The statistical mechanics of money

Slow posting recently because of many real-life things going on after the March Meeting.  We had a very engaging colloquium this week by Victor Yakovenko, a condensed matter theorist from the University of Maryland.   A number of years ago, he got into "econophysics", applying insights from physics to the economy.  A great review is here. 

A classic example is in his highly cited paper, with the same title as this post.  Make some simple assumptions:  Money is a conserved quantity, and the rates of transactions don't depend on the financial direction of the transactions.  Take those assumptions, start with everyone having the same amount of money, and allow randomized transactions between pairs of people.  The long-time result is an exponential (Boltzmann-like) distribution of wealth - the probability of having a certain amount of money \(m\) is proportional to \(\exp(-m/\langle m \rangle)\), where \(\langle m \rangle \) is the average wealth, a monetary "temperature".  The take-away:  complete equality is unstable just because of entropy, the number of possible transactions.

Apparently similar arguments can be applied to income, because it would appear that you can describe the distribution of incomes in many countries as an exponential distribution (more than 90% of the population).  Basically, for a big part of the population, it seems like income distribution is dominated by these transactional dynamics, while the income distribution for the top 3-ish% of the population follows a power-law distribution, likely because that income comes from returns on investments rather than wages.  The universality is quite striking, largely independent of governmental policies on managing the economy.

Yakovenko would be the first to say not to over-interpret these results, but the power of statistical arguments familiar from physics is impressive.  Now all we have to do is figure out the statistical mechanics of people....

APS March Meeting wrapup

I spent the lion's share of today talking w/ my collaborators.  This was great scientifically, but meant that I only went to a couple of talks. 

• This one was pretty slick.  If you look at the conduction properties of a Josephson junction as a function of magnetic field through it, you see a Frauenhofer pattern as a function of the enclosed flux (see this pdf, fig 2).  In principle, taking the inverse Fourier transform of this should reveal the real-space current distribution as a function of the distance along the width of the junction.  This group made Josephson junctions using oriented thin pieces of WTe2.  When the current flowed along one direction, they found that the Josephson current was mostly flowing near the edges of the strip of material.  When current flowed along a different direction in the plane, the current distribution was much more uniform.  
• Similarly evocative, this talk presented work using magnetic focusing plus scanning gate microscopy plus collimating contacts to look at the real-space paths of electrons in a graphene-hBN bilayer w/ a Moire superlattice.  They could then infer the shape of the Fermi surface in momentum-space, confirming that the Moire superlattice results in a roughly triangular (miniband) Fermi surface.  Cooler than my jargon-heavy description sounds.
• I greatly regret that I was unable to attend the invited session in honor of Millie Dresselhaus.  If one of my readers who did make it could please describe it in a comment, I'd appreciate it.
• One other random note:  I did actually speak to the APS person who was in charge of the trade show, and I asked what the heck was up with the two weird "pain relief" booths, which seemed borderline late-night-infomercial/much more like something you'd see at a cheesy shopping mall.  This was apparently an experiment in allowing local vendors in, and it sounds very unlikely that it'll ever happen again.  

If I missed a big story from the meeting, please let me know in the comments.

APS March Meeting Day 3

A handful of semi-random highlights (broken up by my conversations w/ colleagues and catching up on work-related issues):

• Laura Heydermann from ETH spoke about "artificial" magnetic systems, where mesoscopic, lithographically patterned arrays of magnetic islands can yield rich response.  A couple of representative papers are here and here, and recently they've been moving into 3D fabrication and magnetically sensitive imaging.  Very neat stuff.  
• Christian Glatti from Saclay showed a very interesting result, analogous to the ac Josephson effect, but in fractional quantum Hall edge-state tunneling.  The relevant paper, just out in Science, is here.  This idea is, measure electronic shot noise as a function of bias voltage.  Ordinarily this has a minimum at zero bias, and the noise sits at the Johnson-Nyquist level there.  Now shine microwaves of frequency f on the device.  With photon-assisted tunneling, the net result is a change in the noise that has kinks at voltages of +/- hf/e*, where h is Planck's constant, and e* is the effective charge of the low-energy excitations.  Do this in the fractional quantum Hall regime, and you see fractional charge.  
• On a related topic, Michael Pepper from Cambridge showed a very recent result.  In quantum point contacts at very low charge carrier densities, they see quantized conductance at some very surprising rational fractions of the usual conductance quantum 2e²/h.  I still need to digest this.  
• I spent much of the afternoon at the big Kavli Symposium, on topics spanning from unit cell all the way to biological cells.  All excellent speakers.  I won't try to summarize this - rather, when the talks become available streaming, I will put the link here.  (Claudia Felser did bring donuts for the audience to talk about topology, always a crowd-pleaser.)

APS March Meeting, Day 2

A random selection from Day 2:

• Thomas Silva at NIST gave a fun talk about some experiments using the linac coherent light source.  Using pump/probe time-resolved x-ray diffraction, they discovered some surprising acoustic modes in thin, polycrystalline metal films, with systematics suggesting that they might be seeing localization of phonons due to scattering off grain boundaries.
• Along those lines, Gang Chen of MIT spoke about seeing reductions in thermal conductivity due to phonon localization.  His group was working with semiconductor superlattices, with little ErAs nanodots embedded in a disordered way at the superlattice interfaces.  They see systematics in the thermal conductivity that suggest that they are seeing Anderson localization of the heat-carrying phonons.  
• I stopped by the session on conveying physics to a popular audience, and caught most of the talk by Allison Eck chock full of advice for would-be science writers, and a skyped-in talk by Sean Carroll about podcasting.  The depressing truth: If I really want to expand my audience, I should probably join twitter.  (The problem is, that's a conversational medium and I don't see how I could do it well given everything else.)
• Abe Nitzan gave a prize talk that was a nice overview of the last decade's work on understanding electrons, photons, and phonons in molecular junctions.
• I spent much of the afternoon at this session about the copper oxide superconductors.  Dan Dessau's talk primarily about this paper showed the capabilities of a new technique in analyzing angle-resolved photoemission data, to figure out the actual spatial shape of Cooper pairs in these systems. My collaborator Ivan Bozovic spoke (similar to this), showing the power of his tremendous MBE growth approach, able to create epitaxially perfect materials smoothly and systematically spanning the whole doping range.  The other talks in the session were also very interesting.

APS March Meeting, Day 1

A few things I saw at the APS Meeting today, besides 10 inches of fresh, wet snow on the ground this morning (disclaimer:  for various reasons I was session-hopping quite a bit, so this is rather disjointed):

• Ignacio Franco at Rochester spoke about some experiments (here) that I'd not remembered, where carefully controlled, intense femtosecond light pulses were used to turn on a transient current in SiO₂, normally one of the best insulators out there.  The theory is interesting, and made me start thinking about possible opportunities in this area.
• A focus topic session on 2D magnetic materials was extremely crowded - so much so that I literally couldn't get in the room for the first talk.  Interesting talks, including Yujun Deng from Fudan presenting this work; Masaki Nakano from the University of Tokyo spoke about growing epitaxial films of V₅Se₈, a cousin of a material with which we've worked; and Boyi Zhou at Washington University in St. Louis presented this work, which seems to show nontrivial electronic conduction in (ordinarily Mott insulating) monolayer RuCl₃ layered on graphene.  Lots of interesting activity going on here, many fun ideas.
• Naomi Ginsberg at Berkeley talked about some impressive imaging techniques used to follow energy flow in complex materials.  Combining super-resolution methods, interferometry, and time-resolved techniques is a heck of an enabling technique!
• Peter Abbamonte at Illinois presented some remarkable measurements using an angle-resolved electron energy loss technique (M-EELS) to look at the strange metal state of a cuprate superconductor.  The main result is that this material seems to support a very broad plasmon mode with a lot of properties that are inconsistent with what you'd expect in a Fermi liquid, and may make connection with more exotic pictures of strange metals.  
• Wojciech Zurek's talk about the foundations of quantum mechanics (based on this article) was very engaging (and apparently in a superposition of all possible fonts), though again the room was so full that people were sitting on the floor in the aisles and lining three walls.  The session also was running about 10 minutes ahead of schedule, which definitely was not great for people who ended up missing the beginning of Zurek's talk or Rovelli's before it.

The unwieldy size of the meeting is increasingly clear, with lines in the restrooms, and local fastfood places unable to handle the lunch crowd.  

APS March Meeting, Day 0

A brief summary of topics/reading material/things I learned today during DCMP and joint DCMP/DMP executive committee meetings:

• As usual, this will be the biggest March Meeting ever, with 11500 registrants ahead of time.  This is still increasingly problematic in terms of organization and availability of sites.
• New APS Strategic Plan
• New APS report on the Impact of Industrial Physics on the US Economy
• DOE Basic Energy Sciences report (pdf) on the impact of the BES at its 40th anniversary
• The upcoming privatization of the US Strategic Helium Reserve looks depressingly unavoidable.  Sounds like changing this is a non-starter in Congress.

Michelle Simmons and Si-based quantum computing

A last tidbit before the March Meeting.

Earlier this week, Prof. Michelle Simmons came to Rice for our Chapman Lecture series and gave a great talk about her team's project to develop quantum computing in a silicon platform, with individual phosphorus donor atoms as the qubits.   This idea goes back more than twenty years to this proposal by Bruce Kane.   Actually implementing this approach requires overcoming many technical challenges, including positioning individual phosphorus atoms inside single-crystal Si with nearly atomic precision, and similarly fabricating control and read-out electrodes in registry with those.  

Prof. Simmons' group has made truly remarkable progress in this direction.  The key enabling technique is using a scanning tunneling microscope (STM) as a lithography tool.  Single-crystal Si surfaces are prepared in ultrahigh vacuum and terminated with a hydrogen.  The STM tip is then used to strip off the hydrogen atoms with atomic precision.  (This is a serial technique, and so scaling up to the production numbers of the present-day Si industry would require something different, but for now it's fine.)  Phosphine gas decomposes in a particular way when exposed to the dangling bonds left behind by stripping the hydrogen, placing P atoms in particular locations.  This approach can also be used to make highly conductive wires and gates by doping, enabling transport measurements through single dopant atoms.   Growing more single-crystal Si on top of the dopants without having the dopants move around is another success story, making possible 3D fabrication schemes.  With isotopically pure Si, encapsulating the donors can give long coherence times.

There are many competing platforms for possible quantum computer implementations, and this approach is undoubtedly difficult.  In terms of technical achievement, though, this effort has shown the power of sustained support - progress has been truly impressive.