Ignacio García-Mata

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We study numerically the effects of nonlinearity on the Anderson localization in lattices with disorder in one and two dimensions. The obtained results show that at moderate strength of nonlinearity a spreading over the lattice in time takes place with an algebraic growth of number of populated sites Deltan proportional to tnu. This spreading continues up(More)
The linear entropy and the Loschmidt echo have proved to be of interest recently in the context of quantum information and of the quantum to classical transitions. We study the asymptotic long-time behavior of these quantities for open quantum maps and relate the decays to the eigenvalues of a coarse-grained superoperator. In specific ranges of coarse(More)
The Loschmidt echo--also known as fidelity--is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have been identified. For chaotic systems, there is a range of perturbation strengths where the decay of the Loschmidt echo is(More)
We study the relationship between the spectral properties of diffusive open quantum maps and the classical spectrum of Ruelle-Pollicott resonances. The leading resonances determine the asymptotic time regime for several quantities of interest--the linear entropy, the Loschmidt echo, and the correlations of the initial state. A numerical method that allows(More)
The channel induced by a complex system interacting strongly with a qubit is calculated exactly under the assumption of randomness of its eigenvectors. The resulting channel is represented as an isotropic time-dependent oscillation of the Bloch ball, leading to non-Markovian behavior, even in the limit of infinite environments. Two contributions are(More)
We show that nonlinear resonances in a classically mixed phase space allow us to define generic, strongly entangled multipartite quantum states. The robustness of their multipartite entanglement increases with the particle number, i.e., in the semiclassical limit, for those classes of diffusive noise which assist the quantum-classical transition.
We study a version of the mathematical Ruijsenaars-Schneider model and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter. We compare different methods to measure the multifractality of wave packets and identify the best one. We find the(More)
In classical statistical mechanics there is a clear correlation between relaxation to equilibrium and chaos. In contrast, for isolated quantum systems this relation is--to say the least--fuzzy. In this work we try to unveil the intricate relation between the relaxation process and the transition from integrability to chaos. We study the approach to(More)
We study the Anderson transition on a generic model of random graphs with a tunable branching parameter 1<K<2, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a localized phase from an unusual delocalized phase that is ergodic at large scales but strongly nonergodic at smaller scales. In(More)