| While non-Hermitian quantum Hamiltonians are well established for the description of open quantum systems and in PT-symmetric quantum mechanics, their classical analogues have hitherto remained almost unexplored. In this talk the quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian is investigated 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. The effect of the non-Hermiticity that can improve the accuracy of the classical approximation is illustrated in several examples. |
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