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Rational sequences for the conductance in quantum wires from affine Toda field theories

Castro-Alvaredo, O. and Fring, A. (2003). Rational sequences for the conductance in quantum wires from affine Toda field theories. Journal of Physics A: Mathematical and General, 36(26), L425-. doi: 10.1088/0305-4470/36/26/101

Abstract

We analyse the expression for the conductance of a quantum wire which is described by an integrable quantum field theory. In the high temperature regime we derive a simple formula for the filling fraction. This expression involves only the inverse of a matrix which contains the information of the asymptotic phases of the scattering matrix and the solutions of the constant thermodynamic Bethe ansatz equations. Evaluating these expressions for minimal affine Toda field theory we recover several sequences of rational numbers, which are multiples of the famous Jain sequence for the filling fraction occurring in the context of the fractional quantum Hall effect. For instance we obtain ν = 4m/(2m + 1) for A4m−1-minimal affine Toda field theory. The matrices involved have in general non-rational entries and are not part of previous classification schemes based on integral lattices.

Publication Type: Article
Subjects: Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/715
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