Conserved quantities in non-hermitian systems via vectorization method
Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time (PT) symmetry that are best understood as systems with balanced, separated gain and loss. Here, we present an alternative way to ch...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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CTU Central Library
2022-02-01
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| Series: | Acta Polytechnica |
| Subjects: | |
| Online Access: | https://ojs.cvut.cz/ojs/index.php/ap/article/view/7738 |
| _version_ | 1811272757321662464 |
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| author | Kaustubh S. Agarwal Jacob Muldoon Yogesh N. Joglekar |
| author_facet | Kaustubh S. Agarwal Jacob Muldoon Yogesh N. Joglekar |
| author_sort | Kaustubh S. Agarwal |
| collection | DOAJ |
| description | Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time (PT) symmetry that are best understood as systems with balanced, separated gain and loss. Here, we present an alternative way to characterize and derive conserved quantities, or intertwining operators, in such open systems. As a consequence, we also obtain non-Hermitian or Hermitian operators whose expectations values show single exponential time dependence. By using a simple example of a PT-symmetric dimer that arises in two distinct physical realizations, we demonstrate our procedure for static Hamiltonians and generalize it to time-periodic (Floquet) cases where intertwining operators are stroboscopically conserved. Inspired by the Lindblad density matrix equation, our approach provides a useful addition
to the well-established methods for characterizing time-invariants in non-Hermitian systems. |
| first_indexed | 2024-04-12T22:46:01Z |
| format | Article |
| id | doaj.art-6b91b673f1e04fb388f8bd6c99ed9878 |
| institution | Directory Open Access Journal |
| issn | 1805-2363 |
| language | English |
| last_indexed | 2024-04-12T22:46:01Z |
| publishDate | 2022-02-01 |
| publisher | CTU Central Library |
| record_format | Article |
| series | Acta Polytechnica |
| spelling | doaj.art-6b91b673f1e04fb388f8bd6c99ed98782022-12-22T03:13:31ZengCTU Central LibraryActa Polytechnica1805-23632022-02-016211710.14311/AP.2022.62.00014978Conserved quantities in non-hermitian systems via vectorization methodKaustubh S. Agarwal0Jacob Muldoon1Yogesh N. Joglekar2Indiana University Purdue University Indianapolis (IUPUI), Indianapolis, Indiana 46202 U.S.A.Indiana University Purdue University Indianapolis (IUPUI), Indianapolis, Indiana 46202 U.S.A.Indiana University Purdue University Indianapolis (IUPUI), Indianapolis, Indiana 46202 U.S.A.Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time (PT) symmetry that are best understood as systems with balanced, separated gain and loss. Here, we present an alternative way to characterize and derive conserved quantities, or intertwining operators, in such open systems. As a consequence, we also obtain non-Hermitian or Hermitian operators whose expectations values show single exponential time dependence. By using a simple example of a PT-symmetric dimer that arises in two distinct physical realizations, we demonstrate our procedure for static Hamiltonians and generalize it to time-periodic (Floquet) cases where intertwining operators are stroboscopically conserved. Inspired by the Lindblad density matrix equation, our approach provides a useful addition to the well-established methods for characterizing time-invariants in non-Hermitian systems.https://ojs.cvut.cz/ojs/index.php/ap/article/view/7738parity-time symmetrypseudo-hermiticityconserved quantities |
| spellingShingle | Kaustubh S. Agarwal Jacob Muldoon Yogesh N. Joglekar Conserved quantities in non-hermitian systems via vectorization method Acta Polytechnica parity-time symmetry pseudo-hermiticity conserved quantities |
| title | Conserved quantities in non-hermitian systems via vectorization method |
| title_full | Conserved quantities in non-hermitian systems via vectorization method |
| title_fullStr | Conserved quantities in non-hermitian systems via vectorization method |
| title_full_unstemmed | Conserved quantities in non-hermitian systems via vectorization method |
| title_short | Conserved quantities in non-hermitian systems via vectorization method |
| title_sort | conserved quantities in non hermitian systems via vectorization method |
| topic | parity-time symmetry pseudo-hermiticity conserved quantities |
| url | https://ojs.cvut.cz/ojs/index.php/ap/article/view/7738 |
| work_keys_str_mv | AT kaustubhsagarwal conservedquantitiesinnonhermitiansystemsviavectorizationmethod AT jacobmuldoon conservedquantitiesinnonhermitiansystemsviavectorizationmethod AT yogeshnjoglekar conservedquantitiesinnonhermitiansystemsviavectorizationmethod |