Coupled quantum kicked rotors: a study about dynamical localization, slow heating and thermalization

Periodically driven systems are nowadays a very powerful tool for the study of condensed quantum matter: indeed, they allow the observation of phenomena in huge contrast with the expected behavior of their classical counterparts. An outstanding example is dynamical localization: this phenomenon consists in the prevention of heating despite an external periodic perturbation. It has been defined for the first time in a single particle model, the kicked rotor. This chaotic system undergoes an unbounded heating in time in its classical limit; on the opposite, in the quantum regime, the kinetic energy grows until a saturation value is reached and the system stops heating. In my thesis I consider a chain of coupled quantum kicked rotors in order to investigate the fate of dynamical localization in presence of interactions. I remarkably show that a dynamically localized phase persists in the quantum system also in presence of interactions. This is an unexpected behavior since periodically driven, interacting, non-integrable quantum systems heat up to an infinite temperature state. Moreover, I find a genuine quantum dynamics also in the delocalized phase: the heating is not diffusive, as it happens in the classical system, but it follows a sub-diffusive power law. A focus on the properties of the Floquet eigenstates and operators matrix properties gives interesting hints, still under investigation, for a possible justification of the above mentioned slow heating

Real-time-dynamics quantum simulation of (1+1)-dimensional lattice QED with Rydberg atoms

We show how to implement a Rydberg-atom quantum simulator to study the nonequilibrium dynamics of an Abelian (1+1)-dimensional lattice gauge theory. The implementation locally codifies the degrees of freedom of a Z3 gauge field, once the matter field is integrated out by means of the Gauss local symmetries. The quantum simulator scheme is based on currently available technology and thus is scalable to considerable lattice sizes. It allows, within experimentally reachable regimes, us to explore different string dynamics and to infer information about the Schwinger U(1) model

Entanglement generation in (1+1)D(1+1)D QED scattering processes

We study real-time meson-meson scattering processes in $(1+1)$-dimensional QED by means of Tensor Networks. We prepare initial meson wave packets with given momentum and position introducing an approximation based on the free fermions model. Then, we compute the dynamics of two initially separated colliding mesons, observing a rich phenomenology as the interaction strength and the initial states are varied in the weak and intermediate coupling regimes. Finally, we consider elastic collisions and measure some scattering amplitudes as well as the entanglement generated by the process. Remarkably, we identify two different regimes for the asymptotic entanglement between the outgoing mesons: it is perturbatively small below a threshold coupling, past which its growth as a function of the coupling abruptly accelerates.Comment: 21 pages, 15 figure

Discrete Abelian Gauge Theories for Quantum Simulations of QED

We study a lattice gauge theory in Wilson's Hamiltonian formalism. In view of the realization of a quantum simulator for QED in one dimension, we introduce an Abelian model with a discrete gauge symmetry $\mathbb{Z}_n$, approximating the $U(1)$ theory for large $n$. We analyze the role of the finiteness of the gauge fields and the properties of physical states, that satisfy a generalized Gauss's law. We finally discuss a possible implementation strategy, that involves an effective dynamics in physical space.Comment: 13 pages, 3 figure

From localization to anomalous diffusion in the dynamics of coupled kicked rotors

We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on an N-coupled kicked rotors model: We find that the interplay of quantumness and interactions dramatically modifies the system dynamics, inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically through a mapping onto an N-dimensional Anderson model. The thermodynamic limit N\u2192 1e, in particular, always shows unbounded energy growth. This dynamical delocalization is genuinely quantum and very different from the classical one: Using a mean-field approximation, we see that the system self-organizes so that the energy per site increases in time as a power law with exponent smaller than 1. This wealth of phenomena is a genuine effect of quantum interference: The classical system for N 652 always behaves ergodically with an energy per site linearly increasing in time. Our results show that quantum mechanics can deeply alter the regularity or ergodicity properties of a many-body-driven system

Homogeneous Floquet time crystal protected by gauge invariance

We show that homogeneous lattice gauge theories can realize nonequilibrium quantum phases with long-range spatiotemporal order protected by gauge invariance instead of disorder. We study a kicked $\mathbb{Z}_2$-Higgs gauge theory and find that it breaks the discrete temporal symmetry by a period doubling. In a limit solvable by Jordan-Wigner analysis we extensively study the time-crystal properties for large systems and further find that the spatiotemporal order is robust under the addition of a solvability-breaking perturbation preserving the $\mathbb{Z}_2$ gauge symmetry. The protecting mechanism for the nonequilibrium order relies on the Hilbert space structure of lattice gauge theories, so that our results can be directly extended to other models with discrete gauge symmetries.Comment: 6 pages and 4 figures + 3 pages and 3 figures of Supplementary Informatio

Machine-Learning Applications for the Retrieval of Forest Biomass from Airborne P-Band SAR Data

This study aimed at evaluating the potential of machine learning (ML) for estimating forest biomass from polarimetric Synthetic Aperture Radar (SAR) data. Retrieval algorithms based on two different machine-learning methods, namely Artificial Neural Networks (ANNs) and Supported Vector Regressions (SVRs), were implemented and validated using the airborne polarimetric SAR data derived from the AfriSAR, BioSAR, and TropiSAR campaigns. These datasets, composed of polarimetric airborne SAR data at P-band and corresponding biomass values from in situ and LiDAR measurements, were made available by the European Space Agency (ESA) in the framework of the Biomass Retrieval Algorithm Inter-Comparison Exercise (BRIX). The sensitivity of the SAR measurements at all polarizations to the target biomass was evaluated on the entire set of data from all the campaigns, and separately on the dataset of each campaign. Based on the results of the sensitivity analysis, the retrieval was attempted by implementing general algorithms, using the entire dataset, and specific algorithms, using data of each campaign. Algorithm inputs are the SAR data and the corresponding local incidence angles, and output is the estimated biomass. To allow the comparison, both ANN and SVR were trained using the same subset of data, composed of 50% of the available dataset, and validated on the remaining part of the dataset. The validation of the algorithms demonstrated that both machine-learning methods were able to estimate the forest biomass with comparable accuracies. In detail, the validation of the general ANN algorithm resulted in a correlation coefficient R = 0.88, RMSE = 60 t/ha, and negligible BIAS, while the specific ANN for data obtained R from 0.78 to 0.94 and RMSE between 15 and 50 t/ha, depending on the dataset. Similarly, the general SVR was able to estimate the target parameter with R = 0.84, RMSE = 69 t/ha, and BIAS negligible, while the specific algorithms obtained 0.22 ≤ R ≤ 0.92 and 19 ≤ RMSE ≤ 70 (t/ha). The study also pointed out that the computational cost is similar for both methods. In this respect, the training is the only time-demanding part, while applying the trained algorithm to the validation set or to any other dataset occurs in near real time. As a final step of the study, the ANN and SVR algorithms were applied to the available SAR images for obtaining biomass maps from the available SAR images