Husimi dynamics generated by non-Hermitian Hamiltonians

Abstract

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 analyse 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 behaviours. We demonstrate how the full quantum dynamics unfolds on top of the classical Husimi dynamics for two instructive examples.

arXiv comment6 pages and 3 figures

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Cited by in corpus (8)

• Self acceleration from spectral geometry in dissipative quantum-walk dynamics
• Semiclassical Husimi distributions for non-Hermitian quantum systems
• Complex semiclassical theory for non-Hermitian quantum systems
• Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator
• Pseudo-Hermitian extensions of the harmonic and isotonic oscillators
• Correspondence principle, dissipation, and Ginibre ensemble
• Quantum-to-semiclassical Husimi dynamics of non-Hermitian localization transitions
• Quantum signatures and semiclassical limitations in the transmission of Fock states