A quantum-mechanical model for systems of interacting bodies that takes into account noncommutativity of the operators of coordinates and momenta of different particles and correlations of the uncertainties of these quantities is considered. Here, the noncommutativity of these operators is due to the effect of interparticle forces and arises as a natural generalization of the usual commutation relation between the coordinate and momentum operators for a single particle. The efficiency of the model is proven by specific calculations for systems known in atomic and nuclear physics.
For quantum many-body systems with short-range correlations (SRCs), the intimate relationship between their magnitude, the behavior of the single-particle occupation probabilities at momenta larger than the Fermi momentum, and the entanglement entropy is a new qualitative aspect not studied and exploited yet. A large body of recent condensed matter studies indicates that the time evolution of the entanglement entropy describes the nonequilibrium dynamics of isolated and strongly interacting many-body systems, in a manner similar to the Boltzmann entropy, which is strictly defined for dilute and weakly interacting many-body systems. Both theoretical and experimental studies in nuclei and cold atomic gases have shown that the fermion momentum distribution has a generic behavior
n(k)=C/k4 at momenta larger than the Fermi momentum, due to the presence of SRCs, with approximately 20% of the particles having momenta larger than the Fermi momentum. The presence of the long momentum tails in the presence of SRCs changes the textbook relation between the single-particle kinetic energy and occupation probabilities, ${n}_{\text{mf}}(k)=1/{1+exp\ensuremath{\beta}[\ensuremath{\epsilon}(k)\ensuremath{-}\ensuremath{\mu}]}$ for momenta very different form the Fermi momentum, particularly for dynamics processes. SRCs induced high-momentum tails of the single-particle occupation probabilities increase the entanglement entropy of fermionic systems, which in its turn affects the dynamics of many nuclear reactions, such as heavy-ion collisions and nuclear fission.