Very recently, LHCb experiment announced the observation of hidden-charm pentaquark states
The Higgs boson decay channel,
The systematics of energy staggering for the magnetic rotational bands with
We investigate the current-current correlation functions or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density. We study the linear response by using the functional path integral approach and introducing the conjugated gauge fields as external sources. The response functions can be obtained by expanding the generational functional in powers of the external sources. We derive the response functions parallel to two well-established approximations for the equilibrium thermodynamics: the mean-field theory and a beyond-mean-field theory taking into account the mesonic contributions. The response functions based on the mean-field theory recover the so-called quasiparticle random phase approximation. We calculate the dynamical structure factors for the density responses in various channels within the random phase approximation. We show that the dynamical structure factors in the baryon axial vector and isospin axial vector channels can be used reveal the quark mass gap and the Mott dissociation of mesons, respectively. Noting that the mesonic contributions are not taken into account in the random phase approximation, we also derive the response functions parallel to the beyond-mean-field theory. We show that the mesonic fluctuations naturally give rise to three kinds of famous diagrammatic contributions: the Aslamazov-Lakin contribution, the Self-Energy or Density-of-State contribution, and the Maki-Thompson contribution. Unlike the equilibrium case, in evaluating the fluctuation contributions, we need to treat carefully the linear terms in the external sources and the induced perturbations. In the chiral symmetry breaking phase, we find an additional chiral order parameter induced contribution, which ensures that the temporal component of the response functions in the static and long-wavelength limit recovers the correct charge susceptibility defined by using the equilibrium thermodynamic quantities. These contributions from the mesonic fluctuations are expected to have significant effects on the transport properties of hot and dense matter around the chiral phase transition or crossover, where the mesonic degrees of freedom are still important.
One of the major open problems in theoretical physics is a consistent quantum gravity theory. Recent developments in thermodynamic phase transitions of black holes and their van der Waals-like behavior may provide an interesting quantum interpretation of classical gravity. Studying different methods of investigating phase transitions can extend our insight into the nature of quantum gravity. In this paper, we present an alternative theoretical approach for finding thermodynamic phase transitions in the extended phase space. Unlike the standard methods based on the usual equation of state involving temperature, our approach uses a new quasi-equation of state, constructed from the slope of temperature versus entropy. This approach addresses some of the shortcomings of the other methods, and provides a simple and powerful way of studying the critical behavior of a thermodynamical system. Among the applications of this approach, we emphasize the analytical demonstration of possible phase transition points, and the identification of the non-physical range of horizon radii for black holes.
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