In this work we analyse the growth of the cumulative number of confirmed infected cases by the COVID-19 until March 27 th , 2020, from countries of Asia, Europe, North and South America. Our results show (i) that power-law growth is observed for all countries; (ii) by using the distance correlation, that the power-law curves between countries are statistically highly correlated, suggesting the universality of such curves around the World; and (iii) that soft quarantine strategies are inefficient to flatten the growth curves. Furthermore, we present a model and strategies which allow the government to reach the flattening of the power-law curves. We found that, besides the social distance of individuals, of well known relevance, the strategy of identifying and isolating infected individuals in a large daily rate, can help to flatten the power-laws. These are essentially the strategies used in the Republic of Korea. The high correlation between the power-law curves of different countries strongly indicate that the government containment measures can be applied with success around the whole World. These measures must be scathing and applied as soon as possible.

This work analyzes the parameter space of a discrete ratchet model and gives direct connections between chaotic domains and a family of isoperiodic stable structures with the ratchet current. The isoperiodic structures, where larger currents are usually observed inside, appear along preferred direction in the parameter space giving a guide to follow the current. Currents in parameter space provide a direct measure of the momentum asymmetry of the multistable and chaotic attractors times the size of the corresponding basin of attraction. Transport structures are shown to exist in the parameter space of the Langevin equation with an external oscillating force.

We investigate a particle in a ratchet potential (the system) coupled to an harmonic bath of N=1-500 degrees of freedom (the discrete bath). The dynamics of the energy exchange between the system and the discrete bath is studied in the transition regime from low to high values of N . First manifestation of dissipation (energy lost by the system) appears for the bath composed of 10 less, similar N less, similar 20 oscillators, as expected. For low values of N , beside small dissipation effects, the system experiences the bath-induced particle transfer between different potential wells from the ratchet. We show that this effect decreases the mobility of particles along the ratchet. The hopping probability along the ratchet and the energy decay rates for the system are shown to obey the power law for late times, a behavior typical of discrete baths which for low and intermediate values of N always induce a non-Markovian process. The exponential decay is recovered for high bath frequencies distribution and for high values of N , where the Markovian limit is expected. Moreover, by including the external oscillating field with intensity F , we show that current reversal occurs in two situations: By increasing N and by switching from low to high frequencies distribution of the bath. The mobility of particles is shown to have a maximum at F=0.1 , which is N independent (for higher values of N ).

Generalized quantum discord (D q ), Einstein-Podolsky-Rosen steering (S), entanglement (E), and Bell nonlocality (N), are logically distinct quantifiers of quantum correlations. All these measures capture nonclassical aspects of quantum states and play some role as resources in quantum information processing. In this work, we look for the hierarchy satisfied by these quantum correlation witnesses for a class of two-qubit states. We show that N ⊲ S ⊲ E ⊲ D q , meaning that nonlocality implies steering, which in turn implies entanglement, which then implies q-discord. For the quantum states under concern, we show that the invariance of this hierarchy under noisy quantum channels directly implies a death chronology. Additionally, we have found that sudden death of all quantum resources except discord is absent only for a subset of states of measure zero. At last, we provide an illustration of another consequence of the aforementioned hierarchy, namely, the existence of a sudden birth chronology under non-Markovian channels.

Stable periodic structures containing optimal ratchet transport, recently found in the parameter space dissipation versus ratchet parameter by [A. Celestino et al. Phys. Rev. Lett. 106, 234101 (2011)], are shown to be resistant to reasonable temperatures, reinforcing the expectation that they are essential to explain the optimal ratchet transport in nature. Critical temperatures for their destruction, valid from the overdamping to close to the conservative limits, are obtained numerically and shown to be connected to the current efficiency, given here analytically. A region where thermal activation of the rachet current takes place is also found, and its underlying mechanism is unveiled. Results are demonstrated for a discrete ratchet model and generalized to the Langevin equation with an additional external oscillating force.