Correlations and fluctuations of a confined electron gas

The grand potential Ω and the response R=-∂Ω/∂x of a phase-coherent confined noninteracting electron gas depend sensitively on chemical potential μ or external parameter x. We compute their autocorrelation as a function of μ, x, and temperature. The result is related to the short-time dynamics of the corresponding classical system, implying in general the absence of a universal regime. Chaotic, diffusive, and integrable motions are investigated and illustrated numerically. The autocorrelation of the persistent current of a disordered mesoscopic ring is also computed.