Non-Hermitian quantum mechanics and symplectic geometry

July 16 to July 20, 2018

at the

American Institute of Mathematics, San Jose, California

organized by

Eva-Maria Graefe, Michael Hitrik, Roman Schubert, and Alejandro Uribe

Original Announcement

This workshop will be devoted to the exploration of new connections between complex symplectic geometry, quantum mechanics with non-hermitian hamiltonians, and spectral theory of non-selfadjoint operators. Symplectic geometry, as the geometry underlying classical hamiltonian mechanics, has been proven to be extremely useful for understanding problems in quantum mechanics and the spectral theory of self-adjoint operators, in the semiclassical limit. This has lead to the areas of microlocal and semiclassical analysis which underpin a large part of the modern theory of PDEs. While quantum mechanics traditionally uses hermitian hamiltonians to describe closed quantum systems, recently there has been a surge of interest in non-hermitian hamiltonians to describe open quantum systems with losses. This leads to complex hamiltonian flows and hence complex symplectic geometry. Recently new connections between these fields have emerged and the aim of the workshop will be to develop a deeper understanding of these connections and to explore if they can be used to attack some of the open problems in the theory of open quantum systems and non self-adjoint operators.

The main topics of the workshop are:

We wish to bring together experts in complex and symplectic geometry, microlocal and semiclassical analysis, and quantum mechanics, interested in working across areas on at least some of the topics listed above.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.