Bulletin of the American Physical Society
53rd Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics
Volume 67, Number 7
Monday–Friday, May 30–June 3 2022; Orlando, Florida
Session V01: Poster Session III (4:00-6:00pm, EDT)
4:00 PM,
Thursday, June 2, 2022
Room: Grand Ballroom C
Abstract: V01.00121 : Continuous versus discrete truncated Wigner approximation for driven, dissipative spin systems*
Presenter:
Christopher D Mink
(Technical University of Kaiserslautern, Germany)
Authors:
Christopher D Mink
(Technical University of Kaiserslautern, Germany)
David Petrosyan
(Institute of Electronic Structure & Laser (IESL) Foundation for Research & Technology-Hellas (FORTH))
Michael Fleischhauer
(Technical University of Kaiserslautern)
We provide a rigorous derivation of the DTWA based on an embedding in a continuous phase space. We derive a set of operator-differential mappings that yield an exact equation of motion (EOM) for the continuous Wigner function of spins. The truncation approximation is then identified as neglecting specific terms in the exact EOM, allowing for a detailed understanding of the quality of the approximation and possible systematic improvements. Furthermore, we show that the continuous TWA (CTWA) yields a straightforward extension to open spin systems.
We derive exact stochastic differential equations for dephasing, decay and incoherent pump processes, which in the standard DTWA suffer from problems such as non-positive diffusion. We illustrate the CTWA by studying the dynamics of dissipative 1D Rydberg arrays and compare it to exact results for small systems.
*We acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via the Collaborative Research Center SFB/TR185 (Project No. 277625399).
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