Effective Polaron Dynamics of an Impurity Particle Interacting with a Fermi Gas
Abstract
We study the quantum dynamics of a homogeneous ideal Fermi gas coupled to an impurity particle on a threedimensional box with periodic boundary condition. For large Fermi momentum $k_\text{F}$, we prove that the effective dynamics is generated by a Fröhlichtype polaron Hamiltonian, which linearly couples the impurity particle to an almostbosonic excitation field. Moreover, we prove that the effective dynamics can be approximated by an explicit coupled coherent state. Our method is applicable to two relevant settings: first, an interaction coupling $\lambda=1$ and masses of order 1 for time scales of order $k_\text{F}^{1}$; second to the case of $\lambda=k_\text{F}^{1}$ and a heavy Fermi gas with masses of order $k_\text{F}$ for time scales of order 1.
 Publication:

arXiv eprints
 Pub Date:
 June 2024
 DOI:
 10.48550/arXiv.2406.08028
 arXiv:
 arXiv:2406.08028
 Bibcode:
 2024arXiv240608028V
 Keywords:

 Mathematical Physics;
 Condensed Matter  Quantum Gases
 EPrint:
 39 pages, 1 figure