Anderson in an interview

He is certainly among the most creative physicists of last century. I find myself resonating with his style in doing physics, with all modesty. This is an excerpt from an interview [http://www.aip.org/history/ohilist/23362_1.html]:

How about quantum electro-dynamics?

ANDERSON:

It was too hard for me. I'm not a formalist. I did listen to some of those lectures. I found the formalism forbidding. I only later came to understand that kind of formalism. I'm lazy. I'm mentally lazy. I believe in using only the tools that are necessary for the job. If I've got a serious problem and it's my problem that I have to solve, I'll go on inventing formalism until I find the answer. But in general I avoid the formalism if I possibly can.

KOJEVNIKOV:

Among other physicists, who do you think is the closest to you in style?

ANDERSON:

Well some of them are experimentalists. I've always thought that Nicolaas Bloembergen and I were very similar. He's half a theorist, or say six tenths experimentalist and four tenths theorist, and I'm more like six tenths theorist and four tenths experimentalist. So that's fairly close. This is immodest of me, and I say this with all modesty, but I think Fermi worked the way I worked. He really was focused on the experimental question. And then he would do formalism if he had to solve it. And Van very much so. Van was no formalist. The reason I was rescued from complete ignorance of formalism was that I had these courses from Schwinger, and so I learned the Green's function formulas and some of that aspect of physics. But that was another thing about the nuclear physics. The Schwinger group of students and the few students who were working with Furry, they were focused on formalism. And I wanted to really explain experimental facts. So when Van gave me this problem—

Accoustic diode

This is a device that allows one-way propagation of sound. Obviously, such device must break time reversal symmetry. [http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.106.084301]

The device consists of a two-dimensional sonic crystal arranged in a mesh of square steel rods. By rotating the steel rods, Li et al. are able to manipulate the unit cell of the sonic crystal element to turn the diode on (sound waves only propagate one way) and off (sound waves can move back and forth). Furthermore, Li et al. make their device entirely from linear acoustic materials, which allows them to control sound propagation with a simpler and more efficient process, over a broader bandwidth, and with lower power consumption, compared to existing nonlinear sonic-crystal-based devices.

Anderson and Scalapino talk on Science

This is not a latest news but still interesting for those who are working with cuprate superconductors, which are widely thought to be a central problem faced with by contemporary physicists. The two argue about the possibility of a paring glue. [http://www.sciencemag.org/content/316/5832/1705/reply]

[Anderson]:

I do not, however, accept that Scalapino’s calculations, refined as they are, come near to settling the question he has raised. The numerical analysis of Scalapino’s reference 7, and the analysis of experiments in his references 8 and 9, all have, logically, two pieces. To take ref 7 for definiteness, Scalapino’s group does two computations. The first, while difficult, is logically unimpeachable: It is a carefully designed simulation of the properties of the Hubbard model which we both agree is by far the main Hamiltonian candidate. Sure enough, they find d-wave superconductivity and other physical properties that agree with experiments—and also with much simpler mean field theories (1).

In step 2, they attempt to derive from the measured quantities a number of theoretical constructs, such as the "pairing interaction vertex," assuming that the underlying theory is the conventional Feynman-Dyson diagram theory as adapted for condensed matter problems in the 1960s. Thus, the procedure, far from being a purely direct computational result, is a theoretical construct with a very relevant input of unproven assumptions. The interaction vertex which is derived does not look at all like the J term in the Hamiltonian; it is much smaller than it should be, at high energies, growing to its full strength only at the lowest energies.

This is an unlikely result. It says that somehow all the low-frequency spin fluctuations have killed this giant interaction at the high-frequency end, but left it intact at low frequency to do its work on the pairing gap. It amounts to replacing my "elephant" J with almost nothing but its indirect consequences. It also contradicts the simplest mean field theory of the t-J model (ref 1, called because of its simplicity the "Plain Vanilla" theory).

If I found a result which so blatantly did not make physical sense, I might have questioned the method rather than attacking those of us who seem to have found the right answers by doing things otherwise. It is very attractive to abandon these particular methodological assumptions, because the same set of assumptions, applied in the normal state of the same materials, have had zero success in describing its unique and very anomalous properties.

[Scalapino]:

While there is a growing consensus that superconductivity in the high T_c cuprates arises from strong short-range Coulomb interactions between electrons rather than the traditional electron-phonon interaction, the precise nature of the pairing interaction remains controversial (1). This is the case even among those who agree that the essential physics of the cuprates is contained in the Hubbard model (Perspectives, "Is there glue in cuprate superconductors?", by P. W. Anderson, 22 June 2007, p. 1705). For example, both Anderson’s resonating-valence-based (RVB) theory (2) and the spin-fluctuation exchange theory (3, 4) lead to a short-range interaction which forms d _x²−y² pairs. However, the dynamics of the two interactions differ.

In the RVB picture, the superconducting phase is envisioned as arising out of a Mott-liquid of fluctuating singlet pairs. These pairs are bound by a superexchange interaction J which is proportional to t²/U. Here t is the effective hopping matrix element between adjacent sites and U is an onsite Coulomb interaction. J is determined by the virtual hopping of an electron of a given spin to an adjacent site containing an electron with an opposite spin (5). Thus the dynamics of J involves virtual excitations above the Mott gap which is set by U, and the pairing interaction is essentially instantaneous. In this case, as Anderson recently discussed (6), one would not speak of a pairing glue.

In the spin-fluctuation exchange picture, the pairing is viewed as arising from the exchange of particle-hole spin 1 fluctuations whose dynamics reflect the frequency spectrum seen in inelastic magnetic neutron scattering. This spectrum covers an energy range which is small compared with U or the bare bandwidth 8t. In this case, the pairing interaction is retarded and in analogy to the traditional phonon mediated pairing, one says that the spin-fluctuations provide the pairing glue.

Thus, the question of whether there is pairing glue in the cuprates is a question about the dynamics of the pairing interaction. It offers a way of distinguishing different theories. For the Hubbard model, recent numerical calculations (7) have shown that the strongest pairing occurs for U of order the bandwidth 8t. This is also thought to be the parameter regime appropriate to the cuprates. In this regime, these calculations find that the dynamic dependence of the pairing interaction is the same as that of the dynamic spin susceptibility. Thus, there is pairing glue in the Hubbard model.

Of course, the ultimate question is: What does the experiment tell us about the dynamics of the pairing interaction? Just as the spatial structure of the pairing interaction can be determined from the k-dependence of the superconducting gap, the dynamics of the interaction is reflected in the frequency dependence of the gap. In addition, if the interaction is retarded, that is delayed for a time of order ћ/(2J), the gap will have both a real and an imaginary component. This frequency structure of the gap is reflected in a variety of experiments and analysis of structure in the angular resolved photoemission spectrum (8), and the infrared conductivity (9) have suggested that the dynamics is indeed determined by spin-fluctuations. However, as opposed to the Hubbard model, real materials have phonons and alternative explanations have also been proposed (10). Thus, while there is pairing glue in the Hubbard model, more experimental work is needed to settle the question of whether there is glue in the cuprate superconductors.

Superfluid Exists in the core of a neutron star

This is a wonderful discovery. A neutron star 11,000 light years far from us was observed cooling down extrodinarily fast (4% in the past 10 years), which has been deciphered as a signature of the existence of such superfluid. The pressure exerted by gravity on the core of a neutron star is huge and neutrons, which are fermions, were predicted to form boson-like pairs under such high pressure circumstances. Such pairs condense and move coherently and make a superfluid, which is frictionless. More neutrinoes shall be released, and hence more energy shall be taken away, resulting in the faster cooling rate, explain these authors. [http://www.wired.com/wiredscience/2011/02/superfluid-neutron-star/]

Quantum control using unsharp measurements

"For the purpose of controlling a system, two facts appear self-evident. First, the more information one can obtain about the system, the better one can control it. Second, one needs to do more than just obtain information in order to control the system. In the quantum world, however, self-evidence cannot be trusted. Writing in Physical Review A, Ashhab and Nori¹ refute the two 'facts' just given and show that a quantum system can be quickly driven to any desired state using a fixed type of measurement. Although various schemes have been proposed^{2, 3} for driving a quantum system from one state to another using only quantum measurements, this is the first time it has been shown to be achievable using repetitions of a given measurement. Crucially, the authors' proposal requires the measurement to be unsharp. That is, one must avoid obtaining too much information about the system."[http://www.nature.com/nature/journal/v470/n7333/full/470178a.html?WT.ec_id=NATURE-20110210]
[1]Ashhab, S. & Nori, F. Phys. Rev. A 82, 062103 (2010)

Couterflow

This Letter addresses a practical problem that is encountered in, for example, a recent oil gushing in Mexico Gulf. To 'top kill' the oil well, one may pump "mud" from above to suppress the welling from bottom. However, in this "top kill", one needs consider an issue as described in the mentioned Letter, the so-called "Helmholtz instability", namely, "Dense fluids, i.e., mineral suspensions called ‘‘mud’’ [1,2], are introduced into oil wells to provide hydrostatic pressure to offset hydrocarbon (oil and gas) fluid pressure in deep formations, stopping upward flow and reducing the fluid pressure at the surface to near ambient. If hydrocarbon is flowing upward in the well, there is a counterflow between the upwelling hydrocarbon and the descending mud. Successful top kill requires that the mud descend despite this counterflow. However, upwelling at speeds > 1m/s, as in the uncontrolled Macondo well ‘‘blowout’’ in the Gulf of Mexico in 2010, may lead to a Kelvin- Helmholtz instability [3]."[PRL 106, 058301 (2011)] How to avoid the instability ? Suggested to use viscoelastic materials.

Strong interaction makes better clocks !

I have not read this report in Science [331:1043 (2011)], but it catches my attention simply because of its claim ! Anyway, it should be funny to read. "Optical lattice clocks with extremely stable frequency are possible when many atoms are interrogated simultaneously, but this precision may come at the cost of systematic inaccuracy resulting from atomic interactions. Density-dependent frequency shifts can occur even in a clock that uses fermionic atoms if they are subject to inhomogeneous optical excitation. However, sufficiently strong interactions can suppress collisional shifts in lattice sites containing more than one atom. We demonstrated the effectiveness of this approach with a strontium lattice clock by reducing both the collisional frequency shift and its uncertainty to the level of 10⁻¹⁷. This result eliminates the compromise between precision and accuracy in a many-particle system; both will continue to improve as the number of particles increases. "