Robert Harry Kraichnan Scient Undergraduate Thesis, “Quantum Several Years, and Strong Evidence Has

witty presentations of quantum me- Theory of the Linear Gravitational chromodynamics and quantum gravity. chanics and quantum field theory. Field”; he received a PhD from MIT in Kraichnan’s field-theoretic approach to Some of his legendary lectures were 1949 for his thesis, “Relativistic Scatter- nonequilibrium quantum statistical recorded for posterity; others were ing of Pseudoscalar Mesons by Nucle- mechanics is equivalent to the formal- saved as lecture notes by diligent stu- ons,” supervised by Herman Feshbach. ism developed by Julian Schwinger and dents so that their successors might He was one of Albert Einstein’s last as- Leonid Keldysh around the same time. have a taste of Sidney’s inimitable style. sistants at the Institute for Advanced In the late 1950s, Kraichnan tackled In 2005 Harvard hosted a festival to Study in Princeton, New Jersey, in the famously difficult subject of fluid honor Sidney. In attendance were many 1949–50. Kraichnan developed an ap- turbulence. He became a world leader of his former students and many dis- proach to gravitation that started from on the subject and drove major devel- tinguished physicists. Steven Weinberg the linear wave equation of a spin-2 opments for a remarkable 40-year span remarked that “Sidney is a theorist’s massless particle and recovered nonlin- beginning around 1957. For many theorist. He has not been so much con- ear general relativity by a bootstrap. workers in fluid turbulence, it was cerned with accounting for the latest His viewpoint is now popular among enough to say “Bob said. . . .” In 1962 data from experiments as with under- high-energy physicists, but Einstein Kraichnan decided on an unusual ca- standing deeply what our theories re- viewed it with disfavor. Some of reer path, leaving academia and setting ally mean. I can say I learned more Kraichnan’s ideas were rediscovered by up his own scientific consulting busi- about physics from Sidney than from Richard Feynman when he taught a ness. He became an independent re- anyone else.” In that connection let me course on gravity in 1962–63. The bril- search scientist, located first in New recall an oft-told tale: Working late into liance and strong individualist streak Hampshire and later in New Mexico. the night as was his wont, Sidney rarely that were evidenced in his early work His work was funded by grants from appeared at Harvard much before became hallmarks of Kraichnan’s entire agencies such as the Office of Naval noon. He once arrived so late at a sem- career. Research, NSF, and the Department of inar by Weinberg that all he heard was After leaving the institute, Kraich- Energy. He had long associations with Steve’s uncertain response to a question nan worked at Columbia University the National Center for Atmospheric from the audience. “I know the an- and the Courant Institute of New York Research and Los Alamos National swer!” shouted Sidney on entering the University. In the 1950s and 1960s, he Laboratory. room, “What’s the question?” Indeed, made important contributions to sev- Kraichnan made deep and seminal he often answered questions before eral areas of theoretical physics, in par- discoveries on turbulence in many they were asked. Theorists who con- ticular to quantum field theory and the physical systems, as varied as magneto- sulted him were often astounded as quantum many-body problem. At the hydrodynamics, Rayleigh–Benard con- Sidney would patiently explain the im- time, so-called self-consistent ap- vection, and superfluids. In 1957 he plications of their own ideas. proaches, which resummed infinite used the same ideas as in his work on Sidney was both an incomparable subsets of diagrams, became popular. quantum statistics to develop a self- teacher and the most learned sage and In 1957–62 Kraichnan developed an in- consistent theory called the direct- sharpest critic in the world of theoreti- genious method of realizing such ap- interaction approximation (DIA), whose cal physics: He was Pauli’s tongue in proximations as exact solutions of Lagrangian reformulation in 1964–66 Einstein’s image. We have been de- large-N random-coupling models that yielded a quantitative mean-field the- prived all too soon of one of our gener- couple N copies of the microscopic ation’s most profound and imaginative ory of turbulence. Those works were equations with quenched random pa- the first to provide fundamental in- minds. rameters. Similar techniques using ran- Sheldon Lee Glashow sights into the origin of Lord Kelvin’s dom matrices were rediscovered by concept of “vitiating rearrangement” Boston University Gerard ‘t Hooft, Alexander Migdal, and Boston, Massachusetts and the consequent loss of memory and others in the 1980s and applied to eddy viscosity in turbulent flow. The DIA has been applied to diverse prob- Robert Harry lems in fluid turbulence and was an im- portant predecessor to the modern Kraichnan field-theory formalism of Paul Martin, When Robert Kraichnan died on 26 Feb- Eric Siggia, and Harvey Rose. ruary 2008 at his residence in Santa Fe, Kraichnan also discovered the phe- New Mexico, after a long illness, the nomenon of inverse energy cascade in world lost a profound and original the- two-dimensional turbulence. Building oretical physicist. He contributed much on earlier work of Lars Onsager, T. D. to our current understanding of fluid Lee, and others, Kraichnan predicted in turbulence, the subject that occupied 1967 that there should be a Kolmogorov- him for most of his career, and also like energy cascade in 2D fluids with a made fundamental contributions to −5/3 power-law energy spectrum but general relativity, quantum field theory, with energy transferred from small quantum many-body theory, and statis- scales to large scales, the opposite tical physics. direction as in 3D. That idea has proved Kraichnan was born in Philadelphia extremely influential in our current on 15 January 1928. His earliest scien- understanding of the fluid dynamics of tific interest was in general relativity, Earth’s atmosphere and oceans. Inverse which he began to study on his own at cascade has been cleanly observed in age 13. At age 18 he wrote at MIT a pre- laboratory experiments in the past Robert Harry Kraichnan scient undergraduate thesis, “Quantum several years, and strong evidence has

70 May 2008 Physics Today www.physicstoday.org been found for the process in the oceans Charge Sensitive Preamplifiers and atmosphere. COOLFET® STATE-OF-THE-ART Additionally, Kraichnan contributed A250 a large body of work on passive scalars in a turbulent flow, including his intro- External FET duction in 1968 of an exactly soluble FET can be cooled model of advection by a velocity field Noise: <100 e- RMS (Room Temp.) white-noise in time. In a pivotal 1994 <20 e- RMS (Cooled FET) Physical Review Letter, Kraichnan pro- Gain-Bandwidth fT>1.5 GHz posed that the scalar field in that model Power: 19 mW typical should develop anomalous scaling not Slew rate: >475 V/Ms captured by mean-field theory. The ob- Noise @ 0 pF: 670 eV FWHM (Si) servation led to spectacular develop- ~76 electrons RMS ments in turbulence theory in the 1990s, Noise Slope: 13 eV/pF with Low C FET with successful calculations of the scal- iss 11.5 eV/pF with high C FET ing exponents of the passive scalar. The iss Kraichnan model is now widely hailed Fast Rise Time: 2.5 ns as the “Ising model of turbulence.” THE INDUSTRY STANDARD Kraichnan received the 1993 FEATURES A111 Medaille de l’ADION from France’s Ob- servatoire de la Côte d’Azur, the Amer- • Thermoelectrically Cooled FET ican Physical Society’s 1993 Otto La- • 3 internal FETs to match detector porte Award and 1997 Lars Onsager • Lowest Noise and Noise Slope Prize, and the 2003 Dirac Medal from • AC or DC coupling to the detector the Abdus Salam International Centre • Both Energy and Timing outputs for Theoretical Physics. Kraichnan was • Optional input protection A Microchannel Plate elected in 2000 to the National Acad- (MCP) Array Connected emy of Sciences and became in 2003 • Easy to use to Multiple A111s Homewood Professor of the Johns Hop- kins University. Your complete source for high performance preamplifiers and amplifiers In addition to his achievements in AMPTEK INC. Visit Us Now www.amptek.com physics, Kraichnan enjoyed classical 14 DeAngelo Drive, Bedford, MA 01730-2204 U.S.A. Tel: Fax: e-mail: music and was an accomplished violin- +1 781 275-2242 +1 781 275-3470 [email protected] ist. He was also, in better days, an avid See www.pt.ims.ca/16300-31 hiker who took long daily walks and thought deeply about science as he hiked. Much of his best work was done while walking the hills of New Hamp- Don’t Miss This Rare Opportunity! shire and the canyons of New Mexico. With Kraichnan’s passing, the Niels Bohr Collected Works physics community has lost a truly 13-Volume Limited Edition Collector’s Set original theorist. He was a unique and solitary thinker, but never isolated. A new and final opportunity to purchase all of the most relevant and Throughout his career, he took special authenticated materials and facts from Niels Bohr’s life and work as well as interest in mentoring new researchers personal documents previously unpublished. The limited edition set published and was extraordinarily generous in in agreement with and supported by the official Niels Bohr Archive in sharing his own ideas. His many col- Denmark will provide libraries and the scientific community with the leagues and friends will remember his ONLY comprehensive print and online reference of the Nobel Prize winner. warm and kind presence and his pene- trating insights. We’ll miss him very Elsevier much. June 2008 Hardback 8,504 pages Shiyi Chen ISBN: 9780444532862 Gregory Eyink Print List Price: $1,795.00 Johns Hopkins University Baltimore, Maryland Gregory Falkovich Weizmann Institute of Science Rehovot, Israel Uriel Frisch Available online. Visit www.info.sciencedirect.com/reference_works Observatoire de la Côte d’Azur for more information Nice, France Steven Orszag Yale University New Haven, Connecticut Katepalli Sreenivasan Check with your wholesaler to make sure you have access to this extensive reference work. For more Abdus Salam International Centre for information regarding this set please visit our website at http://elsevierdirect.com/nielsbohr Theoretical Physics Trieste, Italy ᭿

May 2008 Physics Today 71 See www.pt.ims.ca/16300-32