Signal reconstructions improved by chaos through the time reversal focusing

HERNAN L. CALVO; RODOLFO A. JALABERT; HORACIO M. PASTAWSKI

Buenos Aires

Workshop; Third workshop on Quantum Chaos: Theory and Applications; 2009

UBA

The focalization of acoustic waves through the time reversal mirror technique is an experimental technique used to accurately reconstruct an initially localized pulse by an array of receiver-emitter transducers that re-inject the recorded signal. The experiments provoked a natural surprise while yielding reconstructions, albeit not perfect, were highly faithful. In this time-reversal focusing (TRF) the play-back signal builds up in the region of the original excitation 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.