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arxiv: 2604.09224 · v1 · submitted 2026-04-10 · ❄️ cond-mat.quant-gas · cond-mat.dis-nn

Many-body dynamical localization in Fock space

Nathan Dupont , Bruno Peaudecerf , David Gu\'ery-Odelin , Gabriel Lemari\'e , Bertrand Georgeot , Christian Miniatura , Nathan Goldman This is my paper

Pith reviewed 2026-05-10 16:35 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.dis-nn
keywords many-body dynamical localizationFock spacekicked-top modelAnderson localizationperiodic drivingbosonic systemsdiscrete time crystalsquantum chaos
0
0 comments X

The pith

Quantum many-body dynamics suppresses transport in Fock space of a periodically driven two-mode bosonic system, unlike the ergodic diffusion of its classical mean-field limit.

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

The paper examines many-body dynamical localization in the Fock space of interacting bosons subject to periodic driving. It maps the system to the kicked-top model to contrast classical chaotic diffusion, which remains bounded along the population imbalance, with quantum interference that halts spreading in Fock space. This produces a localization length whose scaling with particle number and drive parameters is analyzed, together with a shift in spectral statistics from random-matrix to Poisson form. The localization is tied to discrete time crystals and positioned as a route for examining the Anderson transition without external disorder.

Core claim

While the classical mean-field dynamics exhibits bounded ergodic diffusion along the population imbalance axis, the quantum dynamics reveals strong suppression of transport in Fock space, in close analogy with Anderson localization in disordered lattices. The localization length is characterized along with its scaling, the spectral statistics cross over to Poisson upon localization, and the effect is linked to discrete time crystals.

What carries the argument

The mapping of the driven two-mode bosonic system to the kicked-top model, which permits direct comparison of classical diffusion against quantum interference effects in Fock space.

If this is right

  • The localization length and its dependence on particle number and driving parameters become quantifiable.
  • Level statistics cross over from random-matrix to Poisson form once localization sets in.
  • Many-body dynamical localization connects directly to discrete time crystal behavior.
  • The driven bosonic system supplies a platform to investigate the Anderson transition inside Fock space.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Experiments with ultracold atoms could test Fock-space localization by tracking population imbalance and level statistics under periodic driving.
  • The same mapping technique might reveal analogous localization in other periodically driven many-body systems.
  • Suppressed transport could limit entanglement growth or information propagation within the Fock space.

Load-bearing premise

The kicked-top model mapping accurately captures the many-body dynamics of the interacting two-mode bosonic system under periodic driving.

What would settle it

Direct measurement or simulation showing persistent ergodic spreading or Wigner-Dyson level statistics in the quantum regime, rather than bounded localization length and Poisson statistics, would falsify the suppression of transport.

Figures

Figures reproduced from arXiv: 2604.09224 by Bertrand Georgeot, Bruno Peaudecerf, Christian Miniatura, David Gu\'ery-Odelin, Gabriel Lemari\'e, Nathan Dupont, Nathan Goldman.

Figure 1
Figure 1. Figure 1: Kicked system, Fock space picture and dy￾namical localization. (a) Left: Schematics of a two-mode system (1), with two-body interactions U between bosons (black disks) and driven hopping amplitude k(t). Right: Corresponding 1D Fock space. (b) Depiction of the quan￾tum (Eq. (3)) and classical (Eq. (4)) evolutions, with ⃗rm = (x, y, z)m. (c) Evolution of 1000 mean-field trajectories start￾ing from the equato… view at source ↗
Figure 2
Figure 2. Figure 2: (d) shows the saturated variance σ 2 z (m → ∞) as a function of a for N = 50, 200 and 800, revealing three 0 1/3 a = 0.1 (a) classical quantum 0 1/3 σ 2 z (m) a = 0.2 (b) 0 50 100 m = t/T 0 1/3 a = 0.8 (c) 10−5 10−2 10−3 10−2 |ψ(n1)| 2 0 100 200 n1 10−2 10−2 10−1 a 10−5 10−3 10−1 σ 2 z (m → ∞) 2¯h 2 eff ξ 2 (d) N = 50 N = 200 N = 800 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Spectral statistics crossover towards lo￾calization for the RQKT [80]. (a,b,c) Distribution of quasienergy spacings for a = 0.02, 0.1 and 0.8 respectively for N = 200 (solid blue lines) compared to RMT predictions (black lines), in linear scale. (d) Kullback-Leibler divergence DKL of the simulated spacing distributions to the Poisson dis￾tribution as a function of a for N = 200 (dash-dotted line) and ident… view at source ↗
Figure 4
Figure 4. Figure 4: Discrete time crystals from the perspective of MBDL. (a) Left panel: Fock space projection of the two Floquet states with maximal overlap onto |0, N⟩ and |N, 0⟩ for a = π+0.8. Right panels: Expectation value of the population imbalance ⟨Jˆz⟩ as a function of m for |ψ0⟩ = |0, N⟩. (b) Same as (a) for a = π + 0.1. (c) Degeneracy lifting |∆ε± −h/2T| as a function of a−π for N = 50 (light blue) and N = 200 (dar… view at source ↗
read the original abstract

We investigate the emergence of many-body dynamical localization (MBDL) in the Fock space of an interacting two-mode bosonic system subject to periodic driving. Using a mapping to the paradigmatic kicked-top model, we analyze the interplay between classical chaotic diffusion and quantum interference effects. While the mean-field (classical) dynamics exhibits bounded ergodic diffusion along the population imbalance axis, the quantum dynamics reveals strong suppression of transport in Fock space, in close analogy with Anderson localization in disordered lattices. We characterize the localization length, its scaling with particle number and driving parameters, and reveal the spectral crossover from random-matrix to Poisson statistics as the many-body ensemble localizes. We highlight the connection between MBDL and discrete time crystals. Our findings offer a promising avenue to study the Anderson transition in Fock space.

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 investigates the emergence of many-body dynamical localization (MBDL) in the Fock space of an interacting two-mode bosonic system under periodic driving. By mapping the system to the kicked-top model, it contrasts bounded ergodic diffusion in the classical mean-field dynamics along the population imbalance axis with strong suppression of transport in the quantum Fock-space dynamics, drawing an analogy to Anderson localization in disordered lattices. The work characterizes the localization length and its scaling with particle number N and driving parameters, demonstrates a spectral crossover from random-matrix to Poisson statistics upon localization, and highlights connections to discrete time crystals.

Significance. If the mapping is faithful and the numerical results robust, this provides a clean, controllable platform for studying Anderson-like transitions directly in many-body Fock space and the interplay between quantum interference and classical chaos in driven bosonic systems. The explicit link to discrete time crystals and the N-scaling analysis are strengths that could inform experiments with ultracold atoms or trapped ions.

major comments (2)
  1. [Mapping to kicked-top model (near Eq. defining the Floquet operator)] The mapping to the kicked-top model (introduced after the Hamiltonian definition) is load-bearing for the central classical-quantum contrast and Anderson analogy. The manuscript must explicitly derive whether the Floquet operator is unitarily equivalent to the kicked top or only approximates it up to finite-N corrections, interaction renormalization, or extra terms from the specific periodic driving protocol; without this, the observed localization length, its N-dependence, and Poisson spectral statistics could arise from model artifacts rather than genuine MBDL.
  2. [§4 (localization length scaling)] §4 (numerical results on localization length): the scaling of the localization length with N and driving strength is presented without error bars, convergence checks against Hilbert-space truncation, or explicit rules for data exclusion; this undermines the claim that the suppression is a robust many-body effect rather than a finite-N artifact.
minor comments (2)
  1. [Abstract] Abstract: the statement that the quantum dynamics reveals 'strong suppression of transport' should be qualified with a brief mention of the diagnostic used (e.g., participation ratio or return probability) to avoid overstatement.
  2. [Figures] Figure captions (e.g., those showing Fock-space probability distributions): axis labels and color scales should explicitly state the particle number N and driving parameters used, and whether the plots are for a single realization or ensemble average.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We are pleased that the referee recognizes the potential significance of our work on many-body dynamical localization. Below we address each major comment in detail.

read point-by-point responses

  1. Referee: [Mapping to kicked-top model (near Eq. defining the Floquet operator)] The mapping to the kicked-top model (introduced after the Hamiltonian definition) is load-bearing for the central classical-quantum contrast and Anderson analogy. The manuscript must explicitly derive whether the Floquet operator is unitarily equivalent to the kicked top or only approximates it up to finite-N corrections, interaction renormalization, or extra terms from the specific periodic driving protocol; without this, the observed localization length, its N-dependence, and Poisson spectral statistics could arise from model artifacts rather than genuine MBDL.

    Authors: We agree with the referee that an explicit derivation of the mapping is essential to establish the validity of our results. In the revised version, we will include a detailed derivation showing that the Floquet operator for our periodically driven two-mode bosonic system is unitarily equivalent to that of the kicked-top model, with any finite-N corrections explicitly accounted for. This will confirm that the observed localization and spectral statistics arise from genuine many-body dynamical localization rather than artifacts. revision: yes

  2. Referee: [§4 (localization length scaling)] §4 (numerical results on localization length): the scaling of the localization length with N and driving strength is presented without error bars, convergence checks against Hilbert-space truncation, or explicit rules for data exclusion; this undermines the claim that the suppression is a robust many-body effect rather than a finite-N artifact.

    Authors: We thank the referee for pointing out the lack of error bars and convergence checks in §4. In the revised manuscript, we will add error bars to the localization length scaling plots, include explicit convergence tests with respect to the Hilbert space dimension (truncation), and specify the data selection criteria. These additions will demonstrate the robustness of the N-scaling and the many-body nature of the localization effect. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation chain is self-contained.

full rationale

The paper's central claims rest on a stated mapping of the driven two-mode bosonic system to the kicked-top model, followed by direct comparison of classical mean-field diffusion on the Bloch sphere versus quantum spreading in the (N+1)-dimensional Fock basis. Localization length, N-scaling, and Poisson spectral statistics are extracted from the model's time evolution and eigenstate properties rather than being fitted to or defined in terms of the target observables. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations that reduce the result to its own inputs appear in the abstract or described derivation. The Anderson analogy is an interpretive observation from the computed suppression of transport, not a tautological re-labeling. This matches the default expectation for an independent model analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the kicked-top mapping and the interpretation of transport suppression as many-body localization; no free parameters or invented entities are identifiable from the abstract.

axioms (1)
  • domain assumption The two-mode bosonic system with periodic driving can be mapped to the kicked-top model while preserving the essential classical chaotic diffusion and quantum interference effects.
    Explicitly invoked in the abstract as the basis for analyzing mean-field versus quantum dynamics.

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Reference graph

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