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Low-rank numerical approximations for high-dimensional Lindblad equations

Authors: C. Le Bris and P. Rouchon, Physical Review A, Vol. 87 No 2, 022125, 27 February 2013, DOI: 10.1103/PhysRevA.87.022125
A systematic numerical approach to approximate high-dimensional Lindblad equations is described. It is based on a deterministic rank m approximation of the density operator, the rank m being the only parameter to adjust. From a known initial density operator, this rank m approximation gives at each time step an estimate of its largest m eigenvalues with their associated eigenvectors. A numerical integration scheme is also proposed. Its numerical efficiency in the case of a rank m=12 approximation is demonstrated for oscillation revivals of 50 atoms interacting resonantly with a slightly damped coherent quantized field of 200 photons.
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title = {Low-rank numerical approximations for high-dimensional Lindblad equations},
author = {Le Bris, C. and Rouchon, P.},
journal = {Phys. Rev. A},
volume = {87},
issue = {2},
pages = {022125},
numpages = {4},
year = {2013},
month = {Feb},
publisher = {American Physical Society},
doi = {10.1103/PhysRevA.87.022125},
url = {http://link.aps.org/doi/10.1103/PhysRevA.87.022125}