String model of the Cooper pair in the anisotropic superconductor

An analogy between the Cooper pair in high-temperature superconductors and the quark-antiquark pair in quantum chromodynamics (QCD) is proposed. In QCD the nonlinear chromodynamical field between a quark and an antiquark is confined to a tube. So we assume that there exists a strong interaction between phonons which can confine them to some tube as well. This tube is described using the nonlinear Schr\"odinger equation. We show that it has an infinite spectrum of axially symmetric (string) solutions with negative finite linear energy density. The one-dimensional nonlinear Schr\"odinger equation has a finite spectrum (hence, it has a steady state) which describes the Cooper pair squeezed between anisotropy planes in the superconductor. It is shown that in this model the transition temperature is approximately 45 K. \textcopyright{} 1996 The American Physical Society.