Correlations and fluctuations of a confined electron gas

Abstract

The grand potential $Ω$ and the response $R = - \partial Ω/\partial x$ 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.