Writhing geometry at finite temperature: Random walks and geometric phases for stiff polymers

This paper studies the geometry of a semiflexible polymer at finite temperatures. The writhe correlation functions can be calculated from the properties of Gaussian random walks on the sphere. The writhe of a polymer is analogous to geometric or Berry phases studied in optics and wave mechanics. These results can be applied to confocal microscopy studies of stiff filaments and to simulations of short DNA loops.