### Non-Hermitian quantum systems, classical dissipation, and PT-symmetry

**Graefe, E ***(Bristol)*

Thursday 15 April 2010, 14:50-15:10

Seminar Room 1, Newton Institute

#### Abstract

Non-Hermitian operators play a crucial role in various fields of mathematics and physics and have attracted considerable attention recently from both fields. While in quantum mechanics the Hamiltonian is traditionally demanded to be Hermitian for the description of a closed system, there is a rapidly growing interest in the use of non-Hermitian Hamiltonians arising from different areas. The first is the field of open quantum systems where the overall probability decreases in time, such as decay, transport and scattering phenomena. The second motivation arises from the observation that there is a class of non-Hermitian operators (often called PT-symmetric) yielding purely real eigenvalues that can be used to define a fully consistent quantum theory for closed systems. In the present talk we will give a brief overview of non-Hermitian quantum theories, and furthermore introduce their classical analogues, described by dissipative phase space flows.