Khantha, M. ; Balakrishnan, V. (1984) Hopping conductivity of a one-dimensional bond-percolation model in a constant field: exact solution Physical Review B, 29 (8). pp. 4679-4690. ISSN 0163-1829
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Official URL: http://prb.aps.org/abstract/PRB/v29/i8/p4679_1
Related URL: http://dx.doi.org/10.1103/PhysRevB.29.4679
Abstract
The recent work of Odagaki and Lax on the ac hopping conductivity in a one-dimensional bond-percolation model is generalized to include a constant applied field. The corresponding biased random-walk problem on a finite chain of arbitrary length and with properly terminated ends is solved analytically. The solution is extended to include all continuous-time random walks. (It is thus directly applicable, for instance, to spectral diffusion with asymmetric transfer rates and memory effects.) The diffusivity (and thence the conductivity and relative permittivity) on a chain of N sites is obtained exactly, in closed form. A configuration averaging over N yields the diffusivity and relative permittivity for the randomly interrupted infinite chain. Our analytic results are valid at all frequencies, and are in a form amenable to extensive numerical computation. This is done, and the noteworthy features of the results are displayed graphically. All the known results in the field-free case are recovered as special cases of the expressions presented here.
Item Type: | Article |
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Source: | Copyright of this article belongs to American Physical Society. |
ID Code: | 1057 |
Deposited On: | 25 Sep 2010 11:08 |
Last Modified: | 11 May 2011 12:22 |
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