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We investigate the 1/N expansion proposed recently as a strategy to includequantum fluctuation effects in the nonrelativistic, attractive Fermi gas at andnear unitarity. We extend the previous results by calculating thenext-to-leading order corrections to the critical temperature along the wholeBCS-BEC crossover. We demonstrate explicitly that the extrapolation from themean-field approximation, based on the $1/N$ expansion, provides a usefulapproximation scheme only on the BCS side of the crossover. We then apply thetechnique to the study of strongly interacting relativistic many-fermionsystems. Having in mind the application to color superconductivity in colddense quark matter, we develop, within a simple model, a formalism suitable tocompare the effects of order parameter fluctuations in phases with differentpairing patterns. Our main conclusion is that the relative correction to thecritical temperature is to a good accuracy proportional to the mean-field ratioof the critical temperature and the chemical potential. As a consequence, it issignificant even rather deep in the BCS regime, where phenomenologicallyinteresting values of the quark-quark coupling are expected. Possible impact onthe phase diagram of color-superconducting quark matter is discussed.

Strongly interacting Fermi systems in 1/N expansion: From cold atoms to color superconductivity