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Paper Citation Record · LEDGER

Path integral approach to quantum thermalization

As of 14 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 4 inbound Pith citation observations for arXiv:2509.06028.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2509.06028 v1

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T04:45:24.432932Z

measured 49 of 49 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T12:47:29.139078Z

measured 1 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

45 of 45 outbound references displayed

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  • verified fuzzy27
  • unresolved15
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arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 3af25408-4f26-4015-a142-1e33b0cc29d1 · outbound

This paper cites While Eq.

Path integral approach to quantum thermalization While Eq

Reference 1

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Observation e7217549-78a7-4f42-8565-6a05068a3355 · outbound

This paper cites an unresolved cited work.

Path integral approach to quantum thermalization Unresolved cited work

Reference 2

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Observation ae7716d6-2c91-4cfd-bca7-2530540eee8d · outbound

This paper cites Averaging overUyields the generalization of Eq.

Path integral approach to quantum thermalization Averaging overUyields the generalization of Eq

Reference 3

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Observation b203c4ec-95fe-4ce4-80b3-25541a710cdb · outbound

This paper cites How- ever, at this point the advantage of theGΣ-construction becomes evident: the interaction containsψin the form of color singlets Eq.

Path integral approach to quantum thermalization How- ever, at this point the advantage of theGΣ-construction becomes evident: the interaction containsψin the form of color singlets Eq

Reference 4

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Observation 28b0ab85-221a-48a6-b3ac-3be63f84dbd8 · outbound

This paper cites (41) reads as 0=δ Σj S[ ¯G, ¯Σ, B]=D ( ¯Gj+iτ 3(G−1(Bj)−i ¯Σjτ3)−1) , 0=δ Gj S[ ¯G, ¯Σ, B]=D ¯Σj+δ Gj Sint[ ¯G].

Path integral approach to quantum thermalization (41) reads as 0=δ Σj S[ ¯G, ¯Σ, B]=D ( ¯Gj+iτ 3(G−1(Bj)−i ¯Σjτ3)−1) , 0=δ Gj S[ ¯G, ¯Σ, B]=D ¯Σj+δ Gj Sint[ ¯G]

Reference 5

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Observation 595091ea-0fd2-4422-814d-c87ca354a8e2 · outbound

This paper cites an unresolved cited work.

Path integral approach to quantum thermalization Unresolved cited work

Reference 6

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Observation a0a6bef6-3551-4d58-a60f-4ae4594164d1 · outbound

This paper cites Reminiscing a scalar potential coupling, it suggests removingϕfrom the action by a time-dependent gauge transformation.

Path integral approach to quantum thermalization Reminiscing a scalar potential coupling, it suggests removingϕfrom the action by a time-dependent gauge transformation

Reference 7

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Observation 02200b58-553b-4bed-97fe-2b4377a417ba · outbound

This paper cites However, it reappears in opera- tors representing correlation functions in the form of gauge-phase factors containing discrete time integrals overΘ n.

Path integral approach to quantum thermalization However, it reappears in opera- tors representing correlation functions in the form of gauge-phase factors containing discrete time integrals overΘ n

Reference 8

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Observation 03efb411-565d-401f-bcb2-54e3c712a95a · outbound

This paper cites an unresolved cited work.

Path integral approach to quantum thermalization Unresolved cited work

Reference 9

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Observation c543e80d-a234-444b-97c5-cde47b394019 · outbound

This paper cites The representation K1(t)=t−(t−D)Θ(t−D), indicates that the termination of the semiclassical rampK 1,semicl.

Path integral approach to quantum thermalization The representation K1(t)=t−(t−D)Θ(t−D), indicates that the termination of the semiclassical rampK 1,semicl

Reference 10

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Observation 97d298ea-81d5-4b09-ad78-fa9bdd4fcaa8 · outbound

This paper cites particle-hole excitation.

Path integral approach to quantum thermalization particle-hole excitation

Reference 11

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Observation 85cc7a27-7ee5-44a6-898d-9bcca173b5b8 · outbound

This paper cites It implies the vector integral generalization δµρ = ∫ Dψ e− ¯ψψ ψµ ¯ψρ (A1) whereψ={ψ µ}now is aD-component Grassmann vector, Dψ= ∏µ d ¯ψµdψµ and ¯ψψ= ∑µ ¯ψµψµ.

Path integral approach to quantum thermalization It implies the vector integral generalization δµρ = ∫ Dψ e− ¯ψψ ψµ ¯ψρ (A1) whereψ={ψ µ}now is aD-component Grassmann vector, Dψ= ∏µ d ¯ψµdψµ and ¯ψψ= ∑µ ¯ψµψµ

Reference 12

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Observation cc6cebfc-725e-4115-8708-2a7e505d95ff · outbound

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Path integral approach to quantum thermalization Unresolved cited work

Reference 13

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Observation 9fb62256-76ed-4537-bb3e-ba0843a7b6be · outbound

This paper cites Collecting the quadratic terms in Eqs.

Path integral approach to quantum thermalization Collecting the quadratic terms in Eqs

Reference 14

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Observation 6c252034-12b0-4108-8620-9213c85c3858 · outbound

This paper cites Our starting point is the configurations Eq.

Path integral approach to quantum thermalization Our starting point is the configurations Eq

Reference 15

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Observation 9affe1d4-a22c-45fb-b133-2d7b582a8185 · outbound

This paper cites (3) as de- scribed by an integral overG=−iT τ 3T−1 with the action Eq.

Path integral approach to quantum thermalization (3) as de- scribed by an integral overG=−iT τ 3T−1 with the action Eq

Reference 16

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Observation 08113055-acc7-49fc-a845-deb95944e029 · outbound

This paper cites To this end, consider the expansion Eq.

Path integral approach to quantum thermalization To this end, consider the expansion Eq

Reference 17

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Observation f88592fc-4866-4f37-af90-4d6da962d889 · outbound

This paper cites Noting that theT-rotations do not couple to the second and third term in the first line due cyclic invariance, we focus on the first term.

Path integral approach to quantum thermalization Noting that theT-rotations do not couple to the second and third term in the first line due cyclic invariance, we focus on the first term

Reference 18

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Observation 6b796e80-a776-4b7d-a08e-a865a34fb7a3 · outbound

This paper cites We substitute the representationG=T ¯GT−1 with the mean field solution Eq.

Path integral approach to quantum thermalization We substitute the representationG=T ¯GT−1 with the mean field solution Eq

Reference 19

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Observation 54ddfa6b-5770-429e-9bee-f7cec0ea5cfe · outbound

This paper cites Essen- tially, this amounts to taking continuum limits of the for- mulas discussed there.

Path integral approach to quantum thermalization Essen- tially, this amounts to taking continuum limits of the for- mulas discussed there

Reference 20

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Observation be777059-2420-4f6f-b0dc-abe5c78af1f6 · outbound

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Path integral approach to quantum thermalization Unresolved cited work

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Observation 8e2dba2a-855d-412b-b4a4-c78fbb3bb770 · outbound

This paper cites Fran¸ ca, Making quantum dynamics exact, Physics14, 60 (2021), publisher: American Physical Society.

Path integral approach to quantum thermalization Fran¸ ca, Making quantum dynamics exact, Physics14, 60 (2021), publisher: American Physical Society

Reference 22

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Observation 66a62952-93b3-44ed-af0d-7e08d5e164fa · outbound

This paper cites Nandkishore and D.

Path integral approach to quantum thermalization Nandkishore and D

Reference 23

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Observation 3e290156-58cb-4fd2-8579-175c971b7027 · outbound

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Path integral approach to quantum thermalization Unresolved cited work

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Path integral approach to quantum thermalization Unresolved cited work

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Observation 5d2690b7-fc49-4d2b-a48f-2fd352a39808 · outbound

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Path integral approach to quantum thermalization Unresolved cited work

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Observation 88402ff0-0097-475b-8842-6ade0ff9d288 · outbound

This paper cites Fritzsch and T.

Path integral approach to quantum thermalization Fritzsch and T

Reference 27

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Observation 163aa548-8b78-40bd-b73d-7efcec857ffd · outbound

This paper cites Altland and B.

Path integral approach to quantum thermalization Altland and B

Reference 28

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Observation af7fb857-634d-4497-baa2-45f168b3c161 · outbound

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Path integral approach to quantum thermalization Unresolved cited work

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Observation f2da0bb7-25bb-4277-b085-6a78090459e0 · outbound

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Path integral approach to quantum thermalization Unresolved cited work

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Observation 54f4d205-534a-4ebf-975c-eb2c6d63f3ea · outbound

This paper cites Rosenhaus, An introduction to the syk model, Journal of Physics A: Mathematical and Theoretical52, 323001 (2019), publisher: IOP Publishing.

Path integral approach to quantum thermalization Rosenhaus, An introduction to the syk model, Journal of Physics A: Mathematical and Theoretical52, 323001 (2019), publisher: IOP Publishing

Reference 31

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Observation 4375db77-16a7-48f5-af22-c0e0cbeda3b0 · outbound

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Path integral approach to quantum thermalization Unresolved cited work

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source=pdf_text observed=2026-08-05T04:45:23.940783Z digest=sha256:36a3e6335a0abd28ff26237572d403a0eb2cb56c7acfc3f3441976d38a6777d5

Observation fe9ceff8-c5a5-4403-9d62-3d12ee964188 · outbound

This paper cites Alternatively, one may think of them as fermionic or bosonic creation and annihilation operators.

Path integral approach to quantum thermalization Alternatively, one may think of them as fermionic or bosonic creation and annihilation operators

Reference 33

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source=pdf_text observed=2026-08-05T04:45:23.976195Z digest=sha256:46cd09eedc3612247cdfb26b86679f2d7bae627c311306645f53226dddc8cbca

Observation 738ff093-ba66-4b99-baee-166ef270e615 · outbound

This paper cites ⟩will denote path integra- tion, ensemble averaging, or both.

Path integral approach to quantum thermalization ⟩will denote path integra- tion, ensemble averaging, or both

Reference 34

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Observation dec97200-2edf-4859-beb9-232e8708298f · outbound

This paper cites Haake,Quantum signatures of chaos, 4th edition (Springer-Verlag, Berlin, 2018).

Path integral approach to quantum thermalization Haake,Quantum signatures of chaos, 4th edition (Springer-Verlag, Berlin, 2018)

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:45:25.837591Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-05T04:45:24.036348Z digest=sha256:8f808fa33bf7a6b703ccda8de7dd3b6ce940227ec5d035ae0c47f94443d52728

Observation a79052e0-41f5-4e34-80d2-e9c945aad2f9 · outbound

This paper cites an unresolved cited work.

Path integral approach to quantum thermalization Unresolved cited work

Reference 36

Resolution
unresolved
raw_fallback, observed 2026-08-05T04:45:25.692163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-05T04:45:24.051631Z digest=sha256:89b8b7634207be850d21a3d6dde0b454e8f287b9085b7ee65e5ee36c5c42ec88

Observation 89506e9a-8bd2-4e28-afc1-6f74be3aa406 · outbound

This paper cites Coherent states for arbitrary Lie group.

Path integral approach to quantum thermalization Coherent states for arbitrary Lie group

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-05T04:45:24.091217Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T04:45:24.091217Z digest=sha256:de30c7cc4b30a723afd75d8c48dea59c709fe2289acc2ca6616f8d3a55d247b5

Observation 58df5f3e-c4a3-45f9-8c73-12792a8d510f · outbound

This paper cites Kamenev,Field Theory of Non-Equilibrium Systems (Cambridge University Press, 2011).

Path integral approach to quantum thermalization Kamenev,Field Theory of Non-Equilibrium Systems (Cambridge University Press, 2011)

Reference 38

Resolution
unresolved
no resolver link, observed 2026-08-05T04:45:24.155509Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T04:45:24.155509Z digest=sha256:4bc706e4767523bb724c44a38407b0ceb3d2098349edd866d1cddc3570b7b477

Observation ce925315-e02c-40f6-ac4e-c98105fb9d30 · outbound

This paper cites Tyagi and K.

Path integral approach to quantum thermalization Tyagi and K

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:45:25.576597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-05T04:45:24.187594Z digest=sha256:afd3887ae75b2f940e5f0a3baecaf0c93a0972d4eb821cea5e2c20bbef2cb565

Observation a5f5905b-5639-47cc-a75d-69795de43970 · outbound

This paper cites Feynman Path Integrals Over Entangled States.

Path integral approach to quantum thermalization Feynman Path Integrals Over Entangled States

Reference 40

Resolution
verified exact
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-05T04:45:24.221512Z digest=sha256:d2e1b4914d88fe1da427ef13aaf5a49f1b27713f9dbb61baa3fa89ed8dd7a4f3

Observation 86bd5f24-420e-435a-93e0-9c80897490b3 · outbound

This paper cites an unresolved cited work.

Path integral approach to quantum thermalization Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-05T04:45:25.422296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-05T04:45:24.258928Z digest=sha256:f3f73d4fcca747f3db4dbd62d0c5deb56262109e3804f1044daefaa904f350d9

Observation 1a49cebc-f4a8-49de-b922-9cde1d669a2c · outbound

This paper cites Altland and A.

Path integral approach to quantum thermalization Altland and A

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:45:25.247780Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-05T04:45:24.316703Z digest=sha256:abe6d0646f2aaca7f17cc0253b50c32befd2b2ee06d5acb8dafca5aa08629e8a

Observation 8dbdeb92-13ee-48e0-a8a6-775112bbce58 · outbound

This paper cites As an example, we mention rotor models, where the path integral of individual kicked rotors is under excel- lent control [24].

Path integral approach to quantum thermalization As an example, we mention rotor models, where the path integral of individual kicked rotors is under excel- lent control [24]

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:45:25.021267Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-05T04:45:24.324403Z digest=sha256:b41e635395ce1a25914abdae8384b70c62b76ff227760467f26ae6ff193bf62a

Observation e0ab8e99-92d2-425c-a15d-a1086e6a6584 · outbound

This paper cites Tian and A.

Path integral approach to quantum thermalization Tian and A

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:45:24.854896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-05T04:45:24.380311Z digest=sha256:a65dde43cccc141561af385c315c6dd5fd52a73b1783be66b4c88b967dc7e325

Observation febcef7f-3caa-4254-9f3b-22e4664f87f7 · outbound

This paper cites M¨ uller, S.

Path integral approach to quantum thermalization M¨ uller, S

Reference 45

Resolution
malformed identifier
no resolver link, observed 2026-08-05T04:45:24.432932Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T04:45:24.432932Z digest=sha256:f39a59c078d77b23f205bb97a743cdf58eb4577b1f7591ff41b9ed1e4623f779

Pith citing papers

Observation 2588fee3-cd72-4826-8808-67dcd7a2491e · inbound

Chaotic many-body quantum dynamics, spectral correlations, and energy diffusion cites this paper.

Chaotic many-body quantum dynamics, spectral correlations, and energy diffusion Path integral approach to quantum thermalization

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-04T12:47:29.139078Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T12:47:29.139078Z digest=sha256:5825e5c472ea3d9ce1190a1facf92237bbc977ff66e8692e4c08a9e629be2967

Observation d4d53305-6fe5-4aef-bd3c-afb5ae12e325 · inbound

Semiclassical foundation of universality in chaotic quantum circuits cites this paper.

Semiclassical foundation of universality in chaotic quantum circuits Path integral approach to quantum thermalization

Reference 34

Resolution
verified exact
arxiv_id, observed 2026-06-29T16:43:39.969605Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-06-29T16:42:35.507368Z digest=sha256:f236ab07eca99460109223c031b4ed19915b4047ec4974901027062a459587c9

Observation 9db05628-31fd-4bd1-8b73-909da061ca00 · inbound

Provable random-matrix spectral ramp in a static, geometrically local Hamiltonian cites this paper.

Provable random-matrix spectral ramp in a static, geometrically local Hamiltonian Path integral approach to quantum thermalization

Reference 36

Resolution
verified exact
arxiv_id, observed 2026-06-30T05:44:17.326808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-06-30T05:43:25.115431Z digest=sha256:23b21521337805a5a9cb0bf22dc48baafa7a459a6385fb06ec1732a8e898523c

Observation f69fb537-ee4e-44fd-a01d-58ed1ceb9231 · inbound

Entanglement in bipartite systems with symmetry: coupled chaotic kicked Bose-Hubbard systems cites this paper.

Entanglement in bipartite systems with symmetry: coupled chaotic kicked Bose-Hubbard systems Path integral approach to quantum thermalization

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-03T12:31:18.003466Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-03T12:31:18.003466Z digest=sha256:c73f1e66d61fc9531ec6363edfdc2f64887f08cba0a12e084351ffcb88d7331f