(Poster) Time reversal mirror and perfect inverse filter in a microscopic model for sound propagation

HERNAN L. CALVO; ERNESTO P. DANIELI; HORACIO M. PASTAWSKI

Buenos Aires

Workshop; At the Frontiers of Condensed Matter III; 2006

CNEA - Centro Atomico Constituyentes

Time reversal of quantum dynamics can be achieved by changing the sign of the Hamiltonian, as in the Loschmidt Echo experiments in NMR. However, this global procedure, dubbed a "hasty Loschmidt daemon", has an efficiency which is limited by chaos and disorder. In contrast, for classical sound waves, the Time Reversal Mirror (TRM) has proved being very robust precisely for those cases. This procedure, called "stubborn Loschmidt daemon", consists of a persistent injection of wave function amplitude at the periphery of the region we want to control and would work in a quantum system. However, the theory behind this stability is not yet developed. As a first step, we introduce a simple model for onedimensional sound propagation where dissipation and inhomogeneity are achieved by coupling an impurity oscillator to a chain of oscillators. Perfect time reversal requires a procedure, the Perfect Inverse Filter (PIF), where the signals detected at the control points are processed to account for memory effects. In order to ensure numerical stability in the solution of the many-body dynamics, we develop a procedure based on the Trotter-Suzuki algorithm used for quantum dynamics. We show that PIF procedure corrects the imperfections of the TRM that manifest when the initial state is built up from an inhomogeneous spectrum. This leads to substantial qualitative and quantitative improvements of the reversal quality when this system is used as an "acoustic bazooka".