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REVIEW 3 major objections 5 minor 62 references

Solvable Models of Heat Transport in Quantum Mechanics

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Weakly coupled quantum systems exchange heat at a rate set entirely by the two-point function of the coupling operator, and the double-scaled SYK model interpolates between random-matrix and conformal transport.

desk verdict A solid exact-transport paper whose DSSYK interpolation picture is analytically credible but only partially tested numerically. read the letter →

arxiv 2508.09253 v1 pith:U56UGFLS submitted 2025-08-12 hep-th cond-mat.stat-mechcond-mat.str-elnlin.CDnlin.SI

R Loganayagam , Prithvi Narayan , Swathi T S This is my paper · ORCID
classification hep-thcond-mat.stat-mechcond-mat.str-elnlin.CDnlin.SI
keywords heattransportnon-equilibriumsteadystateDSSYKmodelSachdev-Ye-Kitaevrandommatrixtheoryconformalfieldtwo-pointfunctionthermalconductivity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that heat transport between two weakly coupled quantum systems is exactly computable at leading order in the coupling from the two-point function of the coupling operator alone. It derives a closed formula for the heat current and works it out in three toy models—random-matrix, conformal, and Gaussian—each showing a transient peak, an approach to steady state, and a non-equilibrium steady state obeying Fourier's law. It then shows that the double-scaled SYK model realizes all three toy models in different regimes, interpolating from conformal behavior at high temperature to random-matrix behavior at low temperature, with the crossover at inverse temperature $\beta \sim \lambda^{-3/2}$. If correct, the paper gives a parameter-free way to compute transient peaks and thermal conductivities in a strongly interacting solvable model.

What carries the argument

The two-point function $G(t)$ of the operator that couples the hot and cold systems, in particular its frequency-space form satisfying the KMS relation. In the DSSYK model, the exact two-point function is expressed as a sum over chord diagrams, resummed into a $q$-series of Bessel functions; its large-time asymptotics give random-matrix-like power laws, while its $\lambda\to 0$ saddle-point evaluation gives the conformal two-point function with Gamma-function quasinormal poles.

What would settle it

Compute the full heat current from the exact $q$-series two-point function at finite $\lambda$ and compare with the conformal-regime conductivity formula (eq. 4.28) at $\beta\sqrt{\lambda} \sim 1$; a deviation much larger than the roughly 20% seen in the two-point function comparison would falsify the claim that two-point data alone determine transport in this regime.

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Extended reading notes

Core claim

The central claim is that, to leading order in the weak inter-system coupling $\epsilon$, the heat current is determined entirely by the Wightman two-point functions of the coupling operators: $\dot E_c(t) = -\epsilon^2\,\mathrm{Im}\{G_c(t)G_h(t)\} + \epsilon^2\,\mathrm{Im}\int_0^t d\tilde t\,\big(G_c(\tilde t)\dot G_h(\tilde t)-\dot G_c(\tilde t)G_h(\tilde t)\big)$. Consequently, for any system whose two-point function is known—random-matrix, conformal, Gaussian, or DSSYK—the transient peak time and height, the rate of approach to the non-equilibrium steady state, and the steady-state thermal conductivity all follow from that single function. The DSSYK model then serves as a microscopic int

Load-bearing premise

The central premise is that the saddle-point and large-time asymptotic approximations used to evaluate the DSSYK two-point function in the conformal and random-matrix regimes control the transport observables; if subleading corrections are larger than the numerics indicate, the quantitative conductivity predictions could shift.

Editorial extensions

If this is right

  • The transient current peak, the time at which it occurs, and the approach to the steady state are all computable from two-point data alone, without solving the full nonequilibrium dynamics.
  • Different two-point decay profiles produce distinct signatures: random-matrix models approach the steady state as a power law $t^{-5}$, conformal models exponentially, and Gaussian models with a Gaussian falloff.
  • The DSSYK model interpolates between conformal and random-matrix transport as temperature varies, giving a concrete microscopic realization of an RG-like flow between the two toy-model descriptions.
  • The explicit conductivity formulas in the conformal regime, $\sigma \sim \lambda^{-2m}\beta^{1-4m}$ at low temperature and $\sigma \sim \sqrt{\lambda}\,\beta^2$ at high temperature, reproduce earlier coupled-SYK results with now-controlled prefactors.
  • The integrated energy-flux bound $F_\kappa \ge 0$ for $\kappa \ge 2/\beta_h$ is verified in every model considered.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the two-point-function-only formula is general, it suggests a broad dictionary between the analytic structure of $G(t)$ and transport universality classes: poles give exponential approach, branch cuts give power laws, and Gaussian forms give ultra-fast approach.
  • The conformal-to-random-matrix interpolation seen in DSSYK could be a template for other disordered fermion models, including chains of DSSYK systems, where a similar temperature-driven crossover should appear.
  • The conductivity result for unequal operator dimensions (eq. 3.18) may extend naturally to charge transport if the coupling operator is replaced by a conserved charge current, giving a solvable route to electrical conductivity in the same toy-model family.
  • The paper leaves open higher-order corrections in $\epsilon$; if those corrections are controlled, the same chord-diagram machinery could compute leading anharmonic corrections to heat transport.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript studies heat transport between two quantum systems initialized at different temperatures and weakly coupled at t=0. The central technical result is Eq. (2.9), which expresses the leading-order heat current entirely in terms of the two-point functions of the coupling operators of the two isolated systems. Using this formula, the authors analyze three toy models: an RMT-like model with a semicircle density of states and energy-dependent matrix elements (Sec. 3.1), a conformal model with sinh^{-2m} two-point functions (Sec. 3.2), and a Gaussian model (Sec. 3.3). For each, they characterize the transient peak, the approach to the NESS, and the thermal conductivity. They then turn to DSSYK, reviewing its exact two-point function and showing that in suitable limits it reduces to the RMT and conformal toy models (Secs. 4.2.1–4.2.2). The paper closes with numerical comparisons of heat currents and conductivities, and argues that DSSYK interpolates between the conformal and RMT behaviors, with a crossover governed by the scrambling scale.

Significance. If the central claim is correct, the paper provides a useful analytic laboratory for quantum heat transport beyond quasiparticle descriptions: the heat current is computed exactly (to O(epsilon^2)) from two-point data, and the DSSYK model gives a microscopic realization of a UV-conformal to IR-RMT crossover in a transport setting. The manuscript contains a substantial amount of explicit analytic work: closed-form two-point functions, asymptotic expansions, and parameter maps between models. It also verifies general constraints such as the positivity bound on F_kappa from Ref. [6]. The toy models are simple and potentially reusable for other transport questions. However, the quantitative content of the claimed DSSYK-to-toy-model interpolation is not fully demonstrated, as detailed below.

major comments (3)
  1. [§4.3.2, Fig. 22(b), Eq. (4.26)] The central low-temperature claim that DSSYK reduces to the RMT/Cold-RMT model is not quantitatively established by the heat-current data shown. In Fig. 22(b), the RMT result is explicitly normalized to agree with the DSSYK result at t=50. This normalization removes exactly the overall prefactor in the RMT two-point function—the quantity fixed by the parameter map Eq. (4.26)—so the comparison tests only the decay shape, not the transport magnitude. The two-point-function checks in Figs. 17–18 are for beta=1, not in the low-temperature regime. The conductivity comparison in Fig. 23 is a potentially relevant unnormalized test, but the paper does not state clearly whether that comparison is unnormalized or quantify its accuracy over the claimed range. Please provide an unnormalized low-temperature comparison of the heat current (or an explicit, quantified conductivity comparison) using the
  2. [§4.2.1, Appendix C, Fig. 25] The conformal-regime reduction of DSSYK relies on the saddle-point approximation for the partition function and the two-point function, Eqs. (C.2)–(C.8). Fig. 25 shows that the resulting analytical two-point function agrees with numerical DSSYK data only to about 20% at lambda=0.05, and the text itself says the agreement is only “qualitatively well.” Since Eqs. (4.28)–(4.30) use the conformal toy-model form with phi0 determined by the saddle, the finite-lambda conductivity predictions inherit this error. The lambda→0 statement is an asymptotic one, but the paper should state the expected size of subleading corrections and explain how they affect the claimed quantitative agreement in Fig. 23, particularly in the crossover region.
  3. [§3.1, Eq. (3.2); §4.1.1; §4.2.2] The independence of the toy models is somewhat overstated. The RMT matrix-element ansatz Eq. (3.2) is motivated by the form that appears in the DSSYK edge expansion (see footnote 10), and the Gaussian model is exactly the q→1 limit of DSSYK (Sec. 4.1.1). The parameter map Eq. (4.26) is then derived by matching the same edge data. The agreement between DSSYK and the toy models in those limits is therefore partly by construction. This does not invalidate the toy models as useful parametrizations, but the abstract’s phrase “seemingly distinct toy models” should be tempered, and it would strengthen the paper to test at least one prediction in a regime not used to fix the map.
minor comments (5)
  1. [§4.3.2, heading] The section title “for t < (1 − q)^{−3/2}” appears inconsistent with the text and figures, which study large times t ≫ (1 − q)^{−3/2}; the inequality sign is probably inverted.
  2. [§3.3 and §4.1.1] In §4.1.1 the text says the Gaussian matrix elements are “identical” to Eq. (3.20) “with γ = 1,” but the parameter γ is not defined in the Gaussian model of §3.3; the symbol used there is q~.
  3. [§4.2.2, Eq. (4.25)] The normalization of the DSSYK trace is Tr(I)=1, while the RMT model uses an arbitrary normalization N_r. After matching in Eq. (4.26), the relation between the two conventions is not explicitly discussed; please state the normalization assumptions in the parameter map.
  4. [Abstract and §1] The text uses “exact results” for expressions that are often asymptotic (e.g., Eq. (3.6), Eq. (3.16), Eq. (4.25)). Consider using “closed-form” or “exact in the stated limits” to avoid overstatement.
  5. [Figures 4, 9, 13] Several heat-current plots are normalized so that the peak height equals 1. This hides the absolute magnitude, which is important for the quantitative comparisons. Please state in the captions whether and how each curve is normalized.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: transport results are computed from independently specified two-point functions, and the DSSYK-to-toy-model reductions are derived limits rather than fitted predictions.

full rationale

The central formula, eq (2.9), is derived in Appendix A from a weak-coupling expansion and gives the heat current in terms of the isolated two-point functions; it is not defined in terms of the transport quantities it is later used to compute. Each toy model is specified independently: RMT via a semicircle density of states and a matrix-element average, eqs (3.1)-(3.2); the conformal model via a KMS-preserving two-point ansatz, eqs (3.13)-(3.14); the Gaussian model via a Gaussian density of states and matrix elements, eqs (3.18)-(3.20). All transient, NESS, and conductivity statements in Sec. 3 follow by direct integration of these inputs, not by importing the target result. The reductions of DSSYK to the toy models are also derived rather than fitted: the RMT, Gaussian, and conformal limits are obtained from the exact chord-diagram expressions (4.10)-(4.15) and the large-time asymptotic two-point function (4.25), with the parameter map (4.26) fixed by matching those expressions. The disclosed normalization of the RMT curve at t=50 in Fig. 22b is a verification limitation, not a circular fit: the paper uses that plot only to show the decay shape, while the quantitative low-temperature conductivity comparison in Fig. 23 and the analytic conductivities (4.28)-(4.30) are not normalized fits. The ~20% agreement reported for the conformal spectral function (Fig. 25) is likewise an explicitly quantified accuracy caveat. Self-citations to prior chord-diagram results ([39], [40]) supply the known DSSYK correlators, but they are not invoked as a uniqueness theorem or as a substitute for the paper's own transport derivations, and [40] is independent of the present authors. Consequently, no load-bearing step reduces to its own input by construction.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The derivation leans on the standard weak-coupling transport formula, on chosen two-point function ansatze, and on the DSSYK chord-diagram formalism. The toy models carry several free parameters (Delta, phi_0, m, alpha, Je, E0) that are either matched to DSSYK or left as model constants. No new physical entities are introduced.

free parameters (6)
  • Delta = free in RMT toy model; in DSSYK matching: (1+Delta)/(1-Delta) = (-q_tilde;q)^4_infinity / (q_tilde;q)^4_infinity (eq 4.2
    Controls suppression of operator matrix elements between energetically distant states in the RMT model.
  • phi_0 = in DSSYK conformal regime fixed by 4*phi_0/(beta*E0*lambda) = cos(phi_0) (eq 4.22); free in conformal toy model
    Sets the decay rate of the conformal two-point function and the position of its poles.
  • m = conformal scaling exponent; in DSSYK it is the ratio of fermion numbers in operator and Hamiltonian
    Fixed by the operator dimension; controls the power of the correlator.
  • alpha = 1/2 to match RMT edge behavior; otherwise free in cold RMT
    Exponent of the density-of-states edge singularity in the cold RMT model.
  • Je = J*sqrt(1-q_tilde) in DSSYK to Gaussian matching
    Energy scale of the Gaussian model; sets the width of the Gaussian two-point function.
  • E0 = 2 in DSSYK; free in RMT model
    Spectral cutoff; sets the overall energy scale in RMT and DSSYK.
assumptions (5)
  • domain assumption Heat current to leading order in coupling epsilon is given by eq (2.9), assuming factorized thermal initial states and weak coupling.
    Section 2.2 and Appendix A; standard time-dependent perturbation theory, valid for small epsilon.
  • domain assumption The two-point function of the coupling operator is the only input needed for transport; the averaged matrix elements f(E1,E2) are specified by hand.
    Section 2.1; this defines the toy models.
  • standard math DSSYK chord-diagram results for Z(beta) and G(t) (eqs 4.10-4.15) from refs [39,40] are correct.
    Prior published results taken as input.
  • domain assumption The saddle-point approximation controls the lambda-to-0 conformal regime with beta*sqrt(lambda) fixed (eqs C.2-C.8).
    Section 4.2.1, Appendix C; numerical agreement is about 20%.
  • ad hoc to paper The specific forms of f(E1,E2) in the RMT model (eq 3.2) and Gaussian model (eq 3.20) are simple ansatze chosen for solvability.
    Section 3.1 states the RMT form is 'somewhat crude and ad hoc'.

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Pith. "Pith review of Solvable Models of Heat Transport in Quantum Mechanics." pith.science (2026). https://pith.science/paper/U56UGFLS

@misc{pith2026250809253,
  author       = {Pith},
  title        = {Pith review of: Solvable Models of Heat Transport in Quantum Mechanics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/U56UGFLS}},
  note         = {Machine review of arXiv:2508.09253}
}
abstract

We investigate solvable models of heat transport between a pair of quantum mechanical systems initialized at two different temperatures. At time $t=0$, a weak interaction is switched on between the systems, and we study the resulting energy transport. Focusing on the heat current as the primary observable, we analyze both the transient dynamics and the long-time behavior of the system. We demonstrate that simple toy models - including Random Matrix Theory like models ({\it RMT models}) and Schwarzian like models ({\it conformal models}) - can capture many generic features of heat transport, such as transient current peaks and the emergence of non-equilibrium steady state (NESS). For these models, we derive a variety of exact results characterizing the short time transients, long time approach to NESS and thermal conductivity. Finally, we show how these features appear in a more realistic solvable model, the Double-Scaled SYK (DSSYK) model. We demonstrate that the DSSYK model interpolates between the seemingly distinct toy models discussed earlier, with the toy models in turn providing a useful lens through which to understand the rich features of DSSYK.

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Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [35]

    Energy transport across two interacting quantum baths without quasiparticles,

    A. Larzul and M. Schir` o, “Energy transport across two interacting quantum baths without quasiparticles,” Phys. Rev. B , vol. 108, p. 115120, Sep 2023

    work page 2023

  2. [6]

    Universal constraints on energy flow and syk thermalization,

    A. Almheiri, A. Milekhin, and B. Swingle, “Universal constraints on energy flow and syk thermalization,” JHEP, vol. 04, p. 245, 2020

    work page 2020

  3. [1]

    Zwanzig, Nonequilibrium Statistical Mechanics

    R. Zwanzig, Nonequilibrium Statistical Mechanics. OUP USA, 2001

    work page 2001

  4. [2]

    J. I. Kapusta and C. Gale, Finite-temperature field theory: Principles and applications . Cambridge Monographs on Mathematical Physics, Cambridge University Press, 2011

    work page 2011

  5. [3]

    Kamenev, Field Theory of Non-Equilibrium Systems

    A. Kamenev, Field Theory of Non-Equilibrium Systems . Cambridge University Press, 2011

    work page 2011

  6. [4]

    Balakrishnan, Elements of Nonequilibrium Statistical Mechanics

    V. Balakrishnan, Elements of Nonequilibrium Statistical Mechanics . Springer International Publishing, 2020

    work page 2020

  7. [5]

    Energy flow in non-equilibrium conformal field theory,

    D. Bernard and B. Doyon, “Energy flow in non-equilibrium conformal field theory,” J. Phys. A , vol. 45, p. 362001, 2012

    work page 2012

  8. [7]

    Conformal field theory out of equilibrium: a review,

    D. Bernard and B. Doyon, “Conformal field theory out of equilibrium: a review,” J. Stat. Mech., vol. 1606, no. 6, p. 064005, 2016

    work page 2016

Show all 62 references
  1. [8]

    Generalized Gibbs Ensembles for Quantum Field Theories,

    F. H. L. Essler, G. Mussardo, and M. Panfil, “Generalized Gibbs Ensembles for Quantum Field Theories,” Phys. Rev. A , vol. 91, no. 5, p. 051602, 2015

    2015

  2. [9]

    Nonequilibrium density-matrix description of steady-state quantum transport,

    A. Dhar, K. Saito, and P. H¨ anggi, “Nonequilibrium density-matrix description of steady-state quantum transport,” Phys. Rev. E , vol. 85, p. 011126, January 2012

    2012

  3. [10]

    Nonequilibrium density matrix for thermal transport in quantum field theory,

    B. Doyon, “Nonequilibrium density matrix for thermal transport in quantum field theory,” Communications in Mathematical Physics , vol. 351, no. 1, pp. 155–200, 2017

    2017

  4. [11]

    Nonequilibrium thermal transport and its relation to linear response,

    C. Karrasch, R. Ilan, and J. E. Moore, “Nonequilibrium thermal transport and its relation to linear response,” Phys. Rev. B , vol. 88, p. 195129, Nov 2013

    2013

  5. [12]

    Energy transport in heisenberg chains beyond the luttinger liquid paradigm,

    A. De Luca, J. Viti, L. Mazza, and D. Rossini, “Energy transport in heisenberg chains beyond the luttinger liquid paradigm,” Phys. Rev. B , vol. 90, p. 161101, Oct 2014

    2014

  6. [13]

    Energy transport between two integrable spin chains,

    A. Biella, A. De Luca, J. Viti, D. Rossini, L. Mazza, and R. Fazio, “Energy transport between two integrable spin chains,” Phys. Rev. B , vol. 93, p. 205121, May 2016

    2016

  7. [14]

    Ballistic transport and boundary resistances in inhomogeneous quantum spin chains,

    A. Biella, M. Collura, D. Rossini, A. De Luca, and L. Mazza, “Ballistic transport and boundary resistances in inhomogeneous quantum spin chains,” Nature Commun., vol. 10, no. 1, p. 4820, 2019

    2019

  8. [15]

    Finite-temperature transport in one-dimensional quantum lattice models,

    B. Bertini, F. Heidrich-Meisner, C. Karrasch, T. Prosen, R. Steinigeweg, and M. ˇZnidariˇ c, “Finite-temperature transport in one-dimensional quantum lattice models,” Rev. Mod. Phys. , vol. 93, p. 025003, May 2021

    2021

  9. [16]

    S. A. Hartnoll, A. Lucas, and S. Sachdev, Holographic quantum matter . MIT press, 2018. – 52 –

    2018

  10. [17]

    A simple model of quantum holography

    A.Kitaev, “A simple model of quantum holography.” http://online.kitp.ucsb.edu/online/entangled15/kitaev/, 2015

    2015

  11. [18]

    Gapless spin-fluid ground state in a random quantum heisenberg magnet,

    S. Sachdev and J. Ye, “Gapless spin-fluid ground state in a random quantum heisenberg magnet,” Phys. Rev. Lett. , vol. 70, pp. 3339–3342, May 1993

    1993

  12. [19]

    Remarks on the sachdev-ye-kitaev model,

    J. Maldacena and D. Stanford, “Remarks on the sachdev-ye-kitaev model,” Phys. Rev. D, vol. 94, p. 106002, Nov 2016

    2016

  13. [20]

    The spectrum in the sachdev-ye-kitaev model,

    J. Polchinski and V. Rosenhaus, “The spectrum in the sachdev-ye-kitaev model,” Journal of High Energy Physics , vol. 2016, pp. 1–25, 2016

    2016

  14. [21]

    Strange metals and the AdS/CFT correspondence,

    S. Sachdev, “Strange metals and the AdS/CFT correspondence,” J. Stat. Mech. , vol. 1011, p. P11022, 2010

    2010

  15. [22]

    A bound on chaos,

    J. Maldacena, S. H. Shenker, and D. Stanford, “A bound on chaos,” JHEP, vol. 08, p. 106, 2016

    2016

  16. [23]

    Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space,

    J. Maldacena, D. Stanford, and Z. Yang, “Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space,” PTEP, vol. 2016, no. 12, p. 12C104, 2016

    2016

  17. [24]

    An investigation of AdS2 backreaction and holography,

    J. Engels¨ oy, T. G. Mertens, and H. Verlinde, “An investigation of AdS2 backreaction and holography,” JHEP, vol. 07, p. 139, 2016

    2016

  18. [25]

    Bekenstein-hawking entropy and strange metals,

    S. Sachdev, “Bekenstein-hawking entropy and strange metals,” Phys. Rev. X , vol. 5, p. 041025, Nov 2015

    2015

  19. [26]

    A Generalization of Sachdev-Ye-Kitaev,

    D. J. Gross and V. Rosenhaus, “A Generalization of Sachdev-Ye-Kitaev,” JHEP, vol. 02, p. 093, 2017

    2017

  20. [27]

    SYK Models and SYK-like Tensor Models with Global Symmetry,

    J. Yoon, “SYK Models and SYK-like Tensor Models with Global Symmetry,” JHEP, vol. 10, p. 183, 2017

    2017

  21. [28]

    Supersymmetric syk model with global symmetry,

    P. Narayan and J. Yoon, “Supersymmetric syk model with global symmetry,” Journal of High Energy Physics , vol. 2018, pp. 1–60, 2018

    2018

  22. [29]

    Notes on the complex sachdev-ye-kitaev model,

    Y. Gu, A. Y. Kitaev, S. Sachdev, and G. M. Tarnopolsky, “Notes on the complex sachdev-ye-kitaev model,” Journal of High Energy Physics , vol. 2020, pp. 1–74, 2020

    2020

  23. [30]

    Syk model, chaos and conserved charge,

    R. Bhattacharya, S. Chakrabarti, D. P. Jatkar, and A. Kundu, “Syk model, chaos and conserved charge,” Journal of High Energy Physics , vol. 2017, pp. 1–16, 2017

    2017

  24. [31]

    Note on global symmetry and SYK model,

    J. Liu and Y. Zhou, “Note on global symmetry and SYK model,” JHEP, vol. 05, p. 099, 2019

    2019

  25. [32]

    Supersymmetric sachdev-ye-kitaev models,

    W. Fu, D. Gaiotto, J. Maldacena, and S. Sachdev, “Supersymmetric sachdev-ye-kitaev models,” Phys. Rev. D , vol. 95, p. 026009, Jan 2017

    2017

  26. [33]

    Supersymmetric syk model: bi-local collective superfield/supermatrix formulation,

    J. Yoon, “Supersymmetric syk model: bi-local collective superfield/supermatrix formulation,” Journal of High Energy Physics , vol. 2017, pp. 1–48, 2017. – 53 –

    2017

  27. [34]

    Correlators in the N = 2 Supersymmetric SYK Model,

    C. Peng, M. Spradlin, and A. Volovich, “Correlators in the N = 2 Supersymmetric SYK Model,” JHEP, vol. 10, p. 202, 2017

    2017

  28. [36]

    Are fast scramblers good thermal baths?,

    A. Larzul, S. J. Thomson, and M. Schir` o, “Are fast scramblers good thermal baths?,” Apr. 2022

    2022

  29. [37]

    Phase transition in the density of states of quantum spin glasses,

    L. Erd˝ os and D. Schr¨ oder, “Phase transition in the density of states of quantum spin glasses,” Mathematical Physics, Analysis and Geometry , vol. 17, pp. 441–464, 2014

    2014

  30. [38]

    Black Holes and Random Matrices,

    J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher, and M. Tezuka, “Black Holes and Random Matrices,” JHEP, vol. 05, p. 118, 2017. [Erratum: JHEP 09, 002 (2018)]

    2017

  31. [39]

    Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction,

    M. Berkooz, P. Narayan, and J. Sim´ on, “Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction,” Journal of High Energy Physics , vol. 2018, p. 192, Aug. 2018

    2018

  32. [40]

    Towards a full solution of the large N double-scaled SYK model,

    M. Berkooz, M. Isachenkov, V. Narovlansky, and G. Torrents, “Towards a full solution of the large N double-scaled SYK model,” JHEP, vol. 03, p. 079, 2019

    2019

  33. [41]

    Multi-trace correlators in the SYK model and non-geometric wormholes,

    M. Berkooz, N. Brukner, V. Narovlansky, and A. Raz, “Multi-trace correlators in the SYK model and non-geometric wormholes,” JHEP, vol. 21, p. 196, 2020

    2020

  34. [42]

    The bulk Hilbert space of double scaled SYK,

    H. W. Lin, “The bulk Hilbert space of double scaled SYK,” JHEP, vol. 11, p. 060, 2022

    2022

  35. [43]

    Quantum groups, non-commutative AdS 2, and chords in the double-scaled SYK model,

    M. Berkooz, M. Isachenkov, M. Isachenkov, P. Narayan, and V. Narovlansky, “Quantum groups, non-commutative AdS 2, and chords in the double-scaled SYK model,” JHEP, vol. 08, p. 076, 2023

    2023

  36. [44]

    Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity,

    T. G. Mertens and G. J. Turiaci, “Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity,” Living Rev. Rel. , vol. 26, no. 1, p. 4, 2023

    2023

  37. [45]

    Entanglement and Chaos in De Sitter Space Holography: An SYK Example,

    L. Susskind, “Entanglement and Chaos in De Sitter Space Holography: An SYK Example,” JHAP, vol. 1, no. 1, pp. 1–22, 2021

    2021

  38. [46]

    De sitter space, double-scaled syk, and the separation of scales in the semiclassical limit,

    L. Susskind, “De sitter space, double-scaled syk, and the separation of scales in the semiclassical limit,” Journal of Holography Applications in Physics , vol. 5, no. 1, pp. 1–30, 2025

    2025

  39. [47]

    Scrambling in double-scaled syk and de sitter space,

    L. Susskind, “Scrambling in double-scaled syk and de sitter space,” May 2022

    2022

  40. [48]

    The dilaton gravity hologram of double-scaled SYK,

    A. Blommaert, T. G. Mertens, and J. Papalini, “The dilaton gravity hologram of double-scaled SYK,” JHEP, vol. 06, p. 050, 2025

    2025

  41. [49]

    SYK Model with global symmetries in the double scaling limit,

    P. Narayan and S. T. S, “SYK Model with global symmetries in the double scaling limit,” JHEP, vol. 05, p. 083, 2023. – 54 –

    2023

  42. [50]

    Complex sachdev-ye-kitaev model in the double scaling limit,

    M. Berkooz, V. Narovlansky, and H. Raj, “Complex sachdev-ye-kitaev model in the double scaling limit,” arXiv: High Energy Physics - Theory , 2020

    2020

  43. [51]

    The double scaled limit of Super–Symmetric SYK models,

    M. Berkooz, N. Brukner, V. Narovlansky, and A. Raz, “The double scaled limit of Super–Symmetric SYK models,” JHEP, vol. 12, p. 110, 2020

    2020

  44. [52]

    Remarks on the Sachdev-Ye-Kitaev model,

    J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,” Phys. Rev. D, vol. 94, no. 10, p. 106002, 2016

    2016

  45. [53]

    On a remarkable formula of ramanujan,

    D. Chakrabarti and G. K. Srinivasan, “On a remarkable formula of ramanujan,” Archiv der Mathematik , vol. 99, pp. 125–135, Aug. 2012

    2012

  46. [54]

    Ringdown in the syk model,

    M. Dodelson, “Ringdown in the syk model,” Aug. 2024. CERN-TH-2024-135

    2024

  47. [55]

    A cordial introduction to double scaled syk,

    M. Berkooz and O. Mamroud, “A cordial introduction to double scaled syk,” arXiv.org, July 2024

    2024

  48. [56]

    Continuous q-Hermite polynomials — Wikipedia, the free encyclopedia

    Wikipedia, “Continuous q-Hermite polynomials — Wikipedia, the free encyclopedia.” http://en.wikipedia.org/w/index.php?title=Continuous%20q-Hermite% 20polynomials&oldid=1121109966

  49. [57]

    Koekoek, T

    R. Koekoek, T. Koornwinder, P. Lesky, and R. Swarttouw, Hypergeometric Orthogonal Polynomials and Their q-Analogues . Springer Monographs in Mathematics, Springer Berlin Heidelberg, 2010

    2010

  50. [58]

    Large p SYK from chord diagrams,

    B. Mukhametzhanov, “Large p SYK from chord diagrams,” JHEP, vol. 09, p. 154, 2023

    2023

  51. [59]

    Semiclassical geometry in double-scaled SYK,

    A. Goel, V. Narovlansky, and H. Verlinde, “Semiclassical geometry in double-scaled SYK,” JHEP, vol. 11, p. 093, 2023

    2023

  52. [60]

    Local criticality, diffusion and chaos in generalized sachdev-ye-kitaev models,

    Y. Gu, X.-L. Qi, and D. Stanford, “Local criticality, diffusion and chaos in generalized sachdev-ye-kitaev models,” Journal of High Energy Physics , vol. 2017, May 2017

    2017

  53. [61]

    Nonlinear soft mode action for the large- p syk model,

    M. Bucca and M. Mezei, “Nonlinear soft mode action for the large- p syk model,” 2024

    2024

  54. [62]

    I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products . Elsevier/Academic Press, Amsterdam, seventh ed., 2007. – 55 –

    2007

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.