Classical and quantum coupled oscillators: symplectic structure
  We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum regimes. 
A. R. Bosco de Magalh\~aes, C. H. d'\'Avila Fonseca, and M. C. Nemes