Non-monotonous short-time decay of the Loschmidt echo in quasi-one-dimensional systems
arXiv:1102.1031 · doi:10.1103/PhysRevE.83.056210
Abstract
We study the short-time stability of quantum dynamics in quasi-one-dimensional systems with respect to small localized perturbations of the potential. To this end, we address, analytically and numerically, the decay of the Loschmidt echo (LE) during times short compared to the Ehrenfest time. We find that the LE is generally a non-monotonous function of time and exhibits strongly pronounced minima and maxima at the instants of time when the corresponding classical particle traverses the perturbation region. We also show that, under general conditions, the envelope decay of the LE is well approximated by a Gaussian, and we derive explicit analytical formulas for the corresponding decay time. Finally, we demonstrate that the observed non-monotonicity of the LE decay is only pertinent to one-dimensional (and, more generally, quasi-one-dimensional systems), and that the short-time decay of the LE can be monotonous in higher number of dimensions.
12 pages, 8 figures; added references, corrected typos
References in corpus (10)
- Dynamics of Loschmidt echoes and fidelity decay
- Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
- Dephasing representation of quantum fidelity for general pure and mixed states
- Observation of coherence revival and fidelity saturation in a delta-kicked rotor potential
- Microwave fidelity studies by varying antenna coupling
- Loschmidt Echo and the Local Density of States
- Algebraic fidelity decay for local perturbations
- Loschmidt echo for local perturbations: non-monotonous cross-over from the Fermi-golden-rule to the escape-rate regime
- Probing Localization in Absorbing Systems via Loschmidt Echos
- Fidelity decay for local perturbations: microwave evidence for oscillating decay exponents