title: Percolation, sliding, localization and relaxation in topologically closed circuits.
abstract: Considering a random walk in a random environment in a topologically closed circuit, we explore the implications of the percolation and sliding transitions for its relaxation modes. A complementary question regarding the "delocalization" of eigenstates of non-hermitian Hamiltonians has been addressed by Hatano, Nelson, and followers. But we show that for a conservative stochastic process the implied spectral properties are dramatically different. In particular we determine the threshold for under-damped relaxation, and observe "complexity saturation" as the bias is increased.
authors.affiliation: Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel.
authors.forename: Daniel
authors.initials: D
authors.lastname: Hurowitz
authors.affiliation: Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel.
authors.forename: Doron
authors.initials: D
authors.lastname: Cohen