Giant mass and anomalous mobility of particles in fermionic systems

TL;DR

This paper investigates the mobility of a heavy particle in a Fermi sea, revealing giant mass renormalization and novel low-energy effects across all temperatures using a non-perturbative approach.

Contribution

It introduces a non-perturbative method to analyze particle mobility, uncovering a new low energy scale and giant mass effects in fermionic systems.

Findings

Discovery of a new low energy scale T* affecting mobility.

Identification of giant mass renormalization near resonance.

Mobility follows different power laws above and below T*.

Abstract

We calculate the mobility of a heavy particle coupled to a Fermi sea within a non-perturbative approach valid at all temperatures. The interplay of particle recoil and of strong coupling effects, leading to the orthogonality catastrophe for an infinitely heavy particle, is carefully taken into account. We find two novel types of strong coupling effects: a new low energy scale $T^{\star}$ and a giant mass renormalization in the case of either near-resonant scattering or a large transport cross section $\sigma$. The mobility is shown to obey two different power laws below and above $T^{\star}$. For $\sigma\gg\lambda_f^2$, where $\lambda_f$ is the Fermi wave length, an exponentially large effective mass suppresses the mobility.