Abstract of Proposed Research Jean Bellissard
This award will support the development of a general theory of solids based on the properties of their microscopic structure. Our particular interest is to describe the ground state of a solid. We will investigate the development of a mathematically rigorous description of quantum dissipative transport based on analyses of interactions between particles in an aperiodic solid. Mathematically this research involves the use of noncommutative geometry and probability theory on Polish spaces.
The question of how quantum properties determine the phenomenology of related solids is a fundamental problem in mathematical physics and materials science. The PI has worked on these issues for many years and has obtained many important results on quantum transport in solids and the quantum Hall effect. His research under this award, and with a number of collaborators, continues a program that should help provide a mathematical foundation for such theories.
