Eva-Maria Graefe

Quantum mechanics traditionally focuses on Hermitian operators for the description of closed systems. However, there is a rapidly growing interest arising from different areas in the use of non-Hermitian operators. The classical analogues of non-Hermitian quantum theories, however, have hitherto been rarely investigated. In this talk I present results on the quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian in the semiclassical limit of small h-bar. This yields the non-Hermitian analog of the Ehrenfest theorem for the dynamics of observable expectation values. The resulting equations of motion for dynamical variables are coupled to an equation of motion for the phase-space metric---a phenomenon having no analogue in Hermitian theories.