Theoretical background to position 1
Transport coefficients govern the irreversible exchange of extensive and conserved quantities (such as charge, mass, and energy) in extended systems, by relating their fluxes to the thermodynamical forces (such as temperature and density gradients) acting on them. Within the Green-Kubo theory of linear response, transport coefficients can be expressed in terms of the time correlation function of the conserved fluxes extracted from equilibrium molecular dynamics (MD) simulations. In classical MD these fluxes are usually defined by partitioning the conserved quantities into atomic contributions. This operation is no trivial task in a first-principles framework: for instance, the partition of the total energy or electronic charge amongts different atoms is to a large extent arbitrary. For this reason, ab initio MD simulations of heat transport have long been deemed unfit to properly address heat transport, and similar problems also occur in the simulation of adiabatic charge transport in ionic liquids.
This conundrum was solved by the discovery of a gauge invariance principle for transport coefficients, according to which the only observable quantities, i.e. the transport coefficients themselves, do not depend on the datails of such partitioning [1-3]. This result was successfully applied to heat transport, where accurate thermal conductivities for different classes of insulators, ranging from solids to multi-component fluids, were obtained entirely ab initio, also thanks to the development of new data-analysis techniques for stationary time series [3-5]. Gauge-invariance can be integrated with standard lattice-dynamics to obtain a compact expression for the heat conductivity, which applies to crystalline as well as to disordered solids, which only depends on the system's dynamical matrix in the harmonic approximation and vibrational lifetimes [6]. Gauge invariance can also be combined Thouless’ quantization of adiabatic charge transport to prove that the electrical conductivity of an electronically gapped liquid can be exactly expressed in terms of the atomic oxydation numbers of its constituents, the latter being defined as the integer charge transported by an atom along properly designed periodic paths [7].
- A. Marcolongo, P. Umari, and S. Baroni, Microscopic theory and ab initio simulation of atomic heat transport. , Nat. Phys. 12, 80 (2016).
- L. Ercole, A. Marcolongo, P. Umari, and S. Baroni, Gauge Invariance of Thermal Transport Coefficients. J. Low. Temp Phys. 185, 79 (2016).
- L. Ercole, A. Marcolongo, and. S. Baroni, S. Accurate thermal conductivities from optimally short molecular dynamics simulations, Sci. Rep. 7, 15835 (2017).
- S. Baroni, R. Bertossa, L. Ercole, F. Grasselli, and A. Marcolongo, Heat transport in insulators from ab initio Green-Kubo theory, Handbook of Materials Modeling. Applications: Current and Emerging Materials, edited by W. Andreoni and S. Yip (Springer, 2018) 2nd ed., Chap. 12-1.
- R. Bertossa, F. Grasselli, L. Ercole, and S. Baroni, Theory and numerical simulation of heat transport in multi-component systems, Phys. Rev. Lett. 122, 255901 (2019);
- L. Isaeva, G. Barbalinardo, D. Donadio, S. Baroni, Modeling heat transport in crystals and glasses from a unified lattice-dynamical approach, Nat. Commun. in press (2019);
- F. Grasselli and S. Baroni, Topological quantisation and gauge invariance of charge transport in liquid insulators, Nat. Phys. in press (2019).