Numerical Determination of the Phase Diagram of Nuclear Matter

Principal Investigator:
Owe Philipsen

Universität Frankfurt, ITP (Germany)

Local Project ID:

HPC Platform used:

Date published:

The fundamental theory of the strong interactions is Quantum Chromodynamics (QCD). Its elementary constituents are three families of quarks ("up", "down" and "strange") and gluons, which cannot be observed as isolated particles. Under ordinary conditions on earth, a strong attractive force binds them to form protons and neutrons, the building blocks of the atomic nuclei observed in nature. On the other hand, when these particles meet at very high energies, their interaction weakens and no binding happens. Such conditions are realized at either high temperatures in the early universe, shortly after the big bang, or at high matter density, such as in very compact stars. In these cases nuclear matter "melts" into a quark gluon plasma. This state of matter is also created and studied in current and future heavy ion collision experiments at LHC in Geneva (Large Hadron Collider), RHIC in USA (Relativistic Heavy Ion Collider at the Bookhaven National Laboratory) and FAIR in Darmstadt (Facility for Antiproton and Ion Research in Europe GmbH).

Similar to the phase diagram of water, which shows for which combinations of pressure and temperature it is solid, liquid or gaseous, the QCD phase diagram determines the form of nuclear matter depending on temperature and matter density, Figure 1.

An important question is whether there are first order phase transitions via bubble nucleation (as in boiling water) or the matter forms are smoothly connected. Unfortunately, QCD cannot be solved by analytic methods. However, a version reformulated on a discrete space time grid called "Lattice QCD" is amenable to numerical simulations.

In order to be realistic, the simulated system has to be large enough to avoid boundary effects, and the grid has to be fine enough to approximate the original continuum theory. This can only be achieved with High Performance Computing resources, such as provided by HPC system JUQUEEN of Jülich Supercomputing Centre. Simulation time grows significantly when quark masses are small as the "up" and "down" quark in nature, so that simulations run at larger masses to be extrapolated, while the "strange" quark mass is feasible. Also for theoretical reasons masses are varied. For zero and infinite quark masses, QCD exhibits symmetries whose breaking as a function of temperature T causes the first order phase transitions in the lower left and upper right corner of Fig. 2. The boundary lines represent phase transitions of second order. For quark masses in between, in particular their physical values, there is just a smooth crossover from nuclear matter to plasma.

A particular challenge is the description of finite matter density, which is parametrized by chemical potential µ, adding an additional axis to the diagram. Real chemical potential cannot be simulated directly, so the scientists work at imaginary values and extrapolate to real values.

The boundary lines from Fig. 2 then turn into the surfaces in Fig. 3. The result is that with small but increasing matter density the transition from nuclear to plasma matter is completely smooth, without bubble nucleation. This prediction is being tested in heavy ion experiments.

Scientific Contact:

Prof. Dr. Owe Philipsen
Institut für Theoretische Physik / ITP
Johann Wolfgang Goethe-Universität
Max-von-Laue-Straße 1
Campus Riedberg
60438 Frankfurt am Main (Germany)
e-mail: philipsen@th.physik.uni-frankfurt.de

Tags: Goethe Universität Frankfurt EPP