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Husimi Dynamics Generated by non-Hermitian Hamiltonians.

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Non-Hermitian quantum systems exhibit complex dynamics. Analyzing the semiclassical Husimi distribution reveals how classical trajectories and norm evolution explain surprising quantum behaviors in these systems.

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Area of Science:

  • Quantum mechanics
  • Non-Hermitian systems
  • Semiclassical analysis

Background:

  • Dynamics in non-Hermitian Hamiltonians are counterintuitive compared to Hermitian systems.
  • Even simple models like the complexified harmonic oscillator display unexpected dynamics for generic initial states.

Purpose of the Study:

  • To analyze the semiclassical dynamics of the Husimi distribution.
  • To illuminate the foundations of full quantum evolution in non-Hermitian systems.
  • To explain intriguing dynamical behaviors arising from classical Husimi evolution.

Main Methods:

  • Semiclassical limit analysis of the Husimi distribution.
  • Decomposition of classical Husimi evolution into trajectory-dependent and norm-dependent factors.
  • Comparison of classical Husimi dynamics with full quantum dynamics for specific examples.

Main Results:

  • The classical Husimi evolution is determined by initial distribution along trajectories and the final norm value.
  • These two factors in classical Husimi evolution lead to complex dynamical behaviors.
  • Full quantum dynamics were shown to unfold based on the derived classical Husimi dynamics.

Conclusions:

  • The semiclassical Husimi distribution provides insight into non-Hermitian quantum dynamics.
  • Classical Husimi evolution, with its trajectory and norm components, explains observed quantum phenomena.
  • This framework aids in understanding the counterintuitive dynamics of non-Hermitian systems.