Abstract
Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is difficult to carry out, approximations must often be made to compute these functions. We present a general scheme for the computation of correlation functions, which preserves the full quantum equilibrium structure of the system and approximates the time evolution with quantum-classical Liouville dynamics. Several aspects of the scheme are discussed, including a practical and general approach to sample the quantum equilibrium density, the properties of the quantum-classical Liouville equation in the context of correlation function computations, simulation schemes for the approximate dynamics and their interpretation and connections to other approximate quantum dynamical methods.
Highlights
The dynamical properties of condensed-phase or complex systems are often investigated experimentally by applying external fields to weakly perturb a system and observe its relaxation back to Entropy 2014, 16 the thermal equilibrium state
In the Appendix, we discuss a simplified, but approximate sampling scheme that is useful in the high-temperature limit. Another aim of this paper is to demonstrate how a recently-developed simulation method for the quantum-classical Liouville equation (QCLE), the forward-backward trajectory solution (FBTS), can be used to efficiently obtain quantum correlation functions
The scheme for computing the quantum correlation function in Equation (2) combines a numerically exact quantum initial sampling method with dynamics described by the QCLE; the approximations in the simulation method reside in the dynamics
Summary
The dynamical properties of condensed-phase or complex systems are often investigated experimentally by applying external fields to weakly perturb a system and observe its relaxation back to Entropy 2014, 16 the thermal equilibrium state. For many applications, such as proton and electron transfer in condensed phases, it is desirable to explicitly simulate, even approximately, the bath dynamics, since specific local bath DOF may be crucial for a description of the dynamics of the quantum subsystem. For this purpose, several semiclassical [13,14,15] and mixed quantum-classical [16,17]. Equation (1) is cast in the following form [19,20]: Z h
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