I just completed my first draft of Chapter 8: Topology Matters for Condensed Matter Physics: A Very Short Introduction.
Any comments and suggestions would be appreciated. I learned a lot writing the chapter, but imagine it needs to be made more accessible.
This is a basic question that is worth asking in many situations and contexts. Here are some examples.
John is a postdoc who works seventy hours a week. He is always in the lab. He never takes holidays. He says he will once he gets a paper in a luxury journal. But, then we won't take a break until he gets a faculty job...
The students of Professor X regularly experience verbal abuse from him. He usually apologises for getting "carried away".
A government is corrupt, incompetent and tortures its political opponents and critics.
Suresh is on his fourth postdoc. Each has been in a different country.
Susan is a young faculty member, married and with two young children. She is usually at work or "on the road". At home she is mostly working.
A university borrows huge amounts of money from a bank in order to build very fancy buildings that they hope/claim will attract international students.
Scientists keep telling funding agencies that their research field is going to produce commercial benefits in just a few years.
Humans burn lots of fossil fuels....
Every year a university increases the administrative load on faculty by "just a few hours per week".
What will eventually happen? Something will break. A colleague once said to me "if you treat people like a machine and your drive them hard enough they will break. Just like a machine."
Eventually, we butt up against reality. It does not matter what we wish is true. The reality is that humans are finite. We have only finite physical, emotional, and mental resources. We all only have finite time, money, and abilities. Individuals, families, communities, institutions, and nations have only finite financial, social, and political capital.
Every situation is different. Every person is different. Our resources, whether financial or emotional, may differ significantly from one another. But we are all finite.
So, a good question to ask in any endeavor is "Is this sustainable?"
What do you think? Are there situations where you think this question should be asked?
A property of a system composed of interacting parts is emergent if it has the following characteristics. The property is
1. not present in the parts.
2. difficult to predict solely from knowledge of properties of the parts and how they interact with one another.
3. associated with a modification of the properties of and the relationships between the parts.
4. universal, i.e., it is independent of many of the details of the parts.
Different people have different views on what emergence is, particularly with regard to the second characteristic. “Difficult to predict” is sometimes replaced with “impossible”, “almost impossible”, or “extremely difficult”, or “possible in principle, but impossible in practice.” After an emergent property has been observed sometimes it can be understood in terms of the properties of the parts. An example is the BCS theory of superconductivity. This is a posteriori, rather than a priori, understanding. A key word in my statement is “solely”.
Examples of properties of a system that are not emergent are volume, mass, charge, and number of atoms. These are additive properties.
Associated with emergent properties are also unique entities, concepts, theories, and organizing principles.
The road from materials research to commercial technology is a complex and tortuous one. It is not just a matter of what is physically possible. There are rigorous criteria that must be met along the way: financially competitive, mass production, reliability, durability, non-toxicity, ...
The materials needed don't just have to be available, cheap enough, and sufficiently abundant. One also needs supply chains that are not only reliable but also ethical.
In The Economist there is a fascinating (and disturbing) article that shows the complexities involved with the supply chains for just one of the metals used in our smart phones.
Why it’s hard for Congo’s coltan miners to abide by the lawTantalum, a metal used in smartphone and laptop batteries, is extracted from coltan ore. In 2019 40% of the world’s coltan was produced in the Democratic Republic of Congo, according to official data. More was sneaked into Rwanda and exported from there. Locals dig for the ore by hand in Congo’s eastern provinces, where more than 100 armed groups hide in the bush. Some mines are run by warlords who work with rogue members of the Congolese army to smuggle the coltan out.
Before reading this article I had no idea what coltan is and so I read the Wikipedia page.
On the science side, I wrongly guessed that coltan was some compound containing cobalt and tantalum. It is actually a mixture of two distinct crystals, tantalite [(Fe, Mn)Ta2O6] and columbite [(Fe, Mn)Nb2O6].
On the economic side, I found it interesting that until a few years ago Australia actually supplied most of the world's coltan.
In terms of political economy, this problem is an example of the "resource curse", a common experience of countries in The Bottom Billion.
If you are concerned about these issues and you live in Europe you might consider buying a Fairphone.
What is the relationship between deterministic and stochastic "laws" of motion?
Subtle. It is possible that random behaviour can emerge from underlying deterministic laws and the converse. Deterministic laws can emerge from a system of many interacting parts that are described by stochastic motion.
This is nicely discussed in a Physics Today, column by Leo Kadanoff from 2002. Here are a few quotes. First, he discusses how random behaviour, such as Brownian motion, can emerge from many particles undergoing deterministic motion, or stochastic motion...
the observation of apparently stochastic features in some behavior does not imply that the underlying laws are themselves probabilistic. Often, deterministic motion is so complex or so sensitively dependent on initial conditions that the motion is indistinguishable from a set of random events. For example, the path taken by an individual molecule in a gas is very well modeled as a random walk, entirely probabilistic in its nature.
The random walk model can be derived from more fundamental models of molecular scattering. The scattering events could be realized in at least three different ways: using classical mechanics (fully deterministic), using quantum mechanics (partially deterministic), or prespecifying the probabilities of scattering. Thus the probabilistic single-particle model, the random walk, can be equally well obtained from a many-particle model that is entirely deterministic, partially so, or not deterministic at all. Real gases will all show the same behavior independent of the detailed laws governing the scattering.
We use the word “universality” to describe the rather commonly occurring physical situations in which a set of derived laws remains substantially the same over a wide range of alternative underlying fundamental laws. In these cases, the observable outcome cannot be used to select among the possible underlying laws.
This universality is a characteristic of emergent phenomena. Laughlin and Pines refer to this as "protectorates": whereby the underlying physics is obscured by the phenomena that is observed at a higher level. For example, observation of acoustic modes in a crystal obscures the underlying atomic structure.
Kadanoff then discusses how deterministic laws can emerge from underlying stochastic ones.
Conversely,... if you put together many individual stochastic motions, you may well get an essentially deterministic situation. A dilute classical gas obeys the deterministic gas law, PV = NkT. Through the “miracle” of large numbers, many stochastic molecules have produced a deterministic gas.
Kadanoff's article is actually not primarily concerned with the issues of emergence. It is entitled, Models, Morals, and Metaphors, and is mostly concerned with possible philosophical implications of chance and probability playing a role in evolutionary theory.
I was brought up to believe that spin-singlet superconductors must be s-wave (elemental) or d-wave (cuprates) and spin-triplet must be p-wave (superfluid 3He) or f-wave, and so on... More generally, singlets (triplets) are associated with even (odd) parity.
However, like a lot of things we learn some of us tend to forget what are the necessary assumptions needed for the result/claim to be valid.
Thus, I was intrigued when my colleague Ben Powell showed me this preprint.
Unconventional superconductivity near a flat band in organic and organometallic materials
