Lev Landau

Landau, one of my idols, died 42years ago. He is among the most important physicists in the last century. Here finds a brief tribute to him from Ginzburg.

Landau's occasional abruptness has brought about misconceptions that have become a part (and a rather distorted part) of a legend. I, for instance, have heard people saying, "Landau thinks he is more clever than anyone else." This is completely erroneous, however, and there are many chances for one to see how soberly and modestly Landau assesses his place in science. Many years ago, his love for systematization and clarity led him to classify physicists, by way of a joke, according to the scale of a slide rule. This means that a physicist of second-class standing has achieved ten times less than a physicist of the first class. According to this scale, Albert Einstein, even better than first class, belongs to the 0.5 class, while Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Paul Dirac, Enrico Fermi, and some others belong to the first class. As for himself, Landau used to say that he was in the 2.5 class, and only ten years ago, satisfied with his work, he said he had reached the second class.

Landau's very critical attitude and his opinion that many ideas (or, to be more precise, hints at ideas) are "pathological" spring in a substantial measure from his sober nature and clarity of thinking. His criticism and his denial of certain proposals are always based on scientific grounds and thoroughly deliberated arguments. It is quite a different thing that Landau does not always like to explain his remarks: Often he answers, "Think for yourself." The fact that he is not always ready to answer and explain, however, has nothing in common with conceit or snobbery. A profoundly democratic individual, he is alien to pomposity and respect for rank. Any student could discuss scientific problems with him without difficulty, with the single stipulation that held good for all: The student had to achieve the necessary level of understanding and analyze the problem instead of expecting Landau to think for him and do the things that the student could do himself.

Interview with Roger Penrose

Nature conducted an interview with Professor Roger Penrose, who recently re-captured one's imagination with his consecutive aeons referring to the universe. [http://www.nature.com/nature/journal/v468/n7327/full/4681039a.html]:

You are currently working on a book called Fashion, Faith and Fantasy. What it is about?

I rashly suggested that title for three lectures I gave at Princeton University in 2003. 'Fashion' refers mainly to string theory, which has many merits but is not believable. I don't see how you can make sense of all those extra dimensions. 'Faith' refers to quantum mechanics. It's a wonderful theory and works beautifully, but is self-inconsistent — in my view, when you make a measurement, you violate the Schrödinger equation. At some scale in the Universe, quantum mechanics will have to be replaced by a better theory.

And 'fantasy'?

That's largely directed at cosmic inflation, in which the Universe is supposed to have expanded by an enormous factor just after the Big Bang. I've always been against this — it can only work if you start off in a very special state. In my recent book Cycles of Time, I propose my own fantastical scheme that the entire history of the Universe is just one stage in a succession. What we think of as the Big Bang is not the beginning. It's the continuation of the remote future of a previous aeon.

How might we know if that is true?

The cosmic microwave background — the radiation left over from the Big Bang — would reveal evidence of events taking place in the aeon before ours, mainly encounters between supermassive black holes. When galaxies collide, their central black holes may spiral around and swallow each other up, causing an enormous burst of gravitational radiation. Such a burst from late in the previous aeon would leave its mark as circles around which the temperature is anomalously uniform. My colleague Vahe Gurzadyan sees tentative signs of them [see http://go.nature.com/Lbwiou].

The breakthrough of this year from Science

Near the end of this year, one may ask, what is the breakthrough in science this year ? Every one may have his own answer. The one from Science is the achievement of a tiny quantum vibrator that is less the width of a hair. This article reviews why it is a breakthrough:

A team of American physicists found a quicker route, as they reported in March. Instead of a beam, they fashioned a tiny diving board of aluminum nitride plated with aluminum that vibrated by getting thinner and thicker. As the doohickey hummed away at a very high frequency—a whopping 6 billion cycles per second—the “piezoelectric” material in it produced a warbling electric field that was easy to detect. Most important, through that field, the physicists managed to “couple” the mechanical device to an electronic one called a “phase qubit,” a ring of superconductor that itself has one low-energy and one high-energy quantum state.

Manipulating the qubit with microwaves, the researchers could use it to feed energy quanta into the oscillator or pull them out of it, as one might use an ATM to deposit a $20 bill to a bank account or withdraw one. First they showed that when they cooled the oscillator to a few hundredths of a degree they could get no quanta out of it. That meant it had to be in the cashed-out ground state, jiggling with only zero-point motion. The researchers then put the oscillator in a state with exactly one more quantum of energy. They even coaxed it into both states at once, so that it was literally moving two different amounts simultaneously.

The ingenuity in this scheme lay in the design of the oscillator and the use of a qubit to control it. In fact, in 2009, the team used a phase qubit to feed quanta into a long strip of superconducting metal that would ring with microwaves much as an organ pipe rings with sounds. Once they worked the kinks out, they replaced the microwave cavity with their clever mechanical oscillator, a move that had other physicists slapping their foreheads for not having seen it coming.

Insights of the decade from Science

Now we are coming to the end of not only this year but also the first decade of this century. Science has its list of the insights of this decade in science. In materials physics, the meta-material and the related conformal optics which underlies the operation of these materials are enlisted. The ground breaking papers are as follows: [http://www.sciencemag.org/site/special/insights2010/]

• U. Leonhardt, "Optical Conformal Mapping," Science 312, 1777 (2006).
• J. Pendry et al., "Controlling Electromagnetic Fields," Science 312, 1780 (2006).
• D. Schurig et al., "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977 (2006).
• T. Ergin et al., "Three-Dimensional Invisibility Cloak at Optical Wavelengths," Science 328, 337 (2010).

No evidence for the time before Big Bang

Several years ago, Roger Penrose proposed a different cosmological model, which allows the universe to recycle. His considerations are mainly based on two things: (1) The second law of thermodynamics, which states that, the entropy of the universe as an isolated system must increase with time; (2)The conformal invariance, which states that the metric can be determined up to a scale. Point (1) is strong, but (2) is weak. Recently, Roger and his collaborators claimed evidence for their model. This claimed evidence comes from concentric circular belts discernible on the CMB. However, this claim soon intrigues lots of rebuttals. A good review can be found here and here .

The proton size

In a previous entry, I posted a report on the measurement of the proton size that is based on muons. It gives a smaller size than had been accepted. There came a new measurement, which, nonetheless, disagrees with this smaller proton saying. This new one is based on electrons. [http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.105.242001]

The charge radius of the proton is one of nature’s fundamental parameters. Its currently accepted CODATA (Committee on Data for Science and Technology) value, 0.8768×10^-15 m, has been determined primarily by measurements of the hydrogen Lamb shift and, to lesser accuracy, by electron-proton scattering experiments. This value has recently been called into question by a research team at the Paul Scherrer Institut (PSI) in Villigen, Switzerland. By measuring the Lamb shift in muonic hydrogen, these researchers obtained a value of 0.8418×10^-15 m for the charge radius, five standard deviations below the CODATA value.

In a paper appearing in Physical Review Letters, the A1 Collaboration has determined the electric and magnetic form factors of the proton with higher statistics and precision than previously known, using the Mainz (Germany) electron accelerator MAMI (Mainz Microtron) to measure the electron-proton elastic-scattering cross section. Both form factors show structure at Q²≈ m_π² that may indicate the influence of the proton’s pion cloud. But, in addition, the collaboration’s extracted value for the charge radius agrees completely with the CODATA value. The discrepancy between “electron-based” measurements and the recent PSI “muon-based” measurement thus remains a puzzle. – Jerome Malenfant

Single band or double band ?

It is frequently disputed in the field of cuprate superconductors that, the essential physics may be encapsulated more adequately by a single (let's call it d) or double (s-d) band model. Fairly speaking, throughout the whole span of this arena, from the early days till now, as initialized by Anderson and pushed by Zhang and Rice et al., the d-model has been at the center and unchallenged. This situation was further corroborated by the thinking that, the s-d model can be mapped onto the d-model rigorously [see Ref.1 for a review]. Nevertheless, this situation ha to change for two reasons: (1) the d-model can not address the intervening spin glass phase; (2) the d-model can hardly explain the checkerboard pattern observed at low doping.

Why cant the spin glass phase exist within the d-model ? Suppose one has a half-filled single-band Hubbard model. Now add an extra electron to it. What can this electron do ? It shall try to hop from one site to another. Due to Pauli's principle, to render this hopping, the electrons on the two sites must have their spins aligned parallel. This means that, this extra electron tends to align the already existing electrons. On the other hand, the already existing electrons also try to hop and require their neighbors anti-parallel. And these two effects cancel exactly, because the two electrons on the same site have exactly the same hopping amplitude.

Obviously, in the s-d model, the effects don't cancel. This is where the difference gets in.

[1]SPIN POLARONS AND HIGH-Tc SUPERCONDUCTIVITY, A. L. Chernyshev†,* and R. F. Wood Solid State Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831;