Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra

DOI10.1016/j.aop.2014.04.002zbMath1342.81132arXiv1401.4426OpenAlexW3103925916MaRDI QIDQ530775

Sanjib Dey, Thilagarajah Mathanaranjan, Andreas Fring

Publication date: 1 August 2016

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.4426

zbMATH Keywords

optical latticesquasi-exactly solvable modelseuclidean algebrasMathieu equationsPT-symmetric non-Hermitian systems

Mathematics Subject Classification ID

Symmetry breaking in quantum theory (81R40) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12) Special quantum systems, such as solvable systems (81Q80)

Related Items (6)

A Unifying E2-Quasi Exactly Solvable Model ⋮ Spontaneous PT-symmetry breaking for systems of noncommutative Euclidean Lie algebraic type ⋮ Controlling decoherence via \(\mathcal{PT}\)-symmetric non-Hermitian open quantum systems ⋮ Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians ⋮ A new non-Hermitian \(E_2\)-quasi-exactly solvable model ⋮ A Squeezed Review on Coherent States and Nonclassicality for Non-Hermitian Systems with Minimal Length

Cites Work

• Unnamed Item
• A note on the \(\mathcal PT\) invariant periodic potential \(V(x) = 4\cos^2x + 4iV_0\sin2x\)
• Extending \(\mathcal{P}\mathcal{T}\) symmetry from Heisenberg algebra to E2 Algebra
• Invisible defects in complex crystals
• Metric operators for non-Hermitian quadraticsu(2) Hamiltonians
• PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
• Use of equivalent Hermitian Hamiltonian forPT-symmetric sinusoidal optical lattices
• Normal Form of Antiunitary Operators
• Antilinear deformations of Coxeter groups, an application to Calogero models
• Group theoretic quantisation of strings on tori
• Lie-algebras and linear operators with invariant subspaces
• Generalized PT symmetry and real spectra
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• Some nonunitary, indecomposable representations of the Euclidean algebra \mathfrak {e}(3)
• Time evolution of non-Hermitian Hamiltonian systems
• Non-Hermitian Hamiltonians of Lie algebraic type
• Introduction to Lie Algebras and Representation Theory

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