Conserved quantities in non-hermitian systems via vectorization method


  • Kaustubh S. Agarwal Indiana University Purdue University Indianapolis (IUPUI), Indianapolis, Indiana 46202 U.S.A.
  • Jacob Muldoon Indiana University Purdue University Indianapolis (IUPUI), Indianapolis, Indiana 46202 U.S.A.
  • Yogesh N. Joglekar Indiana University Purdue University Indianapolis (IUPUI), Indianapolis, Indiana 46202 U.S.A.



parity-time symmetry, pseudo-Hermiticity, conserved quantities


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.


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Analytic and Algebraic Methods in Physics