object diffuses to infinity. Other geometries however exhibit a bound state for $T=T'$. E.g. the strip geometry ${\cal D}$ has a normalizable distribution, $${\cal P}_m = \frac{\pi}{L^2 \ln 2} \frac{\sin^2(\pi y/L)}{\cosh(2 \pi x/L)-\cos(2 \pi y/L)}$$ and an exponentially localized bound state, with the length set by the strip width. An algebraic bound state is obtained if, in Fig. \[f:6\] with the two polymers going through $-L$ and $L$, one rotates the real negative axis around $0$ clockwise to form a wedge with angle $\phi<\pi$. Then: $${\cal P}_m(r,\theta) = {\cal N}_a \frac{L^{2 a-2} r^{2 a}  \sin^2(a \theta)}{L^{4 a}+ r^{4 a} - 2 (r L)^{2 a} \cos(2 a \theta)}$$ with $a=\pi/\phi>1$ (the formula remains true for $a<1$ as a non-normalizable density) and $\pi {\cal N}_a=4 a^2/(
\psi(\frac{1}{2 a})-\psi(\frac{1}{2}+\frac{1}{2 a})+a+ (\pi / \sin(\frac{\pi }{ a}))$. Let us compare the force exerted by one and by two polymers. Let us choose the simplest geometry $\cal E$, the infinite strip with the two polymers attached at both ends (Fig. \[f:5\]), where the force is along $y$. For an object in the middle, one has a restoring force towards the neutral axis $y=L/2$ $$f^{\mathrm{m}}_y =  \frac{2 kT \pi}{L} \cot\!\Big({\pi y \over L}\Big)\ ,$$ while the force 