With the help of the Berry curvature and the first Chern number (C1), we both analytically and numerically investigate and thus simulate artificial magnetic monopoles formed in parameter space of the Hamiltonian of a driven superconducting qubit. The topological structure of a spin-1/2 system (qubit) can be captured by the distribution of Berry curvature, which describes the geometry of eigenstates of the Hamiltonian. Degenerate points in parameter space act as sources (C1 = 1, represented by quantum ground state manifold) or sinks (C1 = −1, represented by quantum excited state manifold) of the magnetic field. We note that the strength of the magnetic field (described by Berry curvature) has an apparent impact on the quantum states during the process of topological transition. It exhibits an unusual property that the transition of the quantum states is asymmetric when the degenerate point passes from outside to inside and again outside the manifold spanned by system parameters. Our results also pave the way to explore intriguing properties of Abelian Wu-Yang monopoles in other spin-1/2 systems.

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It has been suggested that ultrahigh-energy cosmic rays (UHECRs) can be produced by turbulent stochastic acceleration in relativistic jets of gamma-ray bursts (GRBs) on set of early afterglow. We develop a time-dependent model for proton energization by cascading compressible waves in GRB jets considering the concurrent effect of the jet's dynamics and the mutual interactions between turbulent waves and particles. Considering fast magnetosonic wave as the dominant particle scatterer and assuming interstellar medium (ISM) for the circumburst environment, our results suggest that protons can be accelerated up to 10 19 eV during the phase of early afterglow. The spectral slope dN/dE ∝ E 0 , which is consistent with the requirement for the performance of intermediate-mass composition of UHECR as measured by the Pierre Auger Observatory.