Non-Hermitian Quantum Mechanics of Bosonic Operators

DOI10.1007/978-3-319-72449-2_3zbMath1428.81087arXiv1705.11153OpenAlexW2618192027MaRDI QIDQ4973483

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Publication date: 27 November 2019

Published in: Operator Theory, Operator Algebras, and Matrix Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.11153

zbMATH Keywords

Riesz basismetricspectral analysisnon-Hermitian Hamiltonianbosonic operator

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Linear accretive operators, dissipative operators, etc. (47B44) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Related Items (13)

Toward non-Hermitian quantum statistical thermodynamics ⋮ Order structures of \((\mathcal{D,E})\)-quasi-bases and constructing operators for generalized Riesz systems ⋮ Non-self-adjoint operators with real spectra and extensions of quantum mechanics ⋮ Ordered structures of constructing operators for generalized Riesz systems ⋮ A quantum system with a non-Hermitian Hamiltonian ⋮ An inverse eigenvalue problem for modified pseudo-Jacobi matrices ⋮ Non-self-adjoint Hamiltonians defined by sesquilinear forms and their physical applications ⋮ Implications of losing hermiticity in quantum mechanics ⋮ Saigo-Maeda operators involving the Appell function, real spectra from symmetric quantum Hamiltonians and violation of the second law of thermodynamics for quantum damped oscillators ⋮ Regular biorthogonal pairs and pseudo-bosonic operators ⋮ An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices ⋮ Generalized inverse spectral problem for pseudo-Jacobi matrices with mixed eigendata ⋮ Some invariant biorthogonal sets with an application to coherent states

Cites Work

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• Examples of pseudo-bosons in quantum mechanics
• Classes of linear operators. Vol. I
• Quasi-Hermitian operators in quantum mechanics and the variational principle
• Pseudo-Hermitian Quantum Mechanics with Unbounded Metric Operators
• Non-Selfadjoint Operators in Quantum Physics
• Pseudospectra in non-Hermitian quantum mechanics
• 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
• Nonlinear pseudo-supersymmetry in the framework of -fold supersymmetry

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