|Welcome to the website for the 2009 Quantum Mechanics in the Complex Domain conference to be held at Washington University in St. Louis, MO on March 27-28, 2009. You'll find links for registration, accommodations, schedule, etc. on the navigation bar above.|
The background figure on the conference poster to the right is taken from "Spontaneous Breaking of Classical PT Symmetry," C. M. Bender and
D. W. Darg, J. Math. Phys. 48, 042703 (2007) [arXiv: hep-th/0703072].
Almost all classical trajectories x(t) of a PT-symmetric Hamiltonian are themselves PT symmetric (that is, they are left-right symmetric in the complex-x plane). However, a set of measure 0 of classical trajectories are not PT symmetric, and these trajectories are up-down symmetric. The classical trajectory shown here is one of these rare non-PT-symmetric trajectories. The shape of the trajectory is governed by the Hamiltonian H = p2 + x2(ix)ε, with ε = 16/15. The trajectory is a closed, periodic orbit in the complex-x plane. This trjectory does not cross itself; the lines that seem to cross actually lie on different sheets of a Riemann surface. The figure has been rotated by 90 degrees to emphasize the smile-like structure at the center.