Linear response theory conductivity

When the linear response theory is applied to electric conductivity in an ionic melt, the total charge current J t) can be defined as... 

Using linear response theory and noting (according to the results at the end of Section 5.1.3) that the (complex) electrical conductivity a is the Fourier transform of the current density autocorrelation function, we obtain from Eqn. (5.75) (see the equivalent Eqn. (5.21))... 

The observation that the rate constant may be expressed in terms of an auto-time-correlation function of the flux, averaged over an equilibrium ensemble, has a parallel in statistical mechanics. There it is shown, within the frame of linear response theory, that any transport coefficients, like diffusion constants, viscosities, conductivities, etc., may also be expressed in terms of auto-time-correlation functions of proper chosen quantities, averaged over an equilibrium ensemble. 

Equations (3) or (4), with refinements as necessary for "local field" effects, are an appropriate and useful basis for discussion of various models of non-conducting solutions of biological species considered in I. In many cases, however, solutions of interest have appreciable ionic concentrations in the natural solvent medium and the polymer or other solute species may also have net charges. Under these conditions, the electrical response is better considered in terms of the total current density Jfc(t) defined and expressed by linear response theory as... 

Different approaches have also been proposed. For instance, Painelli et al. [23] have expressed the frequency-dependent conductivity of dimerized and trimerized organic conductors on the base of vibronic adiabatic Mulliken theory. They have shown that the calculated spectrum is virtually identical to the one obtained from linear response theory. 

Proton conductivity of the systems studied has been considered in the framework of the Kubo linear response theory [154], i.e., the conductivity has been written as... 

We compute effective thermal transport coefficients for proteins using linear response theory and beginning in the harmonic approximation, with anharmonic contributions included as a correction. The correction can in fact be rather large, as we compute anharmonicity to nearly double the magnitude of the thermal conductivity and thermal diffusivity of myoglobin. We expect that anharmonicity will generally enhance thermal transport in proteins, in contrast, for example, to crystals, where anharmonicity leads to thermal resistance, since most of the harmonic modes of the protein are spatially localized and transport heat only inefficiently. 

Several transport properties can be evaluated from equilibrium simulations with use of linear response theory, which relates correlation fimctions of spontaneously fluctuating molecular properties to phenomenological transport coefficients. These relations can be used to evaluate diffusion coefficients, thermal conductivities, viscosities, IR spectra, and so on. However, most of these properties are evaluated more directly using appropriately devised techniques of nonequilibrium molecular dynamics. Particularly challenging for polymers is the direct... 

Evans, D J. (1982). Homogeneous NEMD algoiitfam for thermal conductivity Application of non-canonical linear response theory. Phys. Lett., 91 A, 457-460. 

Another approach to calculate thermal conductivity is equilibrium molecular dynamics (EMD) [125] that uses the Green-Kubo relation derived from linear response theory to extract thermal conductivity from heat current correlation functions. The thermal conductivity X is calculated by integrating the time autocorrelation function of the heat flux vector and is given by... 

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),/, ... 

The calculation of the thermal conductivity of gas hydrate using EMD and the Green-Kubo linear response theory was repeated recently. In that work, convergences of the relevant quantities were monitored carefully as a function of the model size. Subtleties in the numerical procedures were also carefully considered. The thermal conductivity of methane hydrate was found to converge within numerical accuracy for 3 x 3 x 3 and 4x4x4 supercells. In the calculation of the heat flux vector there is an interactive term that is a pairwise summation over the forces exerted by atomic sites on one another. The species (i.e., water and methane) enthalpy correction term requires that the total enthalpy of the system is decomposed into contributions from each species. Because of the partial transformation from pairwise, real-space treatment to a reciprocal space form in Ewald electrostatics, it is necessary to recast the diffusive and interactive terms in this expression in a form amenable for use with the Ewald method using the formulation of Petravic. ... 

Linear response theory provides an alternative, and complementary, approach for evaluating the shear viscosity. This non-equilibrium approach is related to equilibrium calculations described in the previous section through the fluctuation-dissipation theorem. Both methods yield identical results. For the more complicated analysis of the hydrodynamic eqnations, the stress tensor, and the longitudinal transport coefficients such as the thermal conductivity, the reader is referred to [35]. 

We turn first to computation of thermal transport coefficients, which provides a description of heat flow in the linear response regime. We compute the coefficient of thermal conductivity, from which we obtain the thermal diffusivity that appears in Fourier s heat law. Starting with the kinetic theory of gases, the main focus of the computation of the thermal conductivity is the frequency-dependent energy diffusion coefficient, or mode diffusivity. In previous woik, we computed this quantity by propagating wave packets filtered to contain only vibrational modes around a particular mode frequency [26]. This approach has the advantage that one can place the wave packets in a particular region of interest, for instance the core of the protein to avoid surface effects. Another approach, which we apply in this chapter, is via the heat current operator [27], and this method is detailed in Section 11.2. 

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