Spatial-Field Correlation: The Building Block of Mesoscopic Fluctuations

Abstract

The absence of self-averaging in mesoscopic systems is a consequence of long-range intensity correlations. Microwave measurements suggest, and diagrammatic calculations confirm, that the correlation function of the normalized intensity with displacement of the source and detector, $\Delta R$ and $\Delta r$, respectively, can be expressed as the sum of three terms, with distinctive spatial dependences. Each term involves only the sum or the product of the square of the field correlation function, $F\equiv F_E^2$. The leading-order term is the product, $F\left(\Delta R\right)F\left(\Delta r\right)$; the next term is proportional to the sum, $F\left(\Delta R\right)+F\left(\Delta r\right)$; the third term is proportional to $F\left(\Delta R\right)F\left(\Delta r\right)+\left[F\right(\Delta R)+F(\Delta r\left)\right]+1\mathrm{}$.