{"id":"e2866a90-975b-44b1-8fb7-f68e0ceb1ff6","arxiv_id":"2611.07657","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Phase locking in tunnel-coupled 1D condensates is caused by the local curvature of the density profile, with a timescale independent of tunnel coupling and captured by linearized modes.","lead":"A trapped one-dimensional superfluid with a curved density profile spontaneously drives two tunnel-coupled sides toward a locked relative phase, on a time set by the local curvature alone. The result gives an experimentally testable, parameter-free explanation for phase locking that the homogeneous integrable theory cannot produce.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek/deepseek-v4-flash","headline":"The central drift formula Eq. (2) is analytically grounded, but the persistent phase-locked plateau and the suppression of revivals by nonlinearity rest solely on TWA at late times, with no exact-quantum cross-check; the relaxation claim remains conditional.","rationale":"The reader and I identify the same weakest link. The analytic result Eq. (2) is well supported: the inverted-oscillator derivation in Appendix C is a standard local large-mu analysis valid before the light-cone time, and Fig. S.5 shows that the linearized TWA matches it. The same cannot be said for the post-light-cone persistent locking, which is central to describing the experiment as relaxation. There the linear model fails by the paper's own Fig. S.5, and the only evidence for nonlinear suppression of revivals is TWA. The paper itself states in Appendix A that TWA loses validity at larger beta, and the numerical details are deferred to an unpublished same-author arXiv preprint [17]. No exact quantum method (TCSA, MPS, or exact diagonalization) is applied to the inhomogeneous model. This does not make the paper wrong: the semiclassical regime beta = 0.343 is plausibly well captured by TWA, and the homogeneous comparison cited as [9] supports TWA in that regime. But it makes the persistent-locking component conditional rather than established. The arc-profile slope deviation is a secondary quantitative caveat that reinforces the need for an independent check but is not by itself disqualifying. The fitted exponents -0.974(22) and -0.936(17) are close to -1, and the scaling collapse in t/tau_rel is visually convincing; the remaining discrepancy is the kind of finite-size and fit-window systematic the authors describe. On balance, the reader's CONDITIONAL verdict is the appropriate one, and my read does not change it.","tokens_in":18865,"tokens_out":15398,"duration_ms":108653,"concrete_test":"Perform an independent exact-quantum benchmark of the same quench protocol using tensor-network (MPS) time evolution of a lattice-regularized inhomogeneous sine-Gordon model with mR ~ 8–16, beta = 0.343, the same massless-ground-state initial condition for nonzero modes and squeezed zero mode, and compare C(t) = <cos phi(t,0)> with TWA over 0 < t < 4R, including the first light-cone echo. If the exact C(t) exhibits revivals of the linear-model amplitude after t*, the nonlinear-suppression claim is unsupported; if it matches TWA, the persistent phase-locking part of the central claim is validated. Convergence checks in bond dimension and lattice spacing would make the comparison decisive.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing piece is not Eq. (2) itself: the 1/cosh envelope is derived in the linearized model (Appendix C, Eq. S.32) and is cross-checked against TWA in Fig. S.5. What makes the paper a relaxation-to-phase-locking story rather than a transient linear dephasing effect is the statement that non-linearity suppresses the excitation returning from the edges and that C(t) settles at 0.87–0.89 beyond the light-cone time. That statement rests entirely on TWA simulations of the nonlinear sine-Gordon model: the linearized theory revives almost fully (Fig. S.5), so the persistent lock is a purely nonlinear, purely TWA-based result. Appendix A acknowledges that TWA loses validity for larger beta, and no exact-quantum calculation for the inhomogeneous quench is provided; the numerical implementation is deferred to the unpublished same-author preprint [17]. If TWA overestimates nonlinear damping of the returning boundary echo, the long-time locked plateau would be an artifact. The transient drift before t* and its curvature-determined timescale would survive, but the relaxation-to-a-phase-locked-state claim in the abstract would not be established. A secondary, smaller quantitative caveat is the arc-profile fitted exponent -0.936(17) versus the predicted -1, a deviation of about four standard errors that the paper attributes to fit-window and finite-size effects but does not fully resolve.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek/deepseek-v4-flash","summary":"The paper addresses the conflict between homogeneous integrable sine-Gordon theory, which predicts no relaxation to a phase-locked state, and experiments on tunnel-coupled one-dimensional condensates that observe phase locking. The authors study the inhomogeneous sine-Gordon model with a slowly varying density profile f(z), using truncated Wigner approximation (TWA) simulations for the full nonlinear model and an asymptotic analysis of the linearized model. Their central result is Eq. (2): near a density maximum, the relative phase at the trap centre drifts as 1/sqrt(cosh(t/tau_rel)), with 1/tau_rel = (1/R) sqrt(-f''(0)/2), independent of the tunnel coupling. This prediction is tested by fitting relaxation times from TWA data for quadratic and arc profiles, by scaling collapse in t/tau_rel, and by comparison with the homogeneous and ramp profiles. The paper concludes that the experimentally observed phase locking is a local, curvature-controlled linear-mode effect of the trap, and that nonlinearity suppresses the returning boundary echoes, leading to a persistent locked plateau.","tokens_in":19270,"tokens_out":10316,"duration_ms":70960,"significance":"If correct, the result provides a concrete, parameter-free resolution of a longstanding puzzle: the experimentally observed phase locking is neither homogeneous integrable dynamics nor primarily nonlinear thermal relaxation, but a universal local effect of the trap curvature. The main analytic formula Eq. (2) is derived, not fitted, and the paper explicitly checks it against TWA data over a range of system sizes and two density profiles, including an analytic sqrt(2) ratio between quadratic and arc profiles. The derivation in Appendix C is a clean inverted-oscillator calculation with stated validity t = O(1), mu to infinity, and the authors themselves bound the breakdown by O(log mu). The physical conversion to tau_rel = sqrt(2)/omega_parallel for a harmonic trap gives a falsifiable experimental prediction. The main weakness is that the long-time phase-locked plateau and the suppression of revivals rest entirely on TWA simulations of the nonlinear model, with no exact-quantum cross-check; this part of the claim is therefore conditional rather than established.","major_comments":[{"comment":"The claim that the system relaxes to a persistent phase-locked state, rather than merely exhibiting a transient linear drift, rests on the statement that beyond the light-cone time C(t) settles at 0.87-0.89 and that nonlinearity suppresses the returning boundary excitation. This part is not supported by the analytic derivation: Fig. S.5 shows that the linearized model revives almost fully, so the persistence of the plateau is a purely nonlinear effect. The only evidence for this nonlinear effect is TWA, and Appendix A acknowledges that TWA loses validity for larger beta. No exact-quantum calculation, such as a truncated conformal space approach for the inhomogeneous trap, and no independent classical-field or other cross-check of the post-light-cone window is provided. I therefore consider the persistent-locking conclusion conditional on TWA accuracy at late times. In addition, for the largest system size in Fig. 1b (R = 4 R0), the plotted window ends at t/R about 2.77, before the light-cone time t* = pi R, so the claimed plateau is directly demonstrated only for the smaller systems.","section":"Results, Fig. 1b and Fig. S.5; Appendix A","authors_acknowledge":"In this deep quantum regime, the Truncated Wigner Approximation (TW A) eventually loses its validity.","authors_acknowledge_p":0.64},{"comment":"The central nonlinear TWA results depend on numerical implementation details that are delegated to Ref. [17], an unpublished same-author arXiv preprint. The Letter states that 'the detailed numerical implementation and parameter choices can be found in Ref. [17]', but the reader of the present manuscript cannot assess discretization, sampling, regularization, or convergence from the Letter alone. Because these simulations are the only test of the full nonlinear model and the only evidence for the persistent locked plateau, the implementation should be described in the main text or supplement, or a published version of Ref. [17] should be provided.","section":"Model and quench protocol; numerical implementation","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The fit of the arc profile gives exponent -0.936(17), which is about four standard errors from the predicted -1, while the quadratic fit -0.974(22) is consistent. The text attributes the arc deviation to fit-window and finite-size effects but provides no quantitative support for this attribution. Since Fig. 4 is the direct, quantitative test of the parameter-free prediction m tau = 1/epsilon, this discrepancy needs a systematic analysis of fit-window dependence and finite-size corrections; without it, the statement that Eq. (2) is followed 'over more than a decade in epsilon' is stronger than the data demonstrate.","section":"Fig. 4 and Eq. (S.2)","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The fit function appears to be missing a division sign: the intended form is presumably C_fit(t|A,tau,delta) = 1 - A^{1/2}/cosh(t/tau) + delta, consistent with Eq. (S.20). Please correct the typo and define A in terms of phi0, sigma0, and delta.","section":"Eq. (S.2)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The supplement states that time t is measured in units of R, but Eq. (2) and the surrounding main text are written in dimensionful form. Please state the conversion explicitly when Eq. (2) is introduced so that the dimensionless supplement formulas and the dimensionful physical formulas are not confused.","section":"Appendix B, after Eq. (S.3)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The vertical axis label 'm tau' should be defined precisely: tau is the fitted relaxation time from Eq. (S.2), while the analytic result is tau_rel from Eq. (2). Please clarify the relationship between the two symbols, especially because the fit extracts tau rather than predicting it.","section":"Fig. 4","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The normal-ordering prescription uses the cutoff a both as a lattice spacing and in 'log a + reg.'. Please state that phi^2 is evaluated on a lattice with spacing a and that the additive constant is adjusted so that the same regularization is used in the TWA simulations.","section":"Appendix B, Eq. (S.12)-(S.13)","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"The analytic result and the scaling collapse are well supported and likely of significant interest to the quantum-gas and non-equilibrium field-theory communities. The main risk is the TWA dependence of the long-time plateau, which is exactly the part of the paper that goes beyond a transient linear effect. I would not recommend acceptance until either an independent check of the nonlinear late-time dynamics is supplied or the persistent-locking claim is appropriately weakened. The deferred numerical implementation in Ref. [17] should also be made available to the reviewers in a verifiable form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek/deepseek-v4-flash","letter":"The one thing to know: this paper actually answers the question its predecessors left open. Refs [16] and [17] reproduced phase locking numerically, but nobody had said what sets the timescale. Here it is, in Eq. (2): the drift rate is determined solely by the local curvature of the density profile at its maximum, independent of tunnel coupling, giving tau = sqrt(2)/omega_parallel for a harmonic trap. That is a real, clean, testable claim.\n\nWhat is new and good: the Appendix C derivation is a standard Liouville-coordinate + inverted-oscillator calculation, honestly scoped (validity t = O(1), mu -> infinity, breakdown bounded by O(log mu), stated in the text). The parameter-free prediction m*tau = 1/epsilon is checked against fitted relaxation times over more than a decade, and the quadratic-vs-arc sqrt(2) ratio comes out as predicted. The linearized model is cross-checked against TWA quantitatively until revival time (Fig. S.5). The comparison of quadratic, arc, ramp and homogeneous profiles cleanly separates curvature effects from finite-size effects, and the authors are careful to distinguish the drift (local, curvature-set) from revivals (global, finite-size). The universal drift is an intermediate window, and they say so.\n\nSoft spots, in proportion:\n\n1. The load-bearing late-time claim — that nonlinearity suppresses the returning boundary echo and C(t) settles at 0.87-0.89 — rests entirely on TWA. The linearized theory revives almost fully (Fig. S.5), so the persistent lock is a purely nonlinear, purely TWA-based statement. The authors acknowledge TWA loses validity at larger beta (Appendix A), and the mechanism is explicitly semiclassical anyway. So this is not a qualitative hole in the drift mechanism; it is a quantitative reliance in the one place where a TWA artifact would change the abstract's story. An exact cross-check (even small-system TCSA) or a classical-equation comparison in the revival window would settle it. This is the main reason the paper is conditional rather than clean accept.\n\n2. The numerics are delegated to the unpublished same-author preprint [17], with no code or data in this submission. Minor-to-moderate reproducibility concern.\n\n3. Minor: the arc-profile fitted exponent is -0.936(17) against the predicted -1, about four standard errors off, attributed to fit-window and finite-size effects. The authors flag residual fit-window dependence themselves. Against a decade of agreement elsewhere, this is minor.\n\nOne transparency note that is a plus, not a flaw: the acknowledgments credit an AI assistant for substantial help with the asymptotic formula, with the authors verifying all results. That is the right way to do it.\n\nWho this is for: anyone working on sine-Gordon, tunnel-coupled condensates, or integrability-breaking in near-integrable systems. The mechanism — the trap reshapes collective modes into an inverted oscillator, curvature sets the scale — is physically clean and should survive scrutiny.\n\nRecommendation: send it to referees. A serious referee should push on the TWA-late-time question and the unpublished numerical implementation, but the core result is derived, parameter-free, and worth publishing. I would cite it.","headline":"The curvature-only phase-locking timescale is a genuine result backed by a sound asymptotic derivation and a parameter-free check over a decade in epsilon; the real weakness is that the long-time locked plateau rests entirely on TWA with no exact-quantum cross-check.","tokens_in":19715,"tokens_out":2227,"would_cite":true,"duration_ms":16350,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["03.75.Lm","03.75.Kk"],"model":"deepseek/deepseek-v4-flash","headline":"A slowly varying trap density — not tunnel coupling or homogeneous integrable dynamics — drives the phase locking observed in tunnel-coupled one-dimensional condensates, on a timescale set only by the density curvature at its maximum.","keywords":["sine-Gordon model","phase locking","truncated Wigner approximation","tunnel-coupled Bose gases","one-dimensional condensates","inhomogeneous quench dynamics","Josephson oscillations","universal scaling collapse"],"falsifier":"Measure the phase-locking onset time while sweeping the longitudinal trap frequency $\\omega_\\parallel$ at fixed tunnel coupling and central density: the paper predicts $\\tau_{\\rm rel}=\\sqrt{2}/\\omega_\\parallel$ with no dependence on $J$, so a locking time that tracks the coupling or scales differently with $\\omega_\\parallel$ would falsify the curvature-only mechanism. A complementary check is a fully quantum simulation of the inhomogeneous model at large $\\beta$, where the paper itself notes TWA loses validity: the mechanism predicts locking disappears as $\\beta$ grows, so persistent locking at large $\\beta$ would show the effect is not purely the semiclassical curvature drift.","tokens_in":20338,"feed_emoji":"⚛️","tokens_out":16197,"duration_ms":90885,"temperature":0.7,"pith_summary":"Experiments on tunnel-coupled one-dimensional Bose condensates show the relative phase settling into a phase-locked state, a fate the homogeneous, integrable sine-Gordon model — the standard description of these systems — does not predict. This paper claims the trap itself is responsible: a slowly varying density profile, with curvature small on the correlation-length scale, makes the relative phase near the density maximum drift toward zero on a timescale set by the curvature alone, $1/\\tau_{\\rm rel}=(1/R)\\sqrt{-f''(0)/2}$, independent of the tunnel coupling. The drift is a linear effect of the inhomogeneous mode structure, already visible in the linearised theory where the modes near the density maximum behave like an inverted harmonic oscillator, rather than nonlinear thermal relaxation. If the claim holds, the experimentally observed locking becomes a universal, parameter-free consequence of trap shape, and the long-time dynamics of trapped near-integrable quantum fields are governed by a single local scale.","feed_headline":"Trap curvature, not tunneling, sets the phase-locking time","feed_subtitle":"Slowly varying density drives a universal drift of the relative phase toward zero on a timescale set by curvature alone.","key_machinery":"The load-bearing object is the inhomogeneous sine-Gordon action (1) with a slowly varying density profile $f(z)=1-z^2$ (harmonic trap) and small parameter $\\epsilon=\\sqrt{-f''(0)/2}/m\\ll 1$, which for the harmonic trap is precisely $mR\\gg 1$. The argument is carried by the linearised mode structure: in the Liouville coordinate $dy/dz=1/\\sqrt{f(z)}$, with modes rescaled by $f^{1/4}$, the spatial operator near the density maximum becomes an inverted harmonic oscillator $-\\partial_\\eta^2-\\eta^2/4$ with rate $\\nu=\\sqrt{-f''(z_*)/2}/R$, whose propagator supplies the $\\sqrt{\\cosh(t/\\tau_{\\rm rel})}$ envelope in Eq. (2) while the bare mass at the centre supplies the $\\cos(m\\sqrt{f(0)}\\,t)$ factor. That asymptotic formula, $1/\\tau_{\\rm rel}=(1/R)\\sqrt{-f''(0)/2}$, is the identity that carries the claim: it is a parameter-free prediction that the full sine-Gordon dynamics, simulated with the truncated Wigner approximation (quantum fluctuations sampled as stochastic initial conditions, with classical equations of motion thereafter), matches over more than a decade in $\\epsilon$ with fitted exponents $-0.97(2)$ (quadratic) and $-0.94(2)$ (arc). Two further elements close the argument: the scaling collapse in $t/\\tau_{\\rm rel}$ that identifies the curvature as the controlling scale across system sizes and profile shapes, and the demonstration that nonlinearity suppresses the excitation returning from the edges, so the locked state persists beyond the light-cone time.","core_discovery":"The paper's central claim is that the phase locking observed in tunnel-coupled one-dimensional condensates, which the homogeneous integrable sine-Gordon theory cannot produce, is generated by the trap itself. In the post-quench dynamics of the inhomogeneous sine-Gordon model, a slowly varying density profile creates a second, parametrically later dynamical regime: the relative phase distribution near the density maximum drifts toward $\\varphi=0$, so the centre coherence $C(t)=\\langle\\cos\\varphi(t,0)\\rangle$ rises on a timescale $1/\\tau_{\\rm rel}=(1/R)\\sqrt{-f''(0)/2}$ that is fixed by the curvature of the density profile at its maximum and is independent of the tunnel coupling. The drift is already present in the linearised theory: near a non-degenerate maximum of the profile the collective modes of the relative phase reduce to an inverted harmonic oscillator, giving $\\langle\\varphi(t,0)\\rangle\\simeq\\varphi_0\\cos(m\\sqrt{f(0)}\\,t)/\\sqrt{\\cosh(t/\\tau_{\\rm rel})}$, with the fluctuations $\\langle\\varphi^2(t,0)\\rangle$ decaying as $1/\\cosh(t/\\tau_{\\rm rel})$ so that $C(t)$ drifts upward. Nonlinearity does not cause the drift; its role is to damp the fast Josephson oscillations and to suppress the boundary echoes that, in the linearised theory, would revive the phase after the light-cone time $t^*=\\pi R$. When time is rescaled by the analytic $\\tau_{\\rm rel}$, the dynamics for different system sizes and for quadratic versus arc-shaped profiles collapse onto a single curve, and in physical units the prediction is parameter-free: $\\tau_{\\rm rel}^{-1}=\\sqrt{-g_{1D}\\rho_0''(x_*)/2M}$, which for a harmonic trap reduces to $\\sqrt{2}/\\omega_\\parallel$.","pith_inferences":["A cleaner experimental test would engineer a flat-topped or zero-curvature central density profile inside an otherwise bound trap: the paper's mechanism predicts no drift inside the light-cone window, so locking appearing there would point to a non-curvature cause.","The inverted-harmonic-oscillator reduction is generic, so any near-integrable one-dimensional field theory in a slowly varying trap whose effective mass has a local extremum should show the same $1/\\sqrt{\\cosh(t/\\tau_{\\rm rel})}$ envelope for observables tied to that region; probing relative-phase quadratures of other coupled low-dimensional systems would test how far the universality extends.","Since $\\tau_{\\rm rel}\\propto R$, the drift is roughly 90% complete before the first edge echo returns at $t^*=\\pi R$; simulating or measuring the collapse over a wider range of $mR$ than the values 25.5–102 used here would sharpen the fitted exponent and the predicted $\\sqrt{2}$ ratio between quadratic and arc profiles.","The paper leaves the quantitative boundary of the semiclassical regime open; an exact quantum simulation of the inhomogeneous model at large $\\beta$ (where the truncated Wigner approximation is acknowledged to lose validity) could map the $\\beta^2$ suppression of the locked plateau and determine whether any locking survives deep in the quantum regime."],"forward_implications":["Changing the tunnel coupling over a wide range should leave the phase-locking timescale untouched: the locking rate is a direct readout of the density curvature at the trap centre, not of the coupling strength.","In a harmonically trapped condensate the prediction is a single closed-form number, $\\tau_{\\rm rel}=\\sqrt{2}/\\omega_\\parallel$ with $\\omega_\\parallel$ the longitudinal trap frequency, which an experiment can check directly.","Because the dynamics collapse when time is rescaled by $\\tau_{\\rm rel}$, the same cosh-envelope drift should appear for any slowly varying profile with a non-degenerate density maximum, while flat or ramped profiles should show no drift until edge signals return.","The onset and the persistence of locking are distinct effects: the drift itself is a linear collective-mode phenomenon, while nonlinearity only damps Josephson oscillations and suppresses boundary revivals — so the late-time plateau is nonlinear, but its timescale is not.","Phase locking is a semiclassical phenomenon: stronger quantum fluctuations (larger $\\beta$) suppress the drift, and it disappears entirely for sufficiently large $\\beta$."],"supporting_citations":[{"why":"Reports the experimental observation of relaxation to a phase-locked state in a one-dimensional bosonic Josephson junction; the phenomenon this paper sets out to explain.","marker":"[15]"},{"why":"Supplies the homogeneous universal rephasing prediction, the baseline showing universal dephasing at short times that the inhomogeneous system matches before locking.","marker":"[8]"},{"why":"Three-dimensional stochastic classical-field simulations that first reproduced the relaxation in a harmonic trap and introduced the f(z)=1−z² profile; the attribution the paper refines.","marker":"[16]"},{"why":"Earlier effective one-dimensional sine-Gordon–Luttinger simulations showing phase locking is recovered once the trap background is included; also the source of the numerical implementation and parameters.","marker":"[17]"},{"why":"The Supplemental Material containing the asymptotic large-mR solution of the linearised theory and the proof of Eq. (2) for the locking timescale.","marker":"[29]"},{"why":"The truncated Wigner approximation method with quantum corrections that underlies all full sine-Gordon numerics in the paper.","marker":"[22]"},{"why":"The quantum sine-Gordon post-quench and rephasing result establishing the homogeneous plateau that the trapped system leaves on the timescale tau_rel.","marker":"[9]"}],"fun_headline_variants":["Curvature clocks phase locking in coupled condensates","Trap curvature sets the phase-locking rate","Phase locking time comes from density curvature, not tunneling","Density curvature alone drives universal phase locking"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The load-bearing premise is that the truncated Wigner approximation quantitatively captures the post-quench dynamics of the inhomogeneous sine-Gordon model across the entire phase-locking window, including the suppression of boundary echoes; the authors rely on TWA for all full-model numerics, acknowledge that it loses validity as $\\beta$ grows, and provide no independent exact-quantum calculation for the inhomogeneous trap.","fun_headline_variants_meta":{"raw":{"variants":["Curvature clocks phase locking in coupled condensates","Trap curvature sets the phase-locking rate","Phase locking time comes from density curvature, not tunneling","Density curvature alone drives universal phase locking"]},"model":"deepseek/deepseek-v4-flash","effort":"low","cost_usd":9.2e-05,"raw_usage":{"cost":9.19464e-05,"is_byok":false,"cost_details":{"upstream_inference_cost":9.19464e-05,"upstream_inference_prompt_cost":3.51624e-05,"upstream_inference_completions_cost":5.6784e-05},"total_tokens":1460,"prompt_tokens":1148,"completion_tokens":312,"prompt_tokens_details":{"audio_tokens":0,"video_tokens":0,"cached_tokens":952,"cache_write_tokens":0},"completion_tokens_details":{"audio_tokens":0,"image_tokens":0,"reasoning_tokens":263}},"tokens_in":1148,"tokens_out":312,"cost_source":"openrouter_usage","duration_ms":4480,"image_pages":[],"temperature":1.0,"billed_attempts":1,"reasoning_tokens":263,"transport_provider":"openrouter","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-11-06T04:10:13.939041+00:00","model_set":{"reader":"deepseek/deepseek-v4-flash"},"falsifier":"Measure the phase-locking onset time while sweeping the longitudinal trap frequency $\\omega_\\parallel$ at fixed tunnel coupling and central density: the paper predicts $\\tau_{\\rm rel}=\\sqrt{2}/\\omega_\\parallel$ with no dependence on $J$, so a locking time that tracks the coupling or scales differently with $\\omega_\\parallel$ would falsify the curvature-only mechanism. A complementary check is a fully quantum simulation of the inhomogeneous model at large $\\beta$, where the paper itself notes TWA loses validity: the mechanism predicts locking disappears as $\\beta$ grows, so persistent locking at large $\\beta$ would show the effect is not purely the semiclassical curvature drift.","supporting_citations":[{"cited_title":"Inhomogeneous quantum quenches in the sine-Gordon theory","cited_arxiv_id":"2109.06869","evidence_quote":"Reports the experimental observation of relaxation to a phase-locked state in a one-dimensional bosonic Josephson junction; the phenomenon this paper sets out to explain."},{"cited_title":"Mass Scale in the Sine-Gordon Model and its Reductions,","cited_arxiv_id":null,"evidence_quote":"Supplies the homogeneous universal rephasing prediction, the baseline showing universal dephasing at short times that the inhomogeneous system matches before locking."},{"cited_title":"Relaxation to a Phase-locked Equilibrium State in a One-dimensional Bosonic Josephson Junction","cited_arxiv_id":"1711.06635","evidence_quote":"Three-dimensional stochastic classical-field simulations that first reproduced the relaxation in a harmonic trap and introduced the f(z)=1−z² profile; the attribution the paper refines."},{"cited_title":"Relaxation in an Extended Bosonic Josephson Junction","cited_arxiv_id":"2012.05885","evidence_quote":"Earlier effective one-dimensional sine-Gordon–Luttinger simulations showing phase locking is recovered once the trap background is included; also the source of the numerical implementation and parameters."},{"cited_title":"Prethermalization Revealed by the Relaxation Dynamics of Full Distribution Functions","cited_arxiv_id":"1212.4645","evidence_quote":"The Supplemental Material containing the asymptotic large-mR solution of the linearised theory and the proof of Eq. (2) for the locking timescale."},{"cited_title":"Modulational instabilities in Josephson oscillations of elongated coupled condensates","cited_arxiv_id":"physics/0502050","evidence_quote":"The truncated Wigner approximation method with quantum corrections that underlies all full sine-Gordon numerics in the paper."},{"cited_title":"Universal Rephasing Dynamics after a Quantum Quench via Sudden Coupling of Two Initially Independent Condensates","cited_arxiv_id":"1211.5145","evidence_quote":"The quantum sine-Gordon post-quench and rephasing result establishing the homogeneous plateau that the trapped system leaves on the timescale tau_rel."}],"review_version":1}