The DOI matches its Crossref record.
Non-Hermitian Quantum Mechanics
Abstract
Non-Hermitian quantum mechanics (NHQM) is an important alternative to the standard (Hermitian) formalism of quantum mechanics, enabling the solution of otherwise difficult problems. The first book to present this theory, it is useful to advanced graduate students and researchers in physics, chemistry and engineering. NHQM provides powerful numerical and analytical tools for the study of resonance phenomena - perhaps one of the most striking events in nature. It is especially useful for problems whose solutions cause extreme difficulties within the structure of a conventional Hermitian framework. NHQM has applications in a variety of fields, including optics, where the refractive index is complex; quantum field theory, where the parity-time (PT) symmetry properties of the Hamiltonian are investigated; and atomic and molecular physics and electrical engineering, where complex potentials are introduced to simplify numerical calculations.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“The concept of biorthonormal basis [44, 45] plays an important role in non-Hermitian quantum mechanics.”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [44]
In the citing paper
“In addition, the fact that 〈 〈 ξ k | is orthogornal to | ζ k ′ 〉 〉 , (199), even though the two sets {〈 〈 ξ k | } and {| ζ k 〉 〉} are not conjugate transpose of each other, implies that the superoperators {| ζ k 〉 〉〈 〈 ξ k | } constitute what we call a biorthonormal basis [44, 45] for S d .”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [44]
Citations
Cites
Still being checked.
Cited by
Sorted by citations
Items 701–800 of 1,000
Nennig, B., & Perrey‐Debain, E. (2020) · Journal of Computational Physics · doi:10.1016/j.jcp.2020.109425 · Cited by 11
Das, A., Ghosh, N., & Nath, D. (2020) · Physics Letters A · doi:10.1016/j.physleta.2020.126681 · Cited by 11
Fang, Y., Kottos, T., & Thevamaran, R. (2021) · New Journal of Physics · doi:10.1088/1367-2630/ac09c9 · Cited by 11
Quantum computing for atomic and molecular resonances
Bian, T., & Kais, S. (2021) · The Journal of Chemical Physics · doi:10.1063/5.0040477 · Cited by 11
Discrete solitons dynamics in $$\mathscr {PT}$$-symmetric oligomers with complex-valued couplings
Kirikchi, O. B., & Karjanto, N. (2021) · Nonlinear Dynamics · doi:10.1007/s11071-021-06217-5 · Cited by 11
Environment-assisted strong coupling regime
Sergeev, T. T., Vovchenko, I. V., Zyablovsky, A. A., & Andrianov, E. S. (2022) · Quantum · doi:10.22331/q-2022-04-13-684 · Cited by 11
Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
Zeng, Q.-B., & Lü, R. (2022) · Physical Review A · doi:10.1103/physreva.105.042211 · Cited by 11
Schwinn, K., Zapata, F., Levitt, A., Eric Cancès, B., Luppi, E., & Toulouse, J. (2022) · The Journal of Chemical Physics · doi:10.1063/5.0091073 · Cited by 11
Fundamental constraints on the observability of non-Hermitian effects in passive systems
Schomerus, H. (2022) · Physical Review A · doi:10.1103/physreva.106.063509 · Cited by 13
Decay Properties of Spectral Projectors with Applications to Electronic Structure
Michele Benzi, A., Boito, P., & Razouk, N. (2013) · SIAM Review · doi:10.1137/100814019 · Cited by 11
Introduction to the scattering theory
(1996) · Advanced series in mathematical physics · doi:10.1142/9789812798220_0007 · Cited by 11
Controlling vibrational cooling with zero-width resonances: An adiabatic Floquet approach
Leclerc, A., Viennot, D., Jolicard, G., Lefèbvre, R., & Atabek, O. (2016) · Physical Review A · doi:10.1103/physreva.94.043409 · Cited by 11
Absence of Floquet scattering in oscillating non-Hermitian potential wells
Longhi, S., & Valle, G. D. (2013) · Physical Review A · doi:10.1103/physreva.87.052116 · Cited by 11
Mode volume of electromagnetic resonators: let us try giving credit where it is duePreprint
Lalanne, P. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2011.00218 · Cited by 11
The RVP Method—From Real Ab-Initio Calculations to Complex Energies and Transition Dipoles
Landau, A., Haritan, I., & Moiseyev, N. (2022) · Frontiers in Physics · doi:10.3389/fphy.2022.854039 · Cited by 10
Self-citationBiorthogonal topological charge pumping in non-Hermitian systems
Zhang, Z., Li, T., Luo, X.-W., & Yi, W. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.224307 · Cited by 10
Topologically Protected Negative Entanglement
Xue, W., & Lee, C. H. (2025) · Advanced Science · doi:10.1002/advs.202513868 · Cited by 10
Dynamically assisted tunneling in the Floquet picture
Ryndyk, D., Kohlfürst, C., Queißer, F., & Schützhold, R. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.023056 · Cited by 10
Miao, C., Li, Y., Wang, J., Zhang, P., Li, Q., Hu, L.-Z., Xu, Y., & Kong, X.-M. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.014403 · Cited by 11
Fate of non-Hermitian free fermions with Wannier-Stark ladder
Li, H.-Z., Wan, M., & Zhong, J. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.094310 · Cited by 10
Reflections on the Spatial Exponential Growth of Electromagnetic Quasinormal Modes
Wu, T., Jaramillo, J. L., & Lalanne, P. (2025) · Laser & Photonics Review · doi:10.1002/lpor.202402133 · Cited by 10
Universal spreading dynamics in quasiperiodic non-Hermitian systems
Xing, Z.-Y., Chen, S., & Hu, H. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.l180203 · Cited by 10
Toward scalable bound-to-resonance extrapolations for few- and many-body systems
Yapa, N., König, S., & Fossez, K. (2025) · Physical Review C · doi:10.1103/physrevc.111.064318 · Cited by 10
Non-Hermitian oscillators with Td symmetry
Amore, P., Fernández, F. M., & Garcia, J. (2014) · Annals of Physics · doi:10.1016/j.aop.2014.11.018 · Cited by 10
Construction of complex STO-NG basis sets by the method of least squares and their applications
Matsuzaki, R., Asai, S., McCurdy, C. W., & Yabushita, S. (2014) · Theoretical Chemistry Accounts · doi:10.1007/s00214-014-1521-6 · Cited by 10
Tellander, F., & Berggren, K. (2017) · Physical Review A · doi:10.1103/physreva.95.042115 · Cited by 10
Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature
Grimaldi, A., Sergi, A., & Messina, A. (2021) · Entropy · doi:10.3390/e23020147 · Cited by 12
Exceptional points and scattering of discrete mechanical metamaterials
Wang, W., & Amirkhizi, A. V. (2022) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-022-02626-6 · Cited by 10
Application of Box and Voronoi CAPs for Metastable Electronic States in Molecular Clusters
Gayvert, J. R., & Bravaya, K. B. (2022) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.2c04892 · Cited by 10
Kondo effect in a non-Hermitian PT -symmetric Anderson model with Rashba spin-orbit coupling
Kulkarni, V. M., Gupta, A., & Vidhyadhiraja, N. S. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.106.075113 · Cited by 11
Application of Modified Smooth Exterior Scaling Method to Study 2Πg N2– and 2Π CO– Shape Resonances
Banuary, M., & Gupta, A. K. (2023) · ACS Omega · doi:10.1021/acsomega.3c00033 · Cited by 10
Transport effects in non-Hermitian nonreciprocal systems: General approach
Ghaemi-Dizicheh, H. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.125155 · Cited by 10
Husimi Dynamics Generated by non-Hermitian Hamiltonians
Holmes, K., Rehman, W., Malzard, S., & Graefe, E.-M. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.157202 · Cited by 10
Algebraic algorithms for eigen-problems of a reduced biquaternion matrix and applications
Guo, Z., Jiang, T., Wang, G., & Васильев, В. И. (2023) · Applied Mathematics and Computation · doi:10.1016/j.amc.2023.128358 · Cited by 10
Selected Configuration Interaction for Resonances
Damour, Y., Scemama, A., Kossoski, F., & Loos, P. (2024) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.4c02060 · Cited by 10
Entanglement Properties of the Two-Electron Quasi-One Dimensional Gaussian Quantum Dot
Kuroś, A., & Okopińska, A. (2015) · Few-Body Systems · doi:10.1007/s00601-015-0992-x · Cited by 10
Landau, A., Haritan, I., Kaprálová-Žďánská, P. R., & Moiseyev, N. (2015) · Molecular Physics · doi:10.1080/00268976.2015.1080872 · Cited by 10
Self-citationSimulation of X-ray transient absorption for following vibrations in coherently ionized F2 molecules
Dutoi, A. D., & Leone, S. R. (2016) · Chemical Physics · doi:10.1016/j.chemphys.2016.10.006 · Cited by 10
Magnus expansion applied to a dissipative driven two-level system
Begzjav, T., & Eleuch, H. (2020) · Results in Physics · doi:10.1016/j.rinp.2020.103098 · Cited by 10
Design of a non-Hermitian on-chip mode converter using phase change materials
Yang, S., Zhang, X., & Sun, H. (2020) · Optics Letters · doi:10.1364/ol.400251 · Cited by 10
Non-Hermiticity-induced quantum control of localization in quantum walks
Zhang, R., Liu, Y.-F., & Chen, T. (2020) · Physical Review A · doi:10.1103/physreva.102.022218 · Cited by 10
Ultrabroadband beam splitting in a dissipative system of three waveguides
Alrifai, R., Coda, V., Peltier, J., Rangelov, A. A., & Montemezzani, G. (2021) · Physical Review A · doi:10.1103/physreva.103.023527 · Cited by 10
s-Wave resonance in exponential cosine screened Coulomb potential
Jiao, L. G., Ji, X. H., Hu, Z. X., Liu, A., Montgomery, H. E., Jr., & Ho, Y. K. (2021) · The European Physical Journal D · doi:10.1140/epjd/s10053-021-00330-1 · Cited by 10
Du, C.-X., Wang, G., Zhang, Y., & Wu, J. (2022) · Optics Express · doi:10.1364/oe.457299 · Cited by 10
Landau-Zener transitions through a pair of higher-order exceptional points
Melanathuru, R., Malzard, S., & Graefe, E.-M. (2022) · Physical Review A · doi:10.1103/physreva.106.012208 · Cited by 10
Composite Quantum Coriolis Forces
Znojil, M. (2023) · Mathematics · doi:10.3390/math11061375 · Cited by 10
Two generalized Wigner–Yanase skew information and their uncertainty relations
Chen, Z., Liang, L., Li, H.-J., & Wang, W. (2016) · Quantum Information Processing · doi:10.1007/s11128-016-1434-5 · Cited by 10
Thermally induced monochromatic microwave generation in magnon polaritons
Grigoryan, V. L., & Xia, K. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.99.224408 · Cited by 10
Non-Hermitian and Zeno limit of quantum systems under rapid measurements
Thiel, F., & Kessler, D. A. (2020) · Physical Review A · doi:10.1103/physreva.102.012218 · Cited by 10
Coquaternionic Quantum Dynamics for Two-level Systems
Brody, D. C., & Graefe, E.-M. (2011) · Acta Polytechnica · doi:10.14311/1394 · Cited by 10
IR-truncated $\mathcal{PT}-$symmetric $ix^3$ model and its asymptotic spectral scaling graphPreprint
Guenther, U., & Stefani, F. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1901.08526 · Cited by 10
Gomez, I. S., & Castagnino, M. (2014) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2014.11.002 · Cited by 9
Liouvillian exceptional points of an open driven two-level system
Seshadri, N., Li, A., & Galperin, M. (2024) · The Journal of Chemical Physics · doi:10.1063/5.0177714 · Cited by 9
Direct Manipulation of Biphoton Generation From the non‐Hermitian Nature of Light‐matter Interaction
Li, K., Cai, Y., Yan, J., Feng, Z., Fu, L., Zhang, L., Li, F., & Zhang, Y. (2025) · Laser & Photonics Review · doi:10.1002/lpor.202402149 · Cited by 9
Quantum tomography of a third-order exceptional point in a dissipative trapped ion
Chen, Y.-Y., Li, K., Zhang, L., Wu, Y., Ma, J.-Y., Yang, H.-X., Zhang, C., Qi, B., Zhou, Z.-C., Hou, P., et al. (2025) · Nature Communications · doi:10.1038/s41467-025-62573-5 · Cited by 9
Topological dynamics of an adiabatically varying Hamiltonian around third order exceptional points
Bhattacherjee, S., Laha, A., & Ghosh, S. (2019) · Physica Scripta · doi:10.1088/1402-4896/ab1c8b · Cited by 9
Recent advances in coherent perfect absorber-lasers and their future applications
Yang, M., Ye, Z.-L., Zhu, L., Farhat, M., & Chen, P. (2022) · Journal of Central South University · doi:10.1007/s11771-022-5160-0 · Cited by 9
Semiclassical Husimi Distributions of Schur Vectors in Non-Hermitian Quantum Systems
Hall, J., Malzard, S., & Graefe, E.-M. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.040402 · Cited by 9
Chatterjee, K., Koczor-Benda, Z., Feng, X., Krylov, A. I., & Jagau, T. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c00514 · Cited by 9
Experimental observation of exceptional points in coupled pendulums
Even, N., Nennig, B., Lefebvre, G., & Perrey‐Debain, E. (2024) · Journal of Sound and Vibration · doi:10.1016/j.jsv.2024.118239 · Cited by 9
Complex scaling in finite volume
Yu, H., Yapa, N., & König, S. (2024) · Physical Review C · doi:10.1103/physrevc.109.014316 · Cited by 9
Gyamfi, J. A., & Jagau, T. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c01039 · Cited by 9
Third-order exceptional points and frozen modes in planar elastic laminates
Fishman, A., Elbaz, G., Varma, T. V., & Shmuel, G. (2024) · Journal of the Mechanics and Physics of Solids · doi:10.1016/j.jmps.2024.105590 · Cited by 9
Non-adiabatic transitions in a non-symmetric optical lattice
Morales-Molina, L., & Reyes, S. A. (2011) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/44/20/205403 · Cited by 9
Longhi, S. (2013) · Physical Review A · doi:10.1103/physreva.88.062112 · Cited by 9
Long-lived resonances at mirrors
Queißer, F., & Unruh, W. G. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.116018 · Cited by 9
Matsuzaki, R., & Yabushita, S. (2017) · Journal of Computational Chemistry · doi:10.1002/jcc.24766 · Cited by 9
Rapidly oscillating scatteringless non-Hermitian potentials and the absence of Kapitza stabilization
Longhi, S. (2017) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/118/20004 · Cited by 9
SIMPLE MODELS OF THREE COUPLED PT -SYMMETRIC WAVE GUIDES ALLOWING FOR THIRD-ORDER EXCEPTIONAL POINTS
Schnabel, J., Cartarius, H., Main, J., Wunner, G., & Heiss, W. D. (2017) · Acta Polytechnica · doi:10.14311/ap.2017.57.0454 · Cited by 9
Abiogenesis and the Second Law of Thermodynamics
Brändas, E. (2020) · Progress in theoretical chemistry and physics · doi:10.1007/978-3-030-34941-7_15 · Cited by 9
Spectral and transport properties of a P T -symmetric tight-binding chain with gain and loss
Ortega, A., Stegmann, T., Benet, L., & Larralde, H. (2020) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/abb513 · Cited by 9
A new type of non-Hermitian phase transition in open systems far from thermal equilibrium
Sergeev, T. T., Zyablovsky, A. A., Andrianov, E. S., Pukhov, A., Lozovik, Y. E., & Vinogradov, A. P. (2021) · Scientific Reports · doi:10.1038/s41598-021-03389-3 · Cited by 9
Myo, T., & Katō, K. (2022) · Physical Review C · doi:10.1103/physrevc.106.l021302 · Cited by 9
Recent progress of quantum simulation of non-Hermitian systems
Gao, X.-E., Li, D.-L., Liu, Z., & Zheng, C. (2022) · Acta Physica Sinica · doi:10.7498/aps.71.20221825 · Cited by 10
Kaprálová-Žďánská, P. R., Šmydke, J., & Civiš, S. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4819495 · Cited by 9
Molecular Foundation of Evolution
Brändas, E. (2018) · Advances in quantum chemistry · doi:10.1016/bs.aiq.2018.06.008 · Cited by 9
Raj, P., & Balanarayan, P. (2019) · Physical Chemistry Chemical Physics · doi:10.1039/c8cp04812f · Cited by 9
Resonances and PT symmetry in quantum curves
Emery, Y., Mariño, M., & Ronzani, M. (2020) · Journal of High Energy Physics · doi:10.1007/jhep04(2020)150 · Cited by 9
Simkó, I., Szidarovszky, T., & Császár, A. G. (2019) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b00314 · Cited by 9
Compositeness of hadron resonances in finite volume
Tsuchida, Y., & Hyodo, T. (2018) · Physical Review C · doi:10.1103/physrevc.97.055213 · Cited by 9
Disorder-aided pulse stabilization in dissipative synthetic photonic lattices
Derevyanko, S. (2019) · Scientific Reports · doi:10.1038/s41598-019-49259-x · Cited by 9
Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials
Borisov, D. I., & Zezyulin, D. A. (2019) · Applied Mathematics Letters · doi:10.1016/j.aml.2019.106049 · Cited by 9
Krajewska, K., & Kamiński, J. Z. (2019) · Physical Review A · doi:10.1103/physreva.100.062116 · Cited by 9
Zielinski, P., Rommel, P., Schweiner, F., & Main, J. (2019) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/1361-6455/ab6274 · Cited by 9
Roberts, B. W. (2018) · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics · doi:10.1016/j.shpsb.2018.02.002 · Cited by 9
Pawlak, M., Żuchowski, P. S., & Jankowski, P. (2021) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.0c01122 · Cited by 9
Sarkar, S. (2021) · Scientific Reports · doi:10.1038/s41598-021-84485-2 · Cited by 9
Znojil, M. (2021) · Journal of Mathematical Physics · doi:10.1063/5.0041185 · Cited by 9
Banuary, M., Kumar, D., & Gupta, A. K. (2024) · New Journal of Chemistry · doi:10.1039/d3nj04908f · Cited by 8
The eigenvalue problem of one-dimensional Dirac operator
Karwowski, J., Ishkhanyan, A. M., & Poszwa, A. (2020) · Theoretical Chemistry Accounts · doi:10.1007/s00214-020-02685-x · Cited by 8
Anion of Oxalyl Chloride: Structure and Spectroscopy
Dauletyarov, Y., Ru, B., & Sanov, A. (2021) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.1c07451 · Cited by 8
A physical interpretation of coupling chiral metaatoms
Cao, Z., Chen, J., Deng, S., & Chen, H. (2022) · Nanoscale · doi:10.1039/d1nr05065f · Cited by 8
Complex scaled nonlocalized cluster model with continuum level density
Zhang, H., Bai, D., Wang, Z., & Ren, Z. (2023) · Physical Review C · doi:10.1103/physrevc.107.064304 · Cited by 8
Quantum entanglement in non-Hermitian Hubbard model
Lima, L. S. (2023) · Physica E Low-dimensional Systems and Nanostructures · doi:10.1016/j.physe.2023.115861 · Cited by 8
Computing Decay Widths of Autoionizing Rydberg States with Complex-Variable Coupled-Cluster Theory
Creutzberg, J., Skomorowski, W., & Jagau, T. (2023) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.3c02931 · Cited by 8
Defect modes in defective one dimensional parity-time symmetric photonic crystal
Wang, T., & Niu, Y. (2023) · Scientific Reports · doi:10.1038/s41598-023-48737-7 · Cited by 8
Xiao, H., & Zeng, Q.-B. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.024205 · Cited by 8
Parsing skin effect in a non-Hermitian spinless BHZ-like model
Halder, D., & Basu, S. (2024) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/ad4940 · Cited by 8
Quantum criticality at the boundary of the non-Hermitian regime of a Floquet system
Zhao, W.-L., & Liu, J. (2024) · Physical Review A · doi:10.1103/physreva.109.052215 · Cited by 9
Ab Initio Computation of Auger Decay in Heavy Metals: Zinc about It
Ferino-Pérez, A., & Jagau, T. (2024) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.4c01316 · Cited by 8
Metadata
- Authors
- Moiseyev, N.
- Affiliations
- Technion – Israel Institute of Technology (IL)
- Corresponding author
- Moiseyev, Nimrod
- ORCID
- Moiseyev, Nimrod
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 2011-02-17
- OpenAlex
- W1649271673
- Cited by
- 1,490
- References
- 0
- Citations by year
- 2026: 77 · 2025: 109 · 2024: 100 · 2023: 104 · 2022: 139 · 2021: 111 · 2020: 154 · 2019: 153 · 2018: 116 · 2017: 101 · 2016: 77 · 2015: 80 · 2014: 48 · 2013: 63 · 2012: 34
- FWCI
- 12.63
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Cambridge University Press eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- non-Hermitian quantum mechanics, complex potentials, resonance, PT symmetry, PT-symmetric Hamiltonians, complex refractive index, complex Hamiltonian, non-Hermitian photonics, quantum field theory, atomic and molecular physics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
