Boris Valerianovich Chirikov, a pioneering contributor to the foundations of dynamical chaos, died from cancer in Novosibirsk, Russia, on 12 February 2008. His name and ideas are known to everyone working in nonlinear dynamics and chaotic behavior of deterministic classical and quantum systems.
Boris was born in the Russian town of Oryol on 6 June 1928. He did his undergraduate and master’s studies in Moscow State University’s department of physics and technology (now the Moscow Institute of Physics and Technology). Before graduating from MIPT in 1952, Boris began working in the Thermotechnical Laboratory, now the Institute of Theoretical and Experimental Physics; for a few years, he continued to work there, studying meson physics. In 1954 he accepted an offer from Gersh Budker, then head of the Laboratory of Novel Acceleration Methods (now the Kurchatov Institute), to join his group, and Boris began working on problems of accelerator and plasma physics.
In 1958 Budker founded the Institute of Nuclear Physics, which now bears his name, in Akademgorodok, a new scientific center south of Novosibirsk, in western Siberia. Boris joined him there in September 1959. Until his last days, Boris worked at Budker’s institute, first as an experimentalist, then as a theoretician. He became a corresponding member of the Russian Academy of Sciences in 1983 and a full member in 1992.
Boris’s early research at the institute was the experimental study of a few problems formulated by Budker. The first one was related to ionic compensation and stability of a high-density relativistic electron beam. After five years of intensive work on that problem, Boris and his coworkers built the B-3 betatron with parameters that even now are considered extraordinary.
In Boris’s evolution from experimentalist to theorist, the critical problem that he studied, suggested by Budker, was the mysterious loss of electrons in magnetic traps for confinement of hot plasma. In a seminal 1959 paper, Boris developed a new method for analyzing nonlinear resonances; that work led him to understand the physics responsible for the loss of electrons: the overlap of nonlinear resonances resulting in the deterministic diffusion of electrons. That study gave rise to the Chirikov “resonance overlap” criterion of chaotic motion in dynamical systems.
In 1965 Boris applied his approach to the Fermi-Pasta-Ulam paradox and explained it analytically. He showed that the parameters used in the numerical study of the FPU problem were taken well below the border of strong chaos. Later, those results were confirmed numerically. Among other important results from Boris and his group during that period are the derivation of the chaos border in the Fermi acceleration model (1964); the discovery of weak Arnold diffusion in four-dimensional nonlinear maps (1969–75); the analysis of statistical properties of chaos in 2D nonlinear maps, including the discovery of the power-law decay of Poincaré recurrences in Hamiltonian systems with divided phase space (1969–81); and the demonstration that the dynamics of Halley’s comet is chaotic (1989). Those and other results are summarized in Boris’s 1969 professorship thesis and his famous 1979 review paper in Physics Reports.
Boris’s work usually included both analytical methods and numerical experiments, now considered the most effective method of analyzing complex systems. His innovative use of numerical simulations often indicated new directions for both theory and experiment.
Researchers and students in dynamical theory closely associate Boris’s name with the “standard map” that serves as a cornerstone of that field. Many physical systems have mapping approximations whose stability and transition from regular to chaotic motion can be conveniently investigated by expanding around a fixed point to obtain the Chirikov standard map. In 1977 Boris initiated the investigation of the quantum version of the map, also known as the kicked rotator. His early studies of that model with his coworkers resulted in the discovery of dynamical localization of quantum chaos. The effect of such localization later was observed in experiments with hydrogen and Rydberg atoms in a monochromatic microwave field and with cold atoms and Bose–Einstein condensates in optical lattices. In applications to quantum systems with complex behavior, the kicked rotator is considered the basic model demonstrating all essential properties of quantum chaos.
From the founding of the Novosibirsk State University in 1959, Boris participated in the development of physics courses. He helped initiate a modern approach to physics education that was introduced at the university. His original lectures on classical mechanics and electrodynamics are used by hundreds of students around the world. His ideas on classical and quantum chaos theory have been essential both to his students and to readers of his published works.
Boris had a remarkable ability to go deeply into the problems of both theoretical and experimental physics and mathematics. His kindness and goodwill will be remembered by all his friends and colleagues. Borrowing a phrase from his friend Andy Sessler, we say we “feel touched to have had [our lives] touched” by Boris.
