We study analytically and numerically the properties of the Jaynes-Cummings model under monochromatic driving. The analytical results allow us to understand the regime of two branches of multiphoton excitation in the case of close resonance between resonator and driven frequencies. The rotating wave approximation allows us to reduce the description of the original driven model to an effective Jaynes-Cummings model with strong coupling between photons and qubit. The analytical results are in good agreement with the numerical ones even if there are certain deviations between the theory and numerics in the close vicinity of the resonance. We argue that the rich properties of the driven Jaynes-Cummings model represent a new area for experimental investigations with superconducting qubits and other systems.

A set of quantum states, dynamically related to the classical periodic orbits of a chaotic map, is used as a basis in which the description of the eigenstates of its quantum version is greatly simplified. This set can be improved with the inclusion of short time propagation along the stable and unstable manifolds of the periodic orbits resulting in a construction similar to the scar functions of Vergini [J. Phys. A 33, 4709 (2000)]. The average participation ratio is used to quantify the quality of the basis.

We present a broad family of quantum baker maps that generalize the proposal of Schack and Caves to any even Hilbert space with arbitrary boundary conditions. We identify a structure, common to all maps consisting of a simple kernel perturbed by diffraction effects. This “essential” baker’s map has a different semiclassical limit and can be diagonalized analytically for Hilbert spaces spanned by qubits. In all cases this kernel provides an accurate approximation to the spectral properties—eigenvalues and eigenfunctions—of all the different quantizations.

We analyze how the COVID-19 pandemic affected the trade of products between countries. With this aim, using the United Nations Comtrade database, we perform a Google matrix analysis of the multiproduct World Trade Network (WTN) for the years 2018–2020, comprising the emergence of the COVID-19 as a global pandemic. The applied algorithms—PageRank, CheiRank and the reduced Google matrix—take into account the multiplicity of the WTN links, providing new insights into international trade compared to the usual import–export analysis. These complex networks analysis algorithms establish new rankings and trade balances of countries and products considering all countries on equal grounds, independent of their wealth, and every product on the basis of its relative exchanged volumes. In comparison with the pre-COVID-19 period, significant changes in these metrics occurred for the year 2020, highlighting a major rewiring of the international trade flows induced by the COVID-19 pandemic crisis. We define a new PageRank–CheiRank product trade balance, either export or import-oriented, which is significantly perturbed by the pandemic.

Quantum manifestations of isoperiodic stable structures (QISSs) have a crucial role in the current behavior of quantum dissipative ratchets. In this context, the simple shape of the ISSs has been conjectured to be an almost exclusive feature of the classical system. This has drastic consequences for many properties of the directed currents, the most important one being that it imposes a significant reduction in their maximum values, thus affecting the attainable efficiency at the quantum level. In this work we prove this conjecture by means of comprehensive numerical explorations and statistical analysis of the quantum states. We are able to describe the quantum parameter space of a paradigmatic system for different values of ${$\hbar${}}_{\mathrm{eff}}$ in great detail. Moreover, thanks to this we provide evidence on a mechanism that we call parametric tunneling by which the sharp classical borders of the regions in parameter space become blurred in the quantum counterpart. We expect this to be a common property of generic dissipative quantum systems.