pith. sign in

arxiv: 2511.20326 · v1 · submitted 2025-11-25 · ❄️ cond-mat.quant-gas

Bloch oscillations of a mobile impurity in a one-dimensional Bose gas

Saptarshi Majumdar , Aleksandra Petkovi\'c This is my paper

Pith reviewed 2026-05-17 04:57 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas
keywords Bloch oscillationsmobile impurityone-dimensional Bose gasdensity shock wavessolitonsweakly interacting bosonsfar-from-equilibrium dynamicsconstant force
0
0 comments X

The pith

A mobile impurity in a one-dimensional Bose gas under constant force exhibits periodic velocity oscillations by emitting density shock waves and solitons into the gas.

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

The paper studies an impurity driven by a constant force through a weakly interacting one-dimensional Bose gas. For a wide range of forces the impurity velocity does not accelerate without limit but instead oscillates around a steady drift velocity. Momentum is periodically transferred into the gas through the creation of dispersive density shock waves, solitons, density waves, and extra phase gradients. The work maps distinct dynamical regimes that depend on the impurity-boson coupling strength, the impurity mass, and the magnitude of the applied force.

Core claim

Under far-from-equilibrium conditions produced by a finite external force, the interplay of impurity-boson interaction, boson-boson interaction, and driving force channels part of the transferred momentum into the Bose gas via emission of dispersive density shock waves, solitons, density waves, and additional phase gradients, so that the impurity velocity oscillates periodically in time around the drift velocity rather than increasing indefinitely.

What carries the argument

Periodic emission of collective excitations (dispersive density shock waves, solitons, and density waves) that carry momentum away from the impurity-Bose-gas system and thereby produce velocity oscillations.

If this is right

  • The impurity velocity oscillates periodically around the drift velocity for a wide range of forces instead of accelerating indefinitely.
  • Distinct dynamical regimes appear as functions of impurity-boson coupling, impurity mass, and external force strength.
  • At sufficiently large forces the oscillations stop and the impurity accelerates without bound.

Where Pith is reading between the lines

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

  • The oscillation period may provide a direct experimental readout of the effective drag experienced by the impurity.
  • Similar momentum-channelling mechanisms could appear in other driven one-dimensional quantum fluids.
  • Relaxing the weak-interaction assumption might allow study of how stronger boson-boson repulsion modifies or suppresses the oscillations.

Load-bearing premise

The bosons stay weakly interacting so that shock waves, solitons, and density waves can form and periodically remove momentum in a strictly one-dimensional geometry with a constant finite force.

What would settle it

Time-resolved imaging that shows the impurity velocity repeatedly rising and falling around a fixed average value while the Bose gas displays periodic trains of density perturbations whose emission times match the oscillation period.

Figures

Figures reproduced from arXiv: 2511.20326 by Aleksandra Petkovi\'c, Saptarshi Majumdar.

Figure 1
Figure 1. Figure 1: FIG. 1. Impurity velocity as a function of the system momentum [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Phase of the condensate wave function for a) several values of the system momentum in the range [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Time evolution of the impurity velocity for [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Time evolution of the boson density in the reference frame defined in Sec. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Phase (top row) and density profile (bottom row) of the bosons in the reference frame defined in Sec. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Energy of the system [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Impurity velocity as a function of time for [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (a) Drift velocity, (b) Bloch oscillation amplitude and (c) time period of the oscillations as a function of the dimensionless force [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Phase and density profile of the bosons in the reference frame [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Dimensionless mobility, [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Mobility as a function of the dimensionless boson-boson [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
read the original abstract

We study the motion of an impurity under the action of a constant force through a one-dimensional system of weakly-interacting bosons. The interplay of the impurity-boson interaction, the boson-boson interaction, and the driving force gives rise to a rich dynamics. We focus on the influence of a finite external force. Under these far-from-equilibrium conditions, we show that in a wide range of forces, one part of the momentum transferred to the system is periodically channeled into the Bose gas through the emission of dispersive density shock waves, solitons, density waves and the creation of additional phase gradients. As a result, the impurity velocity does not increase indefinitely, but periodically oscillates in time around the drift velocity. We uncover and characterize different dynamical regimes in a wide range of the impurity-boson coupling, the impurity mass and the external force. At a sufficiently large force, the Bloch oscillations cease and the impurity exhibits an unlimited acceleration.

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 manuscript studies the far-from-equilibrium dynamics of a mobile impurity driven by a constant external force through a one-dimensional weakly interacting Bose gas. Using the time-dependent Gross-Pitaevskii equation for the bosonic field coupled to the impurity motion, the authors report that in a wide range of forces the impurity velocity periodically oscillates around a drift velocity. This arises because part of the transferred momentum is periodically emitted into the Bose gas in the form of dispersive density shock waves, solitons, density waves, and additional phase gradients. Multiple dynamical regimes are characterized as functions of the impurity-boson coupling strength, impurity mass, and force magnitude. At sufficiently large forces the oscillations cease and the impurity undergoes unlimited acceleration.

Significance. If the mean-field results hold, the work provides a concrete mechanism by which collective excitations in a 1D Bose gas can periodically absorb momentum and thereby stabilize the impurity velocity against continuous acceleration. The mapping of regimes across coupling, mass, and force offers testable predictions for ultracold-atom experiments. The explicit identification of shock-wave and soliton emission as the momentum sink is a useful addition to the literature on driven impurities and polaron transport.

major comments (2)
  1. [Model and numerical implementation (likely §2)] The central claim of periodic velocity oscillations persisting across a 'wide range' of impurity-boson couplings (including strong values) rests on the validity of the mean-field Gross-Pitaevskii description. For strong impurity-boson repulsion the local density depletion and large phase gradients violate the assumptions of small fluctuations and coherence that underlie the GPE; the manuscript does not provide an independent check (e.g., comparison with Bogoliubov-depleted or exact diagonalization results in the strong-coupling limit) that the reported shock waves and solitons survive beyond mean field. This is load-bearing for the 'wide range' statement.
  2. [Results on dynamical regimes] The transition from oscillatory to unlimited-acceleration behavior at large force is stated but not quantified; no explicit critical-force value or scaling with impurity mass and coupling is given that would allow falsification or direct experimental comparison.
minor comments (2)
  1. [Figures] Figure captions should explicitly list the values of impurity-boson coupling, mass ratio, and force used in each panel so that the different regimes can be unambiguously identified.
  2. [Introduction] A short paragraph clarifying how the observed oscillations relate to conventional Bloch oscillations (lattice band structure versus continuous driving plus nonlinear excitations) would improve accessibility.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which we believe will improve the clarity and impact of the work. We address each major comment below.

read point-by-point responses

  1. Referee: [Model and numerical implementation (likely §2)] The central claim of periodic velocity oscillations persisting across a 'wide range' of impurity-boson couplings (including strong values) rests on the validity of the mean-field Gross-Pitaevskii description. For strong impurity-boson repulsion the local density depletion and large phase gradients violate the assumptions of small fluctuations and coherence that underlie the GPE; the manuscript does not provide an independent check (e.g., comparison with Bogoliubov-depleted or exact diagonalization results in the strong-coupling limit) that the reported shock waves and solitons survive beyond mean field. This is load-bearing for the 'wide range' statement.

    Authors: We appreciate the referee raising this important caveat on the mean-field approximation. The title and abstract explicitly frame the study in terms of a weakly-interacting Bose gas, for which the time-dependent Gross-Pitaevskii equation is the standard and well-controlled description. Our numerical survey covers a range of impurity-boson couplings, but we agree that the phrase 'wide range' should be qualified to exclude regimes of extreme local depletion where quantum fluctuations become dominant. In the revised manuscript we will add a dedicated paragraph (likely in §2) that states the validity criteria (e.g., local density depletion remaining below a few tens of percent and phase gradients not exceeding the inverse healing length) and explicitly limits the claimed regime accordingly. A systematic beyond-mean-field benchmark (Bogoliubov or exact diagonalization) lies outside the present scope and would constitute a separate study. revision: partial

  2. Referee: [Results on dynamical regimes] The transition from oscillatory to unlimited-acceleration behavior at large force is stated but not quantified; no explicit critical-force value or scaling with impurity mass and coupling is given that would allow falsification or direct experimental comparison.

    Authors: We agree that an explicit, falsifiable characterization of the transition would strengthen the manuscript. Although the original text identifies the crossover qualitatively, we have re-examined our existing simulation data and can extract a critical force F_c for each combination of mass and coupling. In the revised version we will report these values, together with a simple scaling argument based on equating the external force to the average rate of momentum carried away by the emitted shock waves and solitons. A new panel or table will display F_c(m, g) to enable direct experimental comparison. revision: yes

standing simulated objections not resolved
  • A direct numerical comparison of the reported shock-wave and soliton structures against beyond-mean-field methods (e.g., Bogoliubov-depleted or exact diagonalization) in the strong-coupling limit.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper models the impurity-Bose gas system via the time-dependent Gross-Pitaevskii equation for weakly interacting bosons coupled to classical impurity motion under constant force. The reported periodic velocity oscillations around the drift velocity, momentum transfer via shock waves/solitons/density waves, and regime boundaries are presented as direct outcomes of solving this dynamical system across parameter ranges. No load-bearing steps reduce to self-definition, fitted inputs renamed as predictions, or self-citation chains; the central results follow from the stated mean-field evolution rather than presupposing the target phenomenology. The derivation remains independent of the target claims.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that a 1D weakly-interacting Bose gas supports the listed collective excitations under constant drive; no free parameters or new entities are explicitly introduced in the abstract.

axioms (1)
  • domain assumption Weakly-interacting bosons in one dimension can be described by hydrodynamic or mean-field models that permit formation of dispersive shock waves and solitons
    Implicit in the description of momentum transfer via these excitations

pith-pipeline@v0.9.0 · 5464 in / 1282 out tokens · 47538 ms · 2026-05-17T04:57:01.955173+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages

  1. [1]

    a linear dependence onFshrinks down asM/mdecreases

    = 0.0025. a linear dependence onFshrinks down asM/mdecreases. Figure 11 shows a typical behaviour of the Bloch amplitude as a function ofM/mfor a fixed force ˜F= 1. For all the shown values ofM/m, the drift velocity is well approximated byσFdependence. BothV d andV B decrease as the impurity becomes heavier while the other parameters are kept fixed. The d...

    work page

  2. [2]

    Programme des Investissements d’Avenir

    = 0.0025. This value of the force is in the linear regime ofV d depen- dence onFfor all gamma apart from the three smallest one. Thus,V d shows almost the same behaviour asσF, it is a de- creasing function ofγ. On the other hand, the Bloch ampli- tude exhibits the opposite behaviour, it is an increasing func- tion ofγ. The impurity mobility was expressed ...

    work page

  3. [3]

    Bloch, ¨Uber die quantenmechanik der elektronen in kristall- gittern, Zeitschrift f¨ur Physik52, 555 (1929)

    F. Bloch, ¨Uber die quantenmechanik der elektronen in kristall- gittern, Zeitschrift f¨ur Physik52, 555 (1929)

    work page 1929

  4. [4]

    Zener, Proc

    C. Zener, Proc. R. Soc. Lond.145, 523 (1934)

    work page 1934

  5. [5]

    Waschke, H

    C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. K ¨ohler, Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice, Phys. Rev. Lett.70, 3319 (1993)

    work page 1993

  6. [6]

    Ben Dahan, E

    M. Ben Dahan, E. Peik, J. Reichel, Y . Castin, and C. Salomon, Bloch oscillations of atoms in an optical potential, Phys. Rev. Lett.76, 4508 (1996)

    work page 1996

  7. [7]

    S. R. Wilkinson, C. F. Bharucha, K. W. Madison, Q. Niu, and M. G. Raizen, Observation of atomic Wannier-Stark ladders in an accelerating optical potential, Phys. Rev. Lett.76, 4512 (1996)

    work page 1996

  8. [8]

    D. M. Gangardt and A. Kamenev, Bloch Oscillations in a One- Dimensional Spinor Gas, Phys. Rev. Lett.102, 070402 (2009)

    work page 2009

  9. [9]

    Lamacraft, Dispersion relation and spectral function of an impurity in a one-dimensional quantum liquid, Phys

    A. Lamacraft, Dispersion relation and spectral function of an impurity in a one-dimensional quantum liquid, Phys. Rev. B 79, 241105 (2009)

    work page 2009

  10. [10]

    Meinert, M

    F. Meinert, M. Knap, E. Kirilov, K. Jag-Lauber, M. B. Zvonarev, E. Demler, and H.-C. N ¨agerl, Bloch oscillations in the absence of a lattice, Science356, 945 (2017)

    work page 2017

  11. [11]

    A. M. Kosevich, Bloch oscillations of magnetic solitons as an example of dynamical localization of quasiparticles in a uni- form external field, Low Temp. Phys.27(2001)

    work page 2001

  12. [12]

    Bresolin, A

    S. Bresolin, A. Roy, G. Ferrari, A. Recati, and N. Pavloff, Oscil- lating solitons and ac Josephson effect in ferromagnetic Bose- Bose mixtures, Phys. Rev. Lett.130, 220403 (2023). 12

    work page 2023

  13. [13]

    Rabec, G

    F. Rabec, G. Chauveau, G. Brochier, S. Nascimbene, J. Dal- ibard, and J. Beugnon, Bloch oscillations of a soliton in a 1d quantum fluid, Nature Physics21, 1541 (2025)

    work page 2025

  14. [14]

    Schecter, D

    M. Schecter, D. Gangardt, and A. Kamenev, Dynamics and Bloch oscillations of mobile impurities in one-dimensional quantum liquids, Ann. Phys.327, 639 (2012)

    work page 2012

  15. [15]

    Schecter, D

    M. Schecter, D. M. Gangardt, and A. Kamenev, Quantum im- purities: from mobile Josephson junctions to depletons, New J. Phys.18, 065002 (2016)

    work page 2016

  16. [16]

    Gamayun, O

    O. Gamayun, O. Lychkovskiy, and V . Cheianov, Kinetic the- ory for a mobile impurity in a degenerate Tonks-Girardeau gas, Phys. Rev. E90, 032132 (2014)

    work page 2014

  17. [17]

    Kinetic theory for a mobile impurity in a degenerate Tonks- Girardeau gas

    M. Schecter, D. M. Gangardt, and A. Kamenev, Comment on “Kinetic theory for a mobile impurity in a degenerate Tonks- Girardeau gas”, Phys. Rev. E92, 016101 (2015)

    work page 2015

  18. [18]

    Comment on ‘Kinetic theory for a mobile impurity in a degen- erate Tonks-Girardeau gas’

    O. Gamayun, O. Lychkovskiy, and V . Cheianov, Reply to “Comment on ‘Kinetic theory for a mobile impurity in a degen- erate Tonks-Girardeau gas’ ”, Phys. Rev. E92, 016102 (2015)

    work page 2015

  19. [19]

    T. D. Lee, F. E. Low, and D. Pines, The motion of slow electrons in a polar crystal, Phys. Rev.90, 297 (1953)

    work page 1953

  20. [20]

    L. P. Pitaevskii and S. Stringari,Bose-Einstein Condensation, International Series of Monographs on Physics (Oxford Uni- versity Press, Oxford, New York, 2003)

    work page 2003

  21. [21]

    A. G. Sykes, M. J. Davis, and D. C. Roberts, Drag force on an impurity below the superfluid critical velocity in a quasi-one- dimensional Bose-Einstein condensate, Phys. Rev. Lett.103, 085302 (2009)

    work page 2009

  22. [22]

    Reichert, Z

    B. Reichert, Z. Ristivojevic, and A. Petkovi ´c, The Casimir-like effect in a one-dimensional Bose gas, New J. Phys.21, 053024 (2019)

    work page 2019

  23. [23]

    S. I. Mistakidis, A. G. V olosniev, N. T. Zinner, and P. Schmelcher, Effective approach to impurity dynamics in one- dimensional trapped Bose gases, Phys. Rev. A100, 013619 (2019)

    work page 2019

  24. [24]

    G. M. Koutentakis, S. I. Mistakidis, and P. Schmelcher, Pattern formation in one-dimensional polaron systems and temporal or- thogonality catastrophe, Atoms10, 3 (2022)

    work page 2022

  25. [25]

    Will and M

    M. Will and M. Fleischhauer, Dynamics of polaron formation in 1d Bose gases in the strong-coupling regime, New J. of Phys. 25, 083043 (2023)

    work page 2023

  26. [26]

    Hakim, Nonlinear Schr¨odinger flow past an obstacle in one dimension, Phys

    V . Hakim, Nonlinear Schr¨odinger flow past an obstacle in one dimension, Phys. Rev. E55, 2835 (1997)

    work page 1997

  27. [27]

    Majumdar and A

    S. Majumdar and A. Petkovi ´c, Relaxation dynamics of a mobile impurity injected in a one-dimensional Bose gas, arXiv:2507.10402 , to appear in Phys. Rev. A (2025)

    work page arXiv 2025

  28. [28]

    Kamenev and L

    A. Kamenev and L. I. Glazman, Dynamics of a one- dimensional spinor Bose liquid: A phenomenological ap- proach, Phys. Rev. A80, 011603 (2009)

    work page 2009

  29. [29]

    V . A. Trofimov and N. V . Peskov, Comparison of finite differ- ence schemes for the Gross Pitaevskii equation, Mathematical Modelling and Analysis14, 109 (2009)

    work page 2009

  30. [30]

    Patankar,Numerical Heat Transfer and Fluid Flow, Series in computational methods in mechanics and thermal sciences (Taylor & Francis, 1980)

    S. Patankar,Numerical Heat Transfer and Fluid Flow, Series in computational methods in mechanics and thermal sciences (Taylor & Francis, 1980)

    work page 1980

  31. [31]

    [35] and [25]

    For the definition of the critical mass see Refs. [35] and [25]

    work page

  32. [32]

    Petrov, D.M

    D.S. Petrov, D.M. Gangardt, and G.V . Shlyapnikov, Low- dimensional trapped gases, J. Phys. IV France116, 5 (2004)

    work page 2004

  33. [33]

    A. H. Castro Neto and M. P. A. Fisher, Dynamics of a heavy particle in a Luttinger liquid, Phys. Rev. B53, 9713 (1996)

    work page 1996

  34. [34]

    Petkovi ´c and Z

    A. Petkovi ´c and Z. Ristivojevic, Dynamics of a mobile impurity in a one-dimensional Bose liquid, Phys. Rev. Lett.117, 105301 (2016)

    work page 2016

  35. [35]

    Petkovi ´c, Microscopic theory of the friction force exerted on a quantum impurity in one-dimensional quantum liquids, Phys

    A. Petkovi ´c, Microscopic theory of the friction force exerted on a quantum impurity in one-dimensional quantum liquids, Phys. Rev. B101, 104503 (2020)

    work page 2020

  36. [36]

    Petkovi ´c and Z

    A. Petkovi ´c and Z. Ristivojevic, Dissipative dynamics of a heavy impurity in a Bose gas in the strong coupling regime, Phys. Rev. Lett.131, 186001 (2023)

    work page 2023

  37. [37]

    Schecter, A

    M. Schecter, A. Kamenev, D. M. Gangardt, and A. Lamacraft, Critical velocity of a mobile impurity in one-dimensional quan- tum liquids, Phys. Rev. Lett.108, 207001 (2012)

    work page 2012