Experience in numerically modelling the mixed state of superconductors, applied to a study of the nonstationary Schrödinger equation

Abstract

Experience in numerically modelling superconducting systems has been used to investigate the behavior of a nonstationary wave function far from equilibrium. It is shown that normalization of the wave function plays the role of an efficient nonlocal interaction that causes the wave function to be localized in one of the wells even for an infinitesimal difference of their depths. This fundamentally differs from the solution of the Fokker-Planck equation, which in equilibrium depends exponentially on the energy and is virtually symmetrical for wells that are similar in depth. When a fluctuational (small) variation causes the relative depths to reverse, the wave function’s maximum tunnels to the other well. A transition in a one-well potential from an excited state to a lower state is also considered. It is shown that this is accompanied by the emission of a localized segment of an electromagnetic wave, which can be identified with a “photon.”