{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/exponential-unitary-integrators-for","title":"Exponential unitary integrators for nonseparable quantum Hamiltonians","arxiv_id":"2211.08155","date":"2022-11-15","proceeding":null,"authors":["Maximilian Ciric","Denys I. Bondar","Ole Steuernagel"],"abstract":"Quantum Hamiltonians containing nonseparable products of non-commuting operators, such as $\\hat{\\bf x}^m \\hat{\\bf p}^n$, are problematic for numerical studies using split-operator techniques since such products cannot be represented as a sum of separable terms, such as $T(\\hat{\\bf p}) + V(\\hat{\\bf x})$. In the case of classical physics, Chin [Phys. Rev. E $\\bf 80$, 037701 (2009)] developed a procedure to approximately represent nonseparable terms in terms of separable ones. We extend Chin's idea to quantum systems. We demonstrate our findings by numerically evolving the Wigner distribution of a Kerr-type oscillator whose Hamiltonian contains the nonseparable term $\\hat{\\bf x}^2 \\hat{\\bf p}^2 + \\hat{\\bf p}^2 \\hat{\\bf x}^2$. The general applicability of Chin's approach to any Hamiltonian of polynomial form is proven.","url_abs":"https://arxiv.org/abs/2211.08155v2","url_pdf":"https://arxiv.org/pdf/2211.08155v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"exponential-unitary-integrators-for","repo_url":"https://github.com/dibondar/nonseparablesplitoperator","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}