Characterization of the stretched-exponential trap-time distributions in one-dimensional coupled map lattices

Short-time Loschmidt gap in dynamical systems with critical chaos

We study the Loschmidt echo F(t) for a class of dynamical systems showing critical chaos. Using a kicked rotor with singular potential as a prototype model, we found that the classical echo shows a gap (initial drop) 1-F_{g} , where F_{g} scales as F_{g}(alpha,,eta)=f_{cl}(chi_{cl} identical witheta;{3-alpha}/) ; alpha is the order of singularity of the potential, eta is the spread of the initial phase-space density, and is the perturbation strength. Instead, the quantum echo gap is insensitive to alpha , described by a scaling law F_{g}=f_{q}(chi_{q}=eta;{2}/) which can be captured by a random matrix theory modeling of critical systems. We trace this quantum-classical discrepancy to strong diffraction effects that dominate the dynamics.

Quantum reversibility: is there an echo?

We study the possibility to undo the quantum mechanical evolution in a time reversal experiment. The naive expectation, as reflected in the common terminology ("Loschmidt echo"), is that maximum compensation results if the reversed dynamics extends to the same time as the forward evolution. We challenge this belief and demonstrate that the time t(r) for maximum return probability is in general shorter. We find that t(r) depends on lambda=epsilon(evol)/epsilon(prep), being the ratio of the error in setting the parameters (fields) for the time-reversed evolution to the perturbation which is involved in the preparation process. Our results should be observable in spin-echo experiments where the dynamical irreversibility of quantum phases is measured.

Relationship between dynamical heterogeneities and stretched exponential relaxation

We identify dynamical heterogeneities as an essential prerequisite for stretched exponential relaxation in dynamically frustrated systems. This heterogeneity takes the form of ordered domains of finite but diverging lifetime for particles in atomic or molecular systems, or spin states in magnetic materials. At the onset of the dynamical heterogeneity, the distribution of time intervals spent in such domains or traps becomes stretched exponential at long times. We rigorously show that once this is the case the autocorrelation function of the renewal process formed by these time intervals is also a stretched exponential at long times.