In this paper, we calibrate the Amati relation (the E p–E iso correlation) of gamma-ray bursts (GRBs) in a cosmology-independent way. By using a Gaussian process to reconstruct the smoothed luminosity distance from the Pantheon type Ia supernovae sample, we utilize the reconstructed results to calibrate the E p–E iso correlation with the Markov Chain Monte Carlo method and construct a Hubble diagram with the A220 GRB data, in which there are A118 GRB data with the higher qualities appropriate for cosmological purposes. With 98 GRBs at 1.4 < z ≤ 8.2 in the A118 sample and the observed Hubble data, we obtain Ωm = 0.346 − 0.069 + 0.048 , h = 0.677 − 0.029 + 0.029 for the flat ΛCDM model, and Ωm = 0.314 − 0.055 + 0.072 , h = 0.705 − 0.069 + 0.055 , w = − 1.23 − 0.64 + 0.33 for the flat wCDM model, which are consistent with those from fitting the coefficients of the Amati relation and the cosmological parameters simultaneously.

An improved Amati correlation was constructed in ApJ 931 (2022) 50 by us recently. In this paper, we further study constraints on the ΛCDM and wCDM models from the gamma-ray bursts (GRBs) standardized with the standard and improved Amati correlations, respectively. By using the Pantheon Type Ia supernova sample to calibrate the latest A220 GRB data set, the GRB Hubble diagram is obtained model-independently. We find that at the high-redshift region (z > 1.4) the GRB distance modulus from the improved Amati correlation is larger apparently than that from the standard Amati one. The GRB data from the standard Amati correlation only give a lower bound limit on the present matter density parameter Ωm0, while the GRBs from the improved Amati correlation constrain the Ωm0 with the 68% confidence level to be 0.308 − 0.230 + 0.066 and 0.307 − 0.290 + 0.057 in the ΛCDM and wCDM models, respectively, which are very consistent with those given by other current popular observational data including baryon acoustic oscillation, cosmic microwave background (CMB) radiation, and so on. Once the H(z) data are added in our analysis, the constraint on the Hubble constant H 0 can be achieved. We find that two different correlations provide slightly different H 0 results but the marginalized mean values seem to be close to that from the Planck 2018 CMB radiation observations.

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Entanglement dynamics of a two-qutrit Heisenberg spin chain with the external magnetic fields and DM interaction under the intrinsic decoherence is investigated. Depending on whether there is inhomogeneous magnetic field, the entanglement amplification, i.e. the phenomenon that the finally stable entanglement is bigger than that of the initial one, is found for one kind of initial states. The reasons for the controllable entanglement amplification are discussed.

Taking into account the intrinsic decoherence effect, we study the tripartite nonlocality of a three-qubit Heisenberg spin system with three-body interaction by the generalized Bell inequality. We have found that there is Bell-nonlocality sudden birth, and the three-body interaction is vital to achieving it.