In this paper, the non-Markovian transfer tensor method (TTM) suggested by Cao's group was utilized in a real chemical reaction in liquids from a classical point of view. From the results of this numerical simulation, dramatic enhancement in speed of calculations and decrease in computational cost are shown by applying TTM method. It is wise to be used in complex systems with lots of degrees, such as the process of protein folding or in treating propagations with mountains of data. For some specific quantities we are interested in, how to find a map from complex systems to simple ones and from huge freedoms to a few ones, such as just to one freedom in this paper, it remains something for us to do in the future.

We investigate quantum dynamics in a double-well system subject to time-dependent perturbation with some incommensurate frequencies using entangled trajectory molecular dynamics method. We first compare time evolution of energy of the driven system with two mode perturbation under classical dynamics with one under quantum dynamics, it is found that quantum dynamics obeys Ehrenfest's theorem and it shows our results obtain from entangled trajectory molecular dynamics method are correct and accurate. Quantum coherence suppresses trajectory which initial energy is higher than barrier to get over it, this process is named coherent destruction of tunneling (CDT). We show this interesting phenomenon through showing entangled trajectory and corresponding classical trajectory in phase space and discuss their energy fluctuation with time. Furthermore, we discuss quantum dynamics with different frequency mode perturbation from the perspective of autocorrelation evolution, classical chaos brings remarkable influence on quantum-mechanical phenomena.

The dissipative quantum systems are treated using Klein-Kramers equation, combined with the Gaussian kernel trajectory ensemble, for time evolution of Wigner function $ρ_ω(q, p, t)$ in phase space. The entangled trajectory molecular dynamics approach is used to obtain trajectory solutions for the Klein-Kramers equation with three models: free particle, damped harmonic oscillator and metastable potential. It is found that the performance of semiclassical Wigner propagation is effectively for the relaxation of damped harmonic oscillator and dissipative decay of a metastable state. In addition, the energy of trajectory ensemble decays faster with smaller friction value and changes slightly with variable temperature parameters.

Wigner function is a fundamental method to study the connection between quantum and classical system. Since negative value can be accepted by Wigner function even from a positive initial condition, they are various issues existing in corresponding interpretation as well as the development of numerical methods. We present the entangled trajectories based on the Wigner distributions with negative values.

In this paper, we summarize the photon emission statistical properties of single molecule system, using the recently developed generating function method. Through the introduce of one or double “auxiliary” variables, we can investigate the first moment and second moment of photon emission statistics driven by different external fields, such as the line shapes and Mandel's Q parameters, the photon emission probabilities, the probability distribution of time between successive emission, the waiting time and the waiting time distribution, the cross correlation, the joint probabilities, etc. Among, the first moment of photon statistics and the experimental results of optical amplification are in good agreement.

In this paper, we introduce a new way to obtain the emission spectrum of single molecule driven by external field. A virtual probe field is introduced to simulate the vacuum field, which causes the spontaneous emission phenomena of the excited single molecule. The statistical properties of the emission photons caused by the virtual probe field could be used to obtain the emission spectrum of the single molecule system. The results demonstrate the well-known Mollow triplet splitting phenomenon as the single molecule is driven by strong external field.The abstract should provide a brief summary of the main findings of the paper.

The appropriate metric of quantum speed limit for the triatomic molecules is discussed using a generalized geometric approach. The researches show the quantum Fisher information metric is tighter than the Wigner-Yanase information metric in realistic molecular dynamical evolution. The quantum speed limit metric is related to the initial evolution state of molecules.

In present study, the dynamics of stretching-stretching and stretching-bending entanglement in $H_2O$ are studied with considering the inherent decoherence process. It is shown that the excitation in the bending vibration can lead to the decrease of the generation rate of stretching-stretching entanglement for the non-superposed state and the degeneration of entanglement for the initial entangled states. For specific initial entangled states, the stretching-stretching entanglement can live for a long time, and the correspondence between energy transfer and entanglement is still maintained for the initial local mode states. For the stretching-bending vibrations, the stretching-bending entanglement is much lower than the stretching-stretching vibration, and the degeneration rate of stretching-bending entanglement is higher than that of the stretching-stretching entanglement. The excitation in the remaining stretching vibration can induce a higher degree of stretching-bending entanglement.