Finite-temperature mass gap and quench dynamics of mobile impurities in a Fermi gas
Abstract
Recently, a mass-gap description of mobile impurities in a Fermi gas was introduced, which connects Anderson's orthogonality catastrophe for static impurities to the quasiparticle picture of Fermi polarons through a recoil-induced energy gap in the fermionic dispersion. That description, however, was restricted to zero temperature and did not address dynamics. Here we generalize the mass-gap model to finite temperature by combining the Lee--Low--Pines transformation with a self-consistent Hartree--Fock decoupling of the recoil-induced interaction, and we study the quench dynamics within this framework using the functional-determinant approach. At finite temperature the effective mass gap obeys the self-consistency equation Δ(T)=2UFtanh[Δ(T)/4kB T], with UF=kF2/2M and M the impurity mass. This equation admits a nonzero solution below the characteristic temperature T*=UF/(2kB) and closes as (T*−T)1/2. We identify this closing as the mean-field signature of the thermal melting of the polaron and molecule quasiparticles. Computing the Ramsey response S(t) after a sudden quench of the impurity--fermion interaction, we find that its long-time oscillations---quantum beats between the bound and in-gap states---disappear precisely above T*. Our work ties the thermodynamic and dynamical fingerprints of polaron formation to a single temperature-dependent mean-field parameter.
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BibTeX
@misc{gong2026finitetemperature,
title = {{Finite-temperature mass gap and quench dynamics of mobile impurities in a Fermi gas}},
author = {Baihua Gong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03656},
eprint = {2609.03656},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03656},
}
RIS
TY - UNPB
TI - Finite-temperature mass gap and quench dynamics of mobile impurities in a Fermi gas
AU - Baihua Gong
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03656
UR - https://arxiv.org/abs/2609.03656
AB - Recently, a mass-gap description of mobile impurities in a Fermi gas was introduced, which connects Anderson's orthogonality catastrophe for static impurities to the quasiparticle picture of Fermi polarons through a recoil-induced energy gap in the fermionic dispersion. That description, however, was restricted to zero temperature and did not address dynamics. Here we generalize the mass-gap model to finite temperature by combining the Lee--Low--Pines transformation with a self-consistent Hartree--Fock decoupling of the recoil-induced interaction, and we study the quench dynamics within this framework using the functional-determinant approach. At finite temperature the effective mass gap obeys the self-consistency equation Δ(T)=2U_Ftanh[Δ(T)/4k_B T], with U_F=k_F^2/2M and M the impurity mass. This equation admits a nonzero solution below the characteristic temperature T^*=U_F/(2k_B) and closes as (T^*−T)^1/2. We identify this closing as the mean-field signature of the thermal melting of the polaron and molecule quasiparticles. Computing the Ramsey response S(t) after a sudden quench of the impurity--fermion interaction, we find that its long-time oscillations---quantum beats between the bound and in-gap states---disappear precisely above T^*. Our work ties the thermodynamic and dynamical fingerprints of polaron formation to a single temperature-dependent mean-field parameter.
ER -