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.

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Cited by in corpus (40)

• Non-Hermitian Physics
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• PT-symmetry with a system of three-level atoms
• Invisibility in PT-symmetric complex crystals
• Observation of Defect States in PT-Symmetric Optical Lattices
• Invisibility and PT-symmetry
• Continuous and discrete Schrodinger systems with PT-symmetric nonlinearities
• PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold
• Supersymmetry-generated complex optical potentials with real spectra
• Nonlinear localized modes in PT-symmetric Rosen-Morse potential well
• Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity
• Transfer Matrices as Non-Unitary S-Matrices, Multimode Unidirectional Invisibility, and Perturbative Inverse Scattering
• Localized modes in ${\chi }^{(2)}$ media with $\PT$-symmetric localized potential
• Supersymmetry generated one-way invisible PT-symmetric optical crystals
• Scattering by finite periodic $\mathcal{P}\mathcal{T}$-symmetric structures
• 2D Solitons in PT-symmetric photonic lattices
• Solitons in $\mathcal{P}\mathcal{T}$-symmetric periodic systems with the quadratic nonlinearity
• Peregrine Rogue Wave dynamics in the continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity
• Invisible defects in complex crystals
• Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
• Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and PT-symmetric potential
• Infinite families of (non)-Hermitian Hamiltonians associated with exceptional $X_m$ Jacobi polynomials
• Scattering amplitudes for the rationally extended P T symmetric complex potentials
• PT-symmetric optical superlattices
• Use of Equivalent Hermitian Hamiltonian for $PT$-Symmetric Sinusoidal Optical Lattices
• Peregrine rogue waves in the nonlocal nonlinear Schrödinger equation with parity-time symmetric self-induced potential
• Spectral Singularity in confined PT symmetric optical potential
• Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians
• Interlace properties for the real and imaginary parts of the wave functions of complex-valued potentials with real spectrum
• A unidirectional invisible PT-symmetric complex crystal with arbitrary thickness
• E2-quasi-exact solvability for non-Hermitian models
• The Spectrum of the Hamiltonian with a PT-symmetric Periodic Optical Potential
• Spontaneous PT-symmetry breaking for systems of noncommutative Euclidean Lie algebraic type
• Spectral Analysis of the Schrodinger Operator with an Optical Potential
• Non-Hermitian systems of Euclidean Lie algebraic type with real eigenvalue spectra
• 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
• Singular Mapping for a $PT$-Symmetric Sinusoidal Optical Lattice at the Symmetry-Breaking Threshold
• Refractive index profiles for a $\mathcal{P}\mathcal{T}$-symmetric optical structure
• A unifying E2-quasi-exactly solvable model