Tuesday, November 25, 2008

A New Project for SETI

The Cepheid Galactic Internet

J.G. Learned, R.P. Kudritzki, S. Pakvasa, and A. Zee


URL: http://arxiv.org/abs/0809.0339

This paper puts forward an interesting proposition for intergalactic communication: frequency modulation of cepheid variable stars.

Cepheids are 1,000 to 10,000 times brighter than our sun and have regular, detectable variations in brightness with a period of 1-50 days. The frequency and luminosity are strongly correlated, so one can measure the period of the stars, deduce the luminosity, compare with the observed brightness, and determine how far away the star is. Parallax is used to calibrate the distance scale on nearby cepheids.

The authors of this paper propose that an advanced race might intentionally modify the period of these stars to send information throughout the galaxy: FM at very low frequencies!

The mechanism by which the brightness varies is similar to the charging and discharging of a capacitor. According to the authors, as the star consumes hydrogen through nuclear fusion, ionized helium builds up on the surface of the star. This decreases the luminosity and increases the temperature of the star. This is followed by "violent expansion and deionization," after which the cycle repeats.

It is interesting that an avalanche process like this leads to a regular cycle of variations in the brightness. The same thing happens in circuits with a capacitor (if I remember my physics lab correctly). A build up of charge is followed by dielectric breakdown (a spark) after which the process repeats. The spark frequency is constant. What makes these systems different from, say, a pile of sand? The avalanches in a sand pile have a power law distribution in both size and frequency. What makes the two systems so different? I assume the circuit and the cepheid have nice, normal, linear equations of motion while the sand pile is governed by nonlinear equations. But what parameter differentiates the two? Is there some control parameter in the circuit that would lead to a crossover between periodic sparks and a frequency distribution more like the avalanches in the sand pile?

I digress. The reason I described the process that gives rise to the periodic variations in a cepheid is that the authors claim it can be influenced by external agents. They suggest that the deionization could be triggered early with a sufficient burst of power. The variation in the period could be used to transmit messages. To make the star fire early, the authors suggest that a neutrino beam focused on the star's core might do the trick.

The authors suggest the neutrino beam could be generated by a large space station orbiting the star running on solar power. We've got a long way to go from our handheld calculators to star-altering neutrino beams! For a society that could build such a device, it would seem a simple matter to build the beacon and leave it in place.

So are aliens broadcasting over the cepheid Internet? The authors say it wouldn't be too hard to find out. Normally astronomers measure the average period of these variable stars. Averaging the data would, of course, wash out any signal. Rather than determining the average, one would simply have to bin the data and look for a splitting of the signal around the fundamental frequency.

The authors don't mention it, but one might also perform an entropy analysis of the time series data. A periodic source would have zero entropy, while a modulated source would appear more ergodic. This would be a secondary analysis. If a splitting of the fundamental peak in the frequency spectrum were observed, one would then analyze the time series data to see if the splitting is also periodic, or if it has more structure to it.

Calling this system a galactic Internet is a bit misleading. It's more like the galactic telegraph. An early flash corresponds to a 1, an on-time flash corresponds to 0. Only one bit can be sent per period, so the maximum transmission rate is on the order of 1 bit per month. It would take forever to download a page from Encyclopedia Galactica!

I wonder what types of message would be transmitted. There seem to be two schools of thought about aliens: the Star Trek school, and the Hitchhiker school. The former envision alien civilizations as refined, peaceful, rational, and technologically advanced. The latter imagine alien civilizations to be more like our own society, with profit-driven pleasure-seekers, petty bickering, advertising, and bureaucracy. Each would certainly use the galactic beacon to transmit different kinds of messages.

The Star Trek variety of civilization might use the beacon as a lighthouse, a simple welcome message for young civilizations pointing them to a source of information with more bandwidth, or a galactic emergency broadcast system. If the cepheids were run by Hitchhikers, we might instead find messages like "Tresspassers will be shot on sight" or "Eat at Joe's." Imagine, after years of trying to crack the code, we discovered the message to be

"At the next pulse, the current time will be ..."

Monday, November 24, 2008

Hidden Interactions?

Hidden One-Electron Interactions in Carbon Nanotubes Revealed in Graphene Nanostrips

C.T. White, J. Li, D. Gunlycke, and J.W. Mintmire

Nanoletters 7, 825--830 (2007)

URL: http://pubs.acs.org/doi/abs/10.1021/nl0627745

The authors explore the band gap of graphene nanoribbons. I was disappointed to discover that the "hidden interactions‚" they refer to are second and third nearest neighbor couplings that must be added to the tight binding model to reproduce the results of a density functional calculation. They predict that all armchair edge nanoribbons will have a gap.

These interactions are hidden in nanotubes because the curvature of a nanotube reduces the coupling between more distant neighbors. However, they should have been observable in large-radius nanotubes, in which curvature effects are very weak. The authors do not appear to have addressed this point.

I realize that density functional theory is a powerful tool for investigating the electronic structure of many materials. However, I do not know that it has been used successfully in graphene. Moreover, the authors state that the particular DFT package they used is "especially tailored to take advantage of helical symmetry"--- a symmetry possessed by carbon nanotubes, but not graphene nanoribbons. Moreover, claims that the method "has been successfully used in wide-ranging studies of single walled carbon nanotubes" only refer to studies carried out by the authors.

I am uncomfortable with the idea of taking an empirical model -- the tight-binding model for electrons in graphene -- and adjusting its parameters to fit the results of a density functional calculation. It would be a different matter entirely if the “hidden interactions” were necessary to fit experimental data.

I was discussing a similar idea with my adivsor the other day. We had just listened to a talk in which a biophysicist described the molecular dynamics simulations he had developed to study fluctuating membranes. Because the model reproduced some features of the experimental data, he inferred that the model captured some important physical property of the real system. White et al. do the same thing here, making the claim that because the amended tight-binding model reproduces the results of the DFT calculation, there must be 2nd and 3rd nearest neighbor interactions in graphene.

What this type of reasoning lacks is a proof of a one-to-one correspondence between models and the physical properties of the system. I.e., one would have to establish that a particular model is the only one they could generate a particular physical property before making any conclusions about real graphene samples or fluctuating membranes. I do not believe this type of correspondence exists. At best, one might be able to argue that the model and the physical system fall into the same universality class in the sense of the renormalization group.

In the end, experimental studies will determine whether or not these hidden interactions are physically relevant. The same experiments will also assess the validity of the DFT calculation. It will be interesting to see whether all armchair nanoribbons are semiconductors.

End Interlude

Well, another 9 months have passed since my last post. Although, judging from the comments, I'm the only one who noticed.

I'm back now, and I've read some interesting articles. Let's not delay any longer.

Monday, February 18, 2008

Welcome Back

It's been quite some time since my last post. All of my writing efforts have gone toward producing the first draft of my Ph.D. dissertation, The Effects of Static Electric Potentials on Single Electrons and Excitons in Carbon Nanotubes: A Theoretical Study. I'm just about done --- with the first draft. I've got a 200 page monster with no figures and incomplete references that I've got to hammer into shape by the middle of May, but it's a lot better than staring at a blank page!

Although I haven't posted anything recently, I've been reading a lot. Going over background materials for my dissertation reminded me of how fascinating semiconductor physics, quantum field theory, and excitons are! I've had some time for deviations from my primary research focus as well. My pile of interesting papers continues to grow, plus I've started reading some textbooks on econophysics and nonlinear dynamics. Fascinating stuff.

Hopefully I'll get back in the habit of posting regularly. I hope to make the blog more friendly to others too. It will still primarily focus on interesting papers I've read (I'm still worried that once they go into my filing cabinet, I may never be able to find them again...), but I'd like to make the blog into more of a journal than a database. Maybe we can get a little dialog going on some topics. Maybe I can sharpen my skills at explaining complicated things in simple terms. Maybe I'll be so busy finishing my dissertation and finding a job that I won't have time for anything else. Who knows?

Check back in from time to time to see what's new. And drop me an e-mail if you like.


Sunday, August 12, 2007

Peapods are the Same as Nanotubes

Transport Properties of Carbon Nanotube C_{60} Peapods

C.H.L. Quay, et al.

PRB 76, 073404 (2007)

URL: http://link.aps.org/abstract/PRB/v76/e073404

In this article, the authors present data that suggest room temperature transport properties of carbon nanotube peapods are basically the same as unfilled carbon nanotubes. The peapods are either semiconducting or metallic and there is a Coulomb blockade.

The authors are surprised by the similarities with unfilled nanotubes. Since the nanotubes tested were selected from an ensemble containing mostly --- but not all --- peapods, one possible explanation is that the authors happened to select 7 unfilled nanotubes from the ensemble. They present a Bayesian statistical analysis to show that the chance of that happening are small, and that the most likely number of peapods in the experiment is roughly 6 of 7.

The authors' conclusion is that the transport properties of fullerene peapods are not that different from unfilled nanotubes. Although their statistical analysis seems correct, they could bolster their claim with more samples. I share their initial surprise that a lattice of buckyballs inside a nanotube has virtually no effect on its transport properties.

If the authors are correct, there are no signatures of the buckyball lattice in the transport spectra of a nanotube. How else might one go about detecting them?

Tuesday, July 10, 2007

Photons and the Aharonov Bohm Effect

Bound on the Photon Charge from the Phase Coherence of Extragalactic Radiation

Brett Altschul

PRL 98, 261801 (2007)

URL: http://link.aps.org/abstract/PRL/v98/e261801

The conclusion of this paper will come as a surprise to very few people: the photon probably doesn't have a charge. Altschul, from Indiana University, has deduced an upper bound on the photon charge that is 32 orders of magnitude less than the electron charge (46 if photons have both a positive and a negative charge). It is his analysis rather than his conclusion that I found interesting.

Altshcul's analysis starts from the observation that we can use interferometry to study astrophysical objects. Basically, one collects light from the same source at two different receivers. By studying the interference between the signals at the two receivers, one can obtain information about the source object. For this to work, the light from the source must be coherent --- i.e., the phase difference between two photons traveling along the same path must be small compared to the phase difference they acquire due to the path difference between the two receivers.

Altschul points out a source of phase difference that does not immediately come to mind: the Aharonov-Bohm Effect. If photons have a charge, then photons at the two detectors of an interferometer will acquire a phase difference that depends on the magnetic flux through the triangle made up of the two detectors and the source. (The assumption here is that a charged photon would interact with an external electromagnetic field exactly the same way an electron does.) The fact that interferometry works means the Aharonov Bohm phase small. (Conservatively, Altschul interprets "small" as "less than one".)

Making order of magnitude estimates for the interstellar magnetic field and using the baseline of the Very Long Baseline Interferometry Space Observatory Program (VSOP) with a source distance of 1 Gpc (about 3 billion light years), Altschul places an upper bound of 10^{-32} on the ratio of the photon charge to the electron charge.

The small bound is possible because of the huge distances involved in astronomical observations. It's almost like running a lab experiment designed to probe the Aharonov Bohm effect for 3 billion years --- that's a lot of data!

If the photon can have both positive and negative charges (like electrons) or positive, negative, and neutral charges (like pions), then the bounds are even tighter. This is because the Aharonov Bohm phase is proportional to the charge of the particle. If a particle with positive charge and a particle with negative charge travel along the same path, they acquire equal and opposite phases. If photons have two charges, the fact that interferometry works places an upper limit of 10^{-46} on the ratio of photon and electron charges.

The major source of uncertainty in this analysis is the current lack of understanding regarding interstellar magnetic fields. Perhaps Altschul's study will inspire new methods of studying these fields using interferometry.

As I said, the fact that the one can place a very small upper bound on the photon charge is not surprising. The fact that it can be done by analyzing the Aharonov Bohm effect is.

Altschul mentions a couple interesting facts about the theory of photons. First, the problem of the photon mass has been studied much more than that of photon charge. He mentions three theories of photon mass (Proca, Higgs, and Stuckleberg). I've never heard of the third. He also points out that not much is known about the consequences of charged photons. This is surprising, given the large number of models studied in quantum field theory --- many of which have little relevance to the physical world as revealed by experiments. It sounds like the kind of problem one might find at the end of a chapter in Peskin and Schroeder.

Wednesday, July 4, 2007

Relativity on the Table-Top

Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion

L. Lamata, J. Leon, T. Schatz, and E. Solano

PRL 98, 253005 (2007)

URL: http://link.aps.org/abstract/PRL/v98/e253005

In this article, the authors demonstrate the experimental possibility of simulating a Dirac Hamiltonian in an atomic system. In short, they propose a table-top experiment that would probe the effects of a relativistic system.

The requirements are relatively modest. To simulate the (1+1)-D or (2+1)-D Dirac equation, one needs a two-level atomic system; for the (3+1)-D Dirac equation, one needs a 4-level system. Three types of couplings are also required:
• Carrier Interaction -- a resonant coupling between two of the internal atomic states (such as a laser tuned to the transition frequency).
• Jaynes-Cummings Interaction -- couples two internal states with a vibrational mode of the center of mass. An upward transition between internal states is accompanied by the destruction of a phonon.
• Anti-Jaynes-Cummings Interaction -- also couples two internal states with a vibrational mode, but the frequency is tuned so that an upward transition between is accompanied instead by the creation of a phonon.

When the phases of the laser fields used to generate the above interactions are appropriately tuned, the effective Hamiltonian for the two-level or four-level system is identical in form with the free Dirac equation. By varying the couplings, one can tune the effective particle mass and velocity of light.

The authors dedicate a lot of space to a discussion of Zitterbewegung, which is a rapid oscillatory motion of an electron about its mean position. It was predicted in 1930 by Schrodinger, but has not yet been observed experimentally. For electrons, the amplitude of the oscillations is on the order of 10^{-13} m, and the frequency is on the order of 10^{21} Hz. In addition, Zitterbewegung is an effect of the single-particle Dirac equation. There is some controversy over whether or not the effect persists in QED.

The authors point out that by controlling the effective electron mass and the effective speed of light, one should be able to bring the amplitude and frequency of the oscillations into an experimentally accessible range. Another point they don't mention: even if the effect does not occur for real electrons, the dynamics of their atomic system are (in theory) accurately described by a single-particle Dirac equation. Whether or not real electrons jitter around, the trapped ions on their desks should.

The authors mention a few other relativistic effects that might be simulated: by controlling the particle mass, one could observe something akin to the Higgs mechanism for mass generation; one could simulate the Klein paradox, in which particle-hole pairs are created in a strong potential; one could simulate a (1+1)-D axial anomaly, the lower-dimensional counterpart of the chiral anomaly in (3+1)-D.

The possibility of tuning the parameters of the Dirac equation is interesting. However, such simulations of relativistic systems is a bit perplexing. A similar situation exists in the theory of graphene and carbon nanotubes, where the low-energy excitations are described by a Dirac equation. On a very fundamental level, the simulation can't be right. So how far can one push the analogy?

How similar are a pseudospinor and a spinor? Electron spin has to do with angular momentum, but pseudospin has nothing to do with it. The simulated system can't have pseudospin-orbit coupling, but the Dirac equation can.

How effective is an effective speed of light? In the table-top simulation, nothing prohibits the electron or the center of mass of the ion system from exceeding the effective speed of light. What then? Would the authors claim they were simulating tachyons?

In the Klein paradox, where are the holes going to come from? No corresponding anti-cesium ion is going to materialize in the trap.

It would be quite interesting to probe these unphysical effects in a trap and see exactly how the effective Dirac physics breaks down.

A final note: This was a well-written paper, but I must criticize the authors for a particular choice of phrase. On page 2, they refer to the "notorious analogy" between the Dirac equation and the effective Hamiltonian of the trapped ion. Jesse James was notorious. The three-body problem is notoriously difficult. An analogy between Hamiltonians is not "famous or well known, typically for some bad quality or deed."