Energy band structure due to a complex, periodic, PT-invariant potential

DOI10.1016/S0375-9601(01)00426-1zbMath0969.81667OpenAlexW1990738387MaRDI QIDQ5938061

Zafar Ahmed

Publication date: 31 July 2001

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0375-9601(01)00426-1

zbMATH Keywords

band gapsBrillouin zone boundariesKronig-Penny type potential

Mathematics Subject Classification ID

Many-body theory; quantum Hall effect (81V70)

Related Items (19)

Time evolution for quantum systems with a dynamical Hilbert space ⋮ A PSEUDO-UNITARY ENSEMBLE OF RANDOM MATRICES, PT-SYMMETRY AND THE RIEMANN HYPOTHESIS ⋮ Non-Hermitian \(d\)-dimensional Hamiltonians with position-dependent mass and their \(\eta\)-pseudo-Hermiticity generators ⋮ Exact solutions of the Schrödinger equation with a complex periodic potential ⋮ A note on the \(\mathcal PT\) invariant periodic potential \(V(x) = 4\cos^2x + 4iV_0\sin2x\) ⋮ REAL SPECTRUM OF NON-HERMITIAN HAMILTONIANS FOR HULTHÉN POTENTIAL ⋮ On the spectral properties of the Schrödinger operator with a periodic PT-symmetric potential ⋮ A criterion for the reality of the spectrum of \(PT\)-symmetric Schrödinger operators with complex-valued periodic potentials ⋮ Contact interactions and Kronig–Penney models in Hermitian and $ \boldsymbol {\mathcal {PT}}$ symmetric quantum mechanics ⋮ Stability boundaries of a Mathieu equation having \textit{PT} symmetry ⋮ Handedness of complex PT-symmetric potential barriers ⋮ Analytically solvable PT-invariant periodic potentials ⋮ Bound state solutions of the Schrödinger equation for a \(\mathcal{PT}\)-symmetric potential with Dirac delta functions ⋮ An ansatz for the eigenstates in \(\mathcal{PT}\)-symmetric quantum mechanics ⋮ \({\mathcal{PT}}\)-symmetric periodic optical potentials ⋮ Pseudo-Hermiticity of Hamiltonians under gauge-like transformation: real spectrum of non-Hermitian Hamiltonians ⋮ \(\eta \)-weak-pseudo-hermiticity generators and radially symmetric Hamiltonians ⋮ ${\mathcal{CPT}}$-CONSERVING HAMILTONIANS AND THEIR NONLINEAR SUPERSYMMETRIZATION USING DIFFERENTIAL CHARGE-OPERATORS ${\mathcal C}$ ⋮ Phase space trajectories and quantization in PT-symmetric quantum mechanics

Cites Work

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• Complex periodic potentials with real band spectra.
• One-dimensional crystal with a complex periodic potential
• Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential

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