Quantum magic squares

Quantum magic squares

In a new paper in the Journal of Mathematical Physics, Tim Netzer and Tom Drescher from the Department of Mathematics and Gemma De las Cuevas from the Department of Theoretical Physics have introduced the notion of the quantum magic square, which is a magic square but instead of numbers one puts in matrices.

This is a non-commutative, and thus quantum, generalization of a magic square. The authors show that quantum magic squares cannot be as easily characterized as their “classical” cousins. More precisely, quantum magic squares are not convex combinations of quantum permutation matrices. “They are richer and more complicated to understand,” explains Tom Drescher. “This is the general theme when generalizations to the non-commutative case are studied. Check out the paper!

Quantum magic squares: Dilations and their limitations: Journal of Mathematical Physics: Vol 61, No 11
— Read on aip.scitation.org/doi/10.1063/5.0022344

Fluorescent Platypuses (??)

I was pleasently surprised and bewildered about this article in the New York Times reporting on a recent paper in the journal Mammalia about fluorescence being observed in platypuses when shining ultraviolet light on them… Yes! Not only are platypuses the most extraordinary collection of oddities from being mammals that lay eggs, webbed feet and duck-like bills as well as being venomous… and now they also fluoresce!

Now it is nothing strictly new. As Cara Giamo reports in the NYT article “A lot of living things do, too.” (That is fluoresce). Scorpionslichens and puffin beaks all pop under UV light. As far as mammals go not many have this ability, but there are some examples such as a rainbow of opossums or a bright pink flying squirrel.

As to why the platypus fluoresces, well, that remains a mystery!

2020 Nobel Prize in Physics – Black holes

I had intended to post this much ealier on, and certainly closer to the actual announcement of the Nobel Prizes in early October. It has however been a very busy period. Better late than never, right?

I was very pleased to see that the winners of the 2020 Nobel Prize in Physics were a group that combined the observational with the theoretical. Sir Roger Penrose, Reinhard Genzel, and Andrea Ghez are the recipients of the 2020 Nobel Prize in Physics. Penrose receives half the 10 million Swedish krona while Ghez and Genzel will share the other half.

Penrose’s work has taken the concept of black holes from the realm of speculation to a sound theoretical idea underpinning modern astrophysics. With the use of topology and general relativity, Penrose has provided us with an explanation to the collapse of matter due to gravity leading to the singularity at the centre of a black hole.

A few decades after the 1960’s work from Penrose we have Genzel and Ghez whose independent work using adaptive optics and speckle imaging enabled them to analyse the motion of stars tightly orbiting Sagittarius A*. Their work led to the conclusion that the only explanation for the radio source at the centre of the Milky Way’s was a black hole.

Ghez is the fourth woman to be named a Nobel physics laureate, after Donna Strickland (2018), Maria Goeppert Mayer (1963), and Marie Curie (1903).

From an Oddity to an Observation

In 1916 Karl Schwarzwild described a solution to Einstein’s field equation for the curved spacetime around a mass of radius r. Some terms in the solution either diverged or vanished for r=\frac{2GM}{c} or r=0. A couple of decades later, Oppenheimer and his student Hartland Snyder realised that the former value corresponded to the radius within which light, under the influence of gravity, would no longer be able to reach outside observers – the so called event horizon. Their work would need more than mathematical assumptions to be accepted.

By 1964 Penrose came up with topological picture of the gravitational collapse described and crucially doing so without the assumptions made by Oppenheimer and Snyder. His work required instead the idea of a trapped surface. In other words a 2D surface in which all light orthogonal to it converges. Penrose’s work showed that inside the event horizon, the radial direction becomes time-like. It is impossible to reverse out of the black hole and the implication is that all matter ends up at the singularity. Penrose’s research established black holes as plausible explanation for objets such s quasars and other active galactic nuclei.

Closer to Home

Although our own galaxy is by no means spewing energy like your average quasar, it still emits X-rays and other radio signals. Could it be that there is a black hole-like object at the heart of the Milky Way? This was a question that Genzel and Ghez would come to answer in time.

With the use of infrared (IR) spectroscopy, studies of gas clouds near the galactic centre showed rising velocities with decreasing distances to the centre, suggesting the presence of a massive, compact source of gravitation. These studies in the 1980s were not definitive but provided a tantalising possibility.

In the mid 1990s, both Genzel and Ghez set out to obtain better evidence with the help of large telescopes operating in the near-IR to detect photons escaping the galactic center. Genzel and colleagues began observing from Chile, whereas Ghez and her team from Hawaii.

Their independent development of speckle imaging, a technique that corrects for the distortions caused by Earth’s atmosphere enabled them to make the crucial observations. The technique improves the images by stacking a series of exposures, bringing the smeared light of individual stars into alignment. In 1997, both groups published their measurements stars movements strongly favouring the black hole explanation.

Further to that work, the use of adaptive optics by both laureates not only improved the resolutions obtained, but also provided the possibility of carrying out spectroscopic analyses which enabled them to get velocities in 3D and therefore obtain precise orbits.

The “star” object in this saga is the so-called S0-2 (Ghez’s group) or S2 (Genzel’s group) star. It approaches within about 17 light-hours of Sagittarius A* every 16 years in a highly elliptical orbit.

Congratulations to Ghez and Genzel, and Penrose.

Let there be light: Florence Nightingale

This year, 2020, the word Nightingale has acquired new connotations. It is no longer just a word to refer to a passerine bird with beautiful and powerful birdsong, it is the name that NHS England has given to the temporary hospitals set up for the COVID-19 pandemic. In normal circumstances it is indeed a very good name to use for a hospital, but given the circumstances, it becomes more poignant. It is even more so considering the fact that this year, 2020, is the bicentenary go Florence Nightingale’s birth.

Florence Nightingale was born on 12th May, 1820 in Florence, Italy (hence the name!) and became a social reformer, statistician, and the founder of modern nursing. She became the first woman to be elected to be a Fellow of the Royal Society in 1874.

With the power of data, Nightingale was able to save lives and change policy. Her analysis of data from the Crimean War was compelling and persuasive in its simplicity. It allowed her and her team to pay attention to time – tracking admissions to hospital and crucially deaths – on a month by month basis. We must remember that the power of statistical tests as we know today were not established tools and the work horse of statistics, regression, was decades in the future. The data analysis presented in columns and rows as supported by powerful graphics that many of us admire today.

In 2014 had an opportunity to admire her Nightingale Roses, or to use its formal name polar area charts, in the exhibition Science is Beautiful at the British Library.

Florence Nightingale’s “rose diagram”, showing the Causes of Mortality in the Army in the East, 1858. Photograph: /British Library

These and other charts were used in the report that she later published in 1858 under the title “Notes in Matters Affecting the Health, Efficiency, and Hospital Administration of the British Army”. The report included charts of deaths by barometric pressure and temperature, showing that deaths were higher in hotter months compared to cooler ones. In polar charts shown above Nightingale presents the decrease in death rates that have been achieved. Let’s read it from her own hand; here is the note the accompanying the chart above:

The areas of the blue, red & black wedges are each measured from the centre as the common vortex.

The blue wedges measured from the centre of the circle represent area for area the deaths from Preventible or Mitigable Zymotic diseases, the red wedged measured from the centre the deaths from wounds, & the black wedged measured from the centre the deaths from all other causes.

The black line across the read triangle in Nov. 1854 marks the boundary of the deaths from all other caused during the month.

In October 1854, & April 1855, the black area coincides with the red, in January & February 1855, the blue area coincides with the black.

The entire areas may be compared bu following the blue, the read & the black lines enclosing them.

Nightingale recognised that soldiers were dying from other causes: malnutrition, poor sanitation, and lack of activity. Her aim was to improve the conditions of wounded soldiers and improve their chances of survival. This was evidence that later helped put focus on the importance of patient welfare.

Once the war was over, Florence Nightingale returned home but her quest did not finish there. She continued her work to improve conditions in hospitals. She became a star in her own time and with time the legend of “The Lady with Lamp” solidified in the national and international consciousness. You may have heard of there in the 1857 poem by Henry Wadsworth Longfellow called “Santa Filomena”:

Lo! in that house of misery
A lady with a lamp I see
Pass through the glimmering gloom,
And flit from room to room

Today, Nightigale’s lamp continues bringing hope to her patients. Not just for those working and being treated in the NHS Nightingale hospitals, but also to to all of us through the metaphorical light of rational optimism. Let there be light.

Screencasting with Macs and PCs

The videos below were made a few years ago to support a Science Communication and Group Project module at the School of Physics Astronomy and Mathematics at the University of Hertfordshire. The work was supported by the Institute of Physics and the HE STEM programme. I also got support from the Institute of Mathematics and its Applications. The tools are probably a bit dated now, but I hope the principles still help some students trying to get their work seen.

Students were asked to prepare a short video to present the results of their project and share it with the world. To support them, the videos below were prepared.

Students were also encouraged to prepare technical documentation and the videos for using LaTeX and structuring their documents with LaTeX were very useful.

Screencasting with a Mac

In this video we will see some tools to capture video from your screen using a Mac. The tools are Quicktime Player, MPEG Streamclip and iMovie.

Screencasting with a PC

In this video we will see some tools to capture video from your screen using a PC. The tools are CamStudio and Freemake Video Converter.

Uploading a Video to Vimeo

In this tutorial we will see how to set up an account in Vimeo and how to upload your screencast. Also you will be able to send a link to your video to you friends and other people.

2019 Nobel Prize in Chemistry

From left: John Goodenough, M. Stanley Whittingham, and Akira Yoshino. Credits: University of Texas at Austin; Binghamton University; the Japan Prize Foundation

Originally published in Physics Today by Alex Lopatka

John Goodenough, M. Stanley Whittingham, and Akira Yoshino will receive the 2019 Nobel Prize in Chemistry for developing lithium-ion batteries, the Royal Swedish Academy of Sciences announced on Wednesday. Goodenough (University of Texas at Austin), Whittingham (Binghamton University in New York), and Yoshino (Asahi Kasei Corp and Meijo University in Japan) will each receive one-third of the 9 million Swedish krona (roughly $900 000) prize. Their research not only allowed for the commercial-scale manufacture of lithium-ion batteries, but it also has supercharged research into all sorts of new technology, including wind and solar power.

At the heart of any battery is a redox reaction. During the discharge phase, the oxidation reaction at the anode frees ions to travel through a liquid electrolyte solution to the cathode, which is undergoing a reduction reaction. Meanwhile, electrons hum through a circuit to power a connected electronic device. For the recharge phase, the redox processes reverse, and the ions go back to the anode so that it’s ready for another discharge cycle.

The now ubiquitous lithium-ion battery that powers smartphones, electric vehicles, and more got its start shortly before the 1973 oil crisis. The American Energy Commission asked Goodenough, who was then at MIT’s Lincoln Laboratory, to evaluate a project by battery scientists at the Ford Motor Company. They were looking into the feasibility of molten-salt batteries, which used sodium and sulfur, to replace the standard but outdated lead–acid batteries developed about a century earlier. But by the late 1960s, it became clear that high operating temperatures and corrosion problems made those batteries impractical (see the article by Matthew Eisler, Physics Today, September 2016, page 30).

Whittingham, then a research scientist at Exxon, instead considered low-temperature, high-energy batteries that could not only power electric vehicles but also store solar energy during off-peak hours. To that end he developed a battery in 1976 with a titanium disulfide cathode paired with a lithium metal anode. Lithium’s low standard reduction potential of −3.05 V makes it especially attractive for high-density and high-voltage battery cells. Critically, Whittingham’s design employed lithium ions that were intercalated—that is, inserted between layers of the TiS2 structure—and provided a means to reversibly store the lithium during the redox reactions.

Illustration of Whittingham's battery.
The lithium-ion battery designed by M. Stanley Whittingham had a titanium disulfide cathode and a lithium metal anode, as illustrated here. John Goodenough and Akira Yoshino improved on the technology by replacing the cathode and anode with lithium cobalt oxide and graphite, respectively. Credit: Johan Jarnestad/The Royal Swedish Academy of Sciences

Lithium’s high reactivity, however, means that it must be isolated from air and water to avoid dangerous reactions. Whittingham solved that problem by using nonaqueous electrolyte solutions that had been carefully designed and tested by other researchers in lithium electrochemistry experiments conducted a few years earlier. The proof of concept was a substantial improvement: Whittingham’s lithium-ion battery had a higher cell potential than the lead–acid battery’s—2.5 V compared with 2 V.

Whittingham’s lithium-ion battery, though, wasn’t particularly stable. After repeated discharging and recharging, whisker-like crystals of lithium would grow on the anode. Eventually the wispy threads would grow large enough to breach the barrier separating the anode from the cathode, and the battery would short-circuit or even explode.

In 1980 Goodenough didn’t solve that problem, but he did come up with a much better material for the cathode. Along with Koichi Mizushima and colleagues at Oxford University, he found that lithium cobalt oxide could be used for the cathode. As with the TiS2, the cobalt oxide structure was tightly intercalated with lithium and could thus provide the cathode with sufficient energy density. Goodenough’s insight into the relationship between the cobalt oxide structure and voltage potential resulted in better battery performance; the voltage increased from 2.5 V to 4 V. Although the new battery was an improvement over Whittingham’s design, the system still used highly reactive lithium metal as the anode, so companies couldn’t safely manufacture the batteries on a commercial scale.

The final piece of the puzzle fell into place in 1985 when Yoshino, working at the Asahi Kasei Corp, replaced the anode material with graphite. It was stable in the required electrochemical conditions and accommodated many lithium ions in graphite’s crystal structure. With Goodenough’s lithium cobalt oxide cathode and the graphite anode, Yoshino, “came up with two materials you could put together without a glove box” in a chemistry laboratory, says Clare Grey, a chemist at the University of Cambridge. Importantly, the graphite anode is lightweight and capable of being recharged hundreds of times before its performance deteriorates. Soon after, Sony teamed up with Asahi Kasei and replaced all the nickel–cadmium batteries in its consumer electronics with lithium-ion ones.

“The story of the lithium-ion battery, like so many stories about innovation, is about contributions from many sources over many years, conditioned by changing economic and social circumstances,” says Matthew Eisler, a historian of science at the University of Strathclyde in Glasgow, UK. When the 1979 oil crisis ended, the automotive industry’s interest in batteries drained, but in 1991 they were commercialized for use in cameras, laptops, smartphones, and other handheld electronics enabled by advancements in microprocessor technology.

To develop transportation that doesn’t rely on fossil fuels, the US Department of Energy in 2013 set an ambitious goal for its Joint Center for Energy Storage Research: Make a battery for electric vehicles that has five times the energy density and is one-fifth the cost of currently available batteries. DOE’s goal hasn’t been reached yet, but the program was renewed in September 2018, with dedicated funding of $120 million over the next five years. In a story on the center, Goodenough told Physics Today (June 2013, page 26), “People are working hard, and I believe the problem is solvable, but to get to the next stage, it’s going to take a little luck and some cleverness.”

Editor’s note: This post was updated at 7:15pm EDT from an earlier summary.

The Year in Math and Computer Science

A reblog from Quanta Magazine:

https://www.quantamagazine.org/quantas-year-in-math-and-computer-science-2018-20181221/

Several mathematicians under the age of 30, and amateur problem-solvers of all ages, made significant contributions to some of the most difficult questions in math and theoretical computer science.

Youth ruled the year in mathematics. The Fields Medals — awarded every four years to the top mathematicians no older than 40 — went out to four individuals who have left their marks all over the mathematical landscape. This year one of the awards went to Peter Scholze, who at 30 became one of the youngest ever to win. But at times in 2018, even 30 could feel old.

Two students, one in graduate school and the other just 18, in two separate discoveries, remapped the borders that separate quantum computers from ordinary classical computation. Another graduate student proved a decades-old conjecture about elliptic curves, a type of object that has fascinated mathematicians for centuries. And amateur mathematicians of all ages rose up to make significant contributions to long-dormant problems.

But perhaps the most significant sign of youth’s rise was when Scholze, not a month after the Fields Medal ceremony, made public (along with a collaborator) his map pointing to a hole in a purported proof of the famous abc conjecture. The proof, put forward six years ago by a mathematical luminary, has baffled most mathematicians ever since.