Phase space representation of non-Hermitian system with $\mathcal{P}\mathcal{T}$-symmetry

Abstract

We present a phase space study of non-Hermitian Hamiltonian with $\mathcal{P}\mathcal{T}$-symmetry based on the Wigner distribution function. For an arbitrary complex potential, we derive a generalized continuity equation for the Wigner function flow and calculate the related circulation values. Studying vicinity of an exceptional point, we show that a $\mathcal{P}\mathcal{T}$-symmetric phase transition from an unbroken $\mathcal{P}\mathcal{T}$-symmetry phase to a broken one is a second-order phase transition.

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Cited by in corpus (3)

• Transport properties in a Non-Hermitian triple-quantum-dot structure
• Unitary vs pseudo-unitary time evolution and statistical effects in the dynamical Sauter-Schwinger process
• $\mathcal{P}\mathcal{T}$-symmetry in compact phase space for a linear Hamiltonian