Wave packet evolution in non-Hermitian quantum systems

Abstract

The quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical limit $\hslash \to 0$ this yields the non-Hermitian analog of the Ehrenfest theorem for the dynamics of observable expectation values. The lack of Hermiticity reveals the importance of the complex structure on the classical phase space: The resulting equations of motion are coupled to an equation of motion for the phase space metric---a phenomenon having no analog in Hermitian theories.

Example added, references updated, 4 pages, 2 figures

References in corpus (6)

• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• PT-Symmetric Wave Chaos
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Fractal Weyl laws for chaotic open systems
• Semiclassical structure of chaotic resonance eigenfunctions
• An efficient and accurate method to obtain the energy-dependent Green function for general potentials