| A semiclassical description of the decoherence process of wave packets evolving in chaotic billiards is presented. The particle in the billiard is coupled to a time dependent fluctuating potential whose spectral properties are chosen in order to model the coupling to an environment in the regime of weak dissipation and high temperature. The decoherence is then characterized by the time evolution of the purity of the reduced density matrix. This quantity is calculated semiclassically inspired by the methods of the Loschmidt echo problem. Starting with a initial state given by a single wave packet, the semiclassical calculation for the purity leads to a sum of two terms: one decaying with the Lyapunov exponent and the other with a rate proportional to the temperature, the friction constant and the area of the billiard. The case of a superposition of two wave packets is briefly sketched. |
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