A canonical approach to quantum fluctuations

[2506.21709] A canonical approach to quantum fluctuations Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Quantum Gases arXiv:2506.21709 (cond-mat) [Submitted on 26 Jun 2025 ( v1 ), last revised 3 Apr 2026 (this version, v3)] Title: A canonical approach to quantum fluctuations Authors: Joanna Ruhl , Vanja Dunjko , Maxim Olshanii View a PDF of the paper titled A canonical approach to quantum fluctuations, by Joanna Ruhl and 2 other authors View PDF HTML (experimental) Abstract: We present a canonical formalism for computing quantum fluctuations of certain discrete degrees of freedom in systems governed by integrable partial differential equations with known Hamiltonian structure, provided these models are classical-field approximations of underlying many-body quantum systems. We then apply the formalism to both the 2-soliton and 3-soliton breather solutions of the nonlinear Schrödinger equation, assuming the breathers are created from an initial elementary soliton by quenching the coupling constant. In particular, we compute the immediate post-quench quantum fluctuations in the positions, velocities, norms, and phases of the constituent solitons. For each case, we consider both the white-noise and correlated-noise models for the fluctuation vacuum state. Unlike previous treatments of the problem, our method allows for analytic solutions. Additionally, in the correlated-noise case, we consider the particle-number-conserving (also called $U(1)$-symmetry-conserving) Bogoliubov modes, i.e., modes with the proper correction to preserve the total particle number. We find that in most (but not all) cases, these corrections do not change the final result. Comments: 25 pages, 7 tables, no figures. Resubmitted to PRA 04/02/2026 Subjects: Quantum Gases (cond-mat.quant-gas) Cite as: arXiv:2506.21709 [cond-mat.quant-gas] (or arXiv:2506.21709v3 [cond-mat.quant-gas] for this version) https://doi.org/10.48550/arXiv.2506.21709 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. A, 2026 Related DOI : https://doi.org/10.1103/4zpr-5hh6 Focus to learn more DOI(s) linking to related resources Submission history From: Joanna Ruhl [ view email ] [v1] Thu, 26 Jun 2025 18:48:06 UTC (27 KB) [v2] Mon, 8 Dec 2025 17:37:26 UTC (44 KB) [v3] Fri, 3 Apr 2026 00:09:49 UTC (62 KB) Full-text links: Access Paper: View a PDF of the paper titled A canonical approach to quantum fluctuations, by Joanna Ruhl and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.quant-gas < prev | next > new | recent | 2025-06 Change to browse by: cond-mat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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