Consequences of a possible adiabatic transition betweenν=1/3andν=1quantum Hall states in a narrow wire

We consider the possibility of creating an adiabatic transition through a narrow neck, or point contact, between two different quantized Hall states that have the same number of edge modes, such as $\nu =1\mathrm{}$ and $\nu =\frac{1}{3}$. We apply both the composite-fermion and Luttinger-liquid formalism to analyze the transition. We suggest that using such adiabatic junctions one could build a dc step-up transformer, where the output voltage is higher than the input. Difficulties standing in the way of an experimental implementation of the adiabatic junction are addressed.