Microscopic theory of memory functions

We define a sequence of microscopic dynamical variables by decomposing a Hilbert space into orthogonal subspaces, and construct for them a new hierarchy of equations which is particularly useful for highly correlated systems. A formal solution is shown to give a microscopic expression of Mori's generalized Langevin equation. With a classical liquid as an example, we demonstrate that the theory facilitates a first-principles calculation of memory functions.