Some classical views on the parameters of the Grothendieck-Teichmüeller group

We present two new formulas concerning behaviors of the standard parameters of the Grothendieck-Teichmüller group GT , and discuss their relationships with classical mathematics. First, considering a non-Galois etale cover of P1 {0 1 infinity} of degree 4, we present a newtype equation satisfied by the Galois image in GT . Second, a certain equation in GL 2 (Z||Z2 ) satisfied by every element of GT is derived as an application of (profinite) free differential calculus.</p

Transport Coefficients of InSb in a Strong Magnetic Field

Improvement of a superconducting magnet system makes induction of a strong magnetic field easier. This fact gives us a possibility of energy conversion by the Nernst effect. As the first step to study the Nernst element, we measured the conductivity, the Hall coefficient, the thermoelectric power and the Nernst coefficient of the InSb, which is one of candidates of the Nernst elements. From this experiment, it is concluded that the Nernst coefficient is smaller than the theoretical values. On the other hand, the conductivity, the Hall coefficient ant the thermoelectric power has the values expected by the theory.Comment: 6 pages, Latex, This article was presented in the XVI International Conference on Thermoelectrics, Dresden, Germany (1997

Quantum Nernst Effect

It is theoretically predicted that the Nernst coefficient is strongly suppressed and the thermal conductance is quantized in the quantum Hall regime of the two-dimensional electron gas. The Nernst effect is the induction of a thermomagnetic electromotive force in the $y$ direction under a temperature bias in the $x$ direction and a magnetic field in the $z$ direction. The quantum nature of the Nernst effect is analyzed with the use of a circulating edge current and is demonstrated numerically. The present system is a physical realization of the non-equilibrium steady state.Comment: 11 pages, 5 figures, to be published in Solid State Com