Presets
Parameters
Kaluza-Klein reduction (units hbar = c = k_B = 1): momentum around the circle is n/R, so each particle is a 1-D particle of mass |n|/R with energy E = sqrt(k^2 + (n/R)^2). A thermal gas populates level n with weight 2 m K1(m/T). When R T << 1 only n = 0 survives and the circle becomes invisible: the world has collapsed to one dimension. Gravity with one compact dimension: V(r) ~ coth(r/2R)/r.