Manifestation of classical bifurcation in the spectrum of the integrable quantum dimer.

  title={Manifestation of classical bifurcation in the spectrum of the integrable quantum dimer.},
  author={Aubry and Flach and Kladko and Olbrich},
  journal={Physical review letters},
  volume={76 10},
We analyze the classical and quantum properties of the integrable dimer problem. The classical version exhibits exactly one bifurcation in phase space, which gives birth to permutational symmetry broken trajectories and a separatrix. The quantum analysis yields all tunneling rates (splittings) in leading order of perturbation. In the semiclassical regime the eigenvalue spectrum obtained by numerically exact diagonalization allows one to conclude about the presence of a separatrix and a… 

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Contents: Introduction.- The Mechanics of Lagrange.- The Mechanics of Hamilton and Jacobi.- Integrable Systems.- The Three-Body Problem: Moon-Earth-Sun.- Three Methods of Section.- Periodic Orbits.-
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