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## Generic examples of PT-symmetric qubit (spin 1/2) Liouvillians

Tomaz Prosen

We outline two general classes of examples of PT-symmetric quantum Liouvillian dynamics of open many qubit systems, namely interacting hard-core bosons (or more general XYZ-type spin 1/2 systems) with, either (i) pure dephasing noise, or (ii) having solely single particle/spin injection/absorption incoherent processes.

http://arxiv.org/abs/1209.6588
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)

## Comment on: `Numerical estimates of the spectrum for anharmonic PT symmetric potentials’ [Phys. Scr. \textbf{85} (2012) 065005]

Paolo Amore, Francisco M Fernández

We show that the authors of the commented paper draw their conclusions from the eigenvalues of truncated Hamiltonian matrices that do not converge as the matrix dimension increases. In one of the studied examples the authors missed the real positive eigenvalues that already converge towards the exact eigenvalues of the non-Hermitian operator and focused their attention on the complex ones that do not. We also show that the authors misread Bender’s argument about the eigenvalues of the harmonic oscillator with boundary conditions in the complex-x plane (Rep. Prog. Phys. 70 (2007) 947).

http://arxiv.org/abs/1209.6357

Quantum Physics (quant-ph)