Hydrodynamics of Nuclear Matter

Hydrodynamics of Nuclear Matter

D.T. Son

Hydrodynamics is the theory describing the low-frequency, long-wavelength dynamics of liquids (or, in an extended sense, of any system). In this regime most degrees of freedom become irrelevant since they relax during the time characteristic of particle collisions; the only ones that survive are either those related to the conservation laws or the phases the orders parameters of broken continuous symmetries. The simplest example is normal fluids, where hydrodynamic variables are related to the conservation of energy, momentum, and particle number. In superfluid He-4 and He-3 additional hydrodynamic variables emerge due to the symmetry breaking by the condensate. Although in all of these systems the physics is quite complicated at the molecular level, at large scales the hydrodynamic equations have simple forms dictated by the symmetries, the pattern of symmetry breaking, and the conservation laws. Such equations typically involves unknown coefficients, which can be computed from the microscopic theory or measured in experiments.

A similar philosophy is shared by the chiral perturbation theory, which describes the lightest degrees of freedom of QCD with light quarks. At low energies, QCD is a strongly coupled theory where not much can be computed, at least at this moment, in a reliable fashion. However, well below the chiral scale (about 1 GeV), the dynamics is determined by the chiral Lagrangian, which can be written down knowing only the chiral symmetry and the pattern of chiral symmetry breaking of QCD. To the lowest order, pions are governed by the nonlinear sigma model, the only free parameter of which is the pion coupling constant, which can be determined by matching the predictions of theory with experiment.

In nuclear matter in the chiral limit, the low-energy degrees of freedom include both the fluid-dynamical variables (the energy-momentum tensor), and the chiral ones that describe the massless Goldstone modes arising from the breaking of chiral symmetry. All these degrees of freedom are coupled to each other; therefore, a full hydrodynamic treatment must include all these modes. In this respect, the hydrodynamics of nuclear matter is more similar to that of superfluids rather than of normal fluids. Treatments so far have largely dealt with the fluid dynamical and chiral variables separately, ignoring the interplay between the two.

The purpose of my work is to construct the hydrodynamic theory of nuclear matter in the chiral limit, capable of describing all low-energy degrees of freedom of the latter. The primary place where such a theory can be applied is in the theory of heavy-ion collisions.

Details will be given in my upcoming article.