Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:25:45.902529Z
Paper Citation Record · LEDGER
As of 8 August 2026, this Paper Citation Record lists 89 of 89 outbound references and 0 inbound Pith citation observations for arXiv:2608.06326.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:25:45.902529Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
89 of 89 outbound references displayed
External citation measurements
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Reference 1
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Multi-State Geometry of Density Matrices and Rectification Sum Rules (B26) is given by a sum of delta functions, it satisfies a general sum rule 1 π Z ∞ 0 dϖ ρσ;νλ K (ϖ) = 1 π X ωac>0 wσ;νλ ac = X ωac>0 (pa −p c) [Bν, Bσ,d]ac (Bλ)ca
Reference 4
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Unavailable: canonical work link unavailable.
Observation 0e8334da-5f48-4f79-9d4b-31abb1e38fcc · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 5
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Observation 4db60fcc-2f6a-424c-9695-a95aa57c3a5c · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules To do so, we make use of Eq
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Observation 37814d0d-9250-4cbc-9c97-5d2b61c87145 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules (117) for the single- particle matrix elements of the position operator in or- der to derive Eq
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Observation 936fa67e-42d0-4054-8d6a-dc3b96cc9c23 · outbound
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Reference 9
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Multi-State Geometry of Density Matrices and Rectification Sum Rules Resta, Macroscopic polarization in crystalline di- electrics: The geometric phase approach, Reviews of Modern Physics66, 899 (1994)
Reference 11
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Observation b7e93894-e972-4017-bc0f-98cd92a2d326 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Marzari and D
Reference 12
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Observation 84eef679-347e-4d72-a825-59cd4646626b · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Souza, T
Reference 13
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Observation 0120320b-2562-4aba-a690-faae40db6a35 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Onishi and L
Reference 14
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Observation f1e34ae6-d071-406c-959f-aaaa90676cc4 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Verma and R
Reference 15
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Observation 09cfb696-4304-4451-b314-fb62e67ea0fd · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Ba lut, B
Reference 16
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Observation eae7ee4b-c0a9-40bd-993e-17e7d1e8bd11 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Ba lut, B
Reference 17
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Observation 7e80a8d9-9702-4a76-9003-beebbc31d14a · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Density Matrix Geometry and Sum Rules
Reference 18
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Observation 2bbaa0f8-8ba1-45cf-a420-00ed400d664a · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Chowdhury, Information, dissipation, and planck- ian optimality, arXiv preprint arXiv:2602.04953 (2026), arXiv:2602.04953
Reference 19
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Observation d31884ae-e7d9-44a3-8457-a2bc1ddd57a1 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 20
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Observation 88290c99-99df-4cd6-8beb-dae556e922ae · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Mendez-Valderrama, D
Reference 21
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Observation c078fe77-6820-4824-9d6e-1f2fd7eb6aee · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Peotta and P
Reference 22
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Observation c8601067-1d00-49a2-995e-15b01984f3b9 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Liang, T
Reference 23
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Observation 5db86d4c-240c-4ee2-9b3c-66ea835b1ad1 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules T¨ orm¨ a, S
Reference 24
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Observation 78c097e9-b96a-4b63-9afc-af4a7adec282 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Herzog-Arbeitman, V
Reference 25
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Observation 04468bf9-8628-4055-af41-c8e7accdbd9d · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Huhtinen, J
Reference 26
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Observation c25f8cf2-371b-41be-9fea-16de275289e6 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Roy, Band geometry of fractional topological insula- tors, Physical Review B90, 165139 (2014)
Reference 27
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Observation 04337bfd-1e94-4e7b-af88-e1a437f5a382 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 28
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Observation 1e13592f-2013-4dea-98ea-863b095b6616 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Neupert, C
Reference 29
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Observation 2945d9b1-2d39-4f2f-a506-b43f5a0bede7 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 30
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Observation bea9c489-abe0-4e62-8b9d-0b69dc59ac10 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 31
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Observation 1fc15176-fbe8-4a9d-80bf-7832b9c470ab · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules De Juan, A
Reference 32
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Observation ff42b301-1819-45d3-b35a-80733d7d240e · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Flicker, F
Reference 33
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Observation 72c4fcad-a35d-4d84-b08e-8b8d844950fb · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Morimoto and N
Reference 34
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Observation f27c9ca6-6b42-4c82-9dfb-0e40702274b9 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 35
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Observation e160146a-6152-4f72-a2a1-ec95fa3fda61 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Kaushik and J
Reference 36
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Observation 1bf481a7-ffc1-4856-b0ad-f02b5c627a0a · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 37
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Observation ab4ea716-8a8c-4d12-99f4-6cf7ca19f798 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Chang, S.-Y
Reference 38
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Observation 619704e0-497a-43a2-83f8-5bd889d7835d · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Ahn, G.-Y
Reference 39
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Observation 9765efef-7161-4cbc-a0a5-90181702172f · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 40
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Observation b7d14b9f-9ad4-4684-9de7-c2aa64218949 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Aversa and J
Reference 41
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Observation 812c627c-37bf-4f44-b3bb-77c613ad21a3 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 42
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Observation 2eb26529-fff1-4b93-ac2d-4e5eac6dedcd · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Sodemann and L
Reference 43
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Observation e4683791-85af-48f5-8296-137633fbfd91 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Matsyshyn and I
Reference 44
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Observation b34a3107-ea8c-44f4-9c47-32513df42180 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Morimoto, S
Reference 45
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Observation f0b0ad99-af7d-40bb-99dd-339158e9071f · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Du, H.-Z
Reference 46
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Observation 693bcc16-7d0b-4e61-bbd0-1c4397267055 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Ortix, Nonlinear hall effect with time-reversal symme- try: Theory and material realizations, Advanced Quan- tum Technologies4, 2100056 (2021)
Reference 47
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Unavailable: canonical work link unavailable.
Observation 0bc7d81e-9b75-488b-baf3-2d2ab02063c1 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Nandy and I
Reference 48
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Observation 9a158176-9953-4e8e-980b-6934e6508d07 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Ahn, G.-Y
Reference 49
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Observation 7704a6e2-2ed1-4b09-9b7a-5b1e1fa2ac17 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Quantum geometry beyond projective single bands
Reference 50
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Observation 31fceff0-c981-4c07-8b3f-2476d6c97a5f · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 51
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Observation dc032f9f-0adc-4dac-8f41-b93595e70828 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Alexandradinata, Quantization of intraband and in- terband Berry phases in the shift current, Physical Re- view B110, 075159 (2024)
Reference 52
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Observation 85fceae6-842c-43ef-8d97-0550454cc985 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Zhu and A
Reference 53
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Observation a881fb53-9952-4511-a7a8-88f2c37b6d8b · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Gauge-invariant projector calculus for quantum state geometry and applications to observables in crystals
Reference 54
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Observation 2697031c-0bc9-40d4-9e41-e72dc97af96a · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Avdoshkin and F
Reference 55
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Observation 6f832529-061b-4028-9eed-c6d50484877c · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules The multi-state geometry of shift current and polarization
Reference 56
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Observation 64e9dedd-1cd9-4369-a3db-8b93de964faf · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 57
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Observation 552e7b3e-6fe7-4356-8aec-dad1b5fd1d1c · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 58
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Observation 454d619a-316f-4de7-9133-21242a65b1f2 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Guan and B
Reference 59
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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 0e54b187-4d66-4ae2-b9ec-a582b0ab8ad2 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 60
Source-reported events for the cited work
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Observation 1b110f3e-1ddf-40a2-9885-e71e01b13887 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Vortex-enhanced photovoltaic current in disordered topological materials
Reference 61
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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e8526639-3faf-43ea-b9ce-7f6d37279519 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Het´ enyi and P
Reference 62
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Observation b258a5e6-16ab-4398-b38e-0de8ccc420f4 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Amari and H
Reference 63
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Observation 9fc242ce-4b8d-4efe-9bb6-0055eb7f4a8e · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Hasegawa,α-divergence of the non-commutative in- formation geometry, Reports on Mathematical Physics 33, 87 (1993)
Reference 64
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Observation f1cf02c1-dfed-4d39-91ab-b1494eb8ae4a · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Hasegawa and D
Reference 65
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Observation dc2878ea-991f-43cb-82dc-1ae693040073 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Nagaoka, Differential geometrical aspects of quantum state estimation and relative entropy, inQuantum Com- munications and Measurement, edited by V
Reference 66
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Observation 96a51cf7-ce1d-4e93-86d3-9f1b43701072 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 67
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Observation 8ddcc70b-b9db-4be5-bbcb-17f76b35f767 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 68
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Observation da01c8e5-f12a-4b5e-99c1-7e52fecbb09d · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Provost and G
Reference 69
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Observation 98b5d821-7528-4d73-8722-ed0d71a3cdde · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Verma, P
Reference 70
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Observation 28345146-c3eb-435d-a7cc-3e4a73606a7b · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Bengtsson and K
Reference 71
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Observation be365b3f-a44d-432e-9f45-bd2bce14d33b · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Uhlmann, The metric of Bures and the geometric phase, Quantum groups and related topics , 267 (1992)
Reference 72
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Observation d3c8c87b-3636-4159-9f61-0519bb639a0d · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Uhlmann, Geometric phases and related structures, Reports on Mathematical Physics36, 461 (1995)
Reference 73
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Observation 7c6bb791-2a92-4a70-b3a3-b317061da61e · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Carollo, D
Reference 74
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Observation c9c7fe19-2983-4579-8a84-45353ceba8fd · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Nakahara,Geometry, topology and physics(CRC press, 2018)
Reference 75
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Observation af1848a9-e37e-4339-aafa-bb43d9006b05 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 76
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Observation 1076fe8d-01f3-4877-968b-6cc6c2cfce6f · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Shimada, K
Reference 77
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Observation 3032433c-239c-46b0-9987-fd94ecb30262 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 78
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Observation 3e079e8c-31fa-40b4-bec2-19b78dd80f94 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Iosifidis and K
Reference 79
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Observation 0164dbbb-6c07-4389-b10e-6c6238e0c3c7 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Bradlyn and P
Reference 80
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Unavailable: canonical work link unavailable.
Observation 994cb572-30ad-494d-ab33-e776ff65a84f · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Resta, Geometrical theory of the shift current in pres- ence of disorder and interaction, Physical Review Letters 133, 206903 (2024)
Reference 81
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Observation c2676c74-5d08-4f0a-8ab9-9b574fc1c515 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules von Baltz and W
Reference 82
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Observation b0b7cd1c-a663-4f1e-8e0c-75916c12bf03 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Nastos and J
Reference 83
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Observation 0d77938c-5369-4dfa-b961-1c83fc2c7914 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 84
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Observation 96b9bd8c-e469-454f-9170-98538d9e22c9 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Unresolved cited work
Reference 86
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Observation 6d1d9f34-e2cf-42f6-a687-3b595656eb77 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Spin Hall conductivity in insulators with non-conserved spin
Reference 87
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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation abc89671-51c3-4a6b-bceb-f1fc503d9f02 · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Souza, R
Reference 88
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Observation 603b60e7-9c3b-49e1-8da4-c14b3a72fb0e · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules Patankar, L
Reference 89
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Observation e02de30f-1e0c-4207-8133-834ce3ffd50e · outbound
Multi-State Geometry of Density Matrices and Rectification Sum Rules 449–452, extended version: METR 94-14, De- partment of Mathematical Engineering and Instrumen- tation Physics, University of Tokyo
Reference 1995
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