Tuesday, September 21, 2021

Nanoscale machines in nature

Part two of the Biology brief in The Economist is Cells and how to run them: All life is made of cells, and cells depend on membranes

A few of the main ideas are the following. Cells are either prokaryotic (bacterium) or eukaryotic (animals). Cell membranes are made of lipids that spontaneously form structures due to an interplay between hydrophobic and hydrophilic interactions. The boundary of prokaryotic cells is the membrane. Eukaryotic cells are more complex, containing many organelles (mitochondria), whose boundary are membranes.


Cells are little factories that can multiply themselves and perform distinct biological functions. It requires energy to maintain the cell shape and for it to manufacture new things. Inside and out is maintained by a difference in the concentration of protons (hydrogen ions) across the membrane. There are two aspects to this. First, the electron transport chain produces the protons. Second, a specific protein in the membrane, ATP synthase, pumps protons across the membrane.

The electron transfer chains are driven either by respiration or photosynthesis. 

Energy for processes in the cell is provided by breaking ATP down to ADP. The reverse process is driven by the kinetic energy of rotation (at about 6000 rpm) of the part of the ATP synthase protein.  ATP is Adenosine triphosphate.

To me the amazing/awesome/cool/miraculous thing is what the hardware can do. These are nanoscale chemical machines and factories. The video below shows a simulation of the ATP synthase protein that is located within cell membranes. It acts as a proton pump to maintain the concentration imbalance between the outside and inside of the cell and to convert ADP to ATP.


I learnt from this how the ATP synthase spins in only one direction and the rotation corresponds to sequential conformational changes in the protein subunits.

There is a beautiful discussion of the underlying physics in a chapter in Biological Physics by Phil Nelson. I have written a brief summary here.

The underlying quantum chemistry is explored in

Monday, September 13, 2021

Vertex corrections do matter

For an experimentalist one of the "easiest" quantities to measure for a metal is the electrical resistivity. Yet, for a many-body theorist working on models for strongly correlated electron systems this is one of the most difficult quantities to calculate, without making strong and debatable assumptions. One of the key questions is whether vertex corrections do matter. Ten years ago I summarised some of the issues.

This issue is nicely addressed in this nice paper from 2019.

Conductivity in the Square Lattice Hubbard Model at High Temperatures: Importance of Vertex Corrections

J. Vučičević, J. Kokalj, R. Žitko, N. Wentzell, D. Tanasković, and J. Mravlje

Besides the general issue of understanding the importance of vertex corrections, the paper is partly motivated by recent experiments on ultracold atoms that were compared to the results of calculations for a Hubbard model, using the finite-temperature Lanczos method (which essentially gives exact results on small finite lattices (e.g. 4 x 4)) and cluster Dynamical Mean-Field Theory (DMFT) (which does not include vertex corrections and has some momentum dependence in the self energy).

Before looking at the results I should point out the parameter values for the calculations. They are done for a Hubbard model on a square lattice. The half-bandwidth D=4t where t is the hopping parameter and U=10t. For the graphs below the doping p=0.1 (comparable to optimal doping in the cuprates).

Most importantly, the lowest temperature for which reliable calculations can be performed is T=0.2D=0.8t. In the cuprates, t is about 0.3 eV and so this lowest temperature corresponds to about 3000 K!, i.e. well above the superconducting Tc and the range of resistivity measurements on real materials. Most solids melt at these high temperatures.

Nevertheless, the results are important for two reasons. 

First, the experiments on ultracold atoms are in this temperature regime. [Aside: again this shows how fermion cold atom experiments are a long long way from simulating cuprates, contrary to some hype a decade ago]. 

Second, we are desperate for reliable results, and so it is worth knowing something about the possible importance of vertex corrections, even at very high temperatures. [Aside: my first guess would have been that they are not very important since I would have thought that correlations would be short-range and hand waving from Ward's identity would suggest that it follows the vertex corrections are small. This is wrong.]

In the figure above the top panel is the charge compressibility versus temperature. This is a thermodynamic quantity and the results show that most of the methods give similar results suggesting that the corresponding vertex corrections are small, at least above 0.1D.

The lower panel shows the temperature dependence of the resistivity and suggests that vertex corrections do lead to quantitative, but not qualitative differences. I guess the resistivity is in units of the quantum of resistance. Each rectangle has a vertical dimension of 5 units and so the resistivity is in excess of the Mott-Ioffe-Regel limit, i.e. the system is a bad metal. 

The figure above shows the frequency dependence of the optical conductivity for T=0.5D. There is a Drude peak at zero frequency and the broad peak near omega=2.5D=U corresponds to transitions between the lower and upper Hubbard band. DMFT is qualitatively correct but does differ from FTLM, showing the importance of vertex corrections.

Tuesday, September 7, 2021

Biology in a nutshell: emergence at many levels

 One of the many great things about The Economist magazine is that they run "Briefing" articles that give brief readable introductions and analyses to important topics, ranging from racism to taxation to climate change. Last year they ran a series about new ideas in economics.

They are currently running a series, Biology Briefs. Each week, for six weeks, there is a two-page article on one key topic in modern biology. They are naturally divided by different scales: molecules, cells, organs, individual lives, species, and living planets. 

The most important idea in molecular biology: DNA encodes information that is used to make specific proteins.

Replication: the protein DNA polymerase makes new DNA molecules with the same sequence of base pairs

Transcription: the protein RNA polymerase makes single strands of RNA that have the same genetic information.

Translation: the protein ribosome reads the information in the mRNA and uses it to make chains of amino acids (with specific sequences determined by the RNA sequence). These polymers then fold spontaneously into proteins with specific functions.

There is much that is amazing and awesome about this, including that people have been able to figure all this out. What I find most amazing/miraculous/awesome/cool is not the software but rather the hardware, i.e. the proteins that act as nanoscale biochemical factories, particularly the ribosome.

Wednesday, September 1, 2021

Towards real materials applications

There is a chasm between finding a material that has a desirable property that is key to a technological application and producing a commercial product. In the hype about materials research, the width of this chasm is too often glossed over.

The Structure of Materials by Samuel M. Allen and Edwin L. Thomas (based on a course in Materials Science and Engineering at MIT) introduces the tetrahedron of
structure, properties, processing, and performance. In condensed matter physics the focus is largely on the relationship between structure and properties. But, for engineering, these are both also related to performance and processing (i.e. ability to make materials and devices).


 The book also emphasises the multiple length scales associated with the structure of "real" materials. The scales range from the atomic scale of Angstroms to the scale of micrometers associated with objects such as grain boundaries, topological defects, and domain walls. These longer length scales are also relevant in liquid crystals, glasses, and polymers.

Wednesday, August 25, 2021

The emergence of condensed matter as a fundamental force in physics

What shapes the emergence and influence of a specific new academic discipline or research field? How much does context matter?

How is the discipline defined? By the objects studied, methods used, central concepts, questions asked, goals, or key discoveries? And, who gets to define the discipline: text-book authors, current researchers, distinguished academics, or university managers?

It may depend on who you ask. A discipline can be viewed from intellectual, historical, institutional, political, economic, and sociological perspectives. It all depends on what questions you ask.

Arguably, for most of the twentieth-century physics was considered the dominant field of science. We also observe today that condensed matter physics is a dominant force in physics. This is reflected in many different measures, such as numbers of practitioners, journal articles, PhDs, citations, and Nobel Prizes.

How did this happen? 

Joseph Martin is a historian who explores this question in his 2018 book, Solid State Insurrection: How the Science of Substance Made American Physics Matter. He looks particularly at physics in the USA in the political and economic context of the Cold War, focusing on the rise of solid-state physics, and its metamorphosis into condensed matter physics. The role of institutions such as government, industry, and the American Physical Society (journals, conferences, divisions) is carefully examined. Public testimony of Phil Anderson against the SSC (Superconducting SuperCollider) in 1989 is considered to be a watershed moment and highly symbolic. 

The book is carefully researched, beautifully written, and contains important new insights. I highly recommend it.

In exploring these issues I think it important to find a balance between two extremes. On the one side, there are purists and idealists who claim that physicists are the best (or even only) people to provide a useful and reliable perspective. Science is all about reality, facts, and truth, and contexts (social, political, economic) are completely irrelevant. At the other extreme are the social constructivists who think science is just about politics and power, both inside and outside the university community. Martin is to be commended that he does not tend towards either of these extremes.

A Physics Today article is adapted from the book When condensed-matter physics became king and gives a useful summary.

To whet your appetite for the whole book, a good place to start is the concluding chapter. Martin offers two fascinating counterfactual histories: one where the Manhattan Project failed, one where APS did not keep industrial physicists in the fold.

the most active frontier of the twentieth century was not the high-energy frontier, but the complexity frontier. It was the demystification of the properties of complex matter and the applications of those properties, which remade our technological world, from home computing, stereo equipment, and cookware to communication, transportation, medicine, and warfare.

This is a tendentious framing, but it serves a purpose: it exposes the historiographical contingency of the disproportionate focus on nuclear physics, high energy physics, and cosmology, alongside the historical contingency of the dominance those fields assumed over public discourse about physics in the second half of the twentieth century. Two counterfactual scenarios help to probe that contingency further, each of which offers heuristic utility by throwing into relief the role solid state physics played, despite lacking the public acclaim of its sibling subfields, in securing the prominence of American physics.

First, given the high degree of institutional volatility in the early post–Second World War era, it is easy to imagine a counterfactual scenario in which solid state physicists migrate away from physics and into chemistry, metallurgy, and engineering, much as electrical engineering had some decades earlier. It was a contingency about which the field’s founders actively worried, and the American Physical Society council was demonstrably squeamish about clearing the type of institutional space that would give the society a more industrial flavor. Without solid state, which accounted for a large proportion of the postwar population boom, physics would have stayed smaller and grown more slowly.

We can imagine a second counterfactual scenario in which the Manhattan Project never acquired the scale or resources it needed to construct a working bomb before the end of the war in the Pacific... Suppose, for whatever reason, the Second World War ends without a dramatic, public demonstration of the power of the nucleus...  In this second scenario, solid state physicists would have been well positioned to become much more politically influential in the early Cold War, in particular on the strength of radar research,..

Aside. Earlier I posted about a nice article Martin wrote about public perceptions about condensed matter physics.

Thursday, August 19, 2021

Einstein on big questions

The mere formulation of a problem is far more essential than its solution, which may be merely a matter of mathematical or experimental skills.

To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science.

I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.

Albert Einstein and Leopold Infeld (1938), The Evolution of Physics

I recently encountered this quotation in The Poetry and Music of Science: Comparing Creativity in Science and Art by Tom McLeish. I have heard many times the "Imagination is more important than knowledge" quote, sometimes as a dubious justification for dubious ideas. However, I did not know the context. 

My postdoctoral advisor, John Wilkins tried to drill into me, the idea in the first paragraph, that just coming up with a well-defined formulation of a problem could be a significant advance. This idea certainly had some impact on me, since I sometimes hear my non-scientist wife quote it!

On reflection, I am afraid that I too easily lose sight of this priority of defining problems, just like the method of multiple alternative hypotheses. Good science is hard.

Why am I reading this article? What question am I trying to answer?

Why am I writing this paper? What question am I trying to answer?

What is the problem I assigning a student to work on? Is it well-formulated?

Defining good research questions is hard work and requires discipline.


Thursday, August 12, 2021

Springy stringy molecular crystals

Perfect crystals are elastic. When a stress is applied and then removed the crystal will bounce back to its original shape. However, in reality no crystal is perfect. If the applied stress is too large the crystal will fracture. Understanding fracture is a big deal in materials science and involves some fascinating physics, including the role of topological defects. 

There are two distinct properties: elasticity and plasticity. They are associated with temporary and permanent changes in shape in response to an applied stress.
They are quantified by the elastic stiffness and the tensile strength, respectively. They reflect material properties at quite different length scales. 

A beautiful and accessible short introduction is 
Bart Kahr & Michael D. Ward 

This is a commentary of some work by a few of my UQ chemistry colleagues, who have made and studied a molecular crystal that is incredibly flexible, as seen in this movie.


Anna Worthy, Arnaud Grosjean, Michael C. Pfrunder, Yanan Xu, Cheng Yan, Grant Edwards, Jack K. Clegg & John C. McMurtrie 

A particular advance is that they use a synchrotron to perform spatially resolved X-ray crystallography to determine how the crystal structure varies spatially within a bent crystal. 

The material of interest has quasi-one-dimensional antiferromagnetic interactions and has been studied theoretically by my condensed matter theory colleagues.

Elise P. Kenny, Anthony C. Jacko, Ben J. Powell

But there is more...
A recent Science paper describes ice fibers that were particularly flexible.


Peizhen Xu, Bowen Cui, Yeqiang Bu, Hongtao Wang, Xin Guo, Pan Wang, Y. Ron Shen, Limin Tong