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.

6 pages and 3 figures

References in corpus (4)

• Quantum trajectories and open many-body quantum systems
• Semiclassical structure of chaotic resonance eigenfunctions
• Wave packet evolution in non-Hermitian quantum systems
• Universal intensity statistics of multifractal resonance states

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