Information geometry of complex Hamiltonians and exceptional points

DOI10.3390/e15093361zbMath1371.82059arXiv1307.4017OpenAlexW2044880278WikidataQ62272434 ScholiaQ62272434MaRDI QIDQ280516

Eva-Maria Graefe, Dorje C. Brody

Publication date: 10 May 2016

Published in: Entropy (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.4017

zbMATH Keywords

perturbation theoryphase transitioninformation geometryPT symmetryFisher-Rao metricexceptional pointnon-Hermitian Hamiltonian

Mathematics Subject Classification ID

Related Items (3)

Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions ⋮ Exact description of coalescing eigenstates in open quantum systems in terms of microscopic Hamiltonian dynamics ⋮ Dynamics of finite dimensional non-hermitian systems with indefinite metric

Cites Work

• Unnamed Item
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• Nongeneric eigenvalue perturbations of Jordan blocks
• Dynamics of quantum systems embedded in a continuum
• Bifurcations and exceptional points in dipolar Bose–Einstein condensates
• Visualization of Branch Points in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:math>-Symmetric Waveguides
• Information-Theoretic Differential Geometry of Quantum Phase Transitions
• Signatures of three coalescing eigenfunctions
• Extension d'une formule de Lagrange à des problèmes de valeurs propres
• A non-Hermitian \mathcal{P}\mathcal{T} symmetric Bose–Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Biorthogonal quantum systems
• Coherent states and rational surfaces
• Quantal phase factors accompanying adiabatic changes
• The Role of Sufficiency and of Estimation in Thermodynamics
• Statistical geometry in quantum mechanics
• Geometrization of statistical mechanics
• Geometry of quantum evolution
• Geometry of Quantum Statistical Inference
• 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 physics of exceptional points
• Quantum phase transitions without thermodynamic limits
• Information geometry in vapour–liquid equilibrium
• Geometric phase for non-Hermitian Hamiltonians and its holonomy interpretation
• ON MATRICES DEPENDING ON PARAMETERS
• Projective Hilbert space structures at exceptional points
• Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation
• Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model

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