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arXiv · 1604.08405

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

Ludmila Praxmeyer·Popo Yang·Ray-Kuang Lee
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Abstract

We present a phase space study of non-Hermitian Hamiltonian with $\mathcal{PT}$-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 $\mathcal{PT}$-symmetric phase transition from an unbroken $\mathcal{PT}$-symmetry phase to a broken one is a second-order phase transition.

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Ludmila Praxmeyer, Popo Yang, Ray-Kuang Lee. 2016-04-28. Phase space representation of non-Hermitian system with $\mathcal{PT}$-symmetry. https://doi.org/10.1103/physreva.93.042122

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