# PT-symmetric hamiltonians: Transition from non-dissipative to dissipative system

It is known that Spectrum of a non-hermitian hamiltonian is complex ($E_n-i\gamma_n$) and they represent the dissipative system. eg, Damped harmonic oscillator(DHO), where $E_n$ are the energies of the DHO and $\gamma_n$ describes the decaying rate of its states. It is also known that Spectrum of a hermitian hamiltonian is real and they represent the Non-dissipative system(HO).

In PT-Symmetric hamiltonians: Spectrum is real if PT-symmetry is unbroken and it is complex if it is broken.

Now my ques is: this transition of PT-symmetry can be understood as transition from dissipative system to non-dissipative system ?.

Could anybody give me a simple example ?

• PT-symmetric 'quantum mechanics' is, as far as I know, an extremely niche subject mostly advocated by a single person (Carl Bender) and colleagues, and there are some strong objections to it. It might thus be best to email Prof. Bender directly. – Al Nejati Sep 18 '18 at 5:48
• @AlNejati, Okay, He is a very busy person, so I wonder whether he will reply to it or not. – Epsilon Sep 18 '18 at 11:50
• @Al Nejati No, properly appreciated, the objectors have nuanced their understanding to a mainstream status. At the most conservative, PTQM is a shortcut of plain QM. – Cosmas Zachos Jul 12 at 20:03