English

Percolation, sliding, localization and relaxation in topologically closed circuits

Statistical Mechanics 2016-03-11 v2

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.

Keywords

Cite

@article{arxiv.1512.00258,
  title  = {Percolation, sliding, localization and relaxation in topologically closed circuits},
  author = {Daniel Hurowitz and Doron Cohen},
  journal= {arXiv preprint arXiv:1512.00258},
  year   = {2016}
}

Comments

11 pages, 6 figures, 1 table, upgraded version

R2 v1 2026-06-22T11:58:32.382Z