Pith. sign in

REVIEW 3 major objections 3 minor 51 references

Quantum walker trapped by self-similarity of the Sierpi\'nski carpet

T0 review · 3 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read On a Sierpiński carpet lattice, a continuous-time quantum walker starting at a corner becomes increasingly trapped there as the fractal order grows, so that no well-defined crossing time emerges for moderate orders.

desk verdict Useful zone-hierarchy numerics that clearly show the trapping trend, but the 'no crossing time' claim outruns the evidence and actually contradicts the paper's own barrier picture. read the letter →

arxiv 2608.04844 v1 pith:P5UJUNER submitted 2026-08-05 quant-ph

Tomasz Sowiński This is my paper · ORCID
classification quant-ph
keywords quantumwalkcontinuous-timeSierpińskicarpetfractallatticetrappingtransportsuppressionself-similarity
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 studies a single quantum particle hopping on a finite Sierpiński carpet lattice and claims that, unlike on a uniform square lattice, the particle does not ballistically cross to the opposite corner as the fractal order grows. For $R \ge 3$ the zone-integrated probability of staying in the initial corner zone stays close to unity, while the probability of reaching the opposite corner zone remains near zero over the whole simulated evolution, and for $R=5,6$ the particle effectively never leaves the initial zone within the simulated time. The trapping is not a simple slowdown: the rescaled escape time $T_K J/(\hbar 3^K)$ grows roughly exponentially with the zone order $K$, instead of saturating as it does on the uniform lattice, so no characteristic crossing time emerges. If the claim is right, lattice geometry alone, without disorder, suppresses quantum transport in a self-similar, scale-by-scale manner.

What carries the argument

The central objects are the finite Sierpiński carpet lattices, built by recursively deleting the middle ninth of each square so that $N=8^R$ sites remain at order $R$, and the zone-integrated probabilities $S(t)=\sum_{\vec{r}\in Z_{\mathrm{INI}}}|\langle\vec{r}|\psi(t)\rangle|^2$ and $F(t)$ defined analogously for the opposite corner zone $Z_{\mathrm{FIN}}$; these coarse-grained observables make lattices of different sizes comparable. The scale-dependence analysis uses the hierarchy of self-similar corner zones $Z^K_{\mathrm{INI}}$ of edge size $3^K$, with escape times $T_K$ defined as the first instant at which the probability outside the $K$-order zone exceeds $3\%$. The explanatory mechanism is the bottleneck picture: every path between opposite corners must pass through single rows or columns of sites bordering removed squares, and because such necks occur at every hierarchical level, the accumulated transmission is expected to decrease roughly exponentially with $R$.

What would settle it

Run the same continuous-time evolution for $R=7$ and $R=8$, or extend the time window well beyond $10\cdot 3^R$; if the particle reaches the opposite zone in a time that grows only polynomially with $R$, the claim that no crossing time emerges would overstate. Alternatively, compute the eigenstates of the finite carpet Hamiltonian: if no eigenstate has significant weight near the initial corner, the trapping is a finite-time dynamical effect that would eventually be undone on longer times.

Watch

Extended reading notes

Core claim

On a finite Sierpiński lattice of fractal order $R$ — constructed from a uniform square lattice of edge $D=3^R$ by recursively removing the middle square of each block, leaving $N=8^R$ sites — a continuous-time quantum walker initialized at the corner $\vec{r}_0=(1,1)$ becomes progressively trapped near that corner as $R$ increases. The zone-integrated probabilities $S(t)$ and $F(t)$ for the initial and opposite corner zones (each one of the nine squares of the first construction level) show that the particle never reaches the opposite zone within the simulated time for moderate orders, while on a uniform lattice it arrives ballistically in time $T_U \approx 2\hbar D/3J$. The paper shows that the confinement builds up self-similarly across the hierarchy of corner zones of edge size $3^K$: the rescaled escape time $T_K J/(\hbar 3^K)$ keeps growing roughly exponentially with $K$, in contrast to the flat behavior on the uniform lattice. The dynamics therefore does not become a slowed-down version of ballistic transport; for sufficiently large $R$ the notion of a well-defined crossing time effectively ceases to apply, with the suppression attributed to narrow necks at every length scale acting as a series of partial barriers.

Load-bearing premise

The load-bearing premise is that the finite-time numerical evolution, run up to $tJ/\hbar = 10\cdot 3^R$ for $R \le 6$, reveals the asymptotic transport character, so that failing to reach the opposite zone within the simulated window is interpreted as trapping and as the loss of a well-defined crossing-time scale.

Editorial extensions

If this is right

  • For fractal order $R \ge 3$, the probability $F(t)$ of finding the particle in the opposite corner zone is suppressed compared with the uniform lattice, and for $R=5,6$ the particle stays in the initial zone within the simulated time window.
  • The escape time from a corner zone does not scale with the zone size on the Sierpiński lattice: $T_K J/(\hbar 3^K)$ grows roughly exponentially with $K$, whereas on the uniform lattice it saturates to a constant.
  • No characteristic crossing time exists for large $R$; the transport changes character rather than merely slowing down.
  • The suppression is purely geometric and deterministic, coming from the hierarchical bottlenecks of the lattice rather than from disorder or from removed site-to-site links.
  • The hierarchy of zone probabilities $S_K(t)$ shows the trapping builds up progressively: small zones are emptied and refilled, while larger zones retain probability increasingly effectively with $K$.

Reading between the lines

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

  • A testable quantitative prediction implied by the bottleneck picture but not computed in the paper is that the crossing probability $F(t)$ at the uniform-lattice crossing time $T_U$ should decay roughly exponentially with $R$; this could be checked from the data for $R=2,\ldots,6$.
  • The same hierarchy of zone observables could be measured in photonic waveguide arrays or cold-atom lattices shaped as Sierpiński carpets, where the retention of probability in corner zones would appear as an intensity pattern concentrated near the initial region.
  • If the spectrum of the finite carpet Hamiltonian turns out to have no localized eigenstates near the corner, the trapping is purely dynamical and would be reversed only on exponentially long times; if localized eigenstates exist, the trapping could persist in the long-time limit.
  • Extending the analysis to discrete-time quantum walks, which add a coin degree of freedom, could modify or suppress the trapping and would clarify how robust the effect is to the choice of walk dynamics.
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 / 3 minor

Summary. The manuscript studies continuous-time quantum walks on finite approximations of the Sierpiński carpet up to fractal order R=6, comparing zone-integrated corner probabilities with those on a uniform square lattice. It reports that, unlike the ballistic crossing on the uniform lattice, the particle becomes increasingly confined to its initial corner zone as R grows, and it interprets the growth of the rescaled escape time T_K J/(ℏ3^K) with zone range K as evidence that no characteristic crossing time emerges. The paper proposes a qualitative bottleneck picture in which narrow necks act as weakly reflecting barriers at each hierarchical level.

Significance. Demonstrated, if correct, the result is valuable: it provides a clean, disorder-free geometric mechanism for transport suppression in a self-similar lattice, with feasible experimental realizations in photonic and cold-atom platforms. The paper's strengths include a clearly defined hierarchy of zones, a uniform-lattice control, and public availability of numerical data. However, the headline claim that 'the notion of a crossing time effectively ceases to apply' goes beyond the numerical evidence and should be replaced by a quantitative scaling statement.

major comments (3)
  1. [Sec. VI and Sec. IV, Fig. 4] The central claim that no characteristic crossing time emerges is not supported by the data. The simulations run only up to tJ/ℏ = 10·3^R for R ≤ 6, and on a finite connected graph the unitary evolution is quasiperiodic, so the absence of a crossing within the simulated window cannot establish the absence of a crossing time. Moreover, the paper's own bottleneck argument and Fig. 4 imply a specific crossing-time scaling: if T_K J/(ℏ3^K) ≈ e^{cK}, then T_R ≈ (3 e^c)^R = D^{1+c/ln 3}, which is a power law in D, not the absence of a time scale. To support the conclusion, the authors should either fit the scaling, test whether the exponent grows with R, or reformulate the conclusion as finite-time suppression rather than loss of a time scale.
  2. [Sec. V, Fig. 4] The escape time T_K depends on an ad hoc 3% threshold, and no tests of threshold sensitivity are reported. The 'roughly exponential' growth is asserted visually; no fit, no error bars, and no R-dependence beyond R=6 are given. Since this growth is the quantitative basis for the 'no crossing-time scale' claim, the authors should provide a quantitative fit, threshold-dependence checks, and ideally multiple R values.
  3. [Sec. III and Figs. 2–4] The numerical solutions are obtained with fourth-order Runge-Kutta, but no convergence checks, time-step choices, or error estimates are reported. Because the trapping claim relies on S(t) remaining close to unity over long simulated intervals, small integration errors could matter; please include error estimates or a unitarity check.
minor comments (3)
  1. [Figs. 2 and 3] The time axes are rescaled by a factor of 3 between consecutive fractal orders, but this scaling is described only in the text; a caption note or axis label would improve readability.
  2. [Sec. VI] The phrase 'for all practical purposes' is not quantified; please specify what practical threshold is meant, for example a fixed upper bound on F(t) over the simulated time window.
  3. [Sec. IV] The statement that the overall transmission decreases 'roughly exponentially with the number of barriers' is qualitative; a short derivation or at least a precise statement of the assumed scaling would make the bottleneck picture more testable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central trapping claim is a direct numerical measurement compared with a uniform-lattice benchmark.

full rationale

The derivation chain is self-contained and does not reduce to its own inputs. The Hamiltonian (2) and Schrödinger evolution (3) are solved numerically from a corner initial state, with no fitted parameter encoding the outcome; the zone-integrated probabilities (4a)-(4b) are coarse-grained observables whose zones are fixed by the lattice construction (one of the nine first-level squares), so the comparison across R is an external benchmark rather than an input that forces the result. The paper's own self-citations ([20], [42], [44]) are contextual references and carry no load-bearing argument. The bottleneck picture in Sec. IV is a post-hoc phenomenological explanation of independently observed numerics, not a premise from which the simulations are derived, and the 3% escape-time threshold is a fixed diagnostic, not a parameter fitted to reproduce the claimed scaling. The finite-time extrapolation to 'no characteristic crossing time' may be arguable as a correctness or evidence question, but it is not circularity.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

No parameters are fitted to make the central claim; the only free parameter is the 3% threshold defining escape times. The model uses standard tight-binding and Schrödinger evolution with one hand-chosen initial state. No new particles, forces, or entities are introduced. The bottleneck barrier picture is an ad hoc explanatory assumption rather than a derived result.

free parameters (1)
  • Escape-time threshold = 3%
    T_K is defined as the first time the outside-zone probability exceeds 3%. This hand-chosen threshold defines the reported escape times, and its influence on the K-scaling is not tested.
assumptions (4)
  • standard math Tight-binding nearest-neighbor Hamiltonian (Eq. 2) and Schrödinger equation (Eq. 3) govern the dynamics.
    Standard continuous-time quantum walk model; not derived in the paper.
  • domain assumption The lattice is a finite Sierpiński carpet of order R with open boundaries and the particle starts at the corner (1,1).
    Defines the system under study; the conclusions are for this specific connection rule and initial condition.
  • domain assumption The fourth-order Runge-Kutta solutions are accurate enough for the reported probabilities and escape times.
    No convergence checks or error bars are provided (Sec. III), so the claims depend on numerical accuracy.
  • ad hoc to paper Narrow necks of the lattice act as weakly reflecting independent barriers, giving roughly exponential transmission suppression.
    Phenomenological bottleneck explanation in Secs. IV and V; assumed to interpret the data, not derived from the Hamiltonian.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantum walker trapped by self-similarity of the Sierpi\'nski carpet." pith.science (2026). https://pith.science/paper/P5UJUNER

@misc{pith2026260804844,
  author       = {Pith},
  title        = {Pith review of: Quantum walker trapped by self-similarity of the Sierpi\'nski carpet},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P5UJUNER}},
  note         = {Machine review of arXiv:2608.04844}
}
read the original abstract

We study the dynamics of a single quantum particle on a finite-size square lattice with a fractal structure resembling the Sierpi\'nski carpet, and compare it to the dynamics on a uniform lattice of the same size. For a particle initially localized at a corner of the lattice, we monitor the probability of finding it near the initial and opposite corners using zone-integrated probabilities, allowing a consistent comparison across fractal orders. While on the uniform lattice the particle reaches the opposite corner ballistically, in a time proportional to the lattice size, on the Sierpi\'nski lattice it becomes increasingly confined to the vicinity of its initial position. We show that this trapping builds up self-similarly across the whole hierarchy of corner zones of the lattice.

Figures

Figures reproduced from arXiv: 2608.04844 by the authors.

Figure 1
Figure 1. FIG. 1. Visualization of the Sierpi [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Probability of finding the particle in the initial zone [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Time evolution of the initial-zone probabilities [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Rescaled escape time [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

51 extracted references · 51 canonical work pages

  1. [1]

    Quantum random walks,

    Y. Aharonov, L. Davidovich, and N. Zagury , “Quantum random walks,” Phys. Rev. A48, 1687–1690 (1993)

    work page 1993

  2. [2]

    Quantum computation and decision trees,

    Edward Farhi and Sam Gutmann, “Quantum computation and decision trees,” Phys. Rev. A58, 915 (1998)

    work page 1998

  3. [3]

    Quantum walks and their algorithmic applications,

    Andris Ambainis, “Quantum walks and their algorithmic applications,” International Journal of Quantum Informa- tion01, 507–518 (2003)

    work page 2003

  4. [4]

    Quantum random walks: an introductory overview,

    Julia Kempe, “Quantum random walks: an introductory overview,” Contemp. Phys.44, 307–327 (2003)

    work page 2003

  5. [5]

    Spatial search by quantum walk,

    Andrew M. Childs and Jeffrey Goldstone, “Spatial search by quantum walk,” Phys. Rev. A70, 022314 (2004)

    work page 2004

  6. [6]

    Local- ization of two-dimensional quantum walks,

    Norio Inui, Yoshinao Konishi, and Norio Konno, “Local- ization of two-dimensional quantum walks,” Phys. Rev. A 69, 052323 (2004)

    work page 2004

  7. [7]

    One- dimensional three-state quantum walk,

    Norio Inui, Norio Konno, and Etsuo Segawa, “One- dimensional three-state quantum walk,” Phys. Rev. E72, 056112 (2005)

    work page 2005

  8. [8]

    Quasiperiodic dy- namics of a quantum walk on the line,

    Antoni W ´ojcik, Tomasz Łuczak, Paweł Kurzy´nski, Andrzej Grudka, and Małgorzata Bednarska, “Quasiperiodic dy- namics of a quantum walk on the line,” Phys. Rev. Lett. 93, 180601 (2004)

    work page 2004

Show all 51 references
  1. [9]

    Exploring topological phases with quantum walks,

    Takuya Kitagawa, Mark S. Rudner, Erez Berg, and Eu- gene Demler, “Exploring topological phases with quantum walks,” Phys. Rev. A82, 033429 (2010)

    2010

  2. [10]

    Trapping a particle of a quantum walk on the line,

    Antoni W ´ojcik, Tomasz Łuczak, Paweł Kurzy ´nski, An- drzej Grudka, Tomasz Gdala, and Małgorzata Bednarska- Bzdega, “Trapping a particle of a quantum walk on the line,” Phys. Rev. A85, 012329 (2012)

    2012

  3. [11]

    Propagation of quantum walks in elec- tric fields,

    C. Cedzich, T. Ryb´ar, A. H. Werner, A. Alberti, M. Genske, and R. F. Werner, “Propagation of quantum walks in elec- tric fields,” Phys. Rev. Lett.111, 160601 (2013)

    2013

  4. [12]

    Two-dimensional quantum walk under artificial magnetic field,

    ˙I. Yalc ¸ ınkaya and Z. Gedik, “Two-dimensional quantum walk under artificial magnetic field,” Phys. Rev. A92, 042324 (2015)

    2015

  5. [13]

    Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks,

    Iv ´an M ´arquez-Mart´ın, Pablo Arnault, Giuseppe Di Molfetta, and Armando P ´erez, “Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks,” Phys. Rev. A98, 032333 (2018)

    2018

  6. [14]

    Quantum walks in weak electric fields and bloch oscillations,

    Pablo Arnault, Benjamin Pepper, and A. P´erez, “Quantum walks in weak electric fields and bloch oscillations,” Phys. Rev. A101, 062324 (2020)

    2020

  7. [15]

    Quantum walks in weak stochastic gauge fields,

    Jan W ´ojcik, “Quantum walks in weak stochastic gauge fields,” Physics Letters A512, 129605 (2024)

    2024

  8. [16]

    Quantum walks and quantum simulations with bloch-oscillating spinor atoms,

    D. Witthaut, “Quantum walks and quantum simulations with bloch-oscillating spinor atoms,” Phys. Rev. A82, 033602 (2010)

    2010

  9. [17]

    Continuous-time quantum walks: Models for coherent transport on com- 7 plex networks,

    Oliver M ¨ulken and Alexander Blumen, “Continuous-time quantum walks: Models for coherent transport on com- 7 plex networks,” Phys. Rep.502, 37–87 (2011)

    2011

  10. [18]

    Realization of quantum walks with negligible decoherence in waveg- uide lattices,

    Hagai B. Perets, Yoav Lahini, Francesca Pozzi, Marc Sorel, Roberto Morandotti, and Yaron Silberberg, “Realization of quantum walks with negligible decoherence in waveg- uide lattices,” Phys. Rev. Lett.100, 170506 (2008)

    2008

  11. [19]

    Continuous-time quantum walks and trapping,

    Elena Agliari, Oliver M ¨ulken, and Alexander Blumen, “Continuous-time quantum walks and trapping,” Int. J. Bifurcation Chaos20, 271–279 (2010)

    2010

  12. [20]

    Lissajous dy- namics of a quantum particle in a tilted two-dimensional discrete lattice,

    Grzegorz Jaczewski and Tomasz Sowi ´nski, “Lissajous dy- namics of a quantum particle in a tilted two-dimensional discrete lattice,” Eur. Phys. J. Plus139, 991 (2024)

    2024

  13. [21]

    Connecting the discrete- and continuous-time quantum walks,

    Frederick W. Strauch, “Connecting the discrete- and continuous-time quantum walks,” Phys. Rev. A74, 030301(R) (2006)

    2006

  14. [22]

    Quantum transport in fractal networks,

    Xiao-Ye Xu, Xiao-Wei Wang, Dao-Yi Chen, Cristiane Morais Smith, and Xian-Min Jin, “Quantum transport in fractal networks,” Nat. Photon.15, 703–710 (2021)

    2021

  15. [23]

    Fractal photonic topological insula- tors,

    Tobias Biesenthal, Mark Kremer, Cem Yuce, Stefan Boettcher, Hamidreza Ramezani, Mordechai Segev, and Alexander Szameit, “Fractal photonic topological insula- tors,” Science376, 1114–1119 (2022)

    2022

  16. [24]

    Design and characterization of elec- trons in a fractal geometry ,

    S. N. Kempkes, M. R. Slot, S. E. Freeney , S. J. M. Zevenhuizen, D. Vanmaekelbergh, I. Swart, and C. Morais Smith, “Design and characterization of elec- trons in a fractal geometry ,” Nat. Phys.15, 127–131 (2019)

    2019

  17. [25]

    Assembling molecu- lar sierpi ´nski triangle fractals,

    Jian Shang, Yongfeng Wang, Min Chen, Jingxin Dai, Xiong Zhou, Julian Kuttner, Georg Hilt, Xiang Shao, J. Michael Gottfried, and Kai Wu, “Assembling molecu- lar sierpi ´nski triangle fractals,” Nat. Chem.7, 389–393 (2015)

    2015

  18. [26]

    Parallel assembly of arbitrary defect- free atom arrays with a multitweezer algorithm,

    Wenqi Tianet al., “Parallel assembly of arbitrary defect- free atom arrays with a multitweezer algorithm,” Phys. Rev. Appl.19, 034048 (2023)

    2023

  19. [27]

    Search on a fractal lattice using a quantum random walk,

    Apoorva Patel and K. S. Raghunathan, “Search on a fractal lattice using a quantum random walk,” Phys. Rev. A86, 012332 (2012)

    2012

  20. [28]

    Quantum walks on sierpinski gaskets,

    Pedro Carlos S. Lara, Renato Portugal, and Stefan Boettcher, “Quantum walks on sierpinski gaskets,” Int. J. Quantum Inf.16, 1850020 (2018), arXiv:1209.2095

    2018 arXiv

  21. [29]

    Spa- tial search on sierpinski carpet using quantum walk,

    Shu Tamegai, Shohei Watabe, and Tetsuro Nikuni, “Spa- tial search on sierpinski carpet using quantum walk,” J. Phys. Soc. Jpn.87, 085003 (2018)

    2018

  22. [30]

    Scaling hypothesis of a spatial search on fractal lattices using a quantum walk,

    Rei Sato, Tetsuro Nikuni, and Shohei Watabe, “Scaling hypothesis of a spatial search on fractal lattices using a quantum walk,” Phys. Rev. A101, 022312 (2020)

    2020

  23. [31]

    A counterintuitive role of geometry in transport by quantum walks,

    Jan Mare ˇs, Jaroslav Novotn´y, Martin ˇStefaˇn´ak, and Igor Jex, “A counterintuitive role of geometry in transport by quantum walks,” Phys. Rev. A101, 032113 (2020)

    2020

  24. [32]

    The localization of quan- tum random walks on Sierpinski gaskets,

    Kai Zhao and Wei-Shih Yang, “The localization of quan- tum random walks on Sierpinski gaskets,” J. Math. Phys. 63, 013508 (2022)

    2022

  25. [33]

    Solutions to the Schr¨odinger equation on some fractal lattices,

    E. Domany , S. Alexander, D. Bensimon, and L. P. Kadanoff, “Solutions to the Schr¨odinger equation on some fractal lattices,” Phys. Rev. B28, 3110–3123 (1983)

    1983

  26. [34]

    Localization in fractal spaces: exact results on the Sierpinski gasket,

    X. R. Wang, “Localization in fractal spaces: exact results on the Sierpinski gasket,” Phys. Rev. B51, 9310–9313 (1995)

    1995

  27. [35]

    Transport prop- erties of continuous-time quantum walks on sierpinski fractals,

    Zolt ´an Dar ´azs, Anastasiia Anishchenko, Tam ´as Kiss, Alexander Blumen, and Oliver M ¨ulken, “Transport prop- erties of continuous-time quantum walks on sierpinski fractals,” Phys. Rev. E90, 032113 (2014)

    2014

  28. [36]

    Localization without disorder: quantum walks on struc- tured graphs,

    Shyam Dhamapurkar and K. Venkata Subrahmanyam, “Localization without disorder: quantum walks on struc- tured graphs,” arXiv preprint (2026), 2603.05643

    2026

  29. [37]

    Quantum transport in Sierpinski carpets,

    E. van Veen, S. Yuan, M. I. Katsnelson, M. Polini, and A. Tomadin, “Quantum transport in Sierpinski carpets,” Phys. Rev. B93, 115428 (2016)

    2016

  30. [38]

    Anomalous quan- tum transport in fractal lattices,

    Abel Rojo-Franc`as, Priyanshu Pansari, Utso Bhattacharya, Bruno Juli´a-D´ıaz, and Tobias Grass, “Anomalous quan- tum transport in fractal lattices,” Commun. Phys.7, 259 (2024)

    2024

  31. [39]

    Aharonov-bohm caging and electron trapping in snowflake-like fractal lattices,

    Bishwajit Palet al., “Aharonov-bohm caging and electron trapping in snowflake-like fractal lattices,” Phys. Status Solidi RRL , 2500129 (2025)

    2025

  32. [40]

    Sur une courbe cantorienne qui con- tient une image biunivoque et continue de toute courbe donn´ee,

    Wacław Sierpi ´nski, “Sur une courbe cantorienne qui con- tient une image biunivoque et continue de toute courbe donn´ee,” Comptes Rendus Hebdomadaires des S ´eances de l’Acad´emie des Sciences162, 629–632 (1916)

    1916

  33. [41]

    Strongly correlated quantum walks in optical lattices,

    Philipp M. Preiss, Ruichao Ma, M. Eric Tai, Alexander Lukin, Matthew Rispoli, Philip Zupancic, Yoav Lahini, Ra- jibul Islam, and Markus Greiner, “Strongly correlated quantum walks in optical lattices,” Science347, 1229– 1233 (2015)

    2015

  34. [42]

    Two bosonic quantum walkers in one-dimensional opti- cal lattices,

    Dariusz Wiater, Tomasz Sowi´nski, and Jakub Zakrzewski, “Two bosonic quantum walkers in one-dimensional opti- cal lattices,” Phys. Rev. A96, 043629 (2017)

    2017

  35. [43]

    Quantum walks of in- teracting mott-insulator defects with three-body interac- tions,

    Suman Mondal and Tapan Mishra, “Quantum walks of in- teracting mott-insulator defects with three-body interac- tions,” Phys. Rev. A101, 052341 (2020)

    2020

  36. [44]

    Correlations in few two-component quantum walkers on a tilted lattice,

    Saubhik Sarkar and Tomasz Sowi ´nski, “Correlations in few two-component quantum walkers on a tilted lattice,” Phys. Rev. A102, 043326 (2020)

    2020

  37. [45]

    Two component quantum walk in one- dimensional lattice with hopping imbalance,

    Mrinal Kanti Giri, Suman Mondal, Bhanu Pratap Das, and Tapan Mishra, “Two component quantum walk in one- dimensional lattice with hopping imbalance,” Scientific Reports11, 22056 (2021)

    2021

  38. [46]

    Multi- particle quantum walks and fisher information in one- dimensional lattices,

    Xiaoming Cai, Hongting Yang, Hai-Long Shi, Chao- hong Lee, Natan Andrei, and Xi-Wen Guan, “Multi- particle quantum walks and fisher information in one- dimensional lattices,” Phys. Rev. Lett.127, 100406 (2021)

    2021

  39. [47]

    Enhanced trans- port of two interacting quantum walkers in a one- dimensional quasicrystal with power-law hopping,

    G. A. Dom´ınguez-Castro and R. Paredes, “Enhanced trans- port of two interacting quantum walkers in a one- dimensional quasicrystal with power-law hopping,” Phys. Rev. A104, 033306 (2021)

    2021

  40. [48]

    Signatures of nontrivial pairing in the quantum walk of two-component bosons,

    Mrinal Kanti Giri, Suman Mondal, B. P. Das, and Tapan Mishra, “Signatures of nontrivial pairing in the quantum walk of two-component bosons,” Phys. Rev. Lett.129, 050601 (2022)

    2022

  41. [49]

    Flux- enhanced localization and reentrant delocalization in the quench dynamics of two interacting bosons on a bose- hubbard ladder,

    Mrinal Kanti Giri, Biswajit Paul, and Tapan Mishra, “Flux- enhanced localization and reentrant delocalization in the quench dynamics of two interacting bosons on a bose- hubbard ladder,” Phys. Rev. A109, 043308 (2024)

    2024

  42. [50]

    Controllable quan- tum walks, gravitational constant, and casimir energy in one-dimensional three-boson systems with on-site inter- actions,

    Hongting Yang and Pinquan Qin, “Controllable quan- tum walks, gravitational constant, and casimir energy in one-dimensional three-boson systems with on-site inter- actions,” Phys. Rev. B110, 014302 (2024)

    2024

  43. [51]

    Supplemental material for

    Tomasz Sowi ´nski, “Supplemental material for ”quantum walker trapped by self-similarity of the sierpi´nski carpet”,” Zenodo (2026)

    2026

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.