# It’s hot when I accelerate!

Let us discuss one of the most intriguing predictions of theoretical physics. Picture yourself moving through empty space with fixed acceleration, carrying along a particle detector. Despite the fact that space is empty, your detector will click sometimes. The number of clicks will increase if you accelerate further, and stop completely if you bring your acceleration to zero. It is called Unruh effect, and was predicted in 1976.

That’s weird, isn’t it? Well, we have not even scratched the surface of weirdness!

So, more weirdness. The particles will be detected at random times, and will have random energies. But, if you plot how many particles you get at each energy, you’ll get a thermal plot. I mean: the same plot that you would get from a thermal bath of particles at a given temperature T. And what is that temperature?

$T = \hbar a / 2\pi c$

That is called the Unruh temperature. So nice! All those universal constants… and an unexpected link between acceleration and temperature. How deep is this? We will try to uncover that.

In our previous Physics Napkin we discussed the geometry of spacetime felt by an accelerated observer: Rindler geometry. Take a look at that before jumping into this new stuff.

Has this been proved in the laboratory?

No, not at all. In fact, I am working, with my ICFO friends, in a proposal for a quantum simulation. But that’s another story, I will hold it for the next post.

So, if we have not seen it (yet), how sure are we that it is real? How far-fetched is the theory behind it? Is all this quantum gravity?

Good question! No, we don’t have any good theory of quantum gravity (I’m sorry, string theoreticians, it’s true). It’s a very clear conclusion from theories which have been thoroughly checked: quantum field theory and fixed-background general relativity. With fixed background I mean that the curvature of spacetime does not change.

Detecting particles where there were none… where does the energy come from?

From the force which keeps you accelerated! That’s true: whoever is pushing you would feel a certain drag, because some of the energy is being wasted in a creation of particles.

It’s hot when I accelerate!! Ayayay!!!

I see $\hbar$ appeared in the formula for the Unruh temperature. Is it a purely quantum phenomenon?

Yes, although there is a wave-like explanation to (most of) it. Whenever you move with respect to a wave source with constant speed, you will see its frequency Doppler-shifted. If you move with acceleration, the frequency will change in time. This change of frequency in time causes makes you lose track of phase, and really observe a mixture of frequencies. If you multiply frequencies by hbar, you get energies, and the result is just a thermal (Bose-Einstein) distribution!

But, really… is it quantum or not?

Yes. What is a particle? What is a vacuum? A vacuum is just the quantum state for matter which has the minimum energy, the ground state. Particles are excitations above it. All observers are equipped with a Hamiltonian, which is just a certain “way to measure energies”. Special relativity implies that all inertial observers must see the same vacuum. If the quantum state has minimal energy for an observer at rest, it will have minimal energy for all of them. But, what happens to non-inertial observers? They are equipped with a Hamiltonian, a way to measure energies, which is full of weird inertial forces and garbage. It’s no big wonder that, when they measure the energy of the vacuum, they find it’s not minimal. And, whenever it’s not minimal, it means that it’s full of particles. Yet… why a thermal distribution?

Is all this related to quantum information?

Short story: yes. As we explained in the previous post, an accelerated observer will always see an horizon appear behind him. Everything behind the horizon is lost to him, can not affect him, he can not affect it. There is a net loss of information about the system. This loss can be described as randomness, which can be read as thermal.

Long story. In quantum mechanics we distinguish two types of quantum states: pure and mixed. A pure quantum state is maximally determined, the uncertainty in its measurements is completely unavoidable. Now imagine a machine that can generate quantum systems at two possible pure states A and B, choosing which one to generate by tossing a coin which is hidden to you. The quantum system is now said to be in a mixed state: it can be in any two pure states, with certain probabilities. The system is correlated with the coin: if you could observe the coin, you would reduce your uncertainty about the quantum state.

The true vacuum, as measured by inertial observers, is a pure state. Although it is devoid of particles, it can not be said to be simple in any sense. Instead, it contains lots of correlations between different points of space. Those correlations, being purely quantum, are called entanglement. But, besides that, they are quite similar to the correlations between the quantum state and the coin.

When the horizon appears to the accelerated observer, some of those correlations are lost forever. Simply, because some points are gone forever. Your vacuum, therefore, will be in a mixed state as long as you do not have access to those points, i.e.: while the acceleration continues.

Where do we physicists use to find mixed states? In systems at a finite temperature. Each possible pure state gets a probability which depends on the quotient between its energy and the temperature. The thermal bath plays the role of a hidden coin. So, after all, it was not so strange that the vacuum, as measured by the accelerated observer, is seen as a thermal state.

Thermal dependence with position

As we explained in the previous post, the acceleration of different points in the reference frame of the (accelerated) observer are different. They increase as you approach the horizon, and become infinite there. That means that it will be hotter near the horizon, infinitely hotter, in fact.

After our explanation regarding the loss of correlations with points behind the horizon, it is not hard to understand why the Unruh effect is stronger near it. Those are the points which are more strongly correlated with the lost points.

But from a thermodynamic point of view, it is very strange to think that different points of space have different temperatures. Shouldn’t they tend to equilibrate?

No. In general relativity, in curved spacetime we learn that a system can be perfectly at thermal equilibrium with different local temperatures. Consider the space surrounding a heavy planet. Let us say that particles near the surface at at a given temperature. Some of them will escape to the outer regions, but they will lose energy in order to do so, so they will reach colder. Thus, in equilibrium systems, the temperature is proportional to the strength of gravity… again, acceleration. Everything seems to come together nicely.

Hawking predicted that, if you stand at rest near a black hole, you will detect a thermal bath of particles, and it will get hotter as you approach the event horizon. Is that weird or not? To us, not any more. Because in order to remain at rest near a black hole, you need a strong supporting force behind your feet. You feel a strong acceleration, which is… your weight. The way to feel no acceleration is just to fall freely. And, in that case, you would detect no Hawking radiation at all. So, Hawking radiation is just a particular case of Unruh effect.

There is the feeling in the theoretical physics community that the Unruh effect is, somehow, more fundamental than it seems. This relation between thermal effects and acceleration sounds so strange, yet everything falls into its place so easily, from so many different points of view. It’s the basis of the so-called black hole information paradox, which we will discuss some other day. There have been several attempts to take Unruh quite seriously and determine a new physical theory, typically a quantum gravity theory, out of it. The most famous may be the case of Verlinde’s entropic gravity. But that’s enough for today, isn’t it?

For references, see: Crispino et al., “The Unruh effect and its applications”.

I’ll deliver a talk about our proposal for a quantum simulator of the Unruh effect in Madrid, CSIC, C/ Serrano 123, on Monday 14th, at 12:20. You are all very welcome to come and discuss!

# Feeling acceleration (Rindler spacetime)

This is the first article of a series on the Unruh effect. The final aim is to discuss a new paper on which I am working with the ICFO guys, about a proposal for a quantum simulator to demonstrate how those things work. We are going to discuss some rather tough stuff: Rindler spacetime, quantum field theory in curved spacetime, Hawking radiation, inversion of statistics… and it gets mixed with all the funny stories of cold atoms in optical lattices. I’ll do my best to focus on the conceptual issues, leaving all the technicalities behind.

Our journey starts with special relativity. Remember Minkowski spacetime diagrams? The horizontal axis is space, the vertical one is time. The next figure depicts a particle undergoing constant acceleration rightwards. As time goes to infinity, the velocity approaches c, which is the diagonal line. But also, as time goes to minus infinity, the velocity approaches -c. We’ve arranged things so that, at time t=0, the particle is at x=1.

Minkowski diagram of an accelerated particle.

Now we are told that the particle is, really, a vehicle carrying our friend Alice inside. Since the real acceleration points rightwards, she feels a leftwards uniform gravity field. Her floor, therefore, is the left wall.

Alice in her left. Acceleration points rightwards, “gravity” points leftwards.

Are you ready for a nice paradox? This one is called Bell’s spaceship paradox. Now, imagine that Bob is also travelling with the same acceleration as Alice, but starting a bit behind her. Their trajectories can be seen in the figure

Alice and Bob travel with the same acceleration. Their distance, from our point of view, is constant.

From our point of view, they travel in parallel, their distance stays constant through time. So, we could have joined them with a rigid bar from the beginning. Wait, something weird happens now. As they gain speed, the rod shrinks for you… This is one of those typical paradoxes from special relativity, which only appear to be so because we don’t take into account that space and time measures depend on the point of view. This paradox is readily solved when we realize that, from Alice’s point of view, Bob lags behind! So, in order to keep up with her, and keep the distance constant, Bob should accelerate faster than her!

So, let us now shift to Alice’s point of view. Objects at a fixed location at her left move with higher acceleration than she does, and objects at her right move with lower acceleration. Her world must be pretty strange. How does physics look to her?

One of the fascinating things about general relativity is how it can be brought smoothly from special relativity when considering accelerating observers. In order to describe gravity, general relativity uses the concept of curved spacetime. In order to describe how Alice feels the world around her we can also use the concept of curved spacetime. It’s only logical, Mr Spock, since the principle of equivalence states that you can not distinguish acceleration from a (local) gravity field.

Fermi and Walker explained how to find the curved spacetime which describes how any accelerated observer feels space around her, no matter how complicated her trajectory is. The case of Alice is specially simple, but will serve as an illustration.

The basic idea is that of tetrad, the set of four vectors which, at each point, define the local reference frame. In German, they call them “vier-bein”, four-legs, which sounds nerdier. Look at the next figure. At any moment, Alice’s trajectory is described by a velocity 4-vector v. Any particle, it its own reference frame, has a velocity 4-vector (1,0,0,0). Therefore, we define Alice’s time-vector as v. What happens with space-vectors? They must be rotated so that the speed of light at her point is preserved. So, if the time-vector rotates a given angle, the space-vector rotates the same vector in the opposite direction, so the bisector stays fixed.

The local frames of reference for Alice, at two different times.

Now, each point can be given a different set of “Alice coordinates”, according to local time and local space from Alice point of view. But this change of coordinates is non-linear, and does funny things. The first problem appears when we realize that the space-like lines cross at a certain point! What can this mean? That it makes no sense to use this system of coordinates beyond that point. That point must be, somehow, special.

In fact, events at the left of the intersection point can not affect Alice in any way! In order to see why, just consider that, from our point of view, a light-ray emmited there will not intersect Alice’s trajectory. Everything at the left of the critical point is lost forever to her. Does this sound familiar? It should be: it is similar to the event horizon of a black hole.

Red: what Alice can’t see. Green: where Alice can’t be seen.

Let us assume that you did all the math in order to find out how does spacetime look to Alice. The result is called Rindler spacetime, described by the so-called Rindler metric. In case you see it around, it looks like this

$ds^2=(ax)^2 dt^2 - dx^2 - dy^2 - dz^2$

Don’t worry if you don’t really know what that means. Long story short: when Alice looks at points at her left (remember, gravity points leftwards), she sees a lower speed of light. Is that even possible? That is against the principle of relativity, isn’t it? No! The principle of relativity talks about inertial observers. Alice is not.

So, again: points at her left have lower speeds of light. Therefore, relativistic effects are “more notorious”. Even worse: as you move leftwards, this “local speed of light” decreases more and more… until it reaches zero! Exactly at the “special point”, where Alice coordinates behaved badly. What happens there? It’s an horizon! Where time stood still.

The world for Alice, Rindler spacetime: speed of light depends on position, and becomes zero at the horizon.

Imagine that Alice drops a ball, just opening her hand. It “falls” leftwards with acceleration. OK, OK, it’s really Alice leaving it behind, but we’re describing things from her point of view. Now imagine that Bob is inside the ball, trying to describe his experiences to Alice. Bob just feels normal, from his point of view… he’s just an inertial observer. But Alice sees Bob talking more and more slowly, as he approaches the horizon. Then, he friezes at that point. Less and less photons arrive, and they are highly redshifted (they lose energy), because they had to climb up against the gravitational potential. Finally, he becomes too dim to be recognized, and Alice loses sight of him.

That description would go, exactly, for somebody staying fixed near a black hole dropping a ball inside it. The event horizons are really similar. In both cases, the observer is accelerated: you must feel an acceleration in order to stay fixed near a black hole! As Wheeler used to say, the problem of weight is not a problem of gravitation. Gravitation only explains free fall. The problem of weight is a problem in solid state physics!!

For more information, see Misner, Thorne and Wheeler’s Gravitation, chapter 6. It’s a classic. I wish to thank Alessio, Jarek and Silvia for suffering my process of understanding…

# On physics, maths and tenure in Spain

The following dialogue, its situations, characters and institutions are completely fictional. Or almost.

Two researchers, in their late thirties, meet at the college cafeteria.

Sandy. Hey, Cris, you’re back from Spain! How did the selection process go?

Cris. Bad, the insiders got the tenure positions, but I knew it was going to be that way. You know  how my country is. My CV was much better than theirs, and my lecture was terrific… but there was nothing to do.

Sandy. Yeah, don’t think it’s much better here…

Cris. Well, I don’t know. They evaluated my CV “logarithmically”, if you catch my drift: for example, by multiplying your papers by 2 you earn one extra point. Then, the evaluation of the lecture is very subjective… and that’s what they use to select the inside candidates.

Sandy. Why would they do so?

Cris. It’s easy: because the professors in the department are completely clueless, they don’t want new professors which can overshadow them.

Sandy. Where was the position?

Cris. It was for the mathematics department of a school of building engineering. That’s one of the most stupid things we have in Spain: the hyperfragmentation of the university. You decide your major at 18, when you reach college, and you can’t change easily. In many cases, such as UPM in Madrid, there are as many mathematics departments as there are schools. Tiny departments which do almost no research, dominated by their feudal lords.

Sandy. Like a community college here.

Cris. Much worse! They can do research, just they choose not to. But you know what was the funniest part? The committee argued endlessly about my research in theoretical physics being inappropriate for an applied mathematics department.

Sandy. No way!

Cris. Yes! I challenged them to tell me what is the difference between theoretical physics and applied mathematics…

Sandy. What did they say?

Cris. What did they say!? They mumbled about the names of the journals I use to publish in! If the title contains “physics”, then it’s physics. If it contains “mathematics”, or  “geometry”, or “algebra”, then it’s mathematics.

Sandy. And what if it’s “Communications in mathematical physics”?

Cris. That’s too mind-boggling for them! One of the guys simply asked me: “can you tell me one of your papers which is really mathematical”? I answered: “what about the one I discussed about the Riemann hypothesis?”

Sandy. Hahaha! Yeah, I remember, your fighting with proving the Riemann hypothesis using quantum mechanics.

Cris. Yeah… they told me that my papers are physics-motivated, not mathematics motivated. So, that’s where I told them that that sentence made no sense. Of course, in kinder terms… I added that it was OK to talk about papers focusing on methodology and papers focusing on the solution of a certain problem.

Sandy. Yeah, that might do as a distinction between math and physics, doesn’t it?

Cris. No, it doesn’t! A lot of physics papers focus on the techniques or the formalism. But, even worse, applied mathematics should focus on problem solving, right? I mean, real life problems. Such as… physics! Then I got a bit pedantic, and told them that mathematics comes from “máthema”, which in Greek means “what we learn”, while physics comes from “physis”, which means “Nature”. And I told them: what can you learn about, other than Nature?

Sandy. Hahaha! That made them hate you, for sure.

Cris. You bet. I even cited Arnol’d, and the speech he gave in Paris in 1999, emphasizing the close nature of mathematics and physics.

Sandy. Yeah, I remember that. Arnol’d was amazing. He hated the Bourbaki spirit in mathematics. He said they had converted mathematics into a game, a purely logical game. All branches of mathematics are inspired in physics, right?

Cris. Right! Arithmetics comes from counting. Geometry and probability are very clearly physical. And calculus is an abstraction of the theory of motion.

Sandy. Exactly. A mathematician which considers herself to be “applied” should be someone who is able to apply all kinds of mathematical tools to real-life problems. And a theoretical physicist is usually good at that.

Cris. Also, they rejected immediately a candidate with a CV which was similar to mine, because her teaching had been in physics.

Sandy. Again, the same thing applies. In fact, the distance between teaching calculus and mechanics is the same as the distance between teaching mechanics and thermodynamics.

Cris. Absolutely.

Sandy. I assume they didn’t teach much advanced mathematics to those building engineers.

Cris. Of course they didn’t. In fact, their calculus didn’t contemplate Taylor’s theorem, their vector calculus stopped at double integrals, and their algebra didn’t include complex numbers. My god! The students never reach the $e^{i\pi}= -1$ level!!

Sandy. Hahaha! Yeah, I know that’s your pet peeve… You think the students only get their mathematical maturity when they understand that formula.

Cris. Of course I do! That’s the moment when they stop being little padawans and they receive their jedi sword!

Sandy. Yeah, you love beauty in mathematics.

Cris. You bet I do! In gave my lecture on eigenvalues and eigenvectors, and I produced some nice animations… But even more important, I started with the Fibonacci numbers.

Sandy. You did what!?

Animation presented by C during the lecture, showing orbits obtained when acting several times with a certain matrix.

Cris. I discussed how to get a closed formula for the n-th Fibonacci number by raising a matrix to a certain power.

Sandy. How can you do that?

Cris. I wish you had seen me! It was like making magic when you do it slowly… the golden section appears as an eigenvalue of the matrix which generates the Fibonacci numbers… it’s wonderful when you see why. Grab a napkin, I will tell you.

Sandy. Sure.

# 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)

# How many dimensions did you say?

My friends and colleagues from ICFO, Alessio Celi and Maciej Lewenstein (along with O. Boada and J.I. Latorre), have just published a surprising article in Physical Review Letters, which appears in its Synopsis. What is the big deal?  They propose a route to simulate the behaviour of quantum matter in extra dimensions. The idea is extremely simple once it has been understood. But let me start by telling you what is the framework, I mean: what do I mean by simulation.

Consider that you would like to design a new material, which you want to have some nice properties, such as superconductivity, or a given response to magnetic fields… whatever. Most of these properties are given by the quantum behaviour of electrons inside the crystal. The problem is that the behaviour of interacting electrons in a given system is very hard to predict theoretically, using either pencil and paper calculations or huge supercomputers. What to do, then?

When aeronautical engineers design a new airplane, they do some complex calculations. After that, since they can not rely completely on them, they make a model plane and test it in a wind tunnel. They perform a controlled simulation. If the solution to their equations
coincides with the results of the simulation, then they feel confident about the airplane, and the manufacture procedure begins.

Quantum simulators follow the same idea as the wind tunnel and the model airplane. Set up many laser beams, making up a 3D lattice. The lattice spacing will be much larger than in crystalline solids, more than one μm. Now, instead of electrons, we put some ultra-cold atoms. But, I hear you say, atoms are not elementary particles, unlike electrons. There is a nice response to that: anything is an elementary particle until you hit them hard enough! In other words: atoms behave totally like elementary particles if the temperature and the interaction energy is low enough. If they have total spin 1/2, then the atoms are fermionic and behave much like electrons.

So, you have all the elements. Now, let us check a possible design for a material with some concrete properties: set up your optical lattice, put some ultra-cold atoms in there and see. The best part is that if you do not strike oil at the first attempt, you can always change your parameters almost on-the-fly and try again: tune the lasers, heavier atoms… whatever.

Now that we know what a quantum simulator is, let us focus on the novel part: the work of my colleagues. Many speculative theories in physics require the existence of extra-dimensions. If they exist, then their extension must be really small not to appear in ordinary experiments. I do not mean that those theories should be taken seriously, only that we might desire to find out what would be the implications!

Imagine that we prepare our optical lattice and leave our atoms inside. Atoms jump from a cell to the next tunneling through the laser beam. Now, consider atoms that can be in N different internal states, which differ, for example, in the nuclear spin direction. So to speak, N atomic flavours which are nearly indistinguishable. Label the internal atomic states from 1 to $N$, and arrange things so that atoms can only move from state $i$ to state $i+1$ or $i-1$. Now, by tuning up the laser intensities, we can make this movement in internal state to be exactly as movement in any other direction!

The image shows in blue the atoms with flavour 1, and in pink those with flavour 2. An atom at site $d$ can jump up, right, back… but it can also change flavour. And that jump would correspond to a movement in the fourth dimension. Of course, the extension of this fourth dimension is extremely reduced if we have only two flavours. In general, we will not be able to achieve huge sizes, but this is not a problem since, as we stated, the extra dimension, if it exists, must be extremely small.

For example, we can arrange a single atom in a given cell, with a given internal state, and let it evolve freely. After some time, it will be in another cell and with another internal state. This internal state will mark how much it has moved in the extra-dimension.

V.I. Arnold, one of the great masters, once said that mathematics is the part of physics where experiments are cheap. Well, the cost of the mathematical experiment must always be compared to the cost of the real one. Using an expensive supercomputer to follow the behaviour of all the atoms of a stone as it falls to the ground does not seem to be a huge saving. But using ultracold atoms in an optical lattice to simulate 4D space qualifies much better… most of all because we are not aware of any other experimental setup! :)

# #occupy_scientific_journals

The main aim of this post is to propose a peer-review system on the ArXiv. We need a revolution in the scientific publication scheme.

1.- What is wrong?

Today I needed a scientific article for my research. My institution is not subscribed to the journal, but the publisher said “No problem, dude, just pay $33 and you can read the paper”. Seriously!? Scientific publishing is a peculiar business model. Authors make no money from publication. Neither do referees. The typesetting of the articles is usually done by the authors themselves. Yet, the alleged cost per article is around$1.000-$10.000… Seriously!? Work in fundamental science is usually paid by governmental funds, through taxes. And, even when the money comes from private hands, still their aim is to create knowledge and make it publicly available. But, as of now, the general public does not have free access to the results of the research they fund. Even professional scientists have frequent problems to obtain articles they need, thus making their research more difficult. This problem is getting worse with the economic crisis, and has always been a major issue in developing countries. If authors do not make any money, why do they publish? For want of reputation and dissemination of their work. Funding agencies need some quality measurements in order to make decisions about which project to support. The accepted system, worldwide, is the number of publications and citations, and the prestige of the journals in which you publish. Journals are ranked by the JCR (journal citations report) index, which is itself… another private company (Thomson Reuters), which charges enormous amounts of money to universities and research institutes to pay for a faulty database. Of course, some publishers are better than others. IOP and the DPG started New Journal of Physics, which is open. The problem is that publishing there is quite expensive. Other open journals can be found here. 2.- What do we want? We want a cheap and open publication scheme. Most of the work is already done already by us. We want a fair reputation system, which rewards high quality research, to serve as a guide for government agencies to direct their funding. And also as an internal guide to the relevant literature (too much to read, otherwise!) 3.- Ideas The most promising point of departure is the ArXiv. It is free and open. It costs its maintainers (a board of worldwide research institutions) around$10 per article. Why not creating a peer-review system on the ArXiv? If authors so desire, they might ask for a “peer-review stamp” on their preprint. It wouldn’t be so difficult. A similar idea was already put forward by John Baez.

The peer-review process, as it stands today, is both too slow and too fast. It’s too slow because it takes months for a regular submission to see the light. By then, it is very often well known by the community, who had access to it through the ArXiv or otherwise. And it is also too fast because the referee process is not good enough to assess whether a paper will have impact or not. It takes time to know. So, why not making two “peer-review” processes? A quick-and-dirty one when the paper appears in the ArXiv. A second one, more detailed, after a few years, to evaluate its real importance.

Another nice idea would be to create an open discussion forum for each paper, where people might be able to make comments and ask questions. In the stack-exchange community style, reputation might be awarded for making questions and providing answers which the community approve. Of course, the forums need not be attached to papers only. The concept of paper as the “unit of research” may become outdated in such a structure. Papers were the natural medium for the exchange of information when the dead-tree technology was dominant… but, just like the mechanical loom, animal traction and congressmen, may be overthrown by history.

# 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.