Page 1301 – Physics World

Home » Page 1301

An afternoon of quantum theory

By Louise Mayor

Yesterday I had an exciting trip out of the office.

Earlier this week, one of Physics World’s freelance writers, Jon Cartwright, told how me he’d been invited to the Bristol University theory department’s weekly seminar. Felix Flicker, a 2nd-year PhD student who organizes these events, had seen Jon’s article “The life of psi” in this month’s Physics World, which discusses a theorem published in Nature Physics. The theorem is interesting because if its assumptions hold, it rules out one of the four interpretations of quantum mechanics and leaves us with three.

I wanted in on the seminar action!

Last year when I was planning the Physics World special issue on quantum frontiers (which was out in March and is still available as a free PDF download), I had approached Jon to ask whether he’d like to tackle a quantum topic, and he let me know he was interested in covering the paper by Matthew Pusey, Jonathan Barrett and Terry Rudolph. Jon had seen the story reported elsewhere but had found these accounts were light on the details and didn’t get to the bottom of the science. I liked the idea and Jon went ahead. Once the story arrived in my inbox I was hooked! I found it to be one of those stories that covers some tricky concepts but if you let yourself become immersed in the story and think through what’s being explained, is very rewarding.

(more…)

Do you try to pronounce physics terms as they sound in their language of origin?

By Hamish Johnston

German words in the physicist’s lexicon. (Image by Mathew Ward)

Like many disciplines, physics incorporates words from a number of different languages – and this can often leave a physicist tongue-tied.

How should a native English speaker pronounce Einstein, for example? Should it be the Germanic “Ein-shtein” or the anglicized “Ein-stein”? How should one say De Broglie, Raman or Bernoulli? Should a native English speaker even attempt zitterbewegung, or translate it to “trembling motion”?

I’m sure that some physics terms of English origin are tricky for native speakers of other languages, and their pronunciations are sometimes adjusted accordingly.

Some believe that making an effort to use the original pronunciation shows respect and knowledge of the origin of a word. Others are happy to use the pronunciation they are most comfortable with.

(more…)

Bose–Einstein condensate is in the can

Calculating the properties of a quantum particle in a box is something most physics students have to do as part of their degree course – but actually creating such a simple system in the lab can be an experimental challenge. Now, however, physicists in the UK are the first to create a Bose–Einstein condensate (BEC) in a 3D optical-box trap, which resembles a tin can. The breakthrough could allow physicists to study a range of multi-body physics phenomena in controlled conditions.

The first BEC was made in 1995 in Nobel-prize-winning work that involved cooling a cloud of rubidium-87 atoms down to temperatures of near absolute zero. The atoms settle into a quantum state that extends over a macroscopic volume, which means that the BEC behaves like a superfluid. In addition to being fascinating in their own right as a new state of matter, BECs are interesting because they are created under very controlled conditions, which allows them to be manipulated to resemble a variety of quantum phenomena.

Earlier this year, for example, physicists carried out an experiment in which a BEC behaved much like a Josephson junction – a device that is normally make from a superconductor. As such, BECs can be used as “quantum simulators” to gain a better understanding of less-accessible quantum systems, ranging from magnets to superconductors and neutron stars. Unfortunately, physicists have so far only been able to create BECs in traps where the trapping potential – and so the atomic density – varies harmonically, which is no good for anyone simulating, say, electrons in solids, as these systems tend to have homogenous particle densities.

Lids on a tin can

Now, however, Zoran Hadzibabic and colleagues at the University of Cambridge are the first to create a BEC in a 3D trap that – for most practical purposes – has a constant potential in all three directions. “Our trap is an optical box made out of green light: a dark region of empty space is surrounded by thin walls of light that repel the atoms and keep them confined inside the box,” says Hadzibabic.

His team created the box by imprinting a phase pattern onto a conventional laser beam. The result is a hollow tube of green laser light and two “sheet-shaped” laser beams lying perpendicular to the tube. “The beams form the end lids that close up our optical tin can,” says Hadzibabic. The effects of gravity, which would otherwise distort the box, were eliminated by suspending the atoms using a magnetic field.

Before creating the BEC, Hadzibabic’s team had to cool down a cloud of rubidium-87 atoms to nanokelvin temperatures. This involved first gradually lowering the harmonic trapping potential so that faster-moving hot atoms escape the trap, leaving only cooler atoms behind. As it undergoes this process of “evaporative cooling”, the cloud shrinks until it is small enough to fit inside the optical box. The box is then switched on and the harmonic trap is turned off slowly.

The next step involves subjecting the atoms to a final round of evaporative cooling to get the gas to a temperature of below about 90 nK, where it turns into a BEC. This was done by adjusting the intensity of the laser light that creates the walls of the trap. Faster-moving hot atoms were able to penetrate the walls and exit the trap, while the cooler atoms cannot – causing evaporative cooling.

Einstein’s right again

To confirm that they actually had a BEC in a uniform potential, the researchers turned off the box trap and let the gas expand freely while measuring the velocity distribution of the atoms. A large peak at very low velocity confirmed that a BEC had formed and the shape of the peak contained information about the shape of the box trap. The velocity distribution also revealed the temperature below which the atoms condensed into a BEC. This temperature was first predicted by Einstein in 1925 and Hadzibabic says their analysis is the best experimental confirmation so far.

While the box trap is a good approximation to a constant potential in 3D, it is not perfect, although Hadzibabic argues that it is good enough for most applications. “In our trap,” he says, “we can estimate that more than 80% of the atoms live within the region where the density deviates by less than 10% from the average value, so these atoms should heavily dominate all experimental signals.” In contrast, less than 20% of the atoms in a conventional harmonic trap lie in a region that is representative of the average density.

Focus on phase transitions

Now that they have created a near-homogenous BEC, the researhcers are keen to use it to simulate a range of quantum systems. In particular, the set-up should be good for studying how a system makes the phase transition from a cold gas to a BEC. The team’s first target is to study the effects of inter-particle interactions on Bose–Einstein condensation of a homogeneous gas or fluid. This problem was first proposed in 1957 by Chen Ning Yang and Tsung-Dao Lee – Chinese-American physicists who also won the Nobel prize that year for unrelated work on particle physics.

“This problem has been studied in liquid helium, but many questions remain open and the agreement between theory and experiment has not been reached,” explains Hadzibabic. The team is also looking at doing other experiments in which the interactions between atoms can be fine-tuned. This will involve modifying the experiment to use potassium-39, which is more difficult to trap but better for creating tuneable interactions.

The results are described in Physical Review Letters and a preprint is available on arXiv.

Google and NASA acquire a D-Wave quantum computer

D-Wave’s Geordie Rose with one of the firm’s quantum computers. (Courtesy: D-Wave)

By Hamish Johnston

Canada’s D-Wave Systems is installing one of its quantum computers at NASA’s Ames Research Center in California. The new 512-qubit system – dubbed D-Wave Two – will be used by NASA, Google and the Universities Space Research Association (USRA) to investigate how quantum computers could be used to solve a range of different problems. According to Vancouver-based D-Wave, the computer will be available for use in the third quarter of this year.

(more…)

Consciousness from the ground up

The book Physics in Mind: a Quantum View of the Brain certainly aims high. Written by the eminent biophysicist Werner Loewenstein, its goal is nothing less than a theory that explains our sense of conscious existence, built from the bottom up. Remarkably, Loewenstein’s arrows of explanation hit their target almost all the time, even though the promise implied in the book’s subtitle remains tantalizingly just out of range.

This book is a fantastic journey for any reader, but especially for a physicist. In Loewenstein’s account, life is a delicate dance between the bits of information and quantized chunks of energy that drive all biological processes. Accordingly, he takes us on an intellectual rollercoaster ride through the microscopic world of signalling molecules, autocatalytic sets, DNA, RNA, natural selection and the electromechanics of cell membranes – before culminating in an account of quantum computing and the role of quantum mechanics in the brain.

The book begins with the relationship between the human sense of time and the abstract concept of time in physics. An exposition of the various “arrows of time” – perceptual, thermodynamic and cosmological – leads up to a discussion of the basic mechanisms of molecular signalling in living systems. Loewenstein takes as his central model Maxwell’s famous demon (see April pp36–39), which gets information about the microscopic motions of molecules and uses that information to reduce entropy. The author encourages the reader to think of all molecular information processing in demonic terms, since a wealth of biological processes – the function of ion channels, photosynthesis, the detection of light in the eye, the absorption of scents by receptors in the nose and many more – all operate via the interplay between information and energy at the microscopic scale.

Loewenstein’s choice to describe biological information processing in terms of “demons” that deal in information and energy is a wise one. By providing a central metaphor for the microscopic mechanisms of biological signalling, he supplies a unified picture of how the brain gathers to it the material of sensation. Our eyes and nose, for example, offer us very different senses of our surroundings; but when one describes them in terms of the dance of information and entropy, it becomes clear that they function in very similar ways. A single photon passing through the lens of the eye excites a molecule of rhodopsin, pushing open an ion channel that excites a neural signal. A single molecule locks into an odour receptor in the nose, allowing charge to flow in a way that again excites a neural signal. The steps in each dance are different, but the results are the same: a slight difference in our surroundings is amplified into a perceived difference in our brain.

At this point, the book transits from the solid ground of molecular biology to the more speculative territory of human perception. Here, too, Loewenstein exhibits sure hands. He admits that we don’t know just how conscious awareness works, but gives hints and clues to the evolutionary origins of perception, and to the way in which the brain integrates the products of the sensory apparatus. He draws on the recent comprehensive investigations of how neural circuitry functions to recognize patterns and extract correlations from sensory data. He speculates on the beginning of self awareness and on the role of perception of space and time. His arguments on language, thought and computation are fascinating, and almost persuade the reader that the age-old problems of human consciousness might be solvable.

The dazzling diversity of topics and the rapid pace of the brilliant exposition are overwhelming: at the end of every chapter, the reader has to stop to catch breath. In general, the author’s skill in unifying the array of molecular mechanisms under the single theme of information processing pulls us through. However, by the end of the book, so much knowledge has been imparted that our brains would indeed need to be quantum computers to assimilate it all.

Yet ironically for a book whose subtitle is “a quantum view of the brain,” it is just at the application of quantum mechanics to neural processes that the book stumbles. The author provides a spirited exposition of quantum mechanics and quantum computing, but when it comes to applying quantum theory to the brain itself, Loewenstein hems and haws. While he speculates on the possible role of quantum weirdness such as quantum superposition and entanglement in consciousness, in the end he is too good a scientist to be taken in by claims that wavefunction collapse plays a role in mental processes. Indeed, in the final chapter he admits that quantum mechanics doesn’t seem to play much of a role in the brain at all. It’s a relief not to be subjected to nonsensical claims of entangled neurons, but it does reveal the book’s subtitle to be nothing more than a tease.

Loewenstein is an engaging writer, one who spices his prose with elaborate wordplay, assonance, internal rhymes, puns, metaphors and quotations. All those verbal high jinks go to good use, put into the noble service of communicating hard stuff in a comprehensible fashion, but it does make for a book that could do with a few more monosyllables. Still, in the final analysis, this is a ripping good read. Each chapter brings novel insights into the fundamental workings of life. Those who buy their ticket and take the ride will emerge breathless, but enlightened.

2013 Basic Books £19.99/$28.99hb

Hofstadter’s butterfly spotted in graphene

Hofstadter’s butterfly – a stunning fractal pattern that describes the behaviour of electrons in a magnetic field – has been measured experimentally for the first time. The breakthrough has been made by three research groups that looked at the electronic properties of graphene placed on a boron-nitride surface. As well as confirming a theoretical prediction made nearly 40 years ago, the results could find use in electronic and optoelectronic devices.

The concept of Hofstadter’s butterfly dates back to 1976 when the American physicist Douglas Hofstadter – best known for his Pulitzer-prize-winning book Gödel, Escher, Bach – calculated the energy levels of electrons exposed to a magnetic field in a 2D lattice. He treated the electrons as idealized “Bloch electrons”, which means they do not interact with one another and move in a periodic electric potential commensurate with the lattice. This approach seemed sensible as it had proved a good way of describing the electronic properties of many metals and semiconductors.

Unfortunately, Hofstadter encountered a difficulty when considering electrons exposed to a magnetic field while moving in a 2D lattice. The problem lies in the fact that electrons respond to an applied magnetic field by swimming in circles at the cyclotron frequency. However, the orbital motion of the electrons is quantized in terms of a frequency that is defined by the properties of the crystal lattice. The presence of these two, often incommensurate, frequencies means that Hofstadter’s calculation of electron energy levels yielded some bizarre results.

Hofstadter tried to make sense of this difficulty by plotting the wavefunction of the electron versus a parameter related to the ratio of the two frequencies. The plot produced a stunning fractal pattern that looks like a butterfly. But since Hofstadter’s prediction, physicists have struggled to observe his butterfly in the lab. The main problem is that the crystal frequencies of conventional lattices – where atoms are separated by less than a nanometre – are relatively high, which means that unfeasibly strong magnetic fields way beyond current capabilities would be needed to see the butterfly pattern. Physicists have also tried looking for the Hofstadter butterfly in artificial lattices with separations of hundreds of nanometres, which would require much smaller magnetic fields, but the effect is washed out by disorder in the system.

2D superlattices

Now, however, three research groups have got round this problem by combining two conventional 2D lattices to create superlattices with periodicities on the order of tens of nanometres. One team involved physicists at Columbia University, the City College of New York, the University of Central Florida – all in the US – and Tohoku University and the National Institute for Material Sciences in Japan. The second group included researchers at the universities of Manchester and Lancaster in the UK, France’s National Lab for High Magnetic Fields in Grenoble and the Institute of Materials Science in Madrid, Spain. The third group involved researchers from the Massachusetts Institute of Technology (MIT) who teamed up with the same Japanese researchers involved in the Columbia team.

Experimental data showing Hofstadter's butterfly — Butterfly seen at long last: plot of electron density (horizontal axis) versus magnetic-field strength from data obtained by the Columbia team. (Courtesy: C R Dean *et al*. *Nature* 10.1038/nature12186)

What the teams did was place graphene – a layer of carbon just one atom thick – on an extremely flat surface of a boron-nitride crystal. As both materials have similar hexagonal structures, the researchers observed “Moiré patterns”, which are regular patterns created whenever two similar 2D lattices are overlaid. (The Manchester and MIT groups used single-layer graphene, while the Columbia-led experiment involved bilayer graphene.) By tweaking the relative orientation of the two lattices, the teams were able to create superlattices with appropriate spacing.

The teams then determined the energy spectrum of their superlattice by measuring its electrical conductivity in strong magnetic fields – up to about 35 T at Columbia, 17 T at Manchester and 43 T at MIT. When they plotted electron density (an observable property of the wavefunction) versus magnetic field strength, the teams saw the long-sought-after Hofstadter butterflies.

‘Rare and tremendously exciting’

“The opportunity to confirm a 40-year-old prediction in physics that lies at the core of most of our understanding of low-dimensional material systems is rare, and tremendously exciting,” says Cory Dean of City College of New York. “Our confirmation of this fractal structure opens the door for new studies of the interplay between complexity at the atomic level in physical systems and the emergence of new phenomenon arising from complexity.”

As well as confirming an important theoretical prediction, the studies provide further verification that the electronic properties of graphene can be controlled by placing the material next to another crystalline structure. This could prove useful because although graphene has several technologically useful properties – such as being brilliant at conducting electricity – it lacks key features, notably an electronic band gap, which would make it useful for creating practical transistors or optical detectors.

New materials

The Hofstadter butterfly observation is the latest in a long line of fascinating new findings involving graphene, which was first isolated by Andre Geim and Kostya Novoselov from the University of Manchester in 2004. “Of course, it is nice to catch the beautiful ‘butterfly’ whose elusiveness tormented physicists for generations,” says Geim, “[but] more importantly, this work shows that we are now able to build up a principally new kind of material by stacking individual atomic planes in a desired sequence.”

Geim’s colleague Roman Gorbachev even thinks such superlattices could have practical applications. “Such artificial crystals would have been science fiction a few years ago [but] now they are reality in our lab. One day you might find these structures in your gadgets.”

The Columbia and Manchester experiments are described in Nature (here and here) and a preprint of the MIT result is on arXiv.

Physics World learns how to make graphene at the University of Manchester

Atmosphere agitated by breaking waves

Ocean waves breaking far from shore impart a greater portion of their energy to the air than they do to the surrounding water. That is the claim of scientists in Italy and Australia who are the first to model the dynamics of the air directly over breaking waves. Although it has not been verified experimentally, the result challenges the previously held belief that most of a breaking wave’s energy remains in the water. If verified, the finding could have important implications for our understanding of cloud formation, climate modelling, oceanic circulation, and wave and weather forecasting.

While most waves do not break until they reach shallow water, particularly strong winds can cause them to do so out at sea – picture a classic storm with an ocean whipped full of whitecaps. But wind is not the only contributor to offshore breaking; modulation instability is a process by which small perturbations cause one or two waves within a set to grow unchecked. These waves draw energy from their neighbours until they reach a certain steepness threshold, when they break.

Current estimates suggest that 1–3% of all waves break at sea via this mechanism but until now it had been assumed that the energy released in the process was returned to the water. Indeed, our theoretical knowledge of what really goes on has been limited because calculations involve solving the nonlinear Schrödinger (NLS) equation. This involves making a number of significant approximations, including ignoring viscosity, vortex formation and, crucially, all air–water interactions. “The NLS equation can give you some ideas, but if you want to make one-to-one comparisons, you just don’t get good results,” explains Miguel Onorato, a physicist at the University of Turin who was involved in this latest work.

Tangled vortices

Onorato spent years studying modulation instability with the NLS equation but was eager to push the simulations to tell him more about the real world. To do so he turned to the Navier–Stokes (NS) equations – the central tenets of fluid mechanics, which incorporate all the complex forces and exchanges that the NLS equation willingly overlooks. However, solving the NS equations is famously difficult to do – both numerically and mathematically.

Onorato and colleagues used the NS equations to simulate wave breaking in two dimensions, by approximating the air and water as one single fluid with density and viscosity smoothly varying across the interface. The complexity of their model meant that each simulation took weeks to complete – unlike standard NLS models, which take minutes. But the investment was worth it: “It turns out there’s a lot going on in the air,” says Onorato.

The simulations showed that right before a wave breaks, it accelerates and its crest becomes sharp. As it breaks, the airflow on top of the wave suddenly separates from the crest and forms a vortex behind it – much like the vortices that form behind a spoon pulled through a cup of coffee. When the vortex makes contact with the water surface, it kicks up a second vortex of opposite sign, and the two tangle together in a capsule of counter-rotating air known as a dipole, and get thrown upwards into the atmosphere.

New perspective

When the scientists investigated just how much of a breaker’s energy is lost to this newly recognized dissipation route, they were staggered to find that up to three times more energy is transmitted to the air as is returned to the water. Onorato is careful to point out that this figure relates only to particularly steep waves, but the fact of the energies being comparable in order of magnitude is noteworthy.

Roger Grimshaw, a mathematician and wave expert at Loughborough University, who was not involved in the work, saw Onorato present the work at a workshop in Toronto last week. The talk “attracted a lot of interest”, he says, adding that the work “opens up a new perspective on air–sea interaction, which I believe has not previously been recognized, or indeed seen, either in numerical simulations, as here, or in observations”.

Climate contribution

Alex Babanin, an oceanographer at Swinburne University of Technology and co-author of the study, says “The implications for air–sea interactions, including weather and climate modelling, are significant but the large-scale models don’t simulate waves at all.” Instead, wind speed is used as a proxy for air–sea fluxes, but this can introduce errors of “hundreds of per cent” in the case of breakers resulting from modulation instability.

Although the team’s results are not immediately applicable in today’s climate models, a combination of scaling up the newly recognized contribution from breaking waves and improving the resolution of climate models should see a much more accurate picture of the interplay unfold. Babanin says “We now have a joint project with the Australian Bureau of Meteorology to do exactly that.”

Elsewhere, the team has already performed wave-tank experiments to confirm its computational results. Using a technique called particle image velocimetry, the team used a sheet laser and camera to reconstruct the velocity field of a smoky layer of air as waves broke underneath it. This new work is yet to be published but, says Onorato, “Visually, my collaborators could see those vortices in the air. Of course, there was no wind. The next step will be to add wind.”

The research is published in Physical Review Letters.

Sounding out the Sun

The “solar wind chime” is the work of Helen White, a designer with an interest in enhancing spaces by blending different media. In this interview, White talks to Physics World journalist James Dacey about her inspiration for the work and the challenges she has faced along the way.

Solar noises

White has developed her solar wind chime in Bristol, UK, as part of a communicating science residency supported by IOP Publishing, which publishes Physics World.

A solar wind chime — Chiming with the Sun: a solar wind chime. (Courtesy: Helen White)

Is Canada giving up on science?

By Hamish Johnston

The good old days. Nobel laureate Bert Brockhouse won his prize for work done at a federally-funded research reactor. (Courtesy: NRC) — The good old days: Nobel laureate Bert Brockhouse won his prize for work done at this federally funded research reactor. (Courtesy: CNA)

I am Canadian by birth and lived in that country for more than 30 years until the mid-1990s. For the past decade I have noticed a disturbing trend in the Canadian government of turning away from the outside world and becoming increasingly parochial in its outlook on important issues. I find this sad because I think the country is a thoroughly decent place that, despite its shortcomings, could provide inspiration for those living under less salubrious social and political systems.

(more…)

Cosmic flashes could herald birth of black holes

The birth of a black hole may be signalled by a characteristic cosmic flash, according to researchers in the US. It was previously thought that only the most massive of black holes would produce gamma-ray bursts – narrow beams of electromagnetic radiation that shoot out of the poles of the collapsing star – when they form. But other dying stars were thought to produce a black hole without any kind of flash – seemingly disappearing from the visible sky in an event known as an "unnova". The US researchers' work suggests that unnovae might also have their own characteristic flash, allowing astronomers to witness the birth of stellar- and intermediate-mass black holes.

"Although we know that black holes exist, we know very little about the observable signal that heralds the moment they first form," says Tony Piro, an astrophysicist at the California Institute of Technology and one of the lead researchers of the new study. As a massive star reaches the end of its life it undergoes core collapse, with its component protons and electrons merging to form neutrons. Before it completes its collapse into a black hole, the star momentarily becomes a super-dense object known as a neutron star.

Telltale flash

A by-product of this collapse is the release of neutrinos, which represents a significant loss of energy/mass from the core that causes a corresponding, sudden decrease in the gravitational pull of the star. This loss of attraction has an effect on the core's surrounding gaseous layers – which are mostly composed of hydrogen – causing them to rush outwards, forming an expanding shockwave that travels at more than three million kilometres per hour.

In a previous study from the University of California, Santa Cruz, astronomers Elizabeth Lovegrove and Stan Woosley had predicted that this shockwave would heat up the gaseous envelope, producing a characteristic glow that would shine for around a year and acting as a potential signal of the birth of such a black hole. Even though this effect would be a million times brighter than the Sun, it would still be dim in comparison with other stars. "It would be hard to see, even in galaxies that are relatively close to us," Piro explains.

One size fits all

However, in his recent study, Piro has identified another signal that should be easier to detect from the Earth – an initial flash generated by the shockwave as it hits the star's outer layers. For a red supergiant progenitor star, this breakout flash should be 10–100 times brighter than the glow predicted in Lovegrove and Woosley's study – with peak wavelengths in the ultraviolet and visible spectrum – and would be observable in nearby galaxies. Piro tells physicsworld.com that if the new flash in detected, it will reveal "the formation of black holes of all masses, offering a new approach from which to study these extraordinary gravitational phenomena".

Chris Reynolds, a professor of astronomy at the University of Maryland who was not involved in this study, says that there is currently "a huge degree of uncertainty about black-hole formation, both in terms of the kind of stars that will form black holes, as well as the nature of the formation event – gamma-ray burst versus supernova versus unnova". He says that theoretical work such as this paper is invaluable in honing our searches across the night sky, explaining that "it's always easier to look for something new if you have an idea what it will look like – for example, how luminous it will be and the timescale on which it will occur".

New window

"We used to think that gamma-ray bursts were the best signals of stellar-mass black-hole formation – however, those mighty explosions are rare and beamed, so only a lucky one in a hundred observers can enjoy them," says Re'em Sari, a professor of astrophysics at the Hebrew University of Jerusalem who was also not involved in this study. "[According to this research], a more frequent and isotropic signal marking the birth of black holes is the shock breakout from the progenitor – a weak but characteristic signal." Sari explains that if we can detect such events, this will open a new window through which we might study black holes.

The challenge now is to actually observe such breakout flashes. According to Piro, we should be able to see at least one of these each year. Wide-field surveys that watch the sky for temporary flashes of light are ideally suited to this task. One such survey is Caltech's Palomar Transient Factory, which Piro is collaborating with in the search for his predicted phenomena. On the theoretical front, Piro is also attempting to simulate the flashes in more detail, using more advanced computer models.

The work is published in Astrophysical Journal Letters.

Browse articles by content type

An afternoon of quantum theory

Do you try to pronounce physics terms as they sound in their language of origin?