We analytically study a system of spinless fermions driven at the boundary with an oscillating chemical potential. Various transport regimes can be observed: At zero driving frequency the particle current through the system is independent of the system's length; at the phase-transition frequency, being equal to the bandwidth, the current decays as $\sim${}n$-${}$\alpha${} with the chain length n, $\alpha${} being either 2 or 3; below the transition the scaling of the current is $\sim${}n$-${}1/2, indicating anomalous transport, while it is exponentially small $\sim${}exp($-${}n2$\xi${}) above the transition. Therefore, by a simple change of frequency of the a.c. driving of the system one can vary transport from ballistic, anomalous to insulating.

Background: Cardiovascular disorders in general are responsible for 30% of deaths worldwide. Among them, hypertrophic cardiomyopathy (HCM) is a genetic cardiac disease that is present in about 1 of 500 young adults and can cause sudden cardiac death (SCD). Objective: Although the current state-of-the-art methods model the risk of SCD for patients, to the best of our knowledge, no methods are available for modeling the patient's clinical status up to 10 years ahead. In this paper, we propose a novel machine learning (ML)-based tool for predicting disease progression for patients diagnosed with HCM in terms of adverse remodeling of the heart during a 10-year period. Methods: The method consisted of 6 predictive regression models that independently predict future values of 6 clinical characteristics: left atrial size, left atrial volume, left ventricular ejection fraction, New York Heart Association functional classification, left ventricular internal diastolic diameter, and left ventricular internal systolic diameter. We supplemented each prediction with the explanation that is generated using the Shapley additive explanation method. Results: The final experiments showed that predictive error is lower on 5 of the 6 constructed models in comparison to experts (on average, by 0.34) or a consortium of experts (on average, by 0.22). The experiments revealed that semisupervised learning and the artificial data from virtual patients help improve predictive accuracies. The best-performing random forest model improved R2 from 0.3 to 0.6. Conclusions: By engaging medical experts to provide interpretation and validation of the results, we determined the models' favorable performance compared to the performance of experts for 5 of 6 targets.

We present a variational quantum adiabatic theorem, which states that, under certain assumptions, the adiabatic dynamics projected onto a variational manifold follow the instantaneous variational ground state. We focus on low-entanglement variational manifolds and target Hamiltonians with classical ground states. Despite highly entangled intermediate states along the exact adiabatic path, the variational evolution converges to the target ground state. We demonstrate this approach with several examples that align with our theoretical analysis.

We investigate the dynamical properties of the XY spin-1/2 chain with infinite-range transverse interactions and find a dynamical phase transition with a chaotic dynamical phase. In the latter, we find nonvanishing finite-time Lyapunov exponents and intermittent behavior signaled by fast and slow entropy growth periods. Further, we study the XY chain with a local self-consistent transverse field and observe a localization phase transition. We show that localization stabilizes the chaotic dynamical phase.

We study the equilibrium properties of the spin-$1/2$ XY chain with an infinite-range transverse interaction. At zero temperature, competition between the XY- and the $z$-ordered phases induced by the infinite-range interactions gives rise to a first-order transition upon increasing the transverse coupling. We show that the two gapless points of the XY model behave in fundamentally different ways: isotropic spin chains experience a first-order transition at finite coupling; maximal anisotropic chains overcome a non-algebraic phase transition at zero coupling strength. The phase diagram depicts a first-order reentrant transition that turns second-order along a tricritical line separating a paramagnetic phase from an ordered one at finite temperature. The mean-field approach captures the local properties of the eigenstates and reveals the appearance of a magnetization gap in the spectrum. Global properties, e.g., entanglement entropy, are well approximated only at spectral boundaries. The mean entanglement entropy and the level-spacing ratio deviate from the Gaussian results, revealing the interacting nature of the problem.