Long-range angular correlations of waves in a tube geometry

We show the existence of unusual angular correlations for transmitted and reflected waves for a random medium in the shape of a long tube. The brightness of the speckle spot extends much above its normal angular size Δθ=λ/W (where W is the width of the tube) and falls off only as a power law with oscillatory strength. We show a gradual disappearance of the memory effect as the length of the tube exceeds its width. We have also performed numerical simulations that confirm our analytical expressions for the correlation functions ${\mathit{C}}_1$ and ${\mathit{C}}_2$ and are able to determine the constant background correlation ${\mathit{C}}_3$.