Imaginary Time Formalism for Causal Nonlinear Response Functions | Paper Citation Record

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This paper cites Mahmood, D.

Imaginary Time Formalism for Causal Nonlinear Response Functions Mahmood, D

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This paper cites Wan and N.

Imaginary Time Formalism for Causal Nonlinear Response Functions Wan and N

Reference 2

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Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

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This paper cites ( 4), and exploiting the fact that Eq.

Imaginary Time Formalism for Causal Nonlinear Response Functions ( 4), and exploiting the fact that Eq

Reference 5

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Observation a6063853-8140-4427-9207-94da53b6b5bb · outbound

This paper cites Thus, to all orders in perturbation theory Ç(n) AB({É+ i }n i=1) = ( −1)n ¯Ç(n) AB({i¿i = É+ i }n i=1), (14) provided the continuation is carried out in the Lehmann representation.

Imaginary Time Formalism for Causal Nonlinear Response Functions Thus, to all orders in perturbation theory Ç(n) AB({É+ i }n i=1) = ( −1)n ¯Ç(n) AB({i¿i = É+ i }n i=1), (14) provided the continuation is carried out in the Lehmann representation

Reference 6

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Observation 02ce7028-8a9c-40a6-a0e6-7dcc11c94650 · outbound

This paper cites In the Supplementary Material (SM), we explicitly demonstrate this for the second or- der causal response and the Matsubara three point func- tions [ 54].

Imaginary Time Formalism for Causal Nonlinear Response Functions In the Supplementary Material (SM), we explicitly demonstrate this for the second or- der causal response and the Matsubara three point func- tions [ 54]

Reference 7

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Observation e6535f58-56f3-444f-a06c-7b8cca5fd3a6 · outbound

This paper cites Therefore, we can use the diagrammatic techniques of Ref.

Imaginary Time Formalism for Causal Nonlinear Response Functions Therefore, we can use the diagrammatic techniques of Ref

Reference 8

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This paper cites In- tegrating by parts, we see that in frequency space the correlation function satisﬁes a similar recurrence relation to Eq.

Imaginary Time Formalism for Causal Nonlinear Response Functions In- tegrating by parts, we see that in frequency space the correlation function satisﬁes a similar recurrence relation to Eq

Reference 9

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Observation 14b1018c-7376-48ad-9e01-5e8528f1fef5 · outbound

This paper cites Symmetrizing over frequencies, we de- ﬁne X (n) ABI1 ···BIn ({zi}n i=1) = (−1)n Ãnn! ∑ Ã ∫ n∏ i=1 d³i ³i −∑ n j=i zÃ(j) ¸(n) ABIσ (1) ···BIσ (n) ({³i}).

Imaginary Time Formalism for Causal Nonlinear Response Functions Symmetrizing over frequencies, we de- ﬁne X (n) ABI1 ···BIn ({zi}n i=1) = (−1)n Ãnn! ∑ Ã ∫ n∏ i=1 d³i ³i −∑ n j=i zÃ(j) ¸(n) ABIσ (1) ···BIσ (n) ({³i})

Reference 10

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Observation edf09c76-c8af-4a1e-8123-aea92f718e5a · outbound

This paper cites (26) Taking BIi = B yields Eq.

Imaginary Time Formalism for Causal Nonlinear Response Functions (26) Taking BIi = B yields Eq

Reference 11

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Observation 56116c0b-62f0-499c-9224-d9e818734235 · outbound

This paper cites Bradlyn and P.

Imaginary Time Formalism for Causal Nonlinear Response Functions Bradlyn and P

Reference 12

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Observation 3961a25c-ac5b-4155-aa66-0db4904ece5b · outbound

This paper cites Regularized lattice theory for spatially dispersive nonlinear optical conductivities.

Imaginary Time Formalism for Causal Nonlinear Response Functions Regularized lattice theory for spatially dispersive nonlinear optical conductivities

Reference 13

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Observation 87debd5d-de8e-4cf9-b366-977849dbdfcc · outbound

This paper cites Additionally, our recur- sion relation Eq.

Imaginary Time Formalism for Causal Nonlinear Response Functions Additionally, our recur- sion relation Eq

Reference 14

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Reference 15

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Observation f2f7e6b2-0964-4872-98dd-c93f4a596889 · outbound

This paper cites Anomalous shift and optical vorticity in the steady photovoltaic current.

Imaginary Time Formalism for Causal Nonlinear Response Functions Anomalous shift and optical vorticity in the steady photovoltaic current

Reference 16

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Observation 0286d6c3-36dc-4169-a337-e59d2a895c34 · outbound

This paper cites Quantization of intra- and inter-band Berry phases in the shift current.

Imaginary Time Formalism for Causal Nonlinear Response Functions Quantization of intra- and inter-band Berry phases in the shift current

Reference 17

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Reference 18

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Observation f605121c-3ea5-4f63-8283-5e6ca4e777b5 · outbound

This paper cites Furthermore, the left hand side of Eq.

Imaginary Time Formalism for Causal Nonlinear Response Functions Furthermore, the left hand side of Eq

Reference 19

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Observation 4482a982-3bda-4abf-9a87-1c8b8db2eccd · outbound

This paper cites Morimoto and N.

Imaginary Time Formalism for Causal Nonlinear Response Functions Morimoto and N

Reference 20

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Observation db109a8d-2178-48ea-9cf9-ab94f36b29f5 · outbound

This paper cites 5 Conclusion We have demonstrated the connection between causal and Matsubara Green’s functions to all orders in perturbation theory, generalizing the textbook result at n = 1.

Imaginary Time Formalism for Causal Nonlinear Response Functions 5 Conclusion We have demonstrated the connection between causal and Matsubara Green’s functions to all orders in perturbation theory, generalizing the textbook result at n = 1

Reference 21

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Observation eba05361-84a3-4f97-afea-e9b77862b043 · outbound

This paper cites Matsyshyn and I.

Imaginary Time Formalism for Causal Nonlinear Response Functions Matsyshyn and I

Reference 22

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Observation 77cf801b-69fc-4442-8936-5b815bacc9da · outbound

This paper cites Sodemann and L.

Imaginary Time Formalism for Causal Nonlinear Response Functions Sodemann and L

Reference 23

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Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 24

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Observation da838b95-ebf6-453a-a333-001b5bfc180d · outbound

This paper cites Third order optical nonlinearity of three dimensional massless Dirac fermions.

Imaginary Time Formalism for Causal Nonlinear Response Functions Third order optical nonlinearity of three dimensional massless Dirac fermions

Reference 25

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Reference 26

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Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 27

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Observation 9e08d825-f2c8-42ff-b65c-641af1469754 · outbound

This paper cites Orenstein, J.

Imaginary Time Formalism for Causal Nonlinear Response Functions Orenstein, J

Reference 28

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Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 29

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Observation 0f4b7b11-20fd-4415-a75c-d2077056d1b1 · outbound

This paper cites Quantum Geometry in Quantum Materials.

Imaginary Time Formalism for Causal Nonlinear Response Functions Quantum Geometry in Quantum Materials

Reference 30

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Observation 0c736bd6-02b2-4fc4-969c-6fea61b7d7d4 · outbound

This paper cites Komissarov, T.

Imaginary Time Formalism for Causal Nonlinear Response Functions Komissarov, T

Reference 31

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Observation 28c3bb69-d0ff-4103-b759-dc01155a0ec9 · outbound

This paper cites Gauge-invariant projector calculus for quantum state geometry and applications to observables in crystals.

Imaginary Time Formalism for Causal Nonlinear Response Functions Gauge-invariant projector calculus for quantum state geometry and applications to observables in crystals

Reference 32

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This paper cites Avdoshkin and F.

Imaginary Time Formalism for Causal Nonlinear Response Functions Avdoshkin and F

Reference 33

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Observation 10563acf-8106-4b32-be7d-40e6e1294930 · outbound

This paper cites The multi-state geometry of shift current and polarization.

Imaginary Time Formalism for Causal Nonlinear Response Functions The multi-state geometry of shift current and polarization

Reference 34

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Observation 72791785-6127-41b2-bd79-2a8eb5cf9c50 · outbound

This paper cites Morimoto, S.

Imaginary Time Formalism for Causal Nonlinear Response Functions Morimoto, S

Reference 35

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Observation 0b333c12-1701-47de-8656-9c0e643b3082 · outbound

This paper cites Gross and W.

Imaginary Time Formalism for Causal Nonlinear Response Functions Gross and W

Reference 36

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Observation dc22fec4-d818-4dc8-9912-6b473cef6e0a · outbound

This paper cites Patankar, L.

Imaginary Time Formalism for Causal Nonlinear Response Functions Patankar, L

Reference 37

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Reference 38

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Reference 39

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Reference 40

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Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 41

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Observation b53a249d-3c17-4767-a6fe-6aada4dd595e · outbound

This paper cites De Juan, A.

Imaginary Time Formalism for Causal Nonlinear Response Functions De Juan, A

Reference 42

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Observation b9399b94-9477-48e0-9f3b-3c73ecb7b37e · outbound

This paper cites Orenstein and J.

Imaginary Time Formalism for Causal Nonlinear Response Functions Orenstein and J

Reference 43

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Observation 552cad12-2c81-4f61-ae7e-90f27a216430 · outbound

This paper cites Kubo, Statistical-mechanical theory of irreversible processes.

Imaginary Time Formalism for Causal Nonlinear Response Functions Kubo, Statistical-mechanical theory of irreversible processes

Reference 44

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Observation 280760d9-e2ae-4e90-9b40-fdc5f9190c3c · outbound

This paper cites Watanabe and M.

Imaginary Time Formalism for Causal Nonlinear Response Functions Watanabe and M

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:09.478236Z

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Observation 17e0afd5-7caf-4253-a9ff-997041bc9c5c · outbound

This paper cites Watanabe, Y.

Imaginary Time Formalism for Causal Nonlinear Response Functions Watanabe, Y

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:09.470645Z

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Observation 5796d6f9-b59d-4020-b6b4-8b2a7058b950 · outbound

This paper cites Ahn, G.-Y.

Imaginary Time Formalism for Causal Nonlinear Response Functions Ahn, G.-Y

Reference 48

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Observation c2fed4cc-f763-4b31-8249-fce9f7a7104d · outbound

This paper cites Sipe and A.

Imaginary Time Formalism for Causal Nonlinear Response Functions Sipe and A

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:09.453995Z

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Observation 25dc94c9-c0df-4b87-8837-f093ccbc2790 · outbound

This paper cites Aversa and J.

Imaginary Time Formalism for Causal Nonlinear Response Functions Aversa and J

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:09.425775Z

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Observation f4ef685a-2e9c-4a8b-b8bd-6517e7b4409d · outbound

This paper cites Lucarini, Response Theory for Equilibrium and Non- Equilibrium Statistical Mechanics: Causality and Gener- alized Kramers-Kronig Relations, J Stat Phys 131, 543 (2008).

Imaginary Time Formalism for Causal Nonlinear Response Functions Lucarini, Response Theory for Equilibrium and Non- Equilibrium Statistical Mechanics: Causality and Gener- alized Kramers-Kronig Relations, J Stat Phys 131, 543 (2008)

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:09.321888Z

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Observation d8a649d3-14a2-4da4-b9d0-73ae5d2ff355 · outbound

This paper cites Passos, GB.

Imaginary Time Formalism for Causal Nonlinear Response Functions Passos, GB

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:09.109038Z

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Observation 7de0acfb-bcca-4be9-baa4-6821e2d8ce60 · outbound

This paper cites Peiponen, Nonlinear susceptibilities as a function of several complex angular-frequency variables, Phys.

Imaginary Time Formalism for Causal Nonlinear Response Functions Peiponen, Nonlinear susceptibilities as a function of several complex angular-frequency variables, Phys

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:08.907807Z

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Observation 276820a6-ee85-422c-b031-c9d3256c41df · outbound

This paper cites Peiponen, E.

Imaginary Time Formalism for Causal Nonlinear Response Functions Peiponen, E

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:08.671620Z

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Observation 727a766a-4845-4849-aafc-77da7263f30b · outbound

This paper cites Peiponen, J.

Imaginary Time Formalism for Causal Nonlinear Response Functions Peiponen, J

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:08.411408Z

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Observation a26f6c89-0d80-44ba-94db-dfcd098b3e86 · outbound

This paper cites an unresolved cited work.

Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 56

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:42:08.149891Z

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Observation ff2d0ba1-ed81-4b8c-a1dd-c8434bf4043a · outbound

This paper cites Matsubara, A new approach to quantum-statistical mechanics, Progress of theoretical physics14, 351 (1955).

Imaginary Time Formalism for Causal Nonlinear Response Functions Matsubara, A new approach to quantum-statistical mechanics, Progress of theoretical physics14, 351 (1955)

Reference 57

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Observation 982c96c8-38d0-40c5-bdc9-7bab809c03a7 · outbound

This paper cites Fradkin, Field theories of condensed matter physics (Cambridge University Press, 2013).

Imaginary Time Formalism for Causal Nonlinear Response Functions Fradkin, Field theories of condensed matter physics (Cambridge University Press, 2013)

Reference 58

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 85a8d121-0ae1-4155-9814-abbb8cc11c75 · outbound

This paper cites an unresolved cited work.

Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-06T22:42:00.922763Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6ee045e8-b144-429d-be29-20c108d578c3 · outbound

This paper cites Evans, N-point ﬁnite temperature expectation values at real times, Nuclear Physics B 374, 340 (1992).

Imaginary Time Formalism for Causal Nonlinear Response Functions Evans, N-point ﬁnite temperature expectation values at real times, Nuclear Physics B 374, 340 (1992)

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:07.896065Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation cdf6f9ea-d170-4e5d-a332-00d081516eb7 · outbound

This paper cites an unresolved cited work.

Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 61

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:42:07.664745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f21fad77-3bd6-401c-ac3d-ba4dabbd4383 · outbound

This paper cites an unresolved cited work.

Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 62

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:42:07.430590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d391296a-2d08-4715-9143-4b474f254551 · outbound

This paper cites an unresolved cited work.

Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 63

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:42:07.111892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 97c3ea02-275b-4c3a-acfe-6c4d35917697 · outbound

This paper cites Michishita and R.

Imaginary Time Formalism for Causal Nonlinear Response Functions Michishita and R

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:06.851228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f75eb295-def7-4beb-896c-955d6dcceff8 · outbound

This paper cites an unresolved cited work.

Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 65

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:42:06.634757Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 851c1c12-d4bf-4e8f-a3c7-4896cff30a57 · outbound

This paper cites [ 12] for an expression of [ ν (N ) AB ]2 in terms of the second order spectral density.

Imaginary Time Formalism for Causal Nonlinear Response Functions [ 12] for an expression of [ ν (N ) AB ]2 in terms of the second order spectral density

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:06.508975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9096a515-5c05-4d41-8389-bb80980999e9 · outbound

This paper cites Souza, T.

Imaginary Time Formalism for Causal Nonlinear Response Functions Souza, T

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:06.351351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 507dc932-c015-4c3c-825f-2e96808e6deb · outbound

This paper cites T¨ orm¨ a, S.

Imaginary Time Formalism for Causal Nonlinear Response Functions T¨ orm¨ a, S

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-06T22:42:01.460252Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c4ca8a19-801a-4d5c-b478-28b93670eae9 · outbound

This paper cites Quantum weight: A fundamental property of quantum many-body systems.

Imaginary Time Formalism for Causal Nonlinear Response Functions Quantum weight: A fundamental property of quantum many-body systems

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-06T22:42:01.540732Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ec48ecd-79d7-4239-a3da-1324eddb4368 · outbound

This paper cites Holder, D.

Imaginary Time Formalism for Causal Nonlinear Response Functions Holder, D

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:06.186594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation db20e088-a6de-43e6-b42b-3247d8c0a8d5 · outbound

This paper cites Ba/suppress lut, B.

Imaginary Time Formalism for Causal Nonlinear Response Functions Ba/suppress lut, B

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-06T22:42:01.640405Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 13429571-9ac5-4930-946b-68b59f0b2cb2 · outbound

This paper cites Ba/suppress lut, X.

Imaginary Time Formalism for Causal Nonlinear Response Functions Ba/suppress lut, X

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:06.000088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3d1f2dbd-6615-465e-a397-58da9c1d459b · outbound

This paper cites Verma, P.

Imaginary Time Formalism for Causal Nonlinear Response Functions Verma, P

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-06T22:42:01.780901Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eee9eb49-509e-4807-8c0c-01cff2f32313 · outbound

This paper cites Verma and R.

Imaginary Time Formalism for Causal Nonlinear Response Functions Verma and R

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-06T22:42:01.845648Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a414a8a7-2864-4402-b1cd-ae971a8d75bb · outbound

This paper cites Gubernatis, M.

Imaginary Time Formalism for Causal Nonlinear Response Functions Gubernatis, M

Reference 75

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:05.800750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6cbf776b-4635-4b96-9a94-6543e8eb6201 · outbound

This paper cites Boehnke, H.

Imaginary Time Formalism for Causal Nonlinear Response Functions Boehnke, H

Reference 76

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:05.655340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 57cdfa77-3e53-4dbb-ab53-bf703f6825b9 · outbound

This paper cites an unresolved cited work.

Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 77

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:42:05.471897Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 17725128-208b-45d0-8194-dec7c7d3a9cc · outbound

This paper cites Wentzell, G.

Imaginary Time Formalism for Causal Nonlinear Response Functions Wentzell, G

Reference 78

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:05.350002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f73ac336-4bcc-4407-9c2e-6fe9b87b4796 · outbound

This paper cites Shinaoka, J.

Imaginary Time Formalism for Causal Nonlinear Response Functions Shinaoka, J

Reference 79

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:05.246774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation dd146375-262a-4b3a-9ddd-eb39aa6b9029 · outbound

This paper cites Shinaoka, J.

Imaginary Time Formalism for Causal Nonlinear Response Functions Shinaoka, J

Reference 80

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:05.139721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a7071900-4e52-490e-ae1f-877360e9a504 · outbound

This paper cites Shinaoka, D.

Imaginary Time Formalism for Causal Nonlinear Response Functions Shinaoka, D

Reference 81

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:05.055884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d34ecaf7-5816-47dc-9550-b683def418b8 · outbound

This paper cites Imaginary Time Formalism for Causal No nlinear Response Functions.

Imaginary Time Formalism for Causal Nonlinear Response Functions Imaginary Time Formalism for Causal No nlinear Response Functions

Reference 82

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:04.908635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 29ed631a-fe20-4104-bddc-9dfd4a4f5684 · outbound

This paper cites For the second term on the right hand side of Eq.

Imaginary Time Formalism for Causal Nonlinear Response Functions For the second term on the right hand side of Eq

Reference 83

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:04.742153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bba32b6f-5875-4b87-831a-d93808c5e517 · outbound

This paper cites The ﬁrst order expression is, f (1) i1,i2 (É) = e−´ϵi2− e−´ϵi1 É+− ϵi1i2.

Imaginary Time Formalism for Causal Nonlinear Response Functions The ﬁrst order expression is, f (1) i1,i2 (É) = e−´ϵi2− e−´ϵi1 É+− ϵi1i2

Reference 84

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:04.609770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 183993c1-1bf4-4620-8f3c-0a3c2f2bf325 · outbound

This paper cites an unresolved cited work.

Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 85

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:42:04.418400Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d0b094ed-778a-449e-8067-651758ba4942 · outbound

This paper cites Kubo, Statistical-mechanical theory of irreversible proc esses.

Imaginary Time Formalism for Causal Nonlinear Response Functions Kubo, Statistical-mechanical theory of irreversible proc esses

Reference 86

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:04.241506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 54d870fd-3a60-4d8c-a57d-b5f8c31cb0d9 · outbound

This paper cites an unresolved cited work.

Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 87

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:42:04.058845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 902efbe3-0dbb-4af6-82a0-1b81cd3e5d58 · outbound

This paper cites an unresolved cited work.

Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 88

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:42:09.487034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ee2540c1-b1e3-4651-b75e-adbe6941b4f4 · outbound

This paper cites Bradlyn and P.

Imaginary Time Formalism for Causal Nonlinear Response Functions Bradlyn and P

Reference 89

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:42:03.862331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bb381f13-15eb-4d33-a94e-724e3b1655f2 · outbound

This paper cites an unresolved cited work.

Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 90

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:42:03.670281Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 08fd8a12-66ae-4b47-a35c-b2a61aaaba68 · outbound

This paper cites an unresolved cited work.

Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 91

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:42:03.505647Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 83b5227b-f50d-4baa-93e0-fa3d83d21459 · outbound

This paper cites an unresolved cited work.

Imaginary Time Formalism for Causal Nonlinear Response Functions Unresolved cited work

Reference 92

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:42:03.371680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Coverage vector

Reference resolution

Outbound references

Pith citing papers