| Unit name | Quantum Chaos |
|---|---|
| Unit code | MATHM5700 |
| Credit points | 10 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Dr. Muller |
| Open unit status | Not open |
| Pre-requisites |
Mechanics 2 or Mechanics 23 and Quantum Mechanics or equivalent for Physics students. |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Quantum Chaos studies the mathematical and physical properties that in quantum systems are signatures of the chaotic nature of the underlying classical mechanics. At miscropscopic length scales, the chaotic dynamics of the corresponding classical system manifests himself in the behaviour of the eignfunctions and of the energy levels of the quantum Hamiltonian. For example, when the classical motion is regular the eigenvalues of the quantum system appear as a sequence of uniformly distributed random numbers, while if the dynamics is ergodic they manifest a more rigid structure and tend to repel each other. The course will discuss the main features of the spectra and eigenfunctions of quantum Hamiltonians whose classical limit is chaotic. We will introduce the most important mathematical techniques used to study these systems, like the Gutzwiller trace formla and the random wave model. Most of the topics will be presented within the framework of systems with a discrete time dynamics (quantum maps), as they often allow a thorough mathematical treatment. The unit will also include the main ideas behind two of the most important areas of research in the subject: the random matrix theory conjecture and the problem of quantum unique ergodicity.
