# QCD: In some phase diagrams, the axis are temperature and baryon chemical potential - what does it have to do with densities?

In this figure

one axis is the temperature (this one is no problem), the other one is the baryon chemical potential which causes my confusion.
Figure from here: Phase diagram of simplified QCD.
The text I'm referring to (with a similar figure): http://www.fair-center.eu/for-users/experiments/cbm/introduction.html.

Anyway, in a text about phases of QCD, the authors referred to this x-axis as the density and not the baryon chemical potential.
So my questions are:
What is the baryon chemical potential? What does it tell me?
What does it have to do with densities? Is it just a "synonym" for densities?
Also, as far as I understood, the phases aren't like the phases of "normal" matter, e.g. hadronic matter is at 0 K and 300 million tons per cm3 (see the link for the text) in a "liquid" phase. So, what do the phases look like? Why is it "liquid" and not liquid?

If you have taken statistical mechanics, you should be familiar with the concept of chemical potential. If not, the Wikipedia article on chemical potential should be sufficient (let me know if it isn't). Essentially, chemical potential is a measure of how the energy of a system changes as you add another particle to it.

As far as its relation to density, the best answer I could find is for the case of a Fermi gas: http://www.physics.udel.edu/~glyde/PHYS825/Lectures/chapter_8.pdf. Here, it is shown that the Fermi momentum $p_F$ is dependent on density$^{1/3}$. Since the Fermi energy is proportional to $p_F^2$, it is also proportional to density$^{2/3}$. The chemical potential is proportional to the Fermi energy, so it is also proportional to density$^{2/3}$.

Baryons in the nucleus are thought to behave as a Fermi liquid, so, barring some changes in the magnitude of certain interactions, the dependency should still be there. Since baryon chemical potential rises with density, the axis labels are interchangeable without much trouble.

• Hi, thanks for your answer, it definitely helps me to understand a few things. I'm not sure though whether I should mark my question as answered, I mean, you answered the for me most important parts, but I'm still curious about what the phases look like. Dec 20, 2016 at 22:37
• If we knew anything about what they looked like, I would tell you; unfortunately I think the jury's still out on that one. When we produce these states at CERN, they barely last long enough to throw out some particles and jets that we can study. To this day, we have only been able to indirectly measure the properties of QGP. Dec 20, 2016 at 22:40
• Ah, well, hopefully FAIR will be able to shed some light on this matter and many more. Thanks again! Dec 20, 2016 at 22:58