Theory and simulation of classical and quantum echoes

Echo phenomena occurring in various physical systems are investigated, and analytical results are checked against computer experiments. It is found that Coulomb self-consistent interactions reduce the amplitude of the echo. Proof is given of the possibility of refocusing an initially localized packet by periodically kicking the particles, and the relation between this behavior and chaotic diffusion is discussed. Quantum echoes are investigated via simulations of the Wigner equation in the case of an anharmonic oscillator. It is shown that quantum effects allow for the appearance of linear echoes. The reversibility properties of classical and quantum many-particle systems are discussed. © 1996 The American Physical Society.