A Model for the Quantization of the Hall Resistance in the Quantum Hall Effect ()
Abstract
Some aspects of anyon physics are reviewed with the intention of establishing a model for the quantization of the Hall conductance. A single particle Schrödinger model is introduced and coupled with a constraint equation formulated from the anyon picture. The Schrödinger equation-constraint system can be converted to a single nonlinear differential equation and solutions for the model can be produced.
Share and Cite:
P. Bracken, "A Model for the Quantization of the Hall Resistance in the Quantum Hall Effect,"
Journal of Modern Physics, Vol. 1 No. 3, 2010, pp. 158-162. doi:
10.4236/jmp.2010.13023.
Conflicts of Interest
The authors declare no conflicts of interest.
References
|
[1]
|
J. K. Jain, “Composite Fermions, Perspectives in Quantum Hall Effects,” In: S. D. Sarma and A. Pinczuk Eds., J. Wiley and Sons, New York, 1987.
|
|
[2]
|
K. von Klitzing, G. Dorda and M. Pepper, “New Method for High-Accuracy Determination of the Fine Structure Constant Based on Quantized Hall Resistance,” Physics Review Letters, Vol. 45, No. 6, 1980, pp. 494-497.
|
|
[3]
|
R. B. Laughlin, “Quantized Hall conductivity in Two dimensions,” Physical Review B, Vol. 23, No. 10, 1981, pp. 5632-5633.
|
|
[4]
|
R. E. Prange and S. M. Girvin, “The Quantum Hall Effect,” Springer Verlag, New York, 1987.
|
|
[5]
|
Z. F. Ezawa, “The Quantum Hall Effects, Field Theoretical Approach and Related Topics,” World Scientific, Singapore, 2000.
|
|
[6]
|
R. B. Laughlin, “Fractional Quantization,” Reviews of Modern Physics, Vol. 71, No. 4, 1999, 863-874.
|