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Quasi-free states on a class of algebras of multicomponent commutation relations

Eugene Lytvynov Orcid Logo, Nedal Othman

Reviews in Mathematical Physics, Volume: 35, Issue: 09

Swansea University Author: Eugene Lytvynov Orcid Logo

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DOI (Published version): 10.1142/s0129055x23500204

Abstract

Multicomponent commutations relations (MCRs) describe plektons, i.e. multicomponent quantum systems with a generalized statistics. In such systems, exchange of quasiparticles is governed by a unitary matrix Q(x1,x2) that depends on the position of quasiparticles. For such an exchange to be possible,...

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Published in: Reviews in Mathematical Physics
ISSN: 0129-055X 1793-6659
Published: World Scientific Pub Co Pte Ltd 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa63565
first_indexed 2023-06-01T11:07:11Z
last_indexed 2024-11-15T18:01:51Z
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spelling 2024-07-29T15:11:11.0626626 v2 63565 2023-06-01 Quasi-free states on a class of algebras of multicomponent commutation relations e5b4fef159d90a480b1961cef89a17b7 0000-0001-9685-7727 Eugene Lytvynov Eugene Lytvynov true false 2023-06-01 MACS Multicomponent commutations relations (MCRs) describe plektons, i.e. multicomponent quantum systems with a generalized statistics. In such systems, exchange of quasiparticles is governed by a unitary matrix Q(x1,x2) that depends on the position of quasiparticles. For such an exchange to be possible, the matrix must satisfy several conditions, including the functional Yang–Baxter equation. The aim of the paper is to give an appropriate definition of a quasi-free state on an MCR algebra, and construct such states on a class of MCR algebras. We observe a significant difference between the classical setting for bosons and fermions and the setting of MCR algebras. We show that the developed theory is applicable to systems that contain quasiparticles of opposite type. An example of such a system is a two-component system in which two quasiparticles, under exchange, change their respective types to the opposite ones (1↦2, 2↦1). Fusion of quasiparticles means intuitively putting several quasiparticles in an infinitely small box and identifying the statistical behavior of the box. By carrying out fusion of an odd number of particles from the two-component system as described above, we obtain further examples of quantum systems to which the developed theory is applicable. Journal Article Reviews in Mathematical Physics 35 09 World Scientific Pub Co Pte Ltd 0129-055X 1793-6659 Anyon, plekton, fusion of quasiparticles, quasi-free state 1 10 2023 2023-10-01 10.1142/s0129055x23500204 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Not Required This paper was mostly written when N.O. was a PhD student in the Department of Mathematics of Swansea University. N.O. is grateful to the Department for their constant support during his studies 2024-07-29T15:11:11.0626626 2023-06-01T11:54:13.3120901 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Eugene Lytvynov 0000-0001-9685-7727 1 Nedal Othman 2 63565__28177__e5af8f875a5649e0bce31e6c82b9dc29.pdf 63565.AAM.pdf 2023-07-25T15:28:04.0052588 Output 424796 application/pdf Accepted Manuscript true 2024-06-13T00:00:00.0000000 true eng
title Quasi-free states on a class of algebras of multicomponent commutation relations
spellingShingle Quasi-free states on a class of algebras of multicomponent commutation relations
Eugene Lytvynov
title_short Quasi-free states on a class of algebras of multicomponent commutation relations
title_full Quasi-free states on a class of algebras of multicomponent commutation relations
title_fullStr Quasi-free states on a class of algebras of multicomponent commutation relations
title_full_unstemmed Quasi-free states on a class of algebras of multicomponent commutation relations
title_sort Quasi-free states on a class of algebras of multicomponent commutation relations
author_id_str_mv e5b4fef159d90a480b1961cef89a17b7
author_id_fullname_str_mv e5b4fef159d90a480b1961cef89a17b7_***_Eugene Lytvynov
author Eugene Lytvynov
author2 Eugene Lytvynov
Nedal Othman
format Journal article
container_title Reviews in Mathematical Physics
container_volume 35
container_issue 09
publishDate 2023
institution Swansea University
issn 0129-055X
1793-6659
doi_str_mv 10.1142/s0129055x23500204
publisher World Scientific Pub Co Pte Ltd
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description Multicomponent commutations relations (MCRs) describe plektons, i.e. multicomponent quantum systems with a generalized statistics. In such systems, exchange of quasiparticles is governed by a unitary matrix Q(x1,x2) that depends on the position of quasiparticles. For such an exchange to be possible, the matrix must satisfy several conditions, including the functional Yang–Baxter equation. The aim of the paper is to give an appropriate definition of a quasi-free state on an MCR algebra, and construct such states on a class of MCR algebras. We observe a significant difference between the classical setting for bosons and fermions and the setting of MCR algebras. We show that the developed theory is applicable to systems that contain quasiparticles of opposite type. An example of such a system is a two-component system in which two quasiparticles, under exchange, change their respective types to the opposite ones (1↦2, 2↦1). Fusion of quasiparticles means intuitively putting several quasiparticles in an infinitely small box and identifying the statistical behavior of the box. By carrying out fusion of an odd number of particles from the two-component system as described above, we obtain further examples of quantum systems to which the developed theory is applicable.
published_date 2023-10-01T20:35:15Z
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