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Numerical Determination of the Phase Diagram of Nuclear Matter

Principal Investigator: Owe Philipsen, Universität Frankfurt, ITP (Germany)
HPC Platform: JUQUEEN of JSC
Date Published: February 2015
JSC Project ID: hkf8

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, Fig. 1.

Numerical Determination of the Phase Diagram of Nuclear MatterFig. 1: The QCD phase diagram, with a hadron phase of ordinary nuclear matter and a quark gluon plasma phase. [At zero matter (baryon) density the phase transition is established to be a smooth crossover, current research searches for a first order transition and a critical point at finite density.]
Copyright: GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt/Germany

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.

Numerical Determination of the Phase Diagram of Nuclear MatterFig. 2: The order of the QCD phase transition at zero density as a function of the quark masses. [For very heavy and very light quarks there is a first order phase transition separated by second order lines from a crossover region, which contains the physical point.]
Copyright: Institut für Theoretische Physik/ITP, Johann Wolfgang Goethe-Universität, Frankfurt

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.

Numerical Determination of the Phase Diagram of Nuclear MatterFig. 3: As Fig. 2, but including chemical potential parametrizing matter density. [The boundary surfaces are mapped out by simulation at imaginary chemical potential and then continued to small real values].
Copyright: Institut für Theoretische Physik/ITP, Johann Wolfgang Goethe-Universität, Frankfurt

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)

February 2015