Iterative solutions to the steadystate density matrix for optomechanical systems
Abstract
We present a sparse matrix permutation from graph theory that gives stable incomplete lowerupper preconditioners necessary for iterative solutions to the steadystate 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 steadystate solutions to otherwise intractable quantum optomechanical systems.
 Publication:

Physical Review E
 Pub Date:
 January 2015
 DOI:
 10.1103/PhysRevE.91.013307
 arXiv:
 arXiv:1411.4356
 Bibcode:
 2015PhRvE..91a3307N
 Keywords:

 02.70.c;
 42.50.Pq;
 42.50.Ct;
 02.10.Ox;
 Computational techniques;
 simulations;
 Cavity quantum electrodynamics;
 micromasers;
 Quantum description of interaction of light and matter;
 related experiments;
 Combinatorics;
 graph theory;
 Quantum Physics;
 Physics  Computational Physics
 EPrint:
 10 pages, 5 figures