QUANTUM OSCILLATIONS OF ELECTRONS AND OF COMPOSITE FERMIONS IN 2 DIMENSIONS - BEYOND THE LUTTINGER EXPANSION

Quantum oscillation phenomena, in conventional two-dimensional electro n systems and in the fractional quantum Hall effect, are usually treat ed in the Lifshitz-Kosevich formalism. This is justified in three dime nsions by Luttinger's expansion, in the parameter omega(c)/mu. We show that in two dimensions this expansion breaks down, and we derive a ne w expression, exact in the limit where rainbow graphs dominate the sel f-energy. Application of our results to the fractional quantum Hall ef fect near half-filling shows very strong deviations from Lifshitz-Kose vich behavior. We expect that such deviations will be important in any strongly interacting two-dimensional electronic system.