We study the decoherence of a one-particle system, whose classical correspondent is chaotic, when it evolves coupled to a weak quenched environment. This is done by analytical evaluation of the Loschmidt echo (i.e., the revival of a localized density excitation upon reversal of its time evolution), in the presence of the perturbation. We predict an exponential decay for the Loschmidt echo with a (decoherence) rate which is asymptotically given by the mean Lyapunov exponent of the classical system, and therefore independent of the perturbation strength, within a given range of strengths. Our results are consistent with recent experiments of polarization echoes in nuclear magnetic resonance and numerical simulations.
Physical Review Letters
- Pub Date:
- March 2001
- Condensed Matter - Disordered Systems and Neural Networks;
- Nonlinear Sciences - Chaotic Dynamics;
- Quantum Physics
- No figures. Typos corrected and minor modifications to the text and references. Published version