Galilean invariant exchange correlation functionals with quantum memory

TL;DR

This paper develops Galilean invariant exchange-correlation functionals with quantum memory for time-dependent density functional theory, incorporating non-local temporal effects while satisfying physical constraints.

Contribution

It introduces a new class of Galilean invariant XC functionals based on the ELT metric tensor, enabling memory effects in TDDFT with proper physical constraints.

Findings

Derived XC potentials respecting Galilean invariance.

Formulated the XC action using the ELT metric tensor.

Obtained the linear response limit of the new functionals.

Abstract

Today, most application of time-dependent density functional theory (TDDFT) use adiabatic exchange-correlation (XC) potentials that do not take into account non-local temporal effects. Incorporating such "memory" terms into XC potentials is complicated by the constraint that the derived force and torque densities must integrate to zero at every instance. This requirement can be met by deriving the potentials from an XC action that is Galilean in-variant (GI). We develop a class of simple but flexible forms for an action that respect these constraints. The basic idea is to formulate the action in terms of the Eularian-Lagrangian transformation (ELT) metric tensor, which is itself GI. The general form of the XC potentials in this class is then derived and the linear response limit is derived as well.