Towards an ab initio derivation of generalised hydrodynamics from a gas of interacting wave packets

Benjamin Doyon; Friedrich H\"ubner

arxiv: 2307.09307 · v3 · submitted 2023-07-14 · ❄️ cond-mat.stat-mech · cond-mat.quant-gas· math-ph· math.MP

Towards an ab initio derivation of generalised hydrodynamics from a gas of interacting wave packets

Benjamin Doyon , Friedrich H\"ubner This is my paper

Pith reviewed 2026-05-24 07:34 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.quant-gasmath-phmath.MP

keywords generalised hydrodynamicsLieb-Liniger modelBethe wave functionswave packetsintegrable systemsscattering shiftsconserved densitiesquantum hydrodynamics

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The pith

Wave packets constructed from Bethe wave functions evolve classically and accumulate two-particle scattering shifts that match those of solitons, offering a route to generalised hydrodynamics equations from the underlying quantum states.

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

The paper works toward an ab initio derivation of generalised hydrodynamics starting from the Bethe wave functions of the repulsive Lieb-Liniger model. It identifies the quasi-particles of generalised hydrodynamics with particular wave packets that follow classical trajectories while collecting scattering shifts upon pairwise encounters. An explicit formula is given for how a spectral phase-space density operator acts on these wave functions to produce local conserved densities. If the identification holds, the average densities in long-wavelength states would obey the generalised hydrodynamics equations directly from this microscopic picture. Readers would gain a concrete link between the quantum many-body wave function and the effective hydrodynamic description without intermediate assumptions about quasiparticle distributions.

Core claim

The generalised hydrodynamics quasi-particles can be identified as wave packets in the quantum model that evolve according to a classical particle model and collect two-particle scattering shifts similar to solitons. The spectral phase-space density operator applied to Bethe wave functions generates the local conserved densities, and this construction supplies potential routes to the generalised hydrodynamics equations for average conserved densities in long-wavelength states.

What carries the argument

The spectral phase-space density operator acting on Bethe wave functions to generate local conserved densities, together with the classical evolution of identified wave packets that accumulate scattering shifts.

If this is right

Average conserved densities in long-wavelength states obey the generalised hydrodynamics continuity equations.
Local observables become expressible through the spectral phase-space density of the wave packets.
The same wave-packet construction applies to other quantum integrable models whose Bethe wave functions are known.
Scattering shifts collected by the wave packets determine the effective velocities in the hydrodynamic equations.

Where Pith is reading between the lines

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

Numerical evolution of many such wave packets could serve as a practical method to simulate generalised hydrodynamics in finite systems.
Cold-atom experiments that prepare and track localised wave packets could directly measure the predicted scattering shifts.
The classical particle picture may connect generalised hydrodynamics to existing theories of soliton gases in classical integrable field theories.

Load-bearing premise

The classical motion of the identified wave packets together with the action of the spectral phase-space density operator will directly produce the generalised hydrodynamics equations for average conserved densities.

What would settle it

A direct computation of the time derivative of average conserved densities obtained from the classical wave-packet trajectories that fails to match the known generalised hydrodynamics continuity equations for the Lieb-Liniger model.

read the original abstract

We present steps towards an ab initio derivation of generalised hydrodynamics in quantum integrable models, starting from the Bethe wave functions, and explained on the example of the repulsive Lieb-Liniger model. This includes an identification of the generalised hydrodynamics quasi-particles as wave packets in the quantum model. These wave packets evolve according to a classical particle model and collect two-particle scattering shifts similar to solitons in integrable PDEs. We then discuss potential routes to obtain the generalised hydrodynamics equation for average conserved densities in long-wavelength states from this description. As part of this, we provide an explicit formula for the action of the spectral phase-space density operator on Bethe wave functions, and show that it generates local conserved densities.

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.

Desk Editor's Note private letter to a colleague

The paper identifies GHD quasi-particles with Bethe wave packets and supplies an explicit operator formula that generates local densities, but stops short of completing the derivation to the hydrodynamic equations.

read the letter

The main advance here is the concrete identification of generalised hydrodynamics quasi-particles with wave packets built from Bethe wave functions in the repulsive Lieb-Liniger model. These packets are shown to follow classical trajectories while accumulating the expected two-particle scattering shifts. The paper also gives an explicit formula for the action of the spectral phase-space density operator on Bethe states and verifies that this action produces the local conserved densities. Both pieces are new relative to the cited prior work and are presented without obvious circularity or fitted parameters. The approach begins from standard Bethe ansatz states and aims at an ab initio route, which is a reasonable starting point. The operator formula and the check on local densities are the parts that look technically solid and reproducible from the description. The limitation is that the paper frames everything as steps toward the GHD equations for average conserved densities in long-wavelength states and only discusses potential routes rather than carrying out the derivation or showing that the classical evolution plus the operator directly yields those equations. This is not hidden; the title and abstract are explicit about the prospective nature of the connection. No load-bearing gaps are claimed to be closed. The work is aimed at specialists already familiar with Bethe ansatz techniques and GHD in integrable systems. Readers in that niche can extract the wave-packet picture and the operator formula as usable intermediate results. It is worth sending to peer review because the technical contributions are grounded and the framing is honest about what remains open.

Referee Report

0 major / 2 minor

Summary. The manuscript presents steps towards an ab initio derivation of generalised hydrodynamics (GHD) starting from Bethe wave functions in the repulsive Lieb-Liniger model. It identifies GHD quasi-particles with wave packets that evolve according to a classical particle model while collecting two-particle scattering shifts. An explicit formula is supplied for the action of the spectral phase-space density operator on Bethe states, shown to generate local conserved densities. Potential routes from this description to the GHD equations for average conserved densities in long-wavelength states are discussed.

Significance. If the outlined routes can be completed, the approach would supply a microscopic, parameter-free link between the Bethe-ansatz wave functions and the GHD hydrodynamic equations. The explicit operator formula for the spectral phase-space density and the concrete identification of wave-packet evolution with scattering shifts constitute tangible technical advances that could be reused in other integrable models.

minor comments (2)

[final discussion section] The discussion of potential routes to the GHD continuity equations remains at the level of sketches; adding one or two explicit intermediate steps (e.g., how the classical trajectories plus the operator action produce the continuity equation for a conserved density) would make the connection more transparent.
Notation for the spectral phase-space density operator and its action on Bethe states is introduced without a compact summary table; a short table listing the operator, its action, and the resulting local density would aid readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of the manuscript, recognition of its potential significance, and recommendation for minor revision. No specific major comments were listed in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation remains prospective and self-contained

full rationale

The paper frames its results explicitly as 'steps towards' an ab initio derivation from standard Bethe wave functions and 'discusses potential routes' to GHD equations rather than asserting a completed reduction. The wave-packet identification, classical evolution with scattering shifts, and explicit formula for the spectral phase-space density operator on Bethe states are presented as intermediate technical advances whose link to average conserved densities is left prospective. No fitted parameters renamed as predictions, self-definitional quantities, or load-bearing self-citations appear in the provided abstract or described content. The approach starts from independent Bethe-ansatz inputs and does not reduce its claims to those inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; cannot perform exhaustive audit. The work relies on the standard domain assumption that Bethe wave functions solve the Lieb-Liniger model.

axioms (1)

domain assumption Bethe wave functions describe the eigenstates of the repulsive Lieb-Liniger model
Invoked as the starting point for constructing wave packets and the operator action.

pith-pipeline@v0.9.0 · 5660 in / 1126 out tokens · 43380 ms · 2026-05-24T07:34:22.016518+00:00 · methodology

discussion (0)

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