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.