March artefact – an early graph

Every month one or several of the objects held at the Nobel Museum’s collections will feature here as Artefact of the month.

Physics Laureate David Thouless donated this early handplotted graph. It was given to him on his 65:th birthday when the University of Washington did a symposium in his honor. The graph hung in his office until last summer, when he moved back to his native England, after many years in the US.

The graph is based on experimental data taken by John Reppy and and his graduate student David Bishop. This was the first experimental data showing that the Kosterlitz-Thouless transitions – until then only predicted in theory – worked.

According to Michael Kosterliz – David Thouless’s co-worker and Nobelprize co-laureate – Reppy and Bishop did the experiments without knowing about Thouless and Kosterliz’s work (KT-theory). Somehow they found out about the KT-theory and that the theory predicted a straight line. When Bishop and Reppy put the theoretical line on their data they found that it fitted their experimental data exactly.

Margaret Thouless – David Thouless’s wife – recalls he had been looking for someone to do these experiments. He looked in England where no one was prepared to do any experiments. For various reasons they got done in America instead. Bishop and Reppy performed their experiments with superfluid helium on a thin plastic substrate. When they increased temperature they observed phase transitions in the superfuid liquid, which are indicated by the even numbers on the vertical line. The even numbers stand for mass per unit area and according to theory it should be proportional to temperature. So when plotting the transitions it resulted in a nice straight line going through zero, just as the graph shows.

David Thouless together with Michael Kosterlitz explained something that had not been explained before the 1970’s. With an unorthodox set of mathematical tools – namely topology – they proved that phases of matter could exist in two-dimensional materials, chilled to almost absolute zero. Previously, the scientific community thought phases of matter were impossible in those materials, as well as phase transitions. Remarkably KT-theory is a very exact theory, something very rare in statistical mechanics, since the field ususally resorts to approximations. This is why KT-theory has been so used in a wide range of areas in physics and also opened up various new research fields in physics.

/Milena Dávila, Nobel Museum

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