Phys. Rev. Lett. 75, 4719–4723 (1995)Thermodynamic Analysis of Inhomogeneous Random Walks: Localization and Phase TransitionsReceived 26 September 1995; revised 6 November 1995; published in the issue dated 25 December 1995 We apply the thermodynamic formalism to discrete random walks in inhomogeneous environments. For simple one-dimensional examples we prove the existence of first and second order phase transitions. A typical mechanism for the latter is identified as localization-delocalization transition of relevant eigenfunctions of the generalized propagator. This can be understood by a mapping to quantum mechanical tight-binding models. Within a bivariate version of the formalism we show the occurrence of anomalous diffusion in the delocalized phase. © 1995 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.75.4719
DOI:
10.1103/PhysRevLett.75.4719
PACS:
05.40.+j, 05.45.+b, 05.60.+w, 64.60.-i
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