Measures of complexity and entanglement in many-fermion systems

There is no unique and widely accepted definition of the complexity measure (CM) a many-fermion wave function in presence interactions. The simplest Slater determinant. In shell-model or configuration interaction (CI) other related methods, state represented as superposition large number determinants, which case CI calculations reaches about 20 billion terms. Although practice this has been used CM for decades, it ill defined: not unique, depends on particular type single-particle functions to construct determinants. canonical functions/natural orbitals their corresponding occupation probabilities are intrinsic properties any many-body function, irrespective representation, they provide solution characterize CM. non-negative orbital entanglement entropy, vanishes determinant, provides CM, while more complete spectrum. We illustrate these aspects complex non-equilibrium time-dependent process, induced nuclear fission described within real-time Density Functional Theory framework extended superfluid systems, can describe simultaneously long-range short range correlations between fermions.