{"id":"192dfb1c-e945-4ac9-8e0b-69c7a48513ff","arxiv_id":"2505.01069","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In small 2D bosonic Josephson junctions, the direction of potential asymmetry controls whether initial transverse fragmentation and tunnel-induced longitudinal fragmentation reinforce each other, a many-body effect with no mean-field analog.","lead":"This paper simulates how asymmetric double-well traps change the tunneling of small Bose-Einstein condensates that start with fragmentation across the direction of motion. It finds that tilting the trap along the tunneling direction versus perpendicular to it has opposite effects on the competition between two types of fragmentation, an effect absent in mean-field theory.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The interference ratio Delta is a post hoc two-process decomposition of a single n2(t)/N curve; its interpretation as competing fragmentations needs a direct test.","rationale":"The reader's weakest_assumption identified the same central issue: the two-process interpretation of the dip-and-rise in n2(t)/N underlies the entire Delta measure and the direction-dependent conclusions. My stress-test agrees and sharpens it. The paper is a legitimate MCTDHB numerical study with convergence checks (M = 8 vs M = 10, 128^2 vs 256^2 grid, Supplemental C) and a parameter-free definition of Delta from the data, so there is no internal inconsistency or suggestion of improper computation. The concern is interpretive: Delta is defined from the same curve it explains, and no auxiliary quantity (e.g., natural-orbital overlap dynamics, two-body correlations, or a mean-field excited-orbital occupation) independently confirms that the POM separates transverse-fragmentation reduction from longitudinal-fragmentation development. The abstract's claim of 'no counterpart in the mean-field theory' specifically needs a mean-field calculation of the analogous quantity; the manuscript only shows mean-field initial-state and uncertainty-product data (Fig. 1), which cannot rule out a mean-field mechanism for the POM timing shifts. The unstated lambda0 is a separate quantitative gap but secondary; it strengthens the case for CONDITIONAL rather than ACCEPT. Because the qualitative trends are plausible, well-resolved numerically, and the decomposition is a reasonable interpretive framework, the verdict should remain CONDITIONAL with a request for the direct test rather than REJECT or UNVERDICTED.","tokens_in":25820,"tokens_out":1997,"duration_ms":18366,"concrete_test":"Recompute the dynamics for a representative case (e.g. V = 12, symmetric and 25Cx) and track the natural orbitals themselves: (i) decompose the POM feature by projecting n2(t)/N onto the instantaneous overlaps of the initial u-orbital with the time-dependent natural orbitals, and (ii) run the same quench at the mean-field (M = 1) level and compute the occupation of the first excited Gross-Pitaevskii eigenstate (e.g. by projecting the GP wavefunction onto the instantaneous excited orbital). If the initial drop and subsequent rise of n2(t)/N correspond to a single avoided-crossing between the two leading natural orbitals, or if a qualitatively similar POM feature appears in the mean-field projection, then Delta does not isolate two separate many-body fragmentation processes. Additionally, rerun one representative panel (Figs.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that longitudinal asymmetry delays and transverse asymmetry accelerates the time of maximal 'interference of fragmentations,' quantified by Delta = TF/LF, where the point of minimum (POM) in n2(t)/N separates an initial reduction of transversal fragmentation from a subsequent development of longitudinal fragmentation (Section IV.A.2.b, Fig. 4). The paper's own presentation makes this a post hoc reading of a single curve: TF is defined as n2(0) - n2(POM) and LF as n2(t) - n2(POM), so the shape of Delta in Figs. 5 and 11 is entirely dictated by the location and depth of the POM of the very same n2(t)/N curves used to infer the two mechanisms. Nothing in the manuscript independently verifies that the initial drop is 'transversal fragmentation being reduced' rather than, say, a dephasing/avoided-crossing transient of the natural orbitals or a mean-field-like pulse of the excited mode. The abstract's stronger claim that the asymmetry dependence of this competition 'arises purely from the many-body effects and has no counterpart in the mean-field theory' is not supported by a direct mean-field computation of the same n2(t)/N-like quantity; the only mean-field results shown are for the initial state and uncertainty product (Fig. 1), not for the POM dynamics. A second quantitative gap is that the interaction strength lambda0 is never stated numerically in Section II, while the text claims the qualitative picture is independent of it; without lambda0 or a Lambda scan, the reader cannot judge whether the reported V-ranges for interference (e.g. V = 7 to 14 for Cx, V = 7 to 16 for Cy) are robust or tuned.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the many-body tunneling dynamics of N=10 bosons in a two-dimensional bosonic Josephson junction with either longitudinal (Cx) or transverse (Cy) asymmetry, using the MCTDHB method with M=8 time-adaptive orbitals. The initial ground state is prepared with a barrier orthogonal to the tunneling direction, so that for sufficiently high barrier heights the system is transversely fragmented. The authors analyze the survival probability on the left side, the occupation of the first excited natural orbital n2(t)/N, and the transverse uncertainty product. They introduce the ratio Delta = TF/LF, where TF and LF are respectively the initial drop and the later growth of n2/N separated by its point of minimum (POM), and they interpret Delta approximately equal to one as 'maximal interference of fragmentations'. The central reported result is that longitudinal asymmetry delays, while transverse asymmetry accelerates, the time at which this POM is reached, and the paper claims that this behavior is a pure many-body effect with no mean-field counterpart.","tokens_in":26096,"tokens_out":5524,"duration_ms":59177,"significance":"If established, the paper would provide a concrete, experimentally accessible observable—the occupation of the first excited natural orbital—through which the direction of the trap asymmetry controls the competition between transverse and longitudinal fragmentation in a 2D bosonic Josephson junction. The study is systematic in barrier height and asymmetry, and the numerical convergence checks in the Supplemental Material (orbital number and grid density) strengthen the reliability of the presented MCTDHB results. The direction-dependent delay/acceleration of the POM is an interesting and potentially useful prediction for atomtronic and fragmented-BEC studies. However, the central measure Delta is currently a post hoc decomposition of a single time series, the interaction strength lambda0 is never specified, and the mean-field comparison needed to support the 'no counterpart' claim is absent; these issues must be addressed before the main claims can be considered established.","major_comments":[{"comment":"The central quantity Delta = TF/LF is a post hoc two-process decomposition of a single curve n2(t)/N. TF is defined as n2(0) - n2(POM) and LF as n2(t) - n2(POM), both using the same point of minimum (POM) of the same curve, so Delta approximately equal to one at the POM is true by construction. The informative content is therefore only the time- and parameter-dependence of the POM location, not an independent measure of 'interference' between two separate fragmentation processes. Nothing in the manuscript independently verifies that the pre-POM drop is specifically a reduction of transversal fragmentation rather than, for example, an avoided-crossing transient of the natural orbitals or a mean-field-like pulse of the excited mode. The authors should either reframe the central claim in terms of the POM location and depth, or provide a direct test of the two-process interpretation, e.g., by analyzing the overlaps between time-dependent natural orbitals and the initial g/u orbitals, or by showing that the POM behavior is absent in a Gross-Pitaevskii simulation of the same observable.","section":"Section IV.A.2.b, Fig. 4(c)"},{"comment":"The interaction strength lambda0 is never specified numerically. The Hamiltonian in Eq. (2.1) contains lambda0, and later Lambda = lambda0(N-1) is introduced, but no value is given in the main text or in the Supplemental Material. The statement in Section II that 'the choices of shape and strength of interaction between bosons do not qualitatively affect the physical phenomena described here' is an assertion without supporting data. Since the initial fragmentation threshold, the POM location, and the values of Delta all depend on the interaction, the manuscript must state lambda0 (or Lambda) and ideally show that the direction-dependent delay/acceleration of the POM persists over a range of interaction strengths.","section":"Section II, Eq. (2.1)"},{"comment":"The claim that the observed asymmetry dependence 'arises purely from the many-body effects and has no counterpart in the mean-field theory' is not supported by the data shown. The only mean-field results are the initial-state fragmentation and the uncertainty product (Fig. 1); no mean-field dynamics of the survival probability, orbital occupations, or any n2-like quantity are presented. To support this central claim, the authors should compute the time-dependent mean-field (M=1) analogues of the same observables and show that the POM and its asymmetry dependence are absent at the mean-field level. Without such a comparison, the 'no mean-field counterpart' statement remains an unsupported extrapolation.","section":"Abstract and Section V"},{"comment":"The assertion that the initial transversal fragmentation is essentially independent of the longitudinal asymmetry Cx is never demonstrated. The text states 'therefore not shown' for the Cx dependence in Fig. 1(a), and the caption claims the results are 'practically insensitive' to Cx without providing the corresponding curves or a quantitative measure. This point is load-bearing because the comparison of dynamics across different Cx values assumes identical initial conditions; if the initial fragmentation actually varies with Cx, the reported dynamical differences could be trivially attributed to different initial states. The authors should show the initial-state data for all Cx values, at least in the Supplemental Material, or explicitly quantify the variation.","section":"Section IV.A.1, Fig. 1(a)"}],"minor_comments":[{"comment":"There are several typos, for example 'tunneling pheomena' in the first paragraph should be 'tunneling phenomena', and the caption of Fig. S.3 uses 'symetric' instead of 'symmetric'.","section":"Introduction"},{"comment":"The text repeatedly refers to 'Delta = 0', 'Delta approximately equal to 1', and 'Delta much greater than 1', but the color bars in Figs. 5 and 11 are not annotated with these thresholds; please add explicit labels or a scale so the reader can connect the text to the figures.","section":"Section IV.A.2.b, Fig. 5 and Fig. 11"},{"comment":"The 'rate of density collapse' is described only qualitatively (e.g., 'the collapse slows', 'accelerates', 'is fastest'), with no extracted decay rate or fitting procedure. If this quantity is intended as a quantitative result, the authors should define an estimator (for example, an exponential decay constant of the survival-probability envelope) and report it for the relevant parameter sets.","section":"Sections IV.A.2.a and IV.B.2.a, Figs. 3 and 9"},{"comment":"The sentence 'A value of Delta corresponds to maximal interference of the transversal and longitudinal fragmentations' is missing the condition 'approximately equal to 1'; as written, it implies any value of Delta corresponds to maximal interference.","section":"Section IV.A.2.b, text near Fig. 4(c)"},{"comment":"The manuscript would benefit from a brief statement of the numerical value of lambda0 in the main text (not only in the Supplemental Material), together with the corresponding Lambda, so that the dimensionless units and the interaction regime are transparent from the outset.","section":"Section II"}],"recommendation":"major_revision","confidential_remarks":"The paper builds directly on the authors' previous work, Ref. [59], and the new element is the asymmetry dependence. The overlap is substantial, so the main text should state more clearly which results are new relative to Ref. [59]. The missing lambda0 value and the unsupported mean-field comparison are the main technical concerns; both are fixable within the scope of a revision. I do not see grounds for rejection, but the central claims need the additional support described in the major comments."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this as a numerical extension of Bhowmik & Alon (NJP 2024), not a new framework. What is actually new: a systematic scan of asymmetry along and orthogonal to the tunneling direction, showing that longitudinal tilt delays the point of minimum in n2(t)/N while transverse tilt brings it earlier. Those are clean, reproducible observations, and the MCTDHB runs are converged (M=8 vs M=10, 128^2 vs 256^2 grids are shown in the supplement). The initial-state finding – that longitudinal asymmetry leaves the initial fragmentation essentially untouched while transverse asymmetry suppresses it – is plausible and partially documented. That part is solid.\n\nThe soft spots are real but not fatal. First, the interaction strength lambda0 is never given a number. The text says the qualitative picture is insensitive to it, but without a Lambda scan the reader cannot judge the reported barrier-height windows (V=7–14 for Cx, V=7–16 for Cy). That is an easy fix. Second, the central quantity Delta = TF/LF is, as the stress-test note says, a post hoc split of one n2(t) curve. The POM is an observable; the ratio is a summary. But the interpretation that the initial drop is 'reduction of transversal fragmentation' and the later rise is 'development of longitudinal fragmentation' is not verified by tracking the natural-orbital character across the POM. The natural orbitals rotate during the dynamics; the second orbital may switch from a u-orbital to an excited g-orbital. A direct check would settle whether Delta isolates two mechanisms or one avoided-crossing pulse. Third, the abstract's 'purely from many-body effects and no counterpart in the mean-field theory' is stronger than what is shown: no mean-field survival probability or two-mode comparison is presented. Fourth, 'rate of density collapse' is used qualitatively; an extracted decay rate would strengthen the claims. These are all addressable in revision.\n\nI agree with the reader's conditional verdict. The paper deserves a serious referee: the method is appropriate, the convergence is documented, and the direction-dependence result would matter to the few-boson tunneling community. But it needs a direct validation of the interference diagnostic, a stated lambda0, and a mean-field baseline before the central claim is fully supported. I would not desk-reject it.","headline":"A numerically honest but diagnostic-heavy follow-up to Ref. [59]: the direction-dependent POM shifts are real observations, but the 'interference of fragmentations' measure needs a direct validation before the central claim is taken as established.","tokens_in":26700,"tokens_out":3131,"would_cite":false,"duration_ms":33997,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A two-dimensional bosonic Josephson junction's tilt direction determines whether the point of maximal fragmentation interference is delayed or accelerated, a purely many-body effect with no mean-field analog.","keywords":["bosonic Josephson junction","many-body tunneling","fragmentation dynamics","two-dimensional Bose-Einstein condensate","asymmetric double well","survival probability","natural orbital occupations","uncertainty product"],"falsifier":"Re-run the same quench dynamics with a single-orbital mean-field equation: because that description cannot fragment, it should show no direction-dependent shift of the point of minimum in $n_2(t)/N$; if the envelope of the survival probability or the density variance reproduces the delay/acceleration pattern anyway, the central 'purely many-body' claim fails. Alternatively, compute the overlap of the two lowest natural orbitals through the dip: if they exchange character at the point of minimum, the two 'fragmentation processes' are one avoided crossing.","tokens_in":25556,"feed_emoji":"⚛️","tokens_out":11028,"duration_ms":110353,"temperature":0.7,"pith_summary":"This paper studies how the direction of asymmetry in a two-dimensional bosonic Josephson junction controls the many-body tunneling dynamics of repulsively interacting bosons. Starting from a ground state that is already fragmented across the transverse direction, the authors let it tunnel through a junction tilted either along or across the tunneling direction. They claim that the two tilt directions have opposite effects: longitudinal asymmetry delays, while transverse asymmetry accelerates, the moment at which the occupation of the first excited orbital reaches its minimum, which they read as maximal interference between transverse and longitudinal fragmentation. They further find that self-trapping suppresses this interference while resonant tunneling enhances it, and that none of these effects appears in a single-orbital mean-field description. The significance is that geometric asymmetry becomes a directional control knob for correlation-driven tunneling dynamics.","feed_headline":"Which way you tilt a bosonic junction shifts fragmentation interference","feed_subtitle":"Tilting along the tunnel delays the point of maximal fragmentation interference; tilting across it accelerates it.","key_machinery":"The machinery is the time evolution of natural-orbital occupations, especially $n_2(t)/N$, computed with a multiconfigurational time-dependent variational treatment ($N=10$ bosons, $M=8$ time-adaptive orbitals, on a $128\\times128$ grid). When the initial state is fragmented, the first excited orbital is the odd transverse (ungerade) orbital; its occupation first falls as transverse fragmentation is reduced and then rises as longitudinal fragmentation develops. The central diagnostic is the ratio $\\Delta = \\mathrm{TF}/\\mathrm{LF}$ of these two changes, and the location of the point of minimum (POM) is the event whose timing is compared across symmetric, longitudinally asymmetric, and transversely asymmetric junctions. The transverse uncertainty product $U(t)=\\frac{1}{N^2}\\Delta^2\\hat{Y}\\,\\Delta^2\\hat{P}_Y$ serves as a second probe: it oscillates when the two fragmentations compete and stays almost frozen when one dominates.","core_discovery":"The paper's central claim is that, for a fixed barrier height, initial transverse fragmentation is essentially insensitive to asymmetry along the tunneling direction but is reduced by asymmetry orthogonal to it, and that the subsequent tunneling dynamics show a direction-dependent competition between longitudinal fragmentation, built up during tunneling, and transverse fragmentation, present from the start. The diagnostic is the occupation of the first excited natural orbital, $n_2(t)/N$: it falls from its initial value to a point of minimum (POM) and then rises again. The paper reads the falling part as reduction of transverse fragmentation (TF) and the rising part as development of longitudinal fragmentation (LF), with the ratio $\\Delta = \\mathrm{TF}/\\mathrm{LF}$ quantifying their interference. Longitudinal tilt delays the POM, transverse tilt brings it earlier, self-trapping suppresses the interference, and the resonant-tunneling asymmetry enhances it. Because a single-orbital mean-field state remains fully condensed, these direction-dependent timing shifts have no mean-field counterpart and are presented as a purely many-body effect of correlated tunneling.","pith_inferences":["The 'two processes' reading of the dip in $n_2(t)/N$ could be tested against an alternative: if the dip is an avoided crossing between natural orbitals, the same timing shifts might be describable as a spectral Landau-Zener problem, and computing the orbital overlaps at the POM would distinguish the two descriptions.","The direction-dependent POM shift suggests a practical metrological or atomtronic use: the time of maximal fragmentation interference is a correlation-based readout of tilt direction and magnitude that a mean-field model cannot mimic.","Because the paper fixes one unstated interaction strength, a natural robustness test is to vary $\\lambda_0$ and $N$ while keeping $\\Lambda = \\lambda_0(N-1)$ fixed and to check whether the longitudinal-delay / transverse-acceleration pattern survives.","The same diagnostic could be carried into dipolar or supersolid setups, where the competition between the two fragmentations might appear at different barrier heights or acquire additional long-range interaction effects."],"forward_implications":["A longitudinal tilt postpones the moment at which the first-excited-orbital occupation bottoms out, until the system crosses into self-trapping, after which the collapse of the survival-probability oscillations accelerates again toward the resonant condition.","A transverse tilt advances that same moment and also reduces the initial transverse fragmentation itself, so the two directions of asymmetry have opposite effects on the fragmentation competition.","The rate of density collapse in the survival probability tracks the interference: it slows with self-trapping, speeds up as the barrier height grows through the intermediate range, and under resonant tunneling it stays faster than at small asymmetry but slower than in the symmetric case.","The normalized uncertainty product along the transverse direction becomes a diagnostic of the fragmentation competition: oscillating when the two fragmentations compete and nearly constant when either one dominates.","Since none of these effects appears in a single-orbital mean-field description, an accurate description of fragmented-state tunneling in asymmetric two-dimensional junctions must retain multiple orbitals.","The same direction-dependent fragmentation competition is expected to shape other correlation-sensitive observables beyond the survival probability and uncertainty product.","If the two-process interpretation holds, the timing of maximal fragmentation interference could serve as a probe of how correlations redistribute among natural orbitals during tunneling."],"supporting_citations":[{"why":"Establishes the interference of longitudinal and transversal fragmentations in a symmetric two-dimensional Josephson junction, the phenomenon this paper extends to asymmetric junctions.","marker":"[59]"},{"why":"Supplies the exact quantum dynamics of a bosonic Josephson junction and the standard many-body tunneling and fragmentation baseline.","marker":"[19]"},{"why":"Provides the longitudinal and transversal resonant tunneling conditions for interacting bosons in a two-dimensional Josephson junction, used for the resonant asymmetry parameter.","marker":"[26]"},{"why":"Supplies the time-dependent variational ansatz used for the many-body wavefunction and the multiconfigurational method behind the numerical results.","marker":"[68]"},{"why":"Provides the software implementation used to produce the numerical many-body dynamics and ground states.","marker":"[82]"},{"why":"Defines the repulsive Gaussian pairwise interaction potential used in the Hamiltonian.","marker":"[66]"},{"why":"Establishes the variance-based uncertainty product as a correlation-sensitive probe, the basis of the transverse uncertainty diagnostics.","marker":"[87]"},{"why":"Contains the convergence checks with more orbitals and a finer grid that support the numerical reliability of the reported quantities.","marker":"[84]"}],"fun_headline_variants":["Tilt direction controls fragmentation interference timing in bosonic junction","Bosonic junction: tilt along tunnel delays interference peak, across speeds it","Asymmetry shifts fragmentation interference in 2D bosonic tunneling","Many-body tunneling: tilt direction determines when fragmentation interference peaks"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole timing comparison stands on treating the dip-and-rise of the second-orbital occupation as two separate fragmentation processes, and on the single fixed interaction strength being representative; if the dip is one dynamical feature or the interaction strength changes the picture, the delay-versus-acceleration conclusion would not isolate two competing mechanisms.","fun_headline_variants_meta":{"raw":{"variants":["Tilt direction controls fragmentation interference timing in bosonic junction","Bosonic junction: tilt along tunnel delays interference peak, across speeds it","Asymmetry shifts fragmentation interference in 2D bosonic tunneling","Many-body tunneling: tilt direction determines when fragmentation interference peaks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000402,"raw_usage":{"total_tokens":2134,"prompt_tokens":1017,"completion_tokens":1117,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":633,"completion_tokens_details":{"reasoning_tokens":1045}},"tokens_in":633,"tokens_out":1117,"duration_ms":9507,"temperature":1.0,"reasoning_tokens":1045,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:27:37.924850+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the same quench dynamics with a single-orbital mean-field equation: because that description cannot fragment, it should show no direction-dependent shift of the point of minimum in $n_2(t)/N$; if the envelope of the survival probability or the density variance reproduces the delay/acceleration pattern anyway, the central 'purely many-body' claim fails. Alternatively, compute the overlap of the two lowest natural orbitals through the dip: if they exchange character at the point of minimum, the two 'fragmentation processes' are one avoided crossing.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the interference of longitudinal and transversal fragmentations in a symmetric two-dimensional Josephson junction, the phenomenon this paper extends to asymmetric junctions."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the longitudinal and transversal resonant tunneling conditions for interacting bosons in a two-dimensional Josephson junction, used for the resonant asymmetry parameter."},{"cited_title":"Amico, M","cited_arxiv_id":null,"evidence_quote":"Supplies the time-dependent variational ansatz used for the many-body wavefunction and the multiconfigurational method behind the numerical results."},{"cited_title":"Chakrabarti, A","cited_arxiv_id":null,"evidence_quote":"Provides the software implementation used to produce the numerical many-body dynamics and ground states."},{"cited_title":"Dumke, Z","cited_arxiv_id":null,"evidence_quote":"Defines the repulsive Gaussian pairwise interaction potential used in the Hamiltonian."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Contains the convergence checks with more orbitals and a finer grid that support the numerical reliability of the reported quantities."}],"review_version":1}