Tunneling and the Band Structure of Chaotic Systems

Leboeuf Patricio ¹, Amaury Mouchet ²

Physical Review Letters 73 (1994) 1360

We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex orbits. These turn out to be fundamental for a proper description of the band structure since they incorporate conduction processes through tunneling mechanisms. The results obtained, illustrated with the kicked-Harper model, are in excellent agreement with numerical simulations, even in the extreme quantum regime.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
  CNRS : UMR8626 – Université Paris XI – Paris Sud
• 2. Laboratoire de Mathématiques et Physique Théorique (LMPT),
  CNRS : UMR6083 – Université François Rabelais – Tours