English

A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x

Quantum Physics 2011-01-04 v1 Mathematical Physics math.MP Spectral Theory

Abstract

It is shown that the PT symmetric Hamiltonian with the periodic potential V(x) = 4 cos^2 x + 4 i V_0 sin 2x can be mapped into a Hermitian Hamiltonian for V0<0.5V_0<0.5, by a similarity transformation. It is also shown that there exist a second critical point of the potential V(x), apart from the known critical point V0=0.5V_0=0.5, for V0c .888437V_0^c ~ .888437 after which no part of the eigenvalues and the band structure remains real. Relevant physical consequence of this finding has been pointed out.

Keywords

Cite

@article{arxiv.1004.3218,
  title  = {A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x},
  author = {Bikashkali Midya and Barnana Roy and Rajkumar Roychoudhury},
  journal= {arXiv preprint arXiv:1004.3218},
  year   = {2011}
}