In recent research perspective this is very important field. Parity operation is reversal of co-ordinate (x->-x, p->-p)and time reversal operation is reversal of time (x->x,p->-p, i->-i).
But talking about this combined PT-symmetry in any field of science and engineering, what it implies?
"The central idea of PT -symmetric quantum theory is to replace the condition that the Hamiltonian of a quantum theory be Hermitian with the weaker condition that it possess space-time reflection symmetry (PT symmetry). This allows us to construct and study many new kinds of Hamiltonians that would previously have been ignored. These new Hamiltonians have remarkable mathematical properties and it may well turn out that these new Hamiltonians will be useful in describing the physical world. It is crucial, of course,that in replacing the condition of Hermiticity by PT symmetry we do not give up any of the key physical properties that a quantum theory must have."(Ref-"Introduction to PT -Symmetric Quantum Theory",C.M Bender)
Appreciate your answer.
Actually, I was thinking it more intuitively, like just inversal of space and time co-ordinates and system able to conserve symmetry under these operations, are showing remarkable consequences. What's happening when this symmetry is conserved leading to those results, symmetry breaking, exceptional points.
Hi,
So far as I'm concerned, it might be related to a question in Quantum Mechanics. Given that: "The eigenvalues of physical obervables should have real spectra" & "Hermitian Hamiltonians operators exhibit real eigenvalues", then "If all physical operators need to be Hermitian operators to have real eigenvalues?"
The answer might be negative. "Non-Hermitian Hamiltonians that respect parity–time (PT) symmetry and exhibit real spectra", which is thought to potentially revolutionize and extend quantum theories into new
regimes.
Meanwhile, "The flexibility of photonics allows for creating and superposing non-Hermitian eigenstates with ease using optical gain and loss, which makes it an ideal platform to explore various non-Hermitian quantum symmetry paradigms for novel device functionalities". The extended reading could be reached to the following review.
L. Feng, et al. " Non-Hermitian photonics based on parity–time symmetry," Nature Photonics 11(12) 2017.
Article Non-Hermitian photonics based on parity–time symmetry
Regards,
Yuan
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