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Wave packet evolution for non-Hermitian quantum systems in the semiclassical limit

Eva-Maria Graefe

Mercredi 15 octobre 2014

à 11h en salle C. Brot

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 first is the field of open quantum systems where the overall probability decrease in time, which can be described via complex energies. Applications include, for example, 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. Interestingly, the classical analogues of non-Hermitian quantum theories have hitherto remained almost unexplored. In this talk I present some results, obtained in collaboration with Roman Schubert (Bristol), on the quantum evolution of Gaussian wave packets generated by a non-Hermitian Hamiltonian in the semiclassical limit of small h-bar. This yields the non-Hermitian analogue 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.