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One key challenge in the study of nonadiabatic dynamics in open quantum systems is to balance computational efficiency and accuracy. Although Ehrenfest dynamics (ED) is computationally efficient and well-suited for large complex systems, ED often yields inaccurate results. To address these limitations, we improve the accuracy of the traditional ED by adding a random force (E$+$$\sigma$). In this work, the construction of random forces is considered in Markovian and non-Markovian scenarios, and we ensure the dynamics satisfy the detailed balance in both scenarios. By comparing our E$+$$\sigma$ with existing methods such as the electronic friction model and surface hopping, we furthermore validate its reliability. In addition, E$+$$\sigma$ model still retains the high efficiency of ED and does not incur much additional computation. We believe that this method provides an alternative to accurately describe mixed quantum-classical dynamics in open quantum systems, particularly for large complex systems.

In this paper, we introduce the Floquet Ehrenfest and Floquet surface hopping approaches to study the nonadiabatic dynamics in the laser-dressed solid systems. We demonstrate that these two approaches can be formulated in both real and reciprocal spaces. Using these approaches, we are able to simulate the interaction between electronic carriers and phonons under periodic drivings, such as strong light-matter interactions. Employing the Holstein and Peierls models, we show that the strong light-matter interactions can effectively modulate the dynamics of electronic population and mobility. Notably, our study demonstrates the feasibility and effectiveness of modeling low-momentum carriers' interactions with phonons using a truncated reciprocal-space basis, an approach impractical in real-space frameworks. Moreover, we reveal that even with significant truncation, carrier populations derived from surface hopping maintain greater accuracy compared to those obtained via meanfield dynamics. These results underscore the potential of our proposed methods in advancing the understanding of carrier-phonon interactions in various laser-dressed materials.

The notion of chiral-induced spin selectivity (CISS) has attracted intensive research interest recently. However, the practical applications of the CISS effects face challenges due to relatively low spin polarization. In this Letter, we propose a non-perturbative theory illustrating how circularly polarized (CP) light enhances CISS effects through strong light-matter interactions. We introduce a Floquet electronic friction model to study the nonadiabatic dynamics and spin transport through a chiral molecule in a molecule junction subjected to external driving. Our results show that the interplay of the nonadiabatic effects and light-matter interactions can significantly ($>90\%$) enhance electron spin polarization under CP light. Our predictions can be very useful in experiments for using CP light to control spin current in chiral molecular junctions., Comment: arXiv admin note: substantial text overlap with arXiv:2310.10929

This study investigates the dynamic behavior of polaritons in an optical cavity containing one million molecules, emphasizing the influence of molecular rotation and level disorder on the coupling between molecules and photons. Through rigorous theoretical simulations and numerical analyses, we systematically explore the formation and spectral characteristics of polaritons in this complex environment. Our findings reveal that the rotational motion of molecules significantly affects the electromagnetic field distribution within the cavity, leading to distinct alterations in polariton properties. Simultaneously, the presence of level disorder induces diverse energy level structures, influencing the energy distribution of polaritons. The comprehensive examination of these factors provides valuable insights into the intricate interplay between molecules and photons in large-scale cavity systems. This research not only advances the fundamental understanding of molecular-photon coupling but also offers theoretical guidance for practical applications in the design and exploration of optical cavities.

We present a non-perturbative theory that describes how light regulates chiral-induced spin selectivity (CISS) from the perspective of strong light-matter interactions. The research results indicate that 1) light can have opposite effects on the CISS, 2) the difference in CISS is caused by the steady states of nuclei coupled to spin electrons and 3) this steady state differences are caused by the different light-induced Lorentz forces felt by spin-up and spin-down electrons. The fundamental reason for these results is the impact of light on spin-orbital coupling (SOC), which is a complex process. This theoretical framework is verified by the calculations of Floquet SOC non-adiabatic nuclear dynamics.

In our recent paper [Mosallanejad et al., Phys. Rev. B 107(18), 184314, 2023], we have derived a Floquet electronic friction model to describe nonadiabatic molecular dynamics near metal surfaces in the presence of periodic driving. In this work, we demonstrate that Floquet driving can introduce an anti-symmetric electronic friction tensor in quantum transport, resulting in circular motion of the nuclei in the long time limit. Furthermore, we show that such a Lorentz-like force strongly affects nuclear motion: at lower voltage bias, Floquet driving can increase the temperature of nuclei; at larger voltage bias, Floquet driving can decrease the temperature of nuclei. In addition, Floquet driving can affect electron transport strenuously. Finally, we show that there is an optimal frequency that maximizes electron current. We expect that the Floquet electronic friction model is a powerful tool to study nonadiabatic molecular dynamics near metal surfaces under Floquet driving in complex systems.

The Born-Oppenheimer (BO) approximation has shaped our understanding on molecular dynamics microscopically in many physical and chemical systems. However, there are many cases that we must go beyond the BO approximation, particularly when strong light-matter interactions are considered. Floquet theory offers a powerful tool to treat time-periodic quantum systems. In this overview, we briefly review recent developments on Floquet nonadiabatic dynamics, with a special focus on open quantum systems. We first present the general Floquet Liouville von-Neumann (LvN) equation. We then show how to connect Floquet operators to real time observables. We proceed to outline the derivation of the Floquet quantum master equation in treating the dynamics under periodic driving in open quantum systems. We further present the Floquet mixed quantum classical Liouville equation (QCLE) to deal with coupled electron-nuclear dynamics. Finally, we embed FQCLE into a classical master equation (CME) to deal with Floquet nonadiabatic dynamics in open quantum systems. The formulations are general platforms for developing trajectory based dynamical approaches. As an example, we show how Floquet QCLE and Floquet CME can be implemented into a Langevin dynamics with Lorentz force and surface hopping algorithms., Comment: 17 pages, 2 figures

When the coupled electron-nuclear dynamics are subjected to strong Floquet driving, there is a strong breakdown of the Born-Oppenheimer approximation. In this article, we derive a Fokker-Planck equation to describe non-adiabatic molecular dynamics with electronic friction for Floquet driven systems. We first provide a new derivation of the Floquet quantum-classical Liouville equation (QCLE) for driven electron-nuclear dynamics. We then transform the Floquet QCLE into a Fokker-Planck equation with explicit forms of frictional force and random force. We recast the electronic friction in terms of Floquet Green's functions such that we can evaluate the electronic friction explicitly. We show that the Floquet electronic friction tensor exhibits antisymmetric terms even at equilibrium for real-valued Hamiltonian, suggesting that there is a Lorentz-like force in Floquet driven non-Born Oppenheimer dynamics even without any spin-orbit couplings., Comment: Main: 5 pages, 3 figuers, Supplement: 5 page