Thermal properties of zero sound in asymmetric nuclear matter

The zero-sound modes at finite temperature are investigated with the relativistic random phase approximation to signal the uncertainty of the equation of state (EOS) of asymmetric nuclear matter. It is observed that in typically selected stiff and soft relativistic mean-field (RMF) models, zero-sound modes arise at low temperature, whereas increasing the temperature gradually breaks the zero sound in soft models, with a smaller density range compared to stiff models. At high density, the presence or absence of zero sound turns out to be correspondingly the character of the stiff or soft RMF EOS. More strikingly, we find by analyzing the dispersion relation and sound velocity that at finite temperature the zero-sound modes in RMF models with the stiff EOS undergo a thermal bifurcation, resulting in the transform of zero sound into the first sound at some momentum $Q>T$. The thermally bifurcated sound branch in the stiff models and the zero-sound branch in the soft models are both highly sensitive to the slope of the symmetry energy, providing promising signals for the pending high-density symmetry energies. In addition, it is found that there exists a nonlinear dispersion relation for both the stiff and soft models that supports the zero sound in the relatively lower density region.