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

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 $V_0<0.5$, 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 $V_0=0.5$, for $V_0^c.888437$ after which no part of the eigenvalues and the band structure remains real. Relevant physical consequence of this finding has been pointed out.

References in corpus (3)

• Making Sense of Non-Hermitian Hamiltonians
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• A complex periodic QES potential and exceptional points

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• PT-symmetric optical superlattices
• Peregrine rogue waves in the nonlocal nonlinear Schrödinger equation with parity-time symmetric self-induced potential
• Interlace properties for the real and imaginary parts of the wave functions of complex-valued potentials with real spectrum
• E2-quasi-exact solvability for non-Hermitian models
• A new non-Hermitian E2-quasi-exactly solvable model
• Polar magneto-optic Kerr and Faraday effects in finite periodic \texorpdfstring{$\mathcal{P}\mathcal{T}$}{PT}-symmetric systems
• Refractive index profiles for a $\mathcal{P}\mathcal{T}$-symmetric optical structure
• Singular Mapping for a $PT$-Symmetric Sinusoidal Optical Lattice at the Symmetry-Breaking Threshold