For his many original and outstanding contributions to the theory of chaotic classical and quantum mechanical systems,

Prof. Dr. Alfredo Miguel Ozorio de Almeida

has been awarded the Martin-Gutzwiller-Fellowship 2002
of the Max Planck Institute for the Physics of Complex Systems.

Dr. Ozorio de Almeida’s research displays a deep interest in the relationship between classical and quantum mechanics.
In the early 1980’s with co-author John Hannay, Dr. Ozorio de Almeida first discussed what is widely known today as the “Hannay-Ozorio sum rule” for periodic orbits. Expressions for both integrable and chaotic systems were given. The version for chaotic systems plays a crucial role in deriving the relationship between random matrix theory and the fluctuation properties of such systems when they are quantized. His book, “Hamiltonian Systems”, is a classic and indispensible text. Work found there and in his Cuernavaca proceedings developed the study of bifurcations in Hamiltonian systems. These results have been applied to deriving a trace formula for near-integrable systems that interpolates between the Berry-Tabor and Gutzwiller trace formulae, for uniformizations of semiclassical expressions of bifurcating orbits, and other effects on quantum densities of states.
Moreover, Dr. Ozorio de Almeida showed how to calculate tunneling effects in resonant systems; models of the kind he treated are relevant for the study of molecular dynamics. Another study of note involves his creative use of the relationship between periodic and homoclinic orbits to effectively quantize the “homoclinic torus”. Moving forward in time, he later introduced action billiards and studied the semiclassical theory of breaking time-reversal symmetry.
Throughout his career, he has contributed to advances in understanding of the Weyl representation of quantum mechanics; a recent treatise is published in Physics Reports. The related semiclassical Wigner function remains one of his primary personal interests. Recently, he has published a Physical Review Letter demonstrating its behavior for eigenstates that exhibit “phase space” localization such as scarring.

Prof. Ozorio's talk
on April 15, 2002

"The birth of 'Semiclassics':
A personal view of the
Gutzwiller Trace Formula"