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arXiv · 1512.00258

Percolation, sliding, localization and relaxation in topologically closed circuits

Daniel Hurowitz·Doron Cohen
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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.

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Daniel Hurowitz, Doron Cohen. 2016-03-10. Percolation, sliding, localization and relaxation in topologically closed circuits. https://doi.org/10.1038/srep22735

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