Passage through exceptional point: case study

DOI10.1098/RSPA.2019.0831zbMath1472.81096arXiv2003.05876OpenAlexW3102124971MaRDI QIDQ5160912

Miloslav Znojil

Publication date: 29 October 2021

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/2003.05876

zbMATH Keywords

phase transitionstransition matricesatomic and molecular physicsmathematical physicsquantum physicsnon-Hermitian degeneraciesclosed-form toy modelsquasi-hermitian quantum Hamiltonians

Mathematics Subject Classification ID

Open systems, reduced dynamics, master equations, decoherence (81S22) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Related Items (3)

Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians ⋮ Zig-zag-matrix algebras and solvable quasi-Hermitian quantum models ⋮ Unitary unfoldings of a Bose–Hubbard exceptional point with and without particle number conservation

Cites Work

• Unnamed Item
• Three solvable matrix models of a quantum catastrophe
• Conditional observability
• Multiply degenerate exceptional points and quantum phase transitions
• Quasi-Hermitian operators in quantum mechanics and the variational principle
• Hermitian-non-Hermitian interfaces in quantum theory
• Two patterns of \(\mathcal{PT}\)-symmetry breakdown in a non-numerical six-state simulation
• Open problems: Matrix Hamiltonians with a chance of being complex symmetric
• Non-Hermitian interaction representation and its use in relativistic quantum mechanics
• Parity-time symmetry and the toy models of gain-loss dynamics near the real Kato's exceptional points
• Generalized Bose-Hubbard Hamiltonians exhibiting a complete non-Hermitian degeneracy
• Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding
• Non-Selfadjoint Operators in Quantum Physics
• PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
• Non-Hermitian Quantum Mechanics
• Pseudospectra in non-Hermitian quantum mechanics
• Horizons of stability
• A non-Hermitian \mathcal{P}\mathcal{T} symmetric Bose–Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• A non-Hermitian Hamilton operator and the physics of open quantum systems
• 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
• The minimally anisotropic metric operator in quasi-Hermitian quantum mechanics
• Coupling of eigenvalues of complex matrices at diabolic and exceptional points
• The physics of exceptional points
• Quantum catastrophes: a case study
• Exceptional points in optics and photonics
• Maximal couplings in -symmetric chain models with the real spectrum of energies
• Tridiagonal {\cal PT} -symmetricN-by-NHamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime

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