Evolution of the eigenvalues and eigenstates of the single-particle reduced density operator during two-particle scattering

Quantum Physics arXiv:2512.02239 (quant-ph) [Submitted on 1 Dec 2025] Title:Evolution of the eigenvalues and eigenstates of the single-particle reduced density operator during two-particle scattering Authors:Arsam Najafian, Mark Van Raamsdonk View a PDF of the paper titled Evolution of the eigenvalues and eigenstates of the single-particle reduced density operator during two-particle scattering, by Arsam Najafian and 1 other authors View PDF HTML (experimental) Abstract:A particle initially in a pure state but interacting with some environment evolves into a discrete ensemble of pure states, the eigenstates of its reduced density operator, with ensemble probabilities given by the corresponding eigenvalues. In this work, we use numerics to present explicit results for the time-dependence of these eigenvalues and eigenstates for simple scattering experiments in one and two dimensions. This provides a time-resolved picture of the scattering process, showing in detail how an initial state described entirely in terms of continuous parameters evolves into a discrete set of possible outcomes, each with an associated probability and time-evolving wavefunction. We find that for scattering of Gaussian wavepackets in one dimension, the late time spectrum is dominated by two large eigenvalues nearly equal to the transmission and reflection probabilities associated with the central value of momentum. The corresponding eigenstates appear as single-peaked reflected or transmitted wavepackets. The remaining smaller eigenvalues, which increase to a maximum during scattering and then decrease to small values, correspond to reflected or transmitted wavepackets with multiple spatially separated parts. In this case and also for two-dimensional scattering, we find that successively smaller eigenvalues correspond to probability distributions with successively more peaks. These multi-peaked states correspond to outcomes of the scattering experiment where a particle initially in a single wavepacket ends up in a superposition of separated wavepackets after scattering. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2512.02239 [quant-ph] (or arXiv:2512.02239v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.02239 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mark Van Raamsdonk [view email] [v1] Mon, 1 Dec 2025 22:07:24 UTC (2,256 KB) Full-text links: Access Paper: View a PDF of the paper titled Evolution of the eigenvalues and eigenstates of the single-particle reduced density operator during two-particle scattering, by Arsam Najafian and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: hep-th References & Citations INSPIRE HEP NASA ADSGoogle 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?) 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?)