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Low-rank numerical approximations for high-dimensional Lindblad equations

Abstract : 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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Contributor : François Chaplais <>
Submitted on : Tuesday, February 4, 2014 - 5:16:32 AM
Last modification on : Thursday, September 24, 2020 - 5:04:18 PM

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Claude Le Bris, Pierre Rouchon. Low-rank numerical approximations for high-dimensional Lindblad equations. Physical Review A, American Physical Society, 2013, 87 (2), pp.022125. ⟨10.1103/PhysRevA.87.022125⟩. ⟨hal-00941530⟩

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