Phase-space representation of a non-Hermitian system with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math>symmetry

Abstract

We present a phase-space study of a 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 the 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.