| Citation | Distinguished for work of great originality in both quantum mechanics and classical mechanics. He has studied relationships between quantal and classical systems and his work on fundamental theoretical problems has had many practical applications.
He has introduced the notion of Correspondence Identities, elucidated their connection with dynamical symmetries and used them in the first applications of Monte Carlo trajectory methods to atomic collisions and to microwave ionisation of atoms. With the aid of new correspondence principle techniques he has obtained accurate electron-impact cross sections essential for the interpretation of radio recombination line observations. He introduced the notions of Regular and Irregular Spectra, thus initiating the study of quantum chaos and is application to molecules. His important contributions to quantal collision theory include studies of bounds, of the polarization of impact radiation and of non-iterative techniques for the solution of integro-differential equations.
He has made outstanding contributions to the theory of non-linear non-integrable Hamiltonian systems. These include the development of Fourier methods to distinguish regular and chaotic motion, the discovery of variational principles and their application to obtain useful bounds on regular motion, the discovery of the invariant Cantor sets known as cantori and of their critical importance in a new theory of transport in the chaotic regions of phase space, the first detailed studies in the plane of the complex angle variable and the provision of a necessary probabilistic definition of stability. He has applied some of these theories to the standard (Chirikov-Taylor) map, which is required for the theory of charged particle containment in storage rings and plasma containment devices, and is finding applications in many other fields. |