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the claim
The Moyal-Liouville equation is utilized in practical applications
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INSUFFICIENT LEANING
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2 sources for · 0 against

Available literature briefly notes that Moyal formulations of quantum dynamics find practical applications, but specific, direct evidence detailing practical uses of the Moyal-Liouville equation is extremely sparse and partial.

Evidence for · 2
2026 · cited by 2
We have recently developed the <i>constraint</i> coordinate-momentum <i>phase space</i> (CPS) formulation for finite-state quantum systems. It has been implemented for the electronic subsystem in nonadiabatic transition dynamics to develop practical trajectory-based approaches. In the generalized CPS formulation for the mapping Hamiltonian of the classical mapping model with commutator variables (CMMcv) method [<i>J. Phys. Chem. A</i> <b>2021</b>, 125, 6845-6863, which followed <i>J. Chem. Phys.</i> <b>2016</b>, 145, 204105 and <i>J. Chem. Phys.</i> <b>2019</b>, 151, 024105], each connected component of the generalized CPS is the <i>complex Stiefel manifold</i> labeled by the eigenvalue set of the mapping kernel. Such a phase space structure allows for exact trajectory-based dynamics for pure discrete (electronic) degrees of freedom (DOFs), where the equations of motion of each trajectory are isomorphic to the time-dependent Schrödinger equation. We employ covariant kernels within the generalized CPS formulation to develop two approaches that naturally yield exact evaluation of time correlation functions (TCFs) for pure discrete (electronic) DOFs. In addition, we briefly discuss the phase space representations where the contribution of each trajectory to the integral expression of the TCF of population dynamics is strictly positive semi-definite. The generalized CPS formulation also indicates that the mapping Hamiltonian in phase space mapping model I of our previous work [<i>J. Chem. Phys.</i> <b>2016</b>, 145, 204105] leads to a complex Stiefel manifold U(F)/U(F-2) . The phase space expressions (of TCFs) proposed in this paper are extensively tested in our subsequent work on nonadiabatic dynamics [<i>J. Chem. Theory Comput.</i> <b>2025</b>, 21, 3775-3813]. It is expected that the generalized CPS formulation will have more implications for studying nonadiabatic transition dynamics and many-body quantum dynamics.
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1981 · cited by 0
finding growing theoreti¬ cal and practical applications. The titles of the various sessions … expectation values of the Weyl unitary operators. Moyal ^ showed that quantum dynamics can be reformulated … reformulated in terms of it using the Moyal sine brackets. Related distribution functions were Optics in four dimensions--1980 (ICO, Ensenada) : Free Download, Borrow, and Streaming : Internet Archive Skip to main content Keep the news in the Wayback Machine. Sign Fight for the Future's letter . 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Enter a URL to save Please enter a valid web address About Blog Events Projects Help Donate Contact Jobs Volunteer About Blog Events Projects Help Donate Contact Jobs Volunteer Optics in four dimensions--1980 (ICO, Ensenada) Bookreader Item Preview remove-circle Share or Embed This Item Share to Twitter Share to Facebook Share to Reddit Share to Tumblr Share to Pinterest Share via email Copy Link EMBED EMBED (for Archive.org item Description fields) [archiveorg opticsinfourdime0065unse width=560 height=384 frameborder=0 webkitallowfullscreen=true mozallowfullscreen=true] Want more? Advanced embedding details, examples, and help ! Favorite Share Flag Flag this item for Graphic Violence Explicit Sexual Content Hate Speech Misinformation/Disinformation Marketing/Phishing/Advertising Misleading/Inaccurate/Missing Metadata texts Optics in four dimensions--1980 (ICO, Ensenada) Publication date 1981 Topics Optics -- Congresses , Space and time -- Congresses Publisher New York : American Institute of Physics Collection internetarchivebooks ; inlibrary ; printdisabled Contributor Internet Archive Language English Volume 65 Item Size 1.5G 745 p., [1] p. of plates : 25 cm Papers presented at a conference organized under the auspices of the International Commission for Optics (ICO) and held in Ensenada, B.C., Mexico, August 4-8, 1980 Includes bibliographical references Notes cut text p 348,398,402 due to tight margin Access-restricted-item true Addeddate 2020-08-19 23:01:15 Associated-names Machado, M. A; Narducci, L. M; International Commission for Optics Bookplateleaf 0004 Boxid IA1903308 Camera USB PTP Class Camera Collection_set printdisabled External-identifier urn:oclc:record:1170335474 urn:lcp:opticsinfourdime0065unse:lcpdf:b2eaa20d-3267-410b-acbc-da951ec8638a urn:lcp:opticsinfourdime0065unse:epub:e190cbe7-0df1-4284-9a10-7fc88bffdc0b Foldoutcount 0 Identifier opticsinfourdime0065unse Identifier-ark ark:/13960/t71w4mf0s Invoice 1652 Isbn 0883181649 Lccn 80070771 //r85 Ocr ABBYY FineReader 11.0 (Extended OCR) Ocr_converted abbyy-to-hocr 1.1.11 Ocr_module_version 0.0.14 Old_pallet IA18448 Openlibrary_edition OL4123288M Openlibrary_work OL19489366W Page_number_confidence 100 Page_number_module_version 1.0.5 Pages 770 Ppi 300 Rcs_key 24143 Republisher_date 20200819203123 Republisher_operator associate-ronamye-cabale@archive.org Republisher_time 599 Scandate 20200807003918 Scanner station54.cebu.archive.org Scanningcenter cebu Scribe3_search_catalog isbn Scribe3_search_id 0883181649 Tts_version 4.0-initial-155-gbba175a5 Show More Show Less Full catalog record MARCXML plus-circle Add Review comment Reviews 19 Previews 1 Favorite DOWNLOAD OPTIONS No suitable files to display here. 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  1. Constraint coordinate-momentum phase space formulations for finite-state quantum systems: The relation between commutator variables and complex Stiefel manifolds.peer-reviewedno side taken
  2. Optics in four dimensions--1980 (ICO, Ensenada)referenceno side taken
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