Coupled Kohn-Sham equations for electrons and phonons

2018/03/20 by C. Y. Wang, Thierry Müller, Wang, Chung-Yu +7
Physics and Astronomy · #Quantum and electron transport phenomena #Physics of Superconductivity and Magnetism #Advanced Chemical Physics Studies

paper · pdf · doi:10.48550/arxiv.1803.07364

Abstract

This work establishes the algebraic structure of the Kohn-Sham equations to be solved in a density formulation of electron and phonon dynamics, including the superconducting order parameter. A Bogoliubov transform is required to diagonalize both the fermionic and bosonic Kohn-Sham Hamiltonians since they both represent a non-interacting quantum field theory. The Bogoliubov transform for phonons is non-Hermitian in the general case, and the corresponding time-evolution is non-unitary. Several sufficient conditions for ensuring that the bosonic eigenvalues are real are provided and a practical method for solving the system is described. Finally, we produce a set of approximate mean-field potentials which are functionals of the electronic and phononic density matrices and depend on the electron-phonon vertex.

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