Husimi Dynamics Generated by non-Hermitian Hamiltonians

The dynamics generated by non-Hermitian Hamiltonians are often less intuitive than those of conventional Hermitian systems. Even for models as simple as a complexified harmonic oscillator, the dynamics for generic initial states shows surprising features. Here we analyze the dynamics of the Husimi distribution in a semiclassical limit, illuminating the foundations of the full quantum evolution. The classical Husimi evolution is composed of two factors: (i) the initial Husimi distribution evaluated along phase-space trajectories and (ii) the final value of the norm corresponding to each phase-space point. Both factors conspire to lead to intriguing dynamical behaviors. We demonstrate how the full quantum dynamics unfolds on top of the classical Husimi dynamics for two instructive examples.

Automated summary

The dynamics generated by non-Hermitian Hamiltonians are often more complex than those of conventional Hermitian systems. This is demonstrated even in simple models like the complexified harmonic oscillator, where the dynamics for generic initial states exhibit surprising features. In this study, we analyze the dynamics of the Husimi distribution in a semiclassical limit and provide insights into the foundations of the full quantum evolution. By studying the classical Husimi evolution, we reveal how the full quantum dynamics manifests on top of the classical dynamics for two informative examples.