Quantum harmonic chain
= Quantum harmonic chain
A <quantum harmonic chain> has quadratic couplings between canonical coordinates and momenta. A <normal mode> transformation turns it into independent <quantum harmonic oscillators>. A continuum elastic <action> with <time> coefficient $\chi$ and spatial stiffness $\kappa$ has long-wave <frequency> $\omega^2=(\kappa/\chi)q^2$, the structure of a smooth condensate phase <action>.