RESUMO
A local excitation in a quantum many-spin system evolves deterministically. A time-reversal procedure, involving the inversion of the signs of every energy and interaction, should produce the excitation revival. This idea, experimentally coined in nuclear magnetic resonance, embodies the concept of the Loschmidt echo (LE). While such an implementation involves a single spin autocorrelation M(1,1), i.e. a local LE, theoretical efforts have focused on the study of the recovery probability of a complete many-body state, referred to here as global or many-body LE MMB Here, we analyse the relation between these magnitudes, with regard to their characteristic time scales and their dependence on the number of spins N We show that the global LE can be understood, to some extent, as the simultaneous occurrence of N independent local LEs, i.e. MMBâ¼(M(1,1))(N/4) This extensive hypothesis is exact for very short times and confirmed numerically beyond such a regime. Furthermore, we discuss a general picture of the decay of M1,1 as a consequence of the interplay between the time scale that characterizes the reversible interactions (T(2)) and that of the perturbation (τ(Σ)). Our analysis suggests that the short-time decay, characterized by the time scale τ(Σ), is greatly enhanced by the complex processes that occur beyond T(2) This would ultimately lead to the experimentally observed T(3), which was found to be roughly independent of τ(Σ) but closely tied to T(2).
RESUMO
Numerically, we study the time fluctuations of few-body observables after relaxation in isolated dynamical quantum systems of interacting particles. Our results suggest that they decay exponentially with system size in both regimes, integrable and chaotic. The integrable systems considered are solvable with the Bethe ansatz and have a highly nondegenerate spectrum. This is in contrast with integrable Hamiltonians mappable to noninteracting ones. We show that the coefficient of the exponential decay depends on the level of delocalization of the initial state with respect to the energy shell.