Predicting rate kernels via dynamic mode decomposition

Abstract

Simulating dynamics of open quantum systems is sometimes a significant challenge, despite the availability of various exact or approximate methods. Particularly when dealing with complex systems, the huge computational cost will largely limit the applicability of these methods. In this work, we investigate the usage of dynamic mode decomposition (DMD) to evaluate the rate kernels in quantum rate processes. DMD is a data-driven model reduction technique that characterizes the rate kernels using snapshots collected from a small time window, allowing us to predict the long-term behaviors with only a limited number of samples. Our investigations show that whether the external field is involved or not, the DMD can give accurate prediction of the result compared with the traditional propagations, and simultaneously reduce the required computational cost.

Polaritons under Extensive Disordered Gas-Phase Molecular Rotations in a Fabry–Pérot Cavity

“…The light–matter interaction in H ̂ MC is given by g normalc nobreak0em0.25em⁡ normalcos ( Ω t + ϕ ) , where Ω means the molecular rotational frequency, and ϕ means the molecular rotational phase. We omit counter-rotating light–matter coupling terms in the Hamiltonian because the collective coupling strength is insufficient for these terms to have a significant impact. , To simplify the calculation of the Schrödinger equation, we leveraged the temporal periodicity of molecular rotations and applied the Floquet theory, − which allows us to transform the original time-dependent Hamiltonian H ̂( t ) into a time-independent Floquet Hamiltonian H ̂ F : italicĤ normalF = prefix∑ n , m = prefix− N normalF N normalF ( Ĥ 0 + n ℏ Ω ⊗ Î ) δ n m + italicĤ 1 ( 1 2 e − normali ϕ δ n , m + 1 + 1 2 e normali ϕ δ n , m − …”

Artificial-Intelligence-Based Surrogate Solution of Dissipative Quantum Dynamics: Physics-Informed Reconstruction of the Universal Propagator

“…Runge–Kutta methods thus provide a versatile tool to solve EOM for a wide variety of scenarios such as rate equations in chemical reactions, , population dynamics in charge and energy transfer processes, , and spectroscopic simulations. , Despite their straightforward implementation, the drawbacks of Runge–Kutta methods are the large computational cost and the presence of numerical instabilities associated with the iterations, especially for long-time dynamics. Improvements have been proposed to overcome these limitations by deriving modified schemes of EOM − or implementing other numerical solvers (e.g., proper orthogonal decomposition). However, since they are usually limited to a few specific scenarios, an efficient universal solver is still to be proposed.…”