# Sutherland, Calogero and Gaudin win 2019 Dannie Heineman Prize for Mathematical Physics

WASHINGTON, D.C., OCTOBER 23, 2018 — The American Institute of Physics (AIP) and the American Physical Society (APS) announced today that Bill Sutherland of the University of Utah, Francesco Calogero of the Sapienza University of Rome and Michel Gaudin of the Commissariat à l'énergie atomique (CEA) Saclay are the winners of the 2019 Dannie Heineman Prize for Mathematical Physics.

Awarded annually by AIP and APS on behalf of the Heineman Foundation, the prize honors significant contributions to the field. Sutherland, Calogero and Gaudin were cited "for profound contributions to the field of exactly solvable models in statistical mechanics and many body physics, in particular the construction of the widely studied Gaudin magnet and the Calogero-Sutherland, Shastry-Sutherland and Calogero-Moser models."

They will share the prize's $10,000 award and will be honored in a special ceremonial session next year at the APS March Meeting in Boston.

"On behalf of AIP and the Heineman Foundation, I am pleased to congratulate Drs. Sutherland, Calogero and Gaudin for their key contributions to mathematical physics," said AIP CEO Michael Moloney. "Each of these three arrived at this pinnacle in their careers following separate paths, along the way making numerous invaluable contributions to science and humanity."

"On behalf of APS, I congratulate the winners of the 2019 Dannie Heineman Prize. I am delighted that the outstanding research contributions of Sutherland, Calogero, and Gaudin have been recognized in this way," said APS CEO Kate Kirby.

The breakthrough accomplishments by Calogero, Sutherland and Gaudin are still influential today among physicists as well as applied and pure mathematicians worldwide.

**BACKGROUNDER: Adding to the House that Hans Bethe Built**

Michel Gaudin began his studies working on random matrices. He built on the work of Hans Bethe by refining the elder scientist's equations that predicted collective behaviors in electrons while trying to solve some of the earliest problems of quantum mechanics. This approach enabled him to obtain the solution of the Schrödinger equation for a system of spin one-half fermions with a delta (attractive) potential. Based on his thesis work, he later developed a magnet model (the Gaudin magnet) that opened the door to thermodynamics.

"It is not specifically one-dimensional," Gaudin said. "It has a large number of parameters that allows for the description of interactions of a photon mode with a mix of atoms represented by two-level systems."

In 1971, Calogero developed the first nontrivial many-body problem with two-body forces that could be exactly solved. Sutherland independently obtained the identification and solution of a variant of this model in a statistical mechanics context.

"I am interested in statistical mechanics, quantum mechanics and the connections between the two," Sutherland said. "In this way, I have proceeded throughout my career."

During his graduate studies with professor C.N. Yang, Sutherland developed an exact solution of a model of two-dimensional ferroelectrics in an arbitrary external electric field. Working one summer with the brothers C.N. Yang and C.P. Yang, Sutherland extended these solutions, showing the connection with the one-dimensional quantum Heisenberg-Ising model. Soon after, he came across Calogero's work using an exact wave function of a one-dimensional quantum system. While Calogero's solution was an unbound scattering state, Sutherland figured out how to put the model "in a box" and calculate the thermodynamics for the Calogero-Sutherland model that has been applied in many branches of physics, including quantum fractional Hall effect, generalized exclusion statistics and even black hole physics.

Later the theoretical Shastry-Sutherland model was introduced and became important with the discovery of magnetization plateaus obtained with SrCu2 (BO3)2 under high magnetic ?elds. This technique enabled various experimental studies, including magnetization, specific heat, inelastic neutron scattering, far-infrared studies of electron spin resonance, Raman scattering and nuclear magnetic resonance.

Finally, the Calogero-Moser model is a one-dimensional many-body problem that can be explicitly solved. The model touches many fields of mathematics, including algebraic geometry, representation theory, deformation theory, homological algebra and Poisson geometry. It now plays a role in research areas from theoretical physics, including soliton theory, quantum field theory, string theory, solvable models of statistical mechanics, condensed matter physics and quantum chaos, to pure mathematics, including representation theory, harmonic analysis, theory of special functions, dynamical systems, random matrix theory and complex geometry.

"I feel, at my old age, greatly honored by this recognition," Calogero said. "Particularly so given the list of previous awardees."

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**ABOUT THE WINNERS**

Bill Sutherland is an emeritus professor in the Department of Physics and Astronomy at the University of Utah. He was a National Science Foundation Fellow, as well as a Fellow of the American Physical Society and Honorary Fellow of the Indian Academy of Sciences. He has authored more than 70 peer-reviewed scientific articles and a book, titled Beautiful Models: 70 years of exactly solved quantum many-body systems. Sutherland received his bachelor's degree from Washington University in 1963, a master's degree from the State University of New York, Stony Brook in 1965 and his doctorate from the State University of New York, Stony Brook in 1968. http://www.physics.utah.edu/index.php/undergraduate-program/research-opportunities/173-people/emeritus-faculty/569-bill-sutherland

Michel Gaudin is a professor in the Department of Physics at the Commissariat à l'énergie atomique (CEA) Saclay. He has authored 65 peer-reviewed scientific articles, with the most prominent collected in the book Modèles exactement résolus and the monograph La fonction d'onde de Bethe. Gaudin received degrees from the Ecole Polytechnique in 1951. He took his "These d'état" (reproduced in Modèles exactement résolus) at the University of Orsay in 1967. Gaudin was promoted to the position of Of?cier de l'ordre des Palmes Académiques in 1994.

Francesco Calogero is an emeritus professor in the Department of Physics at the Sapienza University of Rome. He has served on the five-member Board of the Stockholm International Peace Research Institute (SIPRI) for two consecutive five-year terms (1982 to 1992) and is currently a member of the European Leadership Network. From 1989 to 1997, he served as the Secretary General of Pugwash (Pugwash Conferences on Science and World Affairs), which shared the Nobel Peace Prize in 1995 with Joseph Rotblat for their efforts to diminish the part played by nuclear arms in international politics and work toward elimination of their production. He has authored more than 400 peer-reviewed scientific articles and several texts, including Verification: monitoring disarmament, a feat of international cooperation. Calogero received his Laurea in Fisica from the Sapienza University of Rome in 1958. https://en.wikipedia.org/wiki/Francesco_Calogero

**ABOUT THE HEINEMAN PRIZE**

The Heineman Prize is named after Dannie N. Heineman, an engineer, business executive and philanthropic sponsor of the sciences. The prize was established in 1959 by the Heineman Foundation for Research, Education, Charitable and Scientific Purposes, Inc. The Prize will be presented by AIP and APS on behalf of the Heineman Foundation at the APS March 2019 Meeting in Boston. A special ceremonial session will be held at the meeting where Sutherland, Calogero and Gaudin will share the $10,000 award. https://www.aps.org/programs/honors/prizes/heineman.cfm

**ABOUT AIP**

The American Institute of Physics is a federation of scientific societies in the physical sciences, representing scientists, engineers, educators, and students. AIP offers authoritative information, services and expertise in physics education and student programs, science communication, government relations, career services, statistical research in physics employment and education, industrial outreach and history of the physical sciences. AIP publishes Physics Today, the most closely followed magazine of the physical sciences community and is also home to the Society of Physics Students and the Niels Bohr Library and Archives. AIP owns AIP Publishing LLC, a scholarly publisher in the physical and related sciences. http://www.aip.org

**ABOUT APS**

The American Physical Society is a non-profit membership organization working to advance and diffuse the knowledge of physics through its outstanding research journals, scientific meetings and education, outreach, advocacy and international activities. APS represents more than 53,000 members, including physicists in academia, national laboratories and industry in the United States and throughout the world. Society offices are located in College Park, MD (Headquarters), Ridge, NY and Washington, DC.

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