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We review various numerical approaches to compute transport coefficients in molecular dynamics. These approaches can be broadly classified into three groups: (i) nonequilibrium methods based on applying an external driving field to the…
We propose a variance reduction method for calculating transport coefficients in molecular dynamics using an importance sampling method via Girsanov's theorem applied to Green--Kubo's formula. We optimize the magnitude of the perturbation…
Equilibrium properties in statistical physics are obtained by computing averages with respect to Boltzmann-Gibbs measures, sampled in practice using ergodic dynamics such as the Langevin dynamics. Some quantities however cannot be computed…
We describe a method for computing transport coefficients from the direct evaluation of large deviation function. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based…
Explicit expressions for the transport coefficients of a recently introduced stochastic model for simulating fluctuating fluid dynamics are derived in three dimensions by means of Green-Kubo relations and simple kinetic arguments. The…
A recently introduced particle-based model for fluid flow, called Stochastic Rotation Dynamics, can be made Galilean invariant by introducing a random shift of the computational grid before collisions. In this paper, it is shown how the…
The thermal conductivity of classical multi-component fluids is seemingly affected by the intrinsic arbitrariness in the definition of the atomic energies and it is ill-conditioned numerically, when evaluated from the Green-Kubo theory of…
In this work we elaborate on two recently discovered invariance principles, according to which transport coefficients are, to a large extent, independent of the microscopic definition of the densities and currents of the conserved…
We present a method to compute transport coefficients in molecular dynamics. Transport coefficients quantify the linear dependencies of fluxes in non-equilibrium systems subject to small external forcings. Whereas standard non-equilibrium…
A self-consistent method for calculating electron transport through a molecular device is proposed. It is based on density functional theory electronic structure calculations under periodic boundary conditions and implemented in the…
We show how to evaluate mobility profiles, characterizing the transport of confined fluids under a perturbation, from equilibrium molecular simulations. The correlation functions derived with the Green-Kubo formalism are difficult to sample…
We present generalized Green-Kubo expressions for thermal transport coefficients $\mu$ in non-conservative fluid-type systems, of the generic form, $\mu$ $= \mu_\infty$ $+\int^\infty_0 dt V^{-1} \av{I_\epsilon \exp(t {\cal L}) I}_0$ where…
We address the question of whether transport coefficients obtained from a unitary closed system setting, i.e., the standard equilibrium Green-Kubo formula, are the same as the ones obtained from a weakly driven nonequilibrium steady-state…
A recently introduced stochastic model for fluid flow can be made Galilean invariant by introducing a random shift of the computational grid before collisions. This grid shifting procedure accelerates momentum transfer between cells and…
This review is devoted to the different techniques that have been developed to compute the phase-coherent transport properties of quantum nanoelectronic systems connected to electrodes. Beside a review of the different algorithms proposed…
Directly computing mass transport coefficients in stochastic models requires integrating over time the equilibrium correlations between atomic displacements. Here, we show how to accelerate the computations via \green{correlation splitting…
In Part I of this two-part series, the reverse perturbation method for shearing simple liquids [Phys. Rev. E 59, 4894 (1999)] was extended to systems of interacting particles with time-discrete stochastic dynamics. For verification, in this…
Molecular dynamics (MD) simulations are used to calculate transport coefficients in a two-component plasma interacting through a repulsive Coulomb potential. The thermal conductivity, electrical conductivity, electrothermal coefficient,…
Non-equilibrium Green's function theory and related methods are widely used to describe transport phenomena in many-body systems, but they often require a costly inversion of a large matrix. We show here that the shift-invert Lanczos method…
Using Kubo's linear response theory, we derive expressions for the frequency-dependent electrical conductivity (Kubo-Greenwood formula), thermopower, and thermal conductivity in a strongly correlated electron system. These are evaluated…