Conserved quantities in non-hermitian systems via vectorization method
Type of document
articlePeer-reviewed
publishedVersion
Author
Agarwal, Kaustubh S.
Muldoon, Jacob
Joglekar, Yogesh N.
Rights
Creative Commons Attribution 4.0 International Licensehttp://creativecommons.org/licenses/by/4.0/
openAccess
Metadata
Show full item recordAbstract
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 additionto the well-established methods for characterizing time-invariants in non-Hermitian systems.
Collections
The following license files are associated with this item:
Except where otherwise noted, this item's license is described as Creative Commons Attribution 4.0 International License