Abstract
The resistance between arbitrary sites of infinite square network of identical resistors is studied when the network is perturbed by removing two bonds from the perfect lattice. A connection is made between the resistance and the lattice Green’s function of the perturbed network. By solving Dyson’s equation the Green’s function and the resistance of the perturbed lattice are expressed in terms of those of the perfect lattice. Some numerical results are presented for an infinite square lattice.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Asad, J. H., Sakaji, A., Hijjawi, R. S., and Khalifeh, J. M. (2004). On the Resistance of an Infinite Square Network of Identical Resistors (Theoretical and Experimental Comparison). Hadronic Journal (accepted).
Atkinson, D. and Van Steenwijk, F. J. (1999). American Journal of Physics 67, 486.
Bartis, F. J. (1967). American Journal of Physics 35, 354.
Cserti, J. (2000). American Journal of Physics 68, 896.
Cserti, J., David, G., and Piroth, A. (2002). American Journal of Physics 70, 153.
Doyle, P. G. and Snell, J. L. (1984). Random walks and Electric Networks, The Carus Mathematical Monograph, Series 22, The Mathematical Association of America, USA, 83 pp.
Economou, E. N. (1983). Green’s Functions in Quantum Physics, Spriger-Verlag, Berlin.
Hijjawi, R. (2002). PhD Thesis, University of Jordan (unpublished).
Katsura, S. and Inawashiro, S. (1971). Journal of Mathematical Physics 12(8), 1622.
Kirchhoff, G. (1847). Annals of Physik und Chemie 72, 497.
Lovăsz, L. (1996). Random walks on graphs: A survey, in Combinatorics, Paul Erdös is Eighty, Vol. 2. In D. Miklós, V. T. Sós, and T. Szónyi, eds., János Bolyai Mathematical Society, Budepest, pp. 353–398. Also at http://research.microsoft.com∼Lovăsz/as a survey paper.
Monwhea, J. (2000). American Journal of Physics 68(1), 37.
Morita, T. (1971). Journal of Mathematical Physics 12(8), 1744.
Morita, T. and Horiguchi, T. (1971). Journal of Mathematical Physics 12(6), 986.
Morita, T. and Horiguchi, T. (1972). Journal of Physics A: Mathematics and General 5(1), 67.
Redner, S. (2001). A Guide to First-passage Processes, Cambridge Press, Cambridge, UK.
Van der Pol, B. and Bremmer, H. (1955). Operational Calculus Based on the Two-Sided Laplace Integral, Cambridge University Press, England.
Venezian, G. (1994). American Journal of Physics 62, 1000.
Wu, F. Y. (2004). Journal of Physics A: Mathematics and General (37), 6653.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Asad, J.H., Hijjawi, R.S., Sakaj, A. et al. Remarks on Perturbation of Infinite Networks of Identical Resistors. Int J Theor Phys 44, 471–483 (2005). https://doi.org/10.1007/s10773-005-3977-6
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10773-005-3977-6