Consideration by Carlo Beenakker, Chair of the selection committee for the 2014 Lorentz Medal.
Amsterdam, 23 February 2015.
Real numbers are called that way because they were believed to correspond to reality, unlike the imaginary numbers. We now know that this distinction is only apparent, since quantum physics attaches to each particle both a real and an imaginary number. The ratio of these two numbers determines the phase of the particle. The fact that particles have a phase is at the origin of many of the surprises of quantum physics.
Today we honor a scientist who has made fundamental contributions to our understanding of the interplay between something as elusive as the phase of a particle and something as tangible as the geometry of its path. The geometric phase, or Berry phase, is a memory effect: A particle that returns to its starting point, traveling very slowly ("adiabatically"), remembers the path it took by storing it in the phase. This quantum memory is such a fundamental concept that it has spread to many branches of physics, as diverse as optics and string theory.
The Berry phase gives a real significance to imaginary numbers, with a variety of practical implications. We now know that the Berry phase strongly modifies materials properties, such as the electrical conductivity of carbon nanotubes and graphene. Topological insulators, a recently discovered new class of insulators with a conducting surface, owe their existence to the Berry phase of the surface electrons. In quantum chemistry, the outcome of chemical reactions is modified by the Berry phase of reaction pathways. In quantum computer technology, if Majorana particles live up to their promise it will be because of the Berry phase that appears when we interchange two of them.
The appearance of a geometric phase in adiabatic evolution was missed by the founding fathers of quantum mechanics in the early twentieth century, which is remarkable because it is so close to the foundations. I am inclined to think that our own Paul Ehrenfest, who studied adiabatic processes in quantum physics, might have discovered the geometric phase if he could have benefited from the mathematical talent of his predecessor in Leiden, Hendrik Lorentz.
"I like to find new things in old things." These are the words of Sir Michael Berry, whom we honor today with the Lorentz medal. The geometric phase is just one striking example of a fundamental discovery in an area that others had left behind. His modus operandi is to work at the border between physics and mathematics. This is unusual, we don't typically think of mathematics as a world that borders the real world. Mathematics is taught as a tool or a language to describe physical phenomena in the real world. Some would say that physics is discovered while math is invented.
Michael Berry approaches math differently, as a world with its own phenomena and surprising effects waiting to be discovered, and then used as a source of inspiration for analogous discoveries in the physical world. Mathematical concepts such as fractals, knots, caustics, and catastrophes are linked to rainbows, twinkling starlight, sparkling seas, and tsunamis. We have heard about some of these examples today, in the context of light scattering, a topic close to the heart of Hendrik Lorentz himself.
Professor Berry, I feel strongly that the two of you would have found much common ground. We are proud to honor you as the 22nd recipient of the Lorentz medal.