| We construct a set of states, called scar functions, which accurately describes the spectrum of the quantum baker map. These states are based on the classical invariants of the map, and depend on a propagation time parameter. We find that the distance between the scar function basis and the eigenstates decays exponentially with the propagation time, obtaining the best known approximation with times no longer than a fraction of the Ehrenfest time. On the other hand we propose the homoclinic periodic orbit modes to approximate the scar functions of this basis, avoiding the propagation in time. |
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