Pith. sign in

REVIEW 3 major objections 5 minor 51 references

Quantum Chaos and Diffusive Transport from Geometric Randomness

T0 review · 3 major / 5 minor · reviewed 2026-07-31 · grok-4.5

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Geometric randomness alone on layered random graphs produces quantum chaos and diffusion when layers are extensive, and ballistic transport from a few delocalized states when they are not.

desk verdict Clean numerical Letter showing geometry alone can produce RMT chaos and diffusion on RLTL graphs; finite-W thermodynamic claim is plausible but still pre-asymptotic without scaling control. read the letter →

arxiv 2607.28579 v1 pith:KRXR6NFE submitted 2026-07-30 cond-mat.stat-mech cond-mat.dis-nncond-mat.mes-hallquant-ph

Bibek Saha , Abhishek Dhar , Sthitadhi Roy This is my paper
classification cond-mat.stat-mechcond-mat.dis-nncond-mat.mes-hallquant-ph
keywords quantumchaosgeometricrandomnessdiffusivetransportAndersonlocalizationlevelstatisticsrandomgraphswave-packetdynamicsbipartiteentanglement
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

Quantum chaos and diffusion are usually blamed on microscopic disorder or interactions. This paper shows both can appear in a clean tight-binding model whose only randomness is the geometry of the graph. Sites sit in layers; each site links randomly to a fixed number of sites on the neighboring layers. When the number of sites per layer grows with the number of layers, the spectrum shows level repulsion, essentially all eigenstates are delocalized, and a wave packet spreads diffusively. When the layer size is held fixed, most states localize, level repulsion disappears, yet a finite fraction of perfectly delocalized Bloch waves still drive ballistic transport. The result isolates geometric randomness and effective dimensionality as an independent knob that turns chaos and diffusion on or off.

What carries the argument

Random locally tree-like layered (RLTL) graphs: sites arranged in Lx layers of Ly sites each, with every site joined by exactly K random edges to each neighboring layer. The single control parameter is the effective dimensionality set by whether Ly/Lx stays finite or Ly is held fixed while Lx diverges.

What would settle it

A controlled finite-size scaling collapse of the level-spacing ratio or of the diffusion constant versus W = Ly/Lx that either confirms or rules out a sharp change from Wigner-Dyson plus diffusion to Poisson plus ballistic transport as W approaches zero.

Watch

Extended reading notes

Core claim

On random locally tree-like layered graphs with uniform hoppings, an extensive layer-to-length ratio produces robust quantum chaos (Wigner-Dyson level statistics), delocalized eigenstates, and ordinary diffusion; the quasi-one-dimensional limit instead hosts an extensive mixture of localized states and special delocalized Bloch waves, suppressing level repulsion while the Bloch sector alone produces ballistic transport. Geometric randomness is therefore a fundamental mechanism that can generate and tune quantum chaos without microscopic disorder or interactions.

Load-bearing premise

That finite-size numerics at a few representative points already establish the thermodynamic-limit split between chaos-plus-diffusion for any finite layer ratio and Poisson-plus-ballistic transport for fixed layer size.

Editorial extensions

If this is right

  • Geometric randomness can replace microscopic disorder as the source of chaos and diffusion in non-interacting models.
  • Effective dimensionality (layer-size ratio) becomes a tuning parameter that switches the system between chaotic diffusion and mixed localized-plus-ballistic dynamics.
  • The same graphs supply a natural arena for studying Anderson transitions that interpolate between finite-dimensional and tree-like criticality.
  • Periodic driving of the quasi-1D case may hybridize the coexisting localized and delocalized sectors and produce stable multifractal states.

Reading between the lines

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

  • Adding weak onsite disorder to the extensive-layer regime should leave diffusion intact until a conventional Anderson transition, offering a clean test of how geometric and potential disorder compete.
  • The exact Bloch subspace that survives for any Ly suggests a simple projection that could be used to construct analytically solvable limits of larger random-graph models.
  • Because the graphs remain locally tree-like, the same construction may map onto Fock-space graphs of certain many-body problems, giving a geometry-only route to many-body chaos.
Share X Bluesky LinkedIn Reddit HN

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 non-interacting tight-binding fermions on random locally tree-like layered (RLTL) graphs with uniform hoppings, arguing that geometric randomness alone can generate quantum chaos and control transport. Two thermodynamic limits are contrasted: finite layer-aspect ratio W = Ly/Lx (effective 2D), where the authors report Wigner–Dyson level statistics, IPR scaling I2 ∼ Lx^{-1}, Gaussian wave-packet spreading with σ(t) ∼ t^{1/2}, saturating NEGF conductance, and diffusive bipartite entanglement growth; and fixed Ly with Lx → ∞ (quasi-1D ladders), where an extensive fraction of states are localized while a finite fraction of symmetric-layer Bloch states (Eqs. 4–5) remain delocalized, producing Poisson level statistics, a localized core plus ballistic tails in Π(x,t) (Eq. 8), and Lx-independent conductance. The central claim is that geometric randomness is an independent mechanism for generating and tuning quantum chaos.

Significance. If the finite-W thermodynamic-limit claim holds, the work cleanly isolates geometric (structural) disorder from onsite or hopping-amplitude disorder as a driver of level repulsion and diffusion in a non-interacting setting, and supplies a transparent analytic sector (the symmetric-layer Bloch waves) that explains the quasi-1D dichotomy. Strengths include mutually consistent numerical diagnostics (DoS, P(s), IPR, σ(t), Π(x,t), NEGF G(μ), entanglement), an exact identification of the Bloch subspace from the hopping rule (Eq. 5), and useful End Matter derivations relating number fluctuations to wave-packet spreading and detailing the NEGF setup. These make the quasi-1D results particularly solid and the overall construction of independent interest for Anderson localization on hybrid finite-D/tree-like graphs.

major comments (3)
  1. [Spectrum; Eigenstates; Wavepacket dynamics; Conductance (Fig. 5a)] The load-bearing claim that any finite W yields robust thermodynamic-limit chaos and diffusion (Abstract; Main results; Spectrum/Eigenstates/Wavepacket sections) rests on Wigner surmise collapse, I2 Lx collapse, σ(t)∼t^{1/2}, and apparent G saturation at accessible sizes (Lx ≲ 2×10^3 for spectra/dynamics; Lx ≤ 256 for NEGF in Fig. 5a inset). No controlled finite-size scaling is given (no β-function, localization-length estimate, or collapse of a dimensionless conductance vs Lx at fixed W). Because the finite-W geometry is effectively two-dimensional with purely geometric/off-diagonal disorder, a large but finite localization length is not ruled out; the data cannot yet distinguish a true metal from a long pre-asymptotic diffusive regime. A scaling analysis, larger-Lx conductance, or an explicit bound on ξ is needed to underwrite the thermodynamic-limit statement.
  2. [Conductance; End Matter (NEGF)] For W = 1/2 the authors note that Bloch states still exist and “provide a finite contribution to the total conductance since they are ballistic” (Conductance paragraph), yet Fig. 5a and its inset report raw G(μ) and claim saturation implies finite conductivity = G/W. The Bloch fraction vanishes as 1/Ly ∼ 1/(W Lx), so their contribution to G should be separated (as done analytically for fixed Ly in the End Matter) before interpreting saturation of total G as bulk diffusive conductivity of the random sector. Without that decomposition the conductivity claim is ambiguous.
  3. [Main results; Model] Only single representative points are shown (K = 2, W = 1/2; Ly = 8). The abstract and Main results phrase the dichotomy as holding for “an extensive layer size” / “the quasi-one-dimensional limit” generally. At minimum the manuscript should demonstrate that the Wigner/IPR/diffusion diagnostics persist for at least one other finite W (and preferably one other K), or else qualify the claim as numerical evidence at these points rather than a general geometric mechanism.
minor comments (5)
  1. [Spectrum (Fig. 2)] Fig. 2(c): the drift of P(s) toward Poisson for Ly = 8 is clear, but a quantitative diagnostic (e.g. ⟨r⟩ or integrated deviation from Wigner/Poisson vs Lx) would make the thermodynamic-limit statement sharper.
  2. [Wavepacket dynamics] The diffusion constant D ≈ 5.46 is quoted from a Gaussian fit to Π(x,t) but no fit uncertainty, time window, or disorder average is reported; a brief statement would help reproducibility.
  3. [Model] Notation: T(x,x+1) is introduced as the hopping matrix with exactly K ones per row/column; it would help to state explicitly whether the matrices are drawn uniformly among such (0,1)-matrices and whether left/right degrees are exactly K (configuration-model style) or only in expectation.
  4. Typos/formatting: “W avepacket” in Fig. 4 caption; “End MA TTER”; occasional missing spaces before citations and in “L x”, “L y” throughout. The arXiv note about Ref. [50] should be updated or integrated if that work is public.
  5. [Spectrum] Eq. (2) multiplies raw spacings by the local DoS rather than fully unfolding; while the DoS is approximately flat, a short check that standard unfolding yields the same P(s) would remove a minor ambiguity.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: chaos/diffusion claims are direct numerical outputs of a fully specified Hamiltonian plus one model-derived Bloch sector, not inputs renamed as predictions.

full rationale

The load-bearing claims (Wigner-Dyson P(s) and IPR∼Lx^{-1} for finite W; Poisson plus ballistic Bloch transport for fixed Ly; σ(t)∼t^{1/2} and conductance saturation) are obtained by exact diagonalization, wavepacket evolution, and NEGF on the Hamiltonian of Eq. (1) with the stated random 0-1 hopping matrices T^{(x,x+1)}. Nothing is fitted and then re-presented as a prediction. The only analytic sector—the symmetric-layer Bloch waves at En=4J cos[nπ/(Lx+1)] with ψn of Eq. (4)—follows by direct substitution from the row-sum property of the T matrices (Eq. 5), without circular appeal to the chaos claim. Entanglement–number-fluctuation identities and NEGF formulae in the End Matter are standard free-fermion identities, not self-referential. Background citations (Anderson graphs, Fock-space MBL, Dyson singularity, concurrent Ref. [50]) supply context and are not used as uniqueness theorems that force the present results. Finite-size extrapolation risk is a correctness issue, not circularity. Score 0; steps empty.

Assumptions & free parameters 5 free parameters · 7 assumptions · 1 invented entities

The central claim rests on the RLTL ensemble with uniform hoppings, bipartiteness without onsite potentials, layer-only locality for IPR/transport, and the representative thermodynamic limits (finite W vs fixed Ly). No new particles or forces are postulated. Free choices are the connectivity K, the two geometry cuts, and a measured diffusion constant; background axioms are standard tight-binding quantum mechanics, RMT diagnostics, and NEGF linear response.

free parameters (5)
  • Connectivity K = 2
    Fixed to K=2 for all reported data as a representative of the 2K-regular RLTL family; not scanned.
  • Geometry cut W=Ly/Lx = 1/2
    Chosen as W=1/2 to represent the extensive-layer (effective 2D) regime; other finite W not shown.
  • Fixed layer size Ly = 8
    Chosen as Ly=8 to represent the quasi-1D ladder limit; other O(1) Ly not shown.
  • Diffusion constant D in Gaussian Π(x,t) = ≈5.46
    Read off from wave-packet profiles in the finite-W diffusive regime (Fig. 4b); characterizes transport but is not an input to the chaos claim.
  • Lead and coupling hoppings in NEGF = 2J
    Set to 2J so Bloch modes transmit perfectly (EM); a modeling choice that simplifies G_Bloch=1 but affects quantitative conductance decomposition.
assumptions (7)
  • domain assumption Non-interacting tight-binding fermions on a fixed undirected graph with uniform hopping J and no onsite potentials (Eq. 1).
    Defines the entire Hamiltonian; chaos/transport are single-particle spectral properties of this H.
  • domain assumption RLTL ensemble: each site links to exactly K distinct random sites on each adjacent layer; T matrices are 0-1 with K ones per row/column.
    Encodes ‘geometric randomness’; invoked from Model section and Fig. 1; graphs called locally tree-like following Dhar et al. 2011.
  • domain assumption Bipartite layered structure implies E→−E spectral symmetry and absence of a thermodynamic Dyson singularity at E=0 (observed peak shrinks with Lx).
    Used to interpret DoS in Fig. 2 and to set aside E=0 boundary-localized states for finite W.
  • standard math Unfolded level statistics diagnosed by si=(Ei+1−Ei)ρ((Ei+Ei+1)/2), compared to Wigner surmise vs Poisson as chaos vs no chaos.
    Standard RMT diagnostic (Mehta); justified by approximately flat DoS.
  • ad hoc to paper Layer-projected IPR I2=∑x φ(x)^2 with φ(x)=∑y|ψ(x,y)|^2 diagnoses (de)localization along the only spatial direction.
    Natural given layer locality, but discards intra-layer structure; central to Eigenstates section claims.
  • standard math Zero-temperature linear-response conductance from NEGF with semi-infinite 1d leads on every boundary site diagnoses diffusive vs ballistic transport via G(Lx) scaling.
    Standard mesoscopic formula (Datta; EM Eqs. 14–15); lead hoppings chosen specially as above.
  • ad hoc to paper Thermodynamic limits of interest are (i) W=Ly/Lx fixed finite and (ii) Ly=O(1), Lx→∞; these exhaust the ‘effective dimensionality’ dichotomy.
    Stated in Main results/Model; intermediate scalings (e.g. Ly~log Lx) not considered.
invented entities (1)
  • RLTL graphs as structurally disordered generalizations of square lattices/ladders for quantum chaos independent evidence
    purpose: Provide a finite-dimensional, locally tree-like geometry whose randomness is purely in connectivity, enabling the geometric-chaos claim.
    The graph family itself was introduced earlier for classical hard rods (Dhar, Rajesh, Stilck, PRE 2011). This paper does not invent the graphs but invents their use as a clean setting for single-particle quantum chaos without coupling disorder. independent_evidence is true insofar as the ensemble is externally defined and simulable.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantum Chaos and Diffusive Transport from Geometric Randomness." pith.science (2026). https://pith.science/paper/KRXR6NFE

@misc{pith2026260728579,
  author       = {Pith},
  title        = {Pith review of: Quantum Chaos and Diffusive Transport from Geometric Randomness},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KRXR6NFE}},
  note         = {Machine review of arXiv:2607.28579}
}
read the original abstract

The physics of quantum chaos and diffusive transport is typically studied in settings with microscopic disorder or many-body interactions. In this Letter, we demonstrate that these phenomena can arise purely from geometric randomness. By studying non-interacting quantum particles on random locally tree-like layered graphs with uniform couplings, we show that the geometric randomness and effective graph dimensionality dictates the presence of chaotic dynamics or lack thereof. These graphs can be considered as structurally disordered generalisations of regular square lattices or ladders, or equivalently as multi-component one-dimensional chains with random links between the components. We find that an extensive layer size yields robust quantum chaos, level repulsion, and diffusive transport. Conversely, in the quasi-one-dimensional limit, we find the coexistence of extensive number of localised and delocalised states -- this leads to suppressed level repulsion accompanied by the latter driving ballistic transport. These results establish geometric randomness as a fundamental and independent mechanism for generating and tuning quantum chaos.

Figures

Figures reproduced from arXiv: 2607.28579 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. ), indicating the absence of such a singularity in RLTL graphs. Spectrum: To probe the presence of chaos in the spec￾trum, we study the level-spacing statistics, P(s), where s is defined as si = (Ei+1 − Ei) × ρ [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

51 extracted references · 2 linked inside Pith

  1. [50]

    S. Roy, I. M. Khaymovich, A. Das, and R. Moessner, Mul- tifractality without fine-tuning in a Floquet quasiperiodic chain, SciPost Phys.4, 25 (2018)

    2018

  2. [1]

    =δ x,Lx/2δy,Ly/2. Since the notion of locality exists only alongx, we study the spread of the wavepacket along thexdirection via time-evolving distribution Π(x, t) = LyX y=1 | ⟨x, y|e−iHt |ψ(t= 0)⟩ |2 .(6) To quantify the spread, we consider its width σ(t) =   LxX x=1 x2Π(x, t)− LxX x=1 xΠ(x, t) !2  1/2 ,(7) which typically grows asσ(t)∼t 1/z wherez= ...

  3. [2]

    St¨ ockmann,Quantum Chaos: An Introduction, Cam- bridge Nonlinear Science Series (Cambridge University Press, 1999)

    H. St¨ ockmann,Quantum Chaos: An Introduction, Cam- bridge Nonlinear Science Series (Cambridge University Press, 1999)

    1999

  4. [3]

    Haake,Quantum Signatures of Chaos, Springer Series in Synergetics (Springer Berlin Heidelberg, 2010)

    F. Haake,Quantum Signatures of Chaos, Springer Series in Synergetics (Springer Berlin Heidelberg, 2010)

    2010

  5. [4]

    Rigol, V

    M. Rigol, V. Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature452, 854–858 (2008)

    2008

  6. [5]

    Nandkishore and D

    R. Nandkishore and D. A. Huse, Many-body localiza- tion and thermalization in quantum statistical mechan- ics, Annu. Rev. Condens. Matter Phys.6, 15 (2015)

    2015

  7. [6]

    D’Alessio, Y

    L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Advances in Physics65, 239–362 (2016)

    2016

  8. [7]

    J. M. Deutsch, Eigenstate thermalization hypothesis, Rep. Prog. Phys.81, 082001 (2018)

    2018

Show all 51 references
  1. [8]

    D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Col- loquium: Many-body localization, thermalization, and entanglement, Rev. Mod. Phys.91, 021001 (2019)

    2019

  2. [9]

    Sierant, M

    P. Sierant, M. Lewenstein, A. Scardicchio, L. Vidmar, and J. Zakrzewski, Many-body localization in the age of classical computing, Reports on Progress in Physics88, 026502 (2025)

    2025

  3. [10]

    Abou-Chacra, P

    R. Abou-Chacra, P. W. Anderson, and D. J. Thouless, A self-consistent theory of localization, J. Phys. C6, 1734 (1973)

    1973

  4. [11]

    K. S. Tikhonov, A. D. Mirlin, and M. A. Skvortsov, Anderson localization and ergodicity on random regular graphs, Phys. Rev. B94, 220203 (2016)

    2016

  5. [12]

    K. S. Tikhonov and A. D. Mirlin, Fractality of wave func- tions on a Cayley tree: Difference between tree and lo- 6 cally treelike graph without boundary, Phys. Rev. B94, 184203 (2016)

    2016

  6. [13]

    Garc ´ ıa-Mata, O

    I. Garc ´ ıa-Mata, O. Giraud, B. Georgeot, J. Martin, R. Dubertrand, and G. Lemari´ e, Scaling theory of the Anderson transition in random graphs: Ergodicity and universality, Phys. Rev. Lett.118, 166801 (2017)

    2017

  7. [14]

    G. D. Tomasi, M. Amini, S. Bera, I. M. Khaymovich, and V. E. Kravtsov, Survival probability in General- ized Rosenzweig-Porter random matrix ensemble, SciPost Phys.6, 014 (2019)

    2019

  8. [15]

    De Tomasi, S

    G. De Tomasi, S. Bera, A. Scardicchio, and I. M. Khay- movich, Subdiffusion in the Anderson model on the ran- dom regular graph, Phys. Rev. B101, 100201 (2020)

    2020

  9. [16]

    Roy and D

    S. Roy and D. E. Logan, Localization on Certain Graphs with Strongly Correlated Disorder, Phys. Rev. Lett.125, 250402 (2020)

    2020

  10. [17]

    Biroli and M

    G. Biroli and M. Tarzia, Anomalous dynamics on the ergodic side of the many-body localization transition and the glassy phase of directed polymers in random media, Phys. Rev. B102, 064211 (2020)

    2020

  11. [18]

    Garc ´ ıa-Mata, J

    I. Garc ´ ıa-Mata, J. Martin, O. Giraud, B. Georgeot, R. Dubertrand, and G. Lemari´ e, Critical properties of the Anderson transition on random graphs: Two-parameter scaling theory, Kosterlitz-Thouless type flow, and many- body localization, Phys. Rev. B106, 214202 (2022)

    2022

  12. [19]

    D. E. Logan and P. G. Wolynes, Quantum localization and energy flow in many-dimensional Fermi resonant sys- tems, J. Chem. Phys.93, 4994 (1990)

    1990

  13. [20]

    B. L. Altshuler, Y. Gefen, A. Kamenev, and L. S. Levitov, Quasiparticle lifetime in a finite system: A nonperturba- tive approach, Phys. Rev. Lett.78, 2803 (1997)

    1997

  14. [21]

    Biroli and M

    G. Biroli and M. Tarzia, Delocalized glassy dynamics and many-body localization, Phys. Rev. B96, 201114 (2017)

    2017

  15. [22]

    D. E. Logan and S. Welsh, Many-body localization in Fock space: A local perspective, Phys. Rev. B99, 045131 (2019)

    2019

  16. [23]

    Tarzia, Many-body localization transition in Hilbert space, Phys

    M. Tarzia, Many-body localization transition in Hilbert space, Phys. Rev. B102, 014208 (2020)

    2020

  17. [24]

    Roy and D

    S. Roy and D. E. Logan, Fock-space correlations and the origins of many-body localization, Phys. Rev. B101, 134202 (2020)

    2020

  18. [25]

    De Tomasi, I

    G. De Tomasi, I. M. Khaymovich, F. Pollmann, and S. Warzel, Rare thermal bubbles at the many-body lo- calization transition from the Fock space point of view, Phys. Rev. B104, 024202 (2021)

    2021

  19. [26]

    Roy and D

    S. Roy and D. E. Logan, Fock-space anatomy of eigen- states across the many-body localization transition, Phys. Rev. B104, 174201 (2021)

    2021

  20. [27]

    K. S. Tikhonov and A. D. Mirlin, Eigenstate correlations around the many-body localization transition, Phys. Rev. B103, 064204 (2021)

    2021

  21. [28]

    Tikhonov and A

    K. Tikhonov and A. Mirlin, From Anderson localization on random regular graphs to many-body localization, An- nals of Physics435, 168525 (2021)

    2021

  22. [29]

    Roy and D

    S. Roy and D. E. Logan, The Fock-space landscape of many-body localisation, Journal of Physics: Condensed Matter37, 073003 (2024)

    2024

  23. [30]

    Lepri, R

    S. Lepri, R. Livi, and A. Politi, Heat Conduction in Chains of Nonlinear Oscillators, Phys. Rev. Lett.78, 1896 (1997)

    1997

  24. [31]

    Agarwal, S

    K. Agarwal, S. Gopalakrishnan, M. Knap, M. M¨ uller, and E. Demler, Anomalous diffusion and Griffiths effects near the many-body localization transition, Phys. Rev. Lett.114, 160401 (2015)

    2015

  25. [32]

    D. J. Luitz and Y. Bar Lev, Anomalous thermalization in ergodic systems, Phys. Rev. Lett.117, 170404 (2016)

    2016

  26. [33]

    Khait, S

    I. Khait, S. Gazit, N. Y. Yao, and A. Auerbach, Spin transport of weakly disordered Heisenberg chain at infi- nite temperature, Phys. Rev. B93, 224205 (2016)

    2016

  27. [34]

    ˇZnidariˇ c, A

    M. ˇZnidariˇ c, A. Scardicchio, and V. K. Varma, Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system, Phys. Rev. Lett.117, 040601 (2016)

    2016

  28. [35]

    Gu, X.-L

    Y. Gu, X.-L. Qi, and D. Stanford, Local criticality, diffu- sion and chaos in generalized sachdev-ye-kitaev models, Journal of High Energy Physics2017, 1 (2017)

    2017

  29. [36]

    J. T. Chalker and D. Hahn, Chaotic many-body quan- tum dynamics, spectral correlations, and energy diffusion (2026), arXiv:2510.02198 [quant-ph]

    2026 arXiv

  30. [37]

    Mudry, P

    C. Mudry, P. W. Brouwer, and A. Furusaki, Crossover from the chiral to the standard universality classes in the conductance of a quantum wire with random hopping only, Phys. Rev. B62, 8249 (2000)

    2000

  31. [38]

    D. Dhar, R. Rajesh, and J. F. Stilck, Hard rigid rods on a Bethe-like lattice, Phys. Rev. E84, 011140 (2011)

    2011

  32. [39]

    F. J. Dyson, The Dynamics of a Disordered Linear Chain, Phys. Rev.92, 1331 (1953)

    1953

  33. [40]

    Fleishman and D

    L. Fleishman and D. C. Licciardello, Fluctuations and localization in one dimension, J. Phys. C10, L125 (1977)

    1977

  34. [41]

    P. L. Krapivsky and J. M. Luck, Dynamics of a quan- tum particle in low-dimensional disordered systems with extended states, J. Stat. Mech.2011, P02031 (2011)

    2011

  35. [42]

    De Tomasi, S

    G. De Tomasi, S. Roy, and S. Bera, Generalized Dyson model: Nature of the zero mode and its implication in dynamics, Phys. Rev. B94, 144202 (2016)

    2016

  36. [43]

    M. L. Mehta,Random Matrices: Revised and Enlarged Second Edition(Elsevier Science, 2014)

    2014

  37. [44]

    Datta,Electronic Transport in Mesoscopic Systems, Cambridge Studies in Semiconductor Physics and Mi- croelectronic Engineering (Cambridge University Press, 1995)

    S. Datta,Electronic Transport in Mesoscopic Systems, Cambridge Studies in Semiconductor Physics and Mi- croelectronic Engineering (Cambridge University Press, 1995)

    1995

  38. [45]

    D. A. Ryndyk,Theory of quantum transport at nanoscale, Springer Series in Solid-State Sciences (Springer Cham)

  39. [46]

    Dhar and D

    A. Dhar and D. Sen, Nonequilibrium green’s function for- malism and the problem of bound states, Phys. Rev. B 73, 085119 (2006)

    2006

  40. [47]

    Peschel and V

    I. Peschel and V. Eisler, Reduced density matrices and entanglement entropy in free lattice models, J. Phys. A 42, 504003 (2009)

    2009

  41. [48]

    Klich and L

    I. Klich and L. Levitov, Quantum Noise as an Entangle- ment Meter, Phys. Rev. Lett.102, 100502 (2009)

    2009

  42. [49]

    Evers and A

    F. Evers and A. D. Mirlin, Anderson transitions, Rev. Mod. Phys.80, 1355 (2008)

    2008

  43. [51]

    Sarkar, V

    M. Sarkar, V. Pagni, T. Enss, and N. Defenu, Emer- gent quantum chaos from correlations on a random graph (2026), arXiv:2607.11662 [cond-mat.dis-nn]. 7 END MA TTER Details of NEGF calculations Here we discuss the details of our conductance calculations using the NEGF formalism...

    2026 arXiv

Pith tools

Reviewed July 31, 2026 · model on record in the stance chip above.