Journal article 22678 views
Quasi-free states on a class of algebras of multicomponent commutation relations
Reviews in Mathematical Physics
Swansea University Author: Eugene Lytvynov
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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,...
Published in: | Reviews in Mathematical Physics |
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ISSN: | 0129-055X 1793-6659 |
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URI: | https://cronfa.swan.ac.uk/Record/cronfa63565 |
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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 SMA 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 World Scientific Pub Co Pte Ltd 0129-055X 1793-6659 Anyon, plekton, fusion of quasiparticles, quasi-free state 0 0 0 0001-01-01 10.1142/s0129055x23500204 http://dx.doi.org/10.1142/s0129055x23500204 COLLEGE NANME Mathematics COLLEGE CODE SMA 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 2023-10-12T15:09:10.6019989 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 Under embargo Under embargo 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 |
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e5b4fef159d90a480b1961cef89a17b7 |
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e5b4fef159d90a480b1961cef89a17b7_***_Eugene Lytvynov |
author |
Eugene Lytvynov |
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Eugene Lytvynov Nedal Othman |
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Journal article |
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Reviews in Mathematical Physics |
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Swansea University |
issn |
0129-055X 1793-6659 |
doi_str_mv |
10.1142/s0129055x23500204 |
publisher |
World Scientific Pub Co Pte Ltd |
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Faculty of Science and Engineering |
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Faculty of Science and Engineering |
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Faculty of Science and Engineering |
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School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics |
url |
http://dx.doi.org/10.1142/s0129055x23500204 |
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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 |
0001-01-01T15:09:11Z |
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1779559040516358144 |
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11.013148 |