On 26 October 2015, Leo Philip Kadanoff, the John D. and Catherine T. MacArthur Distinguished Service Professor Emeritus of Physics and Mathematics at the University of Chicago, died from complications after surgery. Kadanoff was one of the most profound theoretical physicists of the last half century; his ideas revolutionized the way physicists think about collective phenomena and the structure of matter. The concepts of scaling and of dividing matter iteratively into “Kadanoff blocks,” and the mathematical framework associated with that transformation of scales, have had enormous impact, with applications from condensed matter to elementary particles. In addition to his research, he was a beloved mentor to many students, postdocs, and colleagues and set an example for curiosity-driven, collaborative, interdisciplinary science.
Kadanoff was born in New York City on 14 January 1937. He grew up in the same apartment building on 204th Street as Roy Glauber, his future thesis adviser, and lived about half a block from Gordon Baym, his future collaborator. Kadanoff attended Harvard University, first as an undergraduate and then as a graduate student; he received his doctorate in physics in 1960 with two dissertations—one with Glauber and the other with Paul Martin. He did postdoctoral work at the Niels Bohr Institute in Copenhagen, where he and Baym wrote the classic 1962 text Quantum Statistical Mechanics (W. A. Benjamin), which introduced techniques for treating nonequilibrium interacting quantum systems. That text is still used as a basis for studies of semiconductor devices, plasmas, and elementary particles.
In 1962 Kadanoff joined the physics department at the University of Illinois at Urbana-Champaign. His research focused on properties of condensed matter and critical phenomena, from which emerged his work on block-spin renormalization and scaling. Among the many concepts Kadanoff introduced were two that have been crucial in quantum field theory: the operator product expansion and anomalous scaling dimensions. He also initiated investigations of dynamic critical phenomena and coinvented an elegant lattice representation of fluid mechanics that is still used today.
In 1969 Kadanoff moved to the physics department at Brown University. There he used computer simulations to address issues in urban planning. In 1978 he moved to the University of Chicago, where he remained until his retirement in 2003.
Kadanoff focused on complexity, fluid flow, and applications of computers to physical calculations. His interests led him to study the behavior of systems near critical points, where they are on the verge of changing their character. For example, he looked at possible routes for the onset of chaos in simple systems and for the initiation of turbulence in liquids. He helped introduce the idea of multifractality to characterize certain types of pattern formation arising out of instabilities. He instigated a series of efforts to study singularities in fluids, such as the breakup of a column of liquid into droplets, and the mathematical breakdown of solutions to nonlinear partial differential equations.
Kadanoff was director of the University of Chicago’s Materials Research Center from 1981 to 1984 and 1994 to 1997. He was president of the American Physical Society in 2007.
Widely recognized for his immense research accomplishments, Kadanoff received the US National Medal of Science in 1999. Other honors include the 1980 Wolf Prize in Physics, the 1989 Boltzmann Medal from the International Union of Pure and Applied Physics, both the 1977 Oliver E. Buckley and 1998 Lars Onsager Prizes of the American Physical Society, and the 2011 Isaac Newton Medal of the Institute of Physics. He was also recognized in 1990 with the Quantrell Award for excellence in undergraduate teaching at Chicago.
But to an entire generation of theorists, Leo was regarded as a father figure. Certainly his legacy is as much in the colleagues and students he mentored as in the physics theories he created. As Tom Witten, his longtime colleague at Chicago, said, “The Leo I knew was all about developing people.” His influence on the physicists—young and old—working around him was profound. He was confident in his opinions and warm and generous in his praise when he thought it was deserved. Those traits helped him create an atmosphere in which originality and judgment were prized. Many of his students and postdocs have gone on to distinguished careers, and a lot of their success can be traced back to the training they received from Leo.
While obviously a prodigious mathematical physicist, Leo did not lose sight of the core idea behind his calculations and could explain their significance in very physical terms. He delighted in applying to one area of science ideas that were developed in another. He worked hard to bring scientists and engineers from different disciplines together and thus inspired researchers with many interests—from technical theory, to experiment, to science communication.
Indeed, Leo’s ability to communicate was an important part of why his ideas became so broadly useful, important, and widely adopted, as he himself once noted in conversation. He believed that science progressed when people work together, and his example inspired much collaborative work across disciplines. He had great judgment about what questions were interesting and what results were important, not only in statistical physics, his main subject area, but also in fluids, condensed matter, geophysics, chemistry, and engineering. He would highlight problems that he found exciting and would bring together mathematicians, computer scientists, theorists, and experimentalists to work on a solution.
Being around Leo was never dull. His quips could be outrageously funny but would often contain a kernel of hard and harsh truth. He was forever playful and interested in what was going on in other labs, which he often visited. One of us (Nagel) remembers one visit with particular joy: With Leo’s colleague Heinrich Jaeger we were conducting an experiment on granular avalanches. When he learned that the material consisted of mustard seeds, Leo stuck his hand into the experiment and ate some. Although it is difficult to prove a theory right or wrong when the experiment is eaten before the results are in, it is nevertheless incontrovertible that Leo fully digested our experiment.
