A generalized Heisenberg-Robertson uncertainty inequality holds across unbroken, broken, and exceptional-point regimes in non-Hermitian dynamics when consistent metrics are used to define expectation values and variances.
of the components of⃗ σ: θs = arccos (⟨σ z⟩S), φs = arctan ⟨σy⟩S ⟨σx⟩S .(52) In Figure 7 we plot the anglesθ S andφ S as a function of time, for different sets of parameters
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Uncertainty inequalities in a non-Hermitian scenario
A generalized Heisenberg-Robertson uncertainty inequality holds across unbroken, broken, and exceptional-point regimes in non-Hermitian dynamics when consistent metrics are used to define expectation values and variances.