This study demonstrates that the zeros of diagonal components Green functions are key quantities can detect noninteracting topological insulators. We show traverse band gap in phases. The traverses induce crosses zeros, and zeros' surface gap, analogous to Fermi metals. By calculating microscopic models, we universally appear all six classes conventional utilizing eigenvector-eigenvalue identit...

We consider some classes of Lévy processes for which the estimate of Krylov and Safonov (as in (Potential Anal. 17 (2002) 375–388)) fails and thus it is not possible to use the standard iteration technique to obtain a-priori Hölder continuity estimates of harmonic functions. Despite the failure of this method, we obtain some a-priori regularity estimates of harmonic functions for these processe...

We present a new method for calculating the Green functions for a lattice scalar field theory in D dimensions with arbitrary potential V (φ). The method for non-perturbative evaluation of Green functions for D=1 is generalized to higher dimensions. We define “hole functions” A (i = 0, 1, 2, · · · , N−1) from which one can construct N -point Green functions. We derive characteristic equations of...