Iterative solutions to the steady-state density matrix for optomechanical systems

P. D. Nation, J. R. Johansson, M. P. Blencowe, A. J. Rimberg

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


We present a sparse matrix permutation from graph theory that gives stable incomplete lower-upper preconditioners necessary for iterative solutions to the steady-state density matrix for quantum optomechanical systems. This reordering is efficient, adding little overhead to the computation, and results in a marked reduction in both memory and runtime requirements compared to other solution methods, with performance gains increasing with system size. Either of these benchmarks can be tuned via the preconditioner accuracy and solution tolerance. This reordering optimizes the condition number of the approximate inverse and is the only method found to be stable at large Hilbert space dimensions. This allows for steady-state solutions to otherwise intractable quantum optomechanical systems.

Original languageEnglish
Article number013307
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number1
Publication statusPublished - 2015 Jan 23

Bibliographical note

Publisher Copyright:
© 2015 American Physical Society.

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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