On the PT invariant complex periodic potential V(x) = 4 cos² x + 4 i V₀ sin 2x

Bikashkali Midya

Indian Statistical Institute, Physics and Applied mathematics Unit, Kolkata, India

The equivalent Hermitian Hamiltonian of the PT symmetric Hamiltonian with the complex periodic potential V(x) = 4 cos2 x + 4 i V0 sin 2x has been obtained. It is shown that there exist a second critical point V0~.888437 of the Hamiltonian, apart from the known threshold V0=.5, after which no part of the band structure remains real. Relevant physical consequence of this finding has been pointed out.

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