The minimally anisotropic metric operator in quasi-Hermitian quantum mechanics

DOI10.1098/rspa.2018.0264zbMath1407.81097arXiv1804.06766OpenAlexW3103576753WikidataQ58561648 ScholiaQ58561648MaRDI QIDQ4626132

Miloslav Znojil, Vladimir Lotoreichik, David Krejčiřík

Publication date: 27 February 2019

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.06766

zbMATH Keywords

PT-symmetryquasi-Hermitian quantum mechanicsbasis propertiesmetric operatorsimilarity transforms

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (11)

Anomalous mechanisms of the loss of observability in non-Hermitian quantum models ⋮ Multi-well log-anharmonic oscillators ⋮ Quantum graphs: self-adjoint, and yet exhibiting a nontrivial \(\mathcal{PT}\)-symmetry ⋮ Passage through exceptional point: case study ⋮ Quantum mechanics using two auxiliary inner products ⋮ Unitary unfoldings of a Bose–Hubbard exceptional point with and without particle number conservation ⋮ Spectral analysis of bounded operators on semi-Hilbertian spaces ⋮ Hidden symmetries in non-self-adjoint graphs ⋮ Hybrid form of quantum theory with non-Hermitian Hamiltonians ⋮ Systematics of quasi-Hermitian representations of non-Hermitian quantum models ⋮ The collapse of quasi-self-adjointness at the exceptional points of a PT -symmetric model with complex Robin boundary conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spectral analysis of the diffusion operator with random jumps from the boundary
• On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators
• Traceable integral kernels on countably generated measure spaces
• Unified theory of nuclear reactions
• Quasi-Hermitian operators in quantum mechanics and the variational principle
• Complex Extension of Quantum Mechanics
• Non-Selfadjoint Operators in Quantum Physics
• PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
• Calculation of the metric in the Hilbert space of a {\cal P}{\cal T} -symmetric model via the spectral theorem
• Complex Magnetic Fields: An Improved Hardy--Laptev--Weidl Inequality and Quasi-Self-Adjointness
• One-dimensional Schrödinger operators with -symmetric zero-range potentials
• Closed formula for the metric in the Hilbert space of a -symmetric model
• Metric operator in pseudo-Hermitian quantum mechanics and the imaginary cubic potential

This page was built for publication: The minimally anisotropic metric operator in quasi-Hermitian quantum mechanics