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Cavity exciton-polaritons exhibit ballistic transport and can achieve a distance of 100 $\mu $m in one picosecond. This ballistic transport significantly enhances mobility compared to that of bare excitons, which often move diffusively and become the bottleneck for energy conversion and transfer devices. Despite being robustly reproduced in experiments and simulations, there is no comprehensive microscopic theory addressing the group velocity of polariton transport, and its renormalization due to phonon scattering while still preserving this ballistic behavior. In this work, we develop a microscopic theory to describe the group velocity renormalization using a finite-temperature Green's function approach. Utilizing the generalized Holstein-Tavis-Cummings Hamiltonian, we analytically derive an expression for the group velocity renormalization and find that it is caused by phonon-mediated transitions from the lower polariton states to the dark states. The theory predicts that the magnitude of group velocity renormalization scales linearly with the phonon bath reorganization energy under weak coupling conditions and also linearly depends on the temperature in the high-temperature regime. These predictions are numerically verified using quantum dynamics simulations via the mean-field Ehrenfest method, demonstrating quantitative agreement. Our findings provide theoretical insights and a predictive analytical framework that advance the understanding and design of cavity-modified semiconductors and molecular ensembles, opening new avenues for engineered polaritonic devices.

This paper reports how CdSe core-only nanoplatelets coupled with plasmonic Al nanoparticle lattices can exhibit exciton-polariton lasing. By improving a procedure to synthesize monodisperse 4-monolayer CdSe nanoplatelets, we could resolve polariton decay dynamics and pathways. Experiment and theory confirmed that the system is in the strong coupling regime based on anti-crossings in the dispersion diagrams and magnitude of the Rabi splitting values. Notably, polariton lasing is observed only for cavity lattice periodicities that exhibit specific dispersive characteristics that enable polariton accumulation. The threshold of polariton lasing is 25-fold lower than reported photon lasing values from CdSe nanoplatelets in similar cavity designs. This open-cavity platform offers a simple approach to control exciton polaritons anticipated to benefit quantum information processing, optoelectronics, and chemical reactions.

We present a microscopic theory that aims to explain the vibrational strong coupling (VSC) modified reaction rate constant. The analytic theory is based on a mechanistic conjecture that cavity modes promote the transition from the ground state to the vibrational excited state of the reactant, which is the rate-limiting step of the reaction. The theory explains the observed resonance effect at the normal incident angle. Assuming the coherent vibrational energy transfer picture, the theory can also explain the collective effect and makes several predictions that are experimentally verifiable.

We present the quantum dynamics of a spin coupling to a bath of independent spins via the dissipaton equation of motion (DEOM) approach. The bath, characterized by a continuous spectral density function, is composed of spins that are independent level systems described by the su(2) Lie algebra. This represents an extreme class of anharmonic environment. Based on the conclusion drawn by Suarez and Silbey [J. Chem. Phys. 95, 9115 (1991)] and Makri [J. Chem. Phys. 111, 6164 (1999)] that the spin bath can be mapped to a Gaussian environment under its linear response limit, we derive the fluctuation-dissipation theorem (FDT) of the spin bath from a microscopic perspective, and generalize the discussion to the case of arbitrary bath spin quantum number S. Next, the time-domain Prony fitting decomposition scheme is applied to the bare-bath time correlation function (TCF) given by FDT to generate the exponential decay basis (or pseudo modes) for DEOM construction. The accuracy and efficiency of this strategy has been justified by a variety of numerical results. We envision this work provides new insights to extend the hierarchical equations of motion (HEOM) and DEOM approach to certain types of anharmonic enviroments with arbitrary TCF or spectral density

We derive the non-adiabatic ring polymer molecular dynamics (RPMD) approach in the phase space of the SU(N) Lie Group. This method, which we refer to as the spin mapping non-adiabatic RPMD (SM-NRPMD), is based on the spin-mapping formalism for the electronic degrees of freedom (DOFs) and ring polymer path-integral description for the nuclear DOFs. Using the Stratonovich-Weyl transform for the electronic DOFs, and the Wigner transform for the nuclear DOFs, we derived an exact expression of the Kubo-transformed time-correlation function (TCF). We further derive the spin mapping non-adiabatic Matsubara dynamics using the Matsubara approximation that removes the high frequency nuclear normal modes in the TCF and derive the SM-NRPMD approach from the non-adiabatic Matsubara dynamics by discarding the imaginary part of the Liouvillian. The SM-NRPMD method has numerical advantages compared to the original NRPMD method based on the MMST mapping formalism, due to a more natural mapping using the SU(N) Lie Group that preserves the symmetry of the original system. We numerically compute the Kubo-transformed position auto-correlation function and electronic population correlation function for three-state model systems. The numerical results demonstrate the accuracy of the SM-NRPMD method, which outperforms the original MMST-based NRPMD. We envision that the SM-NRPMD method will be a powerful approach to simulate electronic non-adiabatic dynamics and nuclear quantum effects accurately.

We generalize the quasi-diabatic (QD) propagation scheme to simulate the non-adiabatic polariton dynamics in molecule-cavity hybrid systems. The adiabatic-Fock states, which are the tensor product states of the adiabatic electronic states of the molecule and photon Fock states, are used as the locally well-defined diabatic states for the dynamics propagation. These locally well-defined diabatic states allow using any diabatic quantum dynamics methods for dynamics propagation, and the definition of these states will be updated at every nuclear time step. We use several recently developed non-adiabatic mapping approaches as the diabatic dynamics methods to simulate polariton quantum dynamics in a Shin-Metiu model coupled to an optical cavity. The results obtained from the mapping approaches provide very accurate population dynamics compared to the numerically exact method and outperform the widely used mixed quantum-classical approaches, such as the Ehrenfest dynamics and the fewest switches surface hopping approach. We envision that the generalized QD scheme developed in this work will provide a powerful tool to perform the non-adiabatic polariton simulations by allowing a direct interface between the diabatic dynamics methods and ab initio polariton information.

We provide the analytic expressions of the totally symmetric and anti-symmetric structure constants in the $\mathfrak{su}(N)$ Lie algebra. The derivation is based on a relation linking the index of a generator to the indexes of its non-null elements. The closed formulas obtained to compute the values of the structure constants are simple expressions involving those indexes and can be analytically evaluated without any need of the expression of the generators. We hope that these expressions can be widely used for analytical and computational interest in Physics.

We theoretically demonstrate that chemical reaction rate constant can be significantly suppressed by coupling molecular vibrations with an optical cavity, exhibiting both the collective coupling effect and the cavity-frequency modification of the rate constant. When a reaction coordinate is strongly coupled to the solvent molecules, the reaction rate constant is reduced due to the dynamical caging effect. We demonstrate that collectively coupling the solvent to the cavity can further enhance this dynamical caging effect, leading to additional suppression of the chemical kinetics. This effect is further amplified when cavity loss is considered.

We perform on-the-fly non-adiabatic molecular dynamics simulations using the symmetrical quasi-classical (SQC) approach with the recently suggested molecular Tully models: ethylene and fulvene. We attempt to provide benchmarks of the SQC methods using both the square and the triangle windowing schemes as well as the recently proposed electronic zero-point-energy correction scheme (so-called the gamma correction). We use the quasi-diabatic propagation scheme to directly interface the diabatic SQC methods with adiabatic electronic structure calculations. Our results showcase the drastic improvement of the accuracy by using the trajectory-adjusted gamma-corrections, which outperform the widely used trajectory surface hopping method with decoherence corrections. These calculations provide useful and non-trivial tests to systematically investigate the numerical performance of various diabatic quantum dynamics approaches, going beyond simple diabatic model systems that have been used as the major workhorse in the quantum dynamics field. At the same time, these available benchmark studies will also likely foster the development of new quantum dynamics approaches based on these techniques.

We present a new non-adiabatic ring polymer molecular dynamics (NRPMD) method based on the spin mapping formalism, which we refer to as the spin-mapping NRPMD (SM-NRPMD) approach. We derive the path-integral partition function expression using the spin coherent state basis for the electronic states and the ring polymer formalism for the nuclear degrees of freedom (DOFs). This partition function provides an efficient sampling of the quantum statistics. Using the basic property of the Stratonovich-Weyl transformation, we derive a Hamiltonian which we propose for the dynamical propagation of the coupled spin mapping variables and the nuclear ring polymer. The accuracy of the SM-NRPMD method is numerically demonstrated by computing nuclear position and population auto-correlation functions of non-adiabatic model systems. The results from SM-NRPMD agree very well with the numerically exact results. The main advantage of using the spin mapping variables over the harmonic oscillator mapping variables is numerically demonstrated, where the former provides nearly time-independent expectation values of physical observables for systems under thermal equilibrium, the latter can not preserve the initial quantum Boltzmann distribution. We also explicitly demonstrate that SM-NRPMD provides invariant dynamics upon various ways of partitioning the state-dependent and state-independent potentials.

This work provides the fundamental theoretical framework for the molecular cavity Quantum Electrodynamics by resolving the gauge ambiguities between the Coulomb gauge and the dipole gauge Hamiltonian under the electronic state truncation. Our conjecture for the arising of such gauge ambiguity is that not all operators are properly constrained in the truncated electronic subspace. Based upon this conjecture, we construct a unitary transformation that properly constrains all operators in the subspace, and derive an equivalent and yet convenient expression for the Coulomb gauge Hamiltonian under the truncated subspace. We finally provide the analytical and numerical results of a model molecular system coupled to the cavity to demonstrate the validity of our theory.

We use the polarized Fock states to describe the coupled molecule-cavity hybrid system in quantum electrodynamics. The molecular permanent dipoles polarize the photon field by displacing its vector potential, leading to non-orthogonality between the Fock states of two different polarized photon fields. These polarized Fock states allow an intuitive understanding of several new phenomena that go beyond the prediction of the quantum Rabi model, and at the same time, offer numerical convenience to converge the results. We further exploit this non-orthogonality to generate multiple photons from a single electronic excitation (downconversion) and control the photochemical reactivity.

This paper provides the first ab-initio on-the-fly example of using the Quasi-Diabatic (QD) scheme for non-adiabatic simulations with diabatic dynamics approaches. The QD scheme provides a seamless interface between diabatic quantum dynamics approaches and {\it adiabatic} electronic structure calculations. It completely avoids additional theoretical efforts to reformulate the equation of motion from diabatic to adiabatic representation, or construct global diabatic surfaces. This scheme enables many recently developed diabatic quantum dynamics approaches for ab-inito on-the-fly simulations, providing the non-adiabatic community a wide variety of approaches (such as the real-time path integral method and symmetric quasi-classical approach) beyond the well-explored methods (like trajectory surface-hopping or ab-initio multiple-spawning). The QD scheme also enables using realistic test cases (like ethylene photodynamics) that go beyond simple model systems to assess the accuracy and limitation of recently developed quantum dynamics approaches.

Recently proposed non-adiabatic ring polymer molecular dynamics (NRPMD) approach has shown to provide accurate quantum dynamics by incorporating explicit electronic state descriptions and nuclear quantizations. Here, we present a rigorous derivation of the NRPMD Hamiltonian and investigate its performance on simulating excited state non-adiabatic dynamics. Our derivation is based on the Meyer-Miller-Stock-Thoss (MMST) mapping representation for electronic states and the ring-polymer path-integral description for nuclei, resulting in the same Hamiltonian proposed in the original NRPMD approach. In addition, we investigate the accuracy of using NRPMD to simulate photoinduced non-adiabatic dynamics in simple model systems. These model calculations suggest that NRPMD can alleviate the zero-point energy leakage problem that is commonly encountered in the classical Wigner dynamics, and provide accurate excited states non-adiabatic dynamics. This work provides a solid theoretical foundation of the promising NRPMD Hamiltonian and demonstrates the possibility of using state-dependent RPMD approach to accurately simulate electronic non-adiabatic dynamics while explicitly quantize nuclei.

We apply a recently developed quasi-diabatic (QD) scheme to the symmetric quasi-classical (SQC) approach for accurate quantum dynamics propagation. By using the adiabatic states as the quasi-diabatic states during a short-time quantum dynamics propagation, the QD scheme allows directly interfacing diabatic SQC method with commonly used adiabatic electronic structure calculations, thus alleviate tedious theoretical efforts to reformulate SQC in the adiabatic representation. Further, the QD scheme ensures a stable propagation of the dynamics and allows using a much larger time step compared to directly propagating SQC dynamics in the adiabatic representation. This is due to the fact that the QD scheme does not explicitly require non-adiabatic couplings that could exhibit highly peaked values during non-adiabatic dynamics propagation. We perform the QD-SQC calculations with a wide range of model non-adiabatic systems to demonstrate the accuracy of the proposed scheme. This study opens up the possibility for combining accurate diabatic quantum dynamics methods such as SQC with any adiabatic electronic structure calculations for non-adiabatic on-the-fly propagations.

We investigate photoinduced proton-coupled electron transfer (PI-PCET) reaction through a recently devel- oped quasi-diabatic (QD) quantum dynamics propagation scheme. This scheme enables interfacing accurate diabatic-based quantum dynamics approaches with adiabatic electronic structure calculations for on-the-fly simulations. Here, we use the QD scheme to directly propagate PI-PCET quantum dynamics with the di- abatic Partial Linearized Density Matrix (PLDM) path-integral approach with the instantaneous adiabatic electron-proton vibronic states. Our numerical results demonstrate the importance of treating proton quan- tum mechanically in order to obtain accurate PI-PCET dynamics, as well as the role of solvent fluctuation and vibrational relaxation on proton tunneling in various reaction regimes that exhibit different kinetic iso- tope effects. This work opens the possibility to study the challenging PI-PCET reactions through accurate diabatic quantum dynamics approaches combined with efficient adiabatic electronic structure calculations.

We introduce the coherent state mapping ring-polymer molecular dynamics (CS-RPMD), a new method that accurately describes electronic non-adiabatic dynamics with explicit nuclear quantization. This new approach is derived by using coherent state mapping representation for the electronic degrees of freedom (DOF) and the ring-polymer path-integral representation for the nuclear DOF. CS-RPMD Hamiltonian does not contain any inter-bead coupling term in the state-dependent potential, which is a key feature that ensures correct electronic Rabi oscillations. Hamilton's equation of motion is used to sample initial configurations and propagate the trajectories, preserving the distribution with classical symplectic evolution. In the special one-bead limit for mapping variables, CS-RPMD preserves the detailed balance. Numerical tests of this method with a two-state model system show a very good agreement with exact quantum results over a broad range of electronic couplings.