Topological universality of level dynamics in quasi-one-dimensional disordered conductors

Abstract

Nonperturbative, in inverse Thouless conductance ${g}^{\ensuremath{-}1},$ corrections to distributions of level velocities and level curvatures in quasi-one-dimensional disordered conductors with a topology of a ring subject to a constant vector potential are studied within the framework of the instanton approximation of nonlinear \ensuremath{\sigma} model. It is demonstrated that a global character of the perturbation reveals the universal features of the level dynamics. The universality shows up in the form of weak topological oscillations of the magnitude $\ensuremath{\sim}{e}^{\ensuremath{-}g}$ covering the main bodies of the densities of level velocities and level curvatures. The period of discovered universal oscillations does not depend on microscopic parameters of conductor, and is only determined by the global symmetries of the Hamiltonian before and after the perturbation was applied. We predict the period of topological oscillations to be $4/{\ensuremath{\pi}}^{2}$ for the distribution function of level curvatures in orthogonal symmetry class, and $\sqrt{3}/\ensuremath{\pi}$ for the distribution of level velocities in unitary and symplectic symmetry classes.