Displacement response time-dependent diffusion coefficient

Relation Between the Displacement Response Function and the Time-Dependent Diffusion Coefficient... 

Exactly like its classical analog Eq. (94), Eq. (125) allows one to express the displacement response function in terms of the time-dependent diffusion coefficient. However, contrary to the classical case in which Xxx( 0 is directly proportional to D(t — t ), in the quantum formulation Xxv( 0 is a convolution product, for the value t — t of the argument, of the functions D(t ) and logcoth(7i fi /2 h). Inverting the convolution equation (125) yields an expression for D(t) in terms of the dissipative part of the displacement response function ... 

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... 

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