The classical skeleton of open quantum chaotic maps

Abstract

We have studied two complementary decoherence measures purity and fidelity for a generic diffusive noise in two different chaotic systems (the baker and the cat maps). For both quantities, we have found classical structures in quantum mechanics -the scar functions -that are specially stable when subjected to environmental perturbations. We show that these quantum states constructed on classical invariants are the most robust significant quantum distributions in generic dissipative maps.

Semiclassical matrix elements for a chaotic propagator in the scar function basis

“…These wavefunctions define an optimal basis in chaotic systems [5,12] and they have attracted increasing interest in closed systems [13]. Moreover, they have been shown to be crucial for the understanding of long lived resonances in open systems [14][15][16].…”