Classical description of a quantum particle in a Fermi sea

In this work, we propose a scheme for simulating quantum systems in which some of the degrees of freedom are approximated by classical variables. Starting with a fully quantum-mechanical system, we apply controllable approximations for some of the degrees of freedom, which leads to coupled quantum evolution and Newtonian dynamics. By comparing results obtained within the framework of this quantum-classical dynamics with exact solutions of the original quantum system, we determine the regime of applicability of the proposed approach. The quasi-classical limit of quantum mechanics usually refers to the limit of the Planck constant going to zero, which in a dimensionless version of the Schrödinger equation can be reached by taking the large-mass limit. However, here we show that the strength of the inter-particle interaction is more important for the validity of the approximation than the particle mass. Additionally, we demonstrate how the interaction between the quantum and classical particles induces an effective interactions between the otherwise noninteracting quantum particles and how the proposed simulation scheme can be used to describe the diffusion of a heavy particle in a Fermi see.