Algebraic theory of quantum synchronization and limit cycles under dissipation
Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessar...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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SciPost
2022
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| _version_ | 1826309241805209600 |
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| author | Buča, B Booker, C Jaksch, D |
| author_facet | Buča, B Booker, C Jaksch, D |
| author_sort | Buča, B |
| collection | OXFORD |
| description | Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessary and sufficient algebraic criteria for persistently oscillating eigenmodes (limit cycles) of time-independent quantum master equations. We show these eigenmodes must be quantum coherent and give an exact analytical solution for all such dynamics in terms of a dynamical symmetry algebra. Using our theory, we study both stable synchronization and metastable/transient synchronization. We use our theory to fully characterise spontaneous synchronization of autonomous systems. Moreover, we give compact algebraic criteria that may be used to prove absence of synchronization. We demonstrate synchronization in several systems relevant for various fermionic cold atom experiments. |
| first_indexed | 2024-03-07T07:32:42Z |
| format | Journal article |
| id | oxford-uuid:f5a83030-b9ec-4ce8-b0c5-78f52cdb41a7 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:32:42Z |
| publishDate | 2022 |
| publisher | SciPost |
| record_format | dspace |
| spelling | oxford-uuid:f5a83030-b9ec-4ce8-b0c5-78f52cdb41a72023-01-26T16:54:49ZAlgebraic theory of quantum synchronization and limit cycles under dissipationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f5a83030-b9ec-4ce8-b0c5-78f52cdb41a7EnglishSymplectic ElementsSciPost2022Buča, BBooker, CJaksch, DSynchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessary and sufficient algebraic criteria for persistently oscillating eigenmodes (limit cycles) of time-independent quantum master equations. We show these eigenmodes must be quantum coherent and give an exact analytical solution for all such dynamics in terms of a dynamical symmetry algebra. Using our theory, we study both stable synchronization and metastable/transient synchronization. We use our theory to fully characterise spontaneous synchronization of autonomous systems. Moreover, we give compact algebraic criteria that may be used to prove absence of synchronization. We demonstrate synchronization in several systems relevant for various fermionic cold atom experiments. |
| spellingShingle | Buča, B Booker, C Jaksch, D Algebraic theory of quantum synchronization and limit cycles under dissipation |
| title | Algebraic theory of quantum synchronization and limit cycles under dissipation |
| title_full | Algebraic theory of quantum synchronization and limit cycles under dissipation |
| title_fullStr | Algebraic theory of quantum synchronization and limit cycles under dissipation |
| title_full_unstemmed | Algebraic theory of quantum synchronization and limit cycles under dissipation |
| title_short | Algebraic theory of quantum synchronization and limit cycles under dissipation |
| title_sort | algebraic theory of quantum synchronization and limit cycles under dissipation |
| work_keys_str_mv | AT bucab algebraictheoryofquantumsynchronizationandlimitcyclesunderdissipation AT bookerc algebraictheoryofquantumsynchronizationandlimitcyclesunderdissipation AT jakschd algebraictheoryofquantumsynchronizationandlimitcyclesunderdissipation |