SciPost Submission Page

Hydrodynamics of the interacting Bose gas in the Quantum Newton Cradle setup

by Jean-Sébastien Caux, Benjamin Doyon, Jérôme Dubail, Robert Konik, Takato Yoshimura

This is not the current version.

Submission summary

As Contributors: Benjamin Doyon · Jerome Dubail · Takato Yoshimura
Arxiv Link: (pdf)
Date submitted: 2018-11-10 01:00
Submitted by: Dubail, Jerome
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Experiment
  • Quantum Physics
Approaches: Theoretical, Computational


Describing and understanding the motion of quantum gases out of equilibrium is one of the most important modern challenges for theorists. In the groundbreaking Quantum Newton Cradle experiment [Kinoshita, Wenger and Weiss, Nature 440, 900, 2006], quasi-one-dimensional cold atom gases were observed with unprecedented accuracy, providing impetus for many developments on the effects of low dimensionality in out-of-equilibrium physics. But it is only recently that the theory of generalized hydrodynamics has provided the adequate tools for a numerically efficient description. Using it, we give a complete numerical study of the time evolution of an ultracold atomic gas in this setup, in an interacting parameter regime close to that of the original experiment. We evaluate the full evolving phase-space distribution of particles. We simulate oscillations due to the harmonic trap, the collision of clouds without thermalization, and observe a small elongation of the actual oscillation period and cloud deformations due to many-body dephasing. We also analyze the effects of weak anharmonicity. In the experiment, measurements are made after release from the one-dimensional trap. We evaluate the gas density curves after such a release, characterizing the actual time necessary for reaching the asymptotic state where the integrable quasi-particle momentum distribution function emerges.

Ontology / Topics

See full Ontology or Topics database.

Harmonic traps Hydrodynamics One-dimensional Bose gas Quasiparticles Ultracold atoms
Current status:
Has been resubmitted

Submission & Refereeing History

Resubmission 1711.00873v3 on 30 May 2019

Reports on this Submission

Anonymous Report 2 on 2018-12-31 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1711.00873v2, delivered 2018-12-31, doi: 10.21468/SciPost.Report.773


1. Applies generalized hydrodynamic (GHD) approach to integrable models in an external potential to experimentally relevant (Newton's Cradle) setup.

2. Method is not limited to weak interaction or short times.

3. Investigates the effect of interaction and trap anharmonicity on dephasing.

4. Identifies infinite family of conserved quantities of GHD that constrains thermalization


Only minor weaknesses, identified in the "requested changes"


This paper represents an important part of a series of theoretical developments sparked by the Quantum Newton's Cradle experiment of 2006. The generalized hydrodynamic (GHD) approach to integrable models developed in earlier papers by the same authors and others. The important aspect of the present work is the analysis of realistic conditions that resemble the initial experiment, namely the presence of a trap potential, including anharmonic contributions.

The manuscript itself is extremely clearly written, with the background theory clearly summarized before the numerical simulations of the GHD equations are presented. The various features of the solutions are then discussed, particularly in light of the original experiment.

Requested changes

1. Clarification of the "Euler scale" in the Section "The GHD equation". What is it? The description is purely verbal, and says that the variation of conserved densities is "slow enough". Compared to what? Usually one justifies such an approach via local equilibration, but that is not happening here.

2. "In standard approaches, this would imply....". I see by the citation that the authors refer to application in BEC. In general it isn't true that the distribution function in a nonequilibrium situation is a boosted Gibbs state. If it were, the collision integral in the Boltzmann equation would vanish!

3. I believe the numerical technique used here goes by the name "Smoothed particle hydrodynamics" elsewhere. If the authors agree it may be worth mentioning this.

4. The caption to Fig. 1 contains the term "Flea gas" which I believe is introduced in other work by the authors, but not here. It should be explained or removed.

5. End of the section on harmonic QNC: "...for entropic reasons the particle density spreads mostly towards lower energies...". Can some words of explanation be added here?

6. Some explanation for the chosen anharmonicity could be provided i.e. why not a quartic potential?

  • validity: top
  • significance: high
  • originality: good
  • clarity: high
  • formatting: perfect
  • grammar: excellent

Anonymous Report 1 on 2018-12-14 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1711.00873v2, delivered 2018-12-14, doi: 10.21468/SciPost.Report.746


1. Well formulatied physical questions and motivation
2. Relation to real experiment.
3. Elegant method
4. Convincing results
5. Beautiful figures


1. Absence of discussion of integrability breaking mechanisms (see report).


The manuscript uses Generalized Hydrodynamics (GHD) to describe time evolution
of interacting bosons in one dimension confined by harmonic potential
following the groundbreaking Newton Cradle experiment. The main results are
accurate predictions for the density profiles and quasi-momentum distribution
which can be in principle observed using one-dimensional time of flight. The
results are consistent with the absence of thermalization after several
thousands of oscillations in the trap observed in the original experiment.

The paper provides a valuable application of Generalized Hydrodynamics to real
experiments and illustrates its predictive power. The authors give detailed
account of the method and its limitations. In particular they are able to
show how a smooth phase-space distributions emerge from coarse graining.

My main question is whether the confinement is the main source of the
integrability breaking in this system? Is it possible that other sources of
non-integrability, like three body interactions due to transitions to higher
transverse states, will lead to significant deviations of the idealized picture
and whether they can be accounted for by suitable modifications of Generalized
Hydrodynamic equations? Such discussion can be very valuable for realistic

The manuscript is of clear interest to the theoretical community studying
dynamics of quantum systems close to integrability and the presented method
can be used for efficient simulations of future experiments with ultra cold

Requested changes

No specific changes are required to the current version.

  • validity: top
  • significance: high
  • originality: high
  • clarity: top
  • formatting: perfect
  • grammar: perfect

Login to report or comment