# A personal dream: Journal of Physical Insight

Just a week after I published my post on the scientific publishing industry (#occupy_scientific_journals), the whole world seemed to explode. Tim Gowers started his personal crusade, and articles appeared even in mainstream media about how Elsevier and the strange world of scientific publishing. I was happy.

But complaining is not enough. I have had a dream for a long time: to create a scientific journal. A possible name would be “Journal of Physical Insight”, but others have been proposed by friends, such as “New Points of View in Physics”. Let me explain how it would look like.

Aim and scope. the journal would not aim at publishing original research. It would publish only original insight about known research. New ways of looking at old things. Conquering new territories is not more important than colonizing them.

Examples: revisiting old concepts using new tools, interesting conjectures, exposition of conceptual difficulties and possible ways out, more clever notations, unexpected connections between distant results… Do not misunderstand me, it would be a hard-core research journal, indexed in JCR. It would not be a teachers’ journal, although also teaching might be benefitted from it.

Publication style. I would like it to be a fully free journal, both for readers and authors. Authors would be required to typeset the paper carefully, in final form, check the references, etc. The editors would be volunteers, and they would be required to be young scientists, counting on the help of an advisory committee of senior scientists.

Special emphasis would be given to the writing style. The special aim of the journal suggests that editors and referees should encourage the authors to make a special effort to make concepts very clear. Also, evidently, to peruse the literature as deeply as possible, also outside your field: novel ideas in one field can be known concepts in another.

Peer-review process. That is one of the main novelties brought by the project. First of all, I want it to be double-blind, i.e.: the referees will not know the names of the authors or their affiliation. Also, I advocate for a two-stage peer-review process. The first one would be as quick as possible. Once the paper is published, its refereeing process would not be finished. It would start the second, community-driven process. Comments would be open for each article, and they would be collected for a reasonable amount of time, e.g. two years. It’s already time for scientific research to benefit from the 2.0 revolution! After that trial time, a second refereeing process would be carried out, to assess the impact of the work beyond its number of scitations. This second evaluation would be most beneficial to funding agencies, of course, because by then all scientists in the field would know the article.

Normally, the scientific edition procedure starts when the authors submit their finished work. Given its special scope, this journal would encourage authors to submit article proposals to the editors before embarking in the project, as it is done typically with review papers. The editorial board, if they consider the proposal interesting, will give support to the authors. This is a standard procedure in other areas, but not in science.

Of course, such a project will take a long time to bloom. It will require support from some scientific institution, although money is not an issue in this case: a few dedicated servers would be more than enough. Much more important is to convince a critical mass of colleagues, from all branches of physics, that this idea is worth trying.  Thus, I think time is ripe to ask for feedback… What are your thoughts?

(thanks to Silvia N. Santalla)

# Qubism

Scientists tend to be very visual people. We love to understand through pictures. About one year ago, we had one of those ideas which remind you why it’s so fun to be a theoretical physicist… Simple and deep. The idea was about how to represent quantum many-body wavefunctions in pictures. Speaking very coarsely, the high complexity of the wavefunction maps into fractality of the final image.

So, more slowly. As you know, bit can take only two values: 0 and 1. A qubit is a quantum bit, which can be in any linear combination of 0 and 1, like Schrödinger’s cat, which we denote by $|0\rangle$ and $|1\rangle$. In other terms: a qubit is represented by two complex numbers: $|\Psi\rangle = \alpha |0\rangle + \beta |1\rangle$. If you have two qubits, the basic states are four: 00, 01, 10 and 11, so we get

$|\Psi\rangle = \alpha_{00} |00\rangle + \alpha_{01} |01\rangle + \alpha_{10}|10\rangle + \alpha_{11}|11\rangle$

If you add one qubit, the number of parameters doubles. For N qubits, you need $2^N$ parameters in order to specify completely the state! The task of representing those values in a picture in a meaningful way seems hopeless… Our idea is to start with a square and divide it in four quadrants. Each quadrant will be filled with a color associated with the corresponding parameter.

What if we get a second pair of qubits? Then we move to “level-2”: we split each quadrant into four parts, again, and label them according to the values of the new qubits. We can go as deeply as we want. The thermodynamical limit $N\to\infty$ corresponds to the continuum limit.

The full description of the algorithm is in this paper from arXiv, and we have launched a webpage to publish the source code to generate the qubistic images. So, the rest of this blog entry will be just a collection of pictures with some random comments…

This is the ground state of the Heisenberg hamiltonian for $N=12$ qubits. It is an antiferromagnetic system, which favours neighbouring qubits to be opposite (0-1 or 1-0). The main diagonal structures are linked to what we call a spin liquid.

These four pics correspond to the so-called half-filling Dicke states: systems in which half the qubits are 0 and the other half 1… but you do not know which are which! The four pics show the sequence as you increase the number of qubits: 8, 10, 12 and 14.

This one is the AKLT state for N=10 qu-trits (each can be in three states: -1, 0 or 1). It has some nice hidden order, known as the Haldane phase. The order shows itself quite nicely in its self-similarity.

This one is the Ising model in a transverse field undergoing a quantum phase transition… but the careful reader must have realized that it is not fitting in a square any more! Indeed, it is plotted using a different technique, mapping into triangles. Cute, ein?

But I have not mentioned its most amazing properties. The mysterious quantum entanglement can be visualized from the figures. This property of quantum systems is a strong form of correlation, much stronger than any classical system might achieve.

So, if you want to learn more, browse the paper or visit this webpage, although it is still under construction…

With warm acknowledgments to my coauthors: Piotr Midgał, Maciej Lewenstein (ICFO), Miguel I. Berganza and Germán Sierra (IFT), and also to Silvia N. Santalla and Daniel Peralta.

# The temperature of a single configuration

One of the first things that we learn in thermodynamics is that temperature is the property of an ensemble, not of a single configuration. But is it true? Can we make sense of the idea of the temperature of a single configuration?

I became sure that a meaning could be given to that phrase when I read Kenneth Wilson’s article about the renormalization group in Scientific American long long back. There he gave three pics describing the state of a ferromagnet at low, critical and high temperature. He gave just a single pic for each state!! No probability distributions, no notions of ensemble. Just pictures, that looked like these ones:

Was Wilson wrong? No, he wasn’t! Black spins are down, and green ones are up. So, he wanted to show that, at low temperatures (left pic) you have large domains. At high temperatures (right pic), it is all random. And at the critical temperature, the situation becomes interesting: you have patches within patches, of all sizes… But that is another story, I may tell it some other day.

So, you see: Wilson’s pics make the point, so it is true that a single configuration can give the feeling for the temperature at which it was taken.

In statistical mechanics, each possible configuration C for a system has a certain probability, given by the Boltzmann factor:

$p(C) \propto \exp(-E(C)/kT)$

where $E(C)$ is the energy of the configuration, $T$ is the temperature and $k$ is Boltzmann’s constant. The proportionality is a technical thing: probabilities have to be normalized. In terms of conditional probability, we can say that, given a temperature, we have a probability:

$p(C|T) \propto \exp(-E(C)/kT)$

which means: given that the temperature is $T$, the probability is such and such. Our question is, therefore, what is the probability for each temperature, given the configuration?

$p(T|C)$

Now, remember Bayes theorem? It says that you can reverse conditional probabilities:

$p(A|B) p(B) = p(B|A) p(A)$

So, we can say:

$p(T|C) = p(C|T) p(T)/p(C)$

Great, but… what does that mean? We need the a priori probability distribution for the temperatures and for the configurations. That’s a nice technical problem, which I leave now. But see my main point: given the temperature, you have a probability distribution for the configurations and, given the configuration, you have a probability distribution for the temperatures.

Of course, that distribution might be quite broad… Imagine that you have a certain system at a certain unknown temperature $T$. You get one configuration $C_1$ and, from there, try to estimate the probability. You will get a certain probability distribution $P(T|C_1)$, presumably broad. OK, now get more configurations and iterate: $P(T|C_1,C_2,C_3,\cdots)$. As you get more and more, your distribution should narrow down and you should finally get a delta peak on the right temp! So, you get a sort of visual thermometer…

The idea is in a very alpha release… so comments are very welcome and, if you get something nice and publish, please don’t forget where you got the idea! :)

(Note: I already made an entry of this here, but this one is explained better)