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We study the potential of the Quantum Chromodynamics axion in hot and/or dense quark matter, within a Nambu-Jona-Lasinio-like model that includes the coupling of the axion to quarks. Differently from previous studies, we implement local electrical neutrality and $\beta-$equilibrium, which are relevant for the description of the quark matter in the core of compact stellar objects. Firstly we compute the effects of the chiral crossover on the axion mass and self-coupling. We find that the low energy properties of axion are very sensitive to the phase transition of Quantum Chromodynamics, in particular, when the bulk quark matter is close to criticality. Then, for the first time in the literature we compute the axion potential at finite quark chemical potential and study the axion domain walls in bulk quark matter. We find that the energy barrier between two adjacent vacuum states decrease in the chirally restored phase: this results in a lower surface tension of the walls. Finally, we comment on the possibility of production of walls in dense quark matter., Comment: 10 pages, 7 figures

Dispersion forces (van der Waals force and Casimir force) originating from quantum fluctuations are crucial in the cohesion of microscale and nanoscale particles. In reality, these particles have a variety of irregular shapes that differ considerably from any idealized geometry. Previous experiments have demonstrated that dispersion forces strongly depend on the geometry. Because of the nonadditivity of these forces, commonly used numerical additive methods, such as the Hamaker and Derjaguin approximations, are not suitable for calculations with complex geometries. Moreover, experimental studies are difficult to identify the contributions of the dispersion force from the many forces that constitute the cohesion. Therefore, no general law about the influence of particle geometry on dispersion forces has been established. Thus, in this paper, the fluctuating surface current (FSC) technique, an exact scattering theory-based nonadditive algorithm, was used to study this influence. To characterize complex geometries, a data-adaptive spatial filtering method was introduced to perform scale decomposition, and descriptors at three observation levels (global, local, and surface) were used. Based on the advanced geometric analyses and accurate numerical calculations, the influence of multiscale surface fluctuations on dispersion forces was determined. Furthermore, a convenient formula for predicting the dispersion forces between particles with complex shapes from the exact Lifshitz solution was established via multistage corrections., Comment: 32 pages, 10 figures