NONLINEAR SCHRÖDINGER EQUATION FOR SUPERCONDUCTORS

Abstract

Using the Hartree–Fock–Bogoliubov factorization of the density matrix and the Born–Oppenheimer approximation we show that the motion of a superconducting condensate satisfies a Schrödinger equation at zero temperature. The Galilean invariance of the equation is explicitly manifested. This equation gives a unified description of the condensate dynamics, such as Josephson effects, vortex dynamics and the Bogoliubov–Anderson mode.