Electronic Structure Reading Group: Green-Kubo Method for Computing Transport Coefficients: Heat Transport from Classical to Ab Initio Molecular Dynamics

The Green-Kubo theory of linear response offers a general, rigorous, and elegant framework for computing non-equilibrium transport coefficients from equilibrium molecular dynamics simulations. In this talk, I will present the fundamental concepts behind this technique and illustrate its application to thermal transport, using both classical molecular dynamics and ab initio molecular dynamics (AIMD). I will discuss how to compute the heat current, which relies on partitioning the total energy into local contributions. I will explain why these local contributions are inherently ambiguous and describe strategies to address this issue within both classical and ab initio frameworks.

Bibliography:
- A. Marcolongo, P. Umari, and S. Baroni, Microscopic theory and quantum simulation of atomic heat transport, Nature Physics 12, 80 (2016).
- A. Marcolongo, R. Bertossa, D. Tisi, and S. Baroni, QEHeat: An open-source energy flux calculator for the computation of heat-transport coefficients from first principles, Computer Physics Communications 269, 108090 (2021).
- Baroni, S., Bertossa, R., Ercole, L., Grasselli, F. & Marcolongo, A. Heat Transport in Insulators from Ab Initio Green-Kubo Theory, 1–36 (Springer International Publishing, Cham, 2018).
- Grasselli, F. & Baroni, S. Invariance principles in the theory and computation of transport coefficients. Eur. Phys. J. B 94, 160 (2021).
-  Green, M. S. Markoff random processes and the statistical mechanics of time-
dependent phenomena, ii. Irreversible processes in fluids. J. Chem. Phys. 22, 398–413 (1954).
- Kubo, R. Statistical-mechanical theory of irreversible processes. i. general theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn. 12, 570–586 (1957).

This event is jointly organized with the COSMO seminar.
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The electronic structure reading group brings together researchers and students interested in mathematical aspects of electronic structure problems and adjacent topics, including:

• Density Functional Theory
• Many-body Schrödinger equation for electrons
• Born-Oppenheimer Molecular Dynamics
• Numerical analysis and error control