New physical concepts: Fermionic Exchange Force and Bose-Einstein Force

The particle-exchange symmetry has a strong influence on the behavior and the properties of systems of N identical particles. While fermionic occupation numbers are restricted according to Pauli's exclusion principle, 0 ≦ n_k ≦ 1, bosonic occupation numbers can take arbitrary values 0 ≦ n_k ≦ N. It is also a matter of fact, however, that occupation numbers in realistic systems of interacting fermions and bosons can never attain the maximal possible value, i.e., 1 and N, respectively. By resorting to one-particle reduced density matrix functional theory we provide an explanation for this [1,2]: The gradient of the exact functional diverges repulsively whenever an occupation number n_k tends to attain the maximal value. In that sense we provide in particular a fundamental and quantitative explanation for the absence of complete Bose-Einstein condensation (as characterized by n_k=N) in nature [2]. These new concepts are universal in the sense that the fermionic exchange force and the Bose-Einstein force are present in all systems regardless of the particle number N, the spatial dimensionality and the interaction potentials.
[1] C.Schilling, R.Schilling, Phys. Rev. Lett. 122, 013001 (2019)
[2] J.Liebert, C.Schilling, arXiv:2010.06634 (2020)