Schwarzian derivative as a proof of the chaotic behaviour

Pramana

Zeynep Güven Özdemir1¹ 

[1] Department of Physics, Yıldız Technical University, 34210 Esenler, Istanbul, Turkey$$

关键词: Mercury cuprate superconductors;    nonlinear dynamics and chaotic behaviour;    Schwarzian derivative;    paramagnetic Meissner effect.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In recent years, a sufficient condition for determining chaotic behaviours of the nonlinear systems has been characterized by the negative Schwarzian derivative (Hacıbekiroğlu et al, Nonlinear Anal.: Real World Appl. 10, 1270 (2009)). In this work, the Schwarzian derivative has been calculated for investigating the quantum chaotic transition points in the high-temperature superconducting frame of reference, which is known as a nonlinear dynamical system that displays some macroscopic quantum effects. In our previous works, two quantum chaotic transition points of the critical transition temperature, 𝑇c, and paramagnetic Meissner transition temperature, 𝑇PME, have been phenomenologically predicted for the mercury-based high-temperature superconductors (Onbaşlı et al, Chaos, Solitons and Fractals 42, 1980 (2009); Aslan et al, J. Phys.: Conf. Ser. 153, 012002 (2009); Çataltepe, Superconductor (Sciyo Company, India, 2010)). The 𝑇c, at which the one-dimensional global gauge symmetry is spontaneously broken, refers to the second-order phase transition, whereas the 𝑇PME, at which time reversal symmetry is broken, indicates the change in the direction of orbital current in the system (Onbaşlı et al, Chaos, Solitons and Fractals 42, 1980 (2009)). In this context, the chaotic behaviour of the mercury-based high-temperature superconductors has been investigated by means of the Schwarzian derivative of the magnetic moment versus temperature. In all calculations, the Schwarzian derivatives have been found to be negative at both 𝑇c and 𝑇PME which are in agreement with the chaotic behaviour of the system.

【 授权许可】

Unknown