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.

11 pages, 6 figures, 1 table, upgraded version

References in corpus (4)

• Recent advances in percolation theory and its applications
• Non-equilibrium version of the Einstein relation
• Diffusion in sparse networks: linear to semi-linear crossover
• Non-equilibrium steady state and induced currents of a mesoscopically-glassy system: interplay of resistor-network theory and Sinai physics

Cited by in corpus (6)

• Localization due to topological stochastic disorder in active networks
• The relaxation rate of a stochastic spreading process in a closed ring
• Negative mobility, sliding and delocalization for stochastic networks
• Quantum stochastic transport along chains
• Emergence of Sinai Physics in the stochastic motion of passive and active particles
• Quantum walk in stochastic environment