Consequences of a possible adiabatic transition between ν=1/3 and ν=1 quantum 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 and nu = 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 de 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. [S0163-1829(98)02104-3].