Kubo response theory simulation

MD simulation is advantageous for obtaining dynamic properties directly, since the MD technique provides not only particle positions but also particle velocities that enable us to utilize the response theory (e.g., the Kubo formula [175,176]) to calculate the transport coefficients from time-dependent correlation functions. For example, we will examine the self-diffusion process of a tagged PFPE molecular center of mass (Fig. 1.49) from the simulation to gain insight into the excitation of translational motion, specifically, spreading and replenishment. The squared displacement of the center mass of a molecule or a bead is used as a measure of translational movement. The self-diffusion coefficient D can be represented as a velocity autocorrelation function... 

Transport coefficients of molecular model systems can be calculated by two methods [8] Equilibrium Green-Kubo (GK) methods where one evaluates the GK-relation for the transport coefficient in question by performing an equilibrium molecular dynamics (EMD) simulation and Nonequilibrium molecular dynamics (NEMD) methods. In the latter case one couples the system to a fictitious mechanical field. The algebraical expression for the field is chosen in such a way that the currents driven by the field are the same as the currents driven by real Navier-Stokes forces such as temperature gradients, chemical potential gradients or velocity gradients. By applying linear response theory one can prove that the zero field limit of the ratio of the current and the field is equal to the transport coefficient in question. 

As discussed in the Introduction, considerable effort has been devoted to the study of transport properties. Specifically, viscosity estimates are of potential importance in the rational design of lubricants. In these simulations, two main approaches have been used. The earlier of the two focused on a linear response theory based Green-Kubo formula ... 

Abstract. Kubo s paper on linear-response theory provided a unified language to describe a wide variety of transport phenomena, both quantum and classical, in a suitable microscopic language. The paper has been crucial for subsequent developments in numerical simulation. 

In fact, Kubo s paper also provided much of the language for the subsequent development of nonequilibrium molecular dynamics simulations however, nonequilibrium molecular dynamics adresses problems that could not be handled in the context of the original linear-response theory (see, e.g. Ref. [4]). 

The thermal conductivity of a material can be calculated directly from equilibrium molecular dynamics (EMD) simulation based on the linear response theory Green-Kubo relationship. " The fluctuation-dissipation theorem provides a connection between the energy dissipation in irreversible processes and the thermal fluctuations in equilibrium. The thermal conductivity tensor. A, can be expressed in terms of heat current autocorrelation correlation functions (HCACFs),/, ... 

---