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Dynamical approximations for composite quantum systems: assessment of error estimates for a separable ansatz

Abstract : Abstract Numerical studies are presented to assess error estimates for a separable (Hartree) approximation for dynamically evolving composite quantum systems which exhibit distinct scales defined by their mass and frequency ratios. The relevant error estimates were formally described in our previous work Burghardt et al (2021 J. Phys. A: Math. Theor. 54 414002). Specifically, we consider a representative two-dimensional tunneling system where a double well and a harmonic coordinate are cubically coupled. The time-dependent Hartree approximation is compared with a fully correlated solution, for different parameter regimes. The impact of the coupling and the resulting correlations are quantitatively assessed in terms of a time-dependent reaction probability along the tunneling coordinate. We show that the numerical error is correctly predicted on moderate time scales by a theoretically derived error estimate.
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https://hal.archives-ouvertes.fr/hal-03868449
Contributor : Benjamin Lasorne Connect in order to contact the contributor
Submitted on : Wednesday, November 23, 2022 - 6:20:56 PM
Last modification on : Friday, November 25, 2022 - 4:02:29 AM

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Irene Burghardt, Rémi Carles, Clotilde Fermanian Kammerer, Benjamin Lasorne, Caroline Lasser. Dynamical approximations for composite quantum systems: assessment of error estimates for a separable ansatz. Journal of Physics A: Mathematical and Theoretical, 2022, 55 (22), pp.224010. ⟨10.1088/1751-8121/ac6841⟩. ⟨hal-03868449⟩

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