What the strong interactions, temperature, and density have to do with each other

After the preparation with the last entry, I can now move forward to my next research topic.

Let me just collect what we had so far about the strong interactions, QCD. QCD is the theory that describes the interaction between quarks and gluons. It tells you how these make up the hadrons, like the proton and the neutron. It also describes how these combine to the atomic nuclei. The quarks and gluons cannot be seen alone: The strong force confines them. At the same time, the strong force makes the quarks condense, and thereby creates the illusion of mass. Well, this is what one can call a complicated theory.

Now imagine for a while what happens, if you heat up matter. Really make it hot, much hotter than in the interior of stars. Heat is something like energy. You can imagine that the hotter something is, the faster the movement of particles. The faster they go, he hotter they are. But the higher the energy, the smaller the things are which get involved. Hence, if things get very hot, the quarks and gluons are the one to really feel it.

When this happens, two things occur. One is that the condensate of quarks melts. As a consequence, the quarks can move much more freely. The other is that you can convert some of the energy from the heat to particles. I will come back to the mechanism behind this later. For now, it is enough that this is possible. It is nothing special to the heat case. Anyway, you can convert a small fraction of the heat to particles. If things get hot enough, a small fraction is actually quite a large number. And if things are really hot, you have created so many particles that they do not fit anymore in the space you have available. Then they start to overlap. At that point, even if you have confinement, you can no longer tell the hadrons apart. The things just overlap and you can start to swap quarks and gluons from one to another. You see, when you put enough heat into matter, things start to look very different.

Why is this interesting? I said it must be much hotter than in a star, and actually much hotter even than in a supernova. It does not appear that there is anything in nature being so hot. However, we can create tiny amounts of matter in experiments which is so hot. And also, very far in the past, such super-hot matter existed. Right after the big bang, the whole universe was very densely packed, and the temperature was so high. This was only a fraction of a second after the big bang. So, is this relevant? Well, yes. If we want to look back even further, we have to understand what happened in the transition of the strong force at that time. Since we cannot create universes to study it, we need to extrapolate back in time. And for this, we need to understand each step of going back in time. And hence, we need to understand how QCD works at very high temperatures.

This is not the only case where we need to understand QCD in extreme conditions. The other case is the interior of neutron stars. In these stars, matter is packed incredibly densely. It is very cold there, at least when comparing to the early universe. But it is so dense that hadrons again begin to overlap. Thus, you would expect that you can again exchange quarks and gluons freely between hadrons. But because it is cold, you will keep your quark condensate. In fact, there are quite a lot of speculation, whether you can create also condensates of quarks with different properties than the one usually known. To really understand how neutron stars work, and eventually also how black holes form, we have to understand how QCD works when things become dense.

When you take both cases together, and permit for good measure to also include all possible combinations of dense and hot, you end up with the QCD phase diagram. This phase diagram answers the question: When I have this temperature and that density, how does QCD behave? Determining this phase diagram has been a topic of research ever since these questions were first posed in the 1970s. Very important for this task have been numerical simulations of matter at high temperatures. With them, we have become confident that we start to understand what happens at very small densities and rather high temperature. We understood from this that the universe has undergone a non-violent transition when QCD changed. We can therefore now extrapolate further back in the history of the universe. But we are not yet finished for this case. Right now, we leaned what happens when we are at fixed temperature and density. But these two quantities changed, and we have not yet fully understood how this proceeds.

Things are a lot worse when we turn to the neutron stars. We have not been able to develop efficient programs to simulate the interior of a neutron star. We even suspect that it is not possible at all, for rather fundamental reasons concerning conventional computers. Progress has therefore been mainly made in two ways. One was to rely heavily on (very) simplified models, and more recently using functional methods. Another one was to study artificial theories, which are similar to QCD, but for which efficient programs can be written. From the experience with them we try to indirectly infer what happens really in QCD.

I am involved in the determination of this QCD phase diagram with two angles. One is to develop the functional methods further, such that they become a powerful tool to address these questions. Another one is to learn something from the stand-in theories. Especially in the latter case we just made a breakthrough, on which I will comment in a later entry.