Random matrix theory

Random matrices arise whenever complex systems are described by linear equations. For example, they are central to the mathematical description of complex quantum systems, such as molecular and nano-electrical networks, telecommunications in complex environments, large computer networks, and string theory.

Bristol has an internationally leading research group developing the fundamentals of random matrix theory and exploring significant new applications, for example to number theory and quantum information theory.

Quantum chaos

Newton's laws of motion accurately describe how relatively large objects move, but they fail for very small objects. They then have to be replaced by quantum mechanical laws of motion. For example, quantum mechanics is needed to describe the dynamics of the electrons inside atoms and molecules. The borderland where Newton's laws give way to quantum mechanics is mathematically extremely interesting, particularly when the Newtonian dynamics is chaotic.