In non-hermitian Quantum mechanics states,for certain threshold value of pseudo-hermitian Hamiltonian will give real to complex eigen value spectra and abrupt phase transition have occurred at some point.About this point spontaneous break down of parity-time symmetry(PT symmetry) have occurred but what is meaning of spontaneous breakdown of PT-symmetry????
The meaning is a break-down of the assumptions, and the intuition that a new model exists. Gauge models, for instance, depend on the underlying equation to define congruence. If the underlying model has a degeneracy (two or more results for the same point), that result may be natural (and the theory has to be corrected, to go back to functionality) or artificial (ditto, the theory has also to be corrected).
According to your answer, when spontaneous break down of PT symmetry have occurred there have some degeneracy of energy level but in this context degeneracy break previous condition. This degeneracy have in ground state or any higher energy level??
Let's, first, be a bit more careful in what you summarize of my answer.
When spontaneous break down of PT symmetry has occurred, there MAY be some degeneracy of energy levels. Other causes MAY exist, this is just the simplest, also it keeps the same model. Going back to the gauge models, they depend on the underlying equation to define congruence, thus degeneracy. It can affect any level.
Violation of one of the laws of conservation, namely of preservation of parity in weak couplings, motivated experiments aimed at verification of all known conservation laws, starting in 1957. This is the context of the interest in the spontaneous break down of parity-time symmetry (PT symmetry).
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