Vortex Dynamics, Resistivity Formula, and Fluctuation-dissipation Theorems *

We investigate the problem of forces on moving vortex in a superfluid or superconductor. The main purpose is to locate the source which leads to the contradictory results in the literature. We establish the connection between this problem to the difficult but well studied subject of resistivity formula in transport theory. The relaxation time approximation used in the force calculation via force-force correlation function is shown to be invalid. The roles of Berry's phase and fluctuation-dissipation theorems are discussed. For a vortex moving in a superfluid or superconductor, the only agreement we have reached so far is at zero temperature, in absence of any impurity potentials. Question arises in more complicated cases. Using the Berry's phase calculation [1], as well as the exact total force-force correlation calculation [2], It has been shown that the transverse force is the Magnus force, coming from extended states with no dependence on the core level spacing and other extrinsic details. Other microscopic derivations using core state transitions [3–7] have shown, however, that the transverse force on a moving vortex is greatly reduced in