The QCD phase diagram at zero chemical potential and finite temperature subject to an external magnetic field is studied within the three-flavor Nambu\char21{}Jona-Lasinio (NJL) model and the NJL model with the Polyakov loop. A scalar coupling parameter dependent on the magnetic field intensity is considered. The scalar coupling has been fitted so that the lattice QCD pseudocritical chiral transition temperatures are reproduced and in the limit of large magnetic field decreases with the inverse of the magnetic field intensity. This dependence of the coupling allows us to reproduce the lattice QCD results with respect to the quark condensates and Polyakov loop: due to the magnetic field the quark condensates are enhanced at low and high temperatures and suppressed for temperatures close to the transition temperatures and the Polyakov loop increases with the magnetic field.

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.

The questions of how the bulk of the Universe’s visible mass emerges and how it is manifest in the existence and properties of hadrons are profound, and probe the heart of strongly interacting matter. Paradoxically, the lightest pseudoscalar mesons appear to be key to a further understanding of the emergent mass and structure mechanisms. These mesons, namely, the pion and kaon, are the Nambu–Goldstone boson modes of quantum chromodynamics (QCD). Unravelling their partonic structure and the interplay between emergent and Higgs-boson mass mechanisms is a common goal of three interdependent approaches—continuum QCD phenomenology, lattice-regularised QCD, and the global analysis of parton distributions—linked to experimental measurements of hadron structure. Experimentally, the anticipated electron–ion collider will enable a revolution in our ability to study pion and kaon structures, accessed by scattering from the ‘meson cloud’ of the proton through the Sullivan process. With the goal of enabling a suite of measurements that can address these questions, we examine key reactions that identify the critical detector-system requirements needed to map tagged pion and kaon cross-sections over a wide range of kinematics. The excellent prospects for extracting pion structural, functional, and form-factor data are outlined, and similar prospects for kaon structures are discussed in the context of a worldwide programme. The successful completion of the programme outlined herein will deliver deep, far-reaching insights into the emergence of pions and kaons, their properties, and their role as QCD’s Goldstone boson modes.