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According to perturbation theory predictions, QCD matter in the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential is expected to be in a superfluid Bardeen-Cooper-Schrieffer (BCS) phase of u and d¯ Cooper pairs. It is also expected, on symmetry grounds, that such phase connects via an analytical crossover to the phase with Bose-Einstein condensation (BEC) of charged pions at μI≥mπ/2. With lattice results, showing some indications that the deconfinement crossover also smoothly penetrates the BEC phase, the conjecture was made that the former connects continuously to the BEC-BCS crossover. We compute the spectrum of the Dirac operator, and use generalized Banks-Casher relations, to test this conjecture and identify signatures of the superfluid BCS phase.
The magnetic fields generated in non-central heavy-ion collisions are among the strongest fields produced in the Universe, reaching magnitudes comparable to the scale of the strong interactions. Backed by model simulations, the resulting field is expected to be spatially modulated, deviating significantly from the commonly considered uniform profile. To improve our understanding of the physics of quarks and gluons under such extreme conditions, we use lattice QCD simulations with 2+1 staggered fermion flavors with physical quark masses and an inhomogeneous magnetic background for a range of temperatures covering the QCD phase transition. We assume a 1/cosh2 function to model the field profile and vary its strength to analyze the impact on the computed observables and on the transition. We calculate local chiral condensates, local Polyakov loops and estimate the size of lattice artifacts. We find that both observables show non-trivial spatial features due to the interplay between the sea and the valence effects.