Semiclassical approximations to quantum dynamical time correlation functions
Semiclassical approximations for quantum time correlation functions are presented for both electronically adiabatic and nonadiabatic dynamics along with discussions of the operator ordering and the classical limit. With the combined use of the initial‐value representation of the semiclassical propagator, a discrete algorithm to evaluate the Jacobi matrices, semiclassical operator ordering rules, and the stationary‐phase filter technique, a practical algorithm is developed to calculate quantum time correlation functions. This approach holds considerable promise for simulating the quantum dynamics of realistic many‐body systems. Some simple illustrative examples are used to demonstrate the feasibility and accuracy of the algorithm.
In applying reinforcement learning to continuous space problems, discretization or redefinition of the learning space can be a promising approach. Several methods and algorithms have been introduced to learning agents to respond to this problem. In our previous study, we introduced an FCCM clustering technique into Q-learning (called QL-FCCM) and its transfer learning in the Markov process. Since we could not respond to complicated environments like a non-Markov process, in this study, we propose a method in which an agent updates his Q-table by changing the trade-off ratio, Q-learning and QL-FCCM, based on the damping ratio. We conducted numerical experiments of the single pendulum standing problem and our model resulted in a smooth learning process.