Statistical mechanics of the deformable droplets on Riemannian surfaces: Applications to reptation and related problems

The statistical mechanics treatment of the Laplace–Young‐type problems developed for the flat surfaces is generalized to the case of surfaces of constant negative curvature and connected with them to Riemannian surfaces. Obtained results are mainly used to supply an additional support of the quantum Hall effect (QHE) analogy employed in recent work [J. Phys. 4, 843 (1994)], which provides theoretical justification of the tube concept used in polymer reptation models. As a byproduct, close links between QHE, quantum chaos, and the non‐Abelian Chern–Simons quantum mechanics are indicated.