Models of Markovian and non-Markovian open quantum system dynamics

The papers [1,2] discuss new ways to derivation and simulation of Markovian and non-Markovian open quantum system dynamics. In [1] we develop two approaches leading to Markovian dynamics of a system interacting with a diluted gas: the first one is based on the low density theory for particles with internal degrees of freedom, the second one is based on a semiclassical collision model. We prove that in the high temperature limit the Lamb shift and the dissipator coincide in both approaches for any interaction potential between the system and a gas particle. In [2] we consider the general case on non-Markovian dynamics and propose a new method for learning an unknown system environment model by a series of projective measurements on the system. The method exploits embedding non-Markovian dynamics into a Markovian one for a system and an effective reservoir of finite dimension. The generator of Markovian embedding is inferred by the maximum likelihood estimation. This method allows one to calculate the response of a non-Markovian quantum system to an arbitrary external perturbation.

References

1. S. N. Filippov, G. N. Semin, A. N. Pechen, “Quantum master equations for a system interacting with a quantum gas in the low-density limit and for the semiclassical collision model”, Phys. Rev. A, 101 (2020), 12114, 10 pp.    
2. I. A. Luchnikov, S. V. Vintskevich, D. A. Grigoriev, S. N. Filippov, “Machine learning non-Markovian quantum dynamics”, Phys. Rev. Lett., 124 (2020), 140502, 8 pp.    

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