Phase transition or cross over?

So, since last Friday, finally, I am a happy, new "Dr. phil. nat.". Of course, I am not yet allowed to call myself officially like that - I have to wait until I have in my hands the "Zeugnis". This is only possible in two weeks, after the Promotionsbüro's Easter vacation is over. Everything has to be very orderly in Germany ;-)

In the meantime, I can take a breath, and try to realize what has happened. Getting a PhD is - that is my impression just now - not a sharp phase transition, but a very smooth cross over, starting with the handing in of the written thesis, and ending late after the defense is over.

I was quite a bit nervous before the defense, mainly because I had prepared the final version of my talk only the night before, and thus had not really much time to practice the text I wanted to say. The problem was, I thought that I have 15 to 20 minutes for my presentation, and I knew that it was to long for that period. But then, fortunately, the first thing that Carsten, the head of the examination committee, said was that the procedure begins with a talk of 25 to 30 minutes. I immediately got relaxed.

I think I got through my talk quite successfully in 25 minutes, interrupted by Horst only once or twice, and was ready to face the discussion. The start was a little bumpy: first, there was only colored chalk to write on the blackboard (and remember always to start with the most backward board), and than, I needed a little help to figure out the De Broglie wave length of the particles involved in my code: Roskos open the discussion with the question why the purely classical calculations I am using in my simulations can be justified. Of course, it is easy to write "lambda = hbar/p" on the blackboard, but then, it was not so easy for me any more, at that moment at the blackboard, to expand this fraction by c, use the famous "hbar · c = 197 MeV · fm", and conclude that a nucleus with an energy of 160 GeV (and a corresponding momentum of 160 GeV/c) has a wave length of roughly 1/1000 fm. But with a little help, I reached that conclusion.

It got a bit better when Roskos started asking about Debye screening, a concept he was fond of recognizing from his solid state physics, but then he asked whether I had studied plasma oscillations in my model, which I had to admit I had not, although, of course, I said, this would be an very interesting thing to do, one would expect plasmons to exist in the model, that the search is numerically involved, and that plasma oscillations and plasma instabilities are a hot topic to understand thermalization in the early phase of heavy ion collisions, blah blah. Fortunately, nobody asked about the typical frequencies of plasma oscillations and how to calculate them...

Then, Horst asked me to explain the differences between phase transitions and cross over, and how all this relates to the Kosterlitz-Thouless transition. That later transition was the topic of my diploma thesis, and I was surprised that he really asked this question, since the relation is quite far-fetched, to say the least. Anyway, I was quite successful in plotting the phase diagrams of QCD matter and simple water on the blackboard - although, if you plot the diagram of nuclear matter as a function of density in temperature, keep in mind that there are two lines, tracing the coexistence region of the first order transition, which should meet at the critical point. My first guess of that plot on the blackboard, unfortunately, was a little different.. However, I was quite convincing, I think, in explaining the critical point, critical opalescence, and the absence of sharp differences in density or whatever in a cross over beyond the critical point. I also guess that the audience may have been impressed by my explanations of vortices acting like Coulomb charges and undergoing an ionization transition in the Kosterlitz-Thouless transition, and the analogy to the instanton liquid that drives the chiral transition.

Horst went on asking about some new mechanism to create super-heavy elements, not using the famous cold valley, which I could not answer, since I had skipped the relevant talk of Zagrebaev at last weeks ISHIP conference. Instead, I could make him happy with a schematic plot of collisions of heavy ions at energies in the 100-MeV range and the time scales involved, and the relevance to the creation of conditions suitable for the diving into the lower continuum of the Dirac sea. I guess that everyone who has spent some time in the Frankfurt institute has heard about the funny things that happen when "Z·alpha > 1" and the vacuum spits out positrons ;-)...

The next round of questions went to Klaus Peters, of the IKF, in Frankfurt since last year. He asked me about the different quarks, and the experiments that show the existence of the different families. It is a little bit funny, but one of the relevant plots, the number of hadrons versus dimuons produced in electron-positron annihilation as a function of energy, I knew that from my job as editor of Greiner's textbooks at Harri Deutsch. So, this was really useful for something :-). To his next question, about the prediction of the charm quark, I could, unfortunately, only propose the buzzword GIM mechanism and Glashow, Iliopoulos, Maiani, and that it is related to the weak interactions, but in fact I spent one hour of the afternoon last Sunday to figure out that its about the "suppression of flavor changing neutral currents", which are not observed, but are a consequence of naive Cabbibo mixing - this can even be found in the Wikipedia! His questions about pentaquarks (the reason why I had asked him to take part in my examination committee), again, I could answer. The funny thing is, like in all examinations, that sometimes it is just important to guess what the examiner wants to hear - in this case, "higher Fock states" which are mixed to the valence quark wave function, which can mix with pentaquark states. It took a while until I had figured out that he wanted to hear just this notion.

Finally, in the last round of "official" questions, Carsten came back to the details of my model, asked about comparisons to his Friedberg-Lee model, and about elliptic flow. There is, of course, a big fuzz about elliptic flow at RHIC, which seems to exhibit beautiful quark number scaling for a large number of hadrons. I could tell him something about all this - it was a hot topic at Strange Quark Matter the weak before. I would be happy if I could study it with my model. Unfortunately, it is hard to get enough statistics, and the initial pressure is not high enough, probably because there is no hard core repulsion between quarks in my model. I tried to impress everyone by mentioning the Alder-Wainwright simulations of the early 1960's that showed that hard core repulsion is enough to obtain a reasonable simulation of fluids, and that's why, i tried to argue, my model is not a strongly coupled QGP.

At that point, Carsten decided that the questioning had been long enough. I could have go on for a while, and Walter Greiner gave me the occasion, since in the round "questions from the public", he asked if I had heard Kampert's ISHIP talk about cosmic rays. I had not, but I said it was probably about the first runs of the AUGER experiment in Argentina, and made a plot of the spectrum of cosmic rays with the knee and the ankle and the questionable events at highest energies, where photo-pion production with photons of the microwave background should decelerate protons and prevent them from reaching the earth, and that this may be relevant to possible modifications of special relativity blah blah...

But then, eventually, it was really over. Usually, at this point, the audience has to leave the seminar room, so that the committee can decide about the outcome of the examination. This time however, since the seminar room was completely full with people, the committee left, and found its decision somewhere else. When they came back some 10 minutes later to announce that the result was "sehr gut", and to congratulate me, this was, strictly speaking, the moment of the phase transition to the PhD.

For me, however, it is washed out to a smooth cross over - I have not yet completely reached the new state.