The Nobel Prize in Physics 2016

The Nobel Prize in Physics 2016
The Nobel Prize in Physics 2016 was divided, one half awarded to David J. Thouless, the other half jointly to F. Duncan M. Haldane and J. Michael Kosterlitz "for theoretical discoveries of topological phase transitions and topological phases of matter".

 

Why Did They Win?
Topology is a branch of mathematics that describes properties that change only in increments. In the early 1970s, Dr. Kosterlitz and Dr. Thouless “demonstrated that superconductivity could occur at low temperatures and also explained the mechanism, phase transition, that makes superconductivity disappear at higher temperatures,” the academy found.

In the 1980s, Dr. Thouless showed that the integers by which the conductivity of electricity could be measured were topological in their nature. Around that time, Dr. Haldane discovered how topological concepts could be used to understand the properties of chains of small magnets found in some materials.
“We now know of many topological phases, not only in thin layers and threads, but also in ordinary three-dimensional materials,” the academy said. “Over the last decade, this area has boosted front-line research in condensed matter physics, not least because of the hope that topological materials could be used in new generations of electronics and superconductors, or in future quantum computers.”
Michael S. Turner, a physicist at the University of Chicago, said by email that the work of the three prizewinners was “truly transformational, with long-term consequences both practical and fundamental.”
“It illustrates the importance and surprises associated with curiosity-driven research,” he added.

What Is Topology?

At a news conference in Stockholm, Thors Hans Hansson, a member of the Nobel physics committee, used a bagel, a pretzel and a cinnamon bun to explain topology. While the items vary across many variables, a topologist focuses only on the holes: The pretzel has two, the bagel has one, and the bun has none.
“Things like taste or shape or deformation can change continuously, but the number of holes — something that we call the topological invariant — can only change by integers, like 1, 2, 3, 0,” he said.
This topological insight turned out to be useful in understanding the conductance — the ease with which electric current flows through a substance — in certain two-dimensional materials at extremely low temperatures and in strong magnetic fields. While the research was largely theoretical, it could have practical applications for items like electronics, superconductors and even computers. 
Who Are the Winners?
Dr. Thouless, 82, was born in Bearsden, Scotland, was an undergraduate at Cambridge University and received a Ph.D. in 1958 from Cornell. He taught mathematical physics at the University of Birmingham in England from 1965 to 1978, where he collaborated with Dr. Kosterlitz. He joined the University of Washington in Seattle in 1980, where he is now an emeritus professor.
Dr. Haldane, 65, was born in London. He received his Ph.D. from Cambridge, where he was also an undergraduate, in 1978. He worked at the Institut Laue-Langevin in Grenoble, France, the University of Southern California, Bell Laboratories and the University of California, San Diego, before joining Princeton in 1990.
Dr. Kosterlitz, 73, was born in Aberdeen, Scotland, and received his doctorate in high energy physics from Oxford University in 1969. He has worked at the University of Birmingham; at the Instituto di Fisica Teorica in Turin, Italy; and Cornell, Princeton, Bell Laboratories and Harvard.

 Topology is the mathematical study of those aspects of shapes of things which do not change when they are bent and deformed. For example, if you bend or twist a donut shaped rubber ring, it has still one hole and two distict ways to walk in a loop on it, the long way encircling the hole, and the short way going in a circle round the solid part. These properties are still the same if you deform the donut a bit. So, the topology of an object is described by discrete numbers, not continuous measures such as size or angles - this makes it very powerful because it means that topological properties of materials will not depend on the messy details of how they are made up and shaped, leading to very universal laws which hold with great precision independent of the details of the setup (unlike e.g. the electrical resistance of a piece of metal, whose precise value depends on many unknowns such as the exact shape, purity and temperature.)

 

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