaotic points and XRD analysis of Hg-based superconductors”, Journal of Physics: Conference Series, 153, 012002, 2009.
7. Ö. Aslan Çataltepe, “Some chaotic points in cuprate superconductors”, in: Superconductor, A.M. Luiz, Ed., India: Sciyo http://www.intechopen.com/articles/show/title/some-chaotic-pointsin-cuprate-superconductors) 273-290. (Avaliable from:
8. Z. Güven Özdemir, Ö. Aslan, and Ü. Onbaşlı, “Terahertz oscillations in mercury cuprate Superconductors”, Pramana-J. Phys., vol. 73, pp. 755-763, 2009.

9. Ö Aslan, Z Güven Özdemir, Ü Onbaşlı, Correlation Between The Anisotropy and The Effective Mass of The Quasi‐Particles in Oxide Superconductors, AIP Conference Proceedings 899 (1), 271-272, 2007.
10. Ü Onbaşlı, Z Güven Özdemir, “Superconductors and Quantum- Gravity” in Superconductor edited by A M Luiz, Sciyo Company, India, http://www.intechopen.com/books/superconductor/superconductors- and-quantum-gravity) (Avaliable from:
11. Ö. Aslan Çataltepe, “Mercury cuprates bring symmetry breaking of the Universe to laboratory”, in: Lifetime of the Waves From Nano To Solitons In My Life, Ü. Onbaşlı, Ed., Kerela, India:Transworld Research Network, 2012, pp. 215-243. (Avaliable from: http://www.trnres.com/ebook/uploads/onbaslicontent/T_1350723744 5%20Onbasli.pdf)
12. K Kadowaki, I Kakeya, K Kindo, “Observation of the Nambu- Goldstone Mode in the High Temperature Superconductor Bi2Sr2CaCu2O8+δ.”, Europhys.Lett.,42,203, 1998.
13. P.W. Anderson, “Plasmons, Gauge Invariance, and Mass”, Phys. Rev., 130,439, 1963.
14. Z Güven Özdemir, A Aslan Çataltepe, Ü Onbaşlı, “The Correlation between the Double Helix Quantum Superconductors and Human DNA”, Acta Physica Polonica A, 121,13, 2012. Wave in d-Wave
15. Z. Güven Özdemir, Ö. Aslan, and Ü. Onbaşlı, “Determination of c- axis electrodynamics parameters of mercury cuprates”, J. Phys. Chem. Solids, vo. 67, pp. 453-456, 2006.
16. Z. Güven Özdemir, Ö. Aslan, and Ü. Onbaşlı, “Calculation of microwave Superconductors”, in: The 7th International Conference on Vibration Problems (ICOVP 2005) Springer Proceedings in Physics in high temperature 111, E. İnan, E. Kırış (Eds.), Dordrecht, The Netherlands: Springer, 2007, pp. 377-382.
17. R Ferrell, R Prange, “Self-Field Limiting of Josephson Tunneling of Superconducting Electron Pairs”, Phys. Rev. Lett., 10, 479, 1963.
18. V V Schmidt, in The Physics of Superconductors, Introduction to Fundamentals and Applications edited by P Müller and A V Ustinov Springer, Erlangen, p.81,1997
19. M Tinkham, Introduction to Superconductivity, McGraw-Hill, New York, 1996.
20. P W Anderson, The Theory of Superconductivity in the High-Tc Cuprate Superconductors, Princeton University Press, New Jersey, 1997.
21. M S Li, “Paramagnetic Meissner effect and related dynamical phenomena”, Phys. Rep., 376, 133, 2003.
22. Z. Güven Özdemir, Ö. Aslan, and Ü. Onbaşlı, “Terahertz oscillations in mercury cuprate Superconductors”, Pramana-J. Phys., vol. 73, pp. 755-763, 2009.