pith. sign in

arxiv: 2511.05344 · v2 · submitted 2025-11-07 · ❄️ cond-mat.quant-gas · cond-mat.dis-nn

Engineering Anderson Localization in Arbitrary Dimensions with Interacting Quasiperiodic Kicked Bosons

H. Olsen , P. Vignolo , M. Albert This is my paper

Pith reviewed 2026-05-18 00:02 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.dis-nn
keywords Anderson localizationsynthetic dimensionsquasiperiodic drivingkicked rotorLieb-Liniger bosonstwo-body dynamicslocalization transitionorthogonal universality class
0
0 comments X

The pith

Both interparticle interactions and quasiperiodic modulations generate synthetic dimensions for Anderson localization.

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

The paper explores the Lieb-Liniger model of one-dimensional bosons under periodic delta kicks, incorporating interparticle interactions and quasiperiodic variations in kicking strength. It shows that these interactions alone can create an effective two-dimensional Anderson model through the known kicked rotor mapping. Adding one or two incommensurate frequencies extends the effective dimensionality to three or four. Numerical studies of two-body dynamics with finite-time scaling confirm Anderson localization and the orthogonal critical behavior. The method thus allows emulation of localization phenomena in higher dimensions using one-dimensional systems.

Core claim

Both interparticle interactions and quasiperiodic modulations of the kicking strength can independently and simultaneously generate synthetic dimensions. In the absence of modulation, interactions between two bosons already promote an effective two-dimensional Anderson model. Introducing one or two additional incommensurate frequencies further extends the system to three and four effective dimensions. Through extensive numerical simulations of the two-body dynamics and finite-time scaling analysis, Anderson localization and the associated critical behavior characteristic of the orthogonal universality class are observed.

What carries the argument

The extended mapping of the interacting kicked rotor to a higher-dimensional Anderson model, where interactions and quasiperiodic frequencies serve as generators of synthetic dimensions.

Load-bearing premise

The standard mapping from the kicked rotor to the Anderson model still applies when interactions and quasiperiodic modulations are added to the system.

What would settle it

A failure of the finite-time scaling to show the expected orthogonal universality class critical exponents in the two-body participation ratio for the three- or four-dimensional cases would falsify the claim.

Figures

Figures reproduced from arXiv: 2511.05344 by H. Olsen, M. Albert, P. Vignolo.

Figure 1
Figure 1. Figure 1: Time evolution of the total energy of the two particles for different values of the [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The rescaled quantity ln Λ = ln ⟨E(t)⟩/t2/d as a function of K for different times between t = 10 and t = 200. All curves intersect approximately at the critical point demonstrating the existence of a metal-insulator transition and allowing to locate the critical point Kc. Here c = 10, ε = 0.3 and Nω = 1 for the left figure (d = 3) and Nω = 2 for the right one (d = 4). quantity Λ(K, t) = ⟨E(t)⟩t −2/d = f … view at source ↗
Figure 3
Figure 3. Figure 3: Finite time scaling applied to the numerical results with [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Determination of the critical exponents ν and s by fitting (ln Λ)′ (Kc, t) as function of t in log-log scale. Here c = 10, ε = 0.3 and Nω = 1, 2 for a) and b). 3 4 5 6 7 0.1 0.2 0.3 0.4 0.5 0.5 0.4 0.3 0.2 0.1 0.0 0.1 K ε Localized a) Delocalized 3 4 5 6 7 0.1 0.2 0.3 0.4 0.5 0.2 0.1 0.0 0.1 0.2 0.3 K ε Localized b) Delocalized [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Phase diagram of the dynamical phases in the [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

We study the interplay of interactions and quasiperiodic driving in the Lieb-Liniger model of one-dimensional bosons subjected to a sequence of delta kicks. Building on the known mapping between the kicked rotor and the Anderson model, we show that both interparticle interactions and quasiperiodic modulations of the kicking strength can independently and simultaneously generate synthetic dimensions. In the absence of modulation, interactions between two bosons already promote an effective two-dimensional Anderson model. Introducing one or two additional incommensurate frequencies further extends the system to three and four effective dimensions, respectively. Through extensive numerical simulations of the two-body dynamics and finite-time scaling analysis, we observe Anderson localization and the associated critical behavior characteristic of the orthogonal universality class. This combined use of interactions and quasiperiodic driving thus provides a versatile framework for emulating Anderson localization and its transition in arbitrary dimensions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper studies the Lieb-Liniger Hamiltonian for two bosons in one dimension subjected to periodic delta kicks, with optional quasiperiodic modulation of the kick strength. Building on the single-particle kicked-rotor–Anderson mapping, it argues that interparticle interactions alone generate an effective two-dimensional Anderson model via center-of-mass and relative coordinates, while one or two additional incommensurate frequencies extend the synthetic dimension count to three or four. Extensive two-body numerical simulations combined with finite-time scaling are used to report Anderson localization and critical exponents consistent with the orthogonal universality class.

Significance. If the mapping and numerical evidence hold, the work supplies a controllable route to Anderson localization and its mobility-edge physics in synthetic dimensions d=2,3,4 using only one-dimensional interacting bosons, which is of clear interest for quantum-gas experiments. The explicit use of finite-time scaling to extract universality-class signatures is a methodological strength.

major comments (2)
  1. [§2–3] §2–3 (model and mapping): The central claim that the Floquet operator of the interacting, modulated kicked Lieb-Liniger system maps onto a non-interacting Anderson tight-binding model in synthetic dimensions is stated as an extension of the known single-particle result, but no explicit operator identity, perturbative expansion, or gauge transformation is supplied showing that the interaction term V(|x1−x2|) remains strictly diagonal (on-site) in the center-of-mass/relative lattice basis without generating correlated off-diagonal or long-range hopping. Such terms would alter both the orthogonal-class universality and the location of any mobility edge; their absence must be demonstrated for the load-bearing mapping to be accepted.
  2. [§4] §4 (numerics and scaling): The finite-time scaling analysis reports orthogonal-class critical behavior, yet the manuscript does not quantify how the extracted exponents or the apparent mobility edge shift when the interaction strength or modulation amplitudes are varied over a range that would expose possible residual correlated disorder. A systematic check that the scaling collapse remains stable under these variations is required to confirm that the observed criticality is not an artifact of the two-body truncation or finite-time window.
minor comments (2)
  1. [Figure 3] Figure 3 and associated text: the scaling collapse plots would benefit from explicit error bands on the data points and a statement of the fitting window used for the correlation length.
  2. [§3] Notation: the definition of the synthetic lattice spacing and the precise identification of the on-site disorder strength in the effective Anderson Hamiltonian should be written explicitly rather than left implicit from the single-particle analogy.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and indicate where revisions will be made to strengthen the presentation.

read point-by-point responses

  1. Referee: [§2–3] §2–3 (model and mapping): The central claim that the Floquet operator of the interacting, modulated kicked Lieb-Liniger system maps onto a non-interacting Anderson tight-binding model in synthetic dimensions is stated as an extension of the known single-particle result, but no explicit operator identity, perturbative expansion, or gauge transformation is supplied showing that the interaction term V(|x1−x2|) remains strictly diagonal (on-site) in the center-of-mass/relative lattice basis without generating correlated off-diagonal or long-range hopping. Such terms would alter both the orthogonal-class universality and the location of any mobility edge; their absence must be demonstrated for the load-bearing mapping to be accepted.

    Authors: We agree that an explicit demonstration is required to fully substantiate the mapping. The manuscript presents the result as a direct extension of the single-particle kicked-rotor–Anderson correspondence, with the interaction entering through the relative coordinate. In the revised version we will insert a new subsection deriving the effective Floquet operator in the center-of-mass/relative quasi-momentum basis and explicitly showing that V(|x1−x2|) contributes only a diagonal on-site potential; no correlated off-diagonal or long-range terms appear because the basis states are simultaneous eigenstates of the relative-position operator in the relevant Floquet frame. This addition will confirm that the effective model remains strictly non-interacting Anderson in the orthogonal class. revision: yes

  2. Referee: [§4] §4 (numerics and scaling): The finite-time scaling analysis reports orthogonal-class critical behavior, yet the manuscript does not quantify how the extracted exponents or the apparent mobility edge shift when the interaction strength or modulation amplitudes are varied over a range that would expose possible residual correlated disorder. A systematic check that the scaling collapse remains stable under these variations is required to confirm that the observed criticality is not an artifact of the two-body truncation or finite-time window.

    Authors: For two particles the numerics solve the exact two-body time-dependent Schrödinger equation, so there is no truncation. Nevertheless, we accept that a systematic parameter scan strengthens the claim. In the revised manuscript we will add an appendix (or extended figure) presenting finite-time scaling collapses for several values of the interaction strength and modulation amplitudes. The extracted exponents and mobility-edge location remain consistent with the orthogonal class across this range, indicating that any residual correlated hopping, if present, is negligible within the regime studied. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on external mapping plus independent numerics

full rationale

The paper explicitly builds on the established single-particle kicked-rotor–Anderson mapping (cited as known) and then performs extensive numerical simulations of the two-body Floquet dynamics together with finite-time scaling to observe localization and orthogonal-class critical behavior. No equations or steps in the provided text reduce a reported prediction or synthetic-dimension claim to a fitted parameter or self-citation by construction. The central results are supported by direct dynamical evidence rather than by re-labeling inputs, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the validity of extending the kicked-rotor-to-Anderson mapping to the interacting Lieb-Liniger case and on the assumption that two-body numerics plus finite-time scaling suffice to diagnose higher-dimensional localization transitions.

axioms (1)
  • domain assumption The mapping between the kicked rotor and the Anderson model remains valid when interparticle interactions and quasiperiodic modulations of kick strength are introduced.
    The entire synthetic-dimension construction is built on this extension of the known single-particle mapping.

pith-pipeline@v0.9.0 · 5446 in / 1429 out tokens · 45318 ms · 2026-05-18T00:02:46.916477+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Many-body dynamical localization in Fock space

    cond-mat.quant-gas 2026-04 unverdicted novelty 6.0

    Many-body dynamical localization emerges in the Fock space of a driven interacting bosonic system, suppressing transport and producing a crossover to Poisson spectral statistics.

Reference graph

Works this paper leans on

58 extracted references · 58 canonical work pages · cited by 1 Pith paper

  1. [1]

    Absence of Diffusion in Certain Random Lattices

    P. W. Anderson. “Absence of Diffusion in Certain Random Lattices”. In:Phys. Rev. 109 (1958), p. 1492.doi:10.1103/PhysRev.109.1492

    work page doi:10.1103/physrev.109.1492 1958

  2. [2]

    Fine Tuning of Metal-Insulator Transition in Al0.3Ga0.7As Using Persistent Photoconductivity

    Shingo Katsumoto et al. “Fine Tuning of Metal-Insulator Transition in Al0.3Ga0.7As Using Persistent Photoconductivity”. In:Journal of the Physical Society of Japan56.7 (1987), pp. 2259–2262.doi:10.1143/JPSJ.56.2259

    work page doi:10.1143/jpsj.56.2259 1987

  3. [3]

    Disordered electronic systems

    Patrick A. Lee and T. V. Ramakrishnan. “Disordered electronic systems”. In:Rev. Mod. Phys.57 (2 Apr. 1985), pp. 287–337.doi:10.1103/RevModPhys.57.287

    work page doi:10.1103/revmodphys.57.287 1985

  4. [4]

    and Genack, A

    Rachida Dalichaouch et al. “Microwave localization by two-dimensional random scattering”. In:Nature354.6348 (Nov. 1991), pp. 53–55.doi:10.1038/354053a0

    work page doi:10.1038/354053a0 1991

  5. [5]

    Statistical signatures of photon localization

    AA Chabanov, M Stoytchev, and AZ Genack. “Statistical signatures of photon localization”. In:Nature404.6780 (2000), pp. 850–853. 10

    work page 2000

  6. [6]

    Transport and Anderson localization in disordered two-dimensional photonic lattices

    T. Schwartz et al. “Transport and Anderson localization in disordered two-dimensional photonic lattices”. In:Nature446 (2007), p. 52.doi: 10.1038/nature05623

    work page doi:10.1038/nature05623 2007

  7. [7]

    Experimental Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves

    J. Chab´ e et al. “Experimental Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves”. In:Phys. Rev. Lett.101 (2008), p. 255702. doi:10.1103/PhysRevLett.101.255702

    work page doi:10.1103/physrevlett.101.255702 2008

  8. [8]

    Direct observation of Anderson localization of matter waves in a controlled disorder

    J. Billy et al. “Direct observation of Anderson localization of matter waves in a controlled disorder”. In:Nature453 (2008), p. 891.doi:10.1038/nature07000

    work page doi:10.1038/nature07000 2008

  9. [9]

    URL https://doi.org/10.1038/nature07071

    G. Roati et al. “Anderson localization of a non-interacting Bose–Einstein condensate”. In:Nature453 (2008), p. 895.doi:10.1038/nature07071

    work page doi:10.1038/nature07071 2008

  10. [10]

    Localization of ultrasound in a three-dimensional elastic network

    Hefei Hu et al. “Localization of ultrasound in a three-dimensional elastic network”. In:Nature Physics4.12 (Dec. 2008), pp. 945–948.doi:10.1038/nphys1101

    work page doi:10.1038/nphys1101 2008

  11. [11]

    Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices

    Y. Lahini et al. “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices”. In:Phys. Rev. Lett.100 (2008), p. 013906.doi: 10.1103/PhysRevLett.100.013906

    work page doi:10.1103/physrevlett.100.013906 2008

  12. [12]

    Three-Dimensional Anderson Localization of Ultracold Matter

    S. S. Kondov et al. “Three-Dimensional Anderson Localization of Ultracold Matter”. In:Science334 (2011), p. 66.doi:10.1126/science.1209019

    work page doi:10.1126/science.1209019 2011

  13. [13]

    Three-dimensional localization of ultracold atoms in an optical disordered potential

    F. Jendrzejewski et al. “Three-dimensional localization of ultracold atoms in an optical disordered potential”. In:Nat. Phys.8 (2012), p. 398.doi: 10.1038/nphys2256

    work page doi:10.1038/nphys2256 2012

  14. [14]

    Anderson localization of light

    Segev Mordechai, Christodoulides N. David, and Kip Demetrios. “Anderson localization of light”. In:Nat. Photonics7 (2013), p. 197.doi: 10.1038/nphoton.2013.30

    work page doi:10.1038/nphoton.2013.30 2013

  15. [15]

    Anderson localization of electromagnetic waves in three dimensions

    A. Yamilov, S. E. Skipetrov, and H. Cao. “Anderson localization of electromagnetic waves in three dimensions”. In:Nat. Phys.19 (2023), pp. 716–722.doi: 10.1038/s41567-022-01828-2

    work page doi:10.1038/s41567-022-01828-2 2023

  16. [16]

    Electrons in disordered systems and the theory of localization

    D. J. Thouless. “Electrons in disordered systems and the theory of localization”. In: Physics Reports13 (1974), p. 93.doi:10.1016/0370-1573(74)90029-5

    work page doi:10.1016/0370-1573(74)90029-5 1974

  17. [17]

    W., Licciardello, D

    E. Abrahams et al. “Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions”. In:Phys. Rev. Lett.42 (1979), p. 673.doi: 10.1103/PhysRevLett.42.673

    work page doi:10.1103/physrevlett.42.673 1979

  18. [18]

    Electrons in disordered systems. Scaling near the mobility edge

    F. Wegner. “Electrons in disordered systems. Scaling near the mobility edge”. In:Z. Phys. B25 (1976), pp. 327–337.doi:10.1007/BF01315232

    work page doi:10.1007/bf01315232 1976

  19. [19]

    Anderson transitions

    Ferdinand Evers and Alexander D. Mirlin. “Anderson transitions”. In:Reviews of Modern Physics80.4 (Oct. 2008), pp. 1355–1417.doi: 10.1103/revmodphys.80.1355

    work page doi:10.1103/revmodphys.80.1355 2008

  20. [20]

    Distribution of local densities of states, order parameter function, and critical behavior near the Anderson transition

    Alexander D. Mirlin and Yan V. Fyodorov. “Distribution of local densities of states, order parameter function, and critical behavior near the Anderson transition”. In: Phys. Rev. Lett.72 (4 Jan. 1994), pp. 526–529.doi:10.1103/PhysRevLett.72.526

    work page doi:10.1103/physrevlett.72.526 1994

  21. [21]

    Dimensional Dependence of Critical Exponent of the Anderson Transition in the Orthogonal Universality Class

    Yoshiki Ueoka and Keith Slevin. “Dimensional Dependence of Critical Exponent of the Anderson Transition in the Orthogonal Universality Class”. In:Journal of the Physical Society of Japan83.8 (2014), p. 084711.doi:10.7566/JPSJ.83.084711

    work page doi:10.7566/jpsj.83.084711 2014

  22. [22]

    Critical properties of the Anderson localization transition and the high-dimensional limit

    E. Tarquini, G. Biroli, and M. Tarzia. “Critical properties of the Anderson localization transition and the high-dimensional limit”. In:Phys. Rev. B95 (9 Mar. 2017), p. 094204.doi:10.1103/PhysRevB.95.094204

    work page doi:10.1103/physrevb.95.094204 2017

  23. [23]

    Anderson localization and interactions in one-dimensional metals

    T. Giamarchi and H. J. Schulz. “Anderson localization and interactions in one-dimensional metals”. In:Phys. Rev. B37 (1988), p. 325.doi: 10.1103/PhysRevB.37.325. 11

    work page doi:10.1103/physrevb.37.325 1988

  24. [24]

    Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states

    D. M. Basko, I. L. Aleiner, and B. Altshuler. “Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states”. In:Annals of Physics321 (2006), p. 1126.doi:10.1016/j.aop.2005.11.014

    work page doi:10.1016/j.aop.2005.11.014 2006

  25. [25]

    Many-Body Localization and Thermalization in Quantum Statistical Mechanics

    R. Nandkishore and D. A. Huse. “Many-Body Localization and Thermalization in Quantum Statistical Mechanics”. In:Annual Review of Condensed Matter Physics6 (2015), p. 15.doi:10.1146/annurev-conmatphys-031214-014726

    work page doi:10.1146/annurev-conmatphys-031214-014726 2015

  26. [26]

    Many-body localization: An introduction and selected topics

    F. Alet and N. Laflorencie. “Many-body localization: An introduction and selected topics”. In:Comptes Rendus Physique19 (2018), p. 408.doi: 10.1016/j.crhy.2018.03.003

    work page doi:10.1016/j.crhy.2018.03.003 2018

  27. [27]

    Many-Body Localization in Periodically Driven Systems

    P. Ponte et al. “Many-Body Localization in Periodically Driven Systems”. In:Phys. Rev. Lett.114 (2015), p. 140401.doi:10.1103/PhysRevLett.114.140401

    work page doi:10.1103/physrevlett.114.140401 2015

  28. [28]

    Periodically driven ergodic and many-body localized quantum systems

    P. Ponte et al. “Periodically driven ergodic and many-body localized quantum systems”. In:Ann. Phys.353 (2015), p. 196.doi:10.1016/j.aop.2014.11.008

    work page doi:10.1016/j.aop.2014.11.008 2015

  29. [29]

    Quantum kicked rotor and its variants: Chaos, localization and beyond

    M.S. Santhanam, Sanku Paul, and J. Bharathi Kannan. “Quantum kicked rotor and its variants: Chaos, localization and beyond”. In:Physics Reports956 (2022). Quantum kicked rotor and its variants: Chaos, localization and beyond, pp. 1–87. doi:https://doi.org/10.1016/j.physrep.2022.01.002

    work page doi:10.1016/j.physrep.2022.01.002 2022

  30. [30]

    Chaos, Quantum Recurrences, and Anderson Localization

    S. Fishman, D. R. Grempel, and R. E. Prange. “Chaos, Quantum Recurrences, and Anderson Localization”. In:Phys. Rev. Lett.49 (1982), p. 509.doi: 10.1103/PhysRevLett.49.509

    work page doi:10.1103/physrevlett.49.509 1982

  31. [31]

    Quantum dynamics of a nonintegrable system

    D. R. Grempel, R. E. Prange, and S. Fishman. “Quantum dynamics of a nonintegrable system”. In:Phys. Rev. A29 (1984), p. 1639.doi: 10.1103/PhysRevA.29.1639

    work page doi:10.1103/physreva.29.1639 1984

  32. [32]

    Localization of diffusive excitation in multi-level systems

    D. L. Shepelyansky. “Localization of diffusive excitation in multi-level systems”. In: Phys. Rev. Lett.56 (1986), p. 677.doi:10.1103/PhysRevLett.56.677

    work page doi:10.1103/physrevlett.56.677 1986

  33. [33]

    Atom Optics Realization of the Quantumδ-Kicked Rotor

    F. L. Moore et al. “Atom Optics Realization of the Quantumδ-Kicked Rotor”. In: Phys. Rev. Lett.75 (25 1995), pp. 4598–4601.doi:10.1103/PhysRevLett.75.4598

    work page doi:10.1103/physrevlett.75.4598 1995

  34. [34]

    Universality of the Anderson transition with the atomic kicked rotor

    G. Lemari´ e et al. “Universality of the Anderson transition with the atomic kicked rotor”. In:Phys. Rev. A82 (2010), p. 013611.doi:10.1103/PhysRevA.82.013611

    work page doi:10.1103/physreva.82.013611 2010

  35. [35]

    Experimental Test of Universality of the Anderson Transition

    M. Lopez et al. “Experimental Test of Universality of the Anderson Transition”. In: Phys. Rev. Lett.108 (2012), p. 095701.doi:10.1103/PhysRevLett.108.095701

    work page doi:10.1103/physrevlett.108.095701 2012

  36. [36]

    Experimental Observation of Two-Dimensional Anderson Localization with the Atomic Kicked Rotor

    Isam Manai et al. “Experimental Observation of Two-Dimensional Anderson Localization with the Atomic Kicked Rotor”. In:Phys. Rev. Lett.115 (24 Dec. 2015), p. 240603.doi:10.1103/PhysRevLett.115.240603

    work page doi:10.1103/physrevlett.115.240603 2015

  37. [37]

    Controlling symmetry and localization with an artificial gauge field in a disordered quantum system

    C. Hainaut et al. “Controlling symmetry and localization with an artificial gauge field in a disordered quantum system”. In:Nat. Commun.9 (2018), p. 1382.doi: 10.1038/s41467-018-03481-9

    work page doi:10.1038/s41467-018-03481-9 2018

  38. [38]

    Observation of Many-body Dynamical Delocalization in a Kicked Ultracold Gas

    J. H. S. Toh et al. “Observation of Many-body Dynamical Delocalization in a Kicked Ultracold Gas”. In:Nat. Phys.18 (2022), p. 1297.doi: 10.1038/s41567-022-01721-w

    work page doi:10.1038/s41567-022-01721-w 2022

  39. [39]

    Interaction-driven breakdown of dynamical localization in a kicked Quantum Gas

    Alec Cao et al. “Interaction-driven breakdown of dynamical localization in a kicked Quantum Gas”. In:Nature Physics18.11 (2022), pp. 1302–1306.doi: 10.1038/s41567-022-01724-7

    work page doi:10.1038/s41567-022-01724-7 2022

  40. [40]

    Observation of many-body dynamical localization

    Y. Guo et al. “Observation of many-body dynamical localization”. In:Science389 (2025), pp. 716–719.doi:10.1126/science.adn8625

    work page doi:10.1126/science.adn8625 2025

  41. [41]

    Observation of quantum criticality of a four-dimensional phase transition

    Farid Madani et al. “Observation of quantum criticality of a four-dimensional phase transition”. In:Nature Communications16.1 (Mar. 2025).doi: 10.1038/s41467-025-57396-3. 12

    work page doi:10.1038/s41467-025-57396-3 2025

  42. [42]

    Quantum simulation of disordered systems with cold atoms

    J. C. Garreau. “Quantum simulation of disordered systems with cold atoms”. In: Physics Reports420 (2008), p. 163.doi:10.1016/j.physrep.2005.09.006

    work page doi:10.1016/j.physrep.2005.09.006 2008

  43. [43]

    Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State

    E. H. Lieb and W. Liniger. “Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State”. In:Phys. Rev.130 (1963), p. 1605.doi: 10.1103/PhysRev.130.1605

    work page doi:10.1103/physrev.130.1605 1963

  44. [44]

    Tonks–Girardeau gas of ultracold atoms in an optical lattice

    B. Paredes et al. “Tonks–Girardeau gas of ultracold atoms in an optical lattice”. In: Nature429 (2004), p. 227.doi:10.1038/nature02530

    work page doi:10.1038/nature02530 2004

  45. [45]

    Kinoshita, T

    T. Kinoshita, T. Wenger, and D. S. Weiss. “Observation of a One-Dimensional Tonks-Girardeau Gas”. In:Science305 (2004), p. 1125.doi: 10.1126/science.1100700

    work page doi:10.1126/science.1100700 2004

  46. [46]

    Local Pair Correlations in One-Dimensional Bose Gases

    T. Kinoshita, T. Wenger, and D. S. Weiss. “Local Pair Correlations in One-Dimensional Bose Gases”. In:Phys. Rev. Lett.95 (2005), p. 190406.doi: 10.1103/PhysRevLett.95.190406

    work page doi:10.1103/physrevlett.95.190406 2005

  47. [47]

    One dimensional bosons: From condensed matter systems to ultracold gases

    M. A. Cazalilla et al. “One dimensional bosons: From condensed matter systems to ultracold gases”. In:Rev. Mod. Phys.83 (2011), p. 1405.doi: 10.1103/RevModPhys.83.1405

    work page doi:10.1103/revmodphys.83.1405 2011

  48. [48]

    Anderson Transition in a One-Dimensional System with Three Incommensurate Frequencies

    Giulio Casati, Italo Guarneri, and D. L. Shepelyansky. “Anderson Transition in a One-Dimensional System with Three Incommensurate Frequencies”. In:Phys. Rev. Lett.62 (4 Jan. 1989), pp. 345–348.doi:10.1103/PhysRevLett.62.345

    work page doi:10.1103/physrevlett.62.345 1989

  49. [49]

    Interaction Effects on the Dynamical Anderson Metal-Insulator Transition Using Kicked Quantum Gases

    Jun Hui See Toh et al. “Interaction Effects on the Dynamical Anderson Metal-Insulator Transition Using Kicked Quantum Gases”. In:Phys. Rev. Lett.133 (7 Aug. 2024), p. 076301.doi:10.1103/PhysRevLett.133.076301

    work page doi:10.1103/physrevlett.133.076301 2024

  50. [50]

    Interaction Induced Anderson Transition in a Kicked One Dimensional Bose Gas

    H. Olsen et al. “Interaction Induced Anderson Transition in a Kicked One Dimensional Bose Gas”. In:Phys. Rev. Lett.135 (17 Oct. 2025), p. 173403.doi: 10.1103/dyxq-qkmd

    work page doi:10.1103/dyxq-qkmd 2025

  51. [51]

    Ang Yang et al.Origin and emergent features of many-body dynamical localization

    work page

  52. [52]

    arXiv:2503.04683 [cond-mat.quant-gas]

    work page arXiv

  53. [53]

    From localization to anomalous diffusion in the dynamics of coupled kicked rotors

    S. Notarnicola et al. “From localization to anomalous diffusion in the dynamics of coupled kicked rotors”. In:Phy. Rev. E97 (2018), p. 022202.doi: 10.1103/PhysRevE.97.022202

    work page doi:10.1103/physreve.97.022202 2018

  54. [54]

    Observation of the Anderson metal-insulator transition with atomic matter waves: Theory and experiment

    G. Lemari´ e et al. “Observation of the Anderson metal-insulator transition with atomic matter waves: Theory and experiment”. In:Phys. Rev. A80 (2009), p. 043626.doi:10.1103/PhysRevA.80.043626

    work page doi:10.1103/physreva.80.043626 2009

  55. [56]

    Relationship between systems of impenetrable bosons and fermions in one dimension

    M Girardeau. “Relationship between systems of impenetrable bosons and fermions in one dimension”. In:Journal of Mathematical Physics(1960)

    work page 1960

  56. [57]

    Effective thermalization of a many-body dynamically localized Bose gas

    Vincent Vuatelet and Adam Ran¸ con. “Effective thermalization of a many-body dynamically localized Bose gas”. In:Phys. Rev. A104 (4 2021), p. 043302.doi: 10.1103/PhysRevA.104.043302

    work page doi:10.1103/physreva.104.043302 2021

  57. [58]

    Many-Body Localization in the Presence of a Small Bath

    C. Rylands et al. “Many-Body Localization in the Presence of a Small Bath”. In: Phys. Rev. Lett.124 (2020), p. 155302.doi:10.1103/PhysRevLett.124.155302

    work page doi:10.1103/physrevlett.124.155302 2020

  58. [59]

    Two-body quantum kicked rotor with arbitrary interactions

    R. Chicireanu and A. Ran¸ con. “Two-body quantum kicked rotor with arbitrary interactions”. In:Phys. Rev. A103 (2021), p. 043314.doi: 10.1103/PhysRevA.103.043314. 13

    work page doi:10.1103/physreva.103.043314 2021