Effective dynamics of a tracer particle in a dense homogeneous quantum gas

TL;DR

This paper explores the differing behaviors of a tracer particle in dense bosonic versus fermionic quantum gases, revealing that fermions exhibit free motion despite non-scaled interactions due to their homogeneous distribution and fast degrees of freedom.

Contribution

It demonstrates that fermions behave differently from bosons in the mean field regime, explaining why fermions allow free tracer particle motion without mean field scaling.

Findings

Fermions are more homogeneously distributed than bosons.

Deviations in fermions are due to fast degrees of freedom.

Fermions exhibit free behavior despite non-scaled interactions.

Abstract

We investigate the mean field regime of the dynamics of a tracer particle in a homogenous quantum gas. For a bosonic gas, we show that this regime is constrained by the well known requirement of an appropriate mean field scaling of the interaction. For fermions, however, we find an important qualitative difference. Not only are fermions much more homogeneously distributed than bosons but also deviations from the mean are due only to fast degrees of freedom in the gas. This observation leads to an explanation of why a tracer particle behaves freely in the dense homogeneous fermion gas despite of a non-scaled interaction, i.e., despite of non-vanishing statistical fluctuations. Finally, we indicate how the gained insight can be rigorously justified.