CONICET | Buscador de Institutos y Recursos Humanos

The focalization of acoustic waves through the time reversal mirror technique in a non-homogeneous medium was an experimental deed showing that an initially localized pulse can be accurately reconstructed by an array of receiver-emitter transducers that re-inject the recorded signal. These experiments provoked a natural surprise while yielding reconstructions, that albeit not perfect, were highly faithful. In this time-reversal focusing (TRF) procedure the play back signal builds up in the region of the original excitation, in the form of a reversed wave amplitude and can be viewed as the wave version of the Loschmidt echo. A salient feature of the TRF experiments is that the refocusing improves when the wave-propagation occurs in a disordered medium or in a chaotic cavity, as compared with the homogeneous or integrable case. In this work we develop a semiclassical theory of the TRF in order to explain this robustness and the role played by chaos. Considering the ergodic properties in the cavities, we propose different models for the perturbation and analyze those regimes where the focusing takes place. Finally, we compare the obtained analytical results with numerical simulations.